THE LOW TEMPERATURE SPECIFIC HEATS OF TRANSITION METAL ALLOYS

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THE LOW TEMPERATURE SPECIFIC HEATS OF

TRANSITION METAL ALLOYS

D. Moody, M. Huq

To cite this version:

D. Moody,

M. Huq.

THE LOW TEMPERATURE SPECIFIC HEATS OF

JOURNAL DE PHYSIQUE Colloque C6, suppl6ment au no 8 , Tome 39, aoiit 1978, page C6-779

T H E LOW TEMPERATURE S P E C I F I C HEATS OF T R A N S I T I O N M E T A L ALLOYS

D.E. Moody and M. Huq

(+)

Physics D e p t . , University of

Leeds, Leeds

LS2

9JT, U.K.

~6sumE.-

Nous donnons de nouvelles mesures de chaleur specifique

3

basse temperature de quelques

alliages de mdtaux de transition. A l'aide des rlsultats, nous pouvons obtenir des valeurs de la

chaleur spgcifique Electronique, qui sont diffdrentes des pr6dictions du modsle de Miedema.

Abstract.- New measurements are presented of the low temperature thermal capacity of some transition

metal alloys. From the results we have derived values of the electronic specific heat, which are

quite different to the predictions of Miedema's model.

INTRODUCTION.- In the course of developing highly

successful rules describing the formation of alloys

and intermetallic compounds Miedema /1,2/ introdu-

ced an electronegativity scale, based on experimen-

tally determined work functions and adjusted within

the experimental error to improve the self consis-

tency of the charge transfer model upon which the

rules were based. Estimates of the charge transfer

occurring on alloying indicated that this was sim-

ply related to the difference in electronegativi-

ties of the alloying elements, so that the trans-

fer could now be estimated for any particular alloy.

Subsequently, Miedema showed that both elec-

tronic specific heats and superconducting transi-

tion temperatures of transition metal alloys could

be predicted in terms of electron transfer, and it

seemed that the contributions made by each site to

the density of states at the Fermi level, the at-

tractive electron-phonon interaction, and the re-

pulsive Coulomb pseudopotential are almost entire-

ly determined by the on-site electron concentra-

tion, that is, the atomic number plus the charge

transfer on the site /3,4/. In the initial applica-

tion to y values /3/, which ignored the electron-

phonon enhancement, Miedema suggested that measure-

ments be made on a number of unexplored alloys, cho-

sen on the basis that the rigid band and charge

transfer models gave quite different predictions.

Although this model was later modified to incorpo-

rate electron-phonon enhancement, the predictions

of

y

values were substantially unchanged. Some of

the suggested alloys have now been measured and

these and other results are reported in the follo-

wing.

(+)

Now at University of Mosul, Iraq.

EXPERIMENTAL RESULTS.- Specimens were formed by ar-

gon arc melting, using Johnson Matthey 'Specpure'

materials, and were vacuum annealed at 900°c prior

to measurement in our computer controlled calorime-

ter /5,6/, operated in the temperature range

1 . 4

-

4.2 K. The results are presented in the conventio-

nal graphical form in figure

1

and are shown as

smooth curves since the scatter is imperceptible

on this scale. Most of the curves show some upward

curvature and in these cases the results have been

parametrised by fitting the equation C

=

A

+

yT

+

B T ~

rather than the usual

fl

+ 6T3,

and the coef-

ficients derived by minimising

Z

DC

-

Ccalc

)/cl

are presented in table I. The relationship of the

derived yvalues to the experimental results is al-

so shown in figure

l

by plotting the line of

YT

+

v 3

for each alloy. Apart from five of the alloys

suggested by Miedema, results are also included for

Pd5Mo and PdSNb, which extends earlier work at lo-

wer concentrations /7/.

It is not clear at this stage what significan-

ce should be attached to the constant term

A

in the

specific heat of most of the alloys, but it can be

seen from figure

1

that the only y value which

might be seriously in error is that for Pt30W.

TABLE I

:

Specific heat contributions for the alloys

The concentration of the second element, quoted in

c o l a

1

as atomic percentage, has been calculated

from the weights of the constituents.

Alloy Concentration y

6

A

rms dev

(if analysed) (all in mJ for lmole)

(%)

F i g , I : S p e c i f i c h e a t s o f t h e a l l o y s . The f u l l li- n e s show t h e e x p e r i m e n t a l r e s u l t s , t h e b r o k e n l i n e s yT+f3T3

.

d a t a , b u t s i n c e t h e development o f o u r computer c o n t r o l l e d c a l o r i m e t e r h a s removed a l l impediments t o e x p e r i m e n t a l p r o g r e s s s a v e t h a t of specimen pre- p a r a t i o n any p o s s i b l e r e v i s i o n i s l i k e l y t o be a c o n t i n u i n g p r o c e s s .

The main need now i s t o e x t e n d t h e e x p e r i m e n t a l work t o i n c l u d e many more a l l o y s c h a r a c t e r i s e d by a l a r g e e l e c t r o n / a t o m d i f f e r e n c e between t h e c o n s t i t u e n t s , i n t h e c o u r s e of which we hope t o s e e , f o r example, whether t h e v e r y l o w y v a l u e found i n Pd20Ti and p r o b a b l y o c c u r i n g i n a number of o t h e r Pd b a s e d a l l o y s ( i n d i c a t i n g a s p l i t band regime) w i l l a p p e a r a t some h i g h e r c o n c e n t r a t i o n i n P t a l l o y s . ACKNOWLEDGEMENTS.- We a r e g r a t e f u l t o t h e S c i e n c e R e s e a r c h C o u n c i l f o r f i n a n c i a l s u p p o r t , i n c l u d i n g a r e s e a r c h f e l l o w s h i p (M.H.) R e f e r e n c e s

/ l / Miedema, A.R., J. L e s s Corn. M e t a l s

32

(1973) 117.

121 Miedema, A.R., de Boer, F.R. and d e C h a t e l , P.F. J. Phys. F

2

(1973) 1558.

/ 3 / Miedema, A.R., J . Phys. F

2

(1973) 1803. 141 Miedema, A.R., J. Phys. F.

4

(1974) 120. F i g . 2 : S u p e r i m p o s i t i o n of t h e p r e s e n t r e s u l t s on / 5 / Gregory, I . P . and Moody, D.E.. J. Phys. F

5

f i g u r e 7 o f r e f . 141. The c a l c u l a t e d

Y

v a l u e s f o r (1975) 36.

t h e added p o i n t s were d e r i v e d from t h e v a l u e s of

161

Joseph, O., Moody, D.E. and Whitehead, J . P . , J. e l e c t r o n i c d e n s i t y of s t a t e s and electron-phonon i n - Phys. E 9 (1976) 595.

t e r a c t i o n g i v e n i n t h i s r e f e r e n c e . A5d-5d, @ 4d-5d,

0 4d-4d,

A

5d-3d,0 3d-3d and 1 4 d - 3 d a l l o y s . / 7 / Huq. _485. M. and Moody, D.E., P h y s i c a 86-88B (1977)

DISCU.SSION.- To e f f e c t a comparison between t h e p r e s e n t r e s u l t s and t h o s e c o n s i d e r e d p r e v i o u s l y by Miedema, t h e y a r e shown i n f i g u r e 2 superimposed on a copy of f i g u r e 7 from r e f e r e n c e 141. One i s imme- d i a t e l y tempted t o c o n c l u d e t h a t t h e p r e d i c t i v e ca- p a b i l i t i e s of t h e model compare v e r y b a d l y w i t h i t s a b i l i t y t o f i t e x i s t i n g d a t a , b u t i t s h o u l d b e bor- ne i n mind t h a t , o f t h e n o n - f e r r o m a g n e t i c t r a n s i t i o n m e t a l ' a l l o y s t o which t h e model a p p l i e s , r e l a t i v e l y

few have been s t u d i e d c a l o r i m e t r i c a l 2 y , t h o s e t h a t have t e n d i n g t o b e e i t h e r i s o e l e c t r o n i c o r h a v e si-