LOCAL ATOMIC ARRANGEMENTS 
AND SOLUTION STRENGTHENING 
OF Ta-Mo AND Ta-Nb ALLOYS 
by 
Roamer Edward Predmore 
I I I 
Dissertation submitted to the Faculty of the Graduate School 
of the University of Maryland in partial fulfillment 
of the requirements for the degree of 
Doctor of Philosophy, 1975 
( 
APPROVAL SHEET 
ANO 
Title of Thesis: Local Atomic Arrangements HeBpen:Biale,.49y 1;1,e Solution 
Strengthening of Ta-Mo and Ta-Nb Alloys 
Nam e of Candidate : Roamer Edward Predmore 
Doctor of Ph!losophy, 1975 
Thesi s and Abstract Approved: ....6. ..__./L? -~--'----E_.J_- _  ,_ __________ _ 
Richard J. Arsenault 
Professor of Engineering Materials 
Engineering Materials Group, and 
Department of Chemical Engineering 
Date Approved, ffe/:hr  
ABSTRACT 
ngthening 
tle of Dissertat1?on?. Local Atomic Arrange
ments and Solution Stre
Ti
of Ta-Mo and Ta-Nb Al
loys 
octor of Philosophy, 197
5. 
mer Edward Predmore,
 D
Roa
J. Arsenault 
Dissertation directed by
: Richard 
Professor 
dom solid solutions by x
-ray diffuse 
Nb alloys are shown to 
form ran
Ta-
e atoms in their pure 
scatte ? g measurements. Thes
e a lloys have equal siz
rm
?t? o b ey V egard ' s 
st h  m? van?a nt  m?  compos1 
10n, 
ate With latt?i ce parameters t at ar
e
nce of frac-
bsence of solid solution
 hardening and an abse
Law' and exhibit an a
about 5% 
ture emb ? t high solute concentrati
ons. Ta-Mo atoms of 
nttlement a
arge 
form short range ordere
d solid solutions with l
fference in atomic size di
nd Ta- W, Nb-Mo and N
b-W alloys 
atomic displacement eff
ects. The Ta-Mo, a
that varies in compositi
on with a negative 
have in common a lattic
e parameter 
e heat of mixing which i
s 
deVi t? also a nega
tiv
a ion from Vegard's Law
. There is 
ddition, all these alloys 
show linear 
ge order. In a
Well correlated with sho
rt ran
erature and 
ing to high solute conce
ntrations at room temp
Solid solution harden
? 
ions. Diffuse x-ray sca
ttering 
fractur . embrittlement at high s
olute concentrat
e 
parameters and 
s ts on Ta-Mo alloys give
 the short range order 
:tnea uremen
o a combination of size 
e displacements. The h
ardening is attributed t
atomic siz . 
.  and short range order r
n-
effect 1? nd uced substitutional solid
 solution hardenmg
ducect harde m. ng. 
ACKNOWLEDGMENTS 
The author wishes to express his deep appreciation to Professor R. J. 
Arsenault who suggested the problem and provided guidance and continued en-
couragement throughout the extended period of this work. Special thanks to 
Dr. C. J. Sparks, Jr., of Oak Ridge National Laboratory for his encourage-
ment, discussions and assistance with the diffuse x-ray data analysis. 
Thanks are given to Professor L. Skolnick for providing the x-ray equip-
ment, to Dr. H. A. Beale for aligning and setting up the x-ray equipment, 
Dr. Beale again and Dr. G. C. Das, M.I. T., for zone meeting the alloy crys-
tals and Dr. R. D. Deslottes, N. B. S., for the Si single crystal. I wish to thank 
Mr. L. Kobren, Goddard Space Flight Center, for the electron probe micro-
analysis of the alloy and Miss J. Jellison, Goddard, for the SEM fractographs. 
Thanks are given to Dr. J. E. Epperson, Professor R. W. Armstrong and 
Professor M. J. Marcinkowski for many helpful discussions. I wish to thank 
Mrs. Kay Alexander for typing the dissertation . . 
This author gratefully acknowledges the support of Dr. H. E. Frankel, 
Professor H. W. Price and Mr. C. L. Staugaitis of Goddard. This research 
was sponsored by the Advanced Research Projects Agency and Administered 
through the Center of Materials Research at the University. 
Finally the author wishes to express his appreciation to his wife, Renetta, 
for her never ending devotion and encouragement. 
ii 
TABLE OF CONTENTS - Continued 
TABLE OF CONTENTS 
Chapter Page 
Chapter Page 
G. Atomic Displacement Effect for Mo- Ta Alloys . . . . . 28 
AC KNO\VLEDGMENTS ii 
H. Substitutional Solid Solution Hardening and Short 
LIST OF TABLES V Range Order Har dening ? ? ? ? ? ? ? . . . . . 33 
LIST OF FIGURES vi I. Suggesti ons for F uture Research 35 
I. BACKGROUND 1 
V. CONCLUSIONS . . . 
A. Introduction 1 REFERENCES ? ? ? ? . ? ? . ? ? ? ? ? ? ? ? ? ? ? ? 66 
B. Lattice Par ameter 1 
LIST OF SYMBOLS ?. ?? ? ? ? . . . . 71 
C. Substitutional Solid Solution Har dening 2 
D. Ther modynamic Properties 5 
II. EXPERIMENTAL PROCEDURE 6 
A. Zone Melting and Cr yst al Gr owth 6 
B. Sampl e P r eparation 7 
C. X-Ray Diffraction Techniques 9 
ID. X-RAY DIFFRACTION THE ORY 14 
IV. EXPERIMENTAL RESUL T S AND DISCUSSIONS 19 
A. Microscopic Fra ctur e Processes 19 
B. Lattice P arameter of Ta- Mo Alloys 21 
C. Diffracted Intensity from Ta -Mo Alloys Along the 
h 1 ,00 Axis . . . . . . . . . . . . . . . . . . . . . 21 
D. Diffuse X-Ray Scattering from the h 1 h 2 0 Plane of 
Reciprocal Space from Ta, Mo and Ta-Nb Alloy 22 
E ? Scattering from the h1 h2 O Plane of Reciprocal Space 
from Ta- Mo Alloys . . . . ? ? ? ? ? ? ? ? ? 24 
F ? Short Range Orde r in the Mo-37 at . % Ta and 
Mo- 21 at . % Ta . . ? ? ? ? ? ? ? ? ? ? ? - 26 
iii i v 
LIST OF FIGURES 
LIST OF TABLES 
Figure Page 
Table Page 
1 BCC Substitution Solid Solution Hardening of Ta and 
I. Zone Melting and Crys tal Gr owth Conditions 4 0 Nb at 300 K ......?.......... 49 
II. Diffuse X-Ray Mea surem ent Conditions 43 2 DPH Hardness of Binary Refractory Alloys at 300 K 50 
III. Two Dimensional Short-Range Order Parame ters A 3 DPH Hardness of Binary Refractory Alloys at 300 K 51 
For t h e Mo-21 and Mo-37 at . % Ta Alloys . . . .
Q m.  44 
4 Schematic Representation of the Diffuse Scattering 
IV. Atomic Displacem ent Coeffi c ients rm For Geometry 52 Qm 
Mo-37 at . % Ta . . . . . . . . 45 
5 Geometry of the Three-Circle Single- Crystal 
V. Atomic Displacem ent Coefficie nts rm For Diffractometer . . . . . . . . . . . . ? 53 
Qm 
Mo-21 at . % Ta . . . . . . . . 46 
6 The Method of Scanning the Elementary Volume 54 
VI. Observed and Calculated Short-Range Orde r Parame te r s 
AQm for the Mo-21 and Mo-37 at . % Ta Alloys . . . . 47 7 Fractographs of Refractory Binary Alloys at 300 K 55 
VII. Elastic Strain Te rms L 111 De rived from X- Ray Mea sure- 8 L attice Parameters of Ta-Mo Alloys. Straight line is 
ments of Atomic Displacem ents Compared to Thos e a plot of Vegard' s Law 56 
Calculated from Lattice Constants Assuming Hard 
Spheres . . . . . . . . . . . . . . . . . . . . . . . . . 4 8 9 Diffracted Intensity Along (h , 0, 0) Axis in Reciprocal 1 
Space for Ta-Mo Alloys, Illustrating Asymetry of the 
Short Range Order Peaks about (100) and (300) 
Positions 57 
Diffra cted X-Ray Intensity Distribution in the h h 2 0 Plane 1 
of Reciprocal Space for Mo at Ambient Temperature. 
Counts per 30 sec . . . . . . . . . . . . . . ? ? 58 
11 Diffracted X - Ray Intensity Distribution in the h h 0 Plane 1 2
of Reciprocal Space for Ta at Ambient Temperature. 
Counts per 30 sec . . . . . . . . . . . . . . 59 
12 Diffracted X-Ray Distribution in the h h 0 Plane of 1 2
Reciprocal Space for Nb-22% Ta at Ambient 
Temperature. X-Ray Intensity in Counts 
per 30 sec . . . . . . . . . . . . . . . . ? ? ? 60 
13 Diffracted X-Ray Intensity Distribution in the h h 2 0 Plane of 1
Reciprocal Space for Mo-91% Ta at Ambient Temperature. 
X-Ray Intensity in Counts per 30 sec . . . . . . . . . . 61 
vi 
V 
LIST OF FIGURES - Continued CHAPTER I 
Figure BACKGROUND 
Page 
14 Diff~se Intensity Distribution in the h h O Plane of A. Introduction 
Reciprocal Space for Mo-37% Ta at A1iu6ient 
Temperature. Diffuse X-Ray Intensity in Binary refractory alloys of Nb, Mo, Ta and W form a continuous series of 
Counts per 60 sec . . . ........ 62 
BCC solid solutions. These binary solid solutions exhibit two types of mechan-
15 
RD iff.u se Intensity Distribution in the h h Pl 1 2 O ane o f 
ec1procal Space for Mo-21 a/o Ta at Ambient ical propertie s; alloys of elements with essentially the same atomic size in the 
Temperature. Diffuse X-Ray Intensity in 
Counts per 60 sec . . . . . . . . . . pure st6 a3 t e (0. 0lA or about 0. 3% difference), Ta-Nb and Mo-W, show almost no 
16 Model for the Short Range Ordered structure of Mo-37 substitutional solid solution hardening; whereas the pairs of elements Nb-Mo, 
at. % Ta . . . . . . . . . . . . . . . . . . . 64 
Nb-W, Ta-Mo and Ta-W have about a 5% difference in atomic size and exhibit 
17 Model for the Short Range Ordered Structure of Mo-21 
at ? % Ta . ? . ? ? ? ? ? . . . . . . . . . . . . . 65 substitutional solid solution hardening. The purpose of this investigation was 
to measure the local-order and displacements of atoms in binary alloys of each 
type us ing the diffuse x-ray scattering technique of Cowley, (l) and Warren, 
Averbach and Roberts<2) and to relate this local atomic structure to the ob-
served mechanical properties. 
B. Lattice Parameter 
The Ta-Nb and Mo-W alloys have very small differences in their atomic 
s ize , whereas the other binary combinations have about a 5% atomic size dif-
ference. The lattice parameter of the alloys of Ta-Nb and Mo-Ware found 
invariant with composition in agreement with Vegard's Law when measured 
by Williams and Pechin(3) and Buckle, (4) respectively. However, the binary 
alloys form ed from atoms of different sizes, Ta- Mo, Ta-W, Nb-Mo and Nb-W, 
were found to have a negative deviation from Vegard's Law(5, 6, 7 , 8 , 9) which 
indicates a preference for unlike nearest neighbors . 
vii 1 
3 
2 
C. Subs titutional Solid Solution Hardening The absence of substituti onal solid solution hardening at ambient tempera-
12
The s olute addition can affect both the thermal component of the yield s tress ture wa s observed fo r Nb-Ta . (lO, ) The linea r substitutional solid solution 
ha rdening was obser ved for Nb-W, (l9) for Nb-Mo(ll, 20) and for Ta-W. (21 ? 22) 
(effective s tress r *) and the athermal component (temperature independent s tre s s 
r?) in BCC alloys of different sized a toms. (10, 11, 12, 13, 14) The temperature The above obse rvations were made on tantalum or niobium rich alloys because of 
at which r* i s ze r o is defined as Tc . Above Tc the yield of flow s tress cons i s ts their room temperature ductility. F igure 1 shows the linear solution hardening for 
of the temper ature independent component r ?. Tc i s s lightly above ambient the Ta and Nb rich a lloys a t 300 K. The Ta-Nb alloys with the same atomic size 
t emperature for these alloys . (lO) Though room temperature measurements a r e s how no substitutional solid solution hardening. The alloys with about 5% difference 
s lightly bel ow the plateau tempera ture determine d by Rudolph and Mordike (l0) in atomic size, Ta-Mo, Ta-W and Nb-Mo, show the same linear solution hardening 
and others<11 , 12) on these BCC alloys, their da t a show that the change in the (Fig. 1). Small change s in the slope of the linear solution hardening data as re-
shear stress for varying compositions of the sam e alloying ele m ents is almost ported in the literature can be caused by either varying interstitual concentrations, 
temperature insens itive above 300?C. The change in ou r hardness measurem ents diffe r ences between compression and tensile testing or crystal orientation. The 
made at room temperature are predominantly sensitive to the solid solution hard- obse rvation of an absence of hardening in Ta-Nb and Mo-W alloys composed of 
ening components of the a thermal s tress. Our m easurements extend the com- a toms of the same atomic size but diffe rent shear moduli and the lar ge solution 
positions m ea sured by the previous authors to cover the entire compositional ha rdening in alloys with about 5% a tomic size diffe rence indica tes that atomic size 
range . effe ct and / or short range order m ay be the more predominant cause of hardening. 
An earlie r work(lO) on T a-Nb was inte rpret ed as s howing that the lack of The inherent brittle fracture characteristics of Mo rich and W rich binary 
s trengthening and of s ize diffe r ence in the pure s tate fo r Ta and Nb, even though alloys make it ve ry difficult to perform tensile or compressions tests to measure 
their elastic moduli diffe r ed by 11 x 10 6 psi, precluded an interpretation that s olid solution hardening. Thus diamond pyramid hardness te sts were utilized 
solution strengthening was mos tly dependenton their shear moduli. This whe r e yield strength data was not available. The diamond pyramid hardness 
conclusion has also been r eached by othe rs(l0, 11, 12, 13, 14, 15) and differs with va lues for the binary alloys at ambient temperature are plotted in Figures 2 and 
the FCC solution strengthening interpre tation put forth by Fleischer(16) and the 3. The DPH values measured by the authors we r e obtained using a 100 gram 
BCC solution strengthening interpretation put forth by Suzuki(17) and Boser(18) load. The Mo-W hardness values fit the same hardness curve . (23 , 24 ) The 
which are predominantly based on the modulus difference. hardness values for the Nb-Ta alloys fit on a line joining Ta and Nb which is 
5 
4 
% T 3 a (2.2 x 10- mm) being about equal to the subgrain diameter of Mo-37 at. 
similar in behavior to the yield strengths. Both the Nb-Ta and Mo-W alloys 
% Ta (3.6 x 10-3 mm). The diamond pyramid micro hardness of the Mo-21 at. 
formed from elements of the same atomic size show little increase in hardness 
% Ta alloy subgrain boundari
u ep so  tn a ka ell no  y win itg h.   a 5 gram load on a Reichert Metallo-
graph showed no evidence of subgrain boundary hardening. Subgrain boundary 
The Mo-Ta hardness values shown in Figure 2 are in good agreement with 
23 hardening discussed by Armstrong
7
( 3) is therefore expected to have only limited 
the other measured values.< ) The DPH hardness variation with solute concen-
influence on the rate of alloy hardening in Ta-Mo alloys. The linear variation of 
tration for Nb-W, Nb-Mo and Ta-W are plotted in Figure 3. The data for arc 
25 DPH with alloy content for Mo-Ta alloys is therefore attributed to solution hard-cast Nb-W alloys are from Braun et al. < ) and show a small increase in hard-
ening plus short range order because the hardness values are the same for arc 
ness above the zone refined Nb-W alloys because of larger interstitial concen-
cast alloys as zone melted alloys, the sub grain size is about the
t  r sa at mion e.   foT rh  te h eT  a-W hardness values were reported by Meyers,<24) Westgren et 
26 27 Mo rich alloys and the DPH to critical resolved shear stress ratio agrees a
a pl. -< ) and Kieffer et al.< ) The hardness values agree well and show a relation 
proximately with the expected value. The linear solid solution p
s li um s i sl har o rto t  rt ah ne g N e b-W alloys. The Nb-Mo hardness values in Figure 3 were re-
23 25 order hardening for Mo rich Ta alloys is calculatedp  to or  bte e 1.2 Kg/mm
2 
d by Semchyse un s e int ga  l t.< he ) and Braun et al.< ) The Ta-Mo, Ta-W, Nb-Mo 
ratio of DPH to critical resolved shear stress for Ta rich Mo a
a nn dd   tN heb  - 8W  D B PC HC  p s eu rb  stitutional solid solution alloys with about a 5% atomic size 
atomic percent Ta value. 
difference show a large increase in hardness with solute concentration. When 
the Mo and W atoms are dissolved in the Ta and Nb solid, they produce the same D. Thermodynamic Properties 
linear solution hardening rate of 1. 7 kg/mm 2 per atomic percent solute (Fig. 1) The thermodynamic properties of Ta-Mo, Ta-Wand Nb-Mo alloys at high 
temperature were measured by Singhal and Worrell. (28,29) L t? e heats and a linear hardness increase (Figs. 2, 3) of arge11 D  P nH eg n a u ivm  bers per atomic pe r -
cent solute. of mixing and the negative deviation from Vegard's Law for the lattice parameters 
7 7 normally a
D ssu og cda iale te( d0  ) w a itn hd   sT ha :b :o lr '(  rangh ea  ove r ds eh ro  w wn e rt eh  e o bD sP eH rv ev da .l  ue Ts h eto  pl )  b re im a ab ro yu  t c t ah ur se ee   times 
of the negative heat of mixing 
th ise  
nd 
 afl to trw ib s ut tr ee ds  s p ro if m p ao rl iy lc yr  y tos  t ea ll eli cn te r oa nl il co  y is n. t erT ah ce t if ol no  w a stress is normally 2.5 times 
s ize interaction t
t oh  e a  y lii mel id t es dt r  ee xss te. ntT . he T hy eie sl ed   is nt tr ee rs as c ti is o ntw s i cc ae n nth oe t  bc er  i sti ec pa al r are tes do .l  ve Td h es  hear stress for 
negative excess en
a t rc or py is et sa  l o o f r mie in xt ia nt gio  wn efa rec  t uo sr eo df   tt ow  o c. a lcT uh lu ats e t  h se h oD rtP  H ra nv gal eu  oe ri ds e e r xpected to be about 
parameters of -0.23, -0.20 and -0.14 for Ta-M t< ,h? ., -a Mn o 1 . th 15 times the critical resolved shear stress. For tantalum d t  h Te a -r Wat  i ro e so pf eh ca tir vd en  e Ys  us smg e 
(77) 
to critical resolved shear stress is 25 at 300K. Usin qg u t ah se i -r ca hn eg me io cf a p l r to hp eo or rt yi  o bn ya  Al verbach. 
limits or critical resolved shear stress values from Arsenault et. al., (72) the 
DPH to critical resolve shear stress range from 11 to 36. The ratio of DPH to 
critical resolved shear s tress for Ta is about the same as Mo and within a factor 
of two of the expected ratio of 15. The subgrain size was found to be independent 
of composition for the Mo rich Ta alloys with the subgrain diameter of Mo-21 at. 
7 
into slots. The grain size increased with slower zone speed but even the mini-
CHAPTER JI 
mum zone speed of 1. 2 mm/ min produced an equiaxed polycrystalline structure. 
EXPERIMENTAL PROCEDURE 
A relatively greater evaporation due to the high vapor pressure of Mo was observed 
A. Zone Melting and Crystal Growth 
for Mo-Ta and Mo-W alloys. Concentrated Nb- W alloys were also polycrystalline 
Alloy single crystals and polycrystals were formed by zone melting. A sum-
at the lowest zone speed of 2. 5 to 3. 5 mm/min. The preferential evaporation of 
mary of the melting conditions and resulting alloys are shown in Table I. The 
Nb was expected but not observed. The Ta-Nb polycrystal and single crystal 
zone meu ?m g apparatus and procedure have been described. (30) The materials 
samples were grown from a slotted Nb rod filled with Ta wires. A preferential 
used to make up rod type charges for the zone melter were 1. 6 mm diameter Ta 
evaporation of Nb was observed. 
wire (99. 9wt ? % or greater Ta) supplied by Fansteel, 9.5 mm diameter arc melted 
B. Sample Preparation 
Nb rods (99. 9wt ? % or greater Nb) supplied by Wah Chang, 9. 5 mm diameter Ta 
The single crystals for diffuse x-ray diffraction samples were identified 
rods (99. 999wt ? % Ta) supplied by Materials Research Corp. and 6. 3 mm diameter 
within the zone melted rods by a series of Polaroid Laue photographs taken nor-
arc cast Mo rods (99. 97 wt . % Mo) supplied by Climax Molybdenum. The Mo and 
mal to the axis of the rod. A vise featuring rotation about three axes was mounted 
Ta single crystals were grown by passing either one or two molten zone 
on a Norelco x-ray machine to hold the samples in the x-ray beam. The plane 
passes along the rod charge length to purify the Ta and Mo followed by a 
of the vise and the plane of the XR-7 Polaroid Laue Camera were positioned 
zone pass a t mm? 1? mum speed ( 3. 0-3. 5 mm/min) to grow single crystals. The 
normal to the x-ray beam. The zone melted rod and its supporting bar were 
minimum pressure in the zone melter and the minimum zone speed during 
mounted in the vise with their axis normal to the x- ray beam. Laue photographs 
melting are reported in Table I. The Mo rich Ta alloy single and polycrystal 
were taken at each centimeter interval along the length of the zone melted rod 
samples were grown from rod charges. The Mo rods were slotted by ma-
as it was translated normal to the copper x-ray beam. A series of identical 
chining, cleaned in acetone several t1?mes. T a w?i res were then peened into 
Laue patterns of the same orientation enabled the identification of a single crys-
the slots. The Ta-Mo rod charges were welded and degassed at higher zone 
tal. Laue photographs of several zone melted rods produced either r ings or 
speeds than single crystals were grown at minimum zone speeds (2. 7 to 3. 5 mm/ 
spots because of residual surface effects from zone melting. The surface metal 
min) as reported in Table I. The Ta rich Mo alloys were prepared from a Ta 
was removed by a solution of 10 cc. HF, 10 cc. HNO and 30 cc. l actic acid, or 
rod filled with Mo wires. The rods were zone melted to purify and degas the 3 
a solution of 30 cc. HCl, 30 cc. HF and 15 cc. HNO 3 or by electropolishing in samples before single crystals were grown at 3 mm/min. The Mo-W alloys 
1. 90 cc. H SO and 10 cc. HF. The Laue photographic procedure was repeated were melted from a Mo rod containing three 6 mm diameter W wires peened 2 4 
to identify the single crystals. 
6 
9 
8 
The single crys tals in glass fiber filled, AB diallyl phtha
w lae tr ee   suc pu pt lo iu et d  o bf y  th Be u ez ho ln ee r  m use il nt ge  d a  r ho ed as t ef do  r x-ray diffrac-
tion samples. The e ? d 
r marn er of the r od was used for ha rdness samples, piston-cylindrical die under pres sure. The samples were ground by hand using 
fracture samples and el e ctron probe microanalys is. 180-, 240-, 400- and 600-grit SiC abrasive papT eh re s  cs oin vg el re e dc  wry its ht  a wls a ter. The 
were mounted on a 2. 5 cm by 0. 64 cm by 5 cm stee l plate with s m all pieces of samples were polished on a wheel covered with Buehler Miracloth using a slurry 
Plasticine. The steel plate was mounted in the vise for Laue pictures. By re- of 15 g fine alumina, 35 cc. H 2O and 5 cc. of 20 percent chromic acid. DPH 
positioning the s ample on the plate and t aking L aue photographs a t e ach position, measurements were then taken using a 100 gram load. The DPH values are 
the (lOO) or (110) plane was oriented normal to the copper x-ray beam and paral- reported in Figures 1 and 2. The details of metallographic preparation are re-
lel with the edge of the plate . The sample was bonded to the steel plate with ported in DMIC Memorandum 37. (31 ) 
Hysol epoxy adhesive. The plate was mounted on a magnetic chuck and sectioned The samples for electron probe microanalysis were cut from the zone 
in a plane parallel to the edge of the plate with a Micro-matic Pre cision Wafering melted rods and mounted in glass filled diallyl phthalate (2. 54 cm diameter). 
machine using an alumina (XA 1803-P-RR5) cut off wheel supplied by Allison- Each sample was polished on a new sheet of 180-, 240-, 400- and 600-grit SiC 
Campbell. The x-ray samples were then chipped off the steel plate. The (100) or abrasive paper to avoid contamination. The chemical composition was measured 
(110) cut surface of the sample was placed face down in a 3. 2 cm diameter by electron probe microanalysis at five or more points on each sample and cor-
mounting die, surrounded by a 301 stainless steel ring and mounted in glass rected for absorption effects. ( 32) 
filled diallyl phthalate. The stainless steel ring kept the mount flat during The fracture surfaces of Ta, Nb and Ta-Nb alloys were obtained by tensile 
grinding. The sample was wet ground on 240-, 400-, and 600-grit SiC abrasive l oading rod samples in an Instron tensile machine until fracture. The cleavage 
paper. It was mechanically polished with o. 3 micron alumina in a 20% chromic fra cture surfaces were prepared by clamping the zone melted samples in a vise 
acid water solution, 0. 055 micron alumina in a 20% chromic acid and water and impacting them with a hammer. The fracture surfaces were viewed and 
solution then chemically polished in a solution of 10 cc. HF, 10 cc. HNO and 
3 photographed with an Ultrascan scanning electron microscope. 
30 cc. lactic acid to remove the deformed surface metal. Clear, small Laue C. X-Ray Diffraction Techniques 
spots were taken to indicate an absence of deformed surface metal. Both a The x-ray m e asurements were made using CuK radiation m onochromated 
crystal of (100) and (110) orientation was cut for each composition. by diffraction from a double bent LiF crystal similar to Warren, (33) Cowley(l) 
The samples for hardness testing were cut from zone melted alloy rods and Borie and Spa rks. <34) A General Electric XRD-6 x-ray generator and power 
using a metal cut-off wheel and water as a coolant. The samples were m ounted 
supply formed the basis of the instrument used for these measurements . The 
. I 
11 
10 
G. E. CA8-L copper tub . limit of the discriminator was set at 2. 5 volts tn eliminate low energy noise an
e d  was inserted into a table mounted adjt? Jtable horizontal 
tube support. The t the upper limit was set at 7. 5 volts to eliminate the ~ componen
e tm  op fe  tr ha et  u xr -e r ao yf   the water cooled ~ube wa"' controlled with a 2 
G. E. SPG-4 heat exchange 
r . Th 
beam. Diffuse x-ray
e 1. 
 measurements of the Ta and Mo single crystals showed no 
me voltage was stabi .Lized with a G. E . line 
I\ 
voltage regulator. 4 evidence of the CuKa - peak. The signal was then sF ei ng tu  tr oe   a ds ih go iw tas l  rth ae te a mr era ten rg  ement of the x-ray source, the 2 
monochrometer crystal, sample and detector. (Ortec 434). The output from the digital ratemeter was then sent through a print The doubly bent LiF mono-
chrometer CuK radiat? . out control to a 33C Ti eo ln e tw ya ps e  s pu rp ip nl ti ea e rd   ob ry   tE o l ae  Gct .r  Eo .n  i mcs o da en ld  8  A Hl Fl  o sy trs i, p  I cn hc a. rt T reh ce o rder. 
monochrometer crystal was b ased on a design by Warren, (33) a Tn hd e t  h xe - rf aa yb  r ei qc ua it pio mn e nt was aligned following the procedures described ingreat 
techniques of Chipman, <35) Soarks and Borie<36 ) and Schwartz Morrison and detail by Schwartz, Morrison and Cohen<
37) and Gilmore. (38) The x- ray beam 
? 
Cohen. (37) The doubly bent L1. F monochrometer crystal was supported and from the monochrometer passed over the center of rotation of the goniometer 
aligned using an Electrom ? es and  All oys pri. mary beam monochrometer. The and into the detector through a receiving slit of 20 = O. 02?. A glass slide was 
sample was supported by the Electronics and Alloys adjustable flat sample holder placed in the flat sample holder for alignment. With x = 0?, the slide was moved 
in the General Electric Single Crystal Orienter which was in turn mounted on into the x-ray beam utilizing the y motion to intersect half the beam intensity 
the General Electric SPG-2 x-ray spectrogoniometer. The diffracted x-ray (Fig. 5). Clockwise and counter clockwise adjustments of thew angle positioned 
beam intensity was measured with an Argon filled proportional counter (G. E. the slide and flat sample holder parallel to the x-ray beam by achieving maxi-
SPG-8) with a low noise preamplifier. The parasitic air scattering was reduced mum intensity. The glass slide was rotated 0 = 180? and the goniometer including 
by introducing 1. 2 cm diameter lead tubes extending from the receiver slits and the flat sample holder were moved along they axis to again obtain half the inci-
from the monochrometer to within 4 cm of the crystal center. In addition a knife dent beam intensity. The glass slide was positioned in the vertical center of the 
edge was mounted 1 mm from the crystal and positioned normal to the crystal beam by the procedure of rotating x by 90?, blocking half the beam at both </J = 0? 
plane and the plane of the incident and diffracted beam. The detector bias and 180? and by adjusting the height of the goniometer and the monochrometer. 
potential (?0. 02%) was provided by a model 312A Baird Atomic Super Stable high The alignment of the equipment was checked by measuring the lattice param-
voltage power supply. The Argon detector preamplifier (Ortec 109PC) utilized eters of a high purity Si single crystal from the National Bureau of Standards as 
a field effect transistor for low noise amplification of the detector signal. The well as zone melted Ta and Mo single crystals. The crystals were placed in the 
amplifier (Ortec 485) was set so the peak of the pulse distribution was at a 5 volts flat sample holder. The goniometer was rotated to the 20 angle for the Bragg 
on the Oto 10 volt scale of the single channel analyzer (Ortec 406A). The lower peaks . The I{), 20 and x angles were adjusted to find the maximum Bragg peak 
13 
12 
x- r ay tube power and diffracted intensity for polys tyrene measured at 28 = 100? 
intensity for the CuKO'. radiation. The 28 angles measured at t}, ] i maximum 
4 f or the measurements along the h 1 00 line and in the h h1 2 0 plane in reciprocal 
peak height of each peak were recorded and averavcd. The resulting lattice 
s pace . The 100 and 110 crystallographic planes were not exactly coplanar with 
parameters of Si, Mo and Ta were found to be 5. 428A, 3.147 A and 3. 303A, re-
the cut surface of the sample introducing an absorption error. The crystals 
spectively. The agreement with the reported value of Si of 5. 430A by Schwartz , 
we r e rotated <.p = 18 0? and the diffuse intensity was remeasured near the LRO 
37
Morrison and Cohen( ) and the values of 3. 147 A for Mo and 3 . 303A for Ta from 
positions. The diffuse intensity for ,p = 0? and ,p = 180? were averaged to correct 
39
the ASM Handbook( ) demonstrated accurate equipment alignment. 
for absorption. 
The h 1 h 2 0 planes in the single crystals wer~ aligned with respecttoincident 
Measurement of the short range order and atomic displacement terms using 
beam and the detector by adj?..:sting x, ,p, w, x and y to obtain the maximum in-
powde r samples or one dimensional data was considered in order to reduce the 
tensity from the 110,220 and 200 Bragg peaks at their respective 28 angles with 
. (7
t 6i )m  e required to collect and reduce the data. Walker and Keatmg made 
X set at 0? or 45?. The crystal was translated in the plane of the flat sample 
measurement s along more than one direction in reciprocal space and concluded 
holder to intercept the total incident beam as determined by using a small fluo-
that neither two or three dimensional short range order terms nor the atomic 
rescent screen. The detector was set on the 200 or 220 Bragg peak for a crystal 
displacement terms could be recovered with sufficient accuracy to describe the 
face cut parallel to the 100 or 110 face respectively while the intensity was con-
s hort range order structure in the alloy. In the case of powder samples, the 
tinuously monitored. A knife edge air scattering shield similar to that described 
detailed structure of th
4 e diffuse intensity distribution is lost because of the by Rudman, ( 0) was positioned normal to and within 1 mm of the crystal face 
av eraging of the intensity over a spherical shell about t h e ori?g m? , and  a precise 
without reducing the counting rate on the detector. The data was collected be-
inte rpretation in terms of the order and atomic-displacement parameters is not 
tween 28 = 15? and 28 = 60? in equally spaced 1 ? to 3? steps. The lmife edge was 
36
possible. < ) Therefore it was necessary to collect and reduce two dimensional 
removed at high 28 angles without an increase in the parasitic air scattering. 
data to obtain an accurate measurement of the short range ordered structure. 
The stepwise scan was continued from 28 = 60? to 28 = 140?. The scan was re-
peated for equally spaced 1 ? to 5? increments of x ranging from 0? to 45? to map 
the diffuse x-ray scattering in the h h O plan
I e 2 ( Fig. 6). In order to measure 
the incident beam power, using the method of Warren and Averbach, (56) a poly-
styrene was inserted in the sample holder, x was set at 0?, w was set at 0? and 
diffracted intensity was counted at 28 = 100?. Table II lists the detector slit, 
15 
alloys, can be expressed as 
CHAPTER III 
X - RAY DIP PRACTION THEORY 
l(h1 , h2 , 0) = NXA X 8 (fA - f )
2 
8 L LL aQmn cos 21T h1 Q cos 2rr h2 rn 
The total m easured inte ns1? tY  1. s the sum of the fo Qll  ow min  r
tr, 
n
 c
 
ontribut1. 0ns: 
1o Ro tE hR -++Ao' e modulated Laue monotonic intensity we seek to recover; Ir,+ s , 
- NXA XB(fA - f8)2 LL L [hl 'Y~mn sin 21T hl Q 
the fluorescence from the sampl  e and di. ffraction by objects other than the samp1 e ; Q m n 
l e ' Compton or incoherent scattering from the sample? I temperature-
' TD S ? 
diffuse scattering from the sample; IF u (2) No? sharp fundamental Bragg reflections; 
and 1H' Huang diffuse inten Lsity. L A Lcco  rding to kinematic diffraction theory, the Q m n 
total coherently scattered x-ray intensity ' Icu' a t a given position in reciprocal cos 27T h 1 Q cos 2 7T h2 m 
space is given in electron units as 
f f Q ,iK.Rpq m n 
p q C (l) 
p q 
Th, detailed derivation is presented by Epperson. <42) Relative to an arbitrarily 
where f p and f q are the scattering factors of the atoms situated at sites p and q, 
ch osen origin, the average interatomic vector is given by 
K is 21r times the diffraction vector, and Rpq is the inter atomic vector . According 
to Warren, et al. 2 ( ) it is conventional to consider the coherently scattere (3d )  in-
t ensity from binary solid solutions as divided into two parts: I r u N O which is where ?, m and n are integers and a 1 , a 2 and a 3 are the translation vectors of 
independent of the state of order and which gives rise to the sharp fundamental a cubic unit cell. The continuous variables in reciprocal space, h 1 , h2 and h 3 , 
Bragg reflections, and I 2 , which depends on how the atoms are arranged on the are related to the diffraction vector by the relationship 
atomic sites. A quadratic approximation to the displacements of the atoms off 
(4) 
the average lattice sites , a ccording to Barie and Sparks(4l) gives the diffuse 
/',.A A 11'1 'a' 'a' where bl' b 2 and b are vectors recip
2
r  3 3 ocal to and - ? The Warren intensity associated with the atomic order and atomic displacements (Io Ro ER+ Ao), 2 2 2 
order parameter aQm n is 
Huang diffuse (1 11 ) and first order temperature diffuse scattering (ITps)? The 
pBA 
result specialized for the h
1 h 2 0 plane for body or face-centered cubic binary 
aQmn = I - , Qmn (5) 
XB 
where pQBA i
m s n t he conditional probabilityoffindingaB atom as an (Qmn) neighbor 
14 
17 
16 
of an A atom. Since the x-ray bea 1 As Equati on 6 contains two unknownm   ps aa rm amp ee ts e rm ~a , n iy t  a isto  nm o tp  pa oi sr ss i, b lc eh  e to m  dee ta es ru mr ie nd e  
order parameters a re averaged '1V'3r m ea in thy e a rt .  o om ne p  ua n; ambiguous,: ls coni~..ned y  i fn r om ma  n oy n ec  o so er t d oi f-  data taken at one x-ray wavelength. 
nation shells. Thus, every A atom does not ha li.._, the sar~1e nu Hm ob we er vo ef r B ,  pa lt ao um sas ble assumptions can be made about the relative magnitude of 
;11 the first shell or a ny O the 
th
r e ss h e e tl wl ou  n tl ee rc m;s sth  ae f ta ell ro  dy es th eo rmws in p ine grf  e thc et   l so hn og r- tr -a ran ng ge e  order. 
Q 
order. The alloy is composed of regions sh To hw ei  n mg el ao nc -a sl qo ur ad re er  , d ib su pt l ath ce ey m d eno tn  po at rameters (o)Q mn and (o) ?m n , describe 
have exactly the sa me 1o ca1  arran thg ee  m me en . at nd -i sff qe ur ain rg e  ts hli eg rh mtl ay l f  aro ndm   sr te ag tii co  n d it so p lr ae cg e1 m0n e nts. The superscript indicates 
in the sample. The  s i?z e O f the region to hv ee  r c ow oh ri dc ih n l ao tc ea  dl io rerd cte ir o ne  x ii ns  t ts h ei  s r ere af l le spc ate cd e  lattice and the subscripts specify the 
by the convergence of the orrlP,r parameters. c oordinaT th ee s  a ot fo  tm hi ec   ad tois mpl  a ac t e sm ite en  pt   p rea lr aa tm iv- e to site q. Equation 2 represents a 
eters or 'Y's are defined as follows generalization by Borie and Sparks<41) of the treatment of temperature diffuse 
scattering , second order size effect by Huang, <43) and short-range order due to 
(6) 
Cowley(l) which had been modified by Warren, Averbach and Roberts, (2) to in-
where the superscript Q on 'Y refers to one of the three cube axes, the strain clude the first order size effect. The treatment by Borie and Sparks<
41 ) takes 
parameter L~x mA  n i? s th e f raction of half the cube axis dimension that an A atom a dvantage of the fact that a tomic order and atomic displacement modulations 
has been separated in excess of the average interatomic vector identified by e xhibit different symmetry in reciprocal space to separate the diffuse intensity 
?mn (negative if less separation); f A and f are the atomic scatter ing factors associated with the cx's, -y's and o's. 13 
of atoms A and B of atomic fraction XA and x , respectively. As our x-ray data were only measured in one plane of reciprocal space, 
8
The atomic displacement oA A is given as two dimensiona l parameter s AQm are defined in terms of the thre
Q em  n d imensional 
p arameters, 
= LAQA ('a'I + 'a'2 + ~) (7) 
mn 2 2 2 
(9) 
A = A whe Ar  e a 1 a 2 = a 3 are the three cube axes. A relationship exists among the 
displacements for A-A, A-B and B-B pairs for each coordination shell which The displacem en t paramete r gives the average of the dis tances between all A-B, 
results from the nece ssity to conserve volume< 34) and is given as A- A or B-B atom pairs for a constant interatomic v
2X pll A OB A =
a   -Q rrn  
e
( ct o r . This i s referred to ~ a s thl e_ +    size effect term and was fi rs t trpB A ) 0 X _ X eated bA y A  W arren, Averb 2n Qm n XA  pB 0 (8) ac hA   a) nd B RB o b] e r ts . ( ) A Qmn Qmn B Qmn Qmn 
J3 
1 
CHAPTER IV 
For two dim ens ional data , one obtains the s i ze-effect term~ given as 
EXPERIMENTAL RESULTS AND DISCUSSIONS 
A. Micro( s I c 0 o) p ic Fracture Processes 
The microscopic fracture mechanism of the Ta-Nb and Mo-W alloys at am-
bient temperature are expected to be the same as their elements because the 
alloys do not solution harden. Scanning electron microscope fractographs of 
the elements and alloys were utilized to observe the effect of alloying on the 
microscopic fracture processes. Fractographs of ductile Ta and Nb single 
crystal fracture surfaces were characterized by slip pattern, small cup-and-
cone fractures and tearing. Similar fracture topography has been reported for 
polycrystalline Nb by Wessel, France and Begley<44 ) and Ta single crystals by 
Raffo and Mitchell. <45) Figure 7A shows the same tearing and cup-and-cone 
fracture surface characteristics for the Ta-30 at.% Nb alloy. An alloy of 30 at. % 
Nb in Ta did not produce cleavage fracture. The authors observed the cleav-
age fracture that had been reported for polycrystalline for Mo by Bechtold, (46) 
Lement and Kreder, <47 ) and Wilcox and Gilbert, <48) and Mo single crystals by 
Beardmore and Hull <49) at ambient temperature. ? The cleavage fracture for W 
of single crystals was reported by Beardmore and Hull (50) and a combination of 
cleavage plus intergranular fracture was reported for polycrystalline tungsten 
by Wronski and Fourdeux, (51) Gilbert<52 ) and Forster and Gilbert<53 ) was also 
observed by the authors. Figure 7B shows river pattern cleavage fracture 
in a Mo-30 at ? % W alloy similar to the fracture surface found in Mo-30 wt ? % 
W - 1 wt ? % Ti by Ferriss, Rose and Wulff. <54) The cleavage fracture charac-
teristics are similar for Mo, Wand the Mo-W alloys . The fracture surface 
19 
20 21 
e ithe r ductile Nb or ductile Ta at 300 K was found to produce a transition from 
characteristics of Ta-Nb and Mo-W alloys formed from like S' ,ed atoms are 
duc tile fra cture to cleavage fracture. 
the same as for the elements. 
B . Lattice P aram eter of Ta-Mo Alloys 
The Ta-Mo, Ta-W, Nb-Mo and ~-W alloys are formed from atoms having 
F igure 8 s hows a negative deviation in l attice param et er from 
a Vb eo gu at r5 d% ' s  d Lif af wer  ence in atomic size. Alloying Ta and W results in cleavage frac-
for measurements by Geach a nd Summers- Smith(5) and the pres ent authors. T
t hu ere   at 300 K for alloys with greater than 30 at ? %W  as reported by Ferriss , 
m easurements of Van Torne and Thomas(55) shown in Fi
R go urse e  a 8n  hd a W veu  l af  f. p (54 osi) t ivC el  eavage fracture was observed in Nb-50 at . % Mo single 
deviation from Vegard's Law. Van Torne and Thomas<55
cr )y  gs rta el ws   ta hn ed i rp  r so ib na gb lely  c w ryo sul -d be expected in alloys with as little as 30 at ? % Mo 
tals u sing an electron beam zone melting at a
L  e zc oa nu es  e s po ef e t dh  e o fs  h 25ar . p 4  mre mdu /c mt ? i n. Tv11 in d hu eyc  tility as reported by Milne and Smallman. (11) 
assumed the c rystal compositions to be the sa
A m c eo  m asb  i tn ha et  i so tn a ro tf i nin gt  e cr og mra pn ou sil ta ir o nfr  a oc r ture and cleavage fracture was observed in 
no preferent ial molybde num evaporation dur i
p ngo  ly zoc nry e s mtal el li tn ie n gN . b- C14 o na vt e. r% se W ly ,(  F Ii  g. 7C) and Nb-33 at.% Win addition to W. i 
observed evapora tion w
C el ie ga hv ta  g loe sf sr ea sc  t ou fr  e t ha et   m30 o0 r K e  vis o lt ah te ir lee  f mor oe l ye bx dp ee nc ute md   ii nn   aN llb  - cW as eal sl .o  ys containing 
Ge ach and Sum mers-Smith(5) al
% so  measuredm  to hr ee   t ch ha en m 1 i4 c aa lt   . c omW p. osC itl ie oa nv  a og fe   tf hr ea ic rt  ..ire was observed at ambient temperature 
x-ray diffra ction s ampl e s . Thus the a ppa r
f eo nr t  c po om sp ito is vi et  i do en vs ir aa tin og ni  n fg r ofr mom  V eT ga a-9 rd a ' st  . % Mo ( Fig. 7D) to pure Mo. Alloying 10 
Law f ound by Van Torne and Thom
% as <
55) was caused by negle cti
a nt g  ? t% o t mo e30 a sa ut r e.  Mo or W with either Ta or Nb produces a transition in fracture 
the m olybdenum weigh
s tu  r lf oa sc se   ic nh  a tr ha ec it re  r cis rt yi sc ts a lf sro . m Tte ha er  i ln ag t, t icw ea  v py a rfl ao mw ea tn ed r  c vu ep r- sa un s d-cone topography 
a lloy composition shou
t lo d  c sl he oa wva  g a e n a en gd a ti in vt ee  r dg er va in au til oa nr  ff rra oc mt  u Vre e ga at ra dm 'sb  Lie an wt  t fe om r p ae llr  ature. The strain fie lds 
T a-Mo alloys. 
around the solute atoms with their inherent 5% atomic size difference and the 
c
s .h  ~ iffractedo  Ir nt tr ea nn sg ie ty o  fr rd oe mre  d T a at -o Mm oi  c A a lr lora yn sg  Ae lm one gn  t t hin eh  hibi , t 0th , e 0d  Ais xlo isc  ation movement or 1
The diffracted x-ray inte nsity m easured
p  l aa ls ot nic g  fl to hw e  n h ea , r 0th , e 0c  r la inc ek   t ii np   rth eu -s causing the cleavage fracture . 1
ciprocal spa ce for Mo- 21 at ? % Ta, Mo-37 at ? %
I  n T c ao  an nc dlu  Msio on - 9, 1t  h ae t  r ?a  %n  d To am  i ss  olid solution Ta-Nb alloys exhibit the same am-
shown in F
b igie un rt e  du 9c . tile T f hr ea  c btu ar ce k gc rh oa ur na dc  t xer -i rs at yic  s i nt th ea nt s w itye  re m f eo au sn ud r ei dn   t ah le o nT ga   ta hn ed   hN  b 1 ,  elements. 
0, 0 line on Mo and Ta
T  wh ae s M ao b- o3 ~0 t  a 4t 0 . c% o uW n ts so  pli ed r s  1o 2lu 0t  i so en c  f ao nrm d e 6d 0  cfr oo um nt sl  i pk ee r  si 1z 2e 0d  s ea cto  ms showed the same 
r espe ctively
a .m  b Sie hn ot r tc  l re aa nv ga eg  e o f rr da ec rt  u pr ee a kth sa  at rw ea  s c lp er ae rv lyio  su hs oly w no  b ns ee ar rv  e td he f  o (1r 0 t 0h )e  a M ndo   (a 3n 0d 0)  W ele-
r e c iprocal l
m ate tn icts e  a pn od s ith tie o nM so  f- oW r  a Mll oo -y 2s 1.  aD t.is %so  Tlv ai  n ag n dm  Mor oe - 3t 7h  a an t 1 .0 % t  o T a3 .0   a Tt h . e  % p eM ao k so  r Win 
22 23 
heights for the Mo-37 at . % Ta alloy are much higher than for T lo-21 at . % Ta The Ta crystal gave an intensity band between the 220, 31 0 and 4 00 Bragg 
because of an increase in the den;r.::) C of order and i' . the hib11er alloy content. peak s whereas Mo does not. The temperature diffuse scattering is larger for 
The shift of the (100) and (300) order peaks to higher h 1 values is a result of Ta because of the low Debye temperatu re and soft elastic constants as pointed 
size effect. According to Warren and Averbach, <56) a low background between out by Walker and Keating. (57) Mo, however, has a high Debye temperature 
the (200) ~nd (300) positions followed by a high background between the (300) and and therefore lower I T O s which the absence of interconnecting intensity band. 
the (400) results also from size effect. Low background between the (200) and Surface oxide s or reaction products that may be reacted with Ta or Mo would 
(300) followed by a high background between (300) and (400) is evident for each produce extra peaks. The total absence of extra peaks indicates the surface ox-
crystal. Figure 9 shows diffuse: intensity at the leading edge of the (200) and ides are too thin to produce any effect on the diffraction pattern. 
(400) Bragg peaks for Mo-91 at . % Ta. This diffuse intensity can be explained The Nb-22 a t ? % Ta alloy gave an x-ray diffraction pattern very similar 
by a combination of short range order and atomic displacement modulation. The to that of Ta (Fig. 12). The intensity connecting the 220, 310, and 400 Bragg 
pr eliminary diffuse x-ray measurements along the h 0, 0 line shows that the 
1 peaks resulted from the large temperature diffuse scattering associated with 
Ta- Mo alloys possess short range order and size effect. the low Nb Debye temperature. A very large, uniform increase to 100-125 
D. Diffuse X-Ray Scattering from the h h 2 0 P1 lane of Reciprocal Space from count per 30 sec covering the 300, 210 and 320 order peaks was found. The scat-
Ta, Mo and Ta-Nb Alloy tering factor of Nb (41 at 20 = 0?) is similar to Mo (42 at 20 = 0?) so one would 
The total diffracted intensity from the h 1 h 2 0 plane in reciprocal space was expect a diffracted intensity of about 50 to 60 counts per 30 sec. An increased 
m easured from Mo and Ta and is shown in Figures 10 and 11, respectively. The diffracted intensity from Nb-22 at. % Ta of 100-125 counts per 30 sec above Mo at 50 
very large intensity peaks at the 200, 400, 110 and 220 posit ions are Bragg or counts per 30 sec is 50-75 counts per sec was spread uniformly over the h 1 h 2 0 
fundamental peaks. A minimum uniform intensity of 50 counts per 30 sec for Mo plane. This Laue monotonic diffuse intensity is caused by the large difference 
and 75 counts per 30 sec for Ta was found near the 300 , 210 and 320 order point s. in scattering factors between Nb (41 a t 20 = 0?) and Ta (73 at 20 = 0?), and it is 
The same incident beam power was used for Mo, Ta and Nb-22 at ? % Ta. It expressed mostly by the first two sums of Equation 2. It is possible to have 
produced a diffracted intensity from polystyrene a t 20 = 100?, x = 0?, w = 0? of atomic displacements in the alloy and no diffuse intensity if in Equation 6 the 
1400 counts per 30 sec. The intensity at these super structure points i s p r imarily positive and negative terms cancel. The uniformly distributed Laue monotomic 
incoherent scatter ing and temperatur e diffuse s cattering. The intensity is larger intensity shows the order and atomic displacement on the average of all atom 
for Ta because the coherent and incoher ent scattering fac tors are both larger pairs of the same coordination shell to be near zero. Thus, the alloy is nearly 
while the De bye temperature is lower. a random solid solution. 
24 25 
F, . Sca ttering from the h h 0 Plane of Reciprocal Space frow Ta-Mo Alloys T he data from the Mo-21 and Mo-37 at . % Ta alloys was corrected for ab-
1 2 
The total diffracted in tens it~ f1 r Mo-9 at . % rr a was 111easured u s ing the sorption by m e a s uring the total intensity near the short range order peaks before 
same incident intensity and is shown in Figure 10 . Short range order peaks and after the crystal was rotated 180? about an axis normal to the crystal face 
corresponding to the 300 position and the 210 position are shifted away from the and taking the mean value . The intensity measurements were converted to ab-
300 and 210 order pos i tions in the (110) direction due to the atomic displacement solute units (election units per atom) Ieu/N using the technique of Warren and 
56
effects. The Bragg p0aks a r e round r ather than elliptical when compared to the Ave rbach. ( ) The diffuse intensity was separated into the short range order 
Ta data. This could r esu..lt from the Huang diffusr: intensity which arises from component and the atomic displacement component for both the linear and quad-
6
the quadratic term in the atc:;~ic displacements (43 ) a s it is known to increase ratic terms using the computer programs of Epperson. ( 0) The short range 
in intensity near the Br agg pea ks in the radial dir ection from the origin. order coefficients and atomic displacement coefficients were calculated, and 
The diffuse x-ray scattering from the h 1 h 2 0 plane in recipr ocal space 
reported in Tables III, IV and V. 
from Mo-21 and Mo-37 at .% Ta wa s m easured. A correction for Compton in- The A 00 coefficients for both Mo-21 and Mo-37 at . % Ta are very low. This 
cohe rent s catter ing was computed us ing the incohe r ent scattering factors cal- resulted from using diffuse intensity values that were too low. The estimates 
cula ted by Cromer (58) and Cromer and Mann(59) and subtr acted. An es timate of parasitic scattering and absorption were too high; therefore, the diffuse in-
of the parasitic ai r scattering was subtracted. The intensity around the Bragg tensity remaining after these terms were subtracted was too low. This leads to 
peak including the Huang scatte ring and part of the TDS scattering wa s separated somewhat l e ss accurate AQm values. The AQm values for Mo-37 at . % Ta were 
from the total intensity by smooth extrapolation of the diffuse short range peak c alculated using a linear separation(42) from the data bounded by h 1 , h 2 coordi-
through the Bragg positions. The partially corrected data for Mo- 37 at ? % Ta n ates (0. 5, O; 0. 5, 0. 5; 1, 1; 1, 0) in Figure 14. The AQm short range order 
is similar to the Mo-21 at ? % Ta alloy and are plotted in Figures 14 and 15, c oefficients calculated from the linear separation agreed well with the AQm val-
respectively. For Mo-21 at ? % Ta and Mo-37 at ? % Ta, the atomic displace- u es from the quadratic separation which utilizes data bounded by the coordinate 
m ent effect caused the 210 short range order peak to shift away fr om the origin (0. 5, O; 0. 5, 0. 5; 1, 1; 1. 5 , 1; 1. 5, 0). Agreement between the AQm short 
in the (110) directi on by about 0.1 times the lat tice par am eter. This shift in r ange order coefficients determined from the linear and quadratic separation 
the Mo-91 at ? % Ta alloy i s O. 2 times the lattice parameter. Epperson and indicates there are no significant errors introduced to the coefficients A 11 through 
Spruiell(60) also found a s hift in the short range order peak induced by the a tomic A 44 be cause of the quadratic terms. 
displacement effect because of atomic dis pl a cements for Fe rich Al alloys. 
26 27 
Comparison of the signs of the experimental AQm values fo? Mo-21 and 16 are stacked on top of each other. Plane II is sandwiched between planes I and 
Mo-37 at . % Ta with the signs O!' toth the long raJW"r, ordc 1 _j (LRO) Mo Ta and III to form the model. Molybdenum atoms are represented by closed circles and 
Mo Ta structures shows good agreement from A. thrO\.. . gh the A40 except for tantalum by open circles.0  0 Each box is occupied by 54% Ta. The boxes3   enable 
A = 0. 001 for Mo-37 at . % Ta which is near zero. This shows that both Mo-21 the model to conserve composition. The unoccupied site3 s 3   of the model are atoms 
and Mo-37 at . % Ta alloys have a similar short range order distribution of a toms. having the average alloy composition of 37 % Ta. The model of the Mo-21 at ? % 
These short range ordered alloys tend to form one or a combination of the (B-2) Ta alloy contains 89 atoms and is formed by sandwiching plane B between planes 
or (00 3 ) long range ordered structures found in body centered cubic systems. A and C in Figure 17. The models are created by trial and error. The three 
However, the two dimensional short range order coefficients for both the Mo T a dimensional short range order coefficients ( aQ mn ) are calculated from the model 
(B2) structure and Mo 3 Ta (00 3 ) structure have the same sign variation. Thus and summed according to Equation 8 to obtain the two dimensional A Qm values 
the measured two dimensional A Q m's for the alloys cannot be used to predict as shown in Table VI. In order to get reasonable agreement between the meas-
whether the alloys tend toward a (B2) or a (D0 ) structure. u r ed a3 nd calculated A 1 1 values, very few Ta-Ta first nearest neighbors could 
The atomic displacement coefficients are reported in Table IV and Table V . be permitted. In order to calculate positive values of A 20 and A22 , a preference 
The atomic displacement coefficients for both Mo-21 and Mo-37 at . % Ta have for T a -Ta (200), (220) and (222) neighbors was necessary in each model. Cubic 
the same sign from r! through r: except for r: for the Mo-37 at . % Ta alloy. metals have a high degree of symmetry1  w hich is not exhibited b4 y  the models 4 
With that exception, all the atomic displacement coefficients are positive for having the dimensions of three atomic layers high by six or seven atomic layers 
M = 1 and M = 3 and negative for M = 2 and M = 4 . The similarity of the sign wide . These models may be located at random on any of the three (100) planes 
variation of the atomic displacement coefficients and rate of convergence indi- to inc r ea se the symmetry s o as to encompass about 150 atoms. 
cates the atomic displacement effect is similar for both alloys. The m odels fo r Mo-21 and 37 at . % Ta alloys were calculated independently. 
F. Short Range Order in the Mo-37 at . % Ta and Mo-21 at . % Ta T he probability of finding a Mo atom in the (111) position with respect to a Ta 
To determine local atomic arrangements with alloying compositions, we atom would range from 79 % to 100% if the first nearest neighbors of the Mo-21 
fitted as best we could an atom model of Mo-37 at . % Ta alloy and Mo-21 at . % at . % Ta alloy varied from random to fully ordered, and from 63% to 100% if the 
Ta alloy to the AQm 's. The ordered Mo-37 at. % Ta alloy crystal is described Mo-37 a t . % Ta alloy varied from random to fully ordered. The probability of 
by a model containing 99 atoms in the crystal. The (100) planes shown in Figur e finding a Mo a tom in the (111) position with respect to a Ta atom was calculated 
28 29 
from the models and found to be 85% for Mo-21 at . % Ta and 72 o for the Mo-37 Th e positive s hort range order coefficients indir'ate the origin atom prefers like 
at. % Ta. For both alloys this is about 25% of the .,.,d.nge fo.c first nearest neigh- neighbors for that shell. To understand the sign and magnitude of the displace-
bor between a random solid solution and the perrectly ortlered solution. The ment coefficients , we need to put lmown parameters in Equation 6 and determine 
measured short range order parameters converge to near zero for A 4 4 for both the relative contributions of the two terms . Let the A atom represent Ta and B 
alloys. The common convergence of the short range order parameters as well atom represent Mo. The two terms (Expression 11) in Equation 6 are 
as the common sign variation shows that the short range ordered structure is 
( XTa + O'. ) fT a LT a Ta _ (X_!!_ Q_ + a ) fM o L Mo  Mo  XM (11Q )m  n Qmn X Qmn Qmn 
similar in both alloys. The convergence of the s1'ort rang Oe   order coefficients Ta 
which for the Qmn = 111 of the Mo-3 7 at . % Ta alloy gives approximately (0. 59 -
to zero gives a m easure of thP- size of the region about an atom in which the 
0. 36) fT a L rtia - (1. 7 - O. 36) fM O L~i?t O ? The average value s of fTa and 
short range order persists. Similarly, the extent to which a cooperative ( co-
fM O for the range of 20 at which the data were taken are 30 and 50 respectively. 
ordinated) strain field exists about an atom is measured by the convergence to 
With these va.iues, our two terms become 11. 5 LTaTa - 40. 2 LMoMo. Since 
zero of the atomic displacement paramete 1rs 11.  This occu 1r 1s 1 n  ear the 442 shell 
ou r mea sured r~ was positive (+O . 80) and Mo is the smaller 
1 a tom, we expect 
for both the order and atomic displacement and encompasses about 150 atoms. 
LM oM O to be negative. For the alloy containing 21 at. % Ta, the two terms be-
In fact, the model of the short range order Ji  n 1  lt  he Ta-Mo alloys i s very much like that 
come 3 . 8 Lit~a - 107 L~i?t 0 which makes the strain associated with the Mo-
for Fe-Al alloys, (60) both having a tendency to avoid the like nearest neighbors . 
Mo pairs the most dominant feature of the size effect intensity. In going from 
G. Atomic Displacement Effect for Mo-Ta Alloys 
o. 37 at. fraction of Ta to O. 21, the observed displacement coefficient went 
The atomic displacement coefficients are reported in Tables IV and V. They 
from 0. 080 to 0. 240 ratio. For the Mo-91 at ? % Ta alloy, the dominance of 
are similar in s ign but not in magnitude. With the exception of r! 4 , the coef-
on e of the two terms in the displacement coefficient becomes very large as the 
ficients are positive for M = 1 and 3 and negative for M = 2 and 4. Note that for 
two term s are 500 Li:ia - 0 ifwe set a = -0.1 t
the first coefficients the displaceme 1n 1
h
1 r ough its value has little t coefficients have a sign opposite to that of the 
effect on the result. Since r~ must be positive to shift the SRO diffuse peaks 
short range order coefficients. In general, the l 1o  wer order coefficients are largest 
a way from t he origin in reciprocal space, the L'f fi 8 must to be positive 
and the predominant contribution to the two dimensional coefficients are m os t 
because the Ta-Ta first nearest neighbors are farther apart than the average 
likely the lowest-order three dimensional coefficients. Assuming this to be the ca s e, 
(111) interatomic vector. The large multiplying factor of 500 accounts for the 
these shells for which the short range order coefficients are negative have a pref-
l a r ge shift observed in the x-ray measurements for the Mo-91 at ? % Ta alloy, 
erence_t o be unlike neighbors to the origin atom compared to that of a random alloy. 
30 31 
, Fig. 13) . Similar arguments can be made for the r6 1 a1 a a) 2 terms w iich are negative and OM oTa = 0.0054 (- + .....3_ + 2 . For thE Mo-91 a t . % Ta alloy, the atomic 111 2 2 2 
and represent predominantly second nearest neigh ors. Thus Mo- Mo neighbors dis placement terms calculated from the hard spher e model gave : o~: ~a = 
distances are larger than the average (200) interatomic vector and the Mo 0.0037 (al + ~ + a3) and oTa Mo = -0.010(~ + ~ + a3). 
2 2 2 111 2 2 2 
atoms also prefer like neighbors in their second she Us. The pattern of a prefer- The rate of atomic displa cement (oT fr O ) change as a function of composition 
ence for the like neighbors s ignifying larger than aver age interatomic dis tances for Ta rich and Mo rich alloy is calcula ted using the hard sphere model. The 
and a prefer ence for unlike neighbors having closer than average dis tance s per- atomic displacement from the average lattice s ite for the Ta solute ranges from 
s i s t s thr ough the fourth neighbors. The Ta atoma act as dilatation centers to O. 071A to O. 047 A (LLar O from O. 0150 to O. 0099) for the Mo rich Ta alloys 
its nearest neighbors and M~ i s a contraction center for Mo-Mo neighbors pairs. ranging in composition from Mo to Mo-25 at ? % Ta. The atomic displacement 
When the pr obability of finding an A-B first neare s t ne ighbor (111) for a from the average l attice site ( o'[f ~0 ) for the Mo solute ranges from -0. 063 to 
BCC alloy i s about 100 % as is indicated by the short range or der parame ter, the -0 . 020 A (L Trr 0 from -0. 0127 to - 0. 0041) for Ta to Ta-25 at ? % Mo using the 
fir s t atomic displacement (1'i 1 1 ) can be approxim ate d with a ha r d s phere model hard sphere mode l. The hard sphere model calculations show twice the rate of 
as found by Epper son and Spruiell. (60) The probability of finding Mo (111) near- atomic displacement change or e lastic s t r ain te rm change for Mo dissolved in 
est neighbor adj acent to a Ta atom i s 72 % for Mo-37 at . % Ta and 85% for Mo-21 T a as for Ta dis s olved in Mo. This correlates well wi th the fact that solution 
at . % Ta. These values are less than 100% but show a ve r y strong preference hardening rate for Ta rich Mo alloys (1. 7 kg/ mm2 per atomic percent) have a 
for Mo- Ta neare st neighbors . The s e atomic displacements we r e compared with solution hardening rate that i s proportionately higher than the Mo rich Ta alloys 
a hard sphere model to aid in the explanation of the atomic displacement modu- (1. 2 kg/mm 2 per atomic percent) by about the same ratio. The larger rate of 
l ations as sociated with firs t neare s t neighbors . Knowing the la ttice constant of e l astic strain term change in the Ta rich Mo alloys as calculated from the hard 
the alloys (Fig . 8) and the lattice cons tant of Mo and Ta, one may calculate the sphere model cause the atomic displacement to be greater in the Mo-91 at ? % 
expected difference for the interatomic vector of the Mo-Mo pa i r s, Ta-Ta pairs Ta alloy than either the Mo-21 at ? % Ta alloy or the Mo-37 at ? % Ta alloy. 
and Ta-Mo pairs. These values are listed in Table VII. If we assume that the coefficients are negligible beyond r1 4 , then we may 
For the Mo-21 at . % Ta alloy, the atomic displacement terms calculated write from Equation 10 that for Mo-2..1 a t ? % Ta alloy: 
from the hard sphere model gave, oMoMo ~ -0.0040("!_ + ?, + 2)a nd 6~ ?Ta ~ 
1 1
a a a ) 1 1 1 2 2 2 
0.0101 ....!. + _!. + -2 . For the Mo
( -37 at. % Ta alloy the atomic displacement 
te rms ca~cula:ed fr~m the hard sphere model gave: oM oM O = - 0.0073 \/~
1 
2 + a
2 
2 + a
3
\ 
1 1 1 2) 
33 
32 
in T
~ ab le VII do a gree in sign and s omewhat in m agnitude with the0  . h24 a0 rd -  s0 p.0 h4 e= 9
r
 e 0. 191 
7 1 = 0.095 111 2 model. When the strain parameters LMQ oMo, LTaT a and L
m Tan M o areQ  m on b tained Qmn 
Using Equation 6 for A as Ta and Bas Mo: .. from the Ta rich Mo alloys, the s train ene r gy associated with the SRO r egion 
1 = 2rr [(0.21 -0.1 9) 50LTaT a _(0.79 -0.19\ 30LMoMo] 
'Y111 50-3 co0 u ld0  b.7 e9   c alculated . The in0 te.2 r1 a ct ion be tw) e en dis location strain field and chem -I ll Ill 
i cal en e r gy plus strain field of the SRO region would provide the basis for cal-
cul ating the force necessary to move the disloca tion through the SRO region or 
MoM o - MoMo - -0.095 = -0.0028 
L I I 1 - f I 11 - 33.6 
b a rrier. 
Using the same calculation for Mo-37 at . % Ta alloy: H. Subs titutional Solid Solution Hardening and Short Range Order Hardening 
1 = 21' 1 + 2 I fl 1 1 1 I 'Y 3 l I = 0.080 The Ta-Nb and Mo- W alloys h ave almost the s ame elem ental atomic size, 
rL = 21'1 I 1 +~ = 0.004 t hei r l attice paramet e r i s invariant with composition. They show no substitu-
0 
1 0.080 - 0.004 
')' l 11 = = 0.038 tional s olid solution ha r dening . From the diffuse x - ray sc atte ring measure -2 
ments on Nb-22 at .% Ta, thi s alloy appea
0 rs3  7 t o be a random solid solution with 1 0 63 = 0.038 = 0.3 I 4 [( ? - 0.36) 50
0  . L6 T 3 a Ta -( ? - 0.36) 30 0.  3 L7  M o M 
0
] 
1'111 111 111 the s olute atoms located on the average lattice s ite s. All the Ta-Nb alloys are 
Assuming that LT aTa has the same value for the Mo-37 at . % Ta alloy as f
1 o 1 rl  the r e for e expected to be r andom. Mo-W alloys ar e expected to exhibit a very 
the Mo-21 at . % Ta: small deviation from r andom s olid s olution due to their small elemental 
'Y = 0.038 = 0.314 (l l.5 (-0.0028)- 40.2 L~i? M0 ) 
1 a t omic s iz e difference and limited high temper ature solution hardening.<
2
 3) 
L~i?t O = -0.0038 An absence of s ubstitutional s olid s olution and short range order hardening is 
The two dimensional atomic displacement terms were not recovered for the Mo-91 ob e rve d whe n solutions were fo r m ed from equal s ized atoms with large dif-
at . %TaalloysotheL?[-fTa cannotbecalculated nor can L~f1Ta or <5~i?1Ta be ca l- fe r e nces in thei r shear m odulus values. 
culated for all Mo-Ta alloy using Equation 8. From a similar calculation, the values T he Ta-Mo, Ta-W, Nb-Mo and Nb-W binar y alloys with about 5% diffe r ence 
for L ~ 0 MO L TQ a MO &mn ' mn ' and L&Im a nT a for the second, third and fourth nearest neighbors in the ir atomic s ize show a l attice paramete r variation with composition, a neg-
shells can be cal culated. Two planes of diffuse x-ray dat a should be measured with ativ deviation from Vegard' s Law and line ar ha rdening extended to high solute 
different radiation and reduced from Ta rich Mo rich crystals to obtain the e lastic concentrations at room te mpe rature . The linear hardening r ate of the low 
strain value from the diffuse x-ray data. The two L~1? M0 1 elastic strain value s modulus T a or Nb alloys were found to be 11 DPH values per at.% Mo or W or 
34 35 
1. 7 kg/mm 2 
62
pe r at .% Mo or W. Whe r eas the high modulus Mo alloys were hardening i s not explained by Mott and Nabarro( ) o r Riddhaghi and Asimow<63 ?64) 
.% \vho calculate hardening at OK. Assum ing the solution hardening for these BCC found to harden at a lowe r rate of 8 DP H v alues per at Ta or Nb corre-
alloys a t the plateau t e mpera ture s is high and about equal to the solution hard-
sponding to about 1.2 kg/mm 2 pe r at .% Ta or Nb . 4
c..: ning a t OK as shown for Ta- 9 at % W by Arsenault? ) the solution hardening 
57 64
Flinn' s( ) theory permits the calculation of shor t r ange order strength - c a l c ula t ed by Asimow< ) can be compared to the obse rved substitutional solid 
67 s olut ion hardening. The substitutional solid solution hardening values calculated ening by ordered first nearest neighbors for FCC alloys. Using Flinn's ( ) 
from F i gu res 1 and 2 and from the shear modulus value s of Armstrong and 
theory adjusted for BCC alloys, the SRO strengthe ning of only 0.5 kg/mm 2 
vrordi ke (75) are found to be a factor of 4 to 8 time s higher than predicted by 
= 64
54
for Mo-21 at.% T a ( a 111 -0.069 from the mode l) and of only 1.7 k:g/mm2 As imow( ) for a 1.5 type edge dislocation hardening . Asimow's( ) theory does 
= a gree with the FCC substitutional solid solution harde ning and predicts the ab-for Mo-37 at .% Ta ( a 111 -0 .146 from the model) was calculated. These 65
sence of hardening for Ta-Nb and Mo-W alloys. Foreman and Makin( ) predict 
strengthening values are very low when compared to the obse rved strengthen- 55no p l a t eau hardening for dilute solutions. Friedel( ) predicts zero hardening 
ing produced by the SRO and the solution hardening of about 25 kg/mm 2 fo r \Vith zero a t omic size mismatch at high temperature, a near linear hardening 
2 r a te or c 413 but for dilute solutions. None of these the ories explain the linear Mo-21 at .% Ta and about 44 kg/mm for Mo-37 at .% Ta. If the SRO hard-
plat eau s ubstitutional solid solution hardening observed in these BCC alloys. 
57
ening calculated from Flinn's( ) theory is at all accurate, one can conclude 
s. Suggesti ons for Future Research 
that the predominant hardening mechanism in the Ta-Mo alloys is substit u- With present data a solution hardening theory can be developed which would 
tional solid solution strengthening. Atomic size mismatch appears to be t he be based primarily on the atomic size mismatch effect as the barrier to disloca-
t ion motion in BCC solid solutions. The solid solutions could be assumed random. 
dominant substitutional solid solution hardening parameter for Ta-Nb and 
The sol ution hardening stress should be proportional to the atomic size mismatch 
Ta-Mo alloys as suggested by Rudman,(l3) Harris,(l 5) and Chang_(l4) 
a.nd e q ual t o zero when the atomic mismatch is equal to zero. The plateau stress 
The current substitutional solid solution hardening theories are comp ared c ould be expl ained by distributing the stress fields of the individual solute atoms 
a l ong the full l ength of the dislocation thus preventing thermally activated dis-
with the observed ambient temperature substitutional solid solution harde ninoo- 
location movement. 
rates of Ta-Nb alloys, Mo rich Ta alloys and Ta rich Mo alloys to calculat e th e T h e complexit y of the atomic arrangements that are found in solid solutions 
hardening. The random solid solution hardening theories based on a dominant (local order and at omic displacement) do not permit easy first principle calcu-
16 6 l a tion of the ch ange in strength with concentration. Through x-ray diffuse scat-shear modulus effect by Fleisher,< ) Bose/IS) and Labusch( l) describe 
t e ring provi d ing a better understanding of the atomic arrangements in solid 
hardening for dilute solutions at OK, while Suzuk:i(l 7) included concentrated solu- s ol u t ions , the complexity of the atomic arrangements complicates the modeling 
tions at high or plateau temperatures. The absence of solution hardening for a nd gives only an average configuration. If several regions in the alloy are 
s :impled , we a r e not likely to find the same arrangement in any two of them. 
Ta-Nb and W-Mo corresponding to an absence of atomic mismatch for T a-Nb 
and W-Mo cannot be explained by the above theories. The room tempe r ature 
36 
37 
That the s olid s olution has only short range order, by definition precludes the manne r that the ir average strain terms equal the values measured by diffuse 
alloy from being compared to groups of a toms having a l arge superlattice which 
x - ray d iffra ction. Equating the total force on the dislocation imposed by external 
is not obse rved in Mo-Ta alloys. The SRO parameters (a ) give us the aver age 
configuration of the local order. As a - 0 for t he more dist ant pairs, we h ave l oad on the c rystal t o the interaction force between the SRO region over a solute 
a m e asure of the siz e of the region of local or der beyond which the probability con e ntration r an ge would permit the calculation of solid solution hardening. 
of forming AA, AB and BB pairs becomes that of a random solid solution. The 
T h e che m i c a l inte r a ction e nergy and f orce on the dislocation in both the Ta rich 
length of a di slocation line i s m easured in hundreds of Angstroms in many l at-
tice dis t ances which is much gr eate r than the s ize of the local orde r region. a nd Mo ri ch alloys c ould be calcul ated using a short range order mechanism of 
However, a region of local orde r extends around each at om. The dislocation Lhe typ e of F linn< 6 7) m odified to include a ll the observed SRO shells and the same 
i s subjected to local chemical orde r and cor r el at ed atomic di splacements about 
d i s l ocation inte r a ction m e chani sm proposed for the solution hardening. The 
each atom site along its length, yet from one part of the dis location line to an-
other only 10 l attice constants away, the disloc ati io nn t eh ra as cs ta iom np  l ee nd e e rn go yu  ag nh d  a ft oo rm ci ec   created by the strain fie l d of the dislocation and 
sites to experience the ave rage structure . Lhe str a in field associated with the average atomic displacement in the SRO 
With additional diffuse x-ray diffraction dat a , har dne s s or solution h a rdening regi on could be calcula te d u sing the Lf;,~a, Lr O 1~nM and Lf~~ 0 strain terms 
st rength measur e m ents and el astic m 1odulus values from the T a rich Mo alloys 
and the Nb-V solid solution us s, ina gs  o tl hu et  io fin r h s ta  r sd ee vn ein rg a l th se ho er lly s  c ao nu dld  a b de d ed de  v toe  l to hp ee  d in teraction force caused by the 
from the dis location interaction with the obse rved atomic s tructure of the solu- s h o rt ran ge orde r chemical e nergy t o obta in the total dis l ocation-obstacle inter-
tion. The solution hardening of three types of alloys would be r epresented. The a c t i on f orce . Again a s e t of atomic di s placem ent and associated strain terms 
Nb- V alloys represent solution h ardening for alloys formed from e l e m ents h aving 
the s ame m fo r du ml  us t wb ou  t Td aif  f re ir ce hn  t M a ot o  am lli oc ys si  z we o. uT ldh  e b eT  ra e- qN ub i rs eo dli . d s Ino  l au dti do in tis o nw , ou a ld d irect measure-
exhibit s olution hardening for alloys formed from elements having equal size m e nt of e ach crystal shear m oduli would provide a more accurate cal culati on of 
atoms but unequal modulus values . The Ta-Mo solid solutions exhibit solid the d i s l ocati on inte raction force (short r a nge order atomi c d ispl a cement regi on) 
solution hardening when the alloy i s fo r med from e lements of unequal atomic 
a n d h
s eiz le p  a rn ed m u on ve eq  u ta hl e m  ao mdu bl iu gs u. i tyT  h oe f  t mhe oo dr uy lu c so  u el fd f er ce tp s r oe ns  e sn ot l uth t ie o na  l hlo ay rs d eb ny i na g .s  ta Tti hs et  i-
cal distribution of a toms whose average di s t ribution i s equal to the measured di str ibuti on of the short r a nge order a nd atomic d i s pla cem ent r egi on s a long the 
SRO structure r ather than a r andom atom ic dis t ribution . The average strain d i s l ocation line and throughout the cry stal which ha s the obser ved short r ange 
fie ld in the theory caused by the atomic m isfit in t he alloys could be described 
o r de r and atomic displacement param eter value s could 
b by e t  h de e va ev le or pa eg de   fo of l la o wdi is nt gr  ibution atom s pos itioned off the atomic sites in such a 
~' s h el by . (6 8) T he increase in yi e ld s t r e ss with Ta or Mo s olu te concentra tion 
c ou l d the n be cal culated from such a model b y using the appr oach of For em an 
a nd M a kin. (65) The aver age size of the s h ort range or der regi on tha t interact s 
CHAPTER V 
38 
CONCLUSIONS 
with the strain field can be taken as about 10 la tti ce param e ters or the diameter The obse rved l attice pa r am e ters, substitution solid solution hardening and 
of the 442 shell. The strain parameters can be ob tained from Table VII plus fracture propertie s of Nb , T a , Mo and W binary solid solutions showed two types 
values to be calculated from the two Ta rich Mo alloys that need be measured. of behavior. Ta-Nb and Mo-W alloys formed from equal size atoms and different 
The solid solution hardening calculations s hould e qu a l the 1. 7 kg/ mm2 per modulus have lattice paramet ers that obey Vegard's Law, show an absence of 
at ? % Mo observed in Ta rich Mo alloys a nd 1. 2 kg/ mm2 pe r a t ? % Ta for Mo s ubstitutional solid s olution hardening and exhibit an absence of fracture embrit-
rich Ta alloys. The hardening should be zero for the r andom Ta-Nb alloy s tle ment at high solute concentrations. The Ta-Mo, Ta-W, Nb-Mo and Nb-W 
when the atomic misfit is zero but the modulus diffe r ence is large. The sub- binary solid solutions h aving a 5% diffe rence in their elemental atomic size show 
stitutional solid solution hardening should also be pre sent for the Nb-V BC C a negative deviation in Ve gard' s Law, linear solid solution hardening to high solute 
solutions with equal modulus and substantial atomic misfit as shown by Hobson.(5 9) concentrations at room te mpe rature and fracture embrittlement at high alloy con-
If the correlation between the substitutional solid solution hardening theory and centrations. These observations agree with the data reported in the literature. 
the observation were found to be good, the substitutional solid solution hardening The diffuse x-ray measurement of the Nb-22 at .% Ta alloy from the alloy type 
theory would be expected to predict the hardening in the remaining Ta, Mo, W and having equal size atoms showed the alloy to be a random solid solution. Diffuse 
Nb binary BCC solid solutions. 
x-ray m e asurement of the Ta-Mo alloys of the alloy type with 5% difference in 
atomic s iz e showed short range orde r and atomic displacement to the (442) shell. 
Model s of the Mo-21 at % Ta and the Mo-37 at % Ta alloys were established to 
d e scribe the similar distribution of the short range ordered atoms. Because the 
s hort range order accounts for less than 5% of the alloy strengthening and the 
x-ray data shows very large atomic size effects, the large Ta-Mo strengthening 
i s attributed to the substitutional solid solution hardening controlled by atomic 
s ize mismatch extending to the (442) shell. The solution hardening rate of -s:A.M o 
d Tis  solved in a was shown to be Th  igher than ? d Mi os  so wlve =: ""d  H i  n " '" I f agree-
m ent with the h ard sphere model but not confirmed by x-ray measurement. 
39 
Table I 
Zone Melting and Crystal Gr owth Conditions 
Zone Melting Relat ive 
Crystal Char ge Crystal 
Charge Procedure Evaporation 
Melt Number Sample Composition Composit ion Cr ystal Size 
Description and Minimum Loss 
Number (Atomic %) (Atomic %) 
Pressure (Atomic %) 
Mo-Ta Alloys 
Melt I B-IV 6.3 mm Diam. 3 Passes 100% Mo 100% Mo - 3 Crystals about 
Mo Rod 7 x 10-9 torr 21mm Long x 6mm 
Diam. 
Melt II B-VII-2 6.3mmDiam . 4 Passes Mo-15% Ta Mo- 20. 1% Ta 5% Mo 2 Single Crystals 
B-VII-4 Mo Rods with 5 x 10- 1 o t orr Mo- 215% Ta plus Large Poly-
B-VII-6 2-1. 6 mm 2. 7mm/ min Mo - 20. 5% Ta crystals 
B-VII-8 Diam. Ta Mo-17. 6% Ta 
B-VII-5 Wires Mo - 20. 5% Ta 
Melt ill B-VI-1 6.3mm Diam. 4 Pas ses Mo- 17% Ta Mo-27. 7% Ta 20% Mo 2-25mm Long Crys-
B-VI-3 Mo Rods with 10 -9 torr Mo-39. 5% Ta tals plus Large Poly-
B-VI-4 3-1. 6 mm 3. 5 mm / min Mo - 40. 5%Ta crystals 
B-VI-5 Diam. Ta Mo- 36. 3% Ta 
Wires 
Melt IV B-III 4 . 8 mm Mo- 3 Passes Ta- 31% Mo Ta- 9. 3% Mo 22% Mo 1-4. 3 mm Diam. 
Ta Alloy Rod 2 x 10-8 torr Crystal x 50 mm 
(B-II) Plus 3 mm/ min Long 
15-0. 8 mm ..,. 
Diam. Mo 
0 
Wires 
Table I (Continued) 
Zone Melting Relative 
Crystal Charge Crystal 
Charge Procedure 
Melt Number E
vaporation 
Sample Composition Composition Crystal Size 
Description and Minimum Loss 
Number (Atomic %) (Atomic %) 
Pres sure (Atomic %) 
Melt V B-I 6 . 3mm Ta 3 Passes Ta-11% Mo Ta-3. 9% Mo 7% Mo 5 Single Crystals 
Rod Plus 0. 8 10-8 torr 150mm Long 
mm Diam. 3 mm/ min 
Mo Wires 
Melt VI B-II B-1 2 Passes Ta - 39% Mo Ta-0. 8% Mo 3% Mo ?single Crystal 
10-8 torr 150mm Long 
3mm/ min 
Melt VII B-V 9.5mm Diam. 2 Passes 100% Ta 100% Ta - Single Crystal 
Ta Tod 10-8 torr 
3mm/min 
Mo-W Alloys 
Melt vm B-XV-7 6.3mm Diam. 4 Passes Mo-19% W Mo-20% W 1%Mo Polycrystal ., 
Mo Rod Plus 10-7 torr 0. 3 mm ave. Grain 
3-1.6 mm 12mm/min Diam. 
Diam. W 
Wire 
B-XV-19 1.2mm/min Mo-30%W 11%Mo Polycr ystal o. 5 mm 
ave. Grain Diam. 
..,. 
1--
Table I (Continued) 
Zone Melting Relative 
Charge Crystal 
Charge Procedure Evaporation 
Crystal Composition Composition Crystal Size Description and Minimum Loss 
MeltNumber Sample (Atomic%) (Atomic %) Pressure (Atomic %) 
Number 
Nb- WAlloys 
Melt IX B-XII 6-3 mm Diam. 5 Passes Nb-14% W Nb- 14% W None Polycrystal O. 5 mm 
Nb Rod Plus 2 5 x 10-9 torr ave. Grain Diam. 
1.6mm Diam. 2,5mm/ min 
W Wires 
M-X B-X-2 6. 3mm Diam. 3 Passes Nb-30% W Nb-29% W None Polycrystal O. 2 mm 
Nb Rod Plus 5 x 10-9 torr ave. Grain Diam. 
B-X-5 4-1. 6 mm Nb-32. 7% W 
B-X-6 Diam. W Nb-29. 8% W 
B-X-8 Wires Nb-29 . 8% W 
Nb-Ta Alloys 
M-XI B-XVI 6. 3mm Nb 5 Passes Nb-20% Ta Nb-23% Ta 3% Nb Polycry.:, ..,al 1 S mm 
Plus 3 Ta 2 x 10-8 torr ave. Grain D_ ' ID. 
Wires l.3 mm / min Plus 1-Crystal 
M-XII B-XI-2 6,3mm Nb 3 P asses Nb-29% Ta Nb-33.4% Ta Unknown Polycrystal O. 5 mm 
B-XI-4 Rod Plus 9 x 10-s torr Nb-29. 8% Ta Residual ave. Grain Diam. 
B-XI-6 4 Ta Wires 1.3 mm/ min Nb-30.1% Ta Ta Wires 
B-XI-8 (1. 6 mm Diam.) Nb- 29. 2% Ta 
~ 
N) 
~ ~ -;:.~ -,-3 6 ~ -6 ,-3 ~ -;:. ~ -;:. ~ ~~ - ,-3 - ,-3 0 00 ~~ I - -0 0 0 00 OI 0 0 6~ 6 ~ I 0 0 (') N) N) N) .... -wI  0 0 ti:! - '? -0 wI 01  0 I 0 0 - N) -..:J o:! ~ o:! o:! .... - '? - - 1-1 ,-3 -..:J ~ ~ ~ o:! ~ o:! o:! '<: 00 p) 6' II "-. II 0 ~ .... II "-. II "-. <+ . II 6' II 00 II ~ r-3 ? r-3 ~ 00 00 0 ? ,-3 ? r-3 (0 
p) 0 (0 p) O') 
0 '? :' ~ '? 0 p) (0 ~ .(0 0 0 0 0 0 
0 
.1.-1..  
aa, .
t
 .
1..  
.~...  ~ Ul a, 
0 
~ X 
I 
,:1 
>,j ~ 
~p ~ 
.... 
en .... .... 
f 
p) ~ 
0 w 00 Ul 
O" 
00 
-..:J 0 en 00 ~ t1 0 a, 0 
0 0 0 0 en 0 ~ 0 ~ 0 ~ ~ ~ 0 0 s- ~ ij -0 0 <+ p) a, 
co s ~ 
. a, 0  .0  .0  .0  .0  .0  .0  .0  0 0 0 a 
N) 0 . 0 . . N) N) 
0 N) 
ga 
N) 0 N) 0 0 0 0 0 0 
0 N) 
0 
N) 0 0 N) N) .... 0 N) 0 0 <+ 0 
0 0 [ 
~ ~ w w a: 
0 w 0 w 0 ~ ~ 0 0 0 0 ~ 0 ~ 0 ~ 0 0 0 ~ >u X ~ 
>,j 0 I co 
N) N) .... 
en .... .... 0 .... 
~ !:c 
0 N) N) N) tJ1 en en N) N) 0 ~~ 0 0 0 0 
.... ~ .... 
.... .... ...... ~ -..:J ~ w ~ .. .O..'.)  O') 00 0 N) ~ 0 N) 00 en 0 .'.?..  0 ...... 0 
w D O') D O') D 
0 0 0 W
 D 
0 w D II ~ [ 0 WD 0 0 0 0 0 0 
[ 0 00 Ul a, [ Ul a, a, [ Ol a, [ C .... i ,:1 a,ll  [ Cll a, [ 0 a, II) D C'll D Ul D Cll D Cll D Cll D , <+ Cll 0 ::0 a, a, 
~ 
w 
44 45 
Table m 
Two Dimensional Short-Range Order 
P a ramet ers A Qm For the Mo-21 and Mo-37 at . % T a Alloys 
Signs from Perfect Table IV 
Mo-37 Mo-21 Fe - 18. 3 
MoTa LRO (B2) and 
at. % T a at. % Ta at.% AL 30 fficients 
Mo3 Ta (D0 ) 
Atomic Displacement Coe
3
AQm Experimental Expe r im ental Calculated Experimental rfm For Mo-37 at ? % Ta 
Q 
0.638 284 1.145 m =
 1 
0. m = 2  =3 Ao o + m m =4 
A11 -0. 356 - 0.190 0.412 
0 0.000 -0.134 0.000 -0.070 
1 
A20 0.208 138 0.273 
0.080 0. + 0.000 0.081 0.000 
2 
0.048 0.0
00 
0.051 -0.045 + 0 . 138 0.000 -0.032 A22 
3 0.004 
-0 . 041 -0.056 - 0. 115 0.000 0 . 017 0.000 A31 
4 
0.001 -0.007 -0 . 089 0.000 -0.005 0.000  0.012 A33
A40 0.026 0 . 053 + 0.069 
A4 2 -0 . 003 0.018 + 0.052 
A44 - 0 .009 0.004 + 0. 030 
46 47 
Table VI 
Observed and Calculated Short-Range Order Parameters A.Qm 
for the Mo- 21 and Mo-37 at . % Ta Alloys 
Table V 
Mo- 37 at ? % Ta Mo-21 at . % Ta 
Atomic Displacement Coefficients 
AQm Observed Calculated Observed 
r Cm a lculated 
Qm For Mo-21 at.% Ta 
Aoo 0.638 1.480 0.284 1.108 
Q m = 1 m= 2 m= 3 m =4 
All - 0.356 -0.372 -0.190 -0.204 
0 0. 000 -0.210 0.000 -0.056 
A20 0.208 0.155 0.138 0.137 
1 0.240 0.000 0.041 0.000 
Ai2 0.048 -0.040 0.051 0.045 
2 0. 000 -0.051 0.000 -0.018 
A3 l -0.041 -0.054 -0.056 -0.074 
3 0. 049 0 .000 0.025 0 . 000 
A3 3 0.001 0.020 -0.007 -0.026 
4 0. 000 -0.011 0.000 -0.018 
A40 0.026 -0.015 . o. 053 -0.025 
A4 2 -0.003 0.012 0.018 -0.050 
A44 -0.009 -0.026 0.004 , -0.028 
49 
48 
60 
?- ? -? Ta - W } MITCHELL & RAFFO (Ref . 15) 
---0 Ta- Mo 
50 --x N- b- -- M@ o} 
PETERS & HEND
 RICKSON 0J Nb - TE a  (Ref . 12) 
E 
?-0--.-0-  I 
::::s:::: 
Table VII u 40 I 
~ X 
Elastic strain Terms L
111 Derived from X-Ray Measurements C) 
z 1 1 ~Nb-
o Mf oA  tomic Displacements Compared to Those Calculated z Ta - W 1
u.J   30 
from Lattice Consta 0n  ts Assuming Hard Spheres 0:::: "ii 
c::::i::: 
Mo-21 at.% Ta Mo-37 at.% Ta :I 
~'II 
Mo-91 at ? %
At  o Tm a ic z Ta - Mo 1/' 
Pairs 0 
X-Ray Hard Hard Hard 20 
Sphere X-Ray S Xp -h Re are y  I--Sphe r e =::> 
_J 
Mo-Mo -0.0028 -0.0040 -0.0038 -0.0073 0 tif) x  
Ta-Ta VJ 0 . 0037 10 Nb-Ta 
M ;o- Ta j
f .Ta 0.0101 0~0054 -0. 010 X 
Nb 
50 
10 20 30 
40 
a/o SOLUTE 
F igure Bee1  . Substitution Solid Solution Hardening 
of Ta and Nb at 300 K 
600 VACUUM ARC CAST 
N ? ? REFERENCES 
E 
ZONE MELTED 
~ 500 0 D 6 AUTHORS 
00 
~ -- - _____ Mo-Ta ........... 
Cf) - -. .... ..... 
Cf) 
u.J 400 /., --0 0 ...... ', w 
z ~. ' 
0 
~ p/ / ' ' ? W 
~ /0 -----~ 
I 300 / /J:J ~ ' \ 
o "\?>/ Mo-W __. ' 
::E ()// ,4 ~------ ', 
<( ~/ D ?---- \ 
>~- 200 ~ / / ? -?..D:: ::.------ -- ~~  
~ Mo ,~  ' \ 
0 'tb 
z 
0 DO~ ' 
::E 6 
<( 
?'Nb I I ~ I I I ---1 ?-?-I ?-?- I ?-?-1 
0 
0 10 20 30 40 50 60 70 80 90 100 
ATOM IC PERCENT 
Figure 2. DPH Hardness of Binary Refractory Alloys at 300 K 
CJl 
0 
600 
N 
E 
~ 500 
OD 
~ 
Cf) / Ta-W 
~ 400 
z --- -???-???-???-??????-????-???-???-???-? ----------------
0 ????? Nb-Mo ????-
w 
~ ?? .. ?, 
<( 
I 300 ? .. ? .. 
'? 
0 ?~?? ... 
::E ? 
<( --- ? Ta-W } ...... 
~ 200 REFERENCES >- -? Nb-W ARC MELTED ?????. . Mo ~ 
0 ? ???? ? ? ? Nb-Mo 
z -? Nb-W AUTHORS-ZONE REFINED 
0 
::E 
<( 
0 
0 ..___ _ _..__ _. ..___ _ ___._ __ .__ _. ..__ _ ___,_ _. ..___ _ ___._ __ .___~ 
0 10 20 30 40 50 60 70 80 90 100 
ATOM IC. PERCENT 
Figure 3. DPH Hardness of Binary Refractory Alloys at 300 K 
CJl 
1-4 
52 53 
ex: 
LJ.J 
> 
~!:: _c....,  / 
LJ.J ....J z Cl) ex: s I V) 0 I 
I- 0 Cl) 
<t ex: I CJ 
...JO I 
....J I- bl) 
-u ..i:.:.:.:  I 
I- LJ.J ;.
z .. u u.IJ- Cl) :t I 
V) 0 c,j I 
C) 
U) I 
Q) 
f/l I 
cB I 
~ 
~ 
(.'.J 
z Cl) ,_.s..:.:.,:  
ex: '+-I 
LJ.J 0 0 
I- ....J 
I- i:::: LJ.J 
ex: 0 ?
- <t- _
..-..<.,  
<t u :r: c,j 
/ 
V) V) / 
~ / 
Q) / 
f/l 
Q) -xS 
;... / 0 
p. 
Cl) / / 
(.'.J 0::: 
z C) M 
LJ.J :c 
....J z c,j 
a. ~U:::v, 
~ <tZ 1- s Cl) 
<t LJ.JO:: ,.s::: V) :i co u C) V) U) 
. 
I "Q")'  
0 ;... 
ex: 
I- ~ ?.-< 
~ ex: <t LJ.J i:x.. 
001- (.'.J 
Z I- <.n a: 
Oct> <t 
~~5 I- Figure 5. Geometry of the three-circle single-crystal 
diffractometer. 
54 55 
.c 
.0...  0 0 0 ..., i.
N n 
~ M N .... 
_ o.  0 0 C: 0 0 0 
N 
. .0c ..  0 . 0 N 
0 CX) 
0 N
.C..D.  ...
 . ' -II 
II >< 
>< 
0 
CT> 
0 
0 
1--..-t,--t-,-.. 
?---- 0 A B 
0 
........  1---- -----""-
C D 
Figur e 7. F r a ctogr a phs of Refractory Binary Alloys at 300 K (A) Tearing and 
Cup-and-Cone fracture surface of the Ductile Ta-30 at . % Nb alloy 
(B) Cleavage fra cture showing the river patterns for Mo-30 at. % W 
a lloy (C) Inte r granular fracture and cleavage fracture for polycrystal-
- line Nb-14 a t ? % W (D) clea vage f0 r actu re for Ta-9 a t .
-  %~  M- o a- ll- oy- . ----------------- --- o ? 
56 
57 
650 
....i i----------------------, ~ - ??-Mo-91 AT.~ Ta 
600 
- .. --Mo-37AT.~ Ta 0 "' (/) 550 
(I) a 
..~...  z I 'I  -Mo-21 AT."..... ?.  Ta 
0 ..., 
00 0 500 
.~....  u 
ro w 
.H..,  (/) 
0 lf.l 450 
" . 0 N I 
[/) 
>, I 
......
0
....
 
..  a:: 400 
0 ? 
<O -er: w I 
2 0 0.. I' :::::, 
..J 
<t ~ (/) 350 
I 
I I l- ro 
o 2 
Ln <t E-t ~ I I I Cl! ~ 
I-
~ H z l ' I t-
~ z lf.J ::::> 300 
VJ w [/) 2 0 I I ? <t VJ u H 'U 
2 I a: (I) H 
0 VJ VJ 0 W 
..., ro u l I a: a: s:t c.. (I) I 
I w s bO I- 0 u (I) - 250 2 I 
all 2 I- 2 ro :> 
w ? :::::, :::::, 0 H 
2 ti) <t t- ro ~ ~ 
a: ell I- o <{ P-t ' 
0 M (/) 200 
I- I 
2 (I) 0
u w C) ......
  
2 VJ 
z 
<t w ..... 0.. 
<t w a: ~ ro w > (.'.) c.. ro 
H .lf.J ~ ? )( 0 ..... z 150 N 
I ? . 00 
I (I) 100 
I H ,0- ..?..n.  
~ ........... .. ___,, 
50 
0 
2 100 200 300 
0 0 g 0 g 0 0 0 00 s:t N 0 00 g N N N N ,- ,- ~ ,- 0 
,.; ,.; ,.; ,
N
.;   ,.; ,.; ,.; ,.; ,.; 0.2 0.4 0.6 o.e 1.0 1.2 1.4 1.6 1.e 
\I ij3.l31N'\tij'\td 3::lll.l.'117 
h, ,o,o--.. 
F igure 9. Diffracted Intensity Along (h , O, 0) Axis in Reciproca
1 l Space 
for Ta-Mo Alloys, Illustrating Asymetry of the Short Range 
Order Peaks about (100) and (300) Positions. 
~ 
h2 i 
0.5 , 0.5 , O 110/ ' \ \, 210+ \\  ~(~ 19~ \\ \  \\  410t 
100 
300 
000 100 200 300 400 
0, 0, 0 0.5, 0, 0 1, 0, 0 1.5, 0, 0 2.0, 0, 0 
h1-
Figure 10. Diffracted X-Ray Intensity Distribution in the h1 h2 0 Plane of Reciprocal 
C)1 
Space for Mo at Am 00 bient Temperature. Counts per 30 sec. 
,...... -
h2 f 
05, o.5, o 110..: --- I \ \ ?~?~ \\ \ VM ?.,,,.~\\\ \ \ ?~?" 
200 
100 200 
0,0,0 300 0.5, 0, 0 400 1, 0, 0 1.5,0,0 2,0,0 
h1-
Figure 11. Diffracted X-Ray Intensity Distribution in the h h 0 Plane of Recipr
1 o c2 a l Space 
for Ta at Ambient Temperature. Counts per 30 sec. 
C)1 
~ 
h2 t 
125 
0.5, 0.5, 0 110 
150 
125 
200 
000 100 200 300 400 
0, 0, 0 0.5, 0, 0 1, 0, 0 1.5, 0, 0 2, 0, 0 
h1-
Figure 12. Diffracted X-Ray Distribution in the h1h2 0 Plane of Reciprocal Space for 
O') 
Nb- 22% Ta at Ambient Temperature . X-Ray Intensity in Counts per 30 sec. 0 
( 
300 
~ 
250 
~ 
" \ 4W 
h2 f 
125 
100 '--
o.5, os , o 110,..., ,,,n f ???? , 1'  - ,;v, \t  \'\  \ , rn~  n\\ \ n~  .)< ..,,'  11.10 f 
000 100 200 
0, 0, 0 300 0.5, 0, 0 400 1, 0, 0 1.5, 0, 0 2, 0, 0 
h1-
Figure 13. Diffracted X-Ray Intensity Distribution in the h h
1 0 2 Plane of Reciprocal Space 
for Mo-91 %T a at Ambient Temperature. X-Ray Intensity in Counts per 30 s ec. 
.O...'.)  
1,1,0 220,/ 320 ' 
) 
310 
.5,.5,0 
h2 i ( \~"~) ) 
20, 
! , 
40----
?o 
10 
?c 
100 - 200 300 0,0 ,0 .5,0,0 h1 1,0,0 1.5,0,0 
Figure 14. Diffuse Intensity Distribution in the h h
2 01  Plane of Reciprocal Space for 
Mo-37% Ta at Ambient Temperature. Diffuse X-Ray Intensity in Counts 
o. 
per 60 sec. ~ 
1, 1,0 220 - ------------..... 
320 
0.5,0,5,0 
310 
h
2 f 
40 
80 
120 
000 100 
0,0,0 200 0.5,0,0 300 1,0,0 1.5,0,0 
h
1 -
Figure 15. Diffuse Intensity Distribution in the h
1 ~ 0 Plane of Reciprocal Space for Mo-21 
a/ o Ta at Ambient Temperature. Diffuse X-Ray Intensity in Counts per 60 sec. ~ 
c,:, 
64 
65 
PLANE A PLANE B 
PLANE I PLANE II ? ? ? ? 
a a a a 
a 
a ? 0 0 a ? ? ? ? ? 0 0 ? a 
? ? ? ? 
a
a   ? 0 0 0 a ? 0 ? 0 ? a ? ? ? ? 0 
a a ? 
? ? 
0 ?
?  
a 
a a a  
? 
? 
? a ? ? ? ? 
a a a a ? ? ? ? ? ? ? ? ? ? ? ? a a ? ? ? 0 
PLANE ill 
a a a a PLAN E C a a
a ? ? ?  0 0 ? a 
a ? ? ? ?  Mo ATOMSa  0  ? ? ? ? ? a eT  a ? ? O a
M
 A o
a T
 
 O
A
M TOS MS 
0 0 ? ? 0 0 ? a 
a ? ? ? ? a  .ATOM OF Aa V ERAGE ? ? ? ? o. Ta ATOMS COMPOSITION - 54%Ta ? a 
a a a a a ? ? ?
AT
 ? ? O M OF AVERAGE a COMPOSITION - 27%Ta 
Figure 16. Model for the Short Range Ordered Structure of Mo-37 at . % Ta ? ? ? a 
F igure 17. Model for the Short Range Ordered Structure of Mo-21 at ? % Ta / 
66 
67 
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69 
57. Walker, C. B . and Keating, D. T., Acta . Cryst., 14, 1170 (1961). 
LIST OF SYMBOLS 
T * 
mal component of yield of stress 
58. Cromer , D. T . , J. Chem. P hysics , 50, 4857 (1969) . 
effective stress or ther
athermal component of yield stress 
59. Cromer, D. T. and Mann , J . B ., J . Chem. Phys., 4 7, 1892 (1967). Tc 
temperature at which r* is zero 
X 
60. Epper s on, J. E. and Spr uiell, J . E., J . P hys . Chem. Solids , 30, 1733 diffraction coordinate 
(1969). 'P diffra ction coordinate 
w 
61. Labus ch, R., Phys . Stat. Sol., 41, 659 (1970). diffra ction coordinate 
20 
sea ttering angle 
62. Mott, N. H. and Na barro , F. R. N., Strength of Crystals, Phys . Soc., X 
London, 1948. diffraction coordinate 
y 
diffraction coordinate 
63. Riddhaghi, B. R. and Asim ow, R. M., J. Appl. Phys., 39, 4144 (196 8). /\ 
x-ray wavelength 
64. Riddhaghi, B. R. and As im ow, R. M., J. Appl. Phys., 39, 5169 (196 8). I 0RD E R+AD component of diffracted intensity due to order and atomic displacement 
TF+ s 
65. Foreman, A. J. E. and Makin, J . J., Phil. Mag., 14 , 911 (1966). component of diffracted intensity due to flouresence and submultiple 
wavelength components 
66. Friedel, J., Dislocations , Addison-Wesl ey P ub. Co., Reading , 1964. component of diffracted intensity due to incoherent scattering 
67. Flinn, P. A., Acta . Me t., i , 631 (19 58). component of diffracted intensity due to temperature diffuse scattering 
from the sample 
68. Eshelby, J. D., Solid State Phys ics Volume 3, Edited by F. Seitz and component of diffracted intensity due to sharp fundamental Bragg 
D. Turnbull, Academic Press Inc., New York, 1956. reflections 
I 
69. Hobson, D. 0., Oak Ridge Na tional Laboratory Report, ORNL-3678 , H U A NG component of diffracted intensity due to Huang diffuse scattering 
1964. 1c u intensity in electron units 
fp , fq and q 
70. Dugdale, D.S., J. of Mech. and Phys . of Solids,?_, 85 (1958). scattering factors of atoms situ
ated on sites p 
K 21r A. A. 
71. Tabor, D., Hardne ss of Metals, Clarendon Press, Oxford, 1951. T (S-So ) 
Rpq 
72. Hasson, D. F., Huang , Y., Pink, E., Arsenault, R. J., Met. Trans.,~. interatomic vector 
371 (1974). h h h l ' 2' 3 continuous rectangular coordinates in reciprocal space 
N 
73. Armstrong, R. W., J. of Sci. and Ind. Res., 32, 591 (1973). total number of atoms being irradiated by the x-ray beam 
mole fractions of element A and B 
74. Arsenault, R. J., Acta. Met., 17, 1291 (1969). 
scattering factors for elements A and B 
75. Armstrong, D. A., Mordike, B. L., Z. Metallkde, 61, 356 (1970). Q, m, n discrete variables specifying an atom's position relative to the origin 
~ 
76. Walker, C. B. and Ke)Uing, D. T., Phys. Rev. 130, 1726 (1963). QIZ
m n Warren order parameters 
<o 2 ~ (o 2 ,m 
Qm n ' rQmn mean square atomic displacement parameters 
77. Averbach, B. L., Energetics in Metallurgical Phenomena, Edited by W. M. 
Mueller, Gordon and Breach, New York, 1965. 
71 
72 
(S)i~n, (S>t~n mean square cross atomic displacement parameters 
(S)F~n' (S>F!n 
translational vectors of a cubic unit cell 
base vectors reci ap 1r  oca al 2  to - , a 3 ~ and -
2 2 2 
unit vectors specifying the direction of the scat tered and incident beams, 
respectively 
PBA llmn conditional probability of finding an A atom at the site p if there is an 
atom at site q 
Q 
'YQmn three dimensional first-order size-effect parameters 
Lt~n, Lt~n, LF!n components of the displacement of an atom off the average lattice site 
parallel to ~ , a2 and a3 respectively
2 .  2 2 
A12m two dimensional Warren order parameters 
Q 
rmn two dimensional first order size-effect parameters 
VITA 
Na:rne : Roamer Edward Predmore 
Permanent Address: 14003 Flint Roc k Road 
Rockville, Maryland 20853 
D egree and Date to be Conferred: Ph.D., 1975 
Date of B irth: August 10 , 1937 
P l ace of Birth: Detroit, Michigan 
Seconda ry Edu cation: Caro High School, 1956, Caro, Michigan 
Date of 
Collegiate Institutions Attended: Dates Degree Degree 
Michigan Technological 1956- 60 B . Met. Eng. 1960 
U niversi ty (cum laud) 
Northwestern Univers ity 1960-60 
C a tholic Univers ity of America 1962-64 M. S. (Eng.) 1964 
University o f M aryland 1964-75 P h.D. 1975 
Major : Engineering Materials 
Minor: Chemical E ngineering, Mechanic al Engineering 
Publications: 
1. R. E. Predmore, S. Ahmed and R. Kumar, "Predictions of Solar 
Induced R esponse of Thin-Walled Open- Section Booms for Design. " 
Proceedings o f the Internationa l Symposium on Experimental Mechanics , 
Universit y of Waterloo, Waterloo, Ontario, Canada, June, 1972. 
2. R. E. Predmore, R . J. Arsenault and C. J. Sparks, Jr., "Strengthen-
ing and Fra cture of T a , Nb, Mo and W. Binary Solid Solutions with 
Short Range Order" P roceeding s of the International Conference on 
Mechanica l Beha vior of Materials, Kyoto, Japan, 1971. 
3 . R. E. Predmore, R. J. Arsenault , and C. J. Sparks, Jr., " Local 
At omic Arra ngements in Ta-Mo and Ta-Nb B. C. C. Alloys." 
VITA - Continued 
Proceedings of the Seminar on Metals, August, 1971, Tokyo, Japan, 
The Society of Materials Science, J?apan, Ed. S. Taira. 
4. R. E ? Predmore "Experimental Thermal Mechanics of Deployable Boom 
Structures" t>ignificant Accomplishments in Technology, 1970, National 
Aeronautics and Space Administration, Washington, D. C. 1972. 
5. R. E ? Predmore, J. Jellison and C. L. Staugaitis, "Friction and Wear 
of Steels in Air and Vacuum" ASLE TRANS. 14, 23 (1971) ? 
6. R. E. Predmore and R. J. Arsenault "Short Range Order of Ta-Mo 
Alloys" Scripta Met. _!, 213 (1970) . 
7 ? R. E. Predmore and E. P. Klier "Martensite Start Temperatures 
Versus Pressure for 43:XX Steels" Transactions of ASM 62, 76 8 (1969). 
J ? Jellison, R. E. Predmore, c. L. Staugaitis "Sliding Friction of 
Copper Alloys in Vacuum" ASLE Transactions 12, 771 (1969). 
9 ? H. E . Frankel, A. J. Babecki and R. E. Predmore, "Some Considera-
tions of Advanced Welding Technology" British Welding Journal April 
(1966) 189.