ABSTRACT

Title of Dissertation: TUNING CRYSTALLOGRAPHIC AND MAGNETIC
SYMMETRY IN LITHIUM TRANSITION
METAL PHOSPHATES AND THIOPHOSPHATES

Timothy J. Diethrich
Doctor of Philosophy, 2022

Dissertation Directed by: Professor Efrain E. Rodriguez
Department of Chemistry and Biochemistry

Ferroic ordering needs no introduction; ferromagnetic, ferroelectric, and ferroelastic mate-

rials have had a significant impact on the materials science community for many years. While

these three main types of ferroic ordering are well known, there is a fourth and final, lesser known

ferroic ordering known as ferrotoroidicity. A ferrotoroidic material undergoes a spontaneous,

physical alignment of toroidal moments under a critical temperature. This study is focused on

broadening our current understanding of ferrotoroidics by studying two families of materials:

LiMPO4, and Li2MP2S6, where M = Fe, Mn, and Co. While these two materials initially appear

to be similar in some regards, many differences can be observed as a deeper dive is taken into

their crystallography and magnetic structures.

For a toroidal moment to exist, a specific orientation of magnetic moments is required,

because of this, only certain magnetic point groups are allowed. For example, LiFePO4 has

an “allowed” magnetic point group of m’mm, while it’s delithiated counterpart FePO4 has a



“forbidden” magnetic point group of 222. This work has found that by using a new selective

oxidation technique, lithium concentration can be controlled in the Li1−xFexMn1−xPO4 solid

solution series. Neutron powder diffraction and representational analysis were used to find the

magnetic point groups of each member of this series. In the end, each structure was solved and

the largest transition temperature to date was reported for a potential ferrotoroidic material. The

magnetic exchange interactions can be used to describe the magnetic phase changes that occur

across the Li1−xFexMn1−xPO4 series.

The second group of materials in this study is the lithium transition metal thiophosphates

of the formula Li2MP2S6, where M = Fe, Co. The structure of Li2FeP2S6 has been previously

studied but no magnetic properties of this material have been reported. In addition, neither

the structural nor magnetic properties have been reported for the cobalt analog. Single crystal

XRD was used to confirm the previously reported crystal structure of Li2FeP2S6 and to find the

novel crystal structure of Li2CoP2S6; both crystallize in a trigonal P31m space group. While

isostructural in some regard, there are some crucial differences between these materials. The site

occupancies are different, resulting in non-trivial charge balances and a unique thiophosphate

distortion. Originally, these materials were chosen because their nuclear structure was predicted

to host long-range antiferromagnetic order and potentially ferrotoroidic order. Contrary to expectations,

magnetic susceptibility and field dependent measurements demonstrated paramagnetic behavior

for both the iron and the cobalt sample down to 2 K. This result was further confirmed by a lack

of magnetic reflections in the time-of-flight neutron powder diffraction data.

While the phosphates and the thiophosphates demonstrated very different structural and

magnetic results, they both remain relevant materials for not only ferrotoroidics, but also magneto-

electrics, spintronics, quantum materials, and much more.



TUNING CRYSTALLOGRAPHIC AND MAGNETIC SYMMETRY IN
LITHIUM TRANSITION METAL PHOSPHATES AND THIOPHOSPHATES

by

Timothy J. Diethrich

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

2022

Advisory Committee:
Professor Efrain E. Rodriguez , Chair/Advisor
Professor Jeffery Davis
Professor Andrei Vedernikov
Professor Mercedes Taylor
Professor Ichiro Takeuchi , Dean’s Representative



© Copyright by
Timothy J. Diethrich

2022



Foreword

Below is a list of the manuscripts that I have written or contributed to during my time at the

University of Maryland as a graduate student. Some of the manuscripts have yet to be officially

published, these are marked as under review, in submission, or in preparation.

T. J. Diethrich, S. Gnewuch, K. G. Dold, K. M. Taddei, and E. E. Rodriguez, “Tuning

Magnetic Symmetry and Properties in the Olivine Series Li1−xFexMn1−xPO4 through Selective

Delithiation”, Chem. Mater. 2022, 34, 11, 5039-5053. (invited issue honoring John B. Goodenough).

T. J. Diethrich, P. Y. Zavalij, S. Gnewuch, E. E. Rodriguez “Orbital Contribution to

Paramagnetism and Noninnocent Thiophosphate Anions in Layered Li2MP2S2 Where M = Fe

and Co”, Inorg. Chem. 2021, 60, 14, 10280–10290.

T. E. Shaw, T. J. Diethrich, B. L. Scott, T. M. Gilbert, A. P. Sattelberger, T. Jurca, “MoCl3(dme)

Revisited: Improved Synthesis, Characterization, and X ray and Electronic Structures”, Inorg.

Chem. 2021 60, 12218-12225.

T. Li, R. Jayathilake, L. Balisetty, Y. Zhang, B. Wilfong, T. J. Diethrich, E. E. Rodriguez,

“Crystal field-induced lattice expansion upon reversible oxygen uptake/release in YbMnxFe2xO4”,

Mater. Adv. 2021 3, 1087.

ii



T. E. Shaw, T. J. Diethrich, A. P. Sattelberger, “Synthesis, Characterization, X-ray and

Electronic Structures of Diethyl Ether and 1,2-Dimethoxyethane Adducts of Molybdenum(IV)

Chloride and Tungsten(IV) Chloride”, Dalton Trans. 2022.

N. Katz, T. J. Diethrich, E. E. Rodriguez, “3D Printed VSEPR Models: Bringing Comprehensive

and Free Molecular Model Kits to Classrooms through MolecularCraft”, J. Chem. Ed. 2022

(under review).

T. J. Diethrich, J. Tosado, S. Gnewuch, B. Wilfong, E. E. Rodriguez, “Spin flop and

magnetic phase diagram of potential ferrotoroidics LiFexMn1−xPO4”, Phys. Rev. B, (in preparation).

T. J. Diethrich, H. C. Mandujano, K. G. Dold, E. E. Rodriguez, ”Magnetic Properties

of the Li1−xFexCo1−xPO4 and LiyCoxMn1−xPO4 Solid Solution Series”, Inorg. Chem., (in

preparation).

H. C. Mandujano, T. J. Diethrich, T. Li, E. E. Rodriguez, ”Site occupancy effects on long

range magnetic ordering in Mg1−xCoxPS3 honeycomb lattice through metal site substitution”,

Inorg. Chem., (in preparation).

C. M. Wentz, E. H. R. Tsai, K. G. Yager, L. Gonzalez-Lopez, T. J. Diethrich, M. I. Al-

Sheikhly, L. R. Sita, ”Mesophase Engineering of Neutral and Radical Anion Perylene Bisimide-

Polyolefin Conjugates”, Nat. Chem., (in preparation).

J. Tosado, S. Gnewuch, T. J. Diethrich, N. Qureshi, C. Stock, E. E. Rodriguez, “Ferrotoroidic

order through spherical neutron polarimetry”, (in preparation).

iii



Dedication

To my brothers and sister, who have supported me every step of the way. Knowing when I

need a laugh and knowing when I need encouragement.

To my grandparents, for letting me live in your home the first three years of grad school.

For reminding me how to slow down and for always having a delicious home-cooked meal to

come home to.

To my son Zavian and the little one on the way, I cannot wait to share with you stories of

my graduate school experience and how it shaped me into the father I am today.

To my Dad, for being the primary example in my life of an excellent work ethic, the man I

look up to the most. Showing me what hard work looks like, yet at the same time telling me how

much more important family is.

To my Mom, for homeschooling me all the way through high school, spending countless

hours making sure I had every opportunity to pursue my goals. For all the love, support, texts,

calls, and conversations; pushing me to finish strong, do my best, and always encouraging me.

To my beautiful wife, my best friend, and my love, Beth. You made this possible. You

worked harder so that I could focus when I needed to focus, you know my signs and helped me

take necessary breaks, made sure I was mentally and physically healthy, and cared for me and

supported me with an un-wavering love. I am here because of you. I love you.

iv



Acknowledgments

I would first like to thank my advisor, Professor Efrain Rodriguez for constant support,

teaching, guidance, and mentorship throughout my graduate career. I have learned more than

I could have ever imagined in my five years at University of Maryland. I would also like to

thank my committee members for taking the time to review my work and give me advice as I

move forward: Professor Jeffery Davis, Professor Andrei Vedernikov, Professor Ichiro Takeuchi,

Professor Mercedes Taylor, and Professor Chunsheng Wang.

Secondly, I would like to thank my lab mates, the current and past members of the Rodriguez

group. Stephanie Gnewuch, Jacob Tosado, Matt Leonard, H. Cein Mandujano, Mario Lopez,

Brandon Wilfong, Tianyu Li, Huafei Zheng, Lahari Balisetty, Marcus Carter, Ryan Stadel, Stephanie

Hong, Akil Mondie, Austin Virtue, Rishvi Jayathilake, Justin Yu, and Xiuquan Zhou. Specifically

I would like to thank Stephanie Gnewuch for her mentorship and guidance, teaching me the

ways of solid state chemistry and shaping me into the researcher I am today. I am grateful for

the undergraduates who helped me with my research, Noah Katz, Noah Bender, and especially

Kaitlyn Dold who’s passion and dedication to success helped our project to completion in an

excellent Chemistry of Materials manuscript. I have made some great friends and had excellent

times with all of the Rodriguez group members, past and present.

I would like to thank Dr. Peter Zavalij for his mentorship as I was an instrument teaching

assistant in the X-ray Crystallographic Center. I have learned so much about diffraction and

v



benefited greatly from working with him. I would also like to thank Drs. Qiang Zhang, Shanta

Saha, Marya Anderson, Hui Wu, Nick Butch, Thomas Halloran, and especially Keith Taddei for

their collaboration and help with high end instrumentation; of which I would not have the results

presented in this manuscript. I would also like to thank some my collaborators, Al Sattelberger,

Thomas Shaw, and Charlotte Wentz.

This research would be nothing without funding. The funding for this work at the University

of Maryland came from the U.S. Department of Energy, Office of Science grant number DE-

SC0016434. I would like to acknowledge the support of Oak Ridge National Laboratory and

the National Institutes of Standards and Technology, U.S. Department of Commerce for making

their facilities open for researchers like myself to conduct neutron diffraction experiments. I also

acknowledge support from the National High Magnetic Field Laboratory for access to the high

magnetic field experiments. Finally, I would like to acknowledge support from the Quantum

Materials Center and the X-ray Crystallographic Center for allowing the use of their facilities.

In the end, I could not have done this accomplishment without my family and friends.

Incredible support came from dear friends and members of my church, Grace Church of Clarksburg.

Many other friends and relatives were extremely supportive during my graduate career even if the

phrase ”you done yet?” may have been said a few times. In all seriousness, it would take many

pages to thank each individual person, but I can look back on my graduate career with great

fondness; I have made many life-long friends and memories that I will always hold on to. I

would like to specifically acknowledge my son, Mom, Dad, Grandparents, and four siblings for

all of their support and outpouring of love. And most important of all, my wife Beth for her

constant presence and encouragement and love when I needed it most. While in graduate school,

we started dating, got engaged, got married, and had a baby; for that, I am beyond grateful.

vi



Table of Contents

Foreword ii

Dedication iv

Acknowledgements v

Table of Contents vii

List of Tables x

List of Figures xi

List of Abbreviations xiv

Chapter 1: Introduction 1
1.1 Intrinsic spontaneous order of ferroic materials . . . . . . . . . . . . . . . . . . 1
1.2 Toroidal moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Characterizing ferrotoroidic domains . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Lithium transition metal orthophosphates . . . . . . . . . . . . . . . . . . . . . . 12
1.5 Metal thiophosphates - 2D magnetic materials . . . . . . . . . . . . . . . . . . . 18
1.6 Specific aim and outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Chapter 2: Methods 26
2.1 Synthetic Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.1.1 Solid-state syntheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.1.2 Alkali metal chalcogenides in liquid ammonia . . . . . . . . . . . . . . . 31
2.1.3 Lithium chloride flux single crystal growth . . . . . . . . . . . . . . . . 36
2.1.4 Bridgman-like single crystal growth . . . . . . . . . . . . . . . . . . . . 38
2.1.5 Deintercalating lithium via oxidizing peracetic acid solution . . . . . . . 40

2.2 Characterization Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.2.1 X-ray powder diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.2.2 Single crystal diffraction - Laue diffractometer . . . . . . . . . . . . . . 46
2.2.3 Neutron powder diffraction . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.2.4 MPMS magnetic susceptibility . . . . . . . . . . . . . . . . . . . . . . . 51
2.2.5 MPMS magnetization vs. field . . . . . . . . . . . . . . . . . . . . . . . 55
2.2.6 High field vibrating-sample magnetometer . . . . . . . . . . . . . . . . . 57

vii



Chapter 3: Tuning Magnetic Properties of Li1−xFexMn1−xPO4 Through Selective Delithiation 60
3.1 Introduction to Li1−xFexMn1−xPO4 . . . . . . . . . . . . . . . . . . . . . . . . 60
3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.2.1 LiFexMn1−xPO4 powders and single crystals . . . . . . . . . . . . . . . 65
3.2.2 Chemical delithiation using peracetic acid . . . . . . . . . . . . . . . . . 67
3.2.3 X-ray powder diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.2.4 Magnetic property measurements . . . . . . . . . . . . . . . . . . . . . . 68
3.2.5 Neutron powder diffraction . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.3.1 Initial phase identification of Li1−xFexMn1−xPO4 . . . . . . . . . . . . . 69
3.3.2 Magnetic susceptibility . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.3.3 Neutron powder diffraction . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.3.4 Magnetic structure determination from NPD . . . . . . . . . . . . . . . . 77

3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.4.1 Crystal chemistry upon delithiation . . . . . . . . . . . . . . . . . . . . . 84
3.4.2 Magnetic exchange and symmetry upon delithiation . . . . . . . . . . . . 87
3.4.3 Magnetic properties upon delithiation . . . . . . . . . . . . . . . . . . . 91

3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

Chapter 4: Magnetic Properties of the Li1−xFexCo1−xPO4 and LiyCoxMn1−xPO4 Solid
Solution Series 97

4.1 Introduction to LiyFexCo1−xPO4 and LiyCoxMn1−xPO4 solid solutions . . . . . . 97
4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

4.2.1 Solid solution powders and single crystals . . . . . . . . . . . . . . . . . 101
4.2.2 Peracetic acid treatment - chemical delithiation . . . . . . . . . . . . . . 102
4.2.3 X-ray powder diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.2.4 Magnetic property measurements . . . . . . . . . . . . . . . . . . . . . . 104

4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.3.1 Structural characterization . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.3.2 Cobalt-manganese magnetic property measurements . . . . . . . . . . . 106
4.3.3 Iron-cobalt magnetic property measurements . . . . . . . . . . . . . . . 107

4.4 Conclusions and Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.4.1 Future directions - neutron powder diffraction . . . . . . . . . . . . . . . 113
4.4.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

Chapter 5: Spin Flop and Magnetic Phase Diagrams of LiFexMn1−xPO4 115
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

5.1.1 The magnetic diversity of the LiMPO4 orthophosphates . . . . . . . . . . 115
5.1.2 Spin flop defined . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.1.3 LiFePO4 and LiMnPO4 magnetic phase diagrams . . . . . . . . . . . . . 119

5.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.2.1 Solid-state powder synthesis . . . . . . . . . . . . . . . . . . . . . . . . 121
5.2.2 LiCl flux crystal growth . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.2.3 X-ray diffraction - powder and single crystals . . . . . . . . . . . . . . . 122
5.2.4 MPMS and PPMS magnetic property measurements . . . . . . . . . . . 123

viii



5.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.3.1 Initial magnetic property determination . . . . . . . . . . . . . . . . . . 124
5.3.2 Aligning single crystals - Laue diffractometer . . . . . . . . . . . . . . . 125
5.3.3 Antiferromagnetic field dependence - The ideal spin flop . . . . . . . . . 127
5.3.4 Easy axis throughout the series . . . . . . . . . . . . . . . . . . . . . . . 129
5.3.5 Creating the magnetic phase diagrams . . . . . . . . . . . . . . . . . . . 133
5.3.6 Discussion - Why is HSF so large in LiFePO4? . . . . . . . . . . . . . . 138

5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

Chapter 6: Lithiated Transition Metal Thiophosphates Li2MP2S6 143
6.1 Introduction to lithiated TM thiophosphates . . . . . . . . . . . . . . . . . . . . 143
6.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

6.2.1 Solid-state synthesis of Li2MP2S6 powders . . . . . . . . . . . . . . . . 145
6.2.2 Bridgman-like Li2MP2S6 single crystal growth . . . . . . . . . . . . . . 146
6.2.3 Powder and single crystal XRD . . . . . . . . . . . . . . . . . . . . . . . 147
6.2.4 Magnetic property measurements . . . . . . . . . . . . . . . . . . . . . . 148
6.2.5 Neutron powder diffraction (NPD) . . . . . . . . . . . . . . . . . . . . . 148

6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
6.3.1 Structure determination of Li2.26Fe0.94P2S6 . . . . . . . . . . . . . . . . 149
6.3.2 Structure determination of Li1.56Co0.71P2S6 . . . . . . . . . . . . . . . . 150
6.3.3 Magnetic property measurements of Li2.26Fe0.94P2S6 . . . . . . . . . . . 154
6.3.4 Magnetic property measurements of Li1.56Co0.71P2S6 . . . . . . . . . . . 155
6.3.5 Neutron powder diffraction . . . . . . . . . . . . . . . . . . . . . . . . . 158

6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
6.4.1 Cation order in Li1.56Co0.71P2S6 . . . . . . . . . . . . . . . . . . . . . . 162
6.4.2 The non-innocent P2S6 anion . . . . . . . . . . . . . . . . . . . . . . . . 163
6.4.3 Short-range magnetism and orbitally unquenced moments . . . . . . . . 166

6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

Chapter 7: Conclusions and Future Work 171
7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
7.2 Current and future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

Appendix A: Supplemental Figures 177

Bibliography 199

ix



List of Tables

1.1 Magnetic order summary of MPS3 . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.1 Decomposed representational analysis of the parent space group Pnma . . . . . . 78
3.2 Summary of NPD magnetic structure solution results for the Li1−xFexMn1−xPO4

olivines - part 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.3 Summary of NPD magnetic structure solution results for the Li1−xFexMn1−xPO4

olivines - part 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.4 Bond distances and angles of LixFe0.2Mn0.8PO4 and LixFe0.5Mn0.5PO4 . . . . . . 85
3.5 Summary of NPD magnetic structure solution results from the literature . . . . . 94

4.1 Refined lattice parameters from x-ray powder diffraction of lithiated LiFexCo1−xPO4

samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

5.1 Magnetic properties of the “end members” of the LiMPO4 . . . . . . . . . . . . 120

6.1 Single crystal XRD for Li2.26Fe0.94P2S6 and Li1.56Co0.71P2S6 . . . . . . . . . . . 150
6.2 Structural parameters for the lithiated metal thiophosphates . . . . . . . . . . . . 151
6.3 Structural parameters of lithiated metal phosphates . . . . . . . . . . . . . . . . 163
6.4 Bond valence sums (BVS) calculations . . . . . . . . . . . . . . . . . . . . . . . 165

x



List of Figures

1.1 The four ferroic orders defined . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Defining the toroidal moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Heesch-Shubnikov point groups and ferroic ordering . . . . . . . . . . . . . . . 7
1.4 Second harmonic generation spectroscopy image of LiCoPO4 . . . . . . . . . . . 9
1.5 Spherical neutron polarimetry experiment set up of LiFePO4 single crystal . . . . 10
1.6 LiFePO4 crystal structure as an example orthophosphate structure . . . . . . . . 14
1.7 LiFePO4 compared to NaFePO4 . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.8 General crystal structure of Li2MP2S6 where M . . . . . . . . . . . . . . . . . . 19
1.9 Magnetic structure summary of MPS3 TMCs. . . . . . . . . . . . . . . . . . . . 22

2.1 Solid-state set up for the LiMPO4 phosphates . . . . . . . . . . . . . . . . . . . 29
2.2 Solid-state set up for the Li2MP2S6 thiophosphates . . . . . . . . . . . . . . . . 30
2.3 Air-free cold finger set up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4 Alkali metal chalcogenides experiment set-up . . . . . . . . . . . . . . . . . . . 34
2.5 Graphite ingot used for crystal growth . . . . . . . . . . . . . . . . . . . . . . . 37
2.6 Single crystals of Li2MP2S6 where M = Fe, Co . . . . . . . . . . . . . . . . . . 39
2.7 Miller indices in LiFePO4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.8 Illustration of Bragg’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.9 Laue diffraction theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.10 Classes of magnetic materials and magnetic susceptibility . . . . . . . . . . . . . 53
2.11 Magnetization versus field theory . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.1 Magnetic structures of the transition metal orthophosphates . . . . . . . . . . . . 62
3.2 LiFexMn1−xPO4 single crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.3 Magnetic susceptibility trends of lithiated and delithiated phosphates . . . . . . . 72
3.4 Néel temperature trend - lithiated and delithiated . . . . . . . . . . . . . . . . . . 73
3.5 Inverse susceptibility trends of lithiated and delithiated phosphates . . . . . . . . 74
3.6 Indexed neutron powder diffraction data of LixFe0.3Mn0.7PO4 . . . . . . . . . . 76
3.7 Rietveld refinements of neutron powder diffraction data of LixFe0.3Mn0.7PO4 . . 79
3.8 Bond distances and angles of LixFe0.2Mn0.8PO4 . . . . . . . . . . . . . . . . . . 86
3.9 Super and super-super exchange pathways of orthophosphates . . . . . . . . . . 88
3.10 Summary of Li1−xFexMn1−xPO4 magnetic structures . . . . . . . . . . . . . . . 92

4.1 LiyMxM’1−xPO4 crystals structures . . . . . . . . . . . . . . . . . . . . . . . . . 99

xi



4.2 Single crystals of LiFe0.5Co0.5PO4 and LiCo0.3Mn0.7PO4 . . . . . . . . . . . . . 102
4.3 X-ray powder diffraction of lithiated LiFexCo1−xPO4 samples . . . . . . . . . . 105
4.4 Magnetic susceptibility measurements of LiyCo0.5Mn0.5PO4 . . . . . . . . . . . 107
4.5 Magnetic susceptibility measurements of LiyFe0.5Co0.5PO4 . . . . . . . . . . . . 108
4.6 Magnetic susceptibility trend of Li1−xFexCo1−xPO4 series . . . . . . . . . . . . 109
4.7 Néel temperature (TN ) trends of delithiated Li1−xFexCo1−xPO4 series. . . . . . . 110

5.1 Magnetic phase diagram of a theoretical spin flop . . . . . . . . . . . . . . . . . 118
5.2 Magnetic phase diagrams of LiMnPO4 and LiFePO4 . . . . . . . . . . . . . . . . 120
5.3 Laue images and fits of LiFe0.3Mn0.7PO4 . . . . . . . . . . . . . . . . . . . . . . 126
5.4 Antiferromagnetic field dependence pf a spin flop . . . . . . . . . . . . . . . . . 128
5.5 Magnetization (M) vs. applied field (H) data for LiFe0.1Mn0.9PO4 . . . . . . . . 130
5.6 Magnetization (M) vs. applied field (H) data for LiFe0.2Mn0.8PO4 . . . . . . . . 131
5.7 Magnetization (M) vs. applied field (H) data for LiFe0.9Mn0.1PO4 . . . . . . . . 132
5.8 Summary of the magnetic structures of the LiFexMn1−xPO4 solid solution series. 133
5.9 LiFe0.9Mn0.1PO4 derivative and magnetic phase diagram . . . . . . . . . . . . . 135
5.10 3D Summary of LiFexMn1−xPO4 magnetic phase diagrams . . . . . . . . . . . . 136
5.11 Summary of LiFexMn1−xPO4 HSF values . . . . . . . . . . . . . . . . . . . . . 137
5.12 LiFePO4 anisotropy from susceptibility . . . . . . . . . . . . . . . . . . . . . . 139

6.1 Crystal structure of Li1.56Co0.71P2S6 . . . . . . . . . . . . . . . . . . . . . . . . 151
6.2 Checking for diffuse scattering in the Co-based thiophosphate . . . . . . . . . . . 153
6.3 Bond lengths of Li2MP2S6 from single crystal results . . . . . . . . . . . . . . . 153
6.4 Magnetic susceptibility of Li2.26Fe0.94P2S6 . . . . . . . . . . . . . . . . . . . . . 155
6.5 Magnetic field dependence of Li2.26Fe0.94P2S6 . . . . . . . . . . . . . . . . . . . 156
6.6 Single crystal magnetic susceptibility of Li1.56Co0.71P2S6 . . . . . . . . . . . . . 157
6.7 Magnetic field dependence of Li1.56Co0.71P2S6 . . . . . . . . . . . . . . . . . . . 158
6.8 Neutron powder diffraction of Li2.04Fe1.12P2S6 . . . . . . . . . . . . . . . . . . . 159
6.9 Neutron powder diffraction of Li1.73Co0.43P2S6 . . . . . . . . . . . . . . . . . . 160
6.10 Zoomed neutron powder diffraction of Li1.73Co0.43P2S6 . . . . . . . . . . . . . . 161

7.1 CoPS3 structure and powder x-ray diffraction . . . . . . . . . . . . . . . . . . . 175

A.1 Ferroic orders under space inversion and time reversal symmetry . . . . . . . . . 177
A.2 Allowed point groups for ferrotoroidicity . . . . . . . . . . . . . . . . . . . . . . 177
A.3 X-ray powder diffraction of lithiated and delithiated phosphates . . . . . . . . . . 178
A.4 X-ray powder diffraction showing phosphate delithiation . . . . . . . . . . . . . 179
A.5 Magnetic susceptibility and Curie Weiss fits of phosphates . . . . . . . . . . . . 180
A.6 Magnetic susceptibility and Curie Weiss fits of phosphates . . . . . . . . . . . . 181
A.7 Magnetization versus field - x = 0.5 lithiated and delithiated . . . . . . . . . . . . 182
A.8 Summary of magnetic susceptibility and Curie Weiss fit results . . . . . . . . . . 182
A.9 Summary of representational analysis basis vectors . . . . . . . . . . . . . . . . 183
A.10 Integrated neutron powder diffraction patterns of the x = 0.2 samples . . . . . . . 184
A.11 Integrated neutron powder diffraction pattern of the x = 0.4 sample . . . . . . . . 185
A.12 Integrated neutron powder diffraction patterns of the x = 0.5 samples . . . . . . . 186
A.13 Integrated neutron powder diffraction pattern of the x = 0.6 sample . . . . . . . . 187

xii



A.14 Structural parameters of the neutron powder diffraction refinement results . . . . 187
A.15 Rietveld refinements of neutron powder diffraction of the x = 0.2 samples . . . . 188
A.16 Rietveld refinements of neutron powder diffraction of the x = 0.4 sample . . . . . 189
A.17 Rietveld refinements of neutron powder diffraction of the x = 0.5 samples . . . . 190
A.18 Rietveld refinements of neutron powder diffraction of the x = 0.6 sample . . . . . 191
A.19 Bond distances and angles of the super and super-superexchange pathways . . . . 192
A.20 Diagram to find magnetic subgroups from the parent space group Pnma . . . . . 193
A.21 “Bridgman-like” single crystal heating profiles for the iron and cobalt thiophosphates194
A.22 X-ray powder diffraction and Rietveld fit of Li2.26Fe0.94P2S6 . . . . . . . . . . . 194
A.23 X-ray powder diffraction and Rietveld fit of Li1.56Co0.71P2S6 . . . . . . . . . . . 195
A.24 Susceptibility measurements and CW fits - Li2.26Fe0.94P2S6 . . . . . . . . . . . . 196
A.25 Susceptibility measurements and CW fits - Li1.56Co0.71P2S6 . . . . . . . . . . . . 197
A.26 Zoomed in neutron powder diffraction of Li2.04Fe1.12P2S6 . . . . . . . . . . . . . 198

xiii



List of Abbreviations

AFM Antiferromagnetic
AC Alternating current
BVS Bond Valence Sum
DC Direct current
DFT Density functional theory
FC Field-cooled
FM Ferromagnetic
FTO Ferrotoroidic
HFIR High Flux Isotope Reactor
HC Spin flop saturated field
HSF Spin flop critical field
JHU Johns Hopkins University
MSG Magnetic space group
MPG Magnetic point group
MPMS Magnetic Property Measurement System
NPD Neutron powder diffraction
NHMFL National High Magnetic Field Lab
NCNR NIST Center for Neutron Research
NIST National Institutes of Standards and Technology
ORNL Oak Ridge National Laboratory
PM Paramagnetic
PPMS Physical Property Measurement System
pXRD Powder x-ray diffraction
QMC Quantum Materials Center
SF Spin flop
SHG Spherical Harmonic Generation
SNP Spherical Neutron Polarimetry
SNS Spallation Neutron Source
SQUID Superconducting Quantum Interference Device
TC Curie temperature
TN Néel temperature
TM Transition metal
TMC Transition metal chalcophosphate
UMD University of Maryland

xiv



vdW van der Waals
VSM Vibrating sample magnetometer
XCC X-ray Crystallographic Center
XRD X-ray diffraction
ZFC Zero-field cooled
2D Two-dimensional
µeff Effective magnetic moment
µtot Total magnetic moment
χ Magnetic susceptibility

xv



Chapter 1: Introduction

1.1 Intrinsic spontaneous order of ferroic materials

Symmetry exists in every material, but it manifests in many different ways. Some materials

undergo a spontaneous change in symmetry when an external condition is changed. A simple

example of this is water turning to ice at a specific “critical” temperature where the only external

application to water was cooling. The process of freezing is a spontaneous breaking of directional

symmetry.[1] When a material undergoes a spontaneous, physical change below a critical temperature

thereby introducing some sort of long-range order, it is called a ferroic material.[2] Ferroics

have been closely studied by chemists, physicists, engineers, and materials scientists for many

years. The three primary types of ferroic ordering are ferromagnetism, ferroelectricity, and

ferroelasticity. These materials demonstrate an alignment of magnetic moments, an alignment

of electric dipole moments, and an introduction of strain, respectively.[3] These three ferroic

materials can be seen in Figure 1.1b-c.

Ferromagnet, ferroelectric, and ferroelastic materials can be applied to countless fields and

have been studied for decades. The uniform orientation of magnetic moments (ferromagnetism)

forms what is more commonly known as a standard refrigerator magnet; which have have been

studied for thousands of years.[3] Even now, ferromagnetism is being applied in spintronics [4],

magnetoresistance [5], semiconductors [6], and so much more. The ordered magnetic moments

1



are shown in blue in Figure 1.1b with the electrons shown in black. Many years later, ferroelectric

materials were discovered in the early 1920’s when it was found that electric dipole moments can

spontaneously order with a net polarization (1.1c) [7]. Finally, years later ferroelastic materials

were defined as a material that has orientation states with different spontaneous strain tensors

(1.1d) [8].

Figure 1.1: The four ferroic orders: a) ferrotoroidics break time reversal and space inversion
symmetry, b) ferromagnetics break time reversal symmetry, c) ferroelectrics break space
inversion symmetry, and d) ferroelastics do not break either symmetry.

While each of these phenomena are fascinating on their own, the interplay between more

than one ferroic behavior quickly became of even greater interest to the materials science and

solid-state chemistry fields. When more than one ferroic behavior exists in a material, it is known

as a multiferroic material. Any combination of the primary ferroic materials can be combined to

form a multiferroic. For example, in data storage technology, both ferroelectric and ferromagnetic

behavior are utilized from the multiferroic material in question.[9] These opposite orientations

are used to represent “1” and “0” in common computer storage language. When ferroelectric

2



and ferroelastic behavior exist in a multiferroic, the material can be applied to piezoelectric

transducers.[10] There is a significant benefit to these multiferroic materials because one property,

such as magnetism, can be controlled by an another, like an electric field. This opens up a wide

range of possibilities that can and have been utilized.

While these three primary ferroics have been well studied for hundreds or even thousands of

years, there is a fourth and final, lesser known ferroic order known as ferrotoroidicity. We define

a toroidal moment as the local moment that arises from a local vortex of magnetic moments.[11]

Another way of wording it is a “moment of moments”; an example of a toroidal moment can

be seen in Figure 1.1a. A ferrotoroidic state occurs when the toroidal moments of a material

spontaneously align at some critical temperature. Ferrotoroidic materials have a strong theo-

retical groundwork established [12, 13, 14], however, with the exception of our group at the

University of Maryland, there are few research groups exploring these materials experimentally.[12]

One of the main reasons as to why ferrotoroidics have not been studied experimentally is because

the toroidal moment is not trivial to directly observe via current characterization techniques. This

is discussed in further detail in section 1.3.

The best way to distinguish between and simultaneously relate the four types of ferroic

ordering is through the breaking of time-reversal and space-inversion symmetry. A helpful visual

summary of these symmetry operations can be seen in Figure A.1. Ferromagnets break time-

reversal symmetry; if you consider the movement of the electrons as based in time, if you reverse

this time, the magnetic moment will be facing the opposite direction because of the right hand

rule. Ferroelectrics break space-inversion symmetry; if you put a mirror plane in between the

positive and negative side of the dipole moment, it will flip signs. Ferroelastics don’t break

either of the symmetry operations. Finally, ferrotoroidic materials break both time-reversal and

3



space-inversion symmetry due to the nature at which the electrical current controls the magnetic

moments that then produce a toroidal moment normal to the plane.

Because ferrotoroidic materials break both time-reversal and space-inversion symmetry and

can be controlled by both a magnetic and electric field, a ferrotoroidic material is intrinsically a

multiferroic. More specifically, it demonstrates what is known as the magnetoelectric effect.[12]

Magnetoelectrics can be manipulated by both a magnetic and an electric field; the magnetization

can be controlled by an external electric field and the polarization can be controlled by an applied

magnetic field. The unique thing about ferrotoroidic materials is that there is a linear response of

the magnetization to the applied electric field, meaning that ferrotoroidics express what is known

as the linear magnetoelectric effect. Because of the symmetry elements and the multiferroic

behavior, every ferrotoroidic material must consist of the linear magnetoelectric effect. This

proves useful because as mentioned, measuring a toroidal moment directly is very difficult, one

must instead measure a phenomena that is coupled to that of the toroidal moment.[15] This means

that measuring the linear magnetoelectric effect can be used to show evidence that a toroidal

moment exists.[15]

1.2 Toroidal moments

An example of a toroidal moment can be seen in Figure 1.2a. When enough magnetic

moments are produced by an electrical current and are spontaneously aligned, a torus is formed.

This torus will produce a magnetic field that in turn induces a toroidal moment normal to the

plane. The direction of this toroidal moment is fully dependent on the arrangement of the spins

and therefore the direction of the magnetic moments, following the right hand rule (Figure 1.2b).

4



Figure 1.2: The toroidal moment defined: this figure is from a review article published by our
group in the Journal of Solid State Chemistry.[12] a) The toroidal moment T generated from a
solenoid of magnetic moments. The strength of T depends on the radius r. b) The direction of
the toroidal moment is completely dependent on the arrangement of the magnetic moments. c)
Toroidal moments can be generated from several configurations of magnetic moments.

Now, in a realistic “ system, there won’t be an infinite amount of magnetic moments to create

this ideal closed magnetic field loop seen in 1.2a. Magnetic moments can however form several

other configurations that still have the ability to form a toroidal moment, such as a “head-to-tail”

arrangement.[12] Figure 1.2c demonstrates some examples of when two or more spins can be

arranged in a simple way and still create a toroidal moment. The strength of the toroidal moment

vector is simply a cross product of the radius of the ring r and the localized spin s. The equation

for the toroidal moment strength is

T ∝
N∑

i=1

ri × si (1.1)

5



This helps us in systematically pursuing materials that could demonstrate ferrotoroidicity.

Because the strength of the toroidal moment is directly proportional to the spin, we seek to choose

materials that have metal cations with large magnetic moments. Typically these would be first-

row transitional metals (at least with regard to the materials studied in this work). These metals

have strong magnetic moments, meaning the toroidal moment should be sufficiently large enough

to measure.

As toroidal moments and then the importance of the alignment of these toroidal moments

become more clear, it becomes more and more apparent that the symmetry of the magnetic

moments in the lattice are absolutely crucial in determining if a material can host ferrotoroidicity

or even toroidal moments at all. The crystallographic lattice must allow the magnetic moments

to align in a way that can produce a toroidal moment. Because of this, when searching for new

ferrotoroidic materials, many “ materials can be completely removed as potentials just based off

of their crystallographic and magnetic symmetry. Schmid et al. went through the tedious process

of determining all of the magnetic point groups that allow magnetization (M), polarization (P),

and toroidization (T), as well as all of the overlapping groups that allow multiferroic behavior.[11,

15] The summary of his work is reproduced in a Venn diagram and shown in Figure 1.3.

Out of the 122 Heesch-Shubnikov point groups, 31 magnetic point groups allow ferrotoroidicity,

fourteen of which allow only toroidization, and seventeen of which allow toroidization with

polarization and/or magnetization. There are nine point groups that can host all three primary

types of ferroic behavior shown. The detailed breakdown of these 31 point groups can be seen

in Table A.2. This table proves to be very useful when deciding which materials to pursue with

regard to studying ferrotoroidics experimentally. Now, we know that the desired material should

have metal cations with large magnetic moments and we know what symmetry we are looking

6



Figure 1.3: A Venn diagram reproduced from Shmid et al. [11] where the number of Heesh-
Shubnikov point groups are broken down into those that could demonstrate magnetization (M),
polarization (P), and toroidization (T). Those that are overlapping have the ability to demonstrate
multiferroic behavior. There are 122 Heesh-Shubnikov point groups total, 31 of which could host
toroidization.

for.

1.3 Characterizing ferrotoroidic domains

Before moving on to the types of ferrotoroidic materials that have been studied, it is

important to discuss the instrumentation that has been developed to characterize toroidal moments.

As mentioned, there is still not one all-encompassing technique that can simply observe a toroidal

moment. Over time, there have been three main types of characterization that have been used

to study ferrotoroidics: Second Harmonic Generation (SHG) spectroscopy, Spherical Neutron

Polarimetry (SNP), and magnetoelectric measurements. We will discuss briefly how these instrumentation

techniques have been used to look at ferrotoroidic domains and toroidal moments.

7



Second harmonic generation spectroscopy has many uses on a variety of materials [16, 17]

but is also a useful technique for visualizing ferroic domain structures.[18] In SHG measurements,

an electromagnetic light field denoted E has a frequency of ω and is projected onto a crystal. This

induces a polarization P with a frequency double that of the incident light (2ω). This expression

is represented by the equation [19]:

P(2ω) = ϵ0χ̂E(ω)E(ω) (1.2)

The susceptibility of the material is denoted as χ̂ and ϵ0 is the permittivity of free space.[19]

The susceptibility is arguably the most important, relating the polarization to the electromagnetic

field. Because this tensor relates these two parameters, it is therefore directly coupled to the

toroidization of the crystal. Because χ̂ will change signs depending on the direction of the

polarization, one can use SHG to visualize the domain structure of the ferrotoroidic material.[12]

The most practical example of observing ferrotoroidic domains experimentally was from

Van Aken and Fiebig in 2007 where they characterized the domain structure in LiCoPO4.[19]

They concluded from symmetry arguments that ferrotoroidic domains are allowed in LiCoPO4,

making this material the first to show direct experimental evidence for the existence of ferrotoroidicity.

The SHG image from the LiCoPO4 study can be seen in Figure 1.4. The first image shows the

antiferromagnetic domains when the χyyz component was taken. The dark and light contrast is

very clear in these images, showing the differences between the domains. Figure 1.4c shows the

image from the interface of the χyyz and χzyy components, representing the ferrotoroidic domains

(outlined in red).

While SHG has proven to be helpful in visualizing ferrotoroidic domains, there are still

8



Figure 1.4: Second harmonic generation spectroscopy image of LiCoPO4 reproduced from Van
Aken et al. ([19]). Image down a (100) LiCoPO4 single crystal where a) raw image obtained
from light displaying the AFM domains. b) Clearly shows the domain structures and c) red lines
highlight the ferrotoroidic domain boundary walls.

limitations, it cannot directly observe a toroidal moment, the strength of the toroidal moment,

or even a distinct direction of the toroidal moment. The second major way to characterize

these materials is by using spherical neutron polarimetry (SNP). Neutron scattering is one of the

most useful and versatile techniques to study the structural and magnetic properties of materials.

Neutrons have an intrinsic magnetic dipole moment, meaning they can interact with the magnetic

moments within a sample. The majority of neutron diffraction measurements are unpolarized, this

technique will be described in more detail in Chapter 2. However, sometimes polarized neutrons

are needed to better understand more complicated systems or reveal additional information about

the system.[20]

Polarized neutrons have many additional capabilities, the most useful of these capabilities

9



Figure 1.5: Spherical neutron polarimetry experiment set up of LiFePO4 single crystal. The
incident neutron beam ki has an initial polarization PO. After the neutron scatters, the
scattered neutron beam kf has a final polarization PS . This is the polarization that is analyzed.
The scattering vector (Q) is normal to the interaction. Depending on the alignment of the
magnetization and the response, the polarization is either a) counterclockwise or b) clockwise.

for this work is that spin-polarized neutrons can help detect antiferromagnetic (AFM) domain

population. Not only can it detect AFM domains, there is currently work being done in our group

to prove that the SNP can directly probe scattering from the toroidal moment itself. The details

as to how this method works is extremely detailed and only a summary will be presented here.

A configuration of an SNP experiment on a LiFePO4 single crystal can be seen in Figure 1.5.

One of the unique capabilities of SNP is that there is no restrictions to the polarization of the

incident beam nor how the scattered beam is analyzed. This is contrary to uniaxial scattering

where the polarization of the neutron beam is restricted to being vertical to the scattering plane or

10



along Q in the plane.[21, 22] This means that SNP can analyze the magnetic interaction vector in

its entirety, no matter how complex it may be.[23] This ability to understand complex magnetic

systems like this makes SNP perfect for toroidal moments and ferrotoroidicity.

By using the polarized neutrons and having the ability to determine if the toroidal moments

are pointed up or down (Figure 1.5), SNP can be used to solve the domain population of a

ferrotoroidic material. Our group has performed a successful experiment on a LiFePO4 single

crystal where with no field, equal domain population of the up and down toroidal states were

observed. When a conjugate field is applied: E (electric field) × H (magnetic field), nearly

100% domain population was facing the same direction, indicating ferroic order of the toroidal

domains. This was observed by looking at the off-diagonal terms in the polarization matrix that

was produced during the SNP experiment. When the conjugate field was reversed, the other

domain can be populated. While there is still a lot of room to grow, it appears that spherical

neutron polarimetry is currently the best way to visualize toroidal moments.

Finally, the third way to characterize ferrotoroidic materials is through magnetoelectric

measurements. While SHG and SNP are clearly the better option to visualize ferrotoroidic

domain structure, they are expensive, non-trivial, and time consuming characterization techniques.

In addition, they require millimeter size crystals, which are not always readily available. The

benefit of magnetoelectric measurements is that they can be performed on commercially available

magnetic property measurement systems (MPMS) such as a superconducting quantum interference

device (SQUID) that is much more readily available.[24, 25, 26] The magnetoelectric effect was

already discussed above and will not be discussed in detail here.

The specific aims for magnetoelectric measurements are twofold: first, to determine the off

diagonal components that develop as the material is cooled past the transition temperature. The

11



off diagonal components will determine whether the material demonstrates the linear magnetoelectric

effect, which is essential for ferrotoroidicity to exist. The second aim is to be able to distinguish

between the antiferromagnetic domain contributions and toroidal contributions. Once this is

done, the symmetry and therefore the point group can then be determined.[27] These measurements

are best conducted on single crystals but are also possible with powders or polycrystalline samples.[28,

29, 30] As mentioned, this technique is not nearly as thorough in understanding toroidal domain

structure, but can serve as an affordable, efficient way to collect preliminary results on a potential

ferrotoroidic candidate.

1.4 Lithium transition metal orthophosphates

While it is important to understand our current capabilities to characterize toroidal domain

structure, the work presented here will have more of an experimental focus. The goals for this

research are to synthesize new potential ferrotoroidic materials that can be utilized in the future

when the characterization techniques are more sound and readily available. Our specific aim here

is threefold: first, to develop materials with higher transition temperatures so that ferrotoroidics

can eventually be studied and used in ambient conditions. Secondly, we hope to synthesis

materials that have large magnetic moments and therefore large toroidal moments that are easily

measured. Finally, we hope to synthesize new materials that may not even have been considered

for ferrotoroidicity in the past.

There are an infinite amount of materials that could be chosen to study as potential ferrotoroidic

candidates. Lithiated transition metal orthophosphates of the formula LiMPO4 where M = Fe, Co,

Mn, Ni were of particular interest to our group because LiCoPO4 was arguably the first material

12



with concrete experimental evidence to be a ferrotoroidic. Instead of choosing to work with

cobalt, this study decided to approach the challenge with the iron compound LiFePO4. This is

because the Fe2+ radius is larger, the magnetic moment is stronger, and the Néel temperature is

higher; all three of these properties would probe a larger toroidal moment in the system.

These olivine orthophosphates offer a versatile platform for materials properties exploration.

Whether of physical[31, 32, 33, 34] or electrochemical interest,[35, 36, 37, 38] olivine phosphates

display a rich crystal chemistry by which one can tune their macroscopic properties. Early studies

of the olivine phosphates focused on their magnetic and magnetoelectric properties.[39, 40, 41,

42] Later, the groundbreaking work by Goodenough[43] and others[44, 45, 46, 47, 48] revealed

the M = Fe member to be an outstanding candidate as a cathode in Li-rechargeable batteries. Also

known as triphylite,[49] LiFePO4 displays a working potential of 3.45 V vs Li/Li+ on account of

the facile oxidation of Fe2+ to Fe3+ upon Li+ deintercalation.[50]

On a surface level, each LiMPO4 structure may seem identical, but the subtle changes

in nuclear structure and electron count of the transition metal have a significant impact on the

magnetic ordering within the structure. Ultimately, every physical property stems from the

structural features: electrochemical, magnetic, surface properties, etc. The larger group of oxides

AB2O4 where AO4 is a tetrahedral oxyanion can be broken down into many sub groups, one

of which is the olivine structure type B2(AO4).[51] This work will refer to these materials as

olivines throughout the descriptions as a short hand for materials with the B2(AO4) type structure.

Generally speaking, the AO4 anion is either phosphates [52] or silicates [53, 54], although others

have been studied [55, 56].

The general LiMPO4 crystal structure can be seen in Figure 1.6 where the structure of

LiFePO4 is given as an example. Each member of the series crystallizes in an orthorhombic Pnma

13



Figure 1.6: LiFePO4 crystal structure as an example of an orthophosphate structure. The other
LiMPO4 structures (M = Mn, Co, Ni) strongly resemble this one. Top) View down the [001]-
direction showing the lithium layer that separates the metal phosphates. Bottom) View down the
[100]-direction showing the connectivity of the FeO6 octahedra via the phosphate anions.

space group which can be described as a pseudo-hexagonal close packed (hcp) sublattice of O2−

anions. The Li+ cations fill in the interstitial positions in between the iron phosphate layers in

such a way that the LiO6 octahedra are all edge-sharing with one another. The FeO6 octahedra on

the other hand are corner-sharing; having direct consequences to how the metal cations interact

via exchange pathways (will go in depth on this in Chapter 3). The oxyanion framework that is

formed uses the distorted octahedra to facilitate lithium intercalation and deintercalation when

the metal site is oxidized and reduced. Lastly, it’s important to not overlook the PO4 groups; the

short oxygen to oxygen bonds allow supersuperexchange interactions. This means a metal cation

can interact with another metal that is four atoms away, for example M1 can interact with M2 by

14



the following supersuperexchange path: M1··O1··O2··M2.

Other orthophosphates can take on different structures. For example, when the lithium

cation is changed to sodium, there are a few key differences. In NaFePO4, the structure is similar

to that of LiFePO4 in that the phosphate groups are aligned in the same way and there is still a

layered nature to the unit cell. However, the M1 and M2 sites are completely swapped where

the Fe2+ ions are in between the layers and Na+ takes up the position in between the phosphate

groups; this gives rise to a maricite-type structure.[57] The difference between these structures

can be seen in Figure 1.7. This gives rise to varying connectivity differences across the lattice and

removes the ability to readily deintercalate the cation to form a rechargeable battery. This same

study found that when the transition metal is changed to manganese, both the M1 and M2 sites

are half occupied by Mn2+ and Na+ and is similarly electrochemically inactive. This manganese

structure also adopts a maricite-type structure instead of an olivine structure.[57]

It has been shown that one can change the cation from lithium to ammonia to form NH4FePO4-

•H2O; this material can be readily transformed back into LiFePO4 [58] or LiMnPO4 (using

NH4MnPO4•H2O). [59] The same group that conducted the study above used a similar approach

to synthesize NaMPO4 structures using a direct ion exchange with NH4MPO4 where the NH+
4

cation exchanged with Na+ using molten CH3CO2Na•3H2O.[57] They also successfully substituted

Ca2+ and Mg2+ in place of Mn2+ to attempt to push Na+ out of the M2 site and into the layer

where it can be more mobile. It turns out that this method was successful in developing a new

sodium-ion battery: Na[Mn1−xMx]PO4 where M = Fe, Ca, Mg.[57]

These examples are just scratching the surface of the tunability of the B2(AO4) structure

type. Other studies have used potassium; KMnPO4•H2O has a dittmarite-type structure. This

material can actually be used as a way to synthesize NaMnPO4 with an olivine-type structure

15



Figure 1.7: The crystal structures of a) LiFePO4 compared to that of b) NaFePO4. Just by
changing the cation, the structure undergoes a phase change from an olivine-type structure to
a maricite-type structure that is completely electrochemically inactive. This figure comes from
Lee et al.[57]

instead of a mericite structure.[60] One method that can change the structure of the material is

by removing the cation altogether. Removing lithium from LiFePO4 has a large impact on the

structure of the material because the lithium provides a large amount of structural rigidity to the

framework of the lattice.[61] Upon removal of the cation, many orthophosphate materials are no

longer stable due to the loss of rigidity.

Giving a conclusive review of all transition metal orthophosphates with the B2(AO4) formula

would take an entire dissertation on it’s own, but these examples do demonstrate how tunable

these materials are. By simply changing the B cation or substituting the metal A cation with

16



another, or creating a solid-solution among two metal cations, or removing the B cation all

together, the structure of the material is greatly affected. This begins to show why these materials

have been studied for hundreds of years with no end in sight; the tunability and wide variety of

applications makes them one of the most versatile family of materials ever discovered.

Now that it is understood how versatile the structural properties of these materials are,

one can only imagine how much the structural changes can affect the magnetic properties of the

materials. For the sake of brevity, only the magnetism of each of the four prominent LiMPO4

materials will be discussed (where M = Fe, Co, Mn, Ni). This will demonstrate that by simply

changing the electron count on the transition metal site, the magnetic properties can vary greatly.

First, the most well studied with regard to ferrotoroidicity: LiCoPO4 has Co2+ d7 ions and

demonstrates an m’mm magnetic point group where the antiferromagnetic arrangement of moments

are aligned along the crystallographic b axis.[62] Several sources say that this cobalt phosphate

exhibits long range ordering and alignment of toroidal moments.[19, 57] These toroidal moments

would be aligned along the c direction.

LiFePO4 has one less electron with Fe2+ d6 ions, it has the same magnetic symmetry as

LiCoPO4 (m’mm) with a few distinct differences.[61] First, that magnetic moment is stronger due

to the larger ionic radii, which means that the toroidal moment will also be stronger. Secondly, the

Fe2+ d6 will more readily oxidize to Fe3+ d5, making the removal of lithium easier. Nonetheless,

the AFM moments are still aligned along b and the toroidal moments are predicted to be along c.

LiMnPO4 consists of Mn2+ d5 metal centers, making the magnetic structure unique from

iron and cobalt. The magnetic moments align antiferromagnetically along the a direction ordering

in an m’m’m’ magnetic point group.[62] This material is unique in that it does not demonstrate off

diagonal terms in the magnetoelectric tensor, meaning ferrotoroidicity is not possible. However,

17



recent studies in our group predict that this material will demonstrate anti-ferrotoroidicity with

a net toroidal moment of zero. This makes this material of particular interest, especially when

trying to characterize toroidal moments; having an anti-ferrotoroidic material to compare to a

ferrotoroidic material is very beneficial.

Finally, LiNiPO4 is comprised of Ni2+ d8 ions, making it the orthophosphate with the

smallest magnetic moment (2.22 µB).[63] The antiferromagnetic moments align along the c

direction with a small contribution along the a direction with a final magnetic point group of

mm’m. The amount of research conducted on this material with regard to ferrotoroidicity is slim,

but the toroidal moments are predicted to align along the b axis.

A summary of the magnetic structure of these orthophosphate “backbones” can be seen in

Table 3.5. This introduction to the lithium transition metal orthophosphates has sought to show

how versatile, tunable, and multifaceted these materials can be. This work seeks to continue

studying these materials with the specific application of ferrotoroidicity. Chapters 3-5 will give

in depth descriptions and experiments on the structural and magnetic properties of these materials.

1.5 Metal thiophosphates - 2D magnetic materials

The second main family of materials that will be discussed in this work are the transition

metal thiophosphates of the formula Li2MP2S6 and M2P2S6 where M = Fe, Co, Mn, Ni. The

lithiated thiophosphates had some preliminary structural analysis performed for electrochemical

applications with the hopes of making a new sulfide cathode.[64] However, no magnetic properties

had been published. Structurally, these thiophosphates resembled the orthophosphates but have

some key differences. An example of the general Li2MP2S6 structure can be seen in Figure 1.8.

18



This material crystallizes in a layered-honeycomb like structure with trigonal symmetry and a

space group of P31m.

M2+

Li1+

S

P

a) b)

c)

c

ba
ab

c

ab

c

Figure 1.8: General crystal structure of Li2MP2S6 where M is a transition metal. (a) Layered
structure where the metal thiophosphate octahedra are separated by Li+ cations. (b) Perspective
down the [001]-direction, which shows the trigonal symmetry of the structure in space group
P31m. (c) Metal sublattice only, which better illustrates the honeycomb structure.

The distorted MO6 octahedra are connected via P2S6 groups in a similar way that the

metals are connected with the PO4 groups in LiMPO4. The metals are aligned in a honeycomb

structure which can be visualized when looking down the [001]-direction (1.8c). Similarly to

the orthophosphates, the lithium cations are positioned in the interstitial positions in between

the two layers; this makes it an attractive species for electrochemical interests. These are also

synthesized with first row transition metals, meaning the magnetic moment is expected to be

large and therefore an interesting candidate for ferrotoroidic applications.

To our surprise, after detailed analyses, it became apparent that these thiophosphate materials

19



could not host toroidal moments and therefore could not be considered ferrotoroidic candidates.

This analysis is described in detail in Chapter 6. However, there were many interesting magnetic

properties observed within these materials that were novel in nature and could not be ignored.

For this reason, the final part of this work is focused on finding novel materials that demonstrate

two-dimensional (2D) magnetism; there will be no focus on ferrotoroidicity. This is fitting as this

work with the thiophosphates initiated a pivot in our research group where 2D magnetism has

become a focus.

Research in two-dimensional (2D) magnetism is extremely widespread across many fields

including materials chemistry, physics, and more. The early discovery of 2D magnetism in

van der Waals (vdW) materials focused on compounds such as CrI3 [65, 66, 67], CrGeTe3

[68], and Fe3GeTe2 [69, 70, 71, 72]. As the overwhelming success and versatility of these

materials began to surface, it quickly rose to the forefront of materials research. Since then,

there have been several thorough reviews of magnetism in vdW materials [73, 74, 75, 76, 77,

78]. Here, a brief introduction to these materials will be given, but one should refer to these

reviews for a more detailed summary. One of the most well studied 2D magnetic materials

family is the transition metal chalcophosphates (TMCs). TMCs have been widely studied with

regard to the semi and super conducting properties, displaying large band gaps of 1.6 eV to 3.4

eV [79, 80, 81]. They have also been predicted to be Mott insulators [82, 83, 84] and even

demonstrate ferroic behavior.[73] Arguably the most influence that TMCs have made is in the

fields of microelectronics, spintronics, and magnetoelectrics.[73]

Within a TMC, the metal is generally a first row transition metal and the chalcogenide is

most commonly sulfur or selenium resulting in a final formula of MPX3 where M = Fe, Co, Ni,

Mn and X = S, Se. While this might be one of the most common structures, the metal could

20



also be an alkali or alkaline earth metal and the chalcogenide can be substituted for elements

like tellurium. These materials have a true van der Waals gap where the sulfur or selenide

atoms are above and below the single layer of metals. The structures of these materials are

nearly identical to the lithiated version shown in Figure 1.8 with the exception that in TMCs,

the layer is empty. Most commonly, as shown in 1.8a, the thiophosphates are arranged as P2S4−
6

(or P2Se4−6 ) ethane-like structures with a staggered conformation. These thiophosphates than

coordinate with the metal centers to form a hexagonal array that than form the honeycomb lattice

seen in 1.8c. The honeycomb nature of these materials make them an interesting prospect for

quantum behavior such as quantum spin liquids. Systems like α - RuCl3 [85, 86] or A2IrO3

[87, 88] have demonstrated novel quantum behavior that stem from the honeycomb lattice. The

edge sharing octahedral network of metals facilitate exchange pathways that can result in unique

interactions.

The magnetism of these MPS3 (or otherwise written as M2P2S6), has been extensively

researched. The summary of the magnetic structures of the transition metal thiophosphates can be

seen in Figure 1.9. Each transition metal is well represented in the literature: Manganese [89, 90,

91, 92], iron [93, 94, 95], cobalt [96, 97, 98], and nickel [99]. While the thiophosphates have been

well studied, the selenophosphates (MPSe3) have not, although there have been some attempts

[81, 100]. Similar to the orthophosphates, by simply changing the electron count of the first row

TM, the magnetism can be greatly effected. Three major classes of magnetic Hamiltonians are

represented within this series of four materials: Ising, XXZ, and Heisenberg. The summary of

the magnetic order can be represented in Table 1.1.

Intercalating alkali metals into these 2D thiophosphate layers can change both the structural

and magnetic properties significantly. Given the nature at which the layers form, there is a

21



Figure 1.9: Magnetic structure summary of MPS3 where M = Ni, Mn, Fe, and Co. Each metal
results in a different magnetic symmetry. The details of these structures are listed in Table 1.1.

plethora of cations that can be intercalated. Generally this focus lies in electrochemical or

energy storage applications, leaving a wide gap in the literature with regard to the magnetic

properties of these intercalated thiophosphates. This work is focused on filling this gap by

studying the magnetic properties of these intercalated transition metal thiophosphates with the

goal of broadening the field of 2D magnetism.

Table 1.1: Magnetic order summary of MPS3 where M = Mn, Fe, Co, Ni. Three major classes of
magnetic Hamiltonians are represented: Ising, XXZ, and Heisenberg.

Material Néel Temp. In-plane mag. config. Magnetic model

MnPS3 78 K [101] Néel AFM [101] Heisenberg [73, 99]
FePS3 118 K [101] zigzag AFM [101] Ising [99, 101]
CoPS3 132 K [101] zigzag AFM [99] XXZ [97]
NiPS3 155 K [101] zigzag AFM [99] Heisenberg [73]

Our work starts with looking at lithium intercalation into the FePS3 and CoPS3 layers.

When intercalation is introduced, it’s more intuitive to use the longer notation for these thiophosphates:

22



Li2MP2S6 so this notation will be used primarily for the remainder of this report. Chapter 6

will go in depth into the previously unreported magnetism of Li2FeP2S6 and Li2CoP2S6. As

previously stated, the focus of this work as a whole in our research group has shifted to focus on

these TMCs and 2D magnetism. The final chapter will discuss how the research on the lithium

intercalated thiophosphates has inspired research that is currently underway on other materials.

1.6 Specific aim and outline

One of the leading focuses of materials scientists is to develop new materials with ground-

breaking physical properties. Synthesizing novel ferrotoroidic and 2D magnetic materials would

help strive towards this goal. This chapter has sought to lay the groundwork of the motivation

behind the materials chosen for this research. In reality, the examples mentioned only scratched

the surface of the broad reach of the phosphate and thiophosphate applications. Each chapter will

give a brief introduction that is more specific to the materials that are being discussed to aid in

a smooth read of the entire report. In this thesis document, we describe how the structure and

magnetism of several transition metal phosphates and thiophosphates can be tuned by going into

significant detail of the synthesis, characterization, and analysis of the materials in question.

In Chapter 2, we discuss the synthetic techniques used to make the powders or grow

single crystals. We will also walk through the major characterization techniques used to analyze

the physical and chemical properties of the materials synthesized. There were many synthetic

methods and characterization techniques utilized given the diversity of materials and properties

that we sought to understand.

In Chapters 3-5, we dive into the transition metal phosphates of the formula LiMPO4

23



where M = Fe, Mn, and Co (nickel will not be studied in this work). Chapter 3 introduces

a new synthetic technique to partially delithiate the Li1−xFexMn1−xPO4 solid solution series.

By partially removing lithium and studying the materials with neutron powder diffraction, the

magnetic structure was solved for several members of the series, allowing us to study the affect of

lithium content on magnetic symmetry. In the end, we synthesize a novel potential ferrotoroidic

material with the largest reported Néel temperature (TN ).

Chapter 4 is a shorter chapter that follows up Chapter 3 with preliminary studies on the

effect of selective delithiation on the magnetic structure of the LiyFexCo1−xPO4 and LiyCox-

Mn1−xPO4 solid solution series. While this study is not complete, we see intriguing results

already, especially in the magnetism of the iron-cobalt series. While the cobalt-manganese series

appears to not be affected by delithiation attempts, the iron-cobalt series is all but predictable

with intriguing non-linear TN trends.

Chapter 5 also focuses on a solid solution series with iron and manganese, this time fully

lithiated LiFexMn1−xPO4. This chapter focuses on the unique magnetic phenomena known as

a spin flop. We study the novel spin flop transition in this series as iron concentration increases

and the critical spin flop field (HSF ) increases with it. We then create magnetic phase diagrams

to help us understand why HSF is so large for iron and so low for manganese using spin-orbit

theory arguments. In the end, we synthesized a material with 11.3% iron that demonstrated the

exact same spin flop behavior at iron but at 5 T instead of 32 T, a much more reasonable field

strength.

In Chapter 6, we make the transition away from phosphates and into thiophosphates of the

formula Li2MP2S6 where M = Fe, Co. These materials were originally studied to develop new

ferrotoroidic materials but quickly shifted to 2D magnetic materials applications as it became

24



apparent that there was no long range magnetic ordering. However, the results were all but trivial.

We find that by solving the crystal structure of the novel Li2CoP2S6 material, we discover a

unique structure with what we term as a “non-innocent” P2S3−
6 anion. Neutron powder diffraction

and magnetization measurements are used to better understand these lithiated iron and cobalt

thiophosphates.

Finally, Chapter 7 serves two purposes: 1) to summarize the most important findings in this

doctoral work, and 2) to give a brief direction as to where this project is headed and what research

is currently underway. There will then be a list of the references followed by an appendix with

supplemental figures.

25



Chapter 2: Methods

2.1 Synthetic Methods

This section will not give detailed descriptions of the specific syntheses carried out in this

work such as every mass used, heating profile executed, etc. Those details will be given in each

respective chapter. This section serves to give a more general overview of the primary synthetic

techniques used in this work.

When attempting to synthesize a material for the first time, many things must be considered.

First, has the material been synthesized before? What techniques have been utilized to make it

or materials like it? What are potential safety issues? Does it require extreme conditions such

as high temperature, pressure, or unique/expensive machinery? These are just a few of the many

questions one should ask themselves before attempting a synthesis for the first time. Once a

synthetic method is chosen, more specific questions can be asked.

2.1.1 Solid-state syntheses

In this work, the majority of the powders used were synthesized with what is known as the

solid-state method. Solid-state technique is a broad term referring to combining several starting

reagents in solid form (often powders). These powders are generally ground together with a

26



mortar and pestle before the homogeneous mixture is placed in some kind of crucible. This

crucible is then heated to temperatures that are above the melting point of all starting reagents

but below any degradation temperature. The temperature at which the solid-state procedure is

conducted is crucial and will be discussed more shortly.

The solid-state technique has many advantages. By combining the solids together and

having control over the temperature of the reaction, the amount of impurities introduced into the

system is limited and can often be controlled. The ease of the synthesis allows many trials to

be performed within days or weeks, giving time to attempt many temperatures or concentrations

for a new synthesis. Many “mild” conditions used to synthesize organic compounds will not

work for inorganic metals, making high temperature reactions necessary. While many solid-state

reactions are at or above 1,000 ◦C, there are also many solid-state reactions that can operate at

lower temperatures as well.[102]

Some say that solid-state reaction may not be the most rational way of synthesis design, and

that the scientist does not have enough control; they would be right in some regard.[103] It can be

approached in a more lackadaisical way where precursor powders with the desired elements with

little to no planning are tossed into a crucible and heated at an estimated temperature. On the

contrary, one can carefully plan out each step, balancing a chemical equation and determining

the byproducts and potential impurities. One can do a thorough research of the literature and

calculate the perfect temperature, maybe introduce several annealing steps. One can consider

the environment in which the reaction takes place: under a sealed ampule, under an inert gas

flow, in an open furnace exposed to air. Maybe the best option is to quench the material at high

temperatures, “freezing” a phase in place to avoid a phase change upon cooling. One could

increase or decrease certain precursor concentrations to push metals into the correct site or drive

27



out impurities. In reality, when executed properly, a solid-state reaction can be one of the most

intricate, rational, and controllable synthetic approaches to choose from.

2.1.1.1 Solid-state part 1 - orthophosphate synthesis

Solid-state synthesis was used in both the phosphates and thiophosphates synthetic procedures;

both will be reviewed here. First, solid-state reactions were used to synthesize polycrystalline

powders of LiMPO4 and LiMM’PO4 where M/M’ = Fe, Mn, and Co. This synthesis is inspired

by the work done by Baker [104] and Kellerman [105] on similar phosphates; but several changes

have been made to optimize the synthetic procedure. To synthesize these materials, ammonium

phosphate (NH4H2PO4) is used as the phosphate source, lithium carbonate (Li2CO3) is used as

the lithium source, and metal oxalates (MC2O4·2H2O) or metal carbonates (MCO3) are used as

the transition metal sources.

The first step of this synthesis (after measuring respective stoichiometric ratios) is to mix

the ammonium phosphate with the lithium carbonate. A small amount of ethanol is added to the

mortar and pestle to mix these two reagents into a paste, the ethanol helps the reagents mix and

form a homogeneous mixture. Any excess liquid ethanol must evaporate before the next step.

Once it is a damp paste, the metal oxalates or carbonates are added to the mixture and ground

until homogeneous. The final color completely depends on the content of the metal oxalates

added: iron is yellow, cobalt is pink/purple, and manganese is a faint pink. These powders are

then packed in alumina boat crucibles.

The boat crucibles are then loaded into a quartz tube furnace where an argon gas flow is

introduced. Small cylindrical crucibles are placed on either side to improve gas circulation and

28



a) b)

Argon

Figure 2.1: Solid-state set up for the LiMPO4 phosphates. a) Before the samples are heated. It
is clear that this reaction is synthesizing an iron based compound because the powder is yellow.
The small cylindrical crucibles help introduce a consistent air flow. b) After the heating profile is
complete, the final color of the powder is grey.

reduce the temperature gradient of the furnace. An example of this can be seen in Figure 2.1a.

This method significantly helped remove visible metal oxide impurities that were forming on the

edges of the samples where the temperature was slightly lower than desired. This method may

not be needed for a new furnace, but can help with older furnace designs where the temperature

gradient is larger. The samples are heated to a low temperature (250 ◦C) overnight before heating

to the optimal reaction temperature at 750 ◦C for 3 hours. This reaction forms several by-products

[106], many of which are gas phase and are removed by the argon flow during the low temperature

heating. This reduces the amount of intermediates formed when the high temperature is used to

form the main phase. The final product is a dark grey polycrystalline powder that can be ground

up and characterized. When cobalt is used, there is generally a purple tint to the final powder

color.

2.1.1.2 Solid-state part 2 - thiophosphate synthesis

The first step of the solid-state synthesis of the Li2MP2S6 where M = Fe, Co thiophosphates

is to synthesize one of the starting reagents, Li2S. This synthesis is a complicated liquid ammonia

29



reaction described in detail in the next section. The entire solid-state synthesis process of the

thiophosphate compounds is conducted under an inert atmosphere. The samples are prepped

in an argon filled “dry” glovebox where Li2S, phosphorus pentasulfide (P2S5), and the metal

powder of choice are added to a mortar and pestle and ground together. This mixture is then

placed inside of a graphite crucible with a lid that is then carefully placed inside of a quartz tube.

This quartz tube is fastened to an adapter to maintain an inert atmosphere where it is moved out

of the glovebox, placed under vacuum, and then flame-sealed. The final set up can be seen in

Figure 2.2.

Figure 2.2: Solid-state set up for the Li2MP2S6 thiophosphates. The sample is inside of the
graphite crucible that is then vacuum sealed inside of a quartz ampule before starting the reaction
in the furnace.

The reason that an inert atmosphere is so critical in this synthesis is two-fold. First, there is

a safety hazard; Li2S and P2S5 both degrade upon exposure to moisture in the air. These materials

release toxic H2S gas that smells very strongly of sulfur and rotten eggs. Secondly, when these

30



materials degrade, there are countless impurities introduced and the main phase can no longer

form. The main phase itself is also air-sensitive, making the sealed crucible a necessity. The final

steps are fairly straightforward, the ampule is placed vertically in a furnace where it is heated

to 700 ◦C for 3 hours. The ampule can then naturally cool to room temperature where the final

product is a black polycrystalline powder that is recovered in a glovebox.

While there are some key differences between the phosphate and thiophosphate syntheses,

the overall steps that make up a solid-state synthesis are the same. The precursor solids are

combined together to form a homogeneous mixture. The mixture is then placed inside of a

crucible where it is heated to a desired temperature where every reagent will melt and interact

to form the desired phase. Solid-state methods proved to be extremely useful in achieving all

synthetic goals presented here.

2.1.2 Alkali metal chalcogenides in liquid ammonia

The synthesis of Li2S, needed as a precursor in the solid-state reaction above, can be

described in a more general way as synthesizing any alkali metal chalcogenide of the formula

A2X where A = Li or Na and X = S or Se. Other alkali metals can be used but as the metal

increases in ionic radii, the reaction becomes more aggressive and dangerous. Even with lithium

and sodium, this reaction must be approached with great care. Liquid ammonia is a toxic gas that

will create a hazardous flammable liquid once mixed with the alkali metal. And as mentioned

earlier, the final product will be Li2S (or Na2S) which will release H2S, another toxic gas upon

air exposure. There are also other standard operating procedures utilized to synthesize alkali

metal chalcogenides in liquid ammonia, we found the Youtube video entitled “The Bulk Synthesis

31



of Alkali Metal Chalcogenides in Liquid Ammonia” from Dr. Kanatzidis the most helpful for

inspiration.[107]

To begin this synthesis, it is helpful to set up what we refer to as a “dummy flask”. This

is a round bottom flask that has no contents; it is connected to the Schlenk line set up shown in

Figure 2.3 in place of the reaction flask. The dummy flask will then be purged (by connection

#2) along with the rest of the line, it is helpful to create an inert atmosphere before the reaction

even begins. Make sure that connection #1 is open (and the ammonia tank is closed) so that the

line going to the ammonia tank is purged as well; if this is not done, as the ammonia is added, all

of the O2 in the ammonia line will flow over the lithium, oxidizing the surface.

The full Schlenk line and glassware set up can be seen in Figure 2.3. In this reaction, a cold

finger is used with two barbed connectors, one on the top and one on the bottom; and then at the

very bottom is a round bottom flask male connector. The top is hooked up to special toxic gas

tubing which runs to the ammonia gas tank; it is good to have a stopcock here (if the cold finger

doesn’t already have one), it is denoted connection #1 for clarity. The bottom barbed connector

is hooked up to the Schlenk line where argon flow or vacuum can be initiated (connection #2).

Finally, in order to condense the ammonia gas, a dry ice - acetone bath is used. The cold finger

is filled with dry ice and acetone, and then there is a dry ice - acetone bath for the reaction flask.

Both are critical for a successful reaction. The ammonia gas begins to condense at -33.6 ◦C and

the dry ice-acetone bath is about -78 ◦C. It is important to keep the reaction flask as submerged

into the bath as possible to facilitate a thorough reaction, if the temperature is not low enough,

the ammonia gas will evaporate.

Once the entire set up is complete and the dummy flask is purged and ready for the transfer,

the next step is to measure out the desired alkali metal in the glovebox and put inside of a 3-neck

32



NH4 (g)

Argon

#1

#2

Dry ice
Acetone

Condensed NH4

Li + S

Argon

Vacuum

Cold 
Finger

#3

Figure 2.3: Air-free cold finger set up to synthesize alkali metal chalcogenides, specifically
Li2S. Each connection is designated and labeled to help facilitate the in-text description of the
experiment.

round bottom flask with a glass stir-bar, two glass stoppers, and one stopper with a stopcock

(connection #3). The glass stir-bar is important because liquid ammonia will react with the

common plastic stir bars. This flask is then brought to the Schlenk line where positive argon

pressure is initiated from #2 to prepare for the flask swap. The dummy flask is then swiftly

removed, the reaction flask takes it’s place, and then the vacuum from #2 is initiated. A hose is

attached to connection #3 and then another purging cycle is started. The ammonia line should be

33



back-filled with argon so #1 can be closed here to save time. If this is done correctly, minimal

exposure to air will be introduced. The final set up can be seen in Figure 2.4a; note, this is an old

cold finger that is missing connection #2.

Figure 2.4: a) Alkali metal chalcogenides experiment set-up; this reaction is forming Li2S using
liquid ammonia to facilitate the reaction. b) final product in round bottom flask and then c) the
final product after it is recovered and ground into a powder. Note: this is an old cold finger and
does not have connection #2 from Figure 2.3.

At this time, the reaction flask should be submerged into the dry ice-acetone bath and the

cold finger should already be full of dry ice and acetone. Make sure that the bowl is thin enough

so that the stir plate can still turn the stir bar properly. Now, it is time to introduce the ammonia

gas. NOTE: sulfur powder has not been added yet! This should be measured and ready to go but

not in the reaction flask. Connection #2 should be completely off and argon should be initiated

from #3; this creates a back flow of argon to insure that the toxic ammonia gas does not escape the

set up. After this, the ammonia gas can be turned on at the tank; it will slowly begin to condense

34



where it will run down the cold finger tip and drip onto the lithium.

As the ammonia begins to react with the lithium, the stir plate should be turned on to

facilitate the reaction. A blue solution should form from the solvated electrons introduced by

the lithium and ammonia reacting. The amount of ammonia is always approximate, because it is

nearly impossible to measure the condensed liquid to a precise volume; we estimate approximately

20-30 mL of ammonia is collected. Once it appears that all of the lithium is dissolved, The

ammonia tank and connection #1 are closed off. This will start a reflux where any evaporated

ammonia gas will re-condense back into the solution.

At this point, the glass stopper on the reaction flask is removed (ensuring there is still

positive argon flow coming from #3) and the sulfur is added via funnel to the reaction. It is

absolutely critical to only add sulfur in 0.5 g increments approximately 5 seconds apart, this is

likely the most dangerous step of the reaction. Adding all of the sulfur at once can create a

vigorous reaction that can shoot *flammable toxic liquid* out of the flask. Once the sulfur is

added, the reaction has officially begun and is allowed to reflux for 1 hour.

After the reflux is complete, the dry ice-acetone bath is removed and the ammonia evaporates.

Make sure all sashes are closed throughout this experiment when not directly supervising the

reaction. The evaporation of the ammonia can take several hours, the final flask should look

something like what is shown in Figure 2.4b. After there is clearly no liquid remaining and

the ammonia is evaporated, the reaction flask is removed (while ensuring that connection #3 is

applying positive pressure) and a glass stopper is inserted. Connection #3 is then shut off before

the hose is removed and the flask is moved to a glove box anti-chamber where it is evacuated

for several hours or overnight. The powder is then recovered from the flask, it should be a white

crystalline Li2S powder (Figure 2.4). If there is a lot of yellow in the final product, this is likely

35



unreacted sulfur that formed S8.

Each step mentioned above is specifically designed for minimal to no exposure to oxygen

in the air. This is to prevent any safety hazards as well as to facilitate a successful reaction with

no oxidation. This reaction can be modified to other alkali metal chalcogenides with only minor

changes.

2.1.3 Lithium chloride flux single crystal growth

Powders are useful for many characterization techniques, but often times single crystals

are needed to understand additional structural and magnetic properties that cannot be understood

with powders. There were many techniques used to grow single crystals in this work, only two

of which will be discussed here. Growing single crystals is often not trivial and can require many

attempts before success is achieved. The two method’s described here will be a LiCl flux growth

and a Bridgman-like growth.

Many types of salts, such as lithium chloride, can be used in a flux growth. The main reason

for a flux is it has a lower melting point (605 ◦C for lithium chloride) than the main phase that

is being synthesized. This means that it will create a liquid flux around the main phase that is

still a solid. This liquid-solid mixture is then generally heated past the melting point of the solid

where it becomes a solution. The solution is then slowly cooled, allowing the main phase to form

nucleation sites on the side of the crucible. At this point the flux is still a liquid; the main phase

will continue to grow on the site of nucleation until a large single crystal is grown. When the

temperature decreases past the melting point of the flux, the salt will begin to undergo a phase

change back into a solid and the reaction can be cooled to room temperature.

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The lithium chloride (LiCl) flux growth was used to grow large single crystals (2-6 mm)

of the transition metal orthophosphates. The final crystals of the iron-manganese series can be

seen in Figure 3.2 and examples of the iron-cobalt and cobalt-manganese series can be seen in

Figure 4.2. The synthesis starts by using the polycrystalline powder that was synthesized using

the solid-state methods mentioned above. This powder is ground together with the LiCl flux in

a 1:2 molar ratio for the iron-manganese powders and a 1:3 ratio for the materials with cobalt.

The powder mixture is then placed inside of a graphite ingot (Figure 2.5) with a lid. This ingot

proved to be the most successful crucible to grow single crystals, given it’s large surface area and

room for many nucleation sites. The alternative is a small cylindrical graphite crucible that can

only hold a small amount of powder. This small crucible is useful when testing many conditions

and not wanting to use large amounts of reagents.

3.5 inches

Figure 2.5: Graphite ingot used for orthophosphate crystal growth with a LiCl flux. The small
cylindrical graphite crucible can be used for experimental synthesis where large quantities of
powder are not available.

The ingot is then placed in a tube furnace under argon flow where it is heated to 250 ◦C and

held for two hours. This stage removes any moisture that the hygroscopic lithium chloride salt

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absorbed from the air. The temperature is then heated to 800 ◦C where it is then cooled at 5 ◦C/hr

to 520 ◦C. This slow cool allows the crystals to slowly form while the flux is still in the liquid

phase. After a natural cool to room temperature, the products can be soaked in water because

the salt will dissolve in water while the crystals will remain unaffected. The single crystals

can then be picked and cleaned for further analysis. This method has proven to be successful

in synthesizing many different lithium transition metal orthophosphate single crystals and need

only be slightly modified upon transition metal changes, solid solutions, etc.

2.1.4 Bridgman-like single crystal growth

The second major method used to grow single crystals is what is known as a Bridgman-like

growth. This was used to synthesize the single crystals of Li2MP2S6 where M = Fe, Co. Similar

to the phosphates, the solid-state reaction products were used as the precursor for the crystal

growth. The powders were flame-sealed in a quartz ampule with no additional reagents inside.

It is recommended to use a double sealed ampule, especially when experimenting with different

temperatures.

The most difficult part of this technique is finding the optimal temperature and cooling

rate for the synthesis. When working with sealed ampules, it is important to look up the boiling

point of the reagents to reduce risk of pressure build up. For example, when working with sulfur

compounds in particular, when the samples are heated up too quickly, the mixture will not melt

congruently, causing the sulfur to create gas and build pressure and eventually burst the ampule.

Ramp rate up, target temperature, and ramp rate down should all be considered and experimented

with when designing a crystal growth heating profile.

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a) b)

 

10 mm 

c)

Figure 2.6: Single crystals of Li2MP2S6 where M = Fe, Co. a) bulk crystal coming straight from
the ampule and then b) cleaved crystals separated from the bulk. c) Several hundred Li2CoP2S6

single crystals aligned for a single crystal neutron experiment.

Once the sample is sealed inside of the ampule, it is then propped vertically inside of the

furnace where it is heated at 100 ◦C/hr to 1,000 ◦C for iron and 900 ◦C for cobalt. The sample

dwells at this temperature for a couple of hours to ensure a thorough melting of the phase. The

ampules are then slowly cooled at 5 ◦C/hr to 620 ◦C for iron and 600 ◦C for cobalt. This slow

cooling facilitates a similar type of crystal growth as in the flux method. Instead of using a

flux, these materials will begin to crystallize slowly on their own, creating a repeating layered

structure. One might refer to this type of crystal growth as a self flux. The resultant crystals are

thin, layered, metallic-like crystals that are up to 4 mm x 4 mm in size. They grow stacked along

one another and can easily be cleaved into layers. This synthesis is an excellent example as to

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when complex techniques are step-wise crystal growth methods may not be needed.

2.1.5 Deintercalating lithium via oxidizing peracetic acid solution

The final synthetic method that will be discussed here is the removal of lithium from the

LiMPO4 materials via peracetic acid oxidizing solution. There are many ways in which a cation

like Li+ can be removed from a layered lattice, but most of these methods can be put into one

of two categories: electrochemical delithiation or chemical delithiation. Electrochemistry can be

one of the most effective and efficient ways to remove and then re-intercalate lithium by using

an oxidizing anode and then a reducing cathode. Another way to remove lithium is via chemical

delithiation, which is what will be explored here.

As an example, the delithiation of LiFe(II)PO4 will be explained here. In chemical delithiation,

the sample in question is introduced to an oxidizing solution which is generally an acid. The acid

becomes a conjugate base upon insertion into the solution where there is now a free proton.

This proton will be reduced to hydrogen gas as it removes an electron from the Fe2+ site, thereby

oxidizing it to Fe3+; this kicks the lithium out of the lattice as Li+. The final product is Fe(III)PO4

and can be filtered out via gravity or vacuum filtration.

The oxidizing agent used in the reaction varies depending on the cation being deintercalated

and the transition metal in the main phase. Hydrochloric acid [108], Na2S2O8 [109], oxalic acid

(C2H2O4) [110], and NO2BF4 [111] have all been used as oxidizers in lithium-deintercalation.

This work uses a peracetic acid (CH3CO3H) solution which is a mixture of acetic acid (CH3COOH)

and hydrogen peroxide (H2O2) as the oxidizing solution. This solution is easily obtained and

prepared, making it an attractive candidate for our purposes.

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A 14% peracetic acid solution is prepared from water, acetic acid, and 30% hydrogen

peroxide. It is important to not exceed 40% peracetic acid concentration as it becomes an

explosive hazard, increasing the potential for detonation at 56%. The fully lithiated orthophosphate

powder is soaked in the 14% solution with constant stirring. Sometimes, heat (no more than 50

◦C) is needed to facilitate the removal of the lithium. This reaction is allowed to proceed for

around 3 hours. While the exact reaction time is not critical, it is important to not exceed 24

hrs as the lattice will begin to loose crystallinity and begin to degrade. Generally, the final color

of the powder will change; in the case of LiFePO4, it will turn from a dark grey powder to a

red-orange color.

2.2 Characterization Techniques

Once the desired material is synthesized in powder or single crystal form, the next step is

characterization. There are an endless amount of characterization techniques in materials science:

structural and magnetic property measurements, theoretical calculations, phase separation techniques,

elemental composition analysis, and so much more. These characterization techniques can be as

simple as something done on a bench top in the lab or visiting a neighboring lab from another

department. More complex, extensive analyses may require travel to another university or a

national laboratory. Examples of all of these types of techniques will be given below. While the

methods presented here are not an exhaustive list, they are the primary characterization techniques

used in this work. If more details are desired than what is presented, resources will be listed for

each technique for further inquiry.

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2.2.1 X-ray powder diffraction

X-ray diffraction techniques are ultimately the backbone of the work conducted here and

in many solid-state materials chemistry laboratories. Diffraction data provides a vast amount

of information on the crystal lattice of a material. With simply a small amount of synthesized

powder and x-ray diffraction data, structural information, grain sizes, compositions, impurity

concentration, phase analysis, lattice shifts, and so much more can be determined. It is important

to understand a brief theory of diffraction, to be able to comprehend the wide range of utilities

that it provides.

X-ray diffraction is useless without a crystalline lattice to diffract upon. A unit cell of

a material is the smallest repeating three-dimensional arrangement of atoms within a crystal

structure. A crystalline lattice is then comprised of many of these repeating unit cells. Any

atomic position can then be defined by a set of three coordinates along the x, y, and z axis. The

unit cells uses a, b, and c to define these dimensions. For example, to locate an atom at (1/2, 0,

1/2), one must start at the origin (0,0,0) and then go 1/2 of the unit cell along a, stay stationary

along b, and then go 1/2 of the unit cell along c. This will locate the atom’s position. One can

even use the unit cell dimensions to find distance between two atoms or calculate bond angles.

While this is often automated with today’s technology and software, it is still a useful skill to

understand.

The planes of the atoms are also essential to understand. The reciprocal values of the x,

y, and z coordinates of the intersections are calculated and then converted to integers h, k, and

l.[112] These hkl triplets are referred to as Miller indices and are used to reference a plane of the

material. For example, if a plane intersects the x axis at 1/2a, the y axis at 1/2b, and the z axis at

42



(100) (010)

(110) (111)

Figure 2.7: Four different Miller indices represented in LiFePO4. Each hkl value is displayed
below the unit cell with the plane shown in blue.

2c, the reciprocal positions are (2,2,1/2). These then need to be all integer values so everything

is multiplied by 2 to get (4,4,1). Examples of miller indices in the LiFePO4 lattice can be seen

in Figure 2.7. Four different planes are represented and identified by a blue plane, indicating th