SECOND ORDER ELASTIC CONSTANTS OF Pd, Pd H0.7 AND Pd D0.7 BETWEEN 1.7 AND 50 K

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SECOND ORDER ELASTIC CONSTANTS OF Pd, Pd

H0.7 AND Pd D0.7 BETWEEN 1.7 AND 50 K

D. Poker, R. Schwarz, A. Granato

To cite this version:

JOURNAL DE PHYSIQUE

Colloque C10, supplement au n012, Tome 46, decembre 1985 page (210-123

SECOND ORDER ELASTIC CONSTANTS OF Pd, Pd Ho., AND Pd Do., BETWEEN

1 . 7 AND 50 K*

Department of Physics, University of Illinois, Urbana, IL 61801 U.S.A.

'Center for Materials Science, Los Alamos National Laboratory, Los Alamos, N.M. 87545, U.S.A.

Resum6

-

Les constantes 6 l a s t i q u e s de second ordre, ell, c 4 e t c ' ont 6 t 6 mCsur6es pour l e Pd BlBmentaire, hydrogen6 (PdHOe7) e t d e u t j r 6 (PdDOe7) en f o n c t i o n de l a tempgrature e n t r e 1.8 e t 50 K. Les donn6es ont 6 t 6 ajustges p a r l ' e x p r e s s i o n polyndmiale c i j (1-ai .T2-b. .T4). Dans l e cas du Pd pur, a i j e t b i j valent approximatiyement e$ 10-M. L ' a b s o r p t i o n d ' h y d r o g b e ou de deutgrium diminue cll(0) de 4%, ~ ~ ~ ( 0 ) de 7% e t augmente c ' ( 0 ) de 8%. Le changement l e p l u s s i g n i f i c a t i f a l i e u pour a.., qui diminue d'un f a c t e u r 100. bll demeure inchang6, t a n d i s que b4,, etla' sont m u l t i p l i 6 s d l un fac- t e u r 2 a 4. Les v a r i a t i o n s de c i j ( 0 ) ne peuvent B t r e expliqu6es de manie're simple par 1 'expansion du r6seau de Pd l o r s de 1 'absorption dlhydrogSne e t de deut6rium. La d i m i n u t i o n d' a i j e s t a t t r i b u 6 e

a'

l a d6croissance des deriv6es de premier e t second ordre de l a d e n s i t e d 1 6 t a t s 6 l e c t r o n i q u e s au niveau de Fermi, due au remplissage du niveau d du Pd par l e s 6 l e c t r o n s f o u r n i s par H e t D.

Abstract

-

The second order e l a s t i c constants, ell, c,,,,, and c ' were measured i n pure Pd, PdHoe7 and PdDoa7 as a f u n c t i o n o f temperature between 1.8 and 50 K. The data were f i t t e d w i t h polynomials c i . ( 1

-

a..T2 ₁

_J

-

bijTQ). For Pd, ai j-10-6 and bi j - l O - l O . With t h e a d d i t i o n o# H or D, cll(0) decreases by 4%, ~ ~ ~decreases by 7%, and c l ( 0 ) increases by 8%. ( 0 ) The most s i g n i f i c a n t change occurs f o r the a i

.,

which decrease by a f a c t o r o f 100. Futhermore, bll remains unchanged, w t i l e b,,,, and b' decrease by f a c t o r s o f approximately 2-4. The changes i n the c i j ( 0 ) cannot be explained simply i n terms of t h e expansion o f t h e Pd l a t t i c e w i t h the a d d i t i o n o f H o r D. The decreases o f t h e a i j are a t t r i b u t e d t o a decrease i n t h e f i r s t and second d e r i v a t i v e s o f t h e e l e c t r o n i c d e n s i t y of s t a t e s at the Fermi energy o f Pd t h a t occurs w i t h t h e f i l l i n g o f t h e d-states by the e l e c t r o n s from H o r D.

I

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INTRODUCTION

The temperature dependence o f the e l a s t i c constants o f a m a t e r i a l a t low temperatures can r e f l e c t the e l e c t r o n i c i n t e r a c t i o n s w i t h the l a t t i c e / l / , adding a T2 term t o the usual T4 term due t o l a t t i c e anharmonicity. This a r t i c l e presents t h e r e s u l t s o f measurements o f t h e temperature dependence o f t h e e l a s t i c constants o f Pd w i t h and w i t h o u t 0.7 atomic r a t i o of H o r D. A s u b s t a n t i a l decrease i n t h e magnitude o f t h e T2 term i s concluded t o be caused by the f i l l i n g o f t h e d-states by t h e a d d i t i o n a l e l e c t r o n s o f hydrogen, and t h e s h i f t o f the Fermi energy so as t o reduce t h e d e n s i t y o f s t a t e s and t h e f i r s t and second d e r i v a t i v e s .

*Work supported by U.S. Department o f Energy

f *

Present address : Oak Ridge National Laboratory, Oak Ridge, TN 3 7 8 3 1 ,

U.S.A.

:

operated by Martin Marietta Energy Systems, Inc. under Contract

n o DE-AC05-840R21400 for the U.S. Department of Energy.

JOURNAL

D E PHYSIQUE

I1

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EXPERIMENTAL PROCEDURE

The sample was cut from a s i n g l e c r y s t a l rod o f 99.99% Pd. Two (100) and one (110) p a i r s o f faces were p o l i s h e d f l a t using a s e r i e s o f diamond pastes. Samples were secured t o an aluminum block i n a l i q u i d helium c r y o s t a t . Temperature was measured w i t h a germanium r e s i s t a n c e thermometer. L o n g i t u d i n a l (c 11) and shear

(c4,, and c ' ) transducers were bonded t o t h e sample by condensing propane gas a t 120 K and a l l o w i n g drops o f the l i q u i d t o f a l l onto t h e transducers and t o f i l l t h e space between transducer and sample by c a p i l l a r y a t t r a c t i o n . The sample was then cooled below t h e f r e e z i n g p o i n t o f t h e propane, approximately 80 K. The s o l i d pro- pane provided a good acoustic bond between t h e sample and transducers, w i t h l i t t l e s t r e s s due t o d i f f e r e n t i a l thermal expansion, since t h e bond was formed a t 80 K. Two 10 MHz transducers were used on each p a i r o f p a r a l l e l faces. One transducer produced a d r i v i n g s i g n a l t o resonate the sample a t an i n t e g r a l number o f h a l f - wavelengths, w h i l e t h e second transducer was used as a detector. The d r i v i n g f r e - quency was modulated s l i g h t l y a t a lower frequency and t h e amplitude v a r i a t i o n i n t h e d e t e c t o r was used t o determine t h e resonant frequency. The v e l o c i t y and e l a s t i c constants can be determined through simple r e l a t i o n s as expressed by T r u e l l ,

e t a1 ./2/. This method i s s e n s i t i v e t o changes i n v e l o c i t y approaching one p a r t i n 107.

Measurements were made on t h e sample before and a f t e r charging w i t h H and D t o atomic r a t i o s o f about 0.7. The* sample was annealed a t 1200 C f o r 12 hours a t a nominal vacuum o f 10-9 Torr. The charging was performed by heating t h e sample i n vacuum t o 320 C, p r e s s u r i z i n g w i t h H o r D t o a nominal pressure o f 50 atmospheres, and c o o l i n g t h e sample t o room temperature before r e l e a s i n g t h e pressure. This pro- cedure avoided the production o f l a r g e i n t e r n a l stresses associated w i t h passing through t h e m i s c i b i l i t y gap i n t h e phase diagram. The atomic f r a c t i o n o f hydrogen was determined by weighing. The f r a c t i o n was t i m e dependent, but monotonically decreased t o a value approaching 0.7 f o r both H and D.

I11

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RESULTS

The temperature dependences o f t h e ell, c,,~, and c ' can be seen i n Fig. 1, f o r Pd w i t h and w i t h o u t atomic r a t i o s o f 0.7 H and D. The uncharged data show a much s t r o n g e r temperature dependence than i s seen i n t h e charged data. The r e s u l t s o f f i t t i n g these data w i t h a curve o f t h e form

i s contained i n Table I. The c o e f f i c i e n t o f t h e T4 term i s l a r g e l y unaffected by t h e a d d i t i o n o f hydrogen, remaining unchanged f o r cll, and v a r y i n g by only f a c t o r s o f 2 f o r c" and 4 f o r c,,,,. The c o e f f i c i e n t s o f t h e T2 terms, however, show a very s t r o n g dependence on t h e hydrogen content. The uncharged sample shows T2 coef- f i c i e n t s on t h e order o f K-2, which are reduced by about two orders o f magni- t u d e upon charging w i t h e i t h e r o f t h e hydrogen isotopes.

The temperature independent p a r t o f t h e e l a s t i c constants i s a l s o a f f e c t e d by t h e a d d i t i o n o f hydrogen, as shown i n Table I. With a d d i t i o n o f hydrogen, cll(0) decreases by 4%, ~ ~ ~decreases by 7%, and c ' ( 0 ) increases by 8%. ( 0 ) I f a simple volume expansion o f t h e l a t t i c e o f 13% i s assumed, w i t h no a d d i t i o n a l e f f e c t from t h e hydrogen, then the r e s u l t s o f Weinmann and Steinemann/3/ suggest t h a t t h e decrease i n t h e temperature independent p a r t o f t h e e l a s t i c constants should be an o r d e r o f magnitude l a r g e r than i s observed. Furthermore, on expansion of t h e l a t - t i c e a l l o f t h e e l a s t i c constants should decrease, but an increase i n c ' i s observed, i n d i c a t i n g t h a t the e f f e c t s are not due merely t o an expansion o f t h e l a t t i c e .

c o e f f i c i e n t ' a ' should be reduced by A, and t h e r e s u l t s f o r c o e f f i c i e n t ' b 8 should be reduced by BIZ. The c o r r e c t i o n i s i n s i g n i f i c a n t i n most cases, being on t h e o r d e r o f a few p e r c e n t o f t h e value o f t h e c o e f f i c i e n t . However, t h e expansion c o e f f i c i e n t r e s u l t s o f Smith and White a r e s i m i l a r t o t h e s e e l a s t i c constant r e s u l t s i n t h a t t h e v a l u e o f t h e T2 term i s reduced g r e a t l y by t h e a d d i t i o n o f hydrogen, w h i l e t h e v a l u e o f t h e T4 t e r m remains e s s e n t i a l l y unchanged.

I V

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DISCUSSION

The presence o f a T2 t e r m i n t h e temperature dependence o f e l a s t i c c o n s t a n t s has been shown by B e r n s t e i n t o o r i g i n a t e from t h e e f f e c t s o f e l a s t i c s t r a i n s upon t h e Fermi s u r f a c e o f t h e m e t a l / l / . The magnitude o f t h e e f f e c t i s s t r o n g l y dependent upon t h e d e n s i t y o f e l e c t r o n i c s t a t e s a t t h e Fermi energy and t h e f i r s t and second d e r i v a t i v e s w i t h respect t o e l e c t r o n energy. While t h e c a l c u l a t i o n i s d i f f i c u l t t o p e r f o r m i n d e t a i l , u s i n g an o r d e r o f magnitude e s t i m a t e s i m i l a r t o B e r n s t e i n 8 s / l / y i e l d s a v a l u e f o r a o f about 10-6 K-2. When Pd i s a l l o y e d w i t h hydrogen, some h y b r i d i z a t i o n o f t h e e l e c t r o n i c s t a t e s occurs, b u t t h e most pronounced e f f e c t i s t h a t t h e Fermi energy s h i f t s away from t h e t o p o f t h e d-band t o a h i g h e r energy r e g i o n w i t h a much lower d e n s i t y o f states/5/. T h i s produces a l a r g e decrease i n t h e magnitude o f t h e T2 c o e f f i c i e n t . The T - o e f f i c i e n t , being due t o l a t t i c e c o n t r i b u t i o n s , i s r e l a t i v e l y u n a f f e c t e d .

REFERENCES

/1/ B e r n s t e i n , B. T., Phys. Rev. 132 (1963) 50.

/2/ True11

,

R., Elbaum, C., and

chick,

B. B., U l t r a s o n i c Methods i n S o l i d S t a t e Ph s i c s (Academic Press, New York 1969).

/3/

&A,

C. and Steinemann, S., S o l i d S t a t e Commun. 15 (1974) 281. / 4 / Smith, T. F. and White, G. K., J. Phys. F: Metal ~hys.1 (1977) 1029.

C10-126

J O U R N A L

DE

PHYSIQUE

TABLE I

TEMPDUTURE (K) TEMPoUlURE (K)

C

'

TEMPERATURE DEPENDENCE OF SECOND ORDER ELASTIC CONSTANTS BELOW 2 0 K

U n i t s o f

c(0)

a r e

10"

dynes/cm2, f o r a are 1 0 - 6 K-2, and f o r b a r e

10-lo

K"+.

FIG.

1. TEMPERATURE DEPENDENCE OF