Atomic arrangements in titanium-molybdenum solid solutions

ATOMIC

ARRANGEMENTS

IN TITANIUM-MOLYBDENUM

J. M. DUPOUY

SOLID

SOLUTIONS*

and B. L. AVERBACH?

The short range order and size effect coefficients as well as the thermal and static atomic displacements h&ve been measured in b.c.c. solid solutions of titanium-molybdenum using X-ray diffraction techniques. These solutions exhibit a strong preference for unlike near-neighbors even though a superlattice was not found. The size effect coefficients for the first shell of atoms were negative, indicating that the molybCenter-to-center distances bet,ween denum atoms were smaller than the titanium atoms in solution. the different pairs of nearest neighbor atoms were calculated from the size effect coefficients and the Ti-Ti and MO-MO distances tended to approach the average distance in the solution lattice parameters. At 75 per cent molybdenum the NO-MO distance at compositions between 20 and 50 at.% molybdenum. was smaller than in pure molybdenum and this was taken to indicate an electron exchange in the sohltion. ARRANGEMENT

D’ATOMES

DANS

LES

SOLUTIONS

SOLIDES

DE

TITANE

MOLYBDENE

L’ordre zt courte distance et des coefficients d’effet de dimension einsi que les dbplacements atomiques thermiques et statiques ont 6tB mesur& dans des solutions solides de titane molybdbne de reseau cubique cent& par diffraction de rayons X. Les solutions montrent une grande pr&f&ence pour leurs voisins non semblables, quoiqu’une surstructure n’a pas pu &re trouv8e. Les coefficients d’effet de dimension pour les atomes de la premihre orbite Btaient &g&ifs, co qui indique que les atomes de molybd8ne Btaient plus petits que les atomes de titan0 en solution. Les distances d’un centre iLl’autre entre deux paires diffbrentes d’atomes les plus rapprochbs ant BtB c&x&es d’aprbs le coefficient d’effet ou dimension et d’ap&s les param&res du rkseau. Les distances Ti-Ti et MO-MO tendent iLs’approcher de la distance moyenne dans la solution pour des teneurs entre 20 et 50% atomiques de molybdhne. Pour une teneur de 75% de molybdBne la distance Mo-Mo Qtait plus petite que celle dans le molybdene pur, ce qui indiquerait un &change d’6lectrons dans la solution. ATOMANORDNUNGEN

IN

FESTEN

LiiSUNGEN

AUS

TITAN

UND

MOLYBDliN

RGntgenographisch wurden die Nahordnungsund GrBssaneffekt-Koeffizienten und die therm&hen und statistischen Atomverschiebungen in k.r.z. festen Liisungen aus Titan und Molybdiin bestinunt. Diese Liisungen zeigen ein starkes Vorherrschen van ungleichen niichsten Nachbarn, obwohl keine tiberstruktur gefunden wurde. Die GrGsseneffekt-Koeffizienten der Atome erster Schale waren negativ; des weist darauf hin, dass die Molybdiinatome in der Liisung kleiner sind als die Titanatome. Die Mittelpunktsabstiinde zwischen verschiedenen Paaren niichstbenachbarter Atome wurden &us den Griisseneffekt-Koeffizienten und den Gitterparametern berechnet. Ti-Ti und M+Mo Abstiinde nlihern sich zwischen 20 und 50 At% Molybdiin dem durchschnittlichen Atomabstand in der LGsung an. Bei 75 At% MolybdBn ist der Mo-Mo-Abstand kleiner 81s in reinen Molybdiin, dies wurde alsAnzeichen eines Elektronenaustauschs in der LGsung gedeutet.

1. INTRODUCTION

The

arrangement

of

atoms

averaged in

a

binary

solid

of

the

individual

from the average determined

interatomic

by

distances

by the cell dimensions

is

expressed

in terms of the size effect coefficients for each shell, pi. The spectrum of elastic waves associated with the thermal motion of the atoms may be characterized

by the square of the dynamic

METALLURGICA,

VOL.

displacement

9, AUGUST

1961

position

in

the

lattice,

lattice, Q,

averaged

over

every

position

in the

may also be measured.

The short range order and size effect coefficients are determined from the diffuse scattering and thus provide

averages over small correlation distances in the lattice. In practice it is difficult to obtain information for distances greater than the sixth nearest neighbor, and in polycrystals data are frequently restricted to the first two atomic shells. On the other hand, the thermal and static displacements are determined from the intensities of the diffraction lines and are thus averaged over correlation distances

* Received December 14, 1960; revised February 8, 1961. t Department of Metallurgy, Massachusetts Institute of Technology, Cambridge, Massachusetts. This paper is based on the Sc.D. dissertation of J. Dupouy at M.I.T. ACTA

and

from the average lattice point and the square of this displacement

the short range order coefficients, ui, which indicate the preference for unlike or like neighbors in a particular shell. If the atoms are of different size, the deviation

time

q, or the Debye temperature, 0. If the atoms differ in size there is also a static displacement of each atom

solution may be described in terms of paramet,ers which can be measured by means of X-ray diffraction The average composition of the ith shells techniques. of atoms about an atom at the origin is described

over

which are large enough to provide coherent diffra.ction effects. These longer correlation distances are of the 755

ACTA

756

METALLURGICA,

order of 100 A or greater.

It is interesting

that a difference

in atomic

size produces

both

large

small

and

correlation

allows an independent evaluation although the method of averaging case. Titanium-molybdenum this study.

distances.

This

ofatomic

size effects, is different in each

solutions

The phase diagram(l)

to note effects at

were chosen

for

is shown in Fig. 1.

VOL.

9,

1961

was prepared at the Watertown compositions molybdenum. over

Arsenal.

The actual

were 19.5, 29.5, 40.5, 48.6 and 75.4 at. % Each button was remelted and turned

several

times

in order

to eliminate

dendritic

structure and the final ingot was a cube approximately 1.5 in. on edge. Attempts to use vacuum-sintered scattering

filings for diffuse

samples were unsuccessful.

Long sintering

There is a large b.c.c. phase field with no indication of There is a large ordered phases or compounds.

times were required in order to sharpen the diffracti m lines and to obtain sufficient mechanical strength;

difference in the scattering

the resulting specimens were invariably

contaminated

with

to

the combination atom,

power of these atoms, and

is fairly unique in that the heavier

molybdenum,

has a smaller

distance than the lighter titanium

nearest neighbor

atom.

This should

result in a negative value for the nearest neighbor size effect coefficient, before.

/?i, and this had never been observed

In addition,

the only

which had been investigated

other b.c.c.

previously

solutions

were lithium-

sufficient

hexagonal ingot

phase.

along

helium

in Vycor

1100°C.

at a logarithmic

are described in the following sections. attention is focussed on an improved method reduction

and the results are discussed 2. EXPERIMENTAL

only

the

for 24 hr at from

and the other was cooled

rate from 1100 to 350°C over a period

superficially

These samples were

contaminated; polishing

the surfaces followed

were

by electro-

polishing in a solution of 5 per cent perchloric in glacial acetic acid. These samples all showed marked preferred

METHOD

the

orientation,

but

subsequent

experiments

showed that the diffuse scattering was not affected by

pure molybdenum

arc-melted

containing

and 50 at. ‘A molybdenum University

temperature

cleaned by mechanical

in the final

directions;

and annealed

of data

The alloys were prepared from iodide titanium Ingots

tubing

of 20 days and then quenched.

(a) Materials

phere.

perpendicular

alloys Special

section.

form

One set of samples was water-quenched

a relatively

on five titanium-molybdenum

nitrogen

Solid samples were cut from each

three

the annealing

sma.11size effect.

and

specimens were packed in foils of a titanium-14 wt. % molybdenum, sealed under a partial pressure of

magnesium solid solutions,(2) and this system exhibited Measurements

oxygen

and

under an argon atmos-

approximately

20, 30, 40

were melted at New York

and an alloy with 75 at. % molybdenum

this amount

of texture.

Samples with random orientation measurements filings.

These

were obtained filings

were

for the Bragg line

by using loosely packed sealed

in Vycor

helium and annealed for 1 hr at 1050°C. time

was long

diffraction

enough

to

lines sufficiently

sharpen

under

The annealing the

high

angle

so that they could be well

resolved but was short enough to avoid contamination. The filings were then mixed with Duco cement and acetone to form a flat diffraction (b) X-Ray

sample.

measurements

The diffuse scattering measurements

were made with

monochromatic

CuK, radiation diffracted from a bent

silicon

cut

crystal

to

the

(111)

orientation.

The

detecting assembly consisted of a proportional counter and a pulse height analyser arranged to eliminate the one-third

wavelength

of the white radiation

(the one-

half component was eliminated by the silicon crystal), the cosmic background and the fluorescence radiation from titanium. Readings were recorded continuously

0

Ti

0.5 Alomic fraction

P MO

FIG. 1. Titanium-molybdenum phase diagram.

1.0 f40

on a horizontal spectrometer with the counter rotating at 0.25” in 2 8/min and measurements were made from 10 to 132’ in 2 8. Flat samples were used and the geometry focussing

of the system condition.

satisfied

the usual

double

DUPOUY

AVERBACH:

AND

The specimens were rotated around the axis normal to the reflecting surface to minimize the effects of preferred orientation and the coarse grain size. The diffuse intensity was found to be insensitive to the preferred orientation. Fig. 2 shows the scattering recorded from samples of the 30 % molybdenum with the greatest difference in texture. One sample was so highly textured that the (200), (220) and (222) lines were almost absent, yet the diffuse intensities for both samples were quite similar. In practice the diffuse intensity was recorded from each of three samples cut at different angles from the ingot and the intensities were averaged. In the case of the 50 ‘A alloy only two samples were available ; only one was availabte for the 75 % alloy. The intensities of the diffraction lines were measured with MoK, radiation and a scintillation counter. A holder filled with a mixture of powder and cement was pressed by a spring against the wall of a small chamber which could be filled with liquid nitrogen. The assembly was enclosed in an evacuated container which had a Mylar window glued with epoxy resin. IIeating tape was wrapped around the window to prevent the condensation of moisture. The temperature was measured by a thermocouple embedded in the powder. The diffraction lines were recorded and the areas under the peaks measured with a planimeter. The first four diffraction lines were ignored because of extinction effects, and the remaining eight to twelve lines were used for the determination of thermal and static displacements.

Ti-Mo

SOLID

SOLUTIONS

757

3. REDUCTION

OF DATA

(a) Thermal and static displacements

The integrated intensity of a diffraction line for a binary alloy is given by I = ANF2m(LP) exp [ -2( B, + B,) sin2 e/A21 (1) where A is a constant, Ii the number of atoms irradiated, m the multiplicity, F the structure factor, _l.Z the Lorentz-polarization factor (1 + cos2 2i3)/sin20 00s 8, B, the Debye-Waller factor for thermal displacements and B, the static displacement factor.(3) The thermal factor may be written in terms of the Debye temperature 0 as follows: 3,

= mk-p [tp(Y) 4 f//4:1

=

where m is the average mass of the atom in solution, h is Planck’s constant, k the Boltzmann constant, T the absolute temperature, y = O/T and v(y) is the Debye integral.t4) Plots of In I versus sin2 S/;l” were straight lines, indicating that the powder samples were quite random. Intensities were measured at 108 and at 295°K and values of 3, and B, were determined for each alloy. The mean square atomic displacements may be calculated from the relat,ionships : B, = 4?+G7 and

80

3, = 4n%hs2 .

\,

60

Ti -30 at~~~~percentMO Specimen 33 ---Specimen 31 i

40 0

-I I

0.5

I

1.0

(2)

I

I

1.5

2.0

I 2.5

I

3.0

I 3.5

I

x.. 20 sin8 A

Pra. 2. Comparison of scattering from two specimens with preferred orientation.

W4

758

ACTA

METALLURGICA,

VOL’.

9,

1961

hydrogen

were taken

incoherent

scattering of hydrogen was calculated from

the tables coefficients

The contribution

average 200-

I

’

/-*

0.4 -

2

I

I

I

I

I

I

-

02

-1 I

x (1 x\

I

I

form

of

the

pattern

to have the following

I

I,

*.

I

I,

tion -;‘. 1.0

are

listed in Table 1 and the variations of Debye temperature and B, are shown in Fig. 3. It is interesting to note that the thermal

and static

of the same magnitude

for each composition. Debye

displacements

temperature

but the present data extrapolate

close

to

300”K,

the

value

are There

of b.c.c.

estimated

in t$he Debye tempera-

on an absolute

scale@)

by

comparison with the scattering from lucite, (C,H@,) ; an intensity measurement at 130’ in 28 was used for standardization. Values for the coherent

and incoherent scattering factors for carbon were taken from Berghuis et aZ.(9) and Keating’lO), respecScattering factors for oxygen were taken from

Freema,n(ll). TALBE

Values

for the coherent

scattering

1. Thermal and static displacements Ti-Mo solutions

in

0.68 0.57 0.47 0.34 0.22

0.46 0.31 0.24 0.18 0.10

and

Averbach for b.c.c. lattices. Values of B, were obtained from the measurements of line intensities 1);

the scattering

for

both

elements

Templeton( temperature A

scattering

for titanium

were

were

taken

from

Dauben

and

It was thus possible to calculate the diffuse scattering from equation (4).

similar

arises from

factors

and for molybdenum from The dispersion corrections

contribution the static

to

the

atomic

diffuse

scattering

displacements.

This

sin2 0/n2]).

(5)

has the form :(20,21)

x

The modulating W(x)

(1

-

exp [-2B,

function

and was calculated

H(z)

is similar in form to

here for a b.c.c.

of

observed

for f.c.c. powder patterns.@n

B, were taken from the diffraction and the static diffuse intensity

powder

0.093 0.085 0.077 0.065 0.052

0.075 0.063 0.055 0.048 0.036

The values of

line data (Table 2)

contribution

was thus

ralcula,ted. The diffuse scattering in absolute units was corrected for polarization and for the contributions indicated above,

and the remaining

diffuse

scattering

which

describes the local atomic arrangement may be written as follows :(s)

I = mAmB(.fA -.fd2

1+

( co9 27rrix -

I-_-

300 314 335 385 449

func-

by Herbstein

pattern. The modulations were small and the function U(Z) was taken as unity. A similar situation was

(b) Short range order and size coeficients were placed

(4)

and fi the scattering

calculated

by

ture at 75 at. % molybdenum.

The intensities

sin2 ~9/1~])

to a value

Kaufman(5) ; the Debye temperature for pure molybdenum was taken as 380”K.‘69’) It is evident that there is a significant maximum

has been

taken from Watson’l’) James and Brindley’ls).

temperature and static displacement fw!tor.

for the

which

(Table

fraction MO

Values for the thermal and static displacements

data

exp [ -2B,

where mi is the atomic fraction

0.5

FIG. 3. Debye

0.2 0.3 0.4 0.5 0.75

The

for a powder

factor for the ith atom, and W(x) is a modulating

xi,

Atomic

tively.

with

to be the weighted

constituent.

has been shown by Warreno5)

\

Lx._

0

quite

each

assumed

x

1’ I

0.1 -’ I I

are no

of the Compton modified scattering

diffuse scattering

,’

0.3

titanium,

for

the

absorption

from the results of Bewiloguao3),

contribution

temperature

and

form :

0.5 -

“a

I

McWeenydz),

of Bewilogua(13). The mass were taken from Barrett?).

was calculated the total

from

sin SC&% +

27rr.x

i:=,

sin 27rr.x -2 29wix

(6)

where Ci is the number of atoms in the ith shell, TV = (distance to shell i)/a, a is the lattice parameter, x = 2a sin e/L, 1 is the X-ray wavelength,

and 8 is the

DUPOUY TABLE Specimen condition

Atom

quenched quenched slowly cooled quenched slowly cooled quenched slowly cooled quenched

Bragg angle.

AVERBACH:

AND

Ti-Mo

SOLID

fraction

%3

-0.29 -0.20 -0.27 -0.19 -0.29 -0.24

0.4

!

0.5 0.75

ui is

neighborhood transforms

where pi is the probability

p,lmB

(7)

of finding a B atom in the

ith shell about an ,4 atom at the origin.

The size effect

is given by

similar.

t%

-0.06 -0.04 -0.15 -0.14 -0.21 -0.12 -0.24 -0.12

0.08 0.07 0.10 0.06 0.12 0.05 0.11 0.07

0.02 0.04 0.04 0.02 0.03 0.03 0.04 0.07

i

The short range order parameter ui = 1 -

759

2. Short range order coefficients mi and size coefficients, /li

defined

parameter

SOLUTIONS

-0.079 -0.071 -0.073 -0.060 -0.063 -0.046 -0.056 -0.052

of the fourth

0.013 0.033 0.032 0.025 0.033 0.030 0.032 0.057

-

and sixth. shells.

for all of the alloys

The

were qualitatively

It was assumed therefore that the region in

the transform

from r = 0.4 to r = 1.3 was associated

only with the first two shells. Nineteen values of r were taken in this interval and values of yi, y2, /3i and /12 were obtained

by a least squares

fitting.

This

procedure

gave values of ui, tc2, ,$ and p2 which were

physically

plausible.

Values for CQand c+, were then

estimated

from

transform,

the

assuming

that

all

values above p2 were zero ; the transforms consistently indicated negligible values for cl3 and I+ The values of the local arrangement coefficients calculated in this where The &ha = (TAB - ri)/ri. 17 = f~lf~ and distance rbA is the distance between two A atoms with

manner are listed in Table 2.

one at the origin and the other in the ith shell, and ri is

synthesizing

the average distance to the ith shell determined the lattice parameter. The values

of ui and pi were derived

from

from

the

measurements of the diffuse intensity by means of a Fourier transform.(22) The transform may be written approximately F(r) =

arbitrary

scattering

(- g

(r-

with the observed

coefficients

damping

factor

in this way

diffuse intensity

A is

in Fig.

is quite good and was consistently

is estimated

It is difficult to calculate but the precision

to be ho.005

&O.Ol for u4 and a6 and *0.002

of the

for cc1 and cc2,

for B1 and /12.

Lattice parameters were also determined from spectrometer data during the course of the investiga-

ri)2)

K(x) = I/[m,r~(f,

calculated

the overall error accurately,

cipi;~2

The

by errors of the latter type.

curve

good for each set of data.

&$&-. exp (- g(r - riJ2)

(6).

values of r. On the other hand, the intensity curves are

5 ; the agreement

m

2 and equation

slowly varying errors have an effect only at very small

compared

exp ( -bb2x2) sin 2rrrx dx

(r - ri) t-Z--i=, b3

where

CX~and & listed in Table

may be made by using the values of

transforms are most affected by errors which oscillate with frequencies between 2nri and 2nri; constant or

typical

s0

exp

the diffuse intensity

very much influenced

as

&IX& S(z)

= ,f

A critical test of the coefficients

tion. -fs)2]

-

1,

b

is

an

to reduce the fluctuations

arising by cutting off the data at x(max) instead of infinity, and yi = ai - pi. A typical transform, evaluated by means of Lipson-Beever strips is shown in Fig. 4. It is obvious that contributions of u and /I to the first shell cannot be separated from the contributions to the second shell. The coefficients for the third shell are negligible, but there appear to be some contributions in the

These

values,

estimated

to

be

accurate

to

f0.003 A, are shown in Fig. 6 and agree reasonably well with other measurements.(l) Body-centered titanium does not exist at room temperature and the value for pure titanium is that obtained by Levinger(23) from extrapolations of similar curves with many alloying elements. The agreement in lattice parameters was taken to be an indication that the samples were not contaminated by hydrogen, oxygen or nitrogen

during

would have parameters.

heat

treatment.

had a significant

These

effect

impurities

on the lattice

760

ACTA

METALLURGICA,

VOL.

9,

1961

FIG. 4. Fourier transform for 0.5 MO, quenched alloy.

140

I

I

I

Cl20 .c5 $00 L t z 00 s =60 t

I

I

I

I

Experimental ---Calculated with coefficients from Fourier tronsform

-

E4020 0

I 1.0

I 0.5

0

I 1.5

I 2.0 X= 20 sin 8 A

I 2.5

I 3.0

I 3.5

FIG. 5. Local arrangement diffuse scattering, 0.5 MO, quenched alloy.

I

I 3.26

I

I

I

L

I -

Hansen et al 0

‘\’

I

this work

‘1

3.26

\

b ; ‘, E 0 $

3.24

J\ \

3.22

S 3

.\

3.20

\

\ 0

\ \

3.16

Atomic

fraction

MO

FIG. 6. Lattice parameters.

I

DUPOUY 4. DISCUSSION

AND

OF

AVERBACH:

thus

show

a strong

SOLID

‘761

SOLUTIONS

for a random f.c.c. solution,

RESULTS

All of the alloys exhibit sizeable negative values of a1 and

Ti-Mo

preference

for

unlike

and a similar calculation

for b.c.c. solutions was used to compute values of & from the values given in Table 1. The variation of

nearest neighbors. Values for ua and a, are positive, but a6 is again negative and quite large in magnitude. This pattern of short range order indicates a strong

& with composition was correctly predicted, but all of the values were too small and the correlation

tendency

range order in these solutions. The relationship between

support

to form

an ordered

of this is indicated

solution,

and further

in that the slowly cooled

solutions exhibited more intense short range order than the quenched alloys. However, no evidence of a superlattice was found in the slowly cooled samples. The average number of molybdenum about a titanium

atom is listed for each composition

in Table 3. The intensity the 75 at. % molybdenum

~_

fraction MO

-_--

Number

I i

of molybdenum neighbors quenched

/-:ydom

0.2 0.3 0.4 o.;, 0.5 _~_____ __~.

of the short range order in alloy is indicated in that

3. Average number of molybdenum neighbors about a titanium atom

TABLE

Atom

nearest neighbors

;:;

~

4:o 6.0

t-

31: 7.5

relationship

and the individual

between

the

average

inter-

interatomic

distances

which may

be written as follows: r1 = mA2rLU1 + 2mAm,rA,l

uniquely

mAmBul [2r~~1 -

calculate

from

these

@aA1 +

the two

procedure

lattice

+ m,,2rBB1 (10)

.r~~l)l

in the case of b.c.c. solutions.

to

approximate The

It:;

is assumed

was not found.

It is also evident that the size effect coefficients and the static displacements occurrence

for these solutions

of negative

values

of &

are large. indicates

clearly, denum

using equation (8), that the heavier molybatoms have the smaller center-to-center This was expected from the distance in solution. nearest neighbor distances in the pure materials. However, the values for pa were consistently positive and quite sizeable, pairs

This requires that MO-MO second

have

a separation

larger than

that

deduced from the lattice parameter. This would only seem reasonable if a second neighbor MO-MO pair has a high probability of including a titanium atom in between,

inter-

individual

It is

distances

relationships

and

an

was used.

parameters

exhibit

a large

negative

that the MO-MO and Ti-Ti

distances

in

the solution are the same as in the pure materials, the

it is surprising that a superlattice

neighbor

individual

deviation from Vegard’s law and this suggests that Ti-Mo distances are smaller than the average. If it

an average of 7.5 out of a possible 8 nearest neighbors about a titanium alloy are molybdenum alloys, and

The

additional

impossible

______ slowly cooled __~_~

the

atomic distance deduced from the lattice parameter or

where rl = al/3/2

nearest

of the high degree of short

atomic distances and the nearest neighbor size effect coefficient #I1 are given in equation (8). There is an

f

3.1 1

failed because

nearest

1.9

~

probably

calculated

values

of & are of the correct

rich alloys.

If only the Ti-Ti

as indicated reasonable

tions of molybdenum. to retain

their

If the MO-MO pairs are assumed

original

the resultant

Ti-Ti

distances

are reasonable at high concentrations of titanium unrealistic in molybdenum-rich alloys.

and

An approximate set of distances was obtained by using the reasonable values of Ti-Ti and MO-MO in Fig. 7 and the resultant Several

Borie has derived such a relationship(20)

values

distances are shown in Fig. 7(b) ; the Ti-Ti

Thus, nearest

values of c.

are

of molybdenum

since they are little affected by the values chosen for Ti-Ti, but the values are implausible in dilute solu-

with the high

the presence of atoms of different size, it should be possible to calculate the values of p1 from the observed

to

varies

in Fig. 7(a) ; the MO-MO distances at the high concentrations

and this is quite consistent

inverse is true for the titanium atoms. Since both the static displacements and the size effect coefficients arise from the same basic effect, i.e.

pairs are assumed

retain their original size, the MO-MO distance

degree of short range order observed.

neighbor MO-MO pairs are closer together and second neighbor MO-MO pairs are farther apart than the the corresponding average interatomic spacings;

sign but

considerably larger in absolute value in titanium-rich alloys and considerably smaller in the molybdenum-

features

independent calculation.

curve is shown

of these interatomic

in Fig. 8.

distances

are

of the detailed assumptions made in the In the region of 20 at. “/g molybdenum

the Ti-Ti distance must be smaller than in pure titanium and in the 75 % molybdenum region the MO-MO distance must be smaller than in pure molybdenum . One of the striking features of the MO-MO distances is the apparent decrease below the pure metal value, even though the molybdenum atom is the smaller to begin with. There are insufficient data to

ACTA

762

METALLURGICA,

VOL.

9,

1961 5. CONCLUSIONS

This

work

indicates

that

titanium-molybdenum

b.c.c. solid solutions exhibit a very strong short range order which

extends

for relatively

large correlation

distances in the lattice. The static displacements and size effect coefficients show that the atoms are of very much different denum

atoms,

size in solution,

and the molyb-

which are smaller than the titanium

atoms, become even smaller in the vicinity of 75 at. % molybdenum. The Debye temperature also exhibits a

2.7 -

maximum in the vicinity of MosTi. There was no evidence for a superlattice or compound in any of these

alloys

although

the

short

range

order

did

increase on slow cooling. ACKNOWLEDGMENTS

The authors would like to acknowledge the assistance of the Office of Naval Research

and the U.S. Atomic

Energy Commission in providing

the financial support

for this research. They are also grateful Abrahamson at the Watertown Arsenal assistance

in alloy preparation

of New York many

2.7 0

I 0.2

I I 0.4 0.6 Atomic fraction MO

I 0.8

I

provide a unique explanation but it would appear that the molybdenum atom would have to lose one or more electrons in forming these solutions. be considered

toward compound

evidence formation

for a strong

of the materials.

and to Dr. Margolin

for his help in providing We

are also indebted

to

Professor M. B. Bever, Dr. Roy Kaplow and Dr. Giinter Nagorsen of M.I.T. for valuable discussions and other assistance.

FIG. 7. Nearest neighbor distances (a) assuming Ti-Ti constant (b) assuming MO-MO constant,.

also

University

to Dr. for his

This could tendency

at 75 at. % molybdenum.

REFERENCES 1. M. HANSEN. E. L. KAMEN. H. 11. KESSLER and D. J. MCPRIRSCJN;Trans. Amer.’ Inst. Min. (Metall.) Engrs 191, 881 (1951). 2. F. H. HERBSTEINand B. L. AVERBACH,Actcc Met. 4, 414 (1956). 3. K. HUANG, PTOC. Roy. Sot. A190, 102 (1947). 4. R. W. JAMES, The Crystalline State Vol. 2. Bell, London (1950). 5. L. KAUFMAN, Acta Met. 7, 575 (1959).

FIG. 8. Probable nearest neighbor distances. b-

2.7

2.6 Atomic

fraction

MO

DUPOUY

AND

AVERBACH:

6. A. Euczax in Wien-Ha,rme’ H~~buch der Expe~~e~t~~phyeik Bd. 6, Teil 1. Springer, Berlin (1929). 7. M. BLACKMAN in Handbuch der PhysitC Bd. 7, Teil 1, S. 325. Springer, Berlin (1955). 8. B. E. WARREN and B. L. AVERBACH, Modern Research Techniquues in Physical Metallurgy p, 95. American Society for Metals, Cleveland (1953). 9. J. BERQHUIS, I. M. HAANPPEL, M. POTTERS, B. C. LOOPSTRA, C. H. MCGILLAVRY and A. L. VEENENDAAL, Acta Cr.@., Camb. 8, 478 (1955). 10. D. T. KEATINO and G. H. VINEYARD, A& Cry&., Camb. 9, 895 (1956). 11. A. FREEMAN, Acta Cry&, Camb. 12, 261 (1959); 12, 929 (1959). 12. R. MCWEENY, Acta Cry&, Camb. 4, 513 (1961). 13. L. BEWILOQUA, Phys. 2. 32, 740 (1931). 14. C. S. BARRETT, Structure of Metals. McGraw-Hill, New York (1952).

Ti-Mo

SOLID

SOLUTIONS

763

15. B. E. WARREN, Acta Csyst., Camb. 6, 803 (1953). 16. F. H. HERBSTEIN and B. L. AVERBACH. Acta Cwst.. Camb. ” 8, 843 (1955). 17. R. E. WATSON, Tech. Rep. No. 12, Solid State ano! Mole-

cular Theory Group, M.I.T. (1959). 18. R. W. JAMES and G. W. BRINDLEY, 2. Kristallogr.

19. 20. 21.

22. 23.

78,

470 (1931). C. H. DAUBEN and D. H. TEMPLETON, Acta Cry&, Camb. 8, 841 (1955). B. BORIE, Acta Cry&., Camb. 10, 89 (1957). C. R. HOVSKA and B. L. AYERBACH, J. Appl. Phye. 80, 1532 (1959). P. A. FLINN, B. L. AVERBACN and P. S. RUDMAN, dcta Cry& Camb. 7, 153 (1954). B. W. LEVINQER, Trans. Amer. Inst. Min. (Metall.) Engrs 197, 195 (1953).