ABSTRACT
Title of dissertation: FRUSTRATED MAGNETISM AND
ELECTRONIC PROPERTIES OF
HOLLANDITE OXIDE MATERIALS
Amber M. Larson, Doctor of Philosophy, 2017
Dissertation directed by: Professor Efrain E. Rodriguez
Department of Chemistry and Biochemistry
Microporous transition metal oxides with the hollandite structure type have
been prepared by standard solid-state techniques with varying compositions. With
a nominal formula of AxM8O16 and a framework of edge and corner-sharing MO6
octahedra, hollandites feature a pseudo-one dimensional tunnel occupied loosely
by cation A. The metastability of these open-framework materials, combined with
the ability of accommodating a variety of redox-active transition metals leads to
unique and indispensable properties. Inherent to the triangular connectivity of the
M cations in the hollandite framework, these materials frequently exhibit frus-
trated magnetic behavior.
This thesis demonstrates that it is possible to significantly affect the magnetic
and transport properties of these microporous materials through tuning of their
chemical compositions. We have shown that it is possible to synthesize polycrys-
talline and single crystal hollandite materials under ambient conditions utilizing
salt flux techniques. Our efforts to characterize the structure-property relation-
ships provide some of the first magnetic structure determinations of these complex
frameworks. The interesting behavior of these materials is a result of the interplay
between charge, orbital, and spin degrees of freedom.
This work shows that the hollandite framework is quite versatile, leading to
the real possibility of tuning the material properties to achieve desired effects and
opening up many potential applications for these microporous oxides.
FRUSTRATED MAGNETISM AND ELECTRONIC PROPERTIES
OF HOLLANDITE OXIDE MATERIALS
by
Amber Marie Larson
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2017
Advisory Committee:
Professor Efrain E. Rodriguez, Chair/Advisor
Professor Bryan Eichhorn
Professor Johnpierre Paglione
Professor Lawrence R. Sita
Professor Andrei Vedernikov
© Copyright by
Amber M. Larson
2017
Dedication
For Christian, Camille, and all of my family.
ii
Acknowledgments
First and foremost I would like to thank Professor Efrain Rodriguez for his
guidance and support. It has been a pleasure to work with and learn from such
an extraordinary scientist. I am grateful for the opportunity he has given me to
work on interesting and challenging projects over the past several years, and also
for his kindness and patience as I have navigated graduate school while becoming a
mother. Gratitude is also due the past and present members of the Rodriguez group.
Their friendships and discussions have provided valuable insights into chemistry,
physics, and life.
I would especially like to thank the support scientists at NCNR and the user
facilities at University of Maryland, particularly Craig Brown, Jeff Lynn, Juscelino
Leao, Peter Zavalij, and Karen Gaskell. I would also like to thank Professors Bryan
Eichhorn, Lawrence Sita, Andrei Vedernikov, and Johnpierre Paglione for serving
on my thesis committee and sparing their time to review this manuscript. I am
grateful for the financial support I received from the National Institute of Stan-
dards and Technology (NIST) Center for Neutron Research (NCNR).
Finally, I owe my deepest thanks to my family. Christian and Camille, I love
you more than anything. Words can not express the gratitude owed to my parents,
who have always stood by and guided me. And special thanks goes to my grand-
mother, Mollyanne Hopkins, who sacrificed food, sleep and time to help me study
for my AP Chemistry exam all those years ago.
iii
Contents
List of Tables vii
List of Figures viii
List of Abbreviations x
1 Introduction 1
1.1 Magnetic frustration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Hollandites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.1 Crystal structure of hollandites . . . . . . . . . . . . . . . . . . . 9
1.2.2 Potential applications for hollandites . . . . . . . . . . . . . . . 12
1.3 Objectives and outline of dissertation . . . . . . . . . . . . . . . . . . . . 14
2 Theory & Techniques 17
2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Synthesis techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.1 Solid state reactions . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.2 Salt flux reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Crystallography & diffraction . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.1 Diffraction theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.2 Diffraction techniques . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3.2.1 Powder X-ray diffraction . . . . . . . . . . . . . . . . . . 28
2.3.2.2 Powder neutron diffraction . . . . . . . . . . . . . . . . 29
2.3.2.3 Single crystal diffraction . . . . . . . . . . . . . . . . . . 34
2.3.3 Powder diffraction data analysis . . . . . . . . . . . . . . . . . . 35
2.3.3.1 Indexing peaks . . . . . . . . . . . . . . . . . . . . . . . 35
2.3.3.2 Rietveld refinement . . . . . . . . . . . . . . . . . . . . 38
2.4 Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.4.1 Mechanisms for magnetic exchange . . . . . . . . . . . . . . . . 47
2.4.2 Measuring magnetic properties . . . . . . . . . . . . . . . . . . . 52
2.4.2.1 SQUID magnetometry . . . . . . . . . . . . . . . . . . . 52
2.4.2.2 Magnetic structure determination from neutron diffrac-
tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.5 Transport measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.6 X-ray photoelectron spectroscopy (XPS) . . . . . . . . . . . . . . . . . . 60
iv
3 Ba1.2Mn8O16 and Ba1.2CoxMn8−xO16 63
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.2 Synthesis & experimental details . . . . . . . . . . . . . . . . . . . . . . 67
3.2.1 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.2.2 Diffraction, magnetization, and spectroscopy . . . . . . . . . . . 68
3.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.3.1 Crystal structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.3.2 Elemental analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.3.3 Magnetic properties . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.3.4 Magnetic structure from neutrons . . . . . . . . . . . . . . . . . 86
3.3.5 Electrical properties . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.3.6 Magnetic exchange interactions in hollandites . . . . . . . . . . 94
3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4 K1.6Mn8O16 107
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.2 Synthesis & experimental details . . . . . . . . . . . . . . . . . . . . . . 110
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.3.1 Crystal structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.3.2 Magnetic properties . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.3.3 Magnetic structure from neutrons . . . . . . . . . . . . . . . . . 122
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5 Bi1.7V8O16 135
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
5.2 Synthesis & experimental details . . . . . . . . . . . . . . . . . . . . . . 138
5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.3.1 Powder diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.3.2 Magnetization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
5.3.3 Magnetotransport . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
5.3.4 Single crystal diffraction . . . . . . . . . . . . . . . . . . . . . . . 152
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
5.4.1 Charge order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
5.4.2 Orbital order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
5.4.3 Spin order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
6 Mixed-metal hollandites 166
6.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
6.1.1 KyMnxTi8−xO16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
6.1.1.1 Synthesis & experimental details . . . . . . . . . . . . 168
6.1.1.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
6.1.1.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 172
6.1.2 Bi1.7CrxV8−xO16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
v
6.1.2.1 Synthesis & experimental details . . . . . . . . . . . . 174
6.1.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
6.1.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 178
7 Overall conclusions & future work 181
7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
7.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
A Further experiments on mixed metal hollandites 185
A.1 Ba1.2FeMn7O16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
A.2 Ba1.2NixMn8−xO16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
A.3 Ba1.2CrxMn8−xO16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
A.4 KyVxMn8−xO16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
A.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
B Extended experimental results and information 194
B.1 Bi1.7V8O16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
Bibliography 195
vi
List of Tables
2.1 BT-1 Monochromator information . . . . . . . . . . . . . . . . . . . . . . 32
3.1 Lattice parameters for BaxMn8O16 and BaxCoyMn8-yO16 . . . . . . . . 77
3.2 Structural parameters for BaxMn8O16 and BaxCoyMn8-yO16 . . . . . . 95
3.3 Select interatomic distances and angles in BaxMn8O16 . . . . . . . . . 96
3.4 Select interatomic distances and angles in BaxCoyMn8-yO16 . . . . . . 97
3.5 Composition Analyses of BMO and BCMO . . . . . . . . . . . . . . . . 98
3.6 Curie-Weiss parameters for Ba1.2Mn8O16 and Ba1.2CoMn7O16 . . . . 98
3.7 Basis functions allowed for Ba1.2Mn8O16 and Ba1.2CoxMn8−xO16 . . . 99
3.8 Comparison of magnetic properties in reported ferromagnetic insulat-
ing hollandites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.1 I4/m Structural parameters for K1.35Mn8O16 (XRD) . . . . . . . . . . . 113
4.2 I2/m Structural parameters for K1.35Mn8O16 (XRD) . . . . . . . . . . . 114
4.3 Select interatomic distances and angles in K1.35Mn8O16 from XRD
(I4/m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.4 Select interatomic distances and angles in K1.35Mn8O16 from XRD
(I2/m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.5 I4/m Structural parameters for K1.35Mn8O16 (NPD) . . . . . . . . . . 118
4.6 I2/m Structural parameters for K1.35Mn8O16 (NPD) . . . . . . . . . . 119
5.1 Structural parameters for Bi1.7V8O16 from NPD . . . . . . . . . . . . . 145
5.2 Structural parameters for Bi1.7V8O16 from single crystal diffraction . 156
6.1 Lattice parameters for KyMnxTi8−xO16 . . . . . . . . . . . . . . . . . . 169
6.2 Curie-Weiss parameters for KyMnxTi8−xO16 . . . . . . . . . . . . . . . 171
6.3 Lattice parameters for BiyCrxV8−xO16 . . . . . . . . . . . . . . . . . . . 177
6.4 Curie-Weiss parameters for BiyCrxV8−xO16 . . . . . . . . . . . . . . . . 178
A.1 Experimental details for Ba1.2FeMn7O16 hollandite . . . . . . . . . . . 186
A.2 Experimental details for Ba1.2NixMn8−xO16 hollandite . . . . . . . . . 188
A.3 Experimental details for Ba1.2CrxMn8−xO16 hollandite . . . . . . . . . 190
vii
List of Figures
1.1 Schematic representation of different octahedral molecular sieve ma-
terials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Magnetic frustration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Geometrically frustrated lattice types . . . . . . . . . . . . . . . . . . . 7
1.4 Hollandite structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1 Representative unit cell and notations . . . . . . . . . . . . . . . . . . . 20
2.2 Bragg’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 Scattering interactions for electrons, X-rays, and neutrons . . . . . . . 25
2.4 Neutron scattering lengths . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.5 Schematic of the BT-1 High Resolution Powder Diffractometer at the
NIST Center for Neutron Research . . . . . . . . . . . . . . . . . . . . . 31
2.6 Schematics for different magnetic orderings . . . . . . . . . . . . . . . 44
2.7 Hysteresis loop for a typical ferromagnet . . . . . . . . . . . . . . . . . 45
2.8 Superexchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.9 Vector diagram for elastic scattering . . . . . . . . . . . . . . . . . . . . 55
2.10 Vector diagram for magnetic scattering . . . . . . . . . . . . . . . . . . 56
2.11 Magnetic time-inversion symmetry . . . . . . . . . . . . . . . . . . . . . 57
2.12 The van der Pauw Technique . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.13 Photoelectric effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.1 Ba1.2Mn8O16 hollandite . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.2 Rietveld refinement of TOF neutron data for BCMO . . . . . . . . . . 71
3.3 Rietveld refinement of TOF neutron data for BMO . . . . . . . . . . . 74
3.4 XPS spectra of Ba1.5Co0.9Mn7.1O16 and Ba1.6Mn8O16 . . . . . . . . . . 78
3.5 Magnetic susceptibility of Ba1.5Co0.9Mn7.1O16 . . . . . . . . . . . . . . 81
3.6 Magnetic susceptibility of Ba1.6Mn8O16 . . . . . . . . . . . . . . . . . . 82
3.7 Standardized inverse magnetic susceptibility for Ba1.6Mn8O16 and
Ba1.5Co0.9Mn7.1O16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.8 Comparison of magnetization versus field measurements for Ba1.6Mn8O16
and Ba1.5Co0.9Mn7.1O16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.9 Magnetic structure of Ba1.6Mn8O16 . . . . . . . . . . . . . . . . . . . . . 88
3.10 Normalized magnetic peak intensity of Ba1.5Co0.9Mn7.1O16 . . . . . . 89
3.11 Magnetic structure of Ba1.5Co0.9Mn7.1O16 . . . . . . . . . . . . . . . . . 91
3.12 Resistivity measurments of Ba1.5Co0.9Mn7.1O16 . . . . . . . . . . . . . 93
3.13 Phase diagram for α-MnO2 Hamiltonian . . . . . . . . . . . . . . . . . 100
viii
3.14 Schematic of magnetic exchange parameters in hollandites . . . . . . 102
4.1 X-ray powder diffraction data for K1.6Mn8O16. . . . . . . . . . . . . . . 112
4.2 100 K Neutron powder diffraction data for K1.7Mn8O16 in I4/m. . . . 120
4.3 100 K Neutron powder diffraction data for K1.7Mn8O16 in I2/m. . . . 121
4.4 Magnetic susceptibility of K1.35Mn8O16 . . . . . . . . . . . . . . . . . . 123
4.5 Magnetization versus field measurements for K1.35Mn8O16 . . . . . . 124
4.6 Neutron powder diffraction data for K1.6Mn8O16. . . . . . . . . . . . . 125
4.7 BT-7 Neutron powder diffraction data of K1.6Mn8O16. . . . . . . . . . . 127
4.8 NG-5 Neutron powder diffraction data for K1.6Mn8O16. . . . . . . . . . 129
5.1 Crystal structure of Bi1.7V8O16 hollandite . . . . . . . . . . . . . . . . . 136
5.2 Neutron powder diffraction data of Bi1.7V8O16 across the MIT. . . . . 141
5.3 Temperature evolution of phase fractions across the MIT. . . . . . . . 143
5.4 Temperature evolution of Bi1.7V8O16 lattice parameters. . . . . . . . . 144
5.5 Molar magnetic susceptibility of Bi1.7V8O16 vs. temperature . . . . . 147
5.6 Magnetization vs. applied magnetic field for Bi1.7V8O16 . . . . . . . . 148
5.7 Electrical resistivity measurements as a function of applied magnetic
field for Bi1.7V8O16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
5.8 Linear dependence of the transition temperature TMI vs. applied
magnetic field for single crystals of Bi1.7V8O16 . . . . . . . . . . . . . . 151
5.9 Single crystal XRD data for Bi1.7V8O16 . . . . . . . . . . . . . . . . . . . 154
5.10 Proposed charge and orbital ordering for Bi1.7V8O16 . . . . . . . . . . . 158
5.11 The Bleaney-Bowers equation for antiferromagnetic exchange between
dimers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
5.12 The Bleaney-Bowers equation for ferromagnetic exchange between
dimers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
6.1 X-ray diffraction for KyMnxTi8−xO16 . . . . . . . . . . . . . . . . . . . . 170
6.2 Magnetic susceptibility of K1.7MnxTi8−xO16 . . . . . . . . . . . . . . . . 170
6.3 Magnetization vs. Field Measurements of K1.7Mn3Ti5O16 . . . . . . . 172
6.4 Rietveld refinement of room temperature XRD data for Bi1.7CrxV8−xO16176
6.5 Trends in θCW , C, and µe f f for BiyCrxV8−xO16. . . . . . . . . . . . . . . 179
A.1 X-ray powder diffraction data for K1.6VxMn8−xO16 . . . . . . . . . . . . 192
B.1 Bi1.7V8O16 single crystal wired for resistivity measurements . . . . . 194
ix
List of Abbreviations
χ magnetic susceptibility
λ wavelength
µe f f effective magnetic moment
θ angle of diffraction
θCW Curie-Weiss temperature
AFM Antiferromagnetim
BCMO Ba1.2CoxMn8−xO16
BMO Ba1.2Mn8O16
BVO Bi1.7V8O16
CMR Colossal Magnetoresistance
CW Constant Wavelength
DM Dzyaloshinsky-Moriya
FC Field-cooled
FM Ferromagnetism
H Magnetic field
HIPD High-Intensity Powder Diffractometer
ICP-AES Inductively Coupled Plasma Atomic Emission Spectroscopy
ICP-MS Inductively Coupled Plasma Mass Spectrometry
J Magnetic exchange interaction
JT Jahn-Teller
LANL Los Alamos National Lab
LNSC Lujan Neutron Scattering Center
M Magnetization
MPMS Magnetic Property Measurement System
MIT Metal-Insulator Transition
NIST National Institute of Standards and Technology
NCNR NIST Center for Neutron Research
NPD Neutron Powder Diffraction
PPMS Physical Property Measurement System
Q Momentum transfer
S Magnetic spin
SQUID Superconducting QUantum Interference Device
TOF Time of Flight
UMD University of Maryland
XPS X-ray Photoelectron Spectroscopy
XRD X-ray Diffraction
ZFC Zero-field cooled
x
Chapter 1: Introduction
Transition metal oxides are a broad class of materials that display a uniquely
wide range of electronic properties. The range of potential applications for transi-
tion metal oxides is vast, and chemists play a vital role in the synthesis and charac-
terization of new materials. Chemical thinking, connecting the composition and the
atomic structure of a material to their observed physical and electronic behaviors
is essential for continued innovations and advances of technology.
Transition metal oxides with relatively open structures can be found in the
form of the so-called octahedral molecular sieves (OMS).1–5 Figure 1.1 shows a va-
riety of Mn-based OMS materials, many of which are found naturally as mineral
deposits. Growing interest in these compounds for potential technological applica-
tions has led to the development of synthetic analogues to these structure types.6
As the name implies, the transition metals in OMS are octahedrally coordinated to
oxide anions, with the connectivity of the octahedra creating microporous tunnels
through the material. The general formula for OMS-materials is AxMO2 where
the A cation is a non-framework cation, typically an alkali or alkaline earth metal,
and the B cation is the framework transition metal, often a redox-active transition
metal.7
1
Figure 1.1: Schematic representation of different octahedral molecular
sieve materials, showing the tunnel and layered structures formed by
the MO6 octahedral units. The mineral names provided are for AxMO2
materials with M = Mn.
2
These OMS materials with regular and open porous structures are generally
metastable with respect to their denser phases,8 and their existence arises from
preparation under special reaction conditions.9 The metastability of porous mate-
rials leads to unique and indispensable properties such as catalytic conversion of
petroleum products into fuels and common feedstocks by zeolites.10,11
Motivated by the success of OMS-materials, zeolites, and other porous inor-
ganic compounds, we have studied the hollandite OMS phase since it displays sig-
nificant flexibility in accommodating different transition metals in its framework.
This thesis details investigations of AxM8O16 hollandites, primarily focusing on
compositions where B = V or Mn and the physical properties arising from their
crystalline structures.
1.1 Magnetic frustration
What is life without a little frustration from time to time? In physics, frus-
tration often leads to exotic properties in materials. In this context, frustration
refers to the existence of competing forces in a material, which cannot be satisfied
simultaneously.12–14
Two geometric motifs recur frequently in materials studied for their magnetic
frustration. In a structure featuring a triangular motif of Ising spins,1 where the
moment is constrained to point in one of two directions, three magnetic moments,
each localized at one corner of the triangle, cannot mutually satisfy a preferred
1More details on magnetism and exchange mechanisms are discussed in Section 2.4.1.
3
Figure 1.2: a) Magnetic frustration of a triangular Ising lattice when
spins are coupled antiferromagnetically. b) Magnetic frustration in a
tetrahedral ‘spin-ice’ model.
nearest-neighbor antiparallel arrangement (left side of Figure 1.2). Instead, the
spins fluctuate, or order, in a less obvious manner. These systems are believed to
not order elegantly at a single energy minimum, but instead display a large degen-
eracy of equally unsatisfied states as the ground state of the system.15,16 In these
systems, only short-range correlations between spins are found for all tempera-
tures, T > 0. Analogous to the correlated state of molecules in an ordinary liquid, a
triangular Ising antiferromagnetic network of spins has been termed a ‘spin liquid’
or described as a cooperative paramagnet.12,17–20
Frustrated arrangements of moments localized on tetrahedral corners have
also been studied, where ferromagnetic nearest-neighbor exchange energies are
stymied by the different Ising axes of the spins. To minimize the energy of this
frustration, six different, energetically equivalent spin configurations are possible
featuring two inward-pointing spins and two spins pointing out of each tetrahedra
(as shown on the right side of Figure 1.2). The frustration in this tetrahedral config-
4
uration is analogous to the distribution of protons around oxygen atoms in frozen
water, and as such has been termed ‘spin ice’, with the spins freezing into a set
configuration below ∼0.5 K.12,17,21
Transition metal oxides with triangular magnetic lattices can lead to new
and interesting phenomena on account of their inherently frustrated geometry. A
few materials known for magnetic frustration due to their triangular and corner-
sharing motifs include kagomé lattices and pyrochlores (as shown in Figure 1.3 a &
b), as well as other structure types including honeycomb lattices, spinels, garnets,
and layered materials such as α-NaMnO2 or NaCoO2 (Figure 1.3 c).
Kagomé lattices have been investigated largely due to their observed mag-
netic frustration, but other interesting electronic behaviors have also been observed,
including multiple magnetic phase transitions at low temperature for Ni3V2O8
and Co3V2O8.22 The KMn3O2(Ge2O7) kagomé structure exhibited weak ferromag-
netism with concomitant insulating behavior.23 Spin glass behavior was observed
in SrCr9pGa12−9pO19, with a θCW ∼ −500 K,2 but no observed spin ordering.24–27
An absence of magnetic order was also observed in the S = 12 kagomé lattice of
herbertsmithite, ZnCu3(OH)6Cl2 exhibiting strong magnetic frustration.28–30
Pyrochlores display properties ranging from electronic insulators (La2Zr2O7),
metallic conductors (Bi2Ru2O7−y), ionic conductors and magnetocaloric materials
(Gd1.9Ca0.1Ti2O6.9),31 mixed ionic and electronic conductors, to spin ice systems
(Dy2Ti2O7), spin glass systems (Y2Mo2O7), Haldane chain systems (Tl2Ru2O7), and
2θCW is a convenient measure of the strength of magnetic interactions, discussed further in Sec-
tion 2.4.
5
superconducting materials (Cd2Re2O7).12,32,33 A tunable response of the colossal
magnetoresistance (CMR) was also observed in the Tl2Mn2O7 pyrochlore upon sub-
stitution of Sc into the Tl atomic site, showing functional improvements for mag-
netic sensing applications compared to Mn-based perovskite materials.34
In two-dimensional (2D) (Delafossite) systems such as AxMO2, where A =
alkali or alkaline earth and M = transition metal, the triangular lattice can ex-
hibit a rich magnetic-structural phase diagram or exotic states such as spin liquids.
No long range magnetic order was observed in NaTiO2 down to 1.4 K, though a
θCW ∼ 1000 K was observed. The S = 12 nature of the Ti3+ suggests the possibility
of exotic quantum behavior at low temperature where there is still no long range
order.24,35 2D spin-half antiferromagnets have also generated considerable inter-
est due to their observed superconductivity (NaCoO2) and spin chirality.12,36,37 The
variation in physical properties in these materials is vast, but is closely related to
their structures and the dimensionality of their correlated magnetic moments.
Less explored are materials in which a 2D triangular lattice is folded into
three-dimensional (3D) space, leading to new topologies for studying magnetism.
By rolling a triangular sheet (such as α-NaMnO2) into a cylindrical tube, the 2D tri-
angular lattice is transformed into a 3D tunnel, which at the same time constrains
the system to a pseudo-1D topology (Figure 1.3 d). Such a folded triangular lattice
can be realized in a group of metal oxides with the so-called hollandite structure
type. This thesis focuses on compositional variations of hollandites and the result-
ing magnetic and electronic properties inherent to the structure and compositions
of these materials.
6
d) tunnelc) layered
b) pyrochlorea) kagome
‘
Figure 1.3: Magnetic frustration stemming from geometric con-
straints inherent in triangular lattices has been repeatedly observed
in a) kagomé lattices (e.g. YCa3(MnO)3(BO3)4),38 b) pyrochlores (e.g.
Tl2Mn2O7), c) layered (e.g. α-NaMnO2) and d) tunnel structures (e.g.
Ba1.2Mn8O16). Some atoms have been omitted from each structure to
provide more clarity in visualizing the triangular connectivity of the
magnetic cations (in gray) in each framework.
7
No long range order is possible in one-dimension for T > 0, so one-dimensional
(1D) magnets might be assumed to be tedious and uninteresting. In reality, the one-
dimensionality allows the possibility of complex excitations which are still far from
being completely understood. The study of systems with magnetic order limited to
only one or two dimensions has been one of the most active areas recently in solid
state physics and chemistry. Interesting magnetic phenomena occur as a result of
the 1D, or even pseudo-1D nature of spin chains, spin ladders, and spinons. Novel
Haldane spin-liquid ground states and spin-Peierls transitions have been observed
in 1D spin-1 and spin-12 systems, respectively, such as the quasi-1D antiferromagnet
PbNi2V2O8.39,40
Though extensive studies have been conducted into the magnetic properties
and the structure of nonporous perovskite and pyrochlore structures, little work
has been done on porous oxide materials. The magnetic ordering in hollandite
and todorokite materials has been reported, with both systems classified as spin
glasses.41 Many of these systems contain manganese in non-integral formal oxida-
tion states, thereby offering interesting correlations between the structure and elec-
tronic interactions. These studies have increased in importance since the discovery
of colossal magnetoresistance (CMR), in mixed-valent manganese perovskites and
pyrochlores.
8
1.2 Hollandites
1.2.1 Crystal structure of hollandites
In 1906, Lewis Leigh Fermor provided the first description of what would
come to be known as the mineral hollandite, honoring Mr. Thomas Henry Holland
(then Director of the Geological Survey of India) as the mineral’s namesake. The
crystal structure of the hollandite mineral was not solved until 1945 by Byström
and Byström, when it was decided to be isostructural to another known manganese-
based mineral called cryptomelane.42 Indeed, a series of minerals, including aka-
ganeite, cryptomelane, coronadite, psilomelane, and others, feature the same crys-
tallographic structure, with different names corresponding to different elemental
compositions.43–46 These materials have since been grouped together into the ’hol-
landite’ family allowing a wide range of compositional flexibility.
With a nominal formula of AxM8O16 (where A ≤ 2), the hollandite structure
can be described as MO6 octahedra that share edges and corners to form a square
tunnel, which is occupied by the A cations (Figure 1.4). Surrounded by eight oxy-
gen atoms from metal-oxide framework, the A cation is often nonstoichiometric
and orders Coulombically depending on its size and valency. This affects the oxida-
tion state of the framework transition metal cations (M),resulting in mixed valency
(usually a mix of 3+ and 4+ oxidation states). The tunnel walls are composed of
edge-sharing MO6 octahedra that connect the M centers in a triangular ladder,
resulting in tunnel dimensions of 2×2×∞ MO6 octahedra.
9
Figure 1.4: a) Tetragonal (I4/m) hollandite structure viewed down the
tunnel direction, b) tunnel wall of hollandite showing the triangular lad-
der. c) Monoclinic (I2/m) hollandite structure viewed down the tunnel
direction. For the nominal formula AxM8O16, A is represented in yellow
or green, M is gray, and O is red. Blue axes indicate the I2/m crystallo-
graphic setting, black axes indicate I4/m.
10
In his original description of the mineral, Fermor wrote that "the crystals
in their simplest form show what looks like a tetragonal prism surmounted by a
flat tetragonal pyramid; but the few angular measurements yet made indicate that
the mineral is either orthorhombic or triclinic, more probably the latter, and in
either case very closely approaching the tetragonal form."47 In the description of
the unit cell, Byström claimed either a tetragonal or pseudotetragonal setting. The
latter case was classified as monoclinic, with a β angle deviation from 90◦ of 0.5 -
1.5◦, and a difference of 0.1-0.2 Å between the a and c unit cell parameters.42 The
debate on whether hollandite materials best fit the tetragonal (usually I4/m) or
monoclinic (I2/m) setting depends on the composition of the material. Cheary et al
observed a trend where hollandites featuring a large A cation, paired with a small
M framework cation were usually tetragonal. Conversely, compositions featuring
small A cations and large M cations were typically observed to fit the monoclinic
setting. The rationale behind this trend was the supposition that the framework
walls collapse in on the A cation, with the corner linkages of the MO6 double chains
acting as hinges, as shown in Figure 1.4. Proposing a correlation based on cation
size, Cheary suggested a line of bifurcation at rM /rA ∼ 0.48 as a predictive indicator
for the hollandite symmetry, where rM , rA, and rO are the ionic radii of M, A, and
O, respectively.48
More recently, however, other researchers have rejected Cheary’s indicator as
overly simplistic. A second predictive measure for determining the symmetry of
hollandites was proposed by Zhang and Burnham, claiming that if rA >
p
2(rO +
rM)− rO, the structure could not be monoclinic, whereas if rA <
p
2(rO+ rM)− rO−
11
0.15 the compound could not be tetragonal.49 They also derived further equations
for predicting the lengths of unit-cell edges,
a(Å)= 5.130(rO+ rM)−0.0291ZM +0.441δA (1.1)
c(Å)=
p
2(rO+ rM)+0.0366ZM +0.552δM (1.2)
where ZM is the charge of the M cation, δA is the excess size of the tunnel
cation A relative to the MO6 framework, and δM is the excess size of the M cation
relative to the octahedral cavity.
1.2.2 Potential applications for hollandites
Hollandites have several unique functionalities over other common microp-
orous materials such as silicates and zeolites, including electrical conductivity, long-
range magnetic ordering, and redox properties arising from partially filled d-states
in the framework. To some extent, the d-orbital filling can be controlled through
systematic incorporation of various transition metals into the frameworks and ma-
nipulation of their oxidation states. Thus, we can manipulate the electronic band
structure of these microporous materials - a functionality lacking in mesoporous
zeolites, for example.
The transition metal sites in hollandite structures can accommodate valen-
cies from 2+ to 5+, and mixed valency is a common phenomenon in OMS materials.
Just as mixed-valence manganates with the perovskite structure display interest-
12
ing and useful behavior such as colossal magnetoresistance (CMR),34,50–52 mixed
valences for M cations in hollandites could also lead to similar phenomena. Mate-
rials displaying CMR properties have aroused great interest due to their possible
application in magnetic storage and sensing devices.53 The tunability of the cations
in the hollandite structure type makes these oxides highly functional for various ap-
plications such as molecular sieves, radiation waste storage, catalysts, and cathode
materials in batteries.
The triangular M–M connectivity, coupled with mixed valency, can lead to
interesting properties including insulating ferromagnetism,54,55 frustrated mag-
netism,56–58 and MITs.59–61 Magnetic insulators are rare materials with potential
applications in spintronics and multiferroics. The hollandites AxM8O16, which con-
tain mixed-valent transition metals, have demonstrated ferromagnetism combined
with insulating behavior and provide a new platform for exploring the effects of
magnetic frustration due to their ‘folded’ triangular lattice.
The most comprehensive studies on the physicochemical properties of these
OMS-materials have been carried out on the Mn-based oxides.5,6,41,62–65 Systematic
studies to find other transition metals that may form these structures have been
scattered and largely unconnected. There are, however, several other transition
metals that can form the hollandite type structure including KxCr8O16,54,55,66,67
KxV8O16,68–70 LaxMo8O16,71 BaxRh8O16,72,73 and AxTi8O16.74–76 The physical prop-
erties of the Cr- and V-analogues show unique behavior, including metal-to-insulator
transitions (MITs) and the unusual combination of semiconducting behavior coex-
isting with ferromagnetism.54,55,59,60,77–80 Thus it is very likely that exploring hol-
13
landite materials containing not just mixed valence but also mixed metals will yield
interesting properties. Indeed, doping and substitution at the M site in hollandites
has already been undertaken by various researchers in efforts to tune the chemical
properties.48,70,74,75,79,81–95 Determining the location(s) of dopant atoms, as well as
any potential charge ordering, is key to understanding new physics in the hollan-
dites as well.
1.3 Objectives and outline of dissertation
In this dissertation, several different hollandite materials will be presented
along with their accompanying magnetic and electronic properties. Developing
magnetic models in complex structures is still very challenging. This dissertation
focuses on a fundamental understanding of the interplay between structure and
physical properties in hollandite materials.
In Chapter 2, fundamental theory and techniques are presented related to the
following experimental results and analyses. The discussion focuses primarily on
the basics of crystallography and magnetism, with some attention paid to transport
and spectroscopic measurements.
In Chapter 3, the barium manganate hollandite, and its cobalt-substituted
derivative are presented. The magnetic structure of BaxMn8O16 was tuned from
a complex antiferromagnet with a Néel temperature (TN) = 25 K to a ferrimagnet
with Curie temperature (TC) = 180 K via partial cobalt substitution for manganese.
Both BaxMn8O16 and BaxCoyMn8−yO16 were prepared by salt flux methods, and
14
combined neutron and X-ray diffraction confirm a monoclinic hollandite structure
for both oxides. X-ray photoelectron spectroscopy reveals that the Co2+ substitu-
tion drives the average Mn oxidation state from 3.7+ to nearly 4.0+, thereby chang-
ing its d-electron count. Magnetization and resistivity measurements show that
the cobalt-doped hollandite belongs to the rare class of ferrimagnetic insulators,
with a high TC of 180 K. Based on neutron diffraction measurements the first pro-
posed solution of the magnetic structure of BaxMn8O16 is described, which consists
of a complex antiferromagnet with a large magnetic unit cell. Upon substituting
cobalt for manganese, the magnetic structure changes dramatically, destroying the
previously large magnetic unit cell and promoting ferromagnetic alignment along
the hollandite tunnel direction. The observed hysteresis at base temperature for
BaxCoyMn8−yO16 is explained as arising from uncompensated spins aligned along
the (200) crystallographic planes.
Chapter 4 discusses the potassium manganate hollandite system, and the at-
tempts made to determine the magnetic structure through several different neutron
diffraction studies. Ambiguity in determining the symmetry (I2/m vs I4/m) of the
polycrystaline K1.6Mn8O16 material complicates indexing the magnetic peaks.
Chapter 5 discusses a metal-insulator transition tuned by application of an ex-
ternal magnetic field that occurs in the quasi-one dimensional system Bi1.7V8O16,
which contains a mix of S = 1 and S = 12 vanadium cations. Unlike all other
known vanadates, the magnetic susceptibility of Bi1.7V8O16 diverges in its insu-
lating state, although no long-range magnetic ordering is observed from neutron
diffraction measurements, possibly due to the frustrated geometry of the triangular
15
ladders. Magnetotransport measurements reveal that the transition temperature
is suppressed upon application of an external magnetic field, from 62.5 K at zero
field to 40 K at 8 T. This behavior is both hysteretic and anisotropic, suggesting t2g
orbital ordering of the V3+ and V4+ cations drives a first-order structural transition.
Single crystal X-ray diffraction reveals a charge density wave of Bi3+ cations with a
propagation vector of 0.846c*, which runs parallel to the triangular chain direction.
Neutron powder diffraction measurements show a first-order structural transition,
characterized by the coexistence of two tetragonal phases near the metal-insulator
transition. Finally, we discuss the likelihood that ferromagnetic V–V dimers coexist
with a majority spin-singlet state below the transition in Bi1.7V8O16.
In Chapter 6, preliminary studies into the mixed metal solid solutions of
Bi1.7CrxV8−xO16 and K1.7MnxTi8−xO16 hollandite materials are discussed. Within
the Bi1.7CrxV8−xO16 set of materials, efforts are ongoing in driving the hollandite
to a completely S=1 state, allowing investigation of the potential existence of Hal-
dane behavior in the pseudo-1D hollandite structure. Understanding the effects of
systematically changing the composition between two known end members of the
hollandite family will allow for future tunability of the K1.7MnxTi8−xO16 materials.
Chapter 7 provides the conclusion to this thesis, outlining future work to be
done on materials with the hollandite structure type.
16
Chapter 2: Theory & Techniques
2.1 Overview
This chapter provides an overview of the experimental techniques and related
theory utilized in characterizing the structure and properties of the materials re-
ported within this thesis.
2.2 Synthesis techniques
Various synthetic techniques have been reported for synthesizing hollandite
materials. Hydro- and solvothermal techniques, as well as redox chemistry result-
ing in precipitation of the desired product are synthetic methods often utilized in
investigating the catalytic activity of hollandite materials.3,41,64,89,96–101 The very
small particles desired for catalytic studies have a high surface-to-area ratio, often
resulting in low crystallinity of the materials, which is less than ideal for detailed
structure-property analysis. Rather, in order to more fully investigate the relation-
ships between the hollandite structure and the accompanying physical properties,
highly crystalline materials are desired, and these wet synthetic techniques were
for the most part disregarded.
17
High pressure techniques have been reported to produce single crystal sam-
ples of different hollandite materials.54,66 Unfortunately, the small physical dimen-
sions of the diamond anvil cells used in this technique limit both product yields
and crystal sizes. Aside from the lack of access to equipment for high pressure syn-
theses, the desire to produce quantities of material suitable for neutron diffraction
studies rendered this synthetic technique unhelpful for the studies herein.
The propensity of OMS materials to develop crystallographic defects, such as
twinning and/or intergrowth of more than one OMS phase, make it difficult to grow
crystals or prepare highly crystalline powders.6 The fact that most inorganic sys-
tems are prepared by mixing dry ingredients and then firing at high temperature
also makes it generically difficult to achieve very high purities. A range of crystal
structures exist and each can often accommodate a range of magnetic ions, so the
limits to this process are generally quite rigid. Further, not all chemical structures
can be prepared with high purity and crystallinity, especially as single crystals, and
particularly those obtainable only by high-pressure synthesis.
Because of the difficulty of preparing polycrystalline or single crystal hollan-
dite materials under ambient conditions, little focus was given to making polycrys-
talline or single crystal samples of hollandites until 2001, when Kato et al and
other researchers observed a metal-insulator transition in BixV8O16.102 Recently,
Talanov et al and Moetakef et al have demonstrated high quality single crystal
growth of hollandite oxides through flux methods.75,103 Therefore, we have sought
to prepare highly crystalline and phase-pure Mn-based hollandites by employing
salt flux methods in order to fully explore the relationship between crystal struc-
18
ture and magnetic properties.
Solid state and salt flux techniques are thus the main focus of the synthetic
work within this thesis.74,85,104–106 Aside from producing polycrystalline or single
crystal hollandites, these techniques have the added advantage of fairly facile scal-
ability and working under ambient conditions.
2.2.1 Solid state reactions
Traditional solid state synthetic techniques are very straightforward. Pow-
dered reactants are mixed together, then often pressed into pellets and heated in a
furnace for a prolonged period of time. This synthetic method is intrinsically slow
because of the inhomogeneity inherent at the atomic level. Nucleation of small crys-
tals is able to occur at interfaces between different precursor grains, but in order
for the9
2.2.2 Salt flux reactions
In contrast to crystal growth methods where the desired crystals have the
same composition as the melt, precipitation methods involve the growth of crystals
from a solvent of different composition. The solvent may be one of the constituents
of the desired crystal, or the solvent may be an entirely separate liquid in which
the crystals of interest are partially soluble. In these cases, the solvent melts are
sometimes referred to as fluxes since they effectively reduce the melting point of
the crystals by a considerable amount.9
19
Figure 2.1: Representative unit cell depicting different features includ-
ing lattice points (purple), directions (orange), and lattice planes (green
and blue).
2.3 Crystallography & diffraction
A crystalline material is defined by the infinite repetition of a basic unit cell
motif in three dimensions, where the unit cell is the smallest repeating unit that
retains the full symmetry of the greater crystal structure. For a three-dimensional
crystal, there are seven possible independent unit cell shapes, determined by the
unit cell axes a, b, and c and angles α,β, and γ in real space (Figure 2.1).
Crystallographic techniques such as X-ray and neutron diffraction (discussed
in subsequent sections) utilize reciprocal space in probing the structure of a crys-
talline material. The relationship between the physical crystal structure and its
20
reciprocal lattice (indicated by *) is given by
a∗ =
~b×~c
VC
;b∗ = ~c×~a
VC
; c∗ = ~a×
~b
VC
(2.1)
where VC is the volume of the unit cell, and hence;
VC =~a · (~b×~c) (2.2)
Within a crystalline material, a general point position is characterized by the
coordinates u, v, w, or by the position vector~ruvw:
~r = u~a+v~b+w~c (2.3)
To indicate the direction along one of the unit cell edges, a, b, or c, the no-
tations [100], [010], and [001] are used, respectively (Figure 2.1). Similarly, the
notation [111] is used to indicate the direction of the cell diagonal.
Lattice planes extend in two dimensions throughout the crystal and are de-
scribed by Miller indices, (hkl). This is achieved by taking the inverse of the point
where the lattice plane intercepts the cell axes ~a/h;~b/k;~c/l. For example, a plane
that intersects the a axis one unit cell length away from the origin has an h value
of 1. If the lattice plane intersects the b axis at its halfpoint, k = 1/2, and likewise
for c with l, resulting in a Miller index of (122), as depicted in blue in Figure 2.1.107
The reciprocal lattice vector d∗ = ha∗+kb∗+ cl∗ is perpendicular to the direct
lattice planes with Miller indices (hkl). The magnitude of d is the reciprocal of the
21
nλ
θ
dhkl
Q
λ
A
B
1
1’
2
2’
Figure 2.2: Bragg’s formulation of diffraction by describing the phe-
nomenon as reflections from uniformly spaced layers.
shortest distance between these (hkl) planes, as seen in Figure 2.2.
|d∗| = 1
dhkl
(2.4)
2.3.1 Diffraction theory
A useful representation of the diffraction process is given by picturing the
atoms as arranged in a set of lattice planes (Figure 2.2). William H. and William L.
Bragg regarded these planes as semi-transparent mirrors such that when a crystal
is bombarded with some type of incident radiation, some of the beams are reflected
by a plane, while the remainder are transmitted and later reflected by subsequent
planes.
The spacing between parallel lattice planes, d, and the angle of incidence, θ,
22
is related to the distance traveled by Bragg’s law,
nλ= 2d sinθ (2.5)
where n is an integer, λ is the wavelength, d is the interlayer spacing, and θ
is the angle of incidence.
If a crystal is comprised of uniformly spaced lattice planes A and B, for the
reflected beams 1’ and 2’ to be in-phase, then the additional distance that beam 22’
has to travel relative to 11’ must be an integer multiple of the wavelength. Coherent
scattering is only observed in the occurrence of constructive interference, where the
path difference between scattered beams is an integer number of wavelengths. Out-
of-phase reflections interfere destructively, resulting in cancellation or weakening
of the reflected signal intensity.108
The position of diffracted radiation is determined by the distance between the
Miller planes, and therefore, the lattice parameters of the crystal. The relative
intensities of the Bragg reflections, Ihkl , are dependent mostly on the position of
the atoms within the unit cell.
2.3.2 Diffraction techniques
Within a crystal, the scattering power for a reflection off the (hkl) lattice plane
is defined by the structure factor, Fhkl , where Ihkl is the square of the amplitude of
23
the structure factor:
Ihkl = |Fhkl |2 (2.6)
For X-rays, the structure factor is written as
Fhkl =
∑
i
f i exp[−2pii(hxi+kyi+ lzi)]exp(−Wi) (2.7)
and the structure factor for neutrons is
Fhkl =
∑
i
bi exp[−2pii(hxi+kyi+ lzi)]exp(−Wi) (2.8)
where xi, yi, and zi are the fractional coordinates of the ith atom, f i is the
scattering amplitude for X-rays, and bi is the neutron scattering length. Wi is the
Debye-Waller isotropic temperature factor taking into account the thermal vibra-
tion of the atoms.
Wi =
8pi2 sin2θ〈u2i 〉
λ2
(2.9)
where 〈u2i 〉 is the mean square displacement of the ith atom
Both X-ray and neutron diffraction techniques were heavily utilized in the
studies herein.
The ability to scatter radiation varies by atom and type of radiation (Figure
2.3). For X-rays, the scattering amplitude ( f i) is proportional to the number of core
electrons, and also depends on the radial distribution of electron density around the
atomic nucleus. As a direct result, X-rays are not always reliable in determining
24
Figure 2.3: Schematic depicting the different scattering interactions of
electrons, X-rays, and neutrons in matter. Electrons (blue) and X-rays
(purple) interact with electron clouds via electrostatic and electromag-
netic mechanisms, respectively. As a result of these interactions, neither
medium is able to penetrate as deeply below the surface as neutrons
(green), which interact with atomic nuclei. The nuclear interactions of
neutrons are limited to very short ranges. Neutrons are also capable of
dipole-dipole interactions with the magnetic moment of unpaired elec-
trons in the material.
25
the location of light atoms within a structure, or for resolving parameters for two
transition metals of close Z. The scattering factor for X-rays is also a function of the
Bragg angle, with intensity dropping at higher values of 2θ.
With neutrons, coherent scattering (bi) by nuclei occurs independently of the
Bragg angle, resulting in higher peak intensities persisting at high values of 2θ.
Unlike X-rays, the scattering strength of neutrons does not follow an intuitive
trend, as depicted in Figure 2.4. The scattering length values result from variation
in the nuclear properties (such as spin, energy levels, etc.) of any given nuclide.
This is observed in the difference between the values for 1H, 2H, and 3H, which are
-3.7409 fm, 6.674 fm, and 4.792 fm, respectively.109
Neutrons are a spin-12 particle with a non-zero magnetic moment. Thus, in
addition to interacting directly with the nucleus of an atom, neutrons are capable
of dipole-dipole interactions with magnetic moments of unpaired electrons in the
material, making neutrons an invaluable probe in determining the magnetic order-
ing in materials. Similar to the scattering factor for X-rays, however, the magnetic
scattering factor is a function of the incident angle of radiation, resulting in mag-
netic Bragg peaks appearing at low values of 2θ.
The limitations of each type of scattering can largely be overcome by com-
bining data collected by the different techniques, which will now be individually
discussed in further detail.
26
Figure 2.4: Neutron scattering lengths for elements Hydrogen through
Francium. Different isotopes of the same element can have significantly
different scattering lengths, as indicated by the values provided for hy-
drogen, deuterium and tritium.109
27
2.3.2.1 Powder X-ray diffraction
Laboratory X-ray diffractometers are composed of three primary components:
a radiation source, a monochromator, and a radiation detector. A typical X-ray setup
consists of a metal target, typically copper, in a tube under high vacuum. A filament
(such as tungsten) is heated at one end of the tube, emitting a beam of electrons,
which are accelerated towards the copper target. When the electrons collide with
the copper, core K-shell electrons are emitted, causing electrons from higher filled
shells to drop into the now vacant 1s orbitals.
The transitions from the outer L and M shells to the K (1s) shell (that is L→K
and M→K) are designated as Kα and Kβ, respectively, resulting in the emission
of electromagnetic radiation with a characteristic wavelength unique to every ele-
ment.2 The relaxation of electrons into the 1s orbital vacancies is governed by the
transition selection rule, which requires a change in orbital angular momentum of
one (∆l =±1), thus dictating that the relaxing electron must come from the L (2p)
or M (3p) orbitals, resulting in two intense lines in the emission spectrum. The
emitted X-rays can then be passed through the monochromator, which diffracts the
beams to produce radiation at a single wavelength.
Powder X-ray diffraction (PXRD) is beneficial for samples where it is difficult
to obtain single crystals. An ideal sample for PXRD measurements is well-ground
and prepared in such a way that the sample particles are randomly distributed over
2This phenomenon is exploited in the fundamentals of X-ray Photoelectron Spectroscopy, dis-
cussed and illustrated in Section 2.6.
28
every possible orientation. Successful powder diffraction measurements thereby
give information for every possible reflection in a structure, producing a diffraction
pattern where diffracted Bragg peaks from three dimensions are superimposed onto
a 1D axis.
Powder X-ray data for the materials discussed in this thesis were collected
using a Bruker D8 Advance X-ray diffractometer with a copper source, located at
the X-ray Crystallography Center at the University of Maryland. Samples were
finely ground and laid on a plastic disk, with efforts taken to minimize the effects of
preferred orientation. Materials were typically studied from 8 to 90◦ two-theta, in
steps of 0.04◦ at 1 second per step to verify phase purity. Collected data were then
refined in most cases using the Rietveld method. Successful use of the Rietveld
method is directly related to the quality of powder diffraction data, with better
quality data increasing the likelihood of a reasonable, reliable structure. Thus, for
the samples discussed herein, longer scans were utilized, measuring from 8 to 140◦
2θ, in steps of 0.013◦ at 0.85 second per step.
2.3.2.2 Powder neutron diffraction
Neutrons are useful as a probe for investigating magnetism in condensed mat-
ter, providing experimental means to observe both light atoms, as well as the ar-
rangements of magnetic moments in a material.
There are two types of facilities that produce neutrons at the appropriate en-
ergies to be used in neutron diffraction studies. The first method of neutron produc-
29
tion involves a fission reaction at a nuclear reactor. Uranium with enriched levels of
235U is a very common fuel at these reactors, and through fission of the radioactive
fuel, very high energy neutrons are produced in a flux of up to 1015 s−1 cm−2.109 It is
then necessary for the neutrons to be slowed down via a moderating material such
as heavy water (D2O) to obtain an approximate energy. These neutrons are then
guided through a collimator to produce a coherent beam, to a large single crystal
monochromator, which directs radiation of a specific wavelength towards the sam-
ple in what is termed Constant Wavelength (CW) diffraction. The monochromation
process results in the loss of a significant percentage of the original neutron flux
produced, but allows for the angular deflections of the neutrons to be interpreted
using the relations described in Bragg’s law. Interaction of the incident neutrons
with the sample then scatters the radiation, which is then measured by the detec-
tor.
A majority of the powder neutron diffraction data in this thesis was collected
using the BT-1 high-resolution powder neutron diffractometer at the National In-
stitute of Standards and Technology (NIST) Center for Neutron Research (NCNR)
(Figure 2.5) in Gaithersburg, Maryland. The reactor at NCNR produces a thermal
flux of 4×104 neutrons/cm2·s using uranium as the reactor fuel. Three different
collimators for the incident radiation allow the instrument response to be tailored
to the experiment, and three different monochromators are available for BT-1 mea-
surements, namely Ge(311), Cu(311), and Ge(733). Details for each monochromator
are provided in Table 2.1. A rotating bank of 32 3He detectors at 5◦ intervals allows
diffraction data to be collected over a 2θ range of 0 - 167◦.110
30
Figure 2.5: Schematic diagram of the BT-1 high-resolution powder neutron diffractometer operating at constant wavelength
(CW). Adapted from Ref.110 Notable features common to all CW neutron diffractometers include collimators to align the beam,
monochromators to select for a particular wavelength, and detectors to measure the scattering after neutrons interact with the
sample.
31
Table 2.1: Monochromator details for the BT-1 constant wavelength neutron powder diffractometer at NCNR.111
Mono-
chromator
In-pile Col-
limation (ar-
cmin)
Mono-
chromator
2θ (◦)
Relative
Bragg Inten-
sities
Flux (n/(cm2 ·
s)
λ (Å) Relative
Number of
Reflections
Ge(311) 60’ 75 5.78 1,160,000 2.079 50
15’ 75 2.86 570,000 2.079 50
7’ 75 1.44 290,000 2.079 50
Cu(311) 60’ 90 1.84 870,000 1.540 100
15’ 90 1.00 440,000 1.540 100
7’ 90 0.54 230,000 1.540 100
Ge(733) 60’ 90 0.31 330,000 1.197 200
15’ 90 0.20 200,000 1.197 200
7’ 90 0.11 120,000 1.197 200
32
Instead of using neutrons produced by a nuclear reactor, nuclear spallation
provides a second technique for producing neutrons. This method requires a heavy
metal source (such as mercury or tungsten) that gets bombarded by protons that
have been accelerated to high energies (up to 1000 MeV), thus also requiring an
accelerator such as those found at synchrotron facilities. Upon the proton’s collision
with the heavy metal, a burst of neutrons and other small particles is ejected from
the source in all directions and at all frequencies, with a flux of ∼20-30 neutrons for
every proton that bombards the target.112
After the original pulse produces a white beam of neutrons, the spalled neu-
trons pass through a moderator, interact with the sample, and finally reach a de-
tector, fixed at scattering angle 2θ0. The total time from the initial pulse until the
final detection event is carefully measured and is then used to calculate the scat-
tered intensity as a function of neutron wavelength.
The relation between the wavelength of the neutron and the total time-of-
flight (t) can be calculated by connecting the de Broglie equation to Bragg’s law:
λ= ht
mnL
= 2dhkl sinθ0 (2.10)
where mn is the neutron mass, h is Planck’s constant, L = L1 + L2 is the
total flight path (L1 is the distance the neutrons travel from the moderator to the
sample, and L2 the distance between the sample and detector), and 2sinθ0 is the
fixed scattering angle. The spectral distribution of the incident beam is modeled
by measuring isotropic scattering from a vanadium standard, accounting also for
33
necessary corrections in detector efficiency as a function of wavelength variation.
The technique utilizing Eq. 2.10 from a spallation source is known as time-
of-flight (TOF) analysis, and allows for greater neutron flux at the sample as there
is no monochromation required. Compared to the incident beams used in x-ray
diffraction, however, even TOF neutron sources are considered to have low flux;
thus all neutron diffraction studies require significantly more sample for analysis.
Two samples in this thesis were measured using TOF neutron diffraction, col-
lected on the High Intensity Powder Diffractometer (HIPD) beamline at Los Alamos
National Lab (LANL) Lujan Neutron Scattering Center (LNSC). HIPD has detector
banks at 14, 40, 90, and 153 degrees, and can access a Q range from 0.2 to 50 Å−1.
2.3.2.3 Single crystal diffraction
Having a single crystal for X-ray diffraction studies can significantly simplify
the structural determination of a material, particularly if it is a novel structure.
Prior to 1970 almost all single crystal diffraction studies used film. The crys-
tal was mounted in the center of the X-ray beam, causing the incident radiation to
diffract, exposing the film. An alternative method of data collection allowed for the
crystal to be rotated, diffracting X-rays from each of the atomic planes, onto a strip
of film encircling the crystal. Modern electronic detectors featuring either X-ray
counters or optical detection by CCD have improved the accuracy of X-ray intensity
and count rates.
Scattering from a crystal is confined to distinct points in reciprocal space. The
34
intensity in each point is modulated by the absolute square of the unit cell structure
factor. With a sufficiently large set of diffracted intensities from a given crystal it is
possible to deduce the positions of the atoms in the unit cell.
The single crystal instrumentation used herein is a Bruker Apex2 diffrac-
tometer equipped with a molybdenum source and a CCD area detector, with a
graphite monochromator. Single crystal X-ray data was measured by rotating crys-
tals mounted in the incident radiation.
2.3.3 Powder diffraction data analysis
When an incident beam is diffracted off of randomly oriented crystallites in
a powder sample, the observed diffraction pattern is a superposition of scattering
that occurs in the three-dimensional crystallographic lattice onto a one-dimensional
representation. Miller planes that have similar d-spacing, regardless of their ori-
entation along the different crystallographic axes, subsequently diffract to similar
2θ angles. Oftentimes, these peaks overlap, making accurate measurement of the
observed intensities difficult. Developing the computational tools to analyze all the
Bragg peaks in a diffraction pattern simultaneously was a major breakthrough in
powder analysis. These tools are described in the subsequent sections.
2.3.3.1 Indexing peaks
In order to solve a structure from powder data it is necessary to extract as
many (hkl) reflectionsand intensity values as possible from the data set. Peak
35
locations tell the size of the crystallographic unit cell, whereas peak intensities
relate to the contents of the unit cell. Atomic identities, partial or full occupancies,
and thermal displacements affect the intensities, and microcrystalline properties
affect the peak shapes.
Initially, peak positions are found in the data. Next, the pattern is indexed in
order to determine the unit cell or lattice parameters. Then, space group determi-
nation follows based on symmetry and the presence or absence of certain reflections.
Either Le Bail or Pawley techniques may be used to extract intensities and refine
the unit cell.
Until the 1980s, accurate extraction of peak intensities was not feasible due
to the overlapping nature of peaks in a powder diffraction profile. However, with
the development of high-speed computers with large memories and high-resolution
diffractometers, pattern decomposition became a viable and important part of the
analyses of powder data.
In the Pawley technique, every reflection is assumed to have a peak position
determined by the unit cell parameters and the 2θ zero error, with peak width
determined by the resolution function parameters U, V, W, and a peak intensity
Ihkl .
Pawley reduced the correlations by introducing both constraints and restraints
into the least-squares procedure. As the difference between the calculated 2θ val-
ues of two adjacent peaks approaches zero, their intensities are constrained to be
equivalent. When the ∆2θ is less than the step size, this is introduced as a hard
constraint, and when larger, it is used as a soft restraint. Negative intensities may
36
occasionally be obtained.
The Pawley technique treats peaks individually, while the Le Bail technique
is a method of whole pattern fitting. Le Bail fits can suggest a potential crystallo-
graphic setting, based off of the combination of peak locations.
When either the Le Bail or Pawley technique is employed to perform a full
pattern decomposition, one must be careful to use suitably determined relevant
parameters (background, peak shape, zero shift, or sample displacement, and unit
cell dimensions) as the initial approximation.
The Le Bail method extracts intensities (Ihkl) from powder diffraction data.
This is done in order to find intensities that are suitable to determine the atomic
structure of a crystalline material and to refine the unit cell. For the Le Bail
method, the unit cell and the approximate space group of the sample must be prede-
termined because they are included as a part of the fitting technique. The algorithm
involves refining the unit cell, the profile parameters, and the peak intensities to
match the measured powder diffraction pattern. It is not necessary to know the
structure factor and associated structural parameters, since they are not consid-
ered in this type of analysis. Le Bail can be used to find phase transitions in high
pressure and temperature experiments, and it generally provides a quick method
to refine the unit cell, which allows better experimental planning.
Le Bail analysis fits parameters using a least squares analysis, which is an it-
erative process. First, the Le Bail method defines an arbitrary starting value for the
intensities (Iobs). This value is ordinarily set to one, but other values may be used.
While peak positions are constrained by the unit cell parameters, intensities are
37
unconstrained. The somewhat arbitrary choice of starting values produces a bias in
the calculated values. The refinement process continues by setting the new calcu-
lated structure to the observed structure factor value. The process is then repeated
with the new estimated structure factor. At this point, the unit cell, background,
peak widths, peak shape, and resolution function are refined, and the parameters
are improved. The structure factor is then reset to the new structure factor value,
and the process begins again.107
The Le Bail technique is much better suited for dealing with overlapping in-
tensities than using the Pawley technique, since the intensity is allotted based on
the multiplicity of the intensities that contribute to a particular peak.
2.3.3.2 Rietveld refinement
In 1969, Hugo Rietveld proposed a refinement method to overcome the prob-
lem of peak overlap in powder diffraction data.113 To a certain extent, the Rietveld
method (known also as full pattern refinement) is similar to the full pattern decom-
position using Pawley and/or Le Bail algorithms, except that values of integrated
intensities are no longer treated as free least squares variables (Pawley), or deter-
mined iteratively after each refinement cycle (Le Bail). They are included into all
calculations as functions of relevant geometrical, specimen, and structural param-
eters.
Rietveld’s approach essentially compares a calculated diffraction model against
the observed experimental data. The experimental powder diffraction data are uti-
38
lized without extracting individual integrated intensities or individual structure
factors, and all structural and instrumental parameters are systematically refined
as the calculated profile is fit to the observed data. This is accomplished by using a
linear least squares minimization of the function, Sy,
Si =
∑
i
wi(yi− yci)2 (2.11)
where yi is the observed intensity for the ith point and yci is the calculated
intensity at the ith point, and wi is the weighting of the observables and is defined
by
wi = 1yi
(2.12)
Since observed intensity is not associated directly with a Bragg reflection, for
an accurate profile to be obtained, a reasonable starting model is required. The
calculated intensity is dependent on the structure factor |Fhkl |2 values taken from
the model, which are calculated by
yi = s
∑
hkl
mhklLhkl
∣∣Fhkl∣∣2A iG(2θi−2θhkl)PhklT+ yib (2.13)
where s is the scale factor, mhkl is the multiplicity factor, Lhkl is the Lorentz-
polarization factor for the reflection (hkl), A i is the symmetry parameter, G(θ) is the
peak shape function, 2θhkl is the calculated position of the Bragg peak, corrected for
the zero point shift, Phkl is the preferred orientation function, T is the absorption
correction, and yib is the background intensity at the ith step.
39
The agreement between the observed and calculated structures is measured
by the goodness of fit factors, defined as Rwp, for ‘weighted profile’, Rp, for ‘profile
R-factor’, and Rexp for ‘expected’ goodness of fit, each defined as follows:
Rwp =
√√√√∑i wi(yi− yci)2∑
i wi y2i
(2.14)
This compares how well the structural model under refinement accounts for
relatively small and large Bragg peaks across the diffraction profile. The weighting
factor is given by wi.
Rp =
∑
i
∣∣yi− yci∣∣∑
i yi
(2.15)
and
Rexp =
√
(N−P+C)∑
i wi y2i
(2.16)
which accounts for the statistical quality of the data and the number of vari-
ables used in the refinements, where N is the number of profile points, P is the
number of refined parameters, and C is the number of constraints used.
During the course of a structural refinement, the goodness of fit factor, χ2, can
be used to compare the quality of the data.
χ2 =
( Rwp
Rexp
)2
(2.17)
When the structural model, which makes both physical and chemical sense
yields integrated intensities with similar peak and background features to the ob-
40
served data, the fully refined crystal structure of a material should result in a
calculated powder diffraction pattern closely resembling collected data. In other
words, the difference between the measured and calculated powder diffraction pro-
files should be close to zero, and a value close to one observed for χ2.
The Rietveld technique provides a wealth of noncrystallographic structural
information including reliable phase composition, amorphous content, grain size,
microstrain information, texture analysis, and more. When a material is only avail-
able in a fine-grained, powdered, untextured thin film or other states, Rietveld re-
finement is by far the most robust approach for analyzing the structure. Further,
powder diffraction provides a more accurate view of the sample bulk, whereas sin-
gle crystals may have slight variations between different specimens.
Various software programs are available, such as GSAS, FullProf,114 or Topas,115
for utilizing the Rietveld refinement technique to analyze diffraction data obtained
from facilities around the world. The majority of refinements carried out within this
thesis were performed using the Topas software suite unless otherwise indicated.
2.4 Magnetism
Because electrons are present in all matter, everything possesses some type of
magnetism. Diamagnetism occurs when electrons are paired, such as the electrons
filling the core levels of an atom, making diamagnetism an underlying property of
all matter. Magnetism becomes much more interesting, however, when considering
unpaired electrons occupying partially filled d or f orbitals.
41
The magnetic properties of unpaired electrons are regarded as arising from
two causes, electron spin and electron orbital motion. These interact to define the
magnetic moment of an ion by
µ(S+L) =
√
4S(S+1)+L(L+1) (2.18)
where L is the orbital angular momentum quantum number for the ion and S
is the sum of the spin quantum numbers of the individual unpaired electrons. For
first row transition metal ions, due to the smaller size of the d-orbitals, it is more
common to calculate effective magnetic moments by using the spin-only formula,
µs = g
√
S(S+1) (2.19)
where g is the gyromagnetic ratio, and usually has a value of approximately
2.00. Such a spin-only formula indicates that all orbital contributions to the mo-
ment have been quenched.
Magnetic susceptibility (χ) is a dimensionless measure of the magnetic re-
sponse (Magnetization, M) of a material upon application of an external magnetic
field (H).
χ= M
H
(2.20)
The relationship between the magnetic moment, µ, of a material and its mag-
42
netic susceptibility, χ, is given by
χ= Nµ
2
Bµ
2
3kBT
(2.21)
where N is Avogadro’s number, µB is the Bohr magneton, and kB is Boltz-
mann’s constant.
The pairing of electrons in a diamagnet results in very low change in the mag-
netic susceptibility of that material, as there are no unpaired electrons to interact
with an external magnetic field. Thus, the susceptibility of a diamagnet is very
small and slightly negative, due to the decrease in flux density experienced under
an applied field.
Paramagnetism occurs when there are unpaired electrons in a system, but the
spins on those electrons are randomly oriented and do not interact with each other
in an ordered manner. In a paramagnetic material, the magnetic susceptibility
diverges at low temperatures according to the Curie law, which states that magnetic
susceptibility is inversely proportional to temperature, T.
χ= C
T
(2.22)
where C is the Curie constant, and is specific to the material being measured.
Truly paramagnetic materials that obey the Curie law yield a positive slope with
an intercept of 0 K when 1/χ is plotted against temperature.
As thermal energy is removed from the system, or as magnetic field is ap-
plied, spins in a paramagnetic state may couple together, with varying magnetic
43
b) Ferromagnetic (FM) c) Antiferromagnetic 
(AFM)
d) Ferrimagnetic (fM)a) Paramagnetic (PM)
Figure 2.6: a) Paramagnetic ordering (PM), where spins are oriented
randomly with no net magnetization in absence of an external field. b)
Ferromagnetic ordering (FM), with spins aligned parallel to produce net
magnetization. c) Spins aligned anti-parallel, yielding no net magne-
tization for antiferromagnetic ordering (AFM). d) Spins aligned anti-
parallel, but with moments of different magnitudes which fail to com-
pletely cancel each other out, producing net magnetization for ferrimag-
netic (fM) ordering.
behaviors occurring in response to this cooperative interaction. The different types
of magnetic order are summarized below.
A system displays a ferromagnetic response when the unpaired electrons are
correlated in such a way that all of the spins are oriented in the same direction
(all spin up or all spin down), giving a net magnetic moment in one direction. This
ordering occurs at and below the Curie temperature, TC. Unlike diamagnets and
paramagnets, the addition of an external field to a ferromagnetic material can cause
a strong coupling interaction as the moments align. This long range magnetic order
can persist even after the field is removed, resulting in magnetic hysteresis, as
shown in Fig. 2.7.
Upon application of the external field, the magnetization increases from the
44
Figure 2.7: Hysteresis loop for a typical ferromagnet. Ms is the satura-
tion magnetization, or the maximum value of observed magnetization.
Mr is the remnant magnetization, or the amount of magnetization re-
maining when the applied field is returned to zero. Hc is the coercive
field (the applied reverse field necessary to bring the magnetization back
to zero).
45
origin until reaching the saturated value Ms. At this point, all available spins have
aligned to the direction of the magnetic field and the value of Ms will not increase
further, even with application of higher field. Once saturation has been achieved,
decreasing the applied field back to zero does not eliminate the magnetization in a
ferromagnetic material, leaving some remnant or residual magnetization (Mr). The
reversed field required to reduce the magnetization to a value of zero is called the
coercive field, Hc. Further reversal of the field achieves magnetic saturation in the
reverse direction, resulting in a hysteresis loop featuring an inversion symmetry
about the origin.
Antiferromagnetism occurs when the spins are antialigned in a 1:1 ratio, such
that for every spin up electron there is a spin down and net magnetization is zero.
The onset of antiferromagnetic ordering corresponds to a decrease in magnetization
below the ordering temperature, called the Néel temperature, TN .
If the magnitude of the spins, either spin up or spin down, are not completely
counterbalanced by the antialigned moments, the ordering is called ferrimagnetic
and a net magnetic response is observed.
Magnetic ordering causes the susceptibility to deviate from the Curie law, in
ways often unique to the specific material. When a material displays magnetic
order below a critical temperature, the Curie-Weiss law then applies to the system,
where
χ= C
(T+θCW )
(2.23)
46
In the Curie-Weiss law, θCW is the Weiss constant, corresponding to the tem-
perature where the straight line (extrapolated from the high T paramagnetic regime
in the observed data) intercepts the x-axis when 1/χ is plotted against temperature.
A negative Weiss constant indicates an antiferromagnetic interaction, whereas a
positive Weiss constant is indicative of ferromagnetic coupling. The magnitude of
the Weiss constant is indicative of the strength of the interaction.
Essentially, θCW is the sum of the exchange interactions in a magnetic system,
thereby setting the energy scale for the magnetic interactions. In a system with
little or no frustration, strong deviations from the Curie-Weiss law are expected
for T ∼ |θCW |, with an onset of long range magnetic order occurring near |θ|. For
ordered ferromagnets this is nearly realized, as |θCW |/TC ∼ 1. In antiferromagnetic
systems the situation is more complex, depending on the exact magnetic structure
which is adopted. Typical values for non-frustrated AFM lattices show |θCW |/TN
values in the range of 2 to 4 or 5, and the somewhat arbitrary condition, |θCW |/TN
> 10, has been proposed as the threshold for notable frustration.12,24
2.4.1 Mechanisms for magnetic exchange
A first approximation of the Hamiltonian for nearest neighbor metal-metal
magnetic exchange is
H =−2∑Ji jSi ·Sj (2.24)
where the sum is taken over all pair-wise interactions of spins i and j in a
47
lattice.
Direct exchange occurs when electrons on neighboring atoms interact with-
out an intermediary. This requires sufficient orbital overlap. The direct exchange
interaction (Ji j) coupling the spins, Si, of localized electrons in insulators can be
described by the model Heisenberg Hamiltonian
Hex =−
∑
i j
Ji jSi ·S j (2.25)
If the two states of interest are electronic states in a free atom, then the ex-
change integral, Ji j that couples them is positive and the spins align parallel, as
reflected in Hund’s rules. If the interaction takes place between electrons local-
ized on different neighboring atoms, Ji j tends to be negative; this corresponds to
the situation in which two electrons align antiparallel to form a covalent bonding
state. The direct-exchange interaction falls off rapidly with distance, so that the
interaction between further neighbors is effectively zero.
There are several different mechanisms possible for indirect exchange.
Superexchange, first described in the La1-xCaxMnO3 oxides with the perovskite
structure, is the mechanism that describes the interaction of magnetic moments
through a nonmagnetic intermediate, such as an O2− anion. The rules were first
formulated by John B. Goodenough and Junjiro Kanamori, and are subsequently
known as the Goodenough-Kanamori rules.116–118 Superexchange can be described
by a Heisenberg Hamiltonian, in which the sign of Ji j is determined by the metal-
oxygen-metal (M-O-M) bond angle and the d electron configuration on the transi-
48
tion metal. This interaction is an important source of metal-metal interactions or
magnetic exchange in insulating compounds of the transition metal ions.
When d-orbitals of two transition metal cations are oriented towards each
other, overlapping with opposing lobes of an intermediate p-orbital of an O2− ion,
the superexchange mechanism leads to antiferromagnetic coupling between pairs
of filled (M1 f and M2 f ) or empty (M1e and M2e) d-orbitals, as shown in Figure
2.8. This occurs in accordance with the Pauli exclusion principle, which states that
for two electrons to occupy the same orbital, their spins must be paired and in op-
posite orientations. The entire M1-O-M2 configuration is arranged linearly, and
this is known as 180◦ exchange. When the oxygen anion is mediating between
one filled (M1 f ) and one empty (M2e) transition metal d-orbital, the resulting in-
teraction is ferromagnetic. M1 f accepts the electron from the oxygen with spin
opposing the electrons already occupying the M1 f d-orbital. The empty d-orbital
of M2 then accepts the other oxygen electron, which has the same spin type as
the other d-electrons forming its magnetic moment in accordance with Hund’s rule.
The strength of the interaction will depend on the amount of overlap.
Ferromagnetic ordering comes about by a 90◦ exchange path. Similar to the
180◦ exchange mechanism, the transfer occurs between d-orbitals of the transition
metal and the p-orbitals of the oxygen, resulting in the overlap of two different p-
orbitals, px and py, with the corresponding d-orbitals of the two transition metal
sites. This results in two electrons or p-holes present on the oxygen in the excited
intermediate state. Depending on the two transition metal ions, the remaining p-
electrons will either have spins which are parallel or antiparallel since Hund’s rules
49
Figure 2.8: a) Schematic of the superexchange mechanism between
two d5 cations, where every d orbital is occupied by one electron. b)
Schematic of the superexchange mechanism between a d5 cation and
another cation with at least one empty orbital. c) Schematic of the su-
perexchange mechanism between two dn cations, where n≤ 4 and each
cation has at least one empty orbital.
50
suggest that the two electrons would have the lowest energy when they are parallel.
This means that the spins on the two transition metal ions must also be parallel,
and therefore, ferromagnetic behavior should be observed. These dependencies are
articulated in the semi-empirical Goodenough-Kanamori-Anderson rules.116–118
Double exchange, introduced in 1951 by Clarence Zener, is a mechanism for
spin coupling that arises from electron delocalization.119 In the double exchange
mechanism, an electron is shuttled from one metal cation to another through an
intervening O2−. As the oxygen p-orbitals are doubly occupied, the translocation
first involves the movement of an electron from oxygen to M1, followed by a transfer
of a second electron from M2 into the newly vacated oxygen orbital. According to
Hund’s rules, metallic conduction from hopping eg electrons can only occur if the
electrons of the t2g orbitals for both the M1 and M2 ions are ferromagnetically
aligned. Used to explain the magneto-conductive properties of mixed-valence solids,
particularly doped Mn perovskites, the double-exchange mechanism thus accounts
for both ferromagnetic and metallic behavior.
Expanding the nearest neighbor Hamiltonian (Eq. 2.25) to read
Hˆ =−2∑Jxy(SixS jx+Si yS j y)+ JzSizS jz (2.26)
three different models for exchange can be considered.
The Heisenberg model lets Jxy = Jz, allowing the spins to point in any direc-
tion. This requires isotropic exchange interactions, suggesting that the metal ions
should reside at atomic sites with high symmetry.120
51
The XY model, where spins are free to point anywhere in a fixed plane, is
obtained when Jz = 0
When Jxy = 0, the Ising exchange model is obtained, where spins are con-
strained to lie parallel or antiparallel to a particular direction.120
A one-dimensional line of spins is a spin chain. Spins may be constrained to
align in one, two, or three dimensions according to the Ising, XY, or Heisenberg
models, respectively. Spin chains can be approximately realized in crystals if the
crystal structure keeps the chains reasonably far apart. The single ion anisotropy
due to the crystal field splitting may lead to the magnetic moments behaving as
Ising, XY, or Heisenberg spins, or somewhere in between. Very often these sys-
tems show three-dimensional long range order at very low temperatures because
there will always be some small interchain interaction which can couple the chains
together.
2.4.2 Measuring magnetic properties
2.4.2.1 SQUID magnetometry
SQUID (Superconducting QUantum Interference Device) instruments are ca-
pable of sensitive magnetization measurements, detecting very minute magnetic
fields. A SQUID consists of two superconductors separated by thin insulating layers
to form two parallel Josephson junctions. These junctions are superconductors sep-
arated by a thin layer small enough to allow the tunneling of Cooper electron pairs
to pass through the junction. The current in the SQUID oscillates with changes
52
in phase at the two junctions, which depend upon the change in the magnetic flux.
Counting the oscillations provides a measurement of how the flux has changed.
The sample being measured produces its own magnetic field, which is mea-
sured by a bridge circuit consisting of a primary coil and two secondary coils, wound
in opposition and connected in series. When the two secondary coils are perfectly
balanced, the induced voltage in the device would perfectly cancel out, but introduc-
ing a sample into one of the coils disturbs the balance of the bridge and produces
a net current. This current then induces a field across the SQUID, causing the
critical current to fluctuate. A constant biasing current is passed through the ring,
so the voltage across the ring will fluctuate. These fluctuations are then measured
while the sample is moved through the pickup coil. The field inducing the current
in the pickup loop is proportional to the magnetic moment of the sample, divided
by the cube of the distance between the sample and the loop. The relationship of
the voltage across the SQUID and this distance allows the calculation of the dipole
moment of the sample, thereby allowing the magnetization and susceptibility of the
sample to be determined.
DC magnetic susceptibility measurements were collected using a Quantum
Design Magnetic Property Measurement System (MPMS) SQUID instrument, lo-
cated at the University of Maryland Center for Nanophysics and Advanced Ma-
terials. Measurements were taken in zero-field cooled (ZFC) and field cooled (FC)
environments, from 1.8 to 300 K. Applied magnetic fields were typically 100 or 1000
Oe.
53
2.4.2.2 Magnetic structure determination from neutron diffraction
All methods of diffraction are sensitive to the structural symmetry of the
probed material. Magnetic ordering within a structure reduces the symmetry of
a material, so materials that undergo magnetic ordering at low temperatures pro-
duce different neutron scattering patterns when measured above and below their
Curie or Néel temperatures. If the magnetic structure is ordered such that there are
repeating patterns of moments, this will be reflected in observed magnetic Bragg
peaks. When a sample is subjected to a temperature high enough to disrupt the
ordering of the magnetic moments, the magnetic behavior of the material becomes
the same as that observed in a paramagnet, and the scattering due to magnetic
interactions fades into incoherent background on the diffraction pattern.
Another way of reaching the relationships observed in Bragg’s law is through
considering Q, where Q represents the momentum transfer that occurs when an
incident wave vector ki is diffracted into final wave vector k f (Figure 2.9), and is
represented by the relationship
Q= 4pisinθ
λ
(2.27)
With magnetic scattering, ki = k f . When this condition is upheld, the scatter-
ing is considered elastic. (Though not discussed in Section 2.3.1, elastic scattering
is a necessary condition in Bragg’s law.) Unlike the variables involved in the tradi-
tional representation of Bragg’s law, Q provides a way to study magnetic structure,
regardless of the wavelength or technique used.
54
Figure 2.9: a) A schematic representation of elastic scattering, where
|ki| = |k f |. b) A rearrangement of the scattering vectors to demonstrate
wavevector transfer Q.
The dipole-dipole interaction involved in magnetic scattering is very specific.
The polarity results in highly anisotropic or directional scattering. Only the mag-
netization component on an atom that is perpendicular to Q will be reflected in the
differential cross-section of the magnetic scattering. Thus, in ferromagnetic materi-
als, the magnetic interaction can be ‘turned off ’ if all of the atomic moments can be
aligned parallel to Q. Even more than the atomic form factor in X-ray diffraction,
the magnetic form factor is dependent on the electrons present in the material, and
decays at high angles of measurement.
In solving the magnetic structure of a material it is helpful to use neutron
diffraction data in conjunction with other analytical techniques such as SQUID
magnetometry, synchrotron X-ray scattering, Mossbauer and/or NMR spectroscopy,
etc. It is not possible to solve the magnetic structure without any pre-existing un-
derstanding of the crystal structure. As mentioned previously, two types of scat-
tering occur due to interaction with a neutron beam, and both contribute to the
55
M = M || + M⊥
Q
M||
M
M⊥
Figure 2.10: For magnetic scattering, only the magnetization component
M⊥ to the scattering vector Q contributes to the magnetic scattering
length.
measured pattern. Without any prior understanding of the crystal structure of the
material, it may be very difficult (if not impossible) to distinguish between the peaks
occurring as a result of magnetic scattering and those caused by nuclear scattering.
Determining a magnetic structure via neutron diffraction is not a trivial pro-
cess, and was first achieved by Shull and Smart in 1949 in a sample of MnO.121,122
With the help of modern computational capabilities, Rietveld analysis may be car-
ried out on a diffraction pattern in efforts to determine the magnetic structure.
Upon obtaining a neutron scattering pattern, there are three possible meth-
ods for refining the magnetic structure of the material. In the case where the system
is simple and the unit cell has P1 symmetry, the magnetic structure can be solved by
refining the moments in all three axis directions. A second method uses the nuclear
space group observed in X-ray diffraction or high temperature neutron diffraction
56
Figure 2.11: a) The time-inversion magnetic symmetry operation on an
electric current loop causes the current to be reversed and the axial vec-
tor, which represents the magnetic moment, to be inverted. b) The effect
of a vertical mirror plane on a current loop. The current is unchanged
when the loop is parallel to the plane of the mirror. When the current
loop is perpendicular to the mirror plane, the reflection symmetry op-
eration causes the loop to reverse direction and the axial vector flips
direction. c) The combination of time-inversion and a reflection symme-
try operation on an electric current loop.
analyses. Anti-symmetry operations (represented by a ’ in Figure 2.11) are then
applied to constrain the magnetic moments within the material until a good fit is
acquired. The anti-symmetry operations involved in this methodology are those
proposed by Shubnikov, and are also known as ‘time-reversal elements’ for spin
(Figure 5). In total, there are over 1600 magnetic space groups to consider when in-
cluding antisymmetry elements in three dimensions, making this route somewhat
tedious.
The third and most rigorous method is to utilize group theory and the irre-
ducible representations of space groups to determine the magnetic structure. The
basis vectors within the space groups will constrain the moment directions, and Ri-
etveld analysis can then determine the goodness-of-fit. Breaking this methodology
57
into more detail, the first step of magnetic structure refinement is to locate and
fit the individual magnetic peaks in the observed neutron data. Next, the propa-
gation vector k is calculated based on the observed magnetic peaks. Using k and
the known nuclear space group of the material, the corresponding irreducible rep-
resentations and basis vectors are systematically applied, fitting the coefficients in
the refinement. The basis vectors resulting in the lowest χ2 represent the magnetic
structure that best fits the observed data.
Magnetic structure refinements carried out within this thesis were predomi-
nantly performed using FullProf.114 Another program, SARAh, is useful in validat-
ing the irreducible representations that correspond to the given space group and
propagation vector.123
2.5 Transport measurements
The four probe van der Pauw method was employed for transport measure-
ments on pellet samples. In order to use the van der Pauw method, the sample
must be flat, of a uniform thickness, and ideally symmetrical. The length and width
of the sample must be significantly larger than the sample thickness, with contacts
located at the sample edge, and the area of contact minimized to the extent possi-
ble.124,125 For transport measurements of samples described herein, contacts were
established by attaching gold wires to samples with silver paint.
To make a measurement, a dc current is applied along one edge of the sample
(for instance, I12 in figure 2.12 a) and the voltage across the opposite edge (in this
58
Figure 2.12: The van der Pauw technique.
case, V43) is measured. From these two values, resistance (R) can be found using
Ohm’s law, R = V /I. The leads are then changed so that current is applied from
contact 3 to contact 2 (I23 in figure 2.12 b) while voltage V14 is measured.
The van der Pauw equation, used to solve for the sheet resistance (RS), is
exp(−piRA/RS)+exp(−piRB/RS)= 1 (2.28)
where RA = V43/I12 and RB = V14/I23.126 Resistivity (ρ) of the material can
then be calculated by
ρ = AR
l
(2.29)
where R is the resistance, A is the area of the pellet and l is the length.
Magnetoresistance (MR) is the relative change in electrical resistance of a
59
material on the application of a magnetic field defined by
MR = ρ(H)−ρ(0)/ρ(0) (2.30)
where MR is the magnetoresistance, ρ(0) is the resistivity in zero field and
ρ(H) is the resistivity in an applied field.
Transport data herein was acquired using a Quantum Design physical prop-
erty measurement system (PPMS) located at the University of Maryland Center for
Nanophysics and Advanced Materials. Typical measurements first record the elec-
trical resistance upon cooling the sample, then again as the sample is heated back
to room temperature.
2.6 X-ray photoelectron spectroscopy (XPS)
X-ray photoelectron spectroscopy is a technique for determining the chemical
composition of a surface, down to the range of parts per thousand. This is done
by irradiating a sample with X-rays in a high-vacuum environment to ionize atoms
and release core-level photoelectrons. The kinetic energy of the escaping photo-
electrons limits the depth from which emitted photoelectrons can emerge to a few
nanometers, making XPS a surface technique. Emitted photoelectrons are detected
and analyzed by the instrument to produce a spectrum of emission intensity versus
electron binding energy.
Since each element has a unique set of binding energies, XPS can be used to
identify the elements on the surface of a material, according to an equation pro-
60
Figure 2.13: Photoelectric effect.
posed by Ernest Rutherford,
EBE = hν− (Ek+φ)
where EBE is the binding energy of the electron, hν is the energy of the inci-
dent X-ray photons, Ek is the kinetic energy of the emitted photoelectron measured
at the detector, and φ is a work function dependent on both the material and the
spectrometer. Peak areas at nominal binding energies can be used to quantify the
concentration and ratios of the elements. Small shifts in these binding energies
provide powerful information about the chemical states and short-range chemistry
in a material.127
XPS measurements herein were taken in a high sensitivity Kratos AXIS 165
61
X-ray photoelectron spectrometer at the Surface Analysis Center at University
of Maryland. Both the monochromatic Al Kα and the dual anode (Mg Kα and
monochromatic Al Kα sources) capabilities were utilized, depending on the experi-
mental needs as described in following chapters.
62
Chapter 3: Ba1.2Mn8O16 and Ba1.2CoxMn8−xO16
The research described within this chapter was published in Chemistry of
Materials 2015, 27, pg. 515-525. Dr. Pouya Moetakef, Dr. Karen Gaskell, Dr. Craig
M. Brown, Dr. Graham King, and Dr. Efrain Rodriguez were contributing authors
on the manuscript.
3.1 Introduction
While extensive studies have been conducted into the magnetic properties and
the structure of Mn-based perovskite and pyrochlore structures, significantly less
has been reported on the magnetic structures of Mn-based hollandites. Studies of
the Mn-based hollandites and todorokites indicate that they are semiconducting
with relatively small band gaps, whereas their magnetic behavior has been de-
scribed as either long-range antiferromagnetic, ferrimagnetic, or spin glassy.41,106
With respect to their oxidation states, the OMS-materials are understood to contain
a mixture of Mn3+/Mn4+ sites, and mineralogists and crystallographers have even
identified the Jahn-Teller distorted Mn3+ cation (t32g, e
1
g electronic configuration)
in certain structures. Electrochemists have studied Mn-based OMS materials for
applications such as cathodes in rechargeable batteries since they are redox active
63
and their tunnel structures allows facile insertion and removal of cations such as
Li+. The research group of Steven Suib has also pursued catalytic studies with
OMS-materials on account of their porosity including oxidation of organics such as
alcohols and formaldehyde.
Manganese oxides show a range of magnetic moments due to the dependence
on valence states, S = 52 ,2, and 32 for Mn2+, Mn3+, and Mn4+ respectively. The mag-
netic moments are also affected by octahedral splitting resulting in high spin/low
spin dependencies. Manganese oxides, MnO, Mn3O4, β-MnO2, have been shown to
have magnetic responses ranging from antiferromagnetic to ferromagnetic to heli-
cal magnetism, respectively. Most OMS materials generally show properties of spin
glasses and paramagnetic behavior for temperatures above 100 K. Among different
OMS materials, KOMS-2 is a stable form that can be synthesized with numerous
methods. KOMS-2 is composed of MnO6 edge- and corner-sharing octahedra with
potassium in the tunnels to provide charge balance and stabilize the structure.
Manganese atoms in the KOMS-2 structures are able to be replaced with other
transition metals, which may be either diamagnetic or paramagnetic in nature. In
replacing Mn with other metals, there is tunability in the magnetic response of the
material.
Within the research that has been done on manganese-based hollandites,
those with tunnel cation Ba2+ are rather under-represented compared to the K+
analogue (Chapter 4). A reported salt flux reaction combined Ba(NO3)2 with Mn2O3
and KCl in a 1.2:4:12 molar ratio to produce polycrystalline samples of BaxMn8O16,
with impurity phases obtained for 1.1 ≤ x ≤ 1.3.104 In another study, nanoribbons
64
of Ba1−δMn8O16 were prepared by mixing BaMnO3 in a 1:1 molar KCl/NaCl flux
and heating to 800◦ C for five hours, achieving phase pure product with good crys-
tallinity.106
Different strategies to modify the physical and chemical properties of Mn-
based hollandites have involved introducing, exchanging, or removing ions in the
tunnels and/or framework, but only two studies have reported these effects on bar-
ium manganate hollandites. In 2014, Liu et al reported a "gel-collection" synthetic
technique to produce mixed metal hollandites, where A = Ba, and M = Mn, Ti hol-
landites.87 Their reported technique combined the more traditional solvothermal
and sol-gel synthetic techniques, with barium isopropoxide, manganese acetylace-
tonate, and titanium isopropoxide mixed together in a 1:3:4 molar atomic ratio,
using pure ethanol as the solvent. Heating this solution in an autoclave at 150◦ C
for 24 hours produces a ‘gel-rod’, which is then removed from the supernatant and
sintered at 700◦ C to yield BaMn3Ti4O14.25. Broad diffraction peaks indicated low
crystallinity, but the hollandite structure was confirmed by synchrotron XRD and
pair distribution function (PDF) refinements, as well as spherical-aberration cor-
rected STEM measurements. Electric and magnetic property measurements of the
sample hinted at multiferroic behavior, though reproducing these measurements
on samples with improved crystallinity would be more convincing.87
Barbato et al used solid state salt flux reactions to synthesize BaMMn7O16,
where M = Mg, Mn, Fe, or Ni.85 Broad diffraction peaks in their X-ray diffrac-
tion data indicated poor crystallinity of the samples, all of which were identified
as monoclinic. In the hollandites synthesized by Barbato et al, small changes were
65
Figure 3.1: a)Ba1.2Mn8O16 hollandite structure viewed down the b axis
in the I2/m setting. b) Tunnel wall of hollandite showing the triangular
ladder.
observed in lattice parameters corresponding to the cationic radius of the M cation
incorporated into the framework. Their study focused on the ability of Li+ cations
to insert into the tunnels of each material for electrochemical applications, with M
= Ni displaying the maximum reactivity.
Despite the paucity of reports on the barium manganate hollandite, doping of
low- or high-valent transition metal ions into the framework should result in novel
physical and electronic properties, especially as the oxidation state of the man-
ganese atoms is so dependent upon the identities of the other framework cations.
In the 2006 investigation of the physical properties of Ba1.2Mn8O16 Ishiwata
et al observed a magnetic transition at 40 K, and at low temperatures, sintered
pellets of Ba1.2Mn8O16 demonstrated high resistivity.104 Low temperature neutron
66
data displayed broad magnetic Bragg reflections indexed with a (1/2 0 1/2) super-
lattice, though no detailed magnetic structure was proposed.
The combination of ferrimagnetism with insulating properties is uncommon,
and further analysis of the Ba1.2Mn8O16 framework was desired. The prescribed
synthetic route producing the polycrystalline Ba1.2Mn8O16 material also accommo-
dated the synthesis of a related derivative with Co incorporated into the framework.
This chapter presents a detailed characterization of the Ba1.2Mn8O16 hollan-
dite system, and its Co-substituted analogue, where one stoichiometric equivalent
of cobalt was added into the Mn8O16 framework. The choice of Co as a dopant is
advantageous due to its magnetic properties, as well as its similarity in size, al-
lowing facile incorporation into the manganese oxide framework. A combination
of inductively coupled plasma- mass spectrometry (ICP-MS), conventional lab and
synchrotron X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), neu-
tron powder diffraction (NPD), magnetometry, and transport measurements have
been employed to study the composition, magnetic structure and physical proper-
ties. Of particular interest is how the presence of cobalt affects the complex, frus-
trated magnetism of the system.
3.2 Synthesis & experimental details
3.2.1 Sample preparation
Samples were synthesized through the salt flux method described by Ishi-
wata et al. to produce the polycrystalline hollandite, Ba1.2Mn8O16.
104 Starting
67
reagents included KCl (99.2%, J.T. Baker), Mn2O3 (99%, Sigma-Aldrich), Co3O4
(74%-gravimetric Co, Sigma-Aldrich), Ba(NO3)2 (99.999%, Sigma-Aldrich). Reagents
were used without further purification.
A powder mixture with molar ratio of 1.2:4:12 of Ba(NO3)2, Mn2O3, and KCl
was ground with an agate mortar and pestle to obtain a target stoichiometry of
Ba1.2Mn8O16 (BMO). For the cobalt-doped sample a stoichiometric mixture of the
metals is mixed with the KCl flux in a 1:12 ratio to target a stoichiometry of Ba1.2CoMn7O16
(BCMO). Both materials were then heated in covered alumina crucibles under am-
bient atmosphere. Heating was maintained at a rate of 100 K/h up to 1123 K,
soaked for 72 h, then cooled to room temperature at 100 K/h. The obtained samples
were washed in DI water to dissolve KCl, then dried at 373 K for one hour. Small
impurities of BaCO3 were removed by stirring samples in 1M HCl for 30 min, then
washing with DI water until pH returned to neutral.
For inductively coupled plasma mass spectrometry (ICP-MS) measurements,
∼10 mg of sample was stirred in 5 mL concentrated HCl until completely dissolved,
then diluted appropriately for analysis. For resistivity measurements sample pow-
ders were pressed into pellets 1 mm thick and 13 mm in diameter. Pellets were
sintered at 1173 K for 24 h.
3.2.2 Diffraction, magnetization, and spectroscopy
Room temperature powder X-ray diffraction (XRD) data was collected on a
Bruker D8 X-ray diffractometer with Cu Kα radiation, λ = 1.5418 Å, (step size=0.013◦,
68
with 2θ range from 8◦-140◦). Time-of-flight (TOF) neutron powder diffraction (NPD)
data was collected on the High Intensity Powder Diffractometer (HIPD) beam line
at the Lujan Neutron Scattering Center at Los Alamos Neutron Science Center.
Low temperature constant wavelength (CW) neutron diffraction data was collected
on the BT-1 high resolution powder neutron diffractometer at the NIST Center for
Neutron Research. Cu(311) and Ge(311) monochromators produced neutron beams
of λ = 1.5403 Å and λ = 2.078 Å, respectively. Scans were taken at 5 K, 10 K, and
50 K for BMO, and at 10 K, 40 K, 80 K, 120 K, 160 K, 180 K, 250 K, and 300 K for
BCMO.
Magnetic susceptibility measurements were carried out using a magnetic prop-
erty measurement system (Quantum Design MPMS). Both field-cooled (FC) and
zero-field-cooled (ZFC) magnetic susceptibility measurements were taken from 2 K
- 300 K in direct current mode with an applied magnetic field of 0.01 T (100 Oe).
Hysteresis measurements were carried out at 2 K in magnetic fields between ± 7 T.
A Quantum Design physical property measurement system (PPMS) was used
for temperature dependent resistivity measurements using a four-probe, or Van
der Pauw geometry.124,125 Sintered pellets were mounted onto a PPMS puck with
electrical continuity established by using silver paste to connect gold wires from the
pellet to the sample mount.
X-ray photoelectron spectroscopy (XPS) measurements were taken in a high
sensitivity Kratos AXIS 165 X-ray photoelectron spectrometer operating in hybrid
mode to analyze the composition and average transition metal oxidation state at
the surface. For the Mn 2p peaks, monochromatic Al Kα at 280 W was used as
69
the X-ray energy source, whereas both Mg Kα and monochromatic Al Kα sources
were utilized (at 280 W) in studying the Co 2p peaks in efforts to better resolve
peak overlaps. CasaXPS software was used for quantification and peak fitting after
application of Shirley backgrounds using relative sensitivity factors from the Kratos
vision library. Pressure was at or below 5×10−8 Torr during data collection, and
charge neutralization was required to minimize surface charging.
3.3 Results and discussion
3.3.1 Crystal structure
As-synthesized XRD patterns were taken to measure crystal structure and
purity. Rietveld refinement of both BMO and BCMO structures were carried out
with the TOPAS 4.2 software.115 The patterns of as-synthesized samples showed
good fit to the structure reported by Ishiwata et al, including an impurity peak at
2θ ∼ 24.1−24.5◦, which was reported in the literature but remained unidentified.104
This peak corresponds to the impurity phase BaCO3. Stirring the sample in 1M HCl
for 30 min followed by washing until the pH returned to neutral removed most of
the BaCO3 phase without diminishing the crystallinity of the oxides.
The crystal structures of BCMO and BMO at room temperature were solved
by simultaneously fitting banks 1, 3, and 5 of the TOF neutron diffraction data mea-
sured on HIPD (Figures 3.2 and 3.3, respectively). The resulting patterns were fit
with a monoclinic cell (space group I2/m) with the parameters presented in Tables
3.1 and 3.2.
70
Figure 3.2: Rietveld refinement of the TOF neutron data (HIPD, Los Alamos) for the structure of BCMO. The highest resolution
is found in the backscattering 153◦ bank, which also has the highest Q-range. The blue tick marks indicate expected positions
of hollandite reflections, the green line indicates the difference between the observed data (black circles) and the calculated
model (pink). The inset allows for better visualization of the structural details and refinement that occur at Q > 6Å−1. The
BCMO fit to the data measured at the 90◦ and 40◦ detector banks are available in Appendix B.
71
The refined occupancy of the Ba site is 0.28(2) in BMO and 0.27(2) in BCMO,
slightly less than the targeted stoichiometry (0.3 per site). This discrepancy can
be accounted for in the BaCO3 impurities removed by HCl washing, which may
have also leached a small amount of Ba cations from the hollandite tunnels. The
large values for the Ba thermal displacement parameters are likely a result of the
loose coordination environment of the Ba cation within the framework, allowing in-
creased tunnel cation mobility. Previous studies of hollandite frameworks have seen
incommensurate modulations of the tunnel cation, visible in electron microscopy
images as sharp satellite peaks or diffuse intensity normal to the tunnel direc-
tion.86,88,128
Composition analysis via Rietveld refinement of neutron data provides a first
approximation of whether or not cobalt was successfully incorporated into the hol-
landite structure. The refined Co occupancy in BCMO is 0.40(8) per unit cell, in
contrast to the expected value of one Co atom per cell. However, as the overall
Co concentration is small, the error relative to the total amount of Co is large.
Although the neutron scattering lengths of Co and Mn have fairly good contrast,
(2.49 fm in Co vs. -3.73 fm in Mn), the absolute values of the scattering lengths
are fairly small relative to those of either Ba (5.07 fm) or O (5.803 fm).109 Thus,
small changes in composition between Mn and Co are expected to only affect small
changes in the observed diffraction pattern. The refined composition from neutron
data therefore are useful in confirming the presence of Co, but other elemental anal-
yses are capable of achieving greater compositional precision between Mn and Co.
These methods are presented in the Elemental Analysis section.
72
Further evaluation of the metal-oxide bond distances determined from diffrac-
tion data allow inference of the amount of Mn3+ and Co2+ present in BMO and
BCMO, respectively. The target stoichiometry of Ba1.2Mn8O16 would lead to an av-
erage oxidation state of 3.7+ per manganese cation. Introduction of Co2+ into the
framework structure should cause the manganese to oxidize in order to maintain
charge balance, with an expected oxidation state per manganese cation of 3.94+ for
the target stoichiometry of Ba1.2CoMn7O16. From a bond valence perspective, the
lower valent cations are larger than Mn4+ and should thus lead to larger average
M-O bond distances.
73
Figure 3.3: Rietveld refinement of the TOF neutron data (HIPD, Los Alamos) for the structure of BMO. The highest resolution
is found in the backscattering 153◦ bank, which also has the highest Q-range. The blue tick marks indicate expected positions
of hollandite reflections, the green line indicates the difference between the observed data (black circles) and the calculated
model (pink). The inset allows for better visualization of the structural details and refinement that occur at Q > 6Å−1. The
BMO fit to the data measured at the 90◦ and 40◦ detector banks are available in Appendix B.
74
To assess the effects of Co-substitution on the crystal structure, the metal-
oxide bond distances in BMO must first be analyzed. As observed in a sample of
pyrolusite MnO2,
129 Mn4+ has an average Mn–O bond length of ∼ 1.89 Å whereas
Mn3+ has an average Mn–O bond length of 2.04 Å.130 The average M–O bond
lengths obtained from room temperature refinements of BMO are 1.893 Å and 1.956
Å for the M1 and M2 sites, respectively (Table 3.3). These bond lengths suggest
that Mn4+ preferentially occupies the M1 site, while both Mn3+ and Mn4+ cations
occupy the M2 position in an approximately 1:1 ratio. These bond distance values
imply an average Mn oxidation state of 3.75+ in BMO, slightly higher than the tar-
get of 3.7+. These values can be further quantified using the bond valence method
of Brown, Brese, and O’Keeffe131–133 and the empirical bond valence parameter for
Mn4+. These calculations lead to the M1 site having a valence of 4.12 and the M2
site 3.53.
In BCMO, the average bond lengths are 1.908 Å and 1.942 Å for the M1 and
M2 positions, respectively (Table 3.4). In a high-spin octahedral configuration, Co2+
should have a bond length of 2.14 Å.130 These values suggest that Mn4+ still favors
the M1 site and that Co2+ mixes with Mn4+ at the M2 position in a nearly 1:3 ratio,
assuming no Mn3+ is found in BCMO. The same bond valence treatment of the bond
distances leads to an M1 valence of 4.02 and an M2 valence of 3.67. From these
calculations, it appears that the charge difference between M sites is diminished in
BCMO relative to BMO, as would be expected from the oxidation of Mn upon Co2+
substitution. Since these results are obtained from the average structure refine-
ment of Bragg peaks, the location of cobalt substitution is not certain based solely
75
on arguments of average bond length. Thus, further investigations into the local
structure are needed to determine possible local ordering in BCMO.
The Mn3+ cation, which seems to favor the M2 atomic position in BMO, could
potentially undergo a Jahn-Teller (JT) distortion, elongating in a direction parallel
to the a-axis of the unit cell. An evaluation of the bond distances in BMO (Table
3.3) shows that M2–O2 and M2–O4 are both over 2.0 Å and longer than the other
distances. However, this elongation does not correspond to the expected JT elon-
gation along one axis, but instead indicates a trigonal distortion of the octahera,
with one trigonal face further from the metal center than the other. In contrast,
the equivalent M2–O bond distances in BCMO are shortened, which is further ev-
idence that the JT-active Mn3+ cation is no longer present in BCMO due to Co2+
substitution. Future TOF neutron experiments at temperatures below the mag-
netic ordering transitions will be helpful to search for possible orbital ordering from
JT distortions.
3.3.2 Elemental analysis
Before presenting the magnetic properties of BMO and BCMO, the elemental
analysis of both BMO and BCMO is presented in order to understand the effects
of Co-substitution on structure and composition. To this end, XPS measurements
were utilized to determine metal oxidation states by studying the 2p and 3s X-
ray core level photoelectron spectra, and ICP-MS was used to verify the elemental
composition of the samples.
76
Table 3.1: Room temperature lattice parameters for BaxMn8O16 and
BaxCoyMn8-yO16 from TOF neutron diffraction refinements. Standard uncer-
tainties are given in parentheses.
Sample Ba1.14Mn8O16 (BMO) Ba1.10CoyMn8-yO16 (BCMO)
No. reflections 2545 2560
No. parameters* 29 31
Space group I2/m I2/m
a (Å) 9.683(2) 9.6468(8)
b (Å) 2.8531(5) 2.8589(2)
c (Å) 9.946(2) 9.9954(8)
β(◦) 88.907(3) 88.654(3)
Volume (Å3) 273.9557(3) 275.6637(1)
Calc. density (g/cm3) 5.161(2) 5.11(8)
77
Figure 3.4: XPS spectra of M 2p and M 3s peaks in BMO (dotted pink)
and BCMO (solid blue). M = Mn in panels a and b, and M = Co in
c and d. Mn 2p1/2 was not shown in panel a to better emphasize the
subtle difference in fit of the higher resolution Mn 2p3/2 peak. Asterisks
indicate M peaks overlapping with Ba peaks. Dashed black lines show
the background used for composition quantification.
78
Qualitatively, the asymmetry present in the Mn 2p3/2 peak of BMO and BCMO
(Figure 3.4a) matches that reported for mixed-valent Mn by Militello et al in LiMn2O4,
134
which is consistent with expected mixed valency in hollandites. Unfortunately, the
splitting of the Mn 2p peaks is not helpful in assigning definitive oxidation states
since literature values for the splitting of Mn4+, Mn3.5+, Mn3+ are 11.7, 11.7, and
11.6 eV, respectively.134–136 Furthermore, overlap of the Ba 4d5/2 peak with the
higher binding energy Mn 3s multiplet (Figure 3.4b) complicated the analysis since
the oxidation state of manganese is most reliably determined via splitting between
the two Mn 3s multiplets.
To extract more information about the Mn state from the XPS data, a careful
comparison of the Mn 2p3/2 peak shape in BMO to that in BCMO was performed.
The peak shape for Mn 2p3/2 shows an asymmetric shoulder at lower binding en-
ergy (Figures 3.4a). The Mn 2p3/2 transition was fit with three peaks constrained to
occur at the same binding energies and with the same full width at half maximum
between the BMO and BCMO spectra. A change in the intensity of the lowest bind-
ing energy peak is observed, increasing from BCMO to BMO. Previously reported
XPS measurements of binary Mn oxides show that the Mn 2p3/2 peak occurred at
a slightly lower binding energy (-0.6 eV) in Mn2O3 than in MnO2.129,130 Thus, if
the intensity of the peak fit at lower binding energy is proportional to the amount
of Mn3+ in the sample, there is more Mn3+ present in BMO, leading to a lower
average Mn oxidation state than in BCMO.
In the BCMO sample, the Co 2p peaks overlapped with Ba 3d peaks. The
presence of the Co 2p satellite peaks, however, is characteristic of cobalt atoms in
79
the high spin 2+ oxidation state (Figures 3.4c). These satellite peaks give good
certainty to the assumption that the cobalt cations within the bulk of the material
are also divalent, since the propensity for oxidation is greatest for exposed cations
at the surface.137
Quantification to obtain surface stoichiometry was carried out using the Ba
3d and 4d peaks for BMO and BCMO, respectively, as well as the Mn 2p and Co 3s
peaks. Composition analyses of all obtained methods are listed in Table 3.5, with
XPS measurements resulting in the surface stoichiometries of Ba1.4Co0.79Mn7.2 and
Ba1.5Mn8. In both samples, the results revealed more Ba than expected based on
initial stoichiometry. The discrepancy in Ba might be due to Ba cations moving to
the surface during either the HCl wash or while the system is in the high vacuum
XPS environment.
Investigating the sample composition via inductively-coupled plasma mass
spectrometry (ICP-MS) gave stoichiometries of Ba1.6Mn8O16 for BMO, which sug-
gests an average manganese oxidation state of 3.6+. The composition of BCMO via
ICP-MS gave a stoichiometry of Ba1.5Co0.9Mn7.1O16. Assuming Co is 2+ (as seen in
the XPS data), this leads to an average manganese oxidation state of 3.83+.
3.3.3 Magnetic properties
Field-cooled (FC) and zero-field-cooled (ZFC) measurements were taken of
both samples with and without acid washing (Figures 3.5 and 3.6). Preliminary
analysis of the magnetic susceptibility of BCMO compared to BMO revealed a dra-
80
Figure 3.5: Magnetic susceptibility as a function of temperature for as-
prepared and acid-washed samples of BCMO.
matic change in the magnetic response of the oxide. FC/ZFC curves of BMO show
the susceptibility to be virtually identical above 25 K irrespective of the applied
magnetic field, with the magnetic responses diverging at low temperature. This is
different than the TN reported for bulk Ba1.2Mn8O16 by Ishiwata et al, but agrees
with the magnetic behavior observed by Yu et al in their single crystal investiga-
tion of Ba1+δMn8O16 nanoribbon crystals.104,106 The low-temperature divergence
of the FC/ZFC curves in the manganese sample supports the observations of Suib
and Iton, who classified manganese oxide hollandite materials as spin-glass sys-
tems.12,41
An increase in magnetic susceptibility (χ) of BCMO was observed with an
onset near 180 K and saturation near 22 K, indicative of long-range ferri- or ferro-
magnetic ordering. The temperature and the magnitude of FC/ZFC divergence of
81
Figure 3.6: Magnetic susceptibility as a function of temperature for as-
prepared and acid-washed sampels of BMO.
BCMO at 180 K contrast significantly with those observed in the pure manganese
sample. At 2 K the ∆χ is approximately 1×10−3 between the FC and ZFC curve
for BMO, whereas in BCMO the ∆χ at 2 K is ∼1, a difference of three orders of
magnitude.
The effective paramagnetic moment (µe f f ), the Curie constant C, and the
Curie-Weiss intercept θCW values for BMO and BCMO were obtained by fitting
the linear high temperature region (T > 225 K) of the χ−1 plots to the Curie-Weiss
equation, χ = C/(T −θCW ). The obtained values are recorded in Table 3.6. Based
on the compositions observed via ICP-MS where the average Mn oxidation state is
3.6+, an effective magnetic moment of 4.28 µB is expected for BMO. The calculated
µe f f value of 4.34 µB for the as-prepared BMO sample agrees relatively well with
the expected value.
82
On the basis of the average Mn oxidation state of 3.83+ in BCMO, the spin-
only contribution from the manganese cations to the effective magnetic moment
should be 4.05 µB. A µe f f of ∼ 4.3µB to 5.2 µB is the reported value for Co2+ cations
in the high-spin configuration, a result of both spin and orbital contributions.9,120
Thus, in BCMO the combination of Mn3.83+ and Co2+ would be expected to result in
a µe f f of ∼ 4.14µB. The obtained value for µe f f in BCMO is instead 4.64 µB, which
is significantly higher than expected. Since the transition temperature observed
in BCMO is 180 K, the linear region used to fit for the Curie-Weiss law (T > 225
K) in the measured data may be too close to the transition temperature to allow
for accurate determination of magnetic constants. The Curie constant from the fits
for both BMO and BCMO are therefore both included, as this may allow a more
straightforward assessment of the consequences of substituting Co2+ on the bulk
magnetic properties.
The decrease in µe f f observed in both samples upon acid washing supports the
conclusion that Ba2+ cations are deintercalating from the tunnels during the acid
wash process, causing the framework transition metal cations to further oxidize.
Although the Néel temperature in BMO is 25 K, the absolute value of θCW for BMO
is quite large, indicating strong antiferromagnetic exchange. Ramirez defined a
frustration index f as the ratio of the Weiss field to the ordering temperature, where
f = |θCW |/TN .12,24 A highly frustrated system is classified as one where f > 10, and
in BMO, f ∼ 17. Such significant spin frustration within the framework is often
seen in triangular lattices of edge-sharing MO6 octahedra (Fig. 3.1). In BCMO, f ∼
3.5, indicating that the Co2+ substitution effectively relieved the highly frustrated
83
Figure 3.7: Standardized inverse magnetic susceptibility, with the dot-
ted line representing the ideal antiferromagnetic Curie-Weiss fit.
state of the hollandite.
The standardized χ−1 plot shown in Figure 3.7 allows for the direct compar-
ison of BMO and BCMO. The dashed line passing through the origin corresponds
to ideal Curie-Weiss behavior and can be used to measure the fit quality in the
high temperature paramagnetic regime. The observed negative deviations from
the ideal Curie-Weiss line indicate uncompensated antiferromagnetism (ferrimag-
netism) present in the sample.138 Overall, the magnetization data support a par-
tially saturated ferrimagnetic ground state in BCMO.
The ferrimagnetic behavior of the BCMO sample contrasts with the Co-doped
analogue of a titanium hollandite, Ba1.3Co1.3Ti6.7O16, studied by Shlyk et al, which
did not demonstrate any long-range magnetic order down to 2 K. Extrapolation
of the high-temperature paramagnetic fit for the titanate hollandite produced a
84
Figure 3.8: Comparison between the experimental measurements of
magnetization as a function of applied field for BCMO (blue), and BMO
(pink).
Curie-Weiss constant of θ = 6.4 K, indicative of very weak ferromagnetic coupling
between the Co ions.81 Likewise, the study by Moetakef et al revealed no long-range
magnetic ordering in the hollandite K1.4Co0.75Ti7.25O16.
75
Magnetization versus magnetic field measurements of BMO and BCMO show
that the presence of cobalt within the hollandite structure opens up a hysteresis
loop with a coercivity of ∼1 T (Figure 3.8). Magnetic saturation of BCMO was
not observed within the field range of the MPMS instrument. To further eluci-
date the magnetic ordering, neutron powder diffraction patterns were taken of the
as-synthesized BCMO sample at 10, 40, 80, 120, 160, 180, 250, and 300 K. One
magnetic peak was observed below 180 K, at 2θ ∼ 25◦, which was indexed as the
(200) reflection. The observed magnetic peak intensity was normalized and plotted
85
with good agreement to the normalized field-cooled susceptibility of BCMO (Figure
3.10). The agreement of these data and successful refinement of the magnetic struc-
ture accounting for the magnetic neutron peaks (discussed in Section 3.3.4) confirm
that the observed magnetization is a property of the bulk sample and is not due to
the presence of minute impurities.
3.3.4 Magnetic structure from neutrons
As indicated by the magnetization measurements, remarkably different long-
rage magnetic ordering is observed between BMO and BCMO. To solve the mag-
netic structures from the base temperature NPD data, the representational analy-
sis method was used.
For BMO, the magnetic Bragg peaks were indexed according to the propa-
gation vector of k = (14 ,
1
8 ,
1
4 ), which corresponds to a large magnetic unit cell with
respect to the chemical unit cell (4a× 8b× 4c). The BASIREPS routine in Full-
Prof produced the irreducible representation associated with this k vector for space
group I2/m (Table 3.7). The representation indicates that Mn sites (M1 and M2)
are each split into two orbits (e.g. M1a and M1b in Table 3.7) so that in total there
are four independent basis functions. The different orbits are due to each Mn-site
having an independent set of basis functions generated by the 2/m symmetry of
the space group. The refinement was only stable, however, if the two orbits corre-
sponding to the same site were ferromagnetically coupled. This constraint is also
due to the paucity of well-defined magnetic reflections in the BMO powder sample.
86
The best fit to the powder data (Figure 3.9b) led to an antiferromagnetic coupling
between M1 and M2 so that BMO exhibited no net magnetization, as anticipated
from the SQUID measurements. The magnetic R-factor from this fit was 46%, while
the next model with antiferromagnetic ordering along the b-direction led to a mag-
netic R-factor of 55%. The next models lead consistently to even higher magnetic
R-factors of ≥ 87%. Thus, the best fit given the quality of the powder data favors a
magnetic moment mostly in the ac-plane.
The complex structure of BMO is depicted in Figure 3.9c, showing antiferro-
magnetic moments aligned along the [1 0 1]-direction. The direction and size of the
moment in the ac-plane is modulated by the propagation vector, indicating that the
structure may be that of a complex helical ordering. This is consistent with the
helical ordering proposed by Sato et al for K1.5Mn8O16, where they expected the
period of the charge ordering (λC) to be an integral multiple of the helical magnetic
structure. Further, they expected the λC to be eight times as large as the unit cell
parameter parallel to the tunnel direction (similar to the 8b component of our mag-
netic propagation vector in BMO).64,139 The maximum moment size in the ac-plane
from fitting the Bragg intensities was 2.3(2)µB, which is lower than the expected
3.2µB for Mn3.8+ cations. Figure 3.9a shows a large diffuse background, however,
around the most intense satellite peak of (-1 0 1). Therefore, a large amount of
the magnetic moment may be disordered leading to the background instead of con-
tributing to the Bragg reflections.
Remarkably, for BCMO only one magnetic peak was observed at low temper-
atures, indicating a dramatic change in the magnetic ordering compared to BMO.
87
Figure 3.9: (a) One structural unit cell, with magnetic moments ori-
ented across the cell diagonal in the ac plane. (b) Magnetic fit of con-
stant wavelength data (λ= 2.078) for BMO, with (c) depicting the result-
ing complex magnetic structure. Four unique magnetic orderings occur
within the structural unit cells, depicted by black, green, magenta, and
purple arrows. These cells tile in a pattern such that cells along the
(101) plane are identical, leading to a long-range modulated magnetic
helix.
88
Figure 3.10: Normalized magnetic neutron peaks (orange) tracing the
field-cooled susceptibility curve of BCMO (blue).
Moreover, the peak is commensurate with the chemical unit cell and indexes to
the (200) peak, which is not symmetry-forbidden in space group I2/m but has no
contribution from the nuclear structure. The intensity of the peak decreased as
the temperature approached 180 K and completely disappeared by 200 K, consis-
tent with the magnetic transition temperature observed in the susceptibility data
(Figure 3.7).
Despite resulting in only one major magnetic peak, the magnetic structure of
BCMO is not trivial. For propagation vector of k = (0 0 0), the irreducible repre-
sentations presented in Table 3.7 were obtained. Using the Reverse Monte Carlo
routine in SARAh, Γ3 gave the lowest residual.123 Combinations of Γ3 with other
representations did not result in a lower residual. This representation leads to the
moment being only in the ac-plane, as in BMO, but with antiferromagnetic coupling
89
between the Mn sites related by the 2-fold rotational symmetry.
Although several combinations of coefficients for the representations could be
chosen to model the magnetic Bragg peaks, three models illustrate the method used
for finding the most plausible magnetic structure. In Model 1, the representation
Γ3 is used to produce an antiferromagnetic ordering with the moments along the
c-direction. Model 1 was ruled out since it leads to extra intensity for the (101)/(-
101) doublet. Model 2 uses Γ3 to antialign the moments along the ac-plane in order
to remove intensity along the (101)/(-101) reflections but still retain some moment
direction along the (200) planes. Model 2 was disqualified, however, since it leads to
a large intensity for the (002) reflection. Finally, Model 3, which best fit the neutron
data, uses Γ3 but breaks the 2-fold symmetry between the Mn sites. This leads to
an antiferromagnetic model, intermediate between Models 1 and 2.
The final antiferromagnetic model in Figure 3.11 illustrates several points
observed in the magnetization data. The source of the uncompensated magnetiza-
tion at zero-field arises from the moments on one set of (200) planes having a larger
component along the c-direction than the anti-aligned moments. Since the underly-
ing structure is antiferromagnetic, the hysteresis curve never fully saturates even
at an applied field of 7 T. Most notably, the moments are ferromagnetically aligned
along the tunnel direction in BCMO, whereas in BMO, the moments were antiferro-
magnetically aligned with the magnetic cell along the tunnel direction being eight
unit cells long.
90
Figure 3.11: Three different models of the magnetic structure of
Ba1.5Co0.9Mn7.1O16 and their corresponding fits to the neutron powder
patterns. The neutron data were taken at the BT-1 powder diffractome-
ter at NIST with a λ = 1.54 Å. The best refinement was achieved in
Model 3, where the moments are mostly in the (200) plane with some
ferrimagnetism arising from uncompensated moments for half of the
metal sites.
91
3.3.5 Electrical properties
The resistivity of BMO was previously measured by Ishiwata et al, where they
observed insulating behavior with room temperature resistivity of∼ 3×102 Ω·cm.104
Figure 3.12 shows the electrical resistivity measurements of pressed pellets of BCMO.
An increase in resistivity upon decreasing temperature indicates insulating behav-
ior, which is likely dominated by grain boundary effects.125 Resistivity values ob-
tained from pressed pellets can be two or three orders of magnitude greater than
their single crystal counterparts, and as such, quantitative conclusions may be in-
accurate.140 This is especially true in materials which could exhibit anisotropic
conduction as the resistivity values obtained for a pressed pellet are averaged over
all crystallographic orientations.
The fit of the linear plot in the inset is consistent with variable range hopping
(VRH) as the mechanism of charge mobility in the cobalt-doped sample. Efros-
Shklovskii (ES) variable range hopping is expressed through the formula:
ρ(T)= ρ(T0)exp(T0/T)
1
2 (3.1)
where T0 is a characteristic temperature. In Mott VRH, the exponent in Eq. 1
changes to 1/(1+d), where d is the dimensionality of the electron hopping within the
system. Very little difference is seen between the one-, two-, and three-dimensional
linear fits of Mott VRH, with the best fit observed for one dimension. The fit to
Eq. 1 is consistent with the observations of 1D Mott VRH made by Ishiwata et
al. in the pure manganese Ba1.2Mn8O16 system.
104 However, due to the doped
92
Figure 3.12: Resistivity of BCMO as a function of temperature. The in-
sert shows linear fitting of resistance versus T−1/2 consistent with either
one-dimensional Mott or Efros-Shklovskii variable range hopping.
93
nature of BCMO, the ES mechanism seems more likely as Coulomb interactions of
dopant atoms would create a gap in the density of states near the Fermi level at
low temperatures.
3.3.6 Magnetic exchange interactions in hollandites
Predicting the magnetic ordering models in hollandites requires an under-
standing of the various exchange interactions between the cation centers. The re-
cent first-principles and modeling work by Seriani et al. has examined the rich
magnetic phase diagrams in hollandite-type α-MnO2,56,141 providing a framework
from which to understand BMO and BCMO. Depending on whether the spin Hamil-
tonian is defined as purely Ising or Heisenberg in nature, Seriani et al. have found
various helical, ferromagnetic, collinear antiferromagnetic, and glassy spin states
in the phase diagram of α-MnO2 (Figure 3.13).56,141 The theoretical framework by
Seriani et al. therefore points to the possible magnetic functional behavior of Mn-
based hollandites that is just beginning to be explored experimentally.
94
Table 3.2: Structural parameters for BaxMn8O16 and BaxCoyMn8-yO16 from TOF
neutron diffraction refinements at 300 K. Standard uncertainties are given in
parentheses.
Ba1.14Mn8O16 (BMO) Ba1.10CoyMn8-yO16 (BCMO)
4g Ba y 0.34(2) 0.47(6)
Occ 0.34(2) 0.47(6)
B (Å2) 8(1) 9(2)
4i M1 x 0.170(4) 0.1663(5)
z 0.353(3) 0.3517(5)
**Occ 1 0.94(1)
***B (Å2) 0.56(6) 0.32(4)
4i M2 x 0.338(1) 0.3442(5)
z 0.843(1) 0.8410(6)
**Occ 1 0.961(9)
4i O1 x 0.1936(7) 0.1910(4)
z 0.165(3) 0.1618(5)
***B (Å2) 0.221(9) 0.034(6)
4i O2 x 0.1408(8) 0.1401(4)
z 0.7998(6) 0.7924(4)
4i O3 x 0.1822(9) 0.1839(5)
z 0.5374(7) 0.5437(5)
4i O4 x 0.5445(7) 0.5500(4)
z 0.8515(7) 0.8507(5)
95
Table 3.3: Select interatomic distances (Å) and angles (◦) in BaxMn8O16 at 300 K.
Standard uncertainties are given in parentheses.
Bond length (Å) Bond angle (◦)
M1–O1 1.948(9) x2 M1–O1–M1 99.144
1.87(1) 94.205
M1–O3 1.84(1) M1–O4–M1 98.950
M1–O4 1.88(2) M2–O3–M2 100.082
M2–O2 2.02(3) x2 M2–O2–M2 93.881
1.97(2) 89.859
M2–O3 1.86(2) x2 M1–O3–M2 128.751
M2–O4 2.01(3) M1–O4–M2 130.502
96
Table 3.4: Select interatomic distances (Å) and angles (◦) in BaxCoyMn8-yO16 at 300
K. Standard uncertainties are given in parentheses.
Bond length (Å) Bond angle (◦)
M1–O1 1.987(8) x2 M1–O1–M1 97.915
1.908(7) 92.028
M1–O3 1.93(1) M1–O4–M1 103.751
M1–O4 1.817(7) M2–O3–M2 101.044
M2–O2 1.958(8) x2 M2–O2–M2 93.775
2.04(1) 95.875
M2–O3 1.852(9) x2 M1–O3–M2 127.132
M2–O4 1.99(1) M1–O4–M2 128.088
97
Table 3.5: Composition Analyses of BMO and BCMO.∗ Standard uncertainties are
given in parentheses.
Sample BMO BCMO
Ba Mn Ba Co Mn
neutron 1.14(6) 8 1.09(9) 0.40(9) 7.60(9)
XRD 1.22(1) 8 1.27(2)
ICP-MS 1.6(3) 8 1.47(5) 0.91(4) 7.09(4)
XPS 1.5(1) 8.0(4) 1.4(1) 0.79(5) 7.2(5)
*Values indicate the molar ratios determined by the given method
Table 3.6: Curie-Weiss parameters extracted from the high temperature paramag-
netic regions of 1/χ plots (Figure 3.7).
Sample TN (K) θCW (K) C (cm3 K mol−1 µe f f (µB)
BMO (as prepared) ∼25 -430 2.34 4.34
BMO (HCl washed) ∼25 -335 2.03 4.05
BCMO (as prepared) ∼180 -630 2.67 4.64
BCMO (HCl washed) ∼180 -499 2.46 4.45
98
Table 3.7: Basis functions allowed for the given propagation vector k for compounds
Ba1.2Mn8O16 and Ba1.2CoxMn8−xO16∗
Irreducible representation Basis functions
BMO Γ1 M1a:(1,0,0);(0,1,0);(0,0,1)
M1b:(1,0,0);(0,1,0);(0,0,1)
M2a:(1,0,0);(0,1,0);(0,0,1)
M2b:(1,0,0);(0,1,0);(0,0,1)
BCMO Γ1 M1,2:(0,1,0)
M1,2+−x, y,−z: (0,1,0)
Γ2 M1,2:(1,0,0);(0,0,1)
M1,2+−x, y,−z:(1,0,0);(0,0,1)
Γ3 M1,2:(1,0,0);(0,0,1)
M1,2+−x, y,−z:(-1,0,0);(0,0,-1)
Γ4 M1,2:(0,1,0)
M1,2+−x, y,−z:(0,-1,0)
∗The functions for the different M-cation sites correspond to the magnetic moment
directions. In both BMO and BCMO, we conducted the magnetic structure refine-
ments with space group I−1.
a,bDifferentiates the two orbits of the M1 and M2 sites, which are related by the
2/m operation.
99
z
y
x
J3/J1
J
2
/
J
1
0
1
2
3
-1
-2
-3
0 0.5 1 1.5 2-0.5-1-1.5-2
A2 - AFM
Corr - GFP
FM
C - AFM
C2 - AFM
1 2
6 5
3
4
8
7
z
y
x
1 2
6 5
3
4
8
7
z
y
x
1 2
6 5
3
4
8
7
Figure 3.13: Phase diagram of the Hamiltonian for J1 > 0, as outlined in the theoretical studies of Seriani et al.56,141 Five
different phases are observed: three AFM (C-AFM, A2-AFM, C2-AFM), one FM, and one geometrically frustrated (corr-GFP)
with perfect anticorrelation along the y axes. Also geometrically frustrated phases with zero area are found at every boundary
between any of the five phases. Green circles represent the points in the phase diagram probed via the Monte Carlo simulations.
100
Given the localized and insulating electronic behavior in BMO and BCMO, we
expect superexchange interactions between the cations to dominate the magnetic
behavior. Using the Ji notation and models of α-MnO2 by Seriani et al, the possi-
ble exchange parameters in the BMO and BCMO structures, can be described.56,141
Figure 3.14 shows the three nearest neighbor exchange interactions arising from
the triangular topology of the Mn-sublattice. Along the tunnel direction is J1, while
J2 and J3 act around the tunnel walls. Crystallographic data shows that J1 occurs
for the shortest M–M distance in BMO and through the smallest M–O–M bond
angle (89.9◦ to 99.1◦). The M–M distances and M–O–M bond angles are subse-
quently larger for J2 and J3. Notably, J3 couples the two different M1 and M2 sites
in BMO, whereas J1 and J2 link the same site within the octahedral dimer chain.
According to the Goodenough–Kanamori rules,116–118 the superexchange mech-
anism favors strong, antiferromagnetic interactions when the M–O–M bond an-
gle is 180◦. The covalent nature of the orbital overlap between the d-orbitals di-
rected toward the same oxygen p-orbital leads to antiferromagnetic coupling be-
tween nearest neighbor cations. When the M–O–M bond angle is 90◦, the same
d-orbitals in the metal cations interact with orthogonal oxygen p-orbitals, which
causes the interaction to be dominated by a Coulombic term that favors a weak,
ferromagnetic coupling. In the hollandites presented here, the M–O–M bond an-
gles range from ∼90◦ to 130◦, which makes the assignment of the exchange con-
stants difficult. Unlike in the perovskite manganites, the O2− anions in hollandites
coordinate to three metal centers, where half of the oxygen sites are in a trigonal
pyramidal geometry, while the other half in trigonal planar. Crespo and Seriani
101
J3
J1
J2
J2
a
b
c
Figure 3.14: Schematic of the three magnetic exchange parameters, Ji,
to model the magnetic behavior in BMO and BCMO. This J1− J2− J3
model is derived from the theoretical work of Seriani et al.56,141
therefore formulated the intermediating orbitals controlling the superexchange as
the sp3 hybrid, sp2 hybrid, and pz-orbitals.56 The sp3 hybrid is thought to favor
ferromagnetic interactions, and the sp2 and pz-orbitals can change from antifer-
romagnetic to ferromagnetic depending on the contribution from the pz-orbital in
hybridizing with the Mn d-orbitals.
The subsequent models from applying these exchange constants led Seriani
et al. to find four collinear models: three antiferromagnetic and one ferromag-
netic,56,141 and they constructed a phase diagram plotting J2/J1 vs J3/J1 (Figure
3.13). In an Ising system when J2 and J3 are smaller than J1, a spin glass state is
formed. In a Heisenberg system when J2 and J3 are smaller than J1, as is likely
for Mn4+, various helical states are found. Unfortunately, none of the collinear an-
tiferromagnetic models proposed by Seriani et al. fit the neutron data for BCMO.
102
This discrepancy may arise from the chemical composition and structural differ-
ences between BCMO and α-MnO2. Nevertheless, the model proposed in Figure
3.11 is closely related to their antiferromagnetic models with moments along the c-
direction as well. However, the J1−J2−J3 model does explain how Co-substitution
could change the ordering in BMO. For BMO, the size of J2 and J3 would have to
be sufficiently small with respect to J1 to lead to helical ordering. The addition of
the Co2+ cation could tune the system from Heisenberg to Ising-like due to its large
single-ion magnetic anisotropy,137 thereby unraveling the helical ordering. In ad-
dition, the Co2+ cations could increase the strength of either J2 or J3 sufficiently to
promote a collinear state. The structural details from the neutron data do not re-
veal any obvious changes between BMO and BCMO, so the tuning of the exchange
parameters implies an electronic effect rather than a structural one.
3.4 Conclusions
The combination of ferrimagnetism with insulating properties is rare as fer-
romagnetic coupling often involves itinerant electrons. Insulating materials, on the
other hand, typically feature localized electrons. Several strategies have been pur-
sued to find magnetic insulators in transition metal oxides,142–144 especially in per-
ovskite materials.145,146 The hollandites represent a new avenue for ferromagnetic
insulators, with the study by Hasegawa et al. representing the first observation
of this phenomenon for hollandites. The high-pressure phase K2Cr8O16 displayed
ferromagnetic half-metal behavior with TC = 180 K and TMIT at 95 K.54 Computa-
103
tional studies on the K2Cr8O16 material suggest two conflicting models to account
for the ferromagnetic insulating properties: Mahadevan et al. suggest the proper-
ties arise from charge-ordering within the framework, induced by electrons from
the donor tunnel cations,55 whereas Toriyama et al. attribute the metal-insulator
transition (TMIT) to a Peierls instability in the quasi-one-dimensional structure
along the CrO6 zigzag chains.
147 Sugiyama et al. lend credence to Toriyama’s pro-
posed mechanism in their reports of muon-spin rotation and relaxation data that
suggest the absence of charge ordering in K2Cr8O16 at TMIT .
78 Deintercalation of
potassium from the K2Cr8O16 framework increased the TC of the material to 250
K, but no report has been given on resulting electronic properties.77 Similarly, the
high-pressure phase Rb2Cr8O16 was reported to be ferromagnetic with a TC = 295
K and semiconducting behavior below 290 K, though this material has only been
minimally investigated.67,78
Mn-based hollandites represent a route towards magnetic insulators with-
out the need for high-pressure synthesis. Comparison of these results for BCMO
with those of other hollandites is shown in Table 3.8. In K1.5Mn8O16, Sato et
al. reported an increase of susceptibility (χ) upon cooling from 52 K to 20 K, al-
though the susceptibility did not feature any saturation; rather, it peaked at 23 K,
then displayed a decrease in susceptibility, characteristic of antiferromagnetic or-
dering.64,139 Magnetic hysteresis measurements of K1.5Mn8O16 at 30 K also failed
to saturate, similar to the measurement of BCMO (Figure 3.8). The magnetic be-
havior of K1.5Mn8O16 looks to be closely related to the pure manganese sample,
BMO. The hysteresis observed by Sato et al appears to have been measured in the
104
Table 3.8: Comparison of magnetic properties in reported ferromagnetic insulating
hollandites.
Composition TC (K) Coercivity (T = x K)
K2Mn8O16 180 « 0.25 T (5 K)
Rb2Cr8O16 295 –
K1.5(H3O)xMn8O16 52 0.4 T (30 K)
BCMO 180 1 T (2 K)
small susceptibility hump observed in the transition between paramagnetic and
antiferromagnetic behaviors. To date, literature searches have not uncovered any
other hollandite materials with this unusual combination of properties.
Complex helical ordering has been proposed as the magnetic structure of pure
manganese-based hollandites K1.5Mn8O16, and Ba1.2Mn8O16.
64,104,139 This study
has provided the first magnetic structure refinement of this material from neutron
diffraction. The expansion and modulation of the magnetic moments relative to the
atomic unit cell support the complex helices that have previously been suggested.
The complex helix could represent a way to lift the frustration in the triangular
lattice, as evidenced by the high frustration index seen in the BMO magnetization
measurements.
By simply substituting enough Mn-sites with Co2+, the magnetic ordering of
BMO was tuned from a complex helix to a ferrimagnetic material with a much
higher ordering temperature of 180 K. This ferrimagnetic response could now rep-
105
resent another mechanism for relieving the inherently frustrated lattice.
The combination of ferrimagnetic and insulating properties suggests that BCMO
and future related hollandite materials may have potential use in multifunctional
applications such as spintronics. The potential to tune TC to higher temperatures
(as seen in K2Cr8O16 and K2V8O16) is especially promising, as future device ap-
plications will require functionality near or above room temperature. Further-
more, K2Cr8O16 and RbCr8O16 require high-pressure preparation,
67,78 whereas
Mn-based hollandites represent a platform for synthesizing magnetic insulators
at ambient pressure. A recent study of BaMn3Ti4O14.25 with the hollandite frame-
work also confirms the possibility of developing these materials for multiferroic
applications.87 Finally, the microporous nature of hollandite materials further pro-
vides interesting possibilities in terms of chemical control of physical applications
through soft chemical techniques. Mn-based hollandites are good candidates for
exploring the possibility of magnetic semiconductors, an important set of materials
for spintronic applications.
106
Chapter 4: K1.6Mn8O16
4.1 Introduction
The Mn-based hollandite with K+ in the tunnels has been studied by many
groups, and is the most-studied manganese hollandite. Synthetic routes to obtain
K1.6Mn8O16 include hydrothermal,64,89,93,99,101,125,139,148–154 redox,84,92,95,100,155–161
reflux,41,90,96,162 electrolysis,166–168 sol-gel,83,160,163,164 microwave,91 solid state/flux
reactions,105 and high-pressure reactions.165 Of these techniques, most of the re-
sulting reported samples display low crystallinity.
Of all the published work regarding KxMn8O16, only a few reports have in-
vestigated the magnetic and transport properties of KxMn8O16, and discrepancies
exist between the properties of samples obtained by wet method and those by dry
techniques. One likely contributing factor to the observed differences is the prob-
able addition of guest ions in hydrothermally synthesized microporous materials,
as wet methods often leave H3O+ or other species inside the tunnels.167 No reports
exist on the magnetic structure of K1.6Mn8O16, and only Sato et al comment on the
susceptibility of a polycrystalline sample.64
Since manganese has a variety of oxidation states ranging from 0 to +7, solid
compounds of manganese have a flexibility for charge transfer without a large
107
degradation of the crystal structure. From a physical point of view, the redox prop-
erty of manganese oxides is often related to their high electrical conductivity. In
addition, a manganese ion has a magnetic moment dependent on its valence (S = 52 ,
2, and 32 for Mn
2+, Mn3+, and Mn4+, respectively). Therefore, it seems very attrac-
tive to investigate the effects of the chemical modifications (ion exchange, oxidation
and reduction, etc.) on the physical properties (conductivity and magnetism, etc.).
Literature accounts of the KxMn8O16 hollandite have reported both mono-
clinic99 and tetragonal167 settings for the crystallographic space group. The K1.5Mn8O16
hollandite had been studied by Sato et al, who used a high temperature synthesis
to produce a polycrystalline sample.64
Single crystals were reportedly obtained via hydrothermal synthesis using
a test-tube autoclave. The referenced synthetic procedure involved 200 mg of γ-
MnOOH and 0.15 cc of KOH charged into a gold ampule, which was subsequently
sealed by welding and inserted into an autoclave.99 The autoclave was heated to
650◦ C at a rate of 400 K/hr, kept at the reaction temperature for a week, then
quenched to room temperature, producing monoclinic crystals. Sato et al do not
discuss the crystal symmetry of their materials, but mention that crystals were
typically sized at 1×0.005×0.005 mm3. Electrical conductivities were measured
by the dc four-terminal method. Gold wires were attached to a single crystal with
carbon paste and the current was applied along the needle axis (the c-axis), which
is parallel to the tunnels. Magnetic measurements were done on a bundle of single
crystals. Unfortunately, all the batches included some non-crystalline impurity in
addition to needle-like KMO crystals.64
108
Mn-based hollandites represent a route towards magnetic insulators with-
out the need for high-pressure synthesis. In K1.5Mn8O16, Sato et al reported an
increase of susceptibility (χ) upon cooling from 52 K to 20 K, although the suscep-
tibility did not feature any saturation; rather, it peaked at 23 K, then displayed
a decrease in susceptibility, characteristic of antiferromagnetic ordering. Magnetic
hysteresis measurements of K1.5Mn8O16 at 30 K also failed to saturate. We believe
that the hysteresis observed by Sato et al in K1.5Mn8O16 was measured in the small
susceptibility hump observed in the transition between paramagnetic and antifer-
romagnetic behaviors.
The symmetry of hollandite compounds depends on the ratio of the average
ionic radius of the octahedral cations to that of the tunnel cations. Structures in
which this ratio is >0.48 distort, reducing the tunnel volume, and thereby lowering
the symmetry from tetragonal to monoclinic. The position occupied by a tunnel
cation is determined primarily by the size of the cation. Relatively small cations,
such as Ba2+ in priderite and Pb2+ in hollandite, displace from the special position,
2a, to more stable sites that are at the sum of the ionic radii from the nearest O
atoms. This study also indicates that the reduced form of Mn in hollandite and
cryptomelane is Mn3+; bond lengths calculated from the refinements suggest that
Mn3+ is more easily accommodated in the structures than the larger Mn2+.6
This chapter presents the work undertaken to synthesize polycrystalline K1.6Mn8O16
under ambient pressure, and then to understand the magnetic behavior of this ma-
terial through several neutron diffraction studies. X-ray diffraction (XRD), neutron
powder diffraction (NPD), and magnetic property measurements have been em-
109
ployed to study the composition, magnetic structure and properties.
4.2 Synthesis & experimental details
KxMn8O16 was synthesized by grinding Mn2O3 (99%, Aldrich) in a mixture
of KNO3 (≥ 99.0%) and KCl (>99%, Sigma-Aldrich) (1:2:0.25 molar ratio of Mn2O3
to KCl to KNO3). The material was heated at 100 K/hr up to 1073 K, soaked for
24 h in ambient atmosphere, then cooled at 100 K/hr. The material was then re-
ground and another 0.25 molar equivalent of KNO3 was added before repeating the
same heating procedure. Upon cooling the second time the material was washed
thoroughly with deionized H2O to remove KCl, then dried on a petri dish at 80◦ C
overnight.
Room temperature powder X-ray diffraction (XRD) data was collected on a
Bruker D8 X-ray diffractometer with Cu Kα radiation, λ = 1.5418 Å, (step size=0.013◦,
with 2θ range from 8◦-140◦). Constant wavelength (CW) neutron diffraction data
was collected on the BT-1 high resolution powder neutron diffractometer at the
NIST Center for Neutron Research, utilizing the Cu(311) monochromators, with
a neutron beam of λ = 1.5403 Å. Scans were taken at 5 K, 30 K, and 100 K for
KxMn8O16 .
Further neutron diffraction measurements were acquired with the BT-7 and
NG-5 beamlines. At BT-7, measurements were taken at 3, 18, 30, 45, 60, 100, 150,
200, 250, and 300 K, with additional scans measuring the temperature dependence
of the magnetic peaks between 22-29◦ 2θ. The BT-7 measurements utilized a py-
110
rolytic graphite monochromator, with d = 3.35416 Å. The neutron energy was 14.7
meV, corresponding to λ = 2.359 Å. NG-5 measurements were taken in five degree
increments from 5 K up to 55 K, at a 40’40’ collimation, with neutron energy of 5
meV (λ = 4.045 Å). Attempts to further separate the magnetic peak(s) at 40-42◦ 2θ
using the 20’20’ collimation (3.7 meV) were unsuccessful.
Magnetic susceptibility was measured using a magnetic property measure-
ment system (Quantum Design MPMS). Field-cooled (FC) and zero-field-cooled (ZFC)
magnetic susceptibility measurements were taken from 2 K - 300 K in direct current
mode with an applied magnetic field of 0.01 T (100 Oe). Hysteresis measurements
were carried out at 2 K in magnetic fields between ± 7 T.
4.3 Results
4.3.1 Crystal structure
Rietveld treatment of both the lab XRD and BT-1 NPD data showed phase
pure KxMn8O16. Refinements were carried out for both the I4/m and I2/m space
groups. For the XRD refinements, final Rwp values of 2.504 and 2.183 were obtained
for the tetragonal and monoclinic settings, respectively. The potassium stoichiome-
try was refined as 0.354(4) in I4/m, and 0.344(3) in I2/m, with respective crystallite
sizes of ∼190 nm and ∼140 nm. The refined K site occupancy leads to an overall
composition of K1.4Mn8O16, with an average oxidation state of 3.83+ per manganese
cation, or approximately seven Mn4+ cations to every one Mn3+ cation. Additional
lattice parameters and atomic positions are detailed in Tables 4.1 and 4.2.
111
20 40 60 80 100 120 140
2µ (±)
0
I
n
t
e
n
s
i
t
y
 
(
a
r
b
.
 
u
n
i
t
s
)
K1. 6Mn8O16
Figure 4.1: X-ray powder diffraction data (UMD) for K1.6Mn8O16 at room temperature, with the I4/m setting.
112
Table 4.1: I4/m Structural parameters for K1.35Mn8O16 from room temperature
XRD data. Standard uncertainties are given in parentheses.
300 K, I4/m, Rwp = 2.504%, 22 independent parameters
a = 9.8403(3) Å, c = 2.86001(7) Å, V = 276.94(2) Å3
atom Site x y z Uiso Occ
K 4e 0 0 0.314(4) 2.7(4) 0.354(4)
Mn 8h 0.3501(2) 0.1660(3) 0 0.92(5) 1
O1 8h 0.1544(0) 0.2030(0) 0 0.63(0) 1
O2 8h 0.5421(0) 0.1650(0) 0 0.63(0) 1
The large values for the K thermal displacement parameters are likely a re-
sult of the loose coordination environment of the K cation within the framework, al-
lowing increased tunnel cation mobility. Previous studies of hollandite frameworks
have seen incommensurate modulations of the tunnel cation, visible in electron mi-
croscopy images as sharp satellite peaks or diffuse intensity normal to the tunnel
direction.86,88,128
Refined Mn–O bond lengths for the I4/m and I2/m settings are provided in
Tables 4.3 and 4.4, respectively. Further evaluation of the metal-oxide bond dis-
tances determined from diffraction data allow speculation about charge ordering in
K1.4Mn8O16 for the I2/m setting. As there is only one Mn site in the I4/m setting,
no charge ordering can be inferred from these refined values.
The average Mn–O bond lengths obtained from room temperature XRD re-
113
Table 4.2: I2/m Structural parameters for K1.35Mn8O16 from room temperature
XRD data. Standard uncertainties are given in parentheses.
300 K, I2/m, Rwp = 2.183%, 25 independent parameters
a = 9.8640(3) Å, b = 2.86039(6) Å, c = 9.8130(3) Å,
β = 90.200(4) Å, V = 276.87 (1) Å3
atom Site x y z Uiso Occ
K 4e 0 0.364(4) 0 2.0(4) 0.344(3)
Mn1 4h 0.1656(3) 0 0.3535(3) 0.35(3) 1
Mn2 4h 0.3516(4) 0 0.8346(3) 0.35(3) 1
O1 4h 0.1980(0) 0 0.1520(0) 0.37(0) 1
O2 4h 0.1620(0) 0 0.7950(0) 0.37(0) 1
O3 4h 0.1610(0) 0 0.5420(0) 0.37(0) 1
O4 4h 0.5500(0) 0 0.8140(0) 0.37(0) 1
114
Table 4.3: Select interatomic distances (Å) and angles (◦) in K1.35Mn8O16, obtained
from XRD data at 300 K (I4/m). Standard uncertainties are given in parentheses.
Bond length (Å) Bond angle (◦)
M–O1 1.93(4) x2 M–O1–M 95.90
1.96(2) 98.58
M–O2 1.886(7) x2 M–O2–M 98.60
1.884(5) 130.35
finements of KMO are 1.920 Å and 1.911 Å for the M1 and M2 sites, respectively
(Table 4.4). In a sample of pyrolusite MnO2,129 Mn4+ has been reported to have an
average Mn–O bond length of ∼ 1.89 Å whereas Mn3+ has an average Mn–O bond
length of 2.04 Å.130 Though the difference in average bond lengths in the KMO hol-
landite is slight, looking at the variance in bond length at each metal site supports
the inference that Mn3+ preferentially occupies the M1 site, while Mn4+ cations
predominantly occupy the M2 position. Using the standard bond lengths as refer-
ence, the average bond length for a site occupied 75% by Mn4+ and 25% by Mn3+
would be 1.9275 Å. These values can be further quantified using the bond valence
method of Brown, Brese, and O’Keeffe131–133 and the empirical bond valence pa-
rameter for Mn4+. These calculations lead to the M1 site having a valence of 3.87
and the M2 site 3.92.
Composition analysis via Rietveld refinement of neutron powder diffraction
(NPD) data showed a higher K occupancy than that obtained by XRD, correspond-
115
Table 4.4: Select interatomic distances (Å) and angles (◦) in K1.35Mn8O16, obtained
from XRD data at 300 K (I2/m). Standard uncertainties are given in parentheses.
Bond length (Å) Bond angle (◦)
M1–O1 1.965(9) x2 M1–O1–M1 93.42
2.005(4) 98.02
M1–O3 1.85(1) M1–O4–M1 99.86
M1–O4 1.87(2) x2 M2–O3–M2 99.11
M2–O2 1.917(3) x2 M2–O2–M2 96.49
1.908(2) 101.57
M2–O3 1.88(1) x2 M1–O3–M2 130.30
M2–O4 1.97(3) M1–O4–M2 125.79
116
ing to an overall stoichiometry of K1.72Mn8O16 The neutron scattering lengths of K
and Mn have fairly good contrast, 3.67 fm in K vs. -3.75 fm in Mn, and the absolute
values of the scattering lengths are very small relative to those of O (5.803 fm).109
A joint Rietveld treatment of the three different temperature datasets col-
lected at BT-1 was utilized to obtain further information about the crystal structure
of K1.6Mn8O16. Both the I4/m and I2/m settings were analyzed. A total of 80 inde-
pendent parameters were used in refining the K1.6Mn8O16 structure with the I4/m
setting across the three datasets, while 104 independent parameters were used in
the I2/m setting. These parameters included the lattice parameters, scale, zero
error, atomic locations, peak shape, isotropic thermal displacement (for Mn and O
atoms), anisotropic thermal displacement (for K), K occupancy, and a 7-order poly-
nomial for fitting the background. With Rwp values of 16.240% for the I4/m setting,
compared to an Rwp of 9.802% for I2/m, Rietveld refinement of the BT-1 neutron
data strongly suggests the I2/m setting to be more accurate for K1.6Mn8O16, though
a better fit is expected due to the additional parameters of the lower symmetry set-
ting. The refinement results for the 100 K data, as well as the diffraction patterns
are given as examples for the I4/m and I2/m analyses in Tables 4.5 and 4.6, and
Figures 4.2 and 4.3, respectively.
117
Table 4.5: Structural parameters for K1.72Mn8O16 from 100 K NPD data in the
I4/m setting. Standard uncertainties are given in parentheses.
100 K, I4/m, Rwp = 16.240%, 80 independent parameters*
a = 9.832(8) Å, c = 2.8563(3) Å
atom Site x y z Uiso Occ
K 4e 0 0 0.38(2) ** 0.43(3)
Mn 8h 0.3508(6) 0.1650(7) 0 0.08(8) 1
O1 8h 0.1553(6) 0.2022(4) 0 0.38(4) 1
O2 8h 0.5426(5) 0.1669(8) 0 0.38(4) 1
**K adp U11=U22 0.03(1) U33 0.09(7)
*Datasets collected at 10, 30, and 100 K were refined simultaneously
118
Table 4.6: Structural parameters for K1.72Mn8O16 from 100 K NPD data in the
I2/m setting. Standard uncertainties are given in parentheses.
100 K, I2/m, Rwp = 9.802%, 104 independent parameters*
a = 9.8767(6) Å, b = 2.88558(1) Å, c = 9.7826(6) Å,
β = 90.327(4) Å,
atom Site x y z Uiso Occ
K 4e 0 0.5(8) 0 ** 0.43(2)
Mn1 4h 0.1681(7) 0 0.3448(7) 0.20(5) 1
Mn2 4h 0.3512(7) 0 0.8351(6) 0.20(5) 1
O1 4h 0.2056(5) 0 0.1524(5) 0.33(2) 1
O2 4h 0.1569(5) 0 0.8012(4) 0.33(2) 1
O3 4h 0.1588(6) 0 0.5435(4) 0.33(2) 1
O4 4h 0.5432(4) 0 0.8313(5) 0.33(2) 1
**K adp U11 0.04(1) U22 0.2(6) U33 0.05(1)
*Datasets collected at 10, 30, and 100 K were refined simultaneously
119
20 40 60 80 100 120 140 160
2µ (±)
0
I
n
t
e
n
s
i
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y
 
(
a
r
b
.
 
u
n
i
t
s
)
Figure 4.2: Rietveld refinement of K1.7Mn8O16 structure in the I4/m setting. Neutron powder diffraction data (NCNR) taken at
100 K is represented by black circles, the calculated fit in pink, the resulting difference is in green, and expected peak locations
are indicated by tick marks below.
120
20 40 60 80 100 120 140 160
2µ (±)
0
I
n
t
e
n
s
i
t
y
 
(
a
r
b
.
 
u
n
i
t
s
)
Figure 4.3: Rietveld refinement of K1.7Mn8O16 structure in the I2/m setting. Neutron powder diffraction data (NCNR) taken at
100 K is represented by black circles, the calculated fit in pink, the resulting difference is in green, and expected peak locations
are indicated by tick marks below.
121
4.3.2 Magnetic properties
Figure 4.4 shows the magnetic susceptibility of K1.35Mn8O16, which increases
rapidly at 53 K upon cooling, followed by a sharp decrease near 26 K. This suscepti-
bility profile is characteristic of antiferromagnetic ordering. Based off a θCW value
of -425 K, the calculated Curie constant of K1.35Mn8O16 is 2.13, with an effective
magnetic moment of 4.12 µB. Using the refined composition of K1.35Mn8O16 and
the resulting average Mn valency of +3.83, the expected µe f f of the sample is 4.047
µB, in fairly good agreement with the observed magnetic data.
Using the transition at 53 K as TN , the frustration index is 8.01. Using the
26 K transition, the frustration index is 16.
Magnetization versus magnetic field measurements of K1.35Mn8O16 show the
opening of a hysteresis loop with a coercivity of ∼0.5 T at 30 K. The magnetization
versus field measurements taken at 2 K and 100 K appear paramagnetic or anti-
ferromagnetic (Figure 4.5). Magnetic saturation of K1.35Mn8O16 was not observed
within the field range of the MPMS instrument.
4.3.3 Magnetic structure from neutrons
No obvious structural changes were observed across the different NPD datasets
collected at BT-1. A broad hump in the background, from ∼ 10-30◦ 2θ, suggesting
significant correlations in the sample, largely obscured the 2θ range where mag-
netic Bragg peaks might be expected. A broad magnetic Bragg peak was observed in
the diffraction pattern at ∼16-18◦ 2θ (Figure 4.6), though the peak center appeared
122
Figure 4.4: Magnetic susceptibility as a function of temperature for K1.35Mn8O16.
to shift to slightly higher 2θ at 30 K relative to its position at base temperature. A
second potential magnetic reflection was potentially observed at ∼ 13◦ 2θ, though
the low intensity of the reflection made it difficult to definitively identify the mag-
netic peak from background noise. This second peak sits very close to the location
of the (200)/(002) pair of reflections for the I2/m setting, or the (020) reflection in
I4/m.
123
Figure 4.5: Comparison between the experimental measurements of
magnetization as a function of applied field for K1.35Mn8O16 at 2 K (or-
ange), 30 K (green), and 100 K (blue).
124
Figure 4.6: Raw neutron powder diffraction data (NCNR) for K1.6Mn8O16 at 5 K (gold), 30 K (orange), and 100 K (maroon).
Inset enhances low 2θ region where magnetic reflections can be seen around 16 2θ in the 5 K-100 K line (black).
125
Measurements were then taken on the BT-7 beamline, which features greater
intensity at the expense of lower peak resolution. As shown in Figure 4.7, measur-
ing as a function of temperature, the magnetic peaks with the greatest intensity
(∼16-18◦ 2θ in Figure 4.6) were observed between 23-25◦ 2θ. The lower resolution
prevented accurate determination of the number and location of overlapping peaks,
but allowed better visualization of where magnetic reflections were occurring. An
abrupt shift in the location of the magnetic peaks was observed as the temperature
passed through 25 K, with the most intense peaks shifting to higher 2θ as observed
in the BT-1 data. A broad hump in the background indicated significant correlations
in the sample.
126
Figure 4.7: Neutron powder diffraction data (BT7, NCNR) for various temperatures of K1.6Mn8O16 as it undergoes a magnetic
transition. The data collected at room temperature has been subtracted from the intensities of each of the other datasets to
isolate the temperature dependence of the magnetic reflections.
127
Measuring K1.6Mn8O16 on NG-5 (SPINS), the overlapping, high-intensity mag-
netic peaks were resolved into a sharper peak on the right, and a broader peak on
the left. The left peak is likely a result of two or more overlapping peaks, but
changing the collimation settings to 20’20’ on the instrument failed to further sep-
arate the broad reflection seen at ∼40-42◦ 2θ in Figure 4.8. The shift to higher
2θ is clearly observed in the NG-5 diffraction data, with a significant decrease in
intensity observed at the higher temperatures.
The shifting of magnetic peak locations suggest that upon cooling, the mag-
netic ordering occurs incommensurately with the nuclear structure. As tempera-
ture continues to decrease, however, the magnetic ordering suddenly locks in to
a commensurate pattern around 25 K. Similar lock-in behavior was noted for the
frustrated kagomé staircase in the Co3V2O8 material.169
128
Figure 4.8: Neutron powder diffraction data (NG-5, NCNR) for K1.6Mn8O16.
129
4.4 Discussion
Literature accounts of the KxMn8O16 hollandite have reported both mono-
clinic99 and tetragonal167 settings for the crystallographic space group. According
to Cheary’s radius ratio rule, with rA = 1.51 Å and rB = 0.530 Å or 0.645 Å (for Mn4+
or Mn3+, respectively), K1.6Mn8O16 should display tetragonal symmetry.48 The in-
dicator proposed by Zhang et al also predicts a tetragonal setting for K1.6Mn8O16.49
Attempts to grow single crystals of K1.35Mn8O16 by flux techniques resulted
in decomposition of the tunnel framework, producing denser phases and binary
oxides. Strobel et al reported that heating a single crystal of K1.33Mn8O16 above
about 550◦ C resulted in decomposition, which is in agreement with a study on
natural crystals by Faulring et al who reported a decomposition temperature of
600◦ C. These authors found the transformation to be ‘topotactic’, as the resulting
Mn2O3 crystallites are highly oriented.167
Analysis of the magnetic susceptibility in KxMn8O16 gave an effective mag-
netic moment of 4.12 µB and a Curie constant of 2.13, which is relatively close to
the expected values of 4.05 µB and 2.03 calculated from the stoichiometry obtained
from the refined X-ray data. The extrapolated Weiss temperature of -425 K is in-
dicative of a high amount of frustration within the material, consistent with other
materials with triangular lattice frameworks.
The magnetism of K1.33Mn8O16 was reported to have an antiferromagnetic
transition at TN = 18 K and Curie-Weiss behavior above TN .167 α-MnO2 displayed
an antiferromagnetic transition at TN = 24.5 K.99 Magnetic susceptibility measure-
130
ments on K1.5Mn8O16 revealed the existence of two magnetic phase transitions- an
increase in magnetization at 52 K and an antiferromagnetic transition at 20 K.64
The magnetization measurements described herein showed behavior simi-
lar to that observed by Sato et al.64 In their studies, Sato et al investigated the
anisotropy of the magnetic phase transition between 52-20 K by aligning needles
in grease, observing clear anisotropic behavior below 52 K. Between 52 and 20 K,
their magnetization curve showed hysteresis due to a weak ferromagnetism, with
the direction of spontaneous magnetization perpendicular to the c-axis (tunnel di-
rection). Again, the magnetization versus magnetic field measurements obtained
for K1.6Mn8O16 at 30 K closely match the observations of Sato et al.64
Strobel et al observed evidence of antiferromagnetic ordering at 18 K for sin-
gle crystals in their magnetic susceptibility vs. temperature measurements. This
TN value is lower than that reported in a previous paper where neither the χ(T)
curve nor the sample composition were given. The discontinuity in χ(T) is much
sharper for the single-crystal sample than the powder sample, with a Curie con-
stant = 2, θCW = 315 K. An effective magnetic moment of 4.00 µB per Mn atom was
observed for the crystal sample, in excellent agreement with the spin-only value
4.04 µB calculated from the formula unit K0.16MnO2.167 The frustration index for
this sample is f = 17.5, similar to that observed in our K1.35Mn8O16 hollandite.
The spontaneous magnetization in our K1.35Mn8O16 hollandite closely matches
that of Sato et al at 30 K, displaying only about 0.3% of the calculated saturation
magnetization of K1.5Mn8O16. They proposed several possible explanations for the
weak ferromagnetism, first suggesting a mechanism of double exchange. However,
131
citing evidence of charge order in their material, Sato et al believe the conduc-
tion electrons are considered to be rather localized at 30 K, calling in to question
whether the double exchange mechanism would still effective at this temperature.
Their second possibility is the so-called Dzyaloshinsky-Moriya (DM) mechanism,
where the antisymmetric exchange term D(S1×S2) is added to the symmetric ex-
change term JS1S2. In the tetragonal setting, a mirror plane bisects the nearest
neighbor path, and the D vector of the DM interaction should be perpendicular to
the c-axis, conflicting with the fact that the spontaneous magnetization is perpen-
dicular to the c-axis when the easy plane is perpendicular to the c-axis. However,
this discussion ignores the same charge ordering effect that the authors used to
discredit their first proposal of double exchange. If charge ordering is taken into
account, DM canting remains as a viable mechanism to explain the weak ferromag-
netic behavior. Their third and final possibility of ‘helical ferrimagnetism’ accounts
for the weak observed spontaneous magnetization compared to that of an ordinary
ferrimagnet, also explaining the anisotropy they observed perpendicular to the c-
axis of their crystal needles.64
In ordinary helical magnetic structures, no net magnetization appears be-
cause the magnetic moments cancel each other. However, in the case of potassium
manganese hollandite there are two kinds of spins, S = 32 for Mn
4+ and S = 2 for
Mn3+. If the repeat period of the helical magnetic structure is completely separate
and unrelated to that of the charge ordering, a cancellation of magnetic moments
occurs. Conversely, if the periodicity of charge ordering is an integral multiple of
the magnetic helix, complete cancellation may not always occur and weak magneti-
132
zation can appear. From their composition of K1.5Mn8O16, Sato et al predicted that
the period of charge ordering to be eight times as large as the unit-cell parameter
along the c-axis.64
4.5 Conclusions
What progress have we made in understanding the crystal and magnetic
structures of K1.35Mn8O16 at low temperatures?
Our diffraction studies of K1.35Mn8O16 do not definitively prove the struc-
ture exhibits tetragonal symmetry as seen by the poor fits obtained by Rietveld
refinement of both neutron and X-ray data. Structural characterization has been
undertaken using both plausible settings, though the quality of the data collected
did not allow for a full solution of the magnetic structure. Temperature dependent
measurements at a synchrotron would provide greater resolution of the Bragg re-
flections, thus resolving the symmetry debate.
Efforts to index the magnetic peaks using the K-search routine in FullProf
were ultimately unsuccessful. Despite multiple attempts, using both the I2/m and
I4/m settings and magnetic peak locations from either 30 K or 10 K, no satisfactory
individual propagation vectors aligned well with all, or even several, of the mag-
netic peak locations. It does not seem improbable that multiple propagation vectors
will be needed in solving the magnetic structure of K1.35Mn8O16.
The broadness of the observed magnetic Bragg peaks relative to the nuclear
Bragg reflections in the BT-1 data may be a result of the ordered magnetic domain
133
size being much smaller than the crystalline size of the nuclear structure, or may be
due to the significant frustration present.104 The ‘helical ferrimagnetism’ described
by Sato et al is still a viable model for the magnetic ordering of K1.5Mn8O16, similar
to the ordering observed for Ba1.2Mn8O16 in Chapter 3. Of course, one of the surest
ways to expand our studies and learn significantly more about the magnetic behav-
ior of this material would be to grow single crystals of the material, so synthetic
efforts in this regard are ongoing.
134
Chapter 5: Bi1.7V8O16
The research described within this chapter has been submitted for publica-
tion. Brandon Wilfong, Dr. Pouya Moetakef, Dr. Craig M. Brown, Dr. Peter Zavalij,
and Dr. Efrain Rodriguez were contributing authors on the manuscript.
5.1 Introduction
Vanadium oxides are well-known to exhibit metal-to-insulator transitions (MIT)
and the underlying mechanisms can involve the ordering of charge, orbital, and/or
spin degrees of freedom.170–178 A lingering question in these materials is whether
Mott-type physics (i.e. electron-electron correlations) drive the MIT or whether
Peierls-type interactions (i.e. electron-phonon interactions) are instead responsi-
ble.179–182 Charge ordering also seems to be a key ingredient in observing MITs,
such as in various β-vanadium bronzes and in NaV2O5, which undergoes charge or-
dering at 34 K.171,172,174–176 The study of vanadates with various geometries affords
the opportunity to better separate the parameters responsible for MITs.
V-based hollandites have been studied through both experimental and theo-
retical investigations, particularly because of their observed MITs combined with
their quasi-one dimensional (1D) geometry. A MIT is observed at ∼ 170 K for
135
a) ladder
rungs
b)
Figure 5.1: (a) Side view of the hollandite double chain showing M–M
triangular connectivity of neighboring MO6 octahedra. (b) Hollandite
structure viewed down [001], showing the square channels where the A
cations reside.
K2V8O16. A superlattice observed in the low-temperature phase suggested the pres-
ence of charge ordering, and the authors proposed a model where half of the zigzag
VO6 chains are V4+, while the other chains are a mixture of V3+/V4+.69 Computa-
tional studies suggested orbital ordering pattern.68
Calculations predicted that changing the A cation from K+ to Rb+ raised the
MIT up to 220 K.70
The higher charge of Bi3+ cations, as opposed to the more typical K+ tunnel
cation, lowers the V oxidation state in the hollandite framework, resulting in a
unique composition of S = 1 and S = 12 cations that allow such parameters to be
better separated in order to shed light on similar systems.
Bi1.7V8O16 belongs to the structural class of materials known as hollandites,
where the structure can be described as a square channel occupied by Bi3+ cations,
with walls composed of edge-sharing VO6 octahedra (Figure 5.1b). The V cations are
arranged in triangular ladders (Figure 5.1a). This topology, coupled with mixed va-
136
lency, can lead to interesting properties including insulating ferromagnetism,54,55,77
frustrated magnetism,56–58 and MITs.59–61 The triangular ladder is known to lead
to magnetic frustration such as in the hollandite Ba1.2Mn8O16.57
Bi1.7V8O16 exhibits a MIT close to 70 K, but unlike all other known vana-
dates that undergo MITs, the magnetic susceptibility of Bi1.7V8O16 diverges upon
entering the insulating phase.170,173 Kato et al. first demonstrated that the di-
vergence in the magnetization of Bi1.7V8O16 is concomitant with the MIT near 70
K.102 The uniqueness of this transition, however, was never investigated by struc-
tural or magnetotransport studies to explore whether the system was undergoing
long-range magnetic ordering at the MIT, which would imply that Mott-type physics
was playing a dominant role. Furthermore, whether or not the vanadium cations
dimerize upon entering the insulating phase has been unresolved up to this point.
The studies described in this chapter aim to resolve whether the orbitally
active V4+ and V3+ cations and their mixed spin states are responsible for the di-
vergence in magnetization at the MIT and to understand how crystal structure and
external magnetic field affect the transport properties. Understanding these ques-
tions would have implications on other vanadates with MITs. The combined X-ray
and neutron diffraction studies along with magnetotransport and magnetization
measurements reveal important details regarding the nature of the charge, orbital,
and spin states in Bi1.7V8O16.
137
5.2 Synthesis & experimental details
Polycrystalline samples of Bi1.7V8O16 hollandite were produced by grinding
together stoichiometric ratios of V2O3 (99.7%, Alfa Aesar), V2O5 (98+%, Sigma
Aldrich), and Bi2O3 (99%, Fisher). Reagents were used without further purifica-
tion. After grinding together, the powdered mixture was pressed into a pellet and
heated to 1173 K at a rate of three degrees per minute, in an evacuated flame-sealed
quartz glass ampule. Once the target temperature was reached the sample soaked
for 72 hours, followed by furnace cooling.183
Needle-like single crystals of Bi1.7V8O16 were grown by two different methods.
One route includes using an excess of Bi2O3 during the solid state reaction followed
by physical removal of crystals from the excess Bi2O3 flux. The other route includes
mixing a KCl/NaCl salt mixture (1:1 molar ratio) with a pre-reacted powder mixture
in an alumina crucible sealed in an evacuated quartz ampule. The product:flux
molar ratio was 1:10, and the mixture was heated to 1273 K for 10 hours, followed
by slow cooling at 5◦ /hr. Flux was removed by washing with deionized H2O.
Synchrotron XRD was collected at the 11-BM instrument at the Advanced
Photon Source with λ = 0.41397 Å from 100 K to 300 K. Constant wavelength neu-
tron powder diffraction data was collected on the high resolution BT-1 instrument
at the National Institute of Standards and Technology (NIST) Center for Neutron
Research (NCNR) with a λ = 2.078 Å (Ge311 monochromator) for various tempera-
tures between 10 K and 300 K. All powder diffraction data was analyzed using the
TOPAS software.115
138
A black needle-like specimen of Bi1.7V8O16 with approximate dimensions of
0.03 mm × 0.03 mm × 0.26 mm was used for single crystal X-ray diffraction (XRD)
analysis. The X-ray intensity data were measured on a Bruker APEX-II CCD sys-
tem equipped with a graphite monochromator and a Mo Kα sealed tube (λ = 0.71073
Å ). Full structures were taken at 90 K, 200K, and 300K, and partial measurements
for lattice constant determination were taken between 90 K and 290 K in 20 K
steps. At 200 K, integration of the data using a tetragonal unit cell yielded a total
of 2244 reflections to a maximum θ angle of 32.42◦ (0.66 Å resolution), of which
299 were independent. The structure was solved and refined using the Bruker
SHELXTL Software Package.184,185 The final anisotropic full-matrix least-squares
refinement on F2 with 27 variables converged at R1 = 1.44% for the observed data
and wR2 = 3.70% for all data.
Field-cooled (FC) and zero-field-cooled (ZFC) magnetization measurements
were taken from 2 K - 300 K with a Quantum Design magnetic property measure-
ment system (MPMS) on a polycrystalline sample. Measurements were in direct
current mode, with an applied magnetic field of 0.01 T (100 Oe). Magnetization ver-
sus field up to 7 T were also taken on the MPMS with a polycrystalline sample at
5 K. Transport measurements were taken in a Quantum Design physical property
measurement system (PPMS). A four-probe geometry was used on both a sintered
pellet and later on single crystals, to measure electrical resistance first upon cool-
ing, then upon heating. For the single crystal measurements, magnetic fields were
measured up to 8 T, with ramp rates of 1◦ /min in the temperature region of the
MIT, and 5◦/min above 100 K. Field was applied either along the needle direction,
139
H∥, or normal to it, H⊥.
5.3 Results
5.3.1 Powder diffraction
To investigate the effects of the temperature-induced MIT on the structure
of Bi1.72V8O16, we performed temperature-dependent X-ray and neutron powder
diffraction (NPD). Rietveld refinements were carried out to extract structural and
lattice parameters from the data. Structural and lattice parameters for represen-
tative temperatures of the NPD data are gathered in Table 5.1.
140
Figure 5.2: Neutron powder diffraction data (BT1, NCNR) for various temperatures of Bi1.7V8O16 as it undergoes a tetragonal-
tetragonal structural distortion during the MIT.
141
Temperature dependent NPD data reveals Bi1.7V8O16 undergoing a first-order
tetragonal-to-tetragonal structural phase transition. While at 10 K and 300 K, far
from the MIT, the crystal structure could be fit with a single tetragonal phase, sig-
nificant peak splitting was observed close to the transition. Figure 5.2 shows three
NPD patterns of polycrystalline Bi1.7V8O16 for the 40 K, 67.5 K, and 80 K tempera-
ture steps upon warming. As seen in the 67.5 K data, the NPD pattern is fit well to
two tetragonal phases, with phase fractions tracking the transition from insulating
to metallic behavior (Figure 5.3). A similar tetragonal-to-tetragonal transition has
been observed in Rb2V8O16 at its MIT of 240 K,186 whereas the MIT in K2V8O16
(155-170 K) is accompanied by a structural distortion from tetragonal to monoclinic.
The most notable structural difference between the low-T (insulating) and
high-T (metallic) phases is the significant expansion in the c-direction, which runs
along the triangular ladders, upon entering the insulating phase. Temperature de-
pendence of the lattice parameters from all three different probes, neutrons, powder
X-ray, and single crystal X-ray, are included in Figure 5.4. This suggests that dimer-
ization must occur along the c-direction rather than the ab-direction, and therefore
that the V–V pair formation occurs along the triangular ladder sides rather than
the ladder rungs (Figure 5.1a).
Another notable result from the NPD data, is the lack of either magnetic or
nuclear satellite reflections in the low-T phase. This result leads to the conclusion
that no long-range magnetic order sets in during the MIT, and therefore electron-
electron correlations leading to a Mott-type transition is unlikely. One must note,
however, that the structure of the low-T phase may indeed be lower in symmetry
142
Figure 5.3: Temperature evolution of phase fractions as Bi1.7V8O16
transitions from a metallic to an insulating phase upon cooling. Phase
fractions were calculated during Rietveld refinement of neutron pow-
der diffraction (NPD) data obtained on the BT-1 beamline at the NCNR.
Error bars are smaller than plot symbols used.
143
single crystal XRD
synchrotron XRD
Neutron powder difraction
insulating phase
metalic phase
Figure 5.4: Temperature evolution of the lattice parameters for the
tetragonal cell of Bi1.7V8O16 from single crystal X-ray, synchrotron pow-
der X-ray, and neutron powder diffraction. The low temperature data
indicates a first order transition below 70 K, arising from the nucleation
of a separate tetragonal phase with a large c-parameter. Error bars are
smaller than plot symbols used.
than the tetragonal phase reported here since the NPD data cannot definitively
prove this. Unfortunately, vanadium atoms do not strongly scatter neutrons, espe-
cially relative to the other elements in Bi1.7V8O16, with neutron scattering lengths
of -0.443 fm for V, compared to 8.532 fm for Bi and 5.805 fm for O.109 The ramifica-
tions of this reality are that any satellite reflections arising from V cation displace-
ments could be missed by the NPD measurements.
144
Table 5.1: Structural parameters for Bi1.7V8O16 from NPD data taken at tempera-
tures across the MIT. Standard uncertainties are given in parentheses.
300 K, I4/m, Rwp = 5.521%
a = 9.9243(1) Å, c = 2.92301(5) Å, V = 287.764(8) Å3
atom Site x y z Uiso Occ
Bi 4e 0 0 0.104(2) 1.5(1) 0.411(4)
V 8h 0.348(3) 0.173(3) 0 0.1(1) 1
O1 8h 0.1518(2) 0.1943(1) 0 0.63(3) 1
O2 8h 0.5404(1) 0.1651(3) 0 0.63(3) 1
67.5 K I4/m, Rwp = 4.720%
Metallic phase (34%)
a = 9.9194(2) Å, c = 2.90391(9) Å, V = 285.79(2) Å3
atom Site x y z Uiso Occ
Bi 4e 0 0 0.110(2) 0.69(8) 0.428(2)
V 8h 0.352(6) 0.168(7) 0 0.1(1) 1
O1 8h 0.1505(4) 0.1939(4) 0 0.37(2) 1
O2 8h 0.5411(4) 0.1664(6) 0 0.37(2) 1
Insulating phase (66%)
a = 9.8978(1) Å, c = 2.94526(6) Å, V = 288.594(9) Å3
atom Site x y z Uiso Occ
Bi 4e 0 0 0.102(2) 0.69(8) 0.428(2)
V 8h 0.358(3) 0.170(3) 0 0.1(1) 1
O1 8h 0.1537(2) 0.1930(2) 0 0.37(2) 1
O2 8h 0.5396(2) 0.1646(3) 0 0.37(2) 1
10 K, I4/m, Rwp = 5.521%
a = 9.8985(1) Å, c = 2.94441(4) Å, V = 288.385(9) Å3
atom Site x y z Beq Occ
Bi 4e 0 0 0.099(1) 0.6(1) 0.44(4)
V 8h 0.351(3) 0.168(4) 0 0.2(2) 1
O1 8h 0.1533(1) 0.1933(2) 0 0.51(3) 1
O2 8h 0.5397(1) 0.1655(3) 0 0.51(3) 1
145
5.3.2 Magnetization
Unlike the hollandites K2V8O16 and Rb2V8O16,69,186 the magnetic suscepti-
bility of Bi1.7V8O16 increases sharply at the transition temperature (TMI) upon
cooling (Figure 5.5a), with two steps of increasing susceptibility observed, indica-
tive of non-spin-singlet formation in the insulating phase. Furthermore, hysteretic
behavior is observed in the magnetic susceptibility with the ZFC (measured upon
heating) having a slightly higher TMI than the FC curve (measured upon cooling).
This is consistent with the NPD data showing a large amount of phase coexistence
during the first-order phase transition.
Interestingly, the susceptibility of the high-T metallic phase does not appear
to be temperature independent as would be expected for a metallic Pauli paramag-
net. Instead, the broad maximum near 275 K is indicative of low-dimensional mag-
netism associated with local moments in a 1D chain, for example. Earlier studies of
Bi1.7V8O16 showed similar broad features in the metallic state,102,187,188 whereas
the TMI and extent of the susceptibility’s divergence were dependent on the Bi3+
content and thus the charge of the V cations. This result indicates that while most
electrons near the Fermi level are delocalized, some localized behavior arises possi-
bly due to significant electron correlations even in the metallic state.
Despite the divergence of the magnetization below the MIT, Bi1.7V8O16 never
enters a ferromagnetic state. While it appears it could be diverging much in the
same way as an antiferromagnet above the Néel temperature, the magnetization
never drops even at the lowest temperature of our SQUID measurement (2 K).
146
a)
b)
Figure 5.5: The molar magnetic susceptibility of Bi1.7V8O16 vs. temper-
ature for zero-field cooling (ZFC) and field-cooling (FC) measurements
with an applied field of 0.01 T. The MI transition occurs near 60 K in
this polycrystalline sample. The inset shows the hysteresis and mul-
tiple step behavior of the transition. Bottom panel shows resistivity
measured of a sintered pellet of polycrystalline Bi1.7V8O16 hollandite.
147
Figure 5.6: Magnetization vs. applied magnetic field for Bi1.7V8O16,
measured at 5 K. The linear response is indicative of paramagnetism in
light of the neutron data not displaying any evidence for antiferromag-
netic ordering. A subtle deviation develops at higher fields, although we
are unsure of its underlying cause.
Finally, measuring the magnetization as a function of magnetic field revealed no
long range magnetic order (Figure 5.6), as the magnetization varied linearly as a
function of H, similar to either paramagnetic or antiferromagnetic behavior. While
the M vs. H curve is neither proof for or against long-range antiferromagnetic
ordering, in the context of other results such as neutron diffraction, Bi1.7V8O16
does not appear to develop long-range magnetic order below the MIT.
148
5.3.3 Magnetotransport
First, electrical transport measurements were carried out on polycrystalline
material. The resistivity data for a sintered pellet of Bi1.7V8O16 is presented in
Figure 5.5b, where a transition from a metallic to an insulating state occurs close to
70 K, concomitant with the observed magnetic transition. The resistivity is 7 orders
of magnitude larger near 40 K than at 300 K, confirming the true MIT nature of
the transition.
To better understand how crystallographic direction influences the transport
properties and the effects of an external magnetic field, single crystals were mea-
sured in the PPMS. The transport measurements of a single crystal of Bi1.7V8O16
as a function of temperature, magnetic field strength, and crystallographic direc-
tion are all presented in Figure 5.7. The crystals were needle-like in morphology
due to the hollandite’s quasi-1D structure, and field was applied either parallel or
perpendicular to the needle axis, which corresponds to the c-axis.
The electrical resistivity data shown in Figure 5.7 demonstrates that field
applied normal to the ladder direction suppresses the MIT. Upon cooling, the zero
field data shows an MIT close to 62.5 K, where resistivity increases over six orders
of magnitude compared to that of room temperature; upon heating, the crystal re-
enters the metallic state but at a higher temperature of 80 K, demonstrating a
first-order MIT with large hysteresis. Figure 5.8a shows an overall linear trend
for the transition temperature TMI plotted versus H⊥, where hysteretic behavior
appears to widen as H⊥ approaches 8 T.
149
Figure 5.7: Electrical resistivity measurements as a function of applied
magnetic field for a) field normal to the ladder, H⊥, and b) field paral-
lel to the ladder sides, H||. The TMI of Bi1.7V8O16 displays significant
field dependence for H⊥ compared to the relatively field independent
behavior of H||.
150
Figure 5.8: The linear dependence of the transition temperature TMI
vs. applied magnetic field for (a) H⊥ and (b) H∥. Filled symbols indicate
TMI as sample was heated, open symbols are for TMI upon cooling.
When field is applied along the needle direction, and therefore along the tri-
angular ladder, TMI appears to be independent of field strength. The MIT is sup-
pressed to approximately 40 K upon cooling and approximately 65 K upon heating
regardless of H (Figure 5.8b). This likely indicates that the external field suppress
formation of the V–V dimers, and the effect is more extreme when it is directly along
the bond-axis.
The metal-insulator transitions have a much more sudden onset for H∥ than
for H⊥, where the resistivity upon cooling suddenly diverged around 35-40 K, be-
yond the detection threshold of the instrument, as seen in Figure 5.7b. These direc-
tional experiments thus demonstrate that the coupling between the V cations must
be anisotropic, with exchange interactions both along the ladder and its rungs driv-
ing the MIT.
151
5.3.4 Single crystal diffraction
To understand the behavior of the insulating phase as observed in the mag-
netization and magnetotransport data, we performed multiple diffraction studies of
single crystal and polycrystalline Bi1.7V8O16 at various temperatures. Full struc-
tures were obtained at 90 K, 200 K, and 300 K, while shorter measurements were
carried out between 90 K to 300 K in 20 K steps to follow the thermal expansion.
The lattice parameters as a function of temperature are presented in Figure 5.4,
and no phase transition is observed in this temperature regime. Structural and
lattice parameters at 200 K can be found in Table 5.2, and crystallographic infor-
mation files for the full 200 K and 300 K structures can be found in Supplemental
Information.
From the single crystal results, Bi1.7V8O16 adopts a body-centered tetragonal
space group I4/m with the a-parameter determined by the size of the hollandite
walls and the c-parameter by the V–V distances down the triangular ladder. At 200
K, the V–V distance in the c-direction is 2.913(1) Å and 2.999(1) Å along the ladder
rungs (Figure 5.1a).
Remarkably, overlapped frames of the reciprocal lattice map of the (h0l) and
(0kl) planes of Bi1.7V8O16 reveal satellite reflections as intense as the main reflec-
tions (Figure 5.9a and b), indicating the presence of a charge density wave (CDW).
Up to fourth order reflections can be observed for the CDW satellites. Interest-
ingly, the CDW in Bi1.7V8O16 is quasi-commensurate with the VO6 framework as
evidenced by the satellite reflections located close to (0 0 0.846c∗) or similarly (0
152
0 −0.154c∗). Since we did not observe a temperature dependence in the location
of the satellite reflections, the CDW is not truly incommensurate or independent
from the VO6 framework. Rather, it is commensurate with a very long unit cell of
a×a×13c. Hence, we refer to this as a quasi-commensurate CDW. Furthermore, no
satellite reflections were observed in the (hk0) reflections (Figure 5.9c) indicating
that the CDW only occurs in the c-direction. Due to electrostatic repulsion between
the cations in the hollandite channels, the Bi3+ cations deviate away from their
average crystallographic position to form the CDW, a well known phenomenon in
Ti-based hollandites.189,190
153
Figure 5.9: (a) Single crystal XRD data showing the main (h0l) reflections (white circles) and the satellite reflections corre-
sponding to the Bi charge density wave, which can be indexed with a modulation vector of 0.154c∗. (b) The (0kl) reflections
of the Bi1.7V8O16 single crystal X-ray diffraction measurement, also showing the satellite reflections indicative of long-range
modulation of the Bi cations within the hollandite channels. Faint streaking between satellite peaks indicates disorder amongst
neighboring channels. No satellite reflections or streaking are observed in (c), showing the (hk0) reflections.
154
5.4 Discussion
In light of the structural and transport data, we would like to discuss the
implications for charge, spin, and orbital order in Bi1.7V8O16.
5.4.1 Charge order
Studies of the MITs in hollandites have revealed charge order as one of the
prerequisites for such behavior. K2V8O16 undergoes a two-step MIT between 155-
170 K, with an accompanying decrease in magnetization.69 Through high-resolution
diffraction studies Komarek et al observed a structural transition from tetragonal
to monoclinic in K2V8O16 and proposed a complex CDW formation down the tri-
angular ladders of the hollandite.61 In their model, Komarek et al find that entire
ladders are composed of either V3+ or V4+. Similarly, the Pb1.6V8O16 hollandite un-
dergoes a MIT at 140 K; however, initial studies have yet to resolve whether charge
ordering or significant structural transitions occur in this system.191
Previous studies on structurally related hollandites that do not undergo MITs,
however, could be revealing in formulating the correct model for CDWs in hollan-
dite oxides.189,190,192 The work of Carter and Withers on titanium-based hollandites
have shown a correlation between the wavelength of the CDW’s modulation and
the occupancy x in AxTi8O16 where A is typically a large cation such as Ba2+ or
K+.189,190,192 Carter and Withers connected the modulation of the propagation vec-
tor to the occupancy of the A cation through the relationship x= 2(1− (1/m)) where
m is the ratio between the repeat period of the CDW.190 For the title compound
155
Table 5.2: Structural parameters for Bi1.7V8O16 from single crystal X-ray diffrac-
tion at 200 K. Standard uncertainties are given in parentheses.
Bi1.72V8O16 (200 K, single crystal XRD), I4/m, wR2 = 3.70%
a = 9.932(2) Å, c = 2.9133(6) Å, V= 287.4(1) Å3
atom x y z Uiso Å2 Occ.
Bi1 0.0 0.0 0.060 (3) 0.0099(7) 0.24(1)
Bi2 0.0 0.0 0.161 (4) 0.0099(7) 0.19(1)
V 0.35520(4) 0.17036(4) 0 0.0053(2) 1
O1 0.1528(2) 0.1934(2) 0 0.0065(3) 1
O2 0.5408(2) 0.1648(2) 0 0.0065(3) 1
156
Bi1.7V8O16, since the propagation vector of the CDW is 0.846c∗ (Figure 5.9a,b),
m = 0.154 from the Carter-Withers expression. This ’compositional ruler’ from the
CDW would lead to x= 1.69, consistent with the nominal and refined values of the
Bi stoichiometry from NPD and X-ray diffraction data. Since 0.154 is very close to
2/13, this would physically correspond to two Bi vacancies occurring across every
13 unit cells along the channel direction.
Our single crystal diffraction data suggests a charge ordering model for Bi1.7V8O16
different from that of the other vanadium hollandites such as K2V8O16 and Rb2V8O16.
The average oxidation state of vanadium in Bi1.7V8O16 is V3.363+, which would im-
ply five V3+ (S = 1) for every three V4+ (S = 12 ) cations in the triangular ladder. The
absence of a Bi3+ cation in the tunnel would require nearby V cations to be in the
higher oxidation state of 4+ in order to maintain charge balance. Therefore, the V4+
cations would order around the 2/13 Bi vacancies in the CDW to charge compensate
the lattice. A schematic of the proposed charge ordering is depicted in Figure 5.10a.
Kanke et al propose a similar CDW for the tunnel cations in the Ba1.09V8O16 hol-
landite,193 and Kuwabara et al a similar CDW for the transition metals in the hol-
landite K1.6Mn8O16.165 Interestingly, Mentré et al found that having x< 1.7 for the
Bi site or mixing it with a variety of cations leads to A-site disorder and the com-
pounds become semiconducting at all temperatures.194 Therefore, the CDW seems
to be key for the observation of the MIT.
Careful inspection of the (h0l) and (0kl) maps in Figure 5.9a and b, respec-
tively, reveal another interesting feature with respect to the CDW. Although the
satellite reflections at ±0.846c∗ are fairly strong, there is some streaking which
157
Figure 5.10: a) Proposed charge ordering for the vanadium triangular
ladder of mixed spin states. b) Proposed orbital ordering.
occur in the h− and k−directions. These arise from a finite amount of disorder
between neighboring CDWs in the hollandite’s tunnels. Indeed, Carter and With-
ers found that quenching titanate hollandites can lead to complete disorder of the
CDWs and the reflections become lines in the electron diffraction patterns.190 Their
XRD powder patterns nicely demonstrate that the satellite reflections are much
stronger when the hollandites are slow cooled. Likewise in our case, we found that
the polycrystalline samples of BixV8O16 to display some evidence for the CDW in
the synchrotron data, but they are particularly weak due to the disorder of the
CDW. Interestingly, the satellite of the (002) reflection seemed the broadest on ac-
count of the disorder along the c-direction.
158
5.4.2 Orbital order
Next, we address orbital ordering. Due to the octahedral coordination of the
vanadium cations, we anticipate the normal ’3 below 2’ crystal field splitting of the
d-orbitals. Since the V cations reside on the 8h Wyckoff position in space group
I4/m (Table 5.1), the local symmetry is actually lower than Oh and only contains a
mirror plane with four unique V–O bond distances ranging from 1.844 Å to 2.021
Å at 200 K. Therefore, the crystal field can only be approximated as octahedral.
Within this scheme, the eg orbitals are aligned along the V–O bonds while the t2g
orbitals are involved in coupling the V cations to one another in the triangular
ladder. In the charge ordered state, all the V cations should be orbitally active since
they are in either the t12g or t
2
2g state.
In the present system, an illustration of the orientation of the t2g orbitals
within the hollandite-type structure is displayed in Figure 5.10b. The dxy orbital is
oriented such that one pair of lobes is parallel to the tunnel direction. The four-fold
crystal symmetry renders the dxz and dyz orbitals equivalent, pointing along the
triangular ladder rung directions.
Orbital ordering is supported by the first-order structural distortion observed
in the NPD data, where a large phase coexistence was observed between the insu-
lating and metallic phases. Coupling of dimers along the tunnel direction would
cause an increase in overlap between paired dxy orbitals, further lifting the three-
fold degeneracy of the t2g orbitals. With an approximate ratio of five V 3+ to three
V 4+ cations, the majority of dimers would then be either V 3+–V 3+ pairs, or V 3+–
159
V 4+ pairs.
The theoretical work on BixV8O16 of Shibata et al suggests that orbital or-
dering is required to observe the MIT.195 By deriving a spin-orbit Hamiltonian by
second-order perturbation theory, Shibata et al. find a variety of orbitally ordered
phases and suggests that each one contains a different ground spin state. Inter-
estingly, one of these phases contains a majority of spin-singlets interspersed with
unpaired S = 12 minority states. This could explain the results from the solid state
NMR studies of BixV8O16 by Waki et al, who propose a charge ordered state along
with orbital ordering, leading to spin singlet formation and finally to long-range
antiferromagnetic ordering near 20 K.188,196 We partially agree with some of the
conclusions of Waki et al in that spin singlet formation comprises the majority of
the states in Bi1.7V8O16. Our NPD data, however, conclusively demonstrate no such
long-range antiferromagnetic phase sets in below 20 K.
The recent computational studies from Kim et al suggest that spin, orbital,
and lattice degrees of freedom are all coupled in the related K2V8O16 hollandite.182
The orbital ordering manifests in a Jahn-Teller type fashion, but Kim et al suggest
that Mott-type physics rather than Peierls-type mechanism predominates with the
electronic bands from the dxy orbital playing the decisive role.
Orbital physics seems to be quite general in hollandites, and goes beyond the
vanadates. In the structurally related system K2Cr8O16, long-range ferromagnetic
ordering sets in below 180 K.54 For this system, the interaction between the charge
and orbitally ordered Cr4+ and Cr3+ cations seems key to the formation of such an
usual ground state–a ferromagnetic insulator. The theoretical work by Mahadevan
160
et al.55 showed that ordering of the t2g orbitals, which are the most significant for
the M–M interactions in hollandites, would lead to ferromagnetic coupling between
the cations.
5.4.3 Spin order
Finally, we address spin ordering in Bi1.7V8O16. As shown in Figure 5.10b,
we label the magnetic exchange along the ladder direction as J1 and that along the
rungs as J2. It appears that the majority of the magnetic exchange interactions are
antiferromagnetic in nature as evidenced by the magnetization data in the high-T
phase. Above the MIT the magnetization data (Figure 5.5) reveals a broad feature
that appears similar to the Bonner-Fisher susceptibility for Heisenberg chains with
a negative J.197 For Bi1.7V8O16, the chains consists of predominately S = 1 cations,
and therefore the Bonner-Fisher relation becomes kTmax/|J| = 2.70 where k is the
Boltzmann constant and Tmax is where the susceptibility is at a maximum. For
the FC data (Figure 5.5) Tmax is approximately 275 K. This value is quite high,
and for one-dimensional materials this causes the susceptibility to broaden out in
temperature.120 Based on this relation, we can estimate the exchange interaction
J1 to be close to 8.31 meV.
At the MIT, the system appears to go from a quasi-1D chain of antiferromag-
netically coupled V cations to a dimerization of V–V pairs. Therefore, the system
goes from an extended solid of N centers to one that could be modeled as akin to
N/2 molecules where N is Avogadro’s number. Although the majority of Js remain
161
negative, it does appear that some of the V–V ‘molecules’ are ferromagnetically cou-
pled.
Consider the Hamiltonian for a system consisting of dimers with the inter-
atomic axis being the z-axis as given by
H = gµBS′zHz−2JS1 ·S2 (5.1)
where S1 and S2 would correspond to the spins of the two nearest neighbors
in the V–V dimers, S′z is the operator for the z-component of the total spin of the
dimer, Hz is the external field applied along the z-axis, and g the Landé factor.
For two interacting spin-12 electrons, Eq. 5.1 leads to the so-called Bleaney-Bowers
equation for susceptibility given by
χ= 2N g
2µ2B
kT(3+ e∆/kT) (5.2)
where ∆ is the energy gap between the two quantum numbers that describe
the spin states of the dimer.198 For a positive value for J in Eq. 5.1, the ground
state of the system would be S = 1 (i.e. triplet state) and the excited state S = 0 (i.e.
singlet state), with an energy gap of ∆ between the states. While Eq. 5.2 does not
necessarily apply to our dimers of V3+ and V4 cations since they are of mixed spin
states, the expression is informative in qualitatively describing the magnetization
data below the MIT. For ferromagnetic coupling between the vanadium cations, a
negative value of ∆ (positive J) is found and therefore the susceptibility of Eq. 5.2 is
seen to diverge at lower temperatures. For antiferromagnetic coupling, this suscep-
162
Figure 5.11: a) The Bleaney-Bowers equation for antiferromagnetic ex-
change between dimers.
tibility decreases to zero as 0 K is approached. Unlike all other vanadates undergo-
ing an MIT, Bi1.7V8O16 clearly shows the former. Figures 5.11 and 5.12 compare the
Bleaney-Bowers model for ferromagnetic and antiferromagnetic coupling between
two S = 12 cations. While this model cannot be used to fit the magnetic susceptibil-
ity data, Figure 5.12 does allow the reader to qualitatively compare the two models
against the low temperature susceptibility of Bi1.7V8O16 below the MIT.
In the case of Bi1.7V8O16, multiple steps are clearly seen in the ZFC and FC
curves, below the MIT indicating the formation of ferromagnetically coupled dimers
(Figure 5.5a). The hysteresis in the ZFC/FC curves should also rule out the possi-
bility that these are just isolated ions producing a Curie tail. Furthermore, the
magnetotransport data clearly indicate that the magnetic field controls the extent
163
Figure 5.12: a) The Bleaney-Bowers equation for ferromagnetic ex-
change between dimers.
of the MIT and therefore enters into the coupling energy between the V–V centers
(Eq. 5.1).
Even though both antiferromagnetic and ferromagnetic coupling is observed
between the V–V dimers, the NPD data clearly indicate that no long-range ferro-
magnetic or antiferromagnetic ordering occurs. This suggests that the nature of
magnetic interactions are either 1D or nearly 1D so that no magnetic Bragg reflec-
tions of long-range ordering ever occur. The triangular nature of the ladders likely
also contribute to a frustration that disallows long-range ordering.
164
5.5 Conclusions
We have described a metal-insulator transition for a quasi-one dimensional
system containing a mix of S = 1 and S = 12 vanadium cations. Unlike all other
known vanadates, the magnetic susceptibility of Bi1.7V8O16 diverges below TMI , al-
though no long-range magnetic ordering is observed from neutron diffraction. The
magnetotransport measurements reveal that the transition temperature is sup-
pressed upon application of an external magnetic field, and this behavior is both
hysteretic and anisotropic. A first-order structural transition is revealed by the co-
existence of two tetragonal phases near the MIT indicative of dimerization between
the mixed-spin cations. The MIT is thus best understood in terms of the interplay
between the charge and orbital ordering of the V cations along the triangular ladder
directions.
165
Chapter 6: Mixed-metal hollandites
6.1 Overview
The pure M hollandites demonstrate a range of properties; K2V8O16 under-
goes a metal-to-insulator transition.69 K2Cr8O16 is a ferromagnetic insulator below
95 K.54 K1.5Ti8O16 is paramagnetic,75 and consistent with previous reports, we
have observed a spin-glassy, antiferromagnetic response in the pure Mn hollan-
dites.41,139
Throughout the work presented in this thesis, connections between the com-
position and the atomic structure of a material have been made in interpreting
the physical behavior of hollandite materials. As seen in the differences between
the Ba1.2Mn8O16 and Ba1.2CoMn7O16 in Chapter 3, the magnetic and electronic
properties of materials can be significantly altered by relatively small changes in
composition. We therefore have good reason to believe that investigations of the
mixed-metal hollandite family will continue to reveal exciting electronic and mag-
netic properties for potential use in advanced material applications. By synthesiz-
ing the solid solutions of materials in between these compositions, we aim to map
out the phase diagram to guide future optimizations for material applications.
Many other groups have studied mixed-metal hollandites,48,70,74,75,79,81–95,156
166
but to date, no comprehensive studies exist where an entire solid solution was de-
scribed. The study that best attempts a solid solution was performed by Ishige et
al on the K2V8−xTixO16 material for x = 0, 0.3, and 4.0.60 Their study was focused
on explaining the mechanism driving the MIT in K2V8O16, which they attribute to
V-V dimerization based on changes observed in the V 2p X-ray absorption spectra.
Developing a systematic understanding of how incremental changes in com-
position affect the physical properties will allow for future hollandite materials to
be tuned and developed for desired properties. Within this chapter, preliminary
results in studying mixed-metal solid solutions of different hollandite compositions
are detailed. Two solid solutions, Bi1.7CrxV8−xO16 and K1.7MnxTi8−xO16, are the
focus of this chapter, while additional experimental work on other mixed-metal hol-
landite materials is detailed in Appendix A.
6.1.1 KyMnxTi8−xO16
Ti4+ is d0, and therefore non-magnetic. The KTi8O16 hollandite has been well-
studied,75,76 as has the KMn8O16 hollandite (Chapter 4). By incrementally chang-
ing the composition between these two end-members, an attempt at understanding
of the development of the complex frustrated magnetic behavior of KMn8O16 was
undertaken.
Kijima et al studied the effects of extracting K+ from the tunnels of KxMn2Ti6O16
hollandite, but they did not vary the ratio of Mn to Ti, primarily focusing on the elec-
trochemical effects and the possibility of replacing K+ with Li+.92 Using the I4/m
167
space group, they observed the Mn valency transition from trivalent to tetravalent
upon removal of K+.
Our research group has published initial findings on doping the KyMxTi8−xO16
for M = Sc-Ni and x= y=∼ 1.5.75 Magnetization versus temperature measurements
indicated that all phases were Curie paramagnets. The µe f f = 4.99 µB and θCW =
-40.04 extracted for the Mn-substituted sample were consistent with the d-electron
count given by combined X-ray diffraction and elemental analysis techniques.75 Us-
ing this material as a starting point, we sought to map out the KyMnxTi8−xO16 solid
solution.
6.1.1.1 Synthesis & experimental details
Samples were synthesized through a salt flux method to produce polycrys-
talline hollandite materials , K1.7MnxTi8−xO16. Starting reagents included KCl
(99.2%, J.T. Baker), Mn2O3 (99%, Sigma-Aldrich), Co3O4 (74%-gravimetric Co, Sigma-
Aldrich), Ba(NO3)2 (99.999%, Sigma-Aldrich). Reagents were used without further
purification.
A powder mixture of TiO2, Mn2O3, and KCl was ground with an agate mortar
and pestle. The reagent mixtures were then heated in covered alumina crucibles
under ambient atmosphere. Heating was maintained at a rate of 100 K/h up to
1123 K, soaked for 72 h, then cooled to room temperature at 100 K/h. The obtained
samples were washed in DI water to dissolve KCl, then dried at 373 K for one hour.
Room temperature powder X-ray diffraction (XRD) data was collected on a
168
Table 6.1: Room temperature lattice parameters for KyMnxTi8−xO16 from powder
X-ray diffraction refinements. Standard uncertainties are given in parentheses.
Sample a (Å) c (Å) Rwp (%)
KyMnTi7O16 10.161(3) 2.958(7) 8.519
KyMn2Ti6O16 10.163(2) 2.956(6) 9.044
KyMn3Ti5O16 10.144(3) 2.958(6) 6.474
Bruker D8 X-ray diffractometer with Cu Kα radiation, λ = 1.5418 Å, (step size=0.013◦,
with 2θ range from 8◦-140◦). Constant wavelength neutron powder diffraction data
was collected on the high resolution BT-1 instrument at the National Institute of
Standards and Technology (NIST) Center for Neutron Research (NCNR) with a λ
= 2.078 Å (Ge311 monochromator) for various temperatures between 10 K and 300
K. All powder diffraction data was analyzed using the TOPAS software.115
Field-cooled (FC) and zero-field-cooled (ZFC) magnetization measurements
were taken from 2 K - 300 K with a Quantum Design magnetic property measure-
ment system (MPMS) on a polycrystalline sample. Measurements were in direct
current mode, with an applied magnetic field of 0.01 T (100 Oe). Magnetization
versus field up to 7 T were also taken on the MPMS with a polycrystalline sample
at 5 K.
169
Figure 6.1: X-ray diffraction for KyMnxTi8−xO16.
Figure 6.2: Magnetic susceptibility of K1.7MnxTi8−xO16.
170
Table 6.2: Curie-Weiss parameters extracted from the high temperature paramag-
netic regions of KyMnxTi8−xO16 1/χ plots.
Sample TN (K) θ (K) C (cm3 K mol−1 µe f f (µB)
KyMnTi7O16 ∼45 -40.3 4.53 6.05
KyMn2Ti6O16 ∼47 -41.5 2.27 4.28
KyMn3Ti5O16 ∼48 -66.6 1.89 3.90
6.1.1.2 Results
The observed magnetic susceptibility of K1.7MnxTi8−xO16 showed a transi-
tion occuring at ∼ 47 K. A representative susceptibility of the K1.7Mn3Ti5O16 com-
pound is shown in Figure 6.3. The FC and ZFC measurements, particularly of the
K1.7Mn3Ti5O16 sample, are very similar to the reported magnetization of BaMn3Ti4O14.25
by Liu et al.87
Calculated effective moments and Curie constants for the different composi-
tions are presented in Table 6.2. The observed values for µe f f do not agree well
with the values expected for the targeted compositions, assuming that Ti is present
in an oxidation state of 4+.
The magnetization versus field measurements of K1.7Mn3Ti5O16 (shown in
Figure 6.3) also closely resemble the reported hysteresis for BaMn3Ti4O14.25 by Liu
et al.87
Measuring the K1.7Mn3Ti5O16 at BT-1 revealed one significant magnetic peak
171
Figure 6.3: Magnetization vs. Field Measurements of K1.7Mn3Ti5O16.
at low temperature, along with some minor nuclear reflections that were not ob-
served in the XRD data. Rietveld refinement of the BT-1 data revealed the presence
of a small amount of hausmannite, Mn3O4, which undergoes a magnetic transition
at ∼ 42 K. We thus concluded that the magnetic behavior we had observed was
likely due to the Mn3O4 impurity, not the KyMnxTi8−xO16 samples.
6.1.1.3 Discussion
Mn3O4 is a magnetically disruptive impurity, easily formed in the solid state
techniques utilized herein. Future efforts to pursue the KyMnxTi8−xO16 solid so-
lution should include elemental analysis techniques such as ICP-AES to verify
the incorporation of both transition metal cations into the material. Microscopy
172
techniques might also give an indication as to whether or not different phases are
present on the surface of the bulk material, as the lab XRD data we utilized did not
reveal the existence of the impurity phase.
6.1.2 Bi1.7CrxV8−xO16
For a long time, researchers have been interested in antiferromagnetic mate-
rials with S = 12 ions on a frustrated lattice due to numerous theoretical predictions
that such systems should exhibit spin liquid or even more exotic behavior due in
part to quantum spin fluctuations. Systems with integer spins, (S = 1, 2, 3) are
also of particular interest, as Haldane conjectured the differences in exchange sym-
metry between half-integer and integer spin systems to have a dramatic effect on
the nature of excitations in the material.12 These so-called ‘Haldane chains’ are an
extension of the one dimensional quantum Heisenberg spin model.
In spite of intensive search efforts, the number of materials featuring the 1D
or pseudo-1D nature of combined with purely integer spin states is small. If one
wanted to design a 1D (or quasi-1D) system with a magnetically-driven MIT, a sys-
tem of predominately S = 1 species mixed with some nearest neighbor S = 12 units
might suffice, assuming that the orbital degrees of freedom allow ferromagnetic
coupling between the two species. In the K2Cr8O16 hollandite, one of the few well-
known ferromagnetic insulators, the average charge of chromium is Cr3.75. This
leads to a mixture of S = 1 and S = 32 cations in the chains where S = 1 species are
the majority. The quasi-1D nature of the transition metal network in hollandites,
173
and the compositional tunability, allow the researcher to target an S=1 framework.
Understanding the magnetic behavior of the Bi1.7V8O16 hollandite, and related
variations may thereby provide a potential material for exploring the properties
of Haldane chains.
6.1.2.1 Synthesis & experimental details
Polycrystalline samples of Bi1.7CrxV8−xO16 hollandites were produced by grind-
ing together stoichiometric ratios of V2O3 (99.7%, Alfa Aesar), V2O5 (98+%, Sigma
Aldrich), and Bi2O3 (99%, Fisher). Reagents were used without further purifica-
tion. After grinding together, the powdered mixture was heated to 1173 K at a rate
of three degrees per minute, in an evacuated flame-sealed quartz glass ampule.
Upon reaching the target temperature the sample soaked for 72 hours, followed by
furnace cooling.183
Room temperature powder X-ray diffraction (XRD) data was collected on a
Bruker D8 X-ray diffractometer with Cu Kα radiation, λ = 1.5418 Å, (step size=0.013◦,
with 2θ range from 8◦-140◦). Powder diffraction data was analyzed using the TOPAS
software.115
Field-cooled (FC) and zero-field-cooled (ZFC) magnetization measurements
were taken from 2 K - 300 K with a Quantum Design magnetic property measure-
ment system (MPMS) on a polycrystalline sample. Measurements were in direct
current mode, with an applied magnetic field of 0.01 T (100 Oe).
174
6.1.2.2 Results
Rietveld refinements were carried out to extract structural and lattice param-
eters from the data (Figure 6.4). These results are presented in Table 6.3.
175
Bi1.7CrxV8-xO16
Figure 6.4: Rietveld refinement of room temperature XRD data (UMD) for Bi1.7CrxV8−xO16. The green line indicates the
difference between the observed data (colored lines) and the calculated model (black dashes).
176
Table 6.3: Room temperature lattice parameters for BiyCrxV8−xO16 from powder
X-ray diffraction refinements. Standard uncertainties are given in parentheses.
Sample a (Å) c (Å) Bi occupancy Rwp (%)
BiyCr0.5V7.5O16 10.161(2) 2.958(2) 0.402 8.519
BiyCrV7O16 10.163(2) 2.956(2) 0.416 9.044
BiyCr1.5V6.5O16 10.144(3) 2.958(2) 0.413 6.474
BiyCr2V6O16 10.144(1) 2.958(2) 0.418 6.474
Rietveld treatment of lab XRD data showed phase pure BiyCrxV8−xO16, for x
= 0.5, 1, 1.5, and 2. Lattice parameters extracted from the Rietveld technique are
presented in Table 6.3. The refined Bi3+ occupancy leads to an average bismuth sto-
ichiometry of 1.65. A slight decrease in the a parameter is observed upon increasing
x, without a noticeable accompanying trend in the c parameter.
Elemental analysis was performed on the samples of BiyCrxV8−xO16 utiliz-
ing inductively coupled plasma atomic emission spectroscopy (ICP-AES). The re-
sulting compositions confirmed the presence of Cr within the material, though the
typical amount was approximately 0.2 molar equivalents lower than the targeted
stoichiometry.
The observed magnetic susceptibility of BiyCrxV8−xO16, was very consistent
across the different compositions. Field-cooled (FC) and zero field cooled measure-
ments (ZFC) trace a traditional Curie-Weiss paramagnetic response until T < ∼ 10
K, at which point the magnetization of the ZFC curve decreases sharply, while the
177
Table 6.4: Curie-Weiss parameters extracted from the high temperature paramag-
netic regions of BiyCrxV8−xO16 1/χ plots.
Sample TN (K) θCW (K) C (cm3 K mol−1 µe f f (µB)
BiyCr0.5V7.5O16 ∼9 848 4.53 6.05
BiyCrV7O16 ∼9 360 2.27 4.28
BiyCr1.5V6.5O16 ∼9 279 1.89 3.90
BiyCr2V6O16 ∼9 176 1.89 3.90
FC continues to increase. Calculated effective moments and Curie constants are
presented in Table 6.4, and trends across the different compositions are shown in
Figure 6.5. A decrease in both the θCW andµe f f values are observed upon increasing
the amount of Cr.
6.1.2.3 Discussion
Both the X-ray data and the ICP-AES results confirm the presence of Cr in
the samples synthesized herein. The profile of the magnetic responses of the sam-
ples did not change substantially across the compositions, though the decrease in
θCW shows that the strength of magnetic interactions is decreasing. Though very
preliminary, these materials warrant further investigation.
X-ray photoelectron spectroscopy would determine the oxidation states of the
V and Cr cations in the framework, giving an idea of whether or not the materials
are approaching a true S = 1 state with the addition of Cr. Neutron diffraction
178
Figure 6.5: Trends in θCW , C, and µe f f for BiyCrxV8−xO16 as a function
of molar Cr content. Error bars are smaller than plot symbols used.
179
measurements will also provide insight, both into the structure of the materials, as
well as regarding the magnetic behavior.
180
Chapter 7: Overall conclusions & future work
7.1 Conclusions
Throughout the work presented in this thesis, connections between the com-
position and the atomic structure of a material have been made in interpreting the
physical behavior of hollandite materials.
Several different hollandite materials have been successfully synthesized and
characterized to varying extents. While much of the previous work done on hollan-
dites concentrates on the possibility of using these materials as electrode materials
in batteries, significantly less attention has been expended in understanding the
bulk magnetic and electronic properties of these materials. This limitation has
likely stemmed from the synthetic difficulties in obtaining bulk, highly crystalline
samples. While this limitation is still very present, work done in the Rodriguez
group, presented herein as well as in titanium-based hollandites, suggests the use
of salt flux techniques as a very promising avenue for crystal growth of hollandites
in the future.75
Crystal structures have been resolved by X-ray and neutron powder diffrac-
tion, as well as single crystal X-ray studies when possible. Magnetic behavior has
been evaluated using both a SQUID magnetometer and neutron diffraction.
181
The intense magnetic frustration observed in Ba1.14Mn8O16 was relieved with
the inclusion of Co2+ cations into the framework of Ba1.10CoyMn8−yO16. Magneti-
zation and resistivity measurements show that the cobalt-substituted hollandite
belongs to the rare class of ferrimagnetic insulators. Neutron diffraction measure-
ments made it possible for us to describe the first magnetic structure solution of
BaxMn8O16, consisting of a complex antiferromagnet with a large magnetic unit
cell.
Contrary to reports in the literature, K1.35Mn8O16 does not appear to exhibit
tetragonal symmetry as seen by the poor fits obtained by Rietveld refinement of
both neutron and X-ray data. While two plausible cells are discussed here, the
quality of the data collected did not allow for a full solution of either the atomic or
magnetic structures.
Bi1.7V8O16 was observed to undergo a metal-insulator transition upon cool-
ing, but unlike all other known vanadates, the magnetic susceptibility of Bi1.7V8O16
diverges below TMI , though no long-range magnetic ordering is observed from neu-
tron diffraction. We also observed revealed both anisotropic and hysteretic behavior
accompanying the field-dependence of the MIT.
Finally, investigations into mixed-metal hollandites are just beginning. The
properties of the Bi1.7CrxV8−xO16 series, where x≤3, were initiated in hopes of driv-
ing the material into a purely S = 1 state and observing Haldane-like behavior. The
effects of systematically changing the composition between two known end mem-
bers to synthesize K1.7MnxTi8−xO16 materials was frustrated by the existence of
an Mn3O4 impurity phase. Future investigations of this material will need to find
182
synthetic routes that avoid this impurity, or ways of separating the Mn3O4 from the
desired material post-synthetically.
It can be seen that the observed properties vary significantly with changes
in hollandite composition. Magnetic behavior is affected by orbital ordering and
charge ordering. These results suggest the possibility of rich electrical and mag-
netic phase diagrams for OMS materials. This work contributes to a greater under-
standing of the correlations between structure and properties, particularly in both
hollandite materials and geometrically frustrated systems, allowing for the design
of materials exhibiting certain physical phenomena.
7.2 Future work
Future TOF neutron experiments of Ba1.2Mn8O16 and its Co-substituted deriva-
tive, measured at temperatures below the magnetic ordering transitions, will be
helpful to search for possible orbital ordering from Jahn-Teller distortions. We
would also like to run the same sample on DCS to obtain an overview of the ex-
citations present in this sample. Based off of theoretical calculations performed by
Seriani et al, we predicted that the addition of Co into the Ba1.2Mn8O16 structure
forces the moments from a Heisenberg-like system into a more restricted Ising-
like configuration. DCS will allow us to focus on low Q values, while selecting the
wavelength with the highest energy resolution. We are interested to see if more
interesting dynamics are at play in the hollandites.
Further good quality diffraction data needs to be collected for the K1.6Mn8O16
183
phase, preferably using facilities such as a synchrotron radiation source. This
would allow us to fully elucidate the structure and may further our attempts at
resolving the magnetic structure allowing the physical properties of the material
to be fully characterized. We would also like to measure K1.4Mn8O16 to determine
a) the spin coupling of these systems and b) elucidate the ordering and behavior of
any spin waves present in these hollandites.
Measuring Bi1.7V8O16 on BT-1 as a function of magnetic field strength would
allow us to investigate our hypothesis that the ferromagnetic coupling drives the
MIT. The formation of such dimers is manifest by tetragonal-to-tetragonal struc-
tural transition. As the neutron scattering cross section for vanadium is negligible,
low-temperature synchrotron X-ray diffraction experiments would be very benefi-
cial in locating the vanadium cations through the structural distortion.
There are numerous routes of inquiry to pursue on our nascent studies of the
mixed metal solid solutions. Performing X-ray photoelectron spectroscopy on he
Bi1.7CrxV8−xO16 hollandite materials would determine the oxidation states of the
V and Cr cations in the framework, giving an idea of whether or not the materials
are approaching a true S = 1 state. Neutron diffraction measurements at will also
provide insight, both into the structure of the materials, as well as regarding the
magnetic behavior.
Of course, growth of single crystals would allow us to expand our studies for
all of the materials described herein. Efforts to merely tune the salt flux and solid
state techniques utilized herein may not be sufficient, and floating-zone furnaces or
hydrothermal furnaces may broaden the scope of our synthetic capabilities.
184
Appendix A: Further experiments on mixed metal hollandites
All samples were synthesized by salt flux methods. Stoichiometric amounts
of starting materials (see below) were ground using an agate mortar and pestle.
They were then transferred to alumina crucibles and placed in a furnace at 850◦CC
for 72 hours ramping at 100◦C/h. Subsequent washing with deionized water was
necessary to remove remaining KCl, which was used as a mineralizer. The samples
were then dried over a hot plate at 100◦C for one hour.
A.1 Ba1.2FeMn7O16
We aimed for an Fe content of 1. The following table summarizes the reagents
used in different trials, specific conditions and refined PXRD results.
185
Table A.1: Experimental details for Ba1.2FeMn7O16 hollandite
Sample No. Starting materials Additional PXRD Results
AML085 Ba(NO3)2 + Mn2O3 + Fe2O3 + KCl under O2 flow 98% hollandite + 2% Mn2O3
NSL035 Ba(NO3)2 + Mn2O3 + Fe(NO3)3 ·
9H2O + KCl
pellets calcined at 650 ◦ 96% hollandite + 4% Mn2O3 + BaCO3
NSL041 NSL035 + Ba(NO3)2 + Fe2O3 + KCl - 98% hollandite + 2% Mn2O3 + BaCO3
NSL039A Ba(NO3)2 + Mn2O3 + FeO + KCl under O2 flow 97% hollandite + 4% Mn2O3 + BaCO3
NSL038 Ba(NO3)2 + Mn2O3 + FeO + KCl - 92% hollandite + 3% Mn2O3 + 5% BaCO3
NSL043B Ba(NO3)2 + Mn2O3 + Fe2O3 + KCl - 88% hollandite + 9% Mn2O3 + 3% BaCO3
NSL047A Ba(NO3)2 + Mn2O3 + FeO + KCl +
KNO3
- 71% hollandite + 4% BaMnO3 + 16%
Ba6.3Mn24O48 + 9% KCl
NSL052 Ba(NO3)2 + Mn(NO3)3 · 4H2O +
Fe2O3 + KCl
pellets calcined at 650 ◦ 96% hollandite + 3% BaCO3 + 12%
BaFe12O19
NSL053B NSL052 stirred in HCl 99% hollandite + 1% BaFe12O19
186
We experimented with the following variables: different sources of iron and
manganese, for oxidation states of +2 or +3, the presence of an oxidizing atmosphere
(O2 flow) to favor oxidation, and the addition of a second mineralizer (KNO3), which
also acts as an oxidizing agent. Since the most common impurity was one of the
starting materials, Mn2O3, we tried refiring the sample with more Ba(NO3)2, KCl
and iron oxide. Although the amount of Mn2O3 was reduced, it was not completely
removed. The sample NSL 053 B was almost phase pure, although the intensity of
the peaks was slightly smaller compared to other samples’. The refined pattern is
shown below.
The peak at around 2θ ∼ 24◦C corresponds to the BaCO3 impurity. This phase
was usually included in the refinement, however, sometimes the software identified
it as a background, in those cases, we left the phase out of the refinement, but
acknowledged its presence.
A.2 Ba1.2NixMn8−xO16
We aimed for a Ni content between 0.5 and 1. The following table summarizes
the reagents used in different trials, specific conditions and refined PXRD results.
187
Table A.2: Experimental details for Ba1.2NixMn8−xO16 hollandite
x Sample No. Starting materials Additional PXRD Results
1 AML122 Ba(NO3)2 + Mn2O3 + NiO + KCl under O2 flow 94% hollandite + 4% Mn2O3 + 2% BaCO3
1 AML123 Ba(NO3)2 + Mn2O3 + Ni(NO3)2 +
KCl
calcined, refired in KCl 91% hollandite + 6% NiO + 3% BaCO3
0.5 NSL024A Ba(NO3)2 + Mn2O3 + NiO + KCl - 97% hollandite + 2% NiO + 1% BaCO3
0.5 NSL030A NSL024A + KCl - 89% hollandite + 7% NiMn2O4 + 4%
BaCO3
0.5 NSL031AA NSL024A stirred in HCl 98% hollandite + 2% NiO
0.75 NSL036A Ba(NO3)2 + Mn2O3 + NiO + KCl - 94% hollandite + 3% NiO + 3% BaCO3
0.75 NSL045B NSL036A + Ba(NO3)2 + Mn2O3 +
KCl
- 88% hollandite + 9% NiMn2O4 + 3%
BaCO3
1 NSL024B Ba(NO3)2 + Mn2O3 + NiO + KCl - 91% hollandite + 6% NiO + 3% BaCO3
1 NSL031BA NSL024B stirred in HCl 93% hollandite + 7% NiO
188
In this case we tried to obtain a phase pure hollandite by: varying the nickel
source, (which in this case did not change its oxidation state), introducing an oxi-
dizing atmosphere and refiring the samples to make the leftover starting materials
react. In addition, our target stoichiometries varied in Ni / Mn content, we observed
that lower amounts of Ni integrated better in the hollandite structure. Although it
contained a NiO impurity, the sample NSL 031AA was our best trial. The refined
pattern is shown below.
Field cooled and Zero Field cooled magnetic susceptibility measurements were
carried out on this sample using a SQUID magnetometer. These are shown below.
A.3 Ba1.2CrxMn8−xO16
We aimed for a Cr content between 0.25 and 1. Table A.3 summarizes the
reagents used in different trials, specific conditions and refined PXRD results.
We did not consider different chromium sources for this set of experiments.
Instead, we tried different conditions in the furnace: reducing and oxidizing at-
mospheres as well as different target temperatures. As seen in the PXRD re-
sults column, the percentage of hollandite in our samples was not great. Indeed,
when washing these samples with DI water, they liquid often turned green, in-
dicating that the chromium was not being successfully inserted in the hollandite
structure. Same as with the Ni samples, we obtained better results at lower Cr
content. Though it contained remaining starting materials and barium carbonate,
AML127B was our best sample.
189
Table A.3: Experimental details for Ba1.2CrxMn8−xO16 hollandite
x Sample No. Starting materials Additional PXRD Results
NSL005 Ba(NO3)2 + Mn2O3 + Cr2O3 + KCl - 78% hollandite + 14% Mn2O3 + 8%
BaCrO4
1 NSL008A Ba(NO3)2 + Mn2O3 + Cr2O3 + KCl - 78% hollandite + 14% Mn2O3 + 8%
BaCrO4
1 NSL008B Ba(NO3)2 + Mn2O3 + MnO2 +
Cr2O3 + KCl
- 17% hollandite + 50% Mn2O3 + 33%
BaCrO4
1 NSL013A Ba(NO3)2 + Mn2O3 + Cr2O3 + KCl 950◦ instead 49% hollandite + 44% Mn3O4 + 6%
BaCrO4
1 NSL013B Ba(NO3)2 + Mn2O3 + Cr2O3 + KCl 750◦ instead 40% hollandite + 50% Mn2O3 + 10%
BaCrO4
1 NSL015 Ba(NO3)2 + Mn2O3 + Cr2O3 + KCl under N2 flow no hollandite – 93% Mn3O4 + 7% BaCrO4
0.25 AML127B Ba(NO3)2 + Mn2O3 + Cr2O3 + KCl - 96% hollandite + 4% Mn3O4 + BaCO3
0.5 NSL020 Ba(NO3)2 + Mn2O3 + Cr2O3 + KCl - 78% hollandite + 13% Mn2O3 + 9%
BaCrO4
0.75 AML127D Ba(NO3)2 + Mn2O3 + Cr2O3 + KCl - 74% hollandite + 2% Mn2O3 + 5% BaCrO4
190
A.4 KyVxMn8−xO16
Samples of KyVxMn8−xO16 were synthesized by grinding Mn2O3 with V2O3
in a mixture of KNO3 and KCl (1:1 molar ratio of KCl to KNO3), with at least an
eight-fold molar excess of the salt flux mixture. The material was heated at 180
K/hr up to 973 K, soaked for 24 h in ambient atmosphere, then cooled at 180 K/hr.
We attempted several compositions for x = 0 - 4. Figure A.1 displays raw PXRD
results for samples with x = 0, 1, and 4.
PXRD measurements appeared reasonably clean for samples up to x = 4.
However, XPS measurements did not show any vanadium in the surface compo-
sition, suggesting that the V cations volatilize during the heating procedure. We
did not consider different vanadium sources for this set of experiments, as our ini-
tial XRD data appeared to be phase pure. Future work on these materials may yet
yield interesting results.
A.5 Conclusions
Our goal was to synthesize mixed metal hollandites with the formula A1.2Mn8−xMxO16
where M = Fe, Ni, Cr or V and A = Ba or K. We changed our initial conditions
and reagents in order to improve the methodology. This included different furnace
temperatures, the presence of oxidizing or reducing atmospheres, intermediate cal-
cining steps. As mentioned, remaining starting materials were common impurities,
which we tried to remove by refiring the samples. Perhaps some starting materi-
191
Figure A.1: X-ray powder diffraction data (UMD) for K1.6VxMn8−xO16
at room temperature, for x = 0 (pink), 1 (green), and 4 (orange).
192
als were not fully reacting because we targeted a stoichiometry that was too opti-
mistic. No phase pure hollandite materials were obtained, although we were close
for Ba1.2Mn7FeO16. Future research can be done on these materials, such as using
different metal oxides as starting materials (e.g. Fe3O4) or nitrates (e.g. Fe(NO3)3),
varying the target and ramping temperatures and improving refiring conditions.
193
Appendix B: Extended experimental results and information
B.1 Bi1.7V8O16
Figure B.1: Bi1.7V8O16 single crystal wired for resistivity measurements.
194
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