CHANGES OF THE YOUNG'S MODULUS INDUCED BY HYDROGEN OR DEUTERIUM IN THE PALLADIUM-SILVER ALLOYS

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CHANGES OF THE YOUNG’S MODULUS INDUCED BY HYDROGEN OR DEUTERIUM IN THE

PALLADIUM-SILVER ALLOYS

F. Mazzolai, G. Paparo, R. Franco

To cite this version:

F. Mazzolai, G. Paparo, R. Franco. CHANGES OF THE YOUNG’S MODULUS INDUCED BY

HYDROGEN OR DEUTERIUM IN THE PALLADIUM-SILVER ALLOYS. Journal de Physique

Colloques, 1983, 44 (C9), pp.C9-411-C9-417. �10.1051/jphyscol:1983960�. �jpa-00223410�

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JOURNAL DE PHYSIQUE

Colloque C9, supplkment a u n012, Tome 44, d e c e m b r e 1983 page C9-411

CHANGES

O F

THE YOUNG'S MODULUS INDUCED BY H Y D R O G E N OR D E U T E R I U M I N THE PALLADIUM-SILVER ALLOYS

F.M. Mazzolai, G. P a p a r o * and R. Franco*

~ i ~ a r t i m e n t o d i F i s i c a , U n i v e r s i t d d i P e m g i a , V i a E k e d i S o t t o , P e m g i a , I t a l y

* ~ s t i t u t o d i A c u s t i c a

D.M.

Corbino', V i a Cassia 1216, Roma, I t a l y

R6sum6

-

On a t r o u v 6 que l e changement t o t a l du module d e Young E

-

e s t dii e n p a r t i e 1 l a d i l a t a t i o n du r 6 s e a u e t e n p a r t i e 1 l a dimi- n u t i o n d e l a d e n s i t 6 d e s 6;ats 6 l e c t r o n i q u e s p r S s du n i v e a u d e F e r m i . La dspendance de E a v e c l a t e m p 6 r a t u r e e s t r e l i 6 e B l a d i l a t a - t i o n du r 6 s e a u e t B l ' e x c i t a t i o n d e s modes l o c a u x d e v i b r a t i o n d e s atomes drhydrogSne.

Abstract

-

It has been found t h a t t h e t o t a l change of t h e Young's modulus E induced by H and (or) Ag results from a negative l a t t i c e expansion term, and a positive electronic t e r m , which increases with decreasing t h e density of s t a t e s a t t h e Fermi 1evel.The t e m p e r a t u r e dependence of E is a f f e c t e d both by l a t t i c e expansion and by excitation of local vibrations of hydrogen.

1

-

INTRODUCTION

A l o t of a t t e n t i o n has recently been paid t o changes of t h e elastic constants of 3d,4d and 5d m e t a l s on alloying with elements of adjacent groups 11-91. The reason f o r this interest is mainly due t o t h e f a c t t h a t f o r some of t h e transition elements such a s Nb, P d and P t t h e shear elastic constant CL14 and t h e Young's modulus E show an anomalous behaviour with changing temperature. The value of C44 is found t o decrease with decreasing temperature up t o a certain minimum value, and then i t increases again; t h e Young's modulus of Pd shows an upwards concavity near 100 K

/lo/.

I t is generally believed t h a t t h e above anomalous behaviours a r e due t o electronic contributions arising from t h e transfer of electrons from s t a t e s situated near t h e boundary of t h e Brillouin zones t o other s t a t e s made favorable by t h e applied external s t r e s s 12-61.

Other properties of Pd alloys such a s magnetic susceptibility, H solubility and H diffusivity,

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983960

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C9-412 JOURNAL DE PHYSIQUE

have been related t o alterations of electronic band s t r u c t u r e and t o t h e density of s t a t e s a t t h e Fermi level

1111.

To some e x t e n t changes in t h e above quantities s e e m t o be related only t o alterations in t h e number of valence electrons per a t o m , e/a, no m a t t e r how e / a is changed, e i t h e r by changing t h e interstitial (H) or t h e substitutional (Ag) e l e m e n t concentration.

The purpose of t h e present work has been t h a t of investigating t h e e f f e c t s on t h e Young's modulus produced by alloying Pd with Ag and (or) with H (D).

2 - EXPERIMENTAL

A series of Pdl-xAg alloys were kindly provided by Jhonson and Matthey Co, with values of x equal t o 0.10,0.23,0.32,0.40 and 0.47, while pure Pd specimens w e r e prepared from Marz grade m a t e r i a l supplied by MRC. The specimens, which were rectangular bars (dimensions (in mm):43x7x0.17), were initially annealed in vacuum (10 -6 torr) f o r 5h a t 500 C, then repeatedly H or D charged electrolytically a t a current density of about 38 m ~ / c m ' . The contents of H or D w e r e estimated from weight changes. A f t e r each charging t r e a t m e n t and before t h e subsequent measurement run over t h e t e m p e r a t u r e range (78bT4293 K), t h e specimens w e r e kept a t room t e m p e r a t u r e for homogenization f o r about 1 5 h. Changes in t h e density

P

associated with H (Dl absorption w e r e determined by means of t h e hydrostatic balance technique.

The resonant frequency f and t h e logarithmic decrement were simultaneously measured during cooling (cooling r a t e = l K/min) f o r t h e fundamental flexural free-free mode, excited electrostatically. Values for Young's modulus have been deduced f r o m t h e resonant frequency (28804f53500 Hz), density and t h e geometrical dimensions (thickness t and Ienght I ) of t h e specimens, by using the relationship

Corrections have been made for dimensional changes due t o t e m p e r a t u r e variations. The values of t h e thermal expansion coefficient O( used f o r such corrections were in all cases those f o r hydrogen-free alloys, which a r e presently t h e only ones available.

3

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RESULTS

A typical s e t of Young's modulus d a t a a r e given in Fig.1, which r e f e r s t o an alloy with

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x=0.40 charged with hydrogen.It c a n b e s e e n t h a t t h e Young's modulus, f o r a given t e m p e a r a t u r e

,

strongly d e c r e a s e s with t h e H c o n t e n t , which i s h e r e expressed as t h e a t o m i c r a t i o n (n=H/(Pd+Ag)). This r e s u l t is in a g r e e m e n t w i t h softening in t h e a c o u s t i c dispersion c u r v e s of P d D with r e s p e c t t o pure Pd, which h a s b e e n observed in neutron s c a t t e r i n g

0.63' e x p e r i m e n t s /12/.

T h e n e g a t i v e t e m p e r a t u r e c o e f f i c i e n t =Ed ( d ~ / d ~ ) -1 (Eo is t h e value of E a t 2 9 3

K)

is approximately c o n s t a n t a b o v e 200 K f o r a l l t h e H c o n t e n t s

.

Below 200 K, b e c o m e s

2(

s o m e w h a t m o r e negative. This behaviour of

r

is due t o relaxation processes which have b e e n found 1131 t o give rise t o p e a k s in t h e dissipation c o e f f i c i e n t v s t e m p e r a t u r e curves, a s shown in Fig.2. P l o t s in f i g u r e 2 r e f e r t o t h e s a m e alloy composition and H c o n t e n t s a s t h o s e in f i g u r e 1.

Fig.1. T e m p e r a t u r e dependence of t h e Young's modulus f o r a s e r i e s of H c o n t e n t s n. T h e a t o m i c r a t i o s n=H/(Pd+Ag) a r e given beside e a c h curve.

Fig.2. E l a s t i c energy dissipation peaks induced by H in P d

6 0 Ag40 alloy a t t h e values of hydrogen c o n t e n t n indicated in t h e figure.

4

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DISCUSSION

a

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L a t t i c e expansion

T h e a b s o l u t e i n c r e a s e of t h e volume of t h e unit cell,AV, a s deduced f r o m density measu- r e m e n t s is r e p o r t e d a s a functiuon of n in Fig.3, w h e r e points c a l c u l a t e d f r o m d a t a of Rosenhall /14/ a r e also included. The dotted-dashed line corresponds t o t h e line drawn by Baranowski et al. 1151 through a number of d a t a points r e f e r r i n g t o s e v e r a l palladium alloy systems. In s o m e c o n t r a s t with a conclusion t h a t all such d a t a could b e r e p r e s e n t e d by a

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J O U R N A L D E PHYSIQUE

single line, the volume expansion per unit H content is

W,.,Ag,H,

shown t o depend on the silver content, sligtly increasing w i t h increasing x. The relative volume changes V,-1 (dV/dn) a t 293 K, as deduced f r o m figure 3 are reported i n table I. Here V is the volume o f the u n i t c e l l a t n=O,

0

calculated using t h e value o f the l a t t i c e parameter d measured by Rosenhall /16/(d=3.883 10-lorn).

b

-

Dependence o f E on volume expansion and on the number o f electrons per a t o m (e/a).

Fig.3. Changes i n the volume The presence o f H (D) i n Pd/Ag alloys may a f f e c t the o f the unit c e l l as a function

t o t a l free energy o f the system through changes of: a) o f the atomic r a t i o n.

the phonon spectrum o f the host lattice; b) the band structure and c ) the optical modes associated w i t h l o c a l vibrations o f hydrogen. The separation of the various contributions t o E arising f r o m the above f r e e energy terms is a d i f f i c u l t task and goes beyond the purposes o f the present work. However,qualitative conclusions can be drawn on the r e l a t i v e importance o f such contributions.

The unrelaxed modulus E", as obtained from the measured values a t 293 K by subtraction o f the negative relaxation contribution, is plotted i n Fig.4 as a function o f the l a t t i c e

TABLE 1 - Relative changes of the unit cell volume per 1 at % of H o r Ag a s deduced from density measurements at 293 K.

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parameter d. D a t a deduced f r o m t h e work by Yoshihara e t al. 1161 a r e included in this figure, where filled symbols r e f e r t o H-free alloys. A relatively large s c a t t e r is observed among t h e experimental points. However, t h e d a t a clearly show t h a t addition of H o r Ag produces similar quantitative effects. I t thus seems t h a t t h e excitation of optical modes, which a r e only associated with H, gives no appreciable contribution t o t h e absolute value of E.

To separate t h e electron and t h e acoustical phonon contributions i t has t o be k e p t in mind t h a t on alloying Pd with Ag t h e density of s t a t e s a t t h e F e r m i level drastically decreases with increasing x from 0 t o 0.45 and remains sensibly constant f o r values of x larger than 0.45 1151. This decrease in t h e density of s t a t e s a t t h e F e r m i level is expected t o parallel a decrease in t h e magnetic susceptibility and an increase in t h e rigidity modulus G.

As noted by Zener 1201 changes in t h e Young's modulus a r e mostly due t o changes in G ; i t is thus expected t h a t E should also increase with x, for x 60.45 and then remain constant. On t h e other hand l a t t i c e expansion, which changes almost linearly with x (small deviations from Vegard's law a r e observed for Pd/Ag alloys), is expected t o give rise t o a steady decrease over t h e e n t i r e range of values of x ( o ~ x 5 1 ) . I t is thus tempting t o assume t h a t t h e linear decrease observed in Fig. 4 f o r x

t

0.45 is essentially due t o l a t t i c e dilation, while the initial increase and t h e peaking of E in t h e E vs n plots results f r o m t h e combined e f f e c t of l a t t i c e expansion and electronic contributions. The l a t t e r appears t o be preponde- r a n t f o r x up t o about 0.45 (d53.97 1 0 -10 m).

c - Changes in t h e t e m p e r a t u r e coefficient )( _V

.

The dependence of f on t h e l a t t i c e p a r a m e t e r d, a s deduced from t h e linear part of E(T) curves (T-ZZOOK), is shown in Fig.5, where points calculated from d a t a by Yoshihara e t al. 1161 a r e also included.

F o r t h e H-free alloys (filled symbols) a linear Fig.4. Unrelaxed Young's modulus decrease of is observed over all t h e concen- a s a function of t h e l a t t i c e para-

J

m e t e r d. tration range (OCX 41). This linear behaviour

suggests t h a t t h e slight increase in t h e t e m p e r a t u r e dependence of E (increase in t h e anharmonicity) is associated with l a t t i c e expansion, not with filling of t h e d-band, a process which t a k e s place f o r x L0.45 (d L 3.97 1 0 - ~ ~ m ) , a s s t a t e d above.

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JOURNAL DE PHYSIQUE

Fig.5. D e p e n d e n c e of t h e t e m p e r a - Fig.6. Isotopic e f f e c t s in t h e normalized t u r e c o e f f i c i e n t

8

on t h e l a t t i c e Young's modulus and t e m p e r a t u r e coef-

p a r a m e t e r d. f i c i e n t

r.

The e f f e c t of H on $(open symbols) is, by comparison with t h e e f f e c t of Ag,much s t r o n g e r and n o t l i n e a r with d. In t h e c a s e of H, in addition t o t h e e f f e c t of l a t t i c e expansion, t h e r e s e e m s t o b e an o t h e r contribution which is presumably d u e t o o p t i c a l phonons

,

a s i t h a s been r e p o r t e d f o r P d c h a r g e d w i t h H o r D 1191.

d

-

Isotopic e f f e c t s

In o r d e r t o m o r e c l e a r l y d e t e c t o p t i c a l phonon e f f e c t s , e x p e r i m e n t s have also been p e r f o r m e d w i t h d e u t e r i u m f o r t h e alloy with ~ ~ 0 . 4 . T h e result& a r e given in Fig.6. T h e upper p a r t of t h i s figure shows t h a t t h e r e is a n isotopic e f f e c t on E. I t s e e m s unlikely t h a t t h i s e f f e c t is a s s o c i a t e d with volume expansion, which h a s been found t o b e sensibly t h e s a m e f o r H a n d D, o r with t h e e l e c t r o n i c s t r u c t u r e , which is also e x p e c t e d n o t t o b e sensibly d e p e n d e n t on t h e isotopic species. Thus t h e d i f f e r e n c e s n o t e d in Fig.6 (a) a r e presumably d u e t o t h e m a s s dependence of t h e o p t i c a l phonon excitations. T h e s e d i f f e r e n c e s are,however, s m a l l in comparison with changes a s s o c i a t e d with l a t t i c e expansion and e l e c t r o n s , a s i t h a s already been noted previously, when c o m m e n t i n g Fig.3.

T h e l o w e r p a r t of f i g u r e 6 clearly r e v e a l s an isotopic e f f e c t in t h e t e m p e r a t u r e c o e f f i c i e n t t ( n o t e t h e d i f f e r e n c e in t h e s c a l e s of t h e o r d i n a t e s between t h e lower a n d t h e upper p a r t of t h i s figure). This observation s e e m s t o c o n f i r m t h e conclusions drawn f r o m t h e discussion of t h e previous figure 5 , t h a t H o r (D) local vibrations a r e responsible f o r t h e e n h a n c e m e n t of t h e c r y s t a l anharmonicity.

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5

-

CONCLUSIONS

It has been shown that the absolute values o f the Young's modulus of Pd 1-x Agx Hn (Dn) alloys are similarly changed by alloying Pd w i t h H (D) or w i t h A g

.

Such changes are related t o l a t t i c e expansion induced either by H (D) or by A g and f o r x50.45 t o the decrease i n the number o f electrons per atom a t the F e r m i level. This is somewhat surprising i n view o f the calculations by Faulkner /20/ for the Pd/H system; according t o such calculations it seems that a reduction i n the density o f states should take place over a wider concentration range for H ( n 5 0.7).The increased anharmonicity (stronger dependence of E on T) is on the other hand mostly due to the excitation of optical modes.

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