GENERAL CONDITION FOR AMORPHISATION OF INTERMETALLIC COMPOUNDS

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GENERAL CONDITION FOR AMORPHISATION OF INTERMETALLIC COMPOUNDS

D. Beke, H. Bakker, P. Loeff

To cite this version:

D. Beke, H. Bakker, P. Loeff. GENERAL CONDITION FOR AMORPHISATION OF IN- TERMETALLIC COMPOUNDS. Journal de Physique Colloques, 1990, 51 (C4), pp.C4-63-C4-69.

�10.1051/jphyscol:1990407�. �jpa-00230767�

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GENERAG CONDITION FOR AMORPHISATION OF INTERMETALLIC COMPOUNDS

D.L. B E K E ' ~ ) ,

H.

BAKKER and P.I. LOEFF

Natuurkundig Laboratorium der Universiteit van Amsterdam, valckenierstraat 65, NL-1018 XE Amsterdam. The Netherlands

A b s t r a c t

-

Using s i m p l e t h e r modynad c c o n s i d e r a t i o n s f o r t h e Gi bbs f r e e e n e r g i e s of t h e c r y s t a l l i n e and amorphous s t a t e s a g e n e r a l c o n d i t i o n f o r t h e s o l i d - s t a t e amorphi s a t i on of i n t e r m e t a l l i c compounds by i r r a d i a t i o n o r mechanical impact w a s d e r i v e d . I t w a s o b t a i n e d t h a t t h e a m o r p h i s a t i o n is p o s s i b l e i f t h e maximum e l a s t i c e n e r g y . A H t l . s t o r e d d u r i n g t h e C chemi c a l 3 o r d e r -di s o r d e r t r a n s i t i o n i S l a r g e r t h a n AHa toD t h e e n t h a l py of t h e t o p o l o g i c a l change of a m o r p h i s a t i o n . T h i s c o n d i t i o n c a n b e r e w r i t t e n i n t o t h e form: t h e a m o r p h i s a t i o n i s n o t p o s s i b l e i f t h e o r d e r -di s o r d e r t e m p e r a t u r e i S lower t h a n t h e m e 1 ti ng t e m p e r a t u r e

.

Tc< Tm.

and i f Tc>Tm

-

i n c o n t r a s t t o Johnson's c o n d i t i o n

-

t h e p o s s i b i l i t y of t h e a m o r p h i s a t i o n depends on t h e r e l a t i v e magnitude of t h e e l a s t i c mismatch e n e r g y and t h e chemical e n e r g y of o r d e r i n g . If t h e i r r a t i o is l a r g e enough t h e a m o r p h i s a t i o n i s p o s s i b l e . D e t a i l e d c a l c u l a t i o n s , c a r r i e d o u t f o r a l a r g e number o f compounds, l e d t o a s a t i s f a c t o r y agreement w i t h t h e e x p e r i m e n t a l o b s e r v a t i o n s .

l. INTRODUCTION

C r y s t a l t o g1 a s s t r a n s f o r m a t i o n s i n s o l i d s t a t e are gener a1 l y observed when t h e e n e r g y of t h e c r y s t a l c a n b e r a i s e d t o h i g h e r v a l u e s t h a n t h e d i f f e r e n c e i n e n e r g i e s of t h e c r y s t a l l i n e and amorphous s t a t e s . The aim of t h i s paper is t o d i s c u s s t h e c o n d i t i o n f o r t h e above t r a n s f o r m a t i o n i n i n t e r m e t a l l i c compounds a t s t o c h i o m e t r i c compositions.

P r a c t i c a l l y t h e r e a r e two main ways t o i n c r e a s e t h e e n e r g y of a n i n i ti a1 1 y o r d e r e d compound: i r r a d i a t i o n /l / o r mechanical d e f o r m a t i o n C b a l l - m i l l i n g /2/ o r p l a s t i c d e f o r m a t i o n /3A. I n b o t h c a s e s , d u r i n g t h e a t t r i t i o n of t h e c r y s t a l , t h e i n c r e a s e i n t h e e n e r g y is r e a c h e d by t h e g e n e r a t i o n of 3 chemical d i s o r d e r . 113 p o i n t d e f e c t s Cvacancies and i n t e r s t i t i a l s 3 and i i i > l a t t i c e d e f e c t s C d i s l o c a t i o n s and d i s c 1 i n a t i 0ns3.

{ h p a r t m e n t of S o l i d S t a t e P h y s i c s . I n s t i t u t e of P h y s i c s . L. Kossuth U n i v e r s i t y . H-4010 Debrecen. P. 0. Box 2.

.

^Hungary

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990407

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COLLOQUE DE PHYSIQUE

O b v i o u s l y , d e p e n d i n g on t h e way o f i r r a d i a t i o n o r mechanical d e f o r m a t i o n t h e q u a n t i t y and t h e r a t i o o f t h e above d e f e c t s c a n b e d i f f e r e n t and some d i f f e r e n c e s i n t h e t r a n s f o r m a t i o n c a n b e e x p e c t e d f r o m c a s e t o c a s e . However.

t h e r e are b o t h e x p e r i m e n t a l and t h e o r e t i c a l i n d i c a t i o n s i n t h e l i t e r a t u r e C see e . g . /4,5/ and / 6 . 7 / r e s p e c t i v e l y 3 t h a t t h e most i m p o r t a n t f a c t o r is t h e p r o d u c t i o n o f t h e chemical d i s o r d e r . C o n s e q u e n t l y , w e w i l l n e g l e c t h e r e t h e c o n t r i b u t i o n of o t h e r d e f e c t s .

F u r t h e r m o r e , e s t i m a t i n g t h e change i n t h e G i b b s - f r e e e n e r g y o f t h e s y s t e m w e w i l l c o n s i d e r n o t on1 y t h e chemical t e r m s C a s i t is g i v e n f o r example by t h e Bragg-Williams a p p r o x i m a t i o n 3 b u t a l s o t h e t e r m c o n n e c t e d w i t h t h e e l a s t i c mismatch e n e r g y s t o r e d d u r i n g t h e o r d e r -di s o r d e r p r o c e s s .

GENERAL CONDITION AMORPHISATI ON

The g e n e r a1 c o n d i ti on f o r amor phi s a t i on o f a n o r i g i n a l 1 y o r d e r e d i n t e r m e t a l l i c compound a t s t o c h i ometr i c c o m p o s i t i o n c a n b e g i v e n as

AG;

>

AGa, C13

where AG' c i s t h e c h a n g e c a u s e d f o r example by i r r a d i a t i o n , b a l l m i l l i n g , e t c . i n t h e s o l i d s t a t e and AG i s t h e d i f f e r e n c e between t h e G i b b s - f r e e e n e r g i e s

a

o f t h e amorphous and c r y s t a l l i n e states. L e t u s s u p p o s e t h a t t h e t e m p e r a t u r e i s low enough t o a v o i d t h e t h e r m a l l y a c t i v a t e d r e c o v e r y p r o c e s s e s and t o n e g l e c t t h e e n t r o p y terms i n Ci3:

AH;

>

AHa. C B>

S i n c e AHA is mainly c o n n e c t e d w i t h t h e d i s o r d e r i n g o f t h e o r d e r e d s t r u c t u r e , i t c a n b e w r i t t e n as

where AHchem i s accompanied by t h e pure chemical d i s o r d e r C a s i t is g i v e n f o r example i n t h e Bragg-Williams model /8/3. AHel a r i s e s f r o m t h e s i z e mismatch C which obvious1 y i n c r e a s e s w i t h i n c r e a s i n g d i s o r d e r > . F i n a l l y AHstruct i S

c o n n e c t e d w i t h t h e c h a n g e o f t h e s t r u c t u r e Cchange o f t o p o l o g y > ; t h i s w i l l b e n e g l e c t e d b e c a u s e w e w i l l s u p p o s e t h a t t h e s t r u c t u r e r e m a i n s c r y s t a l l i n e . S i m i l a r 1 y , as i t was a l r e a d y mentioned i n Sec. l , w e w i l l a l s o n e g l e c t

-

on t h e r i g h t hand s i d e o f C33

-

t h e e n e r g y s t o r e d d u r i n g t h e p l a s t i c d e f o r m a t i o n o r s t o r e d by p r o d u c i n g e x t r a p o i n t d e f e c t s . I t i s worth m e n t i o n i n g t h a t t h e p r e s e n c e o f p l a s t i c d e f o r m a t i o n o r extra p o i n t d e f e c t s , a t least p a r t l y . a r e a l s o r e f l e c t e d i n t h e f i r s t two terms i n C33 s i n c e t h e y a r e u s u a l l y accompanied by t h e p r o d u c t i o n o f a n t i - s i t e d e f e c t s C a s f o r example i n t h e c a s e o f a n t i -phase b o u n d a r i e s 3

.

Obvious1 y i n C 3 > t h e f i r s t two t e r m s depend on t h e o r d e r p a r a m e t e r , r ) . On t h e o t h e r hand. AHa i n C23 i s d e t e r m i n e d by t h e r e l a t i o n

where AHzhem h a s a s i m i l a r meaning as t h e f i r s t t e r m i n C33, b u t s i n c e i n t h e amorphous s t a t e t h e r e i s no l o n g r a n g e o r d e r , w e w i l l s u p p o s e t h a t AHa

chem c o r r e s p o n d s t o t h e v a l u e t a k e n a t r ) = 0:

m2hem = AHzhem. where t h e power m r e f e r s t o t h e maximal v a l u e o f AHchem. The s e c o n d t e r m i n C43 e x p r e s s e s t h e f a c t t h a t t h e amorphous s t a t e i s d i s o r d e r e d n o t o n l y c h e m i c a l l y b u t t o p o l o g i c a l l y a s w e l l . S i n c e t h e r e i s no e l a s t i c mismatch e n e r g y i n t h i s c a s e AHel is m i s s i n g f r o m C43.

I f w e look f o r & g e n e r a l c o n d i t i o n

of

a m o r p h i s a t i o n w e c a n t a k e t h e maximum v a l u e s o f AH

chem and AHel < i . e . t h e i r l i m i t s a t r ) = 03 i n eq.C3> and w e have from Cl3

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where AHf d e n o t e s t h e change i n H accompanied w i t h t h e t o p o l o g i c a l change t o p

d u r i n g f u s i o n and p = 0 . 7 &.10/. Combining Cb3 and C73 w e g e t

According t o t h i s g e n e r a l c o n d i t i o n i f is z e r o i t i s n o t e x p e c t e d t h a t t h e a m o r p h i s a t i o n t a k e s p l a c e i . e. eg C83 emphasizes

the

i m ~ o r t a n c e fo

the

e l a s t i c mismatch

the

a m o r p h i s a t i o n

of

i n t e r m e t a l l i c com~ounds.

Eq C83 c a n be f u r t h e r r e w r i t t e n i f w e e x p r e s s AHf i n t e r m s o f t h e h e a t s t o p

of f u s i o n whi c h are d i r e c t l y measurable q u a n t i t i e s . If t h e o r d e r - d i s o r d e r t e m p e r a t u r e . Tc, is lower t h a n t h e m e l t i n g t e m p e r a t u r e , Tm t h a n

where AHZs and W;: are t h e h e a t of f u s i o n and t h e e l a s t i c mismatch e n e r g y of t h e Cdisordered3 s o l i d s o l u t i o n , r e s p e c t i v e l y . I f Tc

>

Tm

4

^omp⁼^-topf ⁺~ Z h e m C 103

and h e r e Mcomp f is t h e h e a t of f u s i o n of t h e Cordered3 compound. I n a c c o r d a n c e w i t h t h e g e n e r a l l y u s e d s u p p o s i t i o n t h a t t h e r e i s n o elastic mismatch e n e r g y i n t h e o r d e r e d compound, and o b v i o u s l y e i t h e r i n t h e l i q u i d s t a t e as w e l l , t h e e l a s t i c t e r m i s m i s s i n g from C103. Furthermore, a c c o r d i n g t o t h e R i c h a r d ' s r u l e /il/

A H z s = h S f ~ m e a n -

-

2k Tmean C l l a 3

and

= 2': Tm. C l l b 3

where &is t h e e n t r o p y of f u s i o n , k i s t h e Boltzmann c o n s t a n t and T

mean Cthe a v e r a g e v a l u e of t h e s o l i d u s and l i q u i d u s 4 8 4 p l a y f a r o l e o f Tm f o r d i s o r d e r e d s o l i d s o l u t i o n s . Now, def i n i ng t h e o r d e r i n g e n e r g y a s

AHord = AHzhem ⁺AH:l = mzhem 9 , where B i s g i v e n by

e

= l + m:l/AH:hem, e q C 8 1 c a n be r e w r i t t e n as

AH:l/p + ~ z h e m

>

2kTm o r

AHor, C 9-1 +p1 /p9

>

2k Tm i f Tc

>

Tm and

ss

i f Tc

<

Tmean. I t c a n b e s e e n from C143 t h a t i f t h e r e i s no e l a s t i c

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COLLOQUE DE PHYSIQUE

mismatch i . e. when AHt1=0 C8=13 ;

W o r d = ~ r h e m

>

2 k Tm.

But, a c c o r d i n g t o eq. C103 a n d C l 1 b3 t h i s c a n n o t b e f u l f i l l e d b e c a u s e

mcomp >

AHzhem a l w a y s . S i m i l a r l y . Cl53 never c a n b e f u l f i l l e d i f A H t l is z e r o . E q u a t i o n s C143 a n d Cl53 a g a i n g i v e t h e n e c e s s a r y c o n d i t i o n s i n t e r m s o f t h e e l a s t i c mismatch e n e r g i e s Cand i n t h e t e r m o f t h e AHrhem i f Tc

>

Tm3.

Thus, i n o r d e r t o make e s t i m a t i o n s f o r d i f f e r e n t s y s t e m s , w e need e s t i m a t i o n s f o r t h e chemical p a r t of t h e - o r d e r i n g e n e r g y and f o r t h e e l a s t i c mismatch e n e r g i es a s w e 1 l .

3-

RESULTS

I n o u r c a l c u l a t i o n s t h e chemical e n e r g i e s w e r e e s t i m a t e d f r o m t h e Miedema e x p r e s s i o n s f o r t h e h e a t o f f o r m a t i o n o f o r d e r e d a l l o y s . I n t h e Miedema's model /l 3/ t h i s q u a n t i t y i S g i v e n as

mf orm -

o r d - < l + 8 [ c : c ~ 1 2 > ~ ~ ~ ~ .

H e r e i s t h e f o r m a t i o n e n t h a l p y o f a l i q u i d a l l o y a n d c; a n d c; a r e t h e s u r f a c e c o n c e n t r a t i o n s /13/. The f a c t o r 8 w a s f i x e d e m p i r i c a l l y i n /13/ s u c h a way t h a t t h e model is i n a c c o r d a n c e w i t h t h e e x p e r i m e n t a l r e s u l t t h a t t h e e n t h a l p y o f t h e o r d e r i n g i s a b o u t o n e t h i r d of W:%. However. s i n c e i n t h e e x p e r i m e n t a l l y o b s e r v e d n o t on1 y t h e chemical b u t t h e e l a s t i c t e r m s are a l s o i n c l u d e d , t h i s f a c t o r is t o o h i g h i f w e want t o g e t t h e chemical t e r m o n l y . I n d e e d . as w e h a v e shown i n /14/ t h e u s e o f t h e f a c t o r 5.3 i n s t e a d o f 8 i S more a p p r o p r i a t e .

F i n a l l y , s i n c e c a n b e e x p r e s s e d as t h e d i f f e r e n c e between t h e h e a t

& f o r m

of f o r m a t i o n of t h e compound, o r d . a n d t h e l i q u i d a l l o y . AHform l i q v a t t h e same c o m p o s i t i o n , w e u s e d i n our c a l c u l a t i o n s t h e r e l a t i o n

mf o r m

l i q a r e t a b u l a t e d i n /13/ f o r e q u i a t o m i c c o m p o s i t i o n s and c a n b e e a s i l y ca1c;lated f o r a n y c o n c e n t r a t i o n .

I n o n e o f our p r e v i o u s p a p e r s / I S /

.

u s i n g a method s i m i l a r t o t h e t h e o r y of a l m o s t c o m p l e t e l y o r d e r e d a l l o y s , a n e s t i m a t i o n f o r t h e e l a s t i c mismatch e n e r g y o f o r d e r e d compounds was d e r i v e d as t h e f u n c t i o n o f t h e l o n g - r a n g e o r d e r p a r a m e t e r , r ) , f r o m t h e continuum e l a s t i c t h e o r y . I t w a s shown t h a t , s i m i l a r l y t o AHchem, t h i s h a s a s i m p l e C l - r ) 2 > - t y p e dependence;

where

= EoC03/4m.

H e r e m = l/FAFB and Fi Ci=A.B3 i s t h e a t o m i c f r a c t i o n of t h e component i and E CO> is t h e e l a s t i c e n e r g y o f t h e s y s t e m when a " p a i r " o f a n t i - s i t e d e f e c t s

0

C i . e . o n e A atom i n t h e

p

and o n e B atom i n t h e a s u b l a t t i c e , r e s p e c t i v e l y 3 a r e produced a t T = 0 K i n a n o t h e r w i s e i d e a l o r d e r e d c r y s t a l . I t was shown by d e t a i l e d c a l c u l a t i o n s /IS/ t h a t t h e e s t i m a t i o n o f AHm i s r e s t r i c t e d by our

el

knowledge on t h e volumes o f atoms and h o l e s i n t h e compound. I t w a s i l l u s t r a t e d t h a t i f , i n t h e c a l c u l a t i o n o f EoC03, w e u s e d u n c o r r e c t e d v a l u e s f o r t h e above volumes C i

.

e. t h e s a m e volumes a s t h e y have i n p u r e m e t a l s A and B , r e s p e c t i v e l y 3 o r w e c o r r e c t e d t h e volumes a c c o r d i n g t o t h e Miedema model

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t h e c o n d i t i o n o b t a i n e d by Johnson /1€i/, o r n o t . I n d e r i v i n g h i s r e l a t i o n Johnson, s u p p o s i n g t h a t p 2 1 and n e g l e c t i n g t h e e l a s t i c mismatch e n e r g i e s . s t a r t e d from t h e r e l a t i o n

Using t h e R i c h a r d ' s r u l e C2k =

d >

and a s i m p l i f i e d r e l a t i o n between Tc and mzhem ~ ~ z h e m 2 kT 3 h e g o t t h e c o n d i t i o n f o r t h e a m o r p h i s a t i o n a s

C

Tc/Tm 2 l . C 21

>

Now, t a k i n g i n t o a c c o u n t t h a t AHtl i s u s u a l 1 y e q u a l o r less t h a n pAHz;

Cp=O.7 a n d see a l s o A S & , we atso obtain from C i 5 > that the amorphisation is not possible in soLid state if Tc c Tm.

I f Tc>Tm w e have shown i n /14/ by d e t a i l e d c a l c u l a t i o n s t h a t c o n d i t i o n C143 c a n b e r e w r i t t e n as

T c n m

>

M 2qcm A3.8 3 where

H e r e q i s a n u m e r i c a l f a c t o r l y i n g between l and 3 f o r t h e most s i m p l e c

s t r u c t u r e s A 4/.

A t 8 = l , i . e when t h e r e i s n o e l a s t i c mismatch. M = l . But i n t h i s case.

a 1 though

Tc/Tm

>

¹^,t h e i n e q u a l i t y C223 c a n n o t b e f u l f i l l e d C a s i t w a s d i s c u s s e d b e f o r e a f t e r e q s C141 a n d C153> a n d s o the transition temperature.

even if i t is higher than Tm, atways shouLd be Less than Tm?gcm 3 /63.6.

Consequent L y the va Lue of Tc L ies be t ween T and 2qcTmm 3 /63.6 and so m

condition C 2 2 > can be fuLfiLLed only if 4 > 2 CH<f>. I t i s h a r d t o c o n c l u d e a n y t h i n g more from C22> b e c a u s e w e are n o t a b l e t o d e t e r m i n e

=c e x p e r i m e n t a l l y , b u t i t is c l e a r l y s e e n t h a t c o n d i t i o n Tc>Tm

is

E& &

s u f f i c i e n t c o n d i t i o n .

F i n a l l y . b e f o r e a n a l y z i n g t h e r e s u l t s of our c a l c u l a t i o n s , w e n o t e t h a t q u a l i t a t i v e l y C 8 > . Cl43 o r C223 i s i n a c c o r d a n c e w i t h t h e c o n d i t i o n s e s t a b l i s h e d e m p i r i c a l l y by Luzzi and Meshi A/ f o r s o l i d s t a t e a m o r p h i s a t i o n o f compounds under e l e c t r o n i r r a d i a t i o n C s e e f o r t h e d e t a i l s A 4 A .

I n h e f i r s t t h r e e columns o f T a b l e 1 t h e c a l c u l a t e d A H z l . C i n u n i t s KJ/mol3 and 4 v a l u e s a r e g i v e n , r e s p e c t i v e l y . The f o u r t h column shows t h e m e l t i n g p o i n t s and t h e n e x t t h r e e columns list t h e c 1 4 v a l u e s Cin u n i t s o f t e m p e r a t u r e 3 c a l c u l a t e d f r o m c o n d i t i o n C143 ;

The c l 4 and c ' 1 4 " t e m p e r a t u r e s " w e r e o b t a i n e d u s i n g volumes o f t h e h o l e s and atoms w i t h and w i t h o u t Miedema's c o r r e c t i o n s i n EoC03, r e s p e c t i v e l y . The column c"14 g i v e s t h e t e m p e r a t u r e s C a c c o r d i n g a g a i n t o C8433 c a l c u l a t e d from A H z y v a l u e s Cwith c o r r e c t e d volumes3 i n p l a c e of AHzl. C I t w a s shown i n A S / t h a t t h e d i f f e r e n c e between A H ~and ~ AHzl f o r t h e same s y s t e m w a s

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COLLOQUE DE PHYSIQUE

comparable t o t h e d i f f e r e n c e i n AHEl - o b t a i n e d by u s i n g c o r r e c t e d o r u n c o r r e c t e d volumes f o r t h e atoms and h o l e s . 3

TABLE 1 Compound AHzl

LaAu 6. 55

La2Co3 2 3 . 1 3 LaCu2 1 6 . 0 6

LaNi 26.99

GdCo3 1 1 . 2 9 OdX07 9 . 7 1

PdZr 2. 0 4

PtZr 1 . 7 4 P t Z r 2 2 . 9 8 Zr7CulO 8 . 0 4

Zr Cu 8.

NiZr2 1 0 . 7 3 NiZr 1 0 . 8 2 CoZr 1 0 . 8 1

ZrzAl 1.37

Zr3Al 1 . 2 4 RuZr 6 . 7 1 Cr2Zr 9 . 4 9

CuTi2 2.40

CuTi 2 . 5 8 Ti3Cu4 2 . 5 7

Ti2Cu3 2.54

TiCu4 2.01

N i Ti 3.41

NiTi2 3.59

Ni3Ti 2 . 3 2 Co2Ti 2 . 7 5

CoTi 3.41

Fe2Ti 2 . 1 8 FeTi 2 . 7 3 Mn2Ti 2 . 1 2 RuTi 0 . 5 5

AuZn 1.55

Ni6Nb7 5.11

N i Mo 4.47 N i 3 A l 1.37 N i A l 2.30 FeCo 0 . 0 6

PdI n 3.20

CoGa 5. 83

C o A l 2 . 3 2 Cu3Sn 1 1 . 2 4 Pd3Sn 3 . 1 0

exp. c o n c l .

C c ' c "

Y Y Y Y

N Y Y Y

Y N Y Y

Y Y Y Y

Y N Y Y

Y N N N

Y Y Y Y

Y N Y Y

Y Y Y Y

Y N N N

N N N N

Y N Y Y

N N N Y

Y N N N

N N N N

Y N N Y

N N N N

Y N N N

3 N N N

Y N N N

3 N N N

Y N N N

N N N N

Y f J N Y

Y N N N

N N N N

N Y Y Y

N N N N

The l a s t two columns show t h e e x p e r i m e n t a l i n f o r m a t i o n on t h e a m o r p h i s a t i o n i n v e s t i g a t e d by i r r a d i a t i o n /l .6.16/ o r by b a l l - m i l l i n g C s e e r e f e r e n c e s /17/ t o e 4 / and till now unpublished r e s u l t s from t h i s l a b o r a t o r y 2 and t h e c o n c l u s i o n s o b t a i n e d from c14 c ' 1 4 and c"14 c o n d i t i o n s , r e s p e c t i v e l y . Here t h e l e t t e r s Y CyesD and N Cno> i n d i c a t e t h a t t h e a m o r p h i s a t i o n i s p o s s i b l e o r not. For t h e CoTi and FeTi systems t h e q u e s t i o n marks show t h a t t h e e x p e r i m e n t a l r e s u l t s a r e n o t unambiguous C see /l 8 / and

m / ,

r e s p e c t i v e l y3.

From t h e comparison of t h e l a s t two columns of T a b l e 1 w e c a n c o n c l u d e ; i 3 The agreement is s a t i s f a c t o r y i n 26 c a s e s from t h e 4 3 compounds: a t

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w a s neglected here

-

can be i m p o r t a n t . I t is p o s s i b l e t h a t m o r e precise m e a s u r e m e n t s at Low temperatures c o u l d lead t o a m o r p h i s a t i on i n t h e s e a1 l oys.

i i i 3 I n systems c o n t a i n i n g T i t h e a g r e e m e n t is w r o n g ;

u s u a l l y

amorphisation w a s observed

.

b u t t h e c a l c u l a t i o n s l e d t o o p p o s i t e r e s u l t s . The reason of t h i s f a c t is n o t clear a t p r e s e n t .

i v 3 We have t o t a k e i n t o account t h a t c o n d i t i o n C 1 4 3 is a necessary c o n d i t i o n and i n t h e m a j o r i t y of cases w h e r e disagreement w a s obtained t h e increase of ^{t h e} t e m p e r a t u r e calculated f r o m C 2 4 3 w o u l d lead t o a better a g r e e m e n t . For e x a m p l e i f w e estimate t h e energy stored by t h e a c c u m u l a t i o n of i a t t i c e defects C m a i n l y d i s l o c a t i o n s 3 d u r i n g p l a s t i c deformation according t o /l 6/ and &g/, as 1-2 k J / m o l , t h a n t h i S w o u l d increase t h e r i g h t hand side of C 1 4 3 C and consequent1 y C 2 4 3 3 by about 150

-

200 K.

ACKNOWLEDGEMENT

F i nanci a1 s u p p o r t by t h e D u t c h Foundation for F u n d a m e n t a l R e s e a r c h on Matter C FObD is g r a t e f u l l y a c k n o w l e d g e d .

R E F E R E N C E S

/l / K. C . R u s s e l

.

Progress in Hat eria Ls Science. V o l . 28, p. 2ZS. P e r g a m o n P r e s s

,

C 19843

/2/ A. W. W e e b e r a n d H. B a k k e r

.

P h y s i c a

8153

C 1 9 8 8 > 93

/3/ P.D. A s k e n a z y . E.A. K e m e n e t z k y . L . E . T a n n e r , W.L. Johnson, J. Less-Common M e t .

. ¹⁴⁰

C 1 9 8 8 3 1 4 9

/4/ R. B. S h w a r z and R. R. P e t r i c h , J. L e s s - C o m m o n M e t .

.

140 C 1 9 8 8 3 171 /5/ P. R. O k a m o t o . L . E . R e h n . J . Pearson. R. B h a d r a and M. G r i m d i t c h . J.

L e s s - C o m m o n M e t .

.

140 C l 9883 231

/g/ D. E. L u z z i and M. M e s h i i

.

S c r i p t a M e t . 20 C l 9 8 6 3 943 /7/ D. E. L u z z i and M. M e s h i i

.

^J. L e s s - C o m m o n M e t .

140

C 19883 193

/8/ T. M u t o and Y. T a k a g i , Solid State Phys. V o l 1.

.

^p. ^31. A c a d e m i c P r e s s . N . Y . . C 1 9 5 5 3

/9/ T. E g a m i and A u r

.

^J. N o n - C r y s t

.

^Solids

,

89 C 19873 60 /l 0/ T. E g a m i

.

^{R e p .} ^{Pr ogr}

^.

^Phys.

⁴⁷

^{C 19843}¹⁶⁰¹

/ i l / R . A . S w a l i n . "Thermodynamics of SoLids" J . W i l e y . N e w - Y o r k . C 1 9 7 6 3 p 60 /l2/ D. L . B e k e . G. E r d e l y i and F. J. K e d v e s

.

^{J. Phys.} ^{C h e m}^Sol.

^a

^C19793 543 /l 3/ F. R. de B o e r

.

^R. B o o m , W. C. M. Mattens. A. R. Miedema and A. K. N i e s s e n .

"Cohesion in MetaLs. Transition ALLoys" N o r t h - H o l l a n d . A m s t e r d a m . C 1 9883

/14/ D. L . B e k e . H. B a k k e r and P. I . L o e f f , s u b m i t t e d t o A c t a Materials /15/ D. L . B e k e . P. I . L o e f f and H. B a k k e r , s u b m i t t e d t o A c t a Materi a l a /l 6/ W. L . Johnson. Progress in Ma teria L Science. V o l . 30. p. 81

.

P e r g a m o n Press

.

^C¹⁹⁸⁶³

/17/ P . I . L o e f f . a n d H. B a k k e r . S c r i p t a . M e t . 23 C 1 9 8 8 3 401

/18/ A . Y e . Y e r m a k o v . V . A . B a r i n o v and Y e . Y e . Y u r c h i k o v . Phys. M e t a l i M e 1 loved.

.

^{54 C}¹⁹⁸²³⁹⁰

/19/ A . Y e . Y e r m a k o v . Y e . Y e . Y u r c h i k o v and V.A. B a r i n o v . Phys. M e t a l . i M e l l o v e d . .

g

C 1 9 8 1 3 050

/ 2 O / F . H . M . S p i t . P . I . L o e f f and H. B a k k e r . J . N o n - C r y s t . S o l i d s .

108

C 1 9 8 8 3 233

&l/ P . I . L o e f f . F . H . M . S p i t and H. B a k k e r . J . L e s s - C o m m o n M e t .

M

C 1 9 8 8 3 271

/22/ A. W. Weeber

.

H. B a k k e r and F. R. de B o e r

,

E u r o p h y s L e t t .

g

C 1 9 8 6 3 445 /23/ T. J . T i a i n e n and R. B. S c h w a r z . J . L e s s - C o m m o n . M e t .

140

C 1 9 8 8 3 99 /24/ A. W. W e e b e r and H. B a k k e r

,

Z. Phys. C h e m i e N e u e Fol ge

157

C 19883 221 4 2 5 1 M.B. B e v e r , D . L . H o l t and A . L . T i t c h e n e r , Prog. Hater. Sci. 17 1 C 1 9 7 3 3