STRUCTURAL PHASE TRANSFORMATIONS IN THE INDIUM-RICH SOLID SOLUTIONS

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STRUCTURAL PHASE TRANSFORMATIONS IN THE INDIUM-RICH SOLID SOLUTIONS

Y. Koyama, O. Nittono

To cite this version:

Y. Koyama, O. Nittono. STRUCTURAL PHASE TRANSFORMATIONS IN THE INDIUM- RICH SOLID SOLUTIONS. Journal de Physique Colloques, 1982, 43 (C4), pp.C4-145-C4-150.

�10.1051/jphyscol:1982415�. �jpa-00222129�

JOURNAL DE PHYSIQUE

Colloque C4, suppliment au n o 12, Tome 43, dicernbre 1982 page C4-145

STRUCTURAL PHASE TRANSFORMATIONS I N T H E I N D I U M - R I C H S O L I D S O L U T I O N S

Y . Koyama and 0. N i t t o n o

Departmeni; o f Metallurgy, Faculty o f Ekgineering, I'okyo Inst-itute o f Technology, I'okyo 152, Japan

(Accepted 9 August 1982)

A b s t r a c t . - I t i s shown t h a t t h e r e a r e f o u r k i n d s o f phase t r a n s f o r m a t i o n i n Indium-rich a l l o y s c o n t a i n i n g s o l u t e atoms such a s Cd, Hg, T1, Sn and Pb a s f o l l o w s : (1) f c c

=

f c t ( c / a > l ) , (2) f c c

2

f c t ( c / a < l ) , (3) f c t ( c / a q ) f c o

=

f c t ( c / a > l ) and ( 4 ) f c t ( c / a Q ) f f c t ( c / a > l ) . The r e s u l t s o b t a i n e d i n t h e s e t r a n s f o r m a t i o n s a r e d i s c u s s e d In t e r m s o f t h e Landau t h e o r y based on t h e group t h e o r y . I t i s concluded t h a t a r e s p o n s i b l e r e p r e s e n t a t i o n f o r t h e s e t r a n s f o r m a t i o n s i s two-dimensional r e p r e s e n t a t i o n Eg belonging t o t h e c u b i c p o i n t group Oh. The f c c f c t t r a n s f o r m a t i o n i n In-TI, In-Cd, In-Hg and I n - Pb a l l o y s and t h e f c t ( c / a ( l )

:

f c o i n In-Pb-Sn a l l o y s a r e q u a n t i t a t i v e l y analyzed i n terms of t h e Gibbs f r e e energy, which i s e x p r e s s e d by two o r d e r p a r a m e t e r s such a s two spontaneous s t r a i n s c o r r e s p o n d i n g t o t h e two-dimen- s i o n a l r e p r e s e n t a t i o n Eg. The e f f e c t o f t h e e l e c t r o n - a t o m r a t i o and t h e atom- i c s i z e on t h e t r a n s f o r m a t i o n behaviour i s a l s o d i s c u s s e d .

I n t r o d u c t i o n . - We have s t u d i e d phase t r a n s f o r m a t i o n s e x i s t i n g i n I n - r i c h a l l o y s such a s In-T1 [ I ] , In-Cd [ 2 , 3 ] , In-Hg, In-Pb [ 4 ] , In-Sn [ 5 , 6 ] . I t is found t h a t t h e r e a r e f o u r k i n d s o f phase t r a n s f o r m a t i o n a s f o l l o w s : (1) f c c

2

f c t ( c / a > l ) , (2) f c c ⁺ f c t ( c / a q ) , ( 3 ) f c t ( c / a < l )

=

^{f c o}

²

f c t ( c / a > l ) and (4) f c t ( c / a c l )

=

f c t ( c / a > l )

.

$ t i c a l o b s e r v a t i o n s demonstrated t h a t t h e s e t r a n s f o r m a t i o n s a r e d i f f u s i o n l e s s and a banded s u r f a c e r e l i e f due t o {110} t r a n s f o r m a t i o n twinning is observed o n s u r f a c e s o f a l l low-temperature p h a s e s . F u r t h e r , it i s shown t h a t t h e twin p l a n e can bc moved by a p p l y i n g a small s t r e s s . Thus, it i s concluded t h a t t h e a l l o y s o f low-temperature p h a s e s a r e supposed t o be f e r r o e l a s t i c m a t e r i a l s , which a r e d e f i n e d by Aizu [ 7 ] . The shape memory e f f e c t i s a l s o observed i n a l l t h e I n - r i c h a l l o y s . I n t h i s p a p e r , t h e s e t r a n s f o r m a t i o n s a r e t r e a t e d by u s i n g t h e Landau t h e o r y

[a]

c o n c e r n i n g t h e second- o r d e r t r a n s f o r m a t i o n , and f u r t h e r m o r e t h e c h a r a c t e r i s t i c f e a t u r e s o f t h e s e t r a n s - f o r m a t i o n s a r e d i s c u s s e d on t h e b a s i s o f t h e r e s u l t s a n a l y z e d by t h i s theory.

Phenomenological C o n s i d e r a t i o n (symmetry change and Gibbs f r e e e n e r g y ) . - Space group changes o f t h e s e t r a n s f o r m a t i o n s a r e summarized i n Table 1 . These t r a n s f o r m a t i o n s

Table 1 Changes o f t h e space groups i n t h e phase t r a n s f o r m a t i o n s i n t h e I n - r i c h a l l o y s .

TYPE I 11 111

I V

SPACE GROUP CHANGE

0; (Fm3m) - ^Dii

⁽

^{I 4fnmrn)}

0; (Fm3m) - Dl', (I4fnmm)

~ ~ 1 4 f n m m ) - ~ ~ ~ = ~ ~ ~ > + ~ ~ ~ ~ ( 1 ~ m m )

~ Z ( 1 h m m )

⁺

Dz (14~rnm)

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982415

JOURNAL DE PHYSIQUE

a r e n o t accompanied by new t r a n s l a t i o n s and t h u s t a k e p l a c e v i a t h e l a t t i c e s o f t e n - ing a t t h e

r

p o i n t . The low-temperature p h a s e s a p p e a r i n g i n t h e s e t r a n s f o r m a t i o n s have t h e f o l l o w i n g p o i n t groups, i . e . D4h and D2h, which correspond t o subgroups o f t h e c u b i c p o i n t group Oh. Thus, one can conclude t h a t a p o i n t group o f t h e symmet- r i c phase and a r e s p o n s i b l e r e p r e s e n t a t i o n f o r t h e s e t r a n s f o r m a t i o n s a r e t h e c u b i c p o i n t group Oh and t h e two-dimensional i r r e d u c i b l e r e p r e s e n t a t i o n Eg r e s p e c t i v e l y . Landau-condition i s n o t s a t i s f i e d because t h e symmetric p r o d u c t o f t h e r e p r e s e n t a - t i o n [IigI3 c o n t a i n s t h e u n i t r e p r e s e n t a t i o n , Alg, i . e . [€g13= Alg + Azg + Eg. T h i s i n d i c a t e s t h e Gibbs f r e e e n e r g y e x p r e s s i o n c o n t a i n s a t h i r d - o r d e r i n v a r i a n t . On t h e o t h e r hand, t h e a n t i s y m m e t r i c s q u a r e { E ~ } ~ i s e q u i v a l e n t t o Azg, and h a s no common r e p r e s e n t a t i o n s with t h e v e c t o r r e p r e s e n t a t i o n T l u . T h i s r e s u l t shows t h a t L i f s h i t z - c o n d i t i o n i s f u l l f i l l e d . Two components o f t h e b a s i s f o r t h e two-dimensional r e p r e - s e n t a t i o n Eg correspond t o 2z2- x 2 - y 2 and x 2 - y 2 , and t h e n two spontaneous s t r a i n s ,

i . e . two o r d e r p a r a m e t e r s f o r t h e s e t r a n s f o r m a t i o n s , a r e e x p r e s s e d a s ~ L = ( ~ E ~ ~ - E ~ ~ -

E ~ J / & and q 2 = ~ X X - ~ y y , where E E and E~~ d e n o t e s t r a i n s a l o n g t h e x-, y- and xx' YY

z-axes

respectively.- heref fore,

t h e ~ i b b s f r e e e n e r g y i s g i v e n a s f o l l o w s , i n terms o f t h e two spontaneous s t r a i n s ,

where ~ ~ = q 1 ~ + q 2 ~ and ~ 2 = q l ~ - 3 q l q 2 ~ a r e i n v a r i a n t s o f second- and t h i r d - o r d e r , r e - s p e c t i v e l y . Fo is a f r e e energy f o r a c u b i c phase, i . e . ql=n2=0, and t h e c o e f f i - c i e n t s a l , a,, a3,

B1,

62 and y, i n g e n e r a l , a r e f u n c t i o n s o f t e m p e r a t u r e and p r e s - s u r e . S o l u t i o n s o b t a i n e d by u s i n g t h e e q u i l i b r i u m c o n d i t i o n s , aF/aql=aF/aq2=0, show t h e e x i s t e n c e o f t h e f o l l o w i n g p h a s e s : (1) c u b i c (01=n2=0), (2) t e t r a g o n a l ( ~ 1 ~ 0 , q2=0 and 3 ~ 1 ~ = n 2 ~ ) and (3) orthorhombic (ql=O,rl2fO and qlfO,q2+0) [ 9 ] . F i g u r e 1 r e p r e s e n t s t h e e x i s t i n g r e g i o n f o r e a c h phase on t h e ( a l , B l ) diagram, which i s ob- t a i n e d w i t h t h e h e l p o f t h e s t a b i l i t y c o n d i t i o n s . S t r u c t u r a l change o c c u r r i n g i n each t r a n s f o r m a t i o n i s a l s o i n d i c a t e d by t h e arrow. One can s e e t h a t t h e s e t r a n s f o r - mations i n t h e I n - r i c h a l l o y s c a n be reproduced i n t h i s f i g u r e and be well e x p l a i n e d on t h e b a s i s o f t h e Landau t h e o r y .

c u b i c

Fig. 1 E x i s t i n g r e g i o n f o r e a c h phase o n t h e (a1, (31) diagram. Phase t r a n s f o r - m a t i o n s i n t h e i n d i u m - r i c h a l l o y s a r e

4 p l o t t e d i n t h i s diagram.

Here, it is c o n c r e t e l y shown t h a t t h e Landau t h e o r e t i c a l a n a l y s i s i s a p p l i - c a b l e t o t h e e x p l a n a t i o n o f t h e p h a s e t r a n s f o r m a t i o n s i n t h e indium-rich a l l o y s . F i r s t , we a n a l y z e t h e c u b i c - t e t r a g o n a l t r a n s f o r m a t i o n . The Gibbs f r e e e n e r g y f o r t h e t r a n s f o r m a t i o n i s g i v e n , by s u b s t i t u t i n g q2=0 i n t h e e q u a t i o n (1) a s f o l l o w s :

where t h e c o e f f i c i e n t s a l , B1 and a2 correspond t o 2nd-, 3 r d - and 4 t h - o r d e r e l a s t i c c o n s t a n t s , r e s p e c t i v e l y . I n what f o l l o w s , al i s assumed t o depend upon t e m p e r a t u r e i n t h e f o l l o w i n g form: a l = (Cll-C12)/2 = a o ( T - T o ) , where a0 i s a d i f f e r e n t i a l v a l u e w i t h r e s p e c t t o t e m p e r a t u r e f o r t h e second-order e l a s t i c c o n s t a n t and To i s a t e m p e r a t u r e d e f i n e d by al=O. Other c o e f f i c i e n t s a r e p u t t o be c o n s t a n t . I n t h i s t r e a t m e n t , t h e h i g h e r - o r d e r terms t h a n t h e f i f t h - o r d e r one i n t h e f r e e e n e r g y a r e n e g l e c t e d . F u r t h e r , q l i s r e l a t e d t o t h e a x i a l r a t i o o f a t e t r a g o n a l l a t t i c e ( c / a )

and i s e x p r e s s e d by t h e f o l l o w i n g form,

where Tm and r11 a r e a t r a n s f o r m a t i o n t e m p e r a t u r e and a spontaneous s t r a i n a t Tm r e - s p e c t i v e l y . With r e s p e c t t o t h e s i g n s , t h e n e g a t i v e one i s used when t h e a x i a l r a t i o o f a t e t r a g o n a l l a t t i c e i s l a r g e r t h a n u n i t y and t h e p o s i t i v e one when it i s small- e r t h a n u n i t y . The t e m p e r a t u r e dependence of t h e e l a s t i c c o n s t a n t (C'), t h e s t r e s s (0) - s t r a i n ( u ~ ) r e l a t i o n and t h e change o f t h e e n t r o p y a t Tm ( 1 ~ ~ 1 ) a r e a l s o g i v e n by >

On t h e o t h e r hand, i n t h e t e t r a g o n a l - o r t h o r h o m b i c t r a n s f o r m a t i o n , t h e o r d e r param- e t e r s , q1 and 172, can be r e a s o n a b l y assumed t o be a c o n s t a n t (=fil) and a v a r i a b l e r e s p e c t i v e l y , a s w i l l be shown i n Fig. 5. In t h i s c a s e , u s i n g t h e e q u a t i o n ( I ) , t h e Gibbs f r e e e n e r g y i n t h i s t r a n s f o r m a t i o n can be e x p r e s s e d by,

where t h e energy ~ h ( ; l ) i n c l u d e s h i g h e r - o r d e r t e r m s o f

el

thaq t h e t h i r d - o r d e r f o r t h e t e t r a g o n a l l a t t i c e , e x c e p t f o r t h e c o n t r i b u t i o n o f Fo. To i s t h e e x t r a p o l a t e d t e m p e r a t u r e a t which C' becomes e q u a l t o zero, and ~ ( 6 1 ) and E(=a3) correspond t o t h e f o u r t h - and t h e s i x t h - o r d e r e l a s t i c c o n s t a n t s r e s p e c t i v e l y and both a r e assum- e d t o be c o n s t a n t . In t h e t e t r a g o n a l - o r t h o r h o m b i c t r a n s f o r m a t i o n , t h e t e m p e r a t u r e dependence o f t h e spontaneous s t r a i n (172) and t h e e l a s t i c c o n s t a n t (C') and t h e change o f t h e e n t r o p y a t Tm

( 1 ~ ~ 1 )

a r e r e p r e s e n t e d a s f o l l o w s :

r i 2 = = 3 ~ 2 2 ( T m ) [ I 2 + (8)

where 172(Tm) i s a spontaneous s t r a i n a t t h e t r a n s f o r m a t i o n t e m p e r a t u r e , Tm. These p h y s i c a l q u a n t i t i e s mentioned above i n both t r a n s f o r m a t i o n s can be c a l c u l a t e d by u s i n g t h e f o l l o w i n g t r a n s f o r m a t i o n p a r a m e t e r s , T O , ao, 61 and a2 i n t h e c u b i c - t e t r a g o n a l t r a n s f o r m a t i o n and T o # , ao, ~ ( 6 1 ) and E i n t h e t e t r a g o n a l - o r t h o r h o m b i c one.

Experimental Procedure.- The experiments were performed by t h e f o l l o w i n g p r o c e d u r e . F i r s t , t h e v a r i a t i o n w i t h t e m p e r a t u r e o f l a t t i c e p a r a m e t e r s f o r each I n - r i c h a l l o y p o l y c r y s t a l was measured by means o f X-ray d i f f r a c t o m e t r y . In a n In-4.4at%Cd a l l o y , t h e a x i a l r a t i o o f a t e t r a g o n a l l a t t i c e was determined by X-ray topography, u s i n g a s i n g l e c r y s t a l p r e p a r e d by t h e r e c r y s t a l l i z a t i o n method. In-(13-X)at%Pb-Xat%Sn a l l o y p o l y c r y s t a l s were a l s o i n v e s t i g a t e d in o r d e r t o a n a l y z e t h e f e a t u r e o f t h e t e t r a g o n a l - o r t h o r h o m b i c t r a n s f o r m a t i o n . The spontaneous s t r a i n s such a s rll and 172

were o b t a i n e d from t h e measured l a t t i c e parameters o r t h e a x i a l r a t i o . The d e t e r - m i n a t i o n o f t h e t r a n s f o r m a t i o n p a r a m e t e r s was made i n t h e f o l l o w i n g way. The param- e t e r s a r e f i r s t p u t t o be a r b i t r a r y v a l u e s . Using t h e s e v a l u e s , t h e spontaneous s t r a i n s a r e c a l c u l a t e d and a r e compared with t h e measured o n e s . T h i s o p e r a t i o n i s r e p e a t e d u n t i l 1 t h e c a l c u l a t e d v a l u e s show a c o m p a r a t i v e l y good agreement w i t h t h e measured o n e s w i t h i n a n e x p e r i m e n t a l e r r o r . A s a r e s u l t , t h e v a l u e s which have a good agreement with e x p e r i m e n t a l s t r a i n s a r e chosen a s t r a n s f o r m a t i o n parameters.

C4-148 JOURNAL DE PHYSIQUE

For c o n v e n i e n c e , cro i s always p u t t o be 2 . ~ x l 0 ~ ~ / m ' . d e g f o r a l l t h e a l l o y s and t h e p r o p r i e t y f o r t h i s a s s u m p t i o n i s d i s c u s s e d i n o t h e r p a p e r [ 9 ] . Using t h e s e p a - r a m e t e r s d e t e r m i n e d , some p h y s i c a l q u a n t i t i e s a r e c a l c u l a t e d and a r e compared w i t h e x p e r i m e n t a l r e s u l t s . F u r t h e r , t h e c h a r a c t e r i s t i c f e a t u r e s o f t h e phase t r a n s f o r - mation f o r e a c h I n - r i c h a l l o y a r e d i s c u s s e d i n t e r m s o f t h e t r a n s f o r m a t i o n param- e t e r s and t h e p h y s i c a l q u a n t i t i e s .

R e s u l t s and D i s c u s s i o n . (1) f c c f c t p h a s e t r a n s f o r m a t i o n . - F i g u r e 2 shows measured and c a l c u l a t e d v a l u e s o f t h e s p o n t a n e o u s s t r a i n r i l f o r a n In-4.4at%Cd a l l o y s i n g l e c r y s t a l . The s t r a i n n l s h o w s a jump from z e r o t o a f i n i t e v a l u e a t t h e t r a n s f o m a - t i o n t e m p e r a t u r e , Tm, and t h e n i n c r e a s e s a s t h e t e m p e r a t u r e i s lowered i n t h e f c t p h a s e . T h i s r e a s o n a b l c agreement between t h e c a l c u l a t e d and measured s t r a i n s a l s o shows t h a t t h e t r a n s f o r m a t i o n c a n be c h a r a c t e r i z e d by u s i n g t h e Landau t h e o r y f o r t h e second- and n e a r l y s e c o n d - o r d e r t r a n s f o r m a t i o n . Here, t h e c a l c u l a t e d s t r a i n s a r e o b t a i n e d by u s i n g t h e t r a n s f o n n a t i o n p a r a m e t e r s , d e t e r m i n e d by t h e p r o c e d u r e d e -

s c r i b e d above. The t e m p e r a t u r e dependence o f t h e e l a s t i c c o n s t a n t f o r In-Cd and I n - Pb a l l o y s i s a l s o c a l c u l a t e d by u s i n g t h e t r a n s f o r m a t i o n p a r a m e t e r s , a s shown i n F i g . 3 . One c a n s e e i n t h e f i g u r e t h a t t h e e l a s t i c c o n s t a n t depends upon t e m p e r a t u r e and becomes s m a l l n e a r Tm, and t h a t t h e v a l u e o f t h e e l a s t i c c o n s t a n t a t Tm f o r t h e

In-Pb a l l o y i s a b o u t s i x t i m e s l a r g c r t h a n t h a t f o r t h e In-Cd a l l o y . F i g u r e 4 shows

300 320 340 360 3 80

temperature, K

6

- 1 \.,

I _I

L , ln- 4 4 a t0/oCd

2 _I

_---

T",

'E

'320 3 4 0 3 6 0 " 3 i O ' 4b0

,

t e m p e r a t u r e (

K )

F i g . 2 Comparison o f c a l c u l a t e d v a l u e s F i g . 3 C a l c u l a t e d v a l u e s o f e l a s t i c o f s p o n t a n e o u s s t r a i n n l w i t h experimen- c o n s t a n t C' f o r In-4.4at%Cd and I n - 3 2 a t % t a l v a l u e s i n In-4.4at%Cd a l l o y . Pb a l l o y s .

t h e s t r e s s - s t r a i n c u r v e s f o r an In-4.4at%Cd a l l o y a s a f u n c t i o n o f t e m p e r a t u r e , which a r e c a l c u l a t e d by t h e t r a n s f o r m a t i o n p a r a m e t e r s . I t can be s e e n t h a t t h e

s t r e s s - s t r a i n c u r v e r e p r e s e n t s a s t r e s s h y s t e r e s i s which i s drawn by t h e broken l i n e s , and t h e c u r v e s o f t h e h i g h - and l o w - t e m p e r a t u r e p h a s e s c o r r e s p o n d t o s o - c a l l e d s u p e r e l a s t i c and f c r r o c l a s t i c l o o p s , r e s p e c t i v e l y . The C'-T c u r v e s and t h e

0 - n l o n e s a r e q u i t e s i m i l a r t o t h o s e o b t a i n e d e x p e r i m e n t a l l y . The t r a n s f o n n a t i o n p a r a m e t e r s and t h e change o f t h e e n t r o p y f o r e a c h a l l o y a r e summarized i n T a b l e 2 , t o g e t h e r w i t h o t h e r r e s u l t s . The e l e c t r o n - a t o m r a t i o ( c / a ) c o r r e s p o n d i n g t o t h e a l l o y c o m p o s i t i o n i s a l s o l i s t e d i n t h e t a b l e . I t i s found t h a t c a l c u l a t e d v a l u e s such a s Tm-To,

B1,

^a2 and AS show a s i m i l a r tendency o f a change depending upon t h e e l e c t r o n - a t o m r a t i o , w i t h r e s p e c t t o t h e s e a l l o y s , a l t h o u g h t h e t r a n s f o r m a t i o n tcm- p e r a t u r e i s n o t t h e same f o r a l l t h e a l l o y s . Furthermore, it c a n be s e e n from t h e v a l u e s such a s n(Tm), AV(Tm' and a'T=As-Hs t h a t t h e b e h a v i o u r o f t h e f c c - f c t t r a n s - f o r m a t i o n becomes more r e c o g n i z a b l e f i r s t o r d e r w i t h d e v i a t i n g from t h e e l e c t r o n - atom r a t i o o f e / a = 3 . 1 1 .

Fig. 4 C a l c u l a t e d s t r e s s - s t r a i n c u r v e s a s a f u n c t i o n o f t e m p e r a t u r e f o r I n - 4 . 4 a t % Cd a l l o y .

T a b l e 2 Transformation p a r a m e t e r s f o r each a l l o y i n f c c - f c t t r a n s f o r m a t i o n , t o - g e t h e r w i t h o t h e r v a l u e s such a s A S , q(Tm), AV(Tm) and AT=As-Ms.

( 2 ) f c t ( c / a < l )

=

f c o phase t r a n s f o r m a t i o n . - F i g u r e 5 shows t h e spontaneous s t r a i n s , rll and 112, a t e a c h t e m p e r a t u r c d u r i n g t h e f c t ( c / a < l )

;

f c o t r a n s f o r m a t i o n f o r an

In-9at%Pb-4at%Sn a l l o y . The p a r a m e t e r ~2 i s equal t o zero i n t h e f c t ( c / a < l ) phase, and on c o o l i n g it jumps t o 5.60 a t Tm and i n c r e a s e s i n t h e f c o phase. C o n t r a r y t o t h e change o f ~ 2 q l , kecps a c o n s t a n t v a l u e i n both t h e f c t and f c o p h a s e s i n s p i t e of t h e e x i s t e n c e o f a jump Art1 a t Tm. T h i s i n d i c a t e s t h a t one can t a k e t h e s t r a i n q2 a s t h e o r d e r p a r a m e t e r f o r t h e f c t - f c o t r a n s f o r m a t i o n . As a s u p p o r t f o r t h i s i n d i c a t i o n , it i s shown t h a t t h e s t r a i n s c a l c u l a t e d by u s i n g t h e determined t r a n s - formation p a r a m e t e r s a r e i n a remarkable agreement with t h e experimental o n c s . The e l a s t i c c o n s t a n t c a l c u l a t e d f o r t h e In-Pb-Sn a l l o y s , a s shown i n Fig. 6 , becomes small a t Tm, being s i m i l a r t o t h a t i n t h e f c c - f c t t r a n s f o r n l a t i o n . The s t r i k i n g f e a - t u r e can be summarized a s f o l l o w s : t h c r e i s a jump o f t h e e l a s t i c c o n s t a n t a t Tm, and i t s h e i g h t and a l s o t h e e l a s t i c c o n s t a n t i n a low-temperature phasc i n c r e a s e w i t h t h e c o n t e n t of Sn. Table 3 r e p r e s e n t s t h e t r a n s f o r m a t i o n p a r a m e t e r s o b t a i n e d e x p e r i m e n t a l l y f o r s e v e r a l In-Pb-Sn a l l o y s . One can s e e Tm k e e p s c o n s t a n t w i t h i n a t e m p e r a t u r e rangc o f 9K f o r a l l t h e a l l o y s , while v a l u e s such a s Tm-To',

1 ,

E and AS i n c r e a s e with i n c r e a s i n g t h e c o n t e n t o f Sn. T h i s r e s u l t shows t h a t t h e

JOURNAL DE PHYSIQUE

x cal

.

^exp

i ^{1 1 2}

200 220 240 260 280 300 320 360 360 380 4C

Temperature I K Temperature I K

Fig. 5 Temperature dependence o f spon- Fig. 6 C a l c u l a t e d v a l u e s o f e l a s t i c t a n e o u s s t r a i n s , rll and r \ z , f o r In-gat% c o n s t a n t C' f o r In-13at%Pb, In-7at%Pb-6

Pb-4at%Sn a l l o y . a t % S n and In-4at%Pb-9at%Sn a l l o y s .

T a b l e 3 T r a n s f o r m a t i o n p a r a m e t e r s and change o f e n t r o p y a t Tm f o r In-(13-X)at%Pb- Xat%Sn a l l o y s i n f c t ( c / a < l )

2

f c o t r a n s f o r m a t i o n .

f c t - f c o t r a n s f o r m a t i o n o f a n a l l o y c o n t a i n i n g more Sn c o n t e n t becomes more remark- a b l e f i r s t o r d e r . I n t h e s e In-Pb-Sn a l l o y s , t h e r e i s no change i n t h e e l e c t r o n - a t o m r a t i o , b u t o n l y an a v e r a g e atomic s i z e d e c r e a s e s when r e p l a c i n g Pb atom (fk203.4 a . u . ) by Sn one (R:l8l .Sa.u.) [ l o ] . T h e r e f o r e , it can b e concluded t h a t t h e f c t -

f c o t r a n s f o r m a t i o n i s m a i n l y e f f e c t e d by t h e a t o m i c s i z e u n l i k e i n t h e f c c - f c t one.

References

[I] NIITONO 0 . and KOYAMA Y., J. Jpn. I n s t . Met. 42 (1978) 56 [ i n Japanese].

[2] KOYAMA Y. and NITTONO O., J . J p n . I n s t . Met. (1979) 262 [ i n J a p a n e s e ]

.

[3] KOYAMA Y. and NITTONO O., J . Jpn. I n s t . Met. (1979) 696 [ i n J a p a n e s e ] . [U] KOYAMA Y . , UKENA T. and NITTONO O . , J . Jpn. 1 G t . Met. 44 (1980) 1431 [ i n

-

J a p a n e s e ] .

[5] NITTONO O., IWASAKI H . and KOYAMA Y., J . J p n . I n s t . Met.

44

(1980) 899 [ i n J a p a n e s e ] .

[6] IWASAKI H., NIITONO 0. and KOYAMA Y . , J . J p n . I n s t . Met.

5

(1981) 667 [ i n J a p a n e s e ] .

171 AIZU K . , J . Phys, Soc. Jpn. 27 (1969) 387.

[8] LANDAU L. D. and LIFSHITZ E ,M. S t a t i s t i c a l P h y s i c s (Pergamon P r e s s , London.

- . -

1961) Chap. 1 4 .

[9] NITTONO 0. and KOYAMA Y . , J p n . J . Appl. Phys. 21 (1982) 680.

[LO] ANIMALU A.D.E. and HEINE V., P h i l . Mag.

12

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