METALLIC GLASSES - SOME CURRENT ISSUES

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METALLIC GLASSES - SOME CURRENT ISSUES

R. Cahn

To cite this version:

R. Cahn. METALLIC GLASSES - SOME CURRENT ISSUES. Journal de Physique Colloques, 1982,

43 (C9), pp.C9-55-C9-66. �10.1051/jphyscol:1982911�. �jpa-00222414�

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JOURNAL DE PHYSIQUE

Colloque C9, supplément au n°12, Tome 45, décembre 1982 page C9-55

METALLIC GLASSES - SOME CURRENT ISSUES

R. W. Cahn

Laboratoire de Métallurgie Physique, Université de Paris-Sud, 91405 Orsay, France

Résumé'. - On discute quatre aspects du comportement des verres métal- liques en tenant compte des dernières observations et théories:

1) La capacité* de former les verres parmi diverses alliages.

2) La structure et l'ordre à courte distance.

3) La nature du volume libre.

4) La relaxation thermique, réversible ou irréversible.

Car le concept de l'Ordre à courte distance est un aspect commun, on passe en revue l'histoire de ce concept en relation avec les

alliages cristallins, pour en tirer des leçons. On souligne l'importance de la variation de cet ordre en fonction de la température.

Abstract. - Four aspects of the behaviour of metallic glasses are analysed in the light of recent results and theories:

1) Glass-forming ability of different alloys.

2) Structure and short-range order.

3) The nature of free volume.

4) Thermal relaxation, reversible or irreversible.

The concept of chemical short-range order runs as a common thread through these various issues, and some space is devoted to a historical resume of the study of SRO in crystalline solid solutions,

in order to draw some instructive parallels. The special importance of establishing how SRO in glasses varies as a function of temperature is emphasised.

1. Introduction. - Research on metallic glasses has become big business. In 1980, for instance, over 1000 papers were published on rapidly quenched alloys and over 90% of these were concerned with, metallic glasses. The breakeven year as between glasses and rapidly quenched crystalline alloys had been 1974, when papers on rapid quenching totalled only 123 (1), whereas in 1981, the Fourth Inter- national Conference on Rapidly Quenched Alloys, alone, included 336 papers on metallic glasses. It is thus no longer realistic to attempt a general survey of recent developments in this field, be they

fundamental or applied: one would need to be at the same time a polymath and a monomaniac. Accordingly, in this short survey I propose

to focus on a few scientific (as opposed to technological) topics, within the larger field of metallic glasses, which are in a state of especially rapid development^on which, in consequence, ideas are in a state of flux. Since the precursor to an important advance in any branch of science is generally a newfound recognition of the depth of one's ignorance, this survey could without much hyperbole be termed an outline of ignorance.

2. Glass-Forming Ability. - In the 1960*s, everybody Knew that glasses are easily made only if they approximate to the composition M8om20i

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982911

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C9-56 JOURNAL DE PHYSIQUE

where M is a t r a n s i t i o n o r noble metal and m a m e t a l l o i d . Now t h a t many metal-metal g l a s s e s a r e known, t h i n g s a r e recognised t o be more complicated and much e f f o r t h a s gone i n t o a t t e m p t s t o f i n d u n i v e r s a l c r i t e r i a t h a t can d i s t i n g u i s h t h o s e a l l o y compositions t h a t can be made g l a s s y by r a p i d quenching, a t up t o

l o 8

K / s , and t h o s e t h a t cannot.

The proper t e s t f o r qlass-forminq a b i l i t y (GFA) i s t h e c r i t i c a l quenching r a t e , R c , which w i l l j u s t allow t h e c o o l i n g l i q u i d t o m i s s t h e nose of t h e C-curve t h a t r e l a t e s t h e s t a r t of c r y s t a l l i s a t i o n t o temperature; t h e lower R c , t h e h i g h e r t h e GFA. I n t h e l i t e r a t u r e , Rc i s always t r e a t e d r a t h e r s i m p l i s t i c a l l y a s a s i n g l e r a t e , whereas i n f a c t dT/dt i t s e l f v a r i e s d u r i n g t h e c o o l i n g p r o c e s s ; b u t t h i s s u b t l e t y i s a m a t t e r f o r f u t u r e a t t e n t i o n . Many a u t h o r s t a c i t l y t r e a t t h e s t a b i l i t y of a g l a s s , a s measured by i t s c r y s t a l l i s a t i o n tempe- r a t u r e , T,, under s t a n d a r d c o n d i t i o n s , a s e q u i v a l e n t t o GFA, i n t h e s e n s e t h a t i f one i n c r e a s e s , s o must t h e o t h e r . This t a c i t h y p o t h e s i s h a s n o t been c r i t i c a l l y examined and i s probably only v e r y rouyhly v a l i d .

The s i m p l e s t s t r u c t u r a l c r i t e r i o n f o r a h i g h GFA/stability i s i n terms of atomic/ionic r a d i i . I n t h e 1 9 6 0 1 s , model experiments on t h e mixing of two-dimensional r a f t s , e i t h e r of soap bubbles (which mimic p o t e n t i a l s between metal i o n s ) o r of hard s p h e r e s , both i n d i - c a t e d t h a t a s i z e d i f f e r e n c e approaching 15% was n e c e s s a r y f o r ready

" g l a s s w formation. T h i s i s a simple m a t t e r of k i n e t i c hindrance

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a l i m i t a t i o n on d i f f u s i o n k i n e t i c s i n t h e l i q u i d . L a t t e r l y , t h i s simple c r i t e r i o n h a s been made more r e a l i s i t c by t h e p o s t u l a t i o n of " g l a s s - forming maps", i n which one a x i s d e f i n e s t h e atomic r a d i u s r a t i o of t h e elemental components and t h e o t h e r some measure of bond s t r e n g t h i n t h e l i q u i d (which a g a i n , by i m p l i c a t i o n , i s a measure of t h e d i f f i c u l t y of atomic t r a n s p o r t ) . Giessen ( 2 ) f o r t h i s purpose u s e s

a q u a n t i t y , A H ~ , t h e maximum v a l u e of t h e h e a t of mixing f o r a s e r i e s of mixtures between two s p e c i f i e d m e t a l s , i t s e l f c a l c u l a t e d from e l e c t r o n e g a t i v i t i e s and e l e c t r o n c o n c e n t r a t i o n s by a w e l l - t e s t e d procedure ( 3 ) . Sommer ( 4 ) independently introduced g l a s s formation diagrams of t h e same t y p e , b u t h e used AEs ( o r 0 R V ) , t h e mean v a p o r i z a t i o n enthalpy of t h e components. These diagrams were a p p l i e d by b o t h a u t h o r s t o a l a r g e v a r i e t y of b i n a r y mixtures. Both Giessen and Sommer found t h a t t h e atomic r a d i u s r a t i o was preponderant b u t t h a t a s t r o n g i n t e r a t o m i c bond could s e r v e t o r e l a x t h e r a d i u s c r i t e r i o n , which i s normally t h a t rx/ry must d e p a r t from u n i t y by a t l e a s t 10%. Both bond s t r e n g t h and r a d l u s r a t i o determine t h e k i n e t i c s of atomic t r a n s p o r t and t h u s of c r y s t a l l i s a t i o n , and t h e magnitude of AHM i s a l s o l i n k e d w i t h t h e f r e e energy change t h a t d r i v e s c r y s t a l l i s a t i o n .

Sommer and h i s c o l l a b o r a t o r s ( 4

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7 ) have t a k e n t h e thermodynamic-cum-kinetic a n a l y s i s of GFA f u r t h e r t h a n t h i s . B r i e f l y , t h e y have e s t a b l i s h e d s y s t e m a t i c a l l y t h a t ( a s might be expected) small f r e e energy d i f f e r e n c e s between t h e l i q u i d and t h e e q u i l i b r i u m c r y s t a l f o r a supercooled melt f a v o u r s g l a s s formation (6 ) : but t h e m a t t e r i s complicated by t h e tendency of m e l t s t o form s h o r t - r a n g e order o r , more e x a c t l y , c l u s t e r s of an i d e a l l o c a l composition; Sommer u s e s t h e g e n e r a l term a s s o c i a t i o n s . The i d e a l composition and frequency of t h e s e a s s o c i a t i o n s can be determined from measurements of thermodynamic and v a r i o u s p h y s i c a l p r o p e r t i e s ( 6 ) . I f such chemically ordered c l u s t e r s a r e p r e s e n t i n t h e melt and have a d i f f e r e n t composition from t h e s t a b l e c r y s t a l l i n e forms, t h e n t h e n u c l e a t i o n of t h e l a t t e r i s chemically hindered. Thus t h e systems Mg

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Ca, Mg

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S r and M g

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B a behave q u i t e d i f f e r e n t l y : g l a s s e s form r e a d i l y over a wide composition range i n t h e f i r s t , over a narrower range i n t h e second and n o t a t a l l i n t h e t h i r d . Thermodynamic measurements i n d i c a t e c l u s t e r s of composition MgCa i n t h e Mg

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Ca m e l t s , but Mg2Ba i n t h e Mg

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Ba m e l t s . s i n c e i n a l l t h r e e systems t h e r e i s a Laves phase of composition A z B , i t follows t h a t n u c l e a t i o n i n t h e Mg

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Ba system i s e a s y i n view of

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t h e presence of c l u s t e r s of s u i t a b l e composition, whereas n u c l e a t i o n i n Mg

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Ca i s hindered. I n Mg

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S r , t h e r e a l s o Mg2Sr c l u s t e r s , but a s m a l l e r volume f r a c t i o n . Sommerls model presupposes a v a r i a b l e degree of microcompositional h e t e r o g e n e i t y which goes f u r t h e r t h a n t h e conventional p i c t u r e of "short-range order".

The d i s t i n c t i o n can be made c l e a r e r by d i s c u s s i n g t h e thorough- l y s t u d i e d Cu

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T i system i n more d e t a i l . The degree of chemical S R O i n Cu

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T i a l l o y s h a s been measured d i r e c t l y both by d i f f r a c t i o n methods ( 8 ) and by EXAFS ( 9 ) and b o t h approaches a g r e e i n showing very s t r o n g maximum order a t a composition Cu2Ti. G l a s s e s can be made over a wide composition range. S a k a t a e t a l . ( 8 )

,

i n an important paper, have shown t h a t t h e c r y s t a l l i s a t i o n t e m p e r a t u r e , Tx, i s h i g h e s t c l o s e t o t h e Cu2Ti composition, and t h e normalised c r y s t a l l i s a t i o n t e m p e r a t u r e , T d T m (where Tm i s t h e e q u i l i b r i u m melting temperature of t h e c r y s t a l l i z e d g l a s s ) a c c u r a t e l y m i m i c s t h e v a r i a t i o n of t h e

SRO parameter a s a f u n c t i o n of composition. T h i s i s a r e s u l t of g r e a t t h e o r e t i c a l i n t e r e s t .

Sommer e t a l . ( 7 ) have made thermodynamic measurements of a s e r i e s of Cu

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T i m e l t s and conclude t h a t , f o r a range of melt

compositions, a s s o c i a t i o n s having t h e composition Cu3Ti2 ( n o t Cu2Ti) a r e p r e s e n t i n t h e m e l t , i n v a r i a b l e volume f r a c t i o n s . S i n c e t h e s t a b l e c r y s t a l l i n e s p e c i e s a r e CuTi and CuTi2, p l a i n l y t h e presence of t h e a s s o c i a t e s h i n d e r s c r y s t a l n u c l e a t i o n . Sommer e t a l . ( 7 ) d i s c u s s t h e s l i g h t mismatch between t h e neutron d i f f r a c t i o n and t h e thermodynamic d a t a and propose a way of r e c o n c i l i n g t h e two.

N e v e r t h e l e s s , i t i s n o t a t p r e s e n t c l e a r j u s t what t h e s t r u c t u r a l r e l a t i o n i s between an a s s o c i a t i o n model (which i m p l i e s h e t e r o g e n e i t y on a f i n e s c a l e ) and conventional chemical s h o r t - r a n g e o r d e r , which i m p l i e s homogeneity.

However t h i s d i f f i c u l t y i s r e s o l v e d , it i s a l r e a d y c l e a r t h a t SRO p l a y s an important r o l e i n determining GFA of m e t a l l i c m e l t s and t h e r e l a t e d thermal s t a b i l i t y of t h e r e s u l t i n g g l a s s e s .

The Sommer-Giessen approach, r e l a t i n g h i g h GFA woth a small f r e e energy change on c r y s t a l l i s a t i o n combined w i t h k i n e t i c hindrance through atomic s i z e mismatch and through t h e formation of a s s o c i a t i o n s i s somewhat r e l a t e d t o an a l t e r n a t i v e model based on atomic volumes.

Yavari and coworkers (10) have r e c e n t l y e s t a b l i s h e d an impressive c o r r e l a t i o n between GFA and A V , t h e change i n volume on f u s i o n . R volume change c l o s e t o z e r o , o r even a c o n t r a c t i o n , on f u s i o n i s found t o favour g l a s s formation. Y a v a r i ' s i d e a s can be summarised i n terms of t h e i d e a t h a t an expansion on f u s i o n i m p l i e s t h e i n j e c t i o n of f r e e volume i n t o t h e l i q u i d , a d e c r e a s e of i t s v i s c o s i t y and hence an enhanced a b i l i t y of c r y s t a l l i n e n u c l e i t o grow even a t s u b s t a n t i a l undercoolings.

These i d e a s a r e c l o s e l y r e l a t e d t o but independent of t h o s e advanced s l i g h t l y e a r l i e r by Ramachandrarao (11). He a p p l i e d a t h e o r e t i c a l model developed over 20 y e a r s ago by Varley t o an e s t i - mation of t h e v a r i a t i o n , w i t h composition, of t h e molar volume of l i q u i d b i n a r y mixtures of m e t a l s , and showed t h a t i n t h o s e systems where g l a s s e s could be formed by quenching, t h e glass-forming range

of compositions i n v a r i a b l y i n c l u d e s t h e composition of minimum molar volume. A n e g a t i v e d e v i a t i o n of a c t u a l molar volume from t h e i d e a l

( i n t e r p o l a t e d ) molar volume, of 15% o r more, seems t o be r e q u i r e d f o r g l a s s formation. Because of t h e ambiguity a t t a c h e d t o t h e s i z e of m e t a l l o i d atoms i n m e l t s and g l a s s e s ( 1 2 ) , t h i s approach i s v a l i d only f o r metal-metal g l a s s e s . Presumably, t h o s e l i q u i d mixtures with p a r t i c u l a r l y small molar volumes a r e a l s o t h o s e f o r which t h e s o l i d - l i q u i d t r a n s f o r m a t i o n i s a s s o c i a t e d w i t h a minimum volume expansion, s o t h a t Ramachandrarao's and Y a v a r i ' s c r i t e r i a may w e l l be e q u i v a l e n t .

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JOURNAL DE PHYSIQUE

There i s a whole b a t t e r y of e m p i r i c a l a t t e m p t s t o r e l a t e f r e e z i n g - p o i n t d e p r e s s i o n i n e u t e c t i c systems t o GFA; t h e b e s t known i s Donald and D a v i e s ' s (13) c r i t e r i o n based on t h e d i f f e r e n c e between t h e a c t u a l e q u i l i b r i u m melting temperature and t h e weighted mean of t h e m e l t i n g t e m p e r a t u r e s of t h e c o n s t i t u e n t elements. (This c r i t e r i o n h a s t h e d i s t i n c t i o n t h a t it h a s p r e d i c t i v e v a l u e ) . Recently,

Massalski ( 1 4 ) h a s developed t h i s approach by r e l a t i n g t h e e q u i l i - brium m e l t i n g temperatures a c r o s s a phase diagram t o t h o s e lower t e m p e r a t u r e s , To, a t which a l i q u i d t e n d s t o f r e e z e without segrega- t i o n t o form a homogeneous c r y s t a l l i n e s o l i d . I f t h e o n s e t of f r e e z i n g d u r i n g f a s t c o o l i n g can be delayed t o below t h i s t e m p e r a t u r e , t h e formation of a homeganeous, " u n p a r t i t i o n e d " g l a s s i s thermodynamically favoured. This approach by Massalski r e p r e s e n t s a p r e l i m i n a r y attempt t o e x t r a p o l a t e arguments used t o i n t e r p r e t massive phase transforma- t i o n s t o t h e problems of GFA.

A number of o l d e r approaches t o GFA have been r e l a t i v e l y n e g l e c t e d of l a t e . Nagel and T a u c l s famous e l e c t r o n i c c r i t e r i o n f o r GFA (15, 16) h a s n o t been much developed. An i s s u e which i s c u r r e n t l y i n suspended animation i s t h e problem of "Polk s t u f f i n g w ( 1 7 ) . The q u e s t i o n h e r e i s whether a metal-metalloid g l a s s , of t h e t y p e of FegO B2g o r Pd80Si20, i s p a r t i c u l a r l y s t a b l e because t h e h o l e s of t h e Bernal ense random packing s t r u c t u r e a r e s t a b i l i s e d by being

" s t u f f e d " by m e t a l l o i d atoms only s l i g h t l y t o o l a r g e f o r them. T h i s s i m p l i s t i c model h a s r e p e a t e d l y been condemned f o r being o u t d a t e d , b u t it i s not q u i t e c l e a r why t h i s i s thought t o be t h e c a s e and no s e r i o u s a n a l y s i s of t h e model h a s appeared f o r a long t i m e . What i s c l e a r i s t h a t t h e p r o p e r t i e s and f i n e s t r u c t u r e of M m g l a s s

i n s t a n c e , s e r i e s v a r i e s t o a s u r p r i s i n g e x t e n t a s x i s v a r i e d ( f o r

Warlimont, p r i v a t e communication, h a s documented such v a r i a t i o n s f o r Fe-B g l a s s e s , a s indeed have a number of o t h e r i n v e s t i g a t o r s ) . The reaso-for such v a r i a t i o n s a r e a s y e t s p e c u l a t i v e .

Thcre have been e s s e n t i a l l y no a t t e m p t s t o achieve a u n i f i e d t h e o r y of GFA f o r m e t a l l i c , oxide and polymeric g l a s s e s . For i n s t a n c e , Goodman's (18) model r e l a t i n g GFA t o a tendency t o polymorphism i n t h e corresponding c r y s t a l l i n e phases, developed f o r oxide systems, h a s n o t been applied t o m e t a l l i c systems. Occasionally, a paper i s

published which a t t e m p t s t o i d e n t i f y u n i f y i n g f e a t u r e s of t h e g l a s s t r a n s f o r m a t i o n (19) or of r e l a x a t i o n mechanisms ( 2 0 ) , b u t such a t t e m p t s have n o t extended t o a n a l y s e s of which f a c t o r s predispose t o g l a s s formation i n t h e f i r s t p l a c e .

I n connection with M a s s a l s k i ' s a t t e m p t s t o r e l a t e GFA t o t h e form of t h e phase diagram, it i s t o be noted t h a t one i s n o t r e s t r i c t e d t o u l t r a f a s t quenching from t h e melt. I n f a v o u r a b l e c a s e s (up t o now, t h i s h a s meant low-melting systems) g l a s s e s can a l s o be made by s l o w c o o l i n g f i n e l y d i s p e r s e d microdrops of molten a l l o y , r e l y i n g on t h e Turnbull-Cech p r i n c i p l e of preventing heterogeneous n u c l e a t i o n by compartmentalising t h e l i q u i d . When t h i s i s done, t h e thermal c h a r a c t e r i d t c s of t h e a l l o y ( g l a s s t r a n s i t i o n t e m p e r a t u r e s ,

t e m p e r a t u r e s of c r y s t a l l i s a t i o n on r e h e a t i n g ) can be measured d u r i n g slow t e m p e r a t u r e change. T h i s t y p e of experiment h a s been most

c l e a r l y presented with r e g a r d t o Te-Cu a l l o y s ( 2 1 ) : i f ways could be found of extending t h i s technique t o higher-melting a l l o y s

( e . g : by use of a molten-salt d i s p e r s i n g medium), t h e t e c h n i q u e could be wldely a p p l i e d t o GFA s t u d i e s .

2 . S t r u c t u r e and Short-Ranqe Order.

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I n what h a s been s a i d above concerning short-range o r d e r and t h e concept of l o c a l a s s o c i a t i o n s it emerged t h a t t h e r e i s a measure of disagreement whether t h e s t r u c t u r e of a m e t a l l i c g l a s s s u b j e c t t o SRO is t o be regarded i n homogeneous o r heterogeneous terms. T h i s dichotomy has of l a t e become

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i n c r e a s i n g l y pronounced, e s p e c i a l l y i n view of t h e s t r u c t u r a l h e t e r o - g e n e i t y e v i d e n t i n h i g h - r e s o l u t i o n e l e c t r o n microscopy of both oxide and m e t a l l i c g l a s s e s ( 2 2 , 2 3 ) ; t h e r e i s evidence f o r t h e e x i s t e n c e of r e g i o n s of h i g h e r s t r u c t u r a l o r d e r s e p a r a t e d by r e g i o n s of l e s s o r d e r . Since we s h a l l be r e t u r n i n g below t o a c o n s i d e r a t i o n of t h e r o l e of SRO i n r e l a x a t i o n , i t i s worth p o i n t i n g out h e r e t h a t t h e homogeneous/

heterogeneous d i s p u t e h a s a l s o been r i f e i n t h e a n a l y s i s of (chemical) SRO i n c r y s t a l l i n e s o l i d s o l u t i o n s : it appears t o be a p a r t i c u l a r l y d i f f i c u l t problem t o r e s o l v e . I t i s worth devoting a few l i n e s t o t h i s d i s p u t e , s i n c e i t c a r r i e s l e s s o n s f o r t h e s t u d e n t of g l a s s e s .

A long-range ordered c r y s t a l l i n e s o l i d s o l u t i o n such a s Cu3Au i s never q u i t e p e r f e c t l y ordered; t h e ~ r a g g - ~ i l l i a m s o r d e r parameter, S , i s always somewhat l e s s t h a n u n i t y . There h a s been d i s p u t e over whether t h e "wrong" atoms a r e randomly d i s p e r s e d (homogeneous) o r c l u s t e r e d i n minute groups ( h e t e r o g e n e o u s ) . A s t h e mean a n t i p h a s e domain s i z e becomes s m a l l e r , t h e r e i s a continuous t r a n s i t i o n from long-range t o short-range o r d e r , and t h e d i s p u t e i n due c o u r s e becomes one about t h e n a t u r e of short-range o r d e r . I n t h e l i t e r a t u r e of t h i s t o p i c , two k i n d s of h e t e r o g e n e i t y a r e d i s c u s s e d : compositional h e t e r o - g e n e i t y ( o f t e n r e f e r r e d t o a s " c l u s t e r i n g " ) , and v a r a i a t i o n s from p o i n t t o p o i n t of t h e s t a t i s t i c a l e x t e n t t o which A atoms have B atoms a s t h e i r n e a r e s t neighbours ( t h e c l a s s i c a l meaning of "SRO"). The mean " s t a t i c " ( a s opposed t o t h e r m a l ) displacement of atoms from t h e i r l a t t i c e s i t e s i s a f u r t h e r v a r i a b l e ; t h i s reduces a s SRO s t r e n g t h e n s . The two forms of h e t e r o g e n e i t y seem t o be c l o s e l y l i n k e d . The e x p e r i - mental d i f f r a c - c i o n methods, which have become very s o p h i s t i c a t e d , a r e d i s c u s s e d by Chen e t a l . ( 2 4 ) and by Georgopoulos and Cohen ( 2 5 ) ; c l u s t e r i n g e f f e c t s a r e d i s c u s s e d by de Fontaine ( 2 6 ) . The most t h o - roughly s t u d i e d s p e c i a l c a s e i s t h a t of t h e copper-rich Cu

-

A 1 a l l o y s : c a l o r i m e t r i c ( 2 7 ) , d i f f r a c t i o n (28

-

3 1 ) , micrographic (31a) and

r e s i s t o m e t r i c (32, 33) s t u d i e s have g r a d u a l l y produced a u n i f i e d p i c t u r e . Some t h i r t y very v a r i e g a t e d p u b l i c a t i o n s on SRO i n Cu

-

A 1 a l l o y s and t h e main c o n c l u s i o n s from them have r e c e n t l y been

reviewed (33 )

.

The degree of SRO ( i n Cu

-

13 t o 16 a t . % A l ) i s a f u n c t i o n s of temperature: i n e q u i l i b r i u m , SRO i n c r e a s e s a s t h e temperature f a l l s . But e q u i l i b r i u m i s e s t a b l i s h e d very slowly a t t h e lower t e m p e r a t u r e s . I f a l l o y samples a r e quenched from d i f f e r e n t temperatures T t h e degree of SRO i s h i g h f o r Tq = 500

-

9000C. low f o r Tq = 5 5 8 6 ~ o r below. I f however t h e a l l o y i s quenched from a h i g h Tq (6500C) and t h e n held a t a temperature i n t h e range 150

-

3000C, h i g h d e g r e e s of SRO a r e r a p i d l y a t t a i n e d (29, 3 2 ) . T h i s behaviour i s k i n e t i c a l l y determined: only i f t h e a l l o y i s quenched from a h i g h Tq s o t h a t a high vacancy c o n c e n t r a t i o n i s quenched i n can t h e a l l o y t h e n order r a p i d l y and approach e q u i l i b r i u m a t low t e m p e r a t u r e s .

-

The s h o r t - range o r d e r i s s p a t i a l l y heterogeneous. TEM (31a) shows t h a t i s l a n d s of a p p r e c i a l b l e SRO a r e surrounded by r e g i o n s without i t ; a l l t h e evidence s u g g e s t s t h a t the'more ordered r e g i o n s a r e of somewhat d i f f e r e n t composition, and t h e e a r l y c a l o r i m e t r i c d a t a (27) suggest t h a t t h e s e r e g i o n s a r e t r y i n g t o achieve t h e s t a t u s of a l o c a l i s e d Cu3A1 s u p e r l a t t i c e .

The p o i n t of t h i s l i t t l e h i s t o r i c a l excursion i n t o t h e n a t u r e of c r y s t a l l i n e SRO i s t h a t t h e r e a r e l e s s o n s t o be l e a r n e d f o r a p p l i - a t i o n t o m e t a l l i c g l a s s e s . A s we have s e e n , t h e r o l e of SRO i n m e l t s on glass-forming a b i l i t y i s now c l e a r , and a s we s h a l l s e e , i t s r o l e i n g l a s s e s i n determining t h e i r r e l a x a t i o n behaviour i s e q u a l l y c l e a r . However, up t o now t h e study of chemical SRO i n m e t a l l i c g l a s s e s by d i f f r a c t i o n h a s r e p e a t e d an e r r o r made by t h e p h y s i c i s t s , such a s Warren and Averbach, who undertook t h e study of SRO i n c r y s t a l l i n e a l l o y s d u r i n g t h e perlod 1950

-

65: wlth t h e s o l e exception of a few of t h o s e who s t u d i e d Cu

-

A 1 a l l o y s (29, 31, 3 2 ) , a11 o t h e r s

t r e a t e d SRO a s a f u n c t i o n of a l l o y composition but n o t of temperature.

The same h a s been t r u e of most of t h e d i r e c t measurement of SRO i n

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C9-60 JOURNAL DE PHYSIQUE

m e t a l l i c g l a s s e s , such a s t h o s e published i n t h e Proceedings of t h e 1981 Sendai Conference. Sakata e t a l . ( 8 ) , working with Cu

-

T i g l a s s e s have however begun t o study t h e e f f e c t of annealing temperature and have a l r e a d y e s t a b l i s h e d t h a t SRO is g r e a t e r i n a g l a s s t h a n i n t h e melt from which i t i s made ( i . e . , SRO i s g r e a t e r a t T t h a n a t a temperature w e l l above T ) and c o n s i d e r a b l y g r e a t e r

i8

t h e g l a s s a t 700K t h a n a t 1173 K . ~ c o g t (34) h a s j u s t published an important i n d i r e c t s t u d y of t h e v a r i a t i o n of SRO w i t h annealing temperature: he used i s o t h e r m a l c a l o r i m e t r y t o show very c l e a r l y t h a t SRO i n t h e g l a s s Fe,oNi4eB,o v a r i e s r e v e r s i b l y a s t h e temperature i s c y c l e d . S i n c e t h e boron a oms a r e known t o avoid each o t h e r always, t h e SRO i n q u e s t i o n mainly a f f e c t s t h e r e l a t i v e p o s i t i o n s of t h e Fe and N i atoms. This kind of i n v e s t i g a t i o n now u r g e n t l y needs t o be done i n a s y s t e m a t i c way f o r a number of two-metal g l a s s e s such a s Cu

-

T i , N i

-

T i , N i

-

Nb which a r e s p e c i a l l y s u b j e c t t o SRO (Cowlam, p r i v a t e communication).

P r e f e r a b l y , c a l o r i m e t r i c and d i f f r a c t i o n s t u d i e s should be combined t o f i n d how SRO v a r i e s r e v e r s i b l y with annealing temperature and how changes i n SRO a f f e c t s p e c i f i c h e a t . (The d i f f r a c t i o n measurements could be expressed i n terms of an improved SRO parameter, a s proposed by C a r g i l l and Spaepen ( 3 5 ) ) . T h i s kind of knowledge could t h e n be p r o p e r l y c o r r e l a t e d w i t h r e v e r s i b l e r e l a x a t i o n behaviour ( s e e below).

R e c e n t experiments and t h e o r i e s by Radelaar and h i s c o l l e a g u e s (61, 71) mark an e x c e l l e n t s t a r t i n t h i s d i r e c t i o n .

I n s p i t e of some i n d i c a t i o n s ( 5 1 ) t h e r e has been no d i r e c t e v i - dence a s y e t of t h e kind of k i n e t i c hindrance c i t e d above f o r c r y s t a l - l i n e Cu

-

A 1 a l l o y s , i n t h e s e n s e t h a t a g l a s s quenched from j u s t below Tg might o r d e r f a s t e r a t lower t e m p e r a t u r e s t h a n i f it had been slow- cooled t o t h o s e t e m p e r a t u r e s . Such e f f e c t s may w e l l prove t o e x i s t , s i n c e it i s w e l l e s t a b l i s h e d t h a t f r e e volume, which determines

d i f f u s i o n r a t e s , v a r i e s s u b s t a n t i a l l y w i t h temperature. I n some g l a s s e s d i f f u s i o n r a t e s a r e much slower t h a n i n t h e i r c r y s t a l l i n e c o u n t e r p a r t s ,

s o t h a t e s t a b l i s h m e n t of e q u i l i b r i u m SRO might be v e r y slow. Thus, f o r i n s t a n c e , t h e remarkable f a c t h a s very r e c e n t l y been e s t a b l i s h e d t h a t d i f f u s i o n of gold i n a N i - Nb g l a s s i s 5

-

6 o r d e r s of magnitude slower t h a n i n t h e same m a t e r i a l a f t e r c r y s t a l l i s a t i o n ( J . D . Wiley e t a l . ( 3 6 ) ; Wiley, p r i v a t e communication). T h i s s t r i k i n g o b s e r v a t i o n i s being a p p l i e d t o t h e production of m e t a l l i s e d c o n t a c t s on i n t e g - r a t e d c i r c u i t s , which must be v e r y s t a b l e a g a i n s t i n t e r d i f f u s i o n of metal and semiconductor.

3. Nature of Free Volume, G l a s s T r a n s i t i o n and D i f f u s i o n i n M e t a l l i c G l a s s e s .

-

The experimental s t u d y of d i f f u s i o n i n m e t a l l i c g l a s s e s h a s developed a t g r e a t speed i n t h e p a s t few y e a r s , and t h i s h a s been l i n k e d w i t h i n c r e a s e d s p e c u l a t i o n about t h e n a t u r e of f r e e volume, which i n t u r n i s c l o s e l y r e l a t e d t o t h e g l a s s t r a n s i t i o n . I n t h e space a v a i l a b l e h e r e , t h e r e i s room only f o r a summary of r e c e n t i d e a s .

The most s t r i k i n g development i s t h e p u b l i c a t i o n of Cohen and G r e s t ' s model of t h e g l a s s t r a n s i t i o n (1q37,38). The b a s i c i d e ~ of t h i s t h e o r y , which have been worked out i n c o n s i d e r a b l e q u a n t i t a t i v e

d e t a i l , i n v o l v e t h e e x i s t e n c e of a s p e c i f i e d d i s t r i b u t i o n of s t r u c t u - r a l c e l l s of d i f f e r e n t volumes; m o b i l i t y presupposes a minimum c e l l volume, and c e l l s exceeding t h i s a r e s a i d t o be l i q u i d - l i k e . The g l a s s t r a n s i t i o n i s determined by a s o l u t i o n of t h e p e r c o l a t i o n problem i n a population of l i q u i d - l i k e c e l l s contained i n r i g i s , non-diffusing s o l i d - l i k e c e l l s .

T h i s model i s one which presupposes a c o n t i n u o u s l y v a r i a b l e range of f r e e volume i n t h e l i q u i d / g l a s s s t r u c t u r e ( a c o n t i n u o u s l y d i s t r i b u t e d f r e e volume model, C D F V ) , a s opposed t o a

hole

model i n which f r e e volume e x i s t s i n vacancy-like u n i t s . Cantor and Ramachan- d r a r a o (39) have r e c e n t l y published a n o t h e r form of f r e e volume

(8)

t h e o r y , by applylng c o n f i g u r a t i o n a l e n t r o p y c a l c u l a t i o n s t o t h e problem of t h e r e l a t i v e numbers of d i f f e r e n t k i n d s of Bernal polyhedra i n a Bernal DRP s t r u c t u r e . They analysed f o r t h e f i r s t time how t h e s e r e l a t i v e numbers should vary w i t h temperature (which i m p l i e s changes i n f r e e volume s i n c e d i f f e r e n t k i n d s of polyhedra have d i f f e r e n t

volumes per atom); good accord was achieved between t h e o r y and measured s p e c i f i c h e a t s and o t h e r p h y s i c a l q u a n t i t i e s . This important new model i s a l s o a CDFV v e r s i o n

.

Egami e t a l . ( 4 0 ) have worked out some i m p l i c a t i o n s of another CDFV model, based on t h e i d e a t h a t a m e t a l l i c g l a s s c o n t a i n s r e g i o n s of h y d r o s t a t i c t e n s i o n and o t h e r s which a r e l o c a l l y compressed, s o t h a t t h e aggreggate f r e e volume i n t h e former r e g i o n s can be much g r e a t e r t h a n i s u s u a l l y e s t i m a t e d from t h e macroscopic d e n s i t y . K i r i - t a n i and Hamada ( 4 1 ) have advanced a c l o s e l y r e l a t e d model, incorpo- r a t i n g what t h e y c a l l " L a t e n t vacancies".

Others have proposed h o l e models. Ramachandrarao h i m s e l f , w i t h coworkers ( 4 2 , 42) developed i d e a s f i r s t advanced by polymer p h y s i c i s t s i n t o a s e l f - c o n s i s t e n t f r e e volume model f o r m e t a l l i c g l a s s e s which can e x p l a i n a number of experimental f a c t s such a s t h e v a r i a t i o n of v i s c o s i t y w i t h t e m p e r a t u r e , and a l s o t h e r e l a t i v e s t a b i l i t y of d i f - f e r e n t g l a s s e s ( l i n ~ e d c l o s e l y w i t h t h e energy of formation of a h o l e ) ; t h e s i z e of t h e h o l e can a l s o be e s t i m a t e d from t h i s t h e o r y . Buschow (44) independently produced a s i m i l a r t h e o r y r e l a t i n g thermal s t a b i l i t y t o an e s t i m a t e d h o l e formation energy. ( m e r e i s now s o much a c t i v i t y i n t h i s s e c t o r of t h e o r y t h a t people have r e p e a t e d l y published s i m i l a r models i n ignorance of each o t h e r ) .

The balance of c r e d i b i l i t y between CDFV and h o l e models i s a s y e t u n c e r t a i n ( 4 5 ) . There a r e a l s o beginning t o appear d e t a i l e d s t r u c t - u r a l t h e o r i e s of l i n e d e f e c t s

(a

d i s l o c a t i o n s ) i n m e t a l l i c g l a s s e s

( R i v i e r , 46; Venkataraman, p r i v a t e communication), b u t how and indeed whether t h e y a r e r e l a t e d t o f r e e volume, d i f f u s i o n and Tg i s a s y e t u n c l e a r .

Experimental s t u d i e s of d i f f u s i o n i n m e t a l l i c g l a s s e s have suddenly burgeoned i n t h e p a s t t h r e e y e a r s , a s methods were e s t a b - l i s h e d t o measure t h e v e r y shallow d i f f u s i o n p r o f i l e s ( l e s s t h a n 1

ym),

imposed by t h e need t o avoid any c r y s t a l l i s a t i o n d u r i n g t h e d i f f u s i o n anneal. The e x t e n s i v e work r e c e n t l y published i s surveyed i n d e t a i l i n a forthcoming review ( 4 7 ) . S p e c i a l mention should be made of t h e f i r s t o b s e r v a t i o n ( 4 8 ) of a c o n c e n t r a t i o n dependence of D ( r e l a t i n g t o hydrogen i n a Pd-Cu-Si g l a s s ) , accompanied by a s t r u c t u r a l i n t e r p r e - t a t i o n ( 4 9 ) of t h i s a b s e r v a t i o n , i n terms of a reducing t i g h t n e s s of s o l u t e - s o l v e n t binding a s t h e most f a v o u r a b l e s i t e s a r e occupied f i r s t , s o t h a t D i n c r e a s e s w i t h H c o n c e n t r a t i o n .

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The t h e o r e t i c a l i n t e r p r e - t a t i o n of d i f f u s i o n i n m e t a l l i c g l a s s e s i s i n a h i g h l y u n s a t i s f a c t o r y s t a t e : an i n i t i a l approach e x i s t s f o r i n t e r s t i t i a l - t y p e d i f f u s i o n ( 4 9 , 50) b u t none a t a l l f o r d i f f u s i o n of l a r g e atoms. This comes h i g h on any l i s t of c u r r e n t unresolved i s s u e s . On t h e experimental f r o n t , t h e c h i e f d i s p u t e d i s s u e concerns t h e e f f e c t of thermal r e l a x - a t i o n on d i f f u s i v i t i e s i n m e t a l l i c g l a s s e s : published r e s u l t s up t o now have been c o n t r a d i c t o r y , b u t it may be (47) t h a t t h e c o n t r a d i c t i m s a r e more apparent t h a n r e a l . T h i s d i s p u t e w i l l be f u r t h e r complicated by t h e r e c e n t claim ( 5 1 ) t h a t t h e atomic m o b i l i t y i n a m e t a l l i c g l a s s can be p a r t l y r e v e r s i b l e with temperature! Another t o p i c r e q u i r i n g f u r t h e r experimentation i s t h e d i f f u s i o n of carbon, a small atom, and i t s k i n e t i c r e l a t i o n t o t h e d i f f u s i o n of boron ( l a r g e r ) and hydrogen ( s m a l l e r ) . The only e x t a n t measurement, by an e l e g a n t b u t i n d i r e c t method ( 5 2 ) shows t h a t carbon d i f f u s e s s u b s t a n t i a l l y f a s t e r t h a n boron i n a Fe-B-Si-C g l a s s , b u t slower t h a n hydrogen.

Few s y s t e m a t i c s t u d i e s have been undertaken of t h e r e l a t i v e d i f - f u s i o n r a t e s of a component or impurity atom i n a m e t a l l i c g l a s s and t h e same m a t e r i a l a f t e r it has c r y s t a l l i s e d . The above-mentioned (36)

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C9-62 JOURNAL DE PHYSIQUE

dramatic c o n t r a s t between t h e s e two q u a n t i t i e s i n t h e c a s e of gold d i f f u s i n g i n a Ni-Nb g l a s s

-

i t a h a s been suggested t h a t t h e very f a s t d i f f u s i o n i n t h e c r y s t a l l i s e d a l l o y i s due t o m i g r a t i o n along t h e boundaries of t h e very small g r a i n s

-

s u g g e s t s t h a t a s y s t e m a t i c study of t h i s kind f o r s e v e r a l g l a s s e s should be of p r a c t i c a l a s w e l l a s fundamental i n t e r e s t .

4 . Thermal R e l a x a t i o n of M e t a l l i c G l a s s e s .

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T h i s t o p i c h a s a t t r a c t e d r a p i d l y i n c r e a s i n g a t t e n t i o n i n t h e p a s t few y e a r s , and a s f a c t s accumulate, s o do u n c e r t a i n t i e s about t h e proper s t r u c t u r a l i n t e r - p r e t a t i o n of what h a s been observed. I t i s a p a r t i c u l a r l y i n t r i g u i n g s u b j e c t a t i t s present s t a g e .

Four e x c e l l e n t , very r e c e n t t r e a t m e n t s of thermal r e l a x a t i o n c h a r a c t e r i s t i c s a r e by Greer and Spaepen ( 5 3 ) , S c o t t and ~ u r s u m o v i 8

( 5 4 ) , Balanzat e t a 1 ( 5 5 ) and Chambron and Chamberod ( 5 1 , 5 6 ) . These c o n c e n t r a t e , r e s p e c t i v e l y , on changes i n magnetic Curie temperature, e l a s t i c modulus, e l e c t r i c a l r e s i s t i v i t y and induced magnetic a n i s o - t r o p y . The r e l a x a t i o n of t h e c o e r c i v e f i e l d h a s a l s o been s t u d i e d very r e c e n t l y ( ~ r o n m i i l l e r , p r i v a t e communication; Gibbs and E v e t t s , p r i v a t e communication). The e s s e n t i a l f a c t s a r e t h e s e : A l l p r o p e r t i e s change both i r r e v e r s i b l y and r e v e r s i b l y ; t h e l a t t e r component i s c h a r a c t e r i s e d by v a l u e s of t h e p r o e r t y which a r e s p e c i f i c t o t h e annealing temperature and r e v e r t t o t h e s e v a l u e s - a f t e r a period f o r e q u i l i b r a t i o n

-

whatever t h e preceding annealing temperature. I r r e v e r - s i b l e changes a r e much slower a t a given temperature t h a n t h e c o r r e s - ponding r e v e r s i b l e change. The k i n e t i c s of b o t h t y p e s of recovery depend somewhat on t h e previous thermal h i s t o r y , and p a r t i c u l a r l y on t h e temperature from which t h e g l a s s was l a s t quenched. Relaxation k i n e t i c s , g e n e r a l l y s o i n t h e c a s e of i r r e v e r s i b l e and sometimes i n t h e c a s e of r e v e r s i b l e r e l a x a t i o n , follow a l o g t law.

For t h o s e p r o p e r t i e s and annealing t i m e s which l e a d t o predom- i n a n t l y r e v e r s i b l e changes, p l o t s of p r o p e r t y change from t h e i n i t i a l s t a t e i n t h e as-prepared g l a s s show s t a n d a r d c h a r a c t e r i s t i c s . Thus, i f ATc (where T i s t h e magnetic Curie t e m p e r a t u r e ) i s p l o t t e d a g a i n s t annealing temseratrure, T,, f o r c o n s t a n t annealing t i m e , t h e n A Tc v s T a always shows a maximum f o r a p a r t i c u l a r v a l u e of Ta. Recent s t u d i e s by Mizoguchi e t a l . ( 5 7 ) have shown c l e a r l y t h a t t h i s peak i s reduced t o lower temperatures f o r longer i s o c h r o n a l a n n e a l i n g p e r i o d s . S i m i l a r peaks have been e s t a b l i s h e d f o r r e s i s t i v i t y ( 5 5 ) and u n i a x i a l aniso- f r o p y ( 5 6 ) . I t i s c l e a r t h a t , above t h e peak, t h e p r o p e r t y i s a l r e a d y I n e q u l l l b r i u m a t t h e a n n e a l i n g temperature a f t e r an anneal f o r t h e s t a n d a r d i s e d t i m e . Whereas i n e q u i l i b r i u m t h e p r o p e r t y would c o n t i n u e t o r i s e with d e c r e a s i n g t e m p e r a t u r e , i n f a c t it cannot do s o below t h e peak because t h e r e i s n o t enough time a t t h e s e lower temperatures t o a t t a i n e q u i l i b r i u m .

A p a r t i c u l a r l y i n t e r e s t i n g q u e s t i o n which has n o t p r e v i o u s l y been considered i n g e n e r a l terms i s t h e r a t i o between t h e magnitudes of r e v e r s i b l e and i r r e v e r s i b l e changes ( l e t u s c a l l it t h e R / i r a t i o ) . T h i s r a t i o of c o u r s e depends on t h e property i n q u e s t i o n , t h e tempe- r a t u r e , t h e annealing time and t h e composition of t h e g l a s s , but t h e d i f f e r e n t p r o p e r t i e s can a t any r a t e be put i n a sequence. So f a r a s t h e a v a i l a b l e evidence g o e s , R/I q u i t e g e n e r a l l y d e c r e a s e s i n t h e following o r d e r : Curie t e m p e r a t u r e , e l a s t i c modulus (both q u i t e s i m i l a r ) ; u n i a x i a l magnetic a n i s o t r o p y ; c o e r c i v e f i e l d ; e l e c t r i c a l r e s i s t i v i t y ; change i n l e n g t h ( o r d e n s i t y ) . With t h e f i r s t two, t h e i r r e v e r s i b l e com-oonent i s o f t e n q u i t e s l i g h t , and f o r t h e Curie tempe- r a t u r e h a s only r e c e n t l y been observed ( 5 8 ) .

Egami ( 5 9 ) was t h e f i r s t t o propose a d i s t i n c t i o n between

topological ( T S R O ) and chemical ( C S R O ) short-range order: t h e former

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r e f e r s t o geometrical packing, and i s s a i d t o i n c r e a s e when packing becomes d e n s e r , while t h e second h a s i t s u s u a l meaning, f a m i l i a r a s we have seen from c r y s t a l l i n e a l l o y s , and r e f e r s only t o t h e probabi- l i t y of f i n d i n g chemically u n l i k e n e a r e s t n e i g h b i u r s ( r e l a t i v e t o t h e p r o b a b i l i t y f o r a random arrangement of atomic s p e c i e s ) . Egami proposed t h a t r e v e r s i b l e changes, which a r e r a p i d , i n v o l v e only changes i n CSRO, and such chgges involve movements of atoms only over d i s t a n - c e s of t h e o r d e r of i n t e r a t o m i c s e p a r a t i o n s ; whereas i r r e v e r s i b l e changes of p r o e r t i e s i n v o l v e changes of TSRO and concomitant changes of d e n s i t y , and such changes i n v o l v e long-range d i f f u s i o n of atoms.

Egami h a s gone some way towards confirming h i s i d e a s (which remain extremely c o n t r o v e r s i a l ) by h i s r e c e n t very e x a c t experiments on changes i n x-ray d i f f r a c t i o n p a t t e r n s of g l a s s e s on i r r e v e r s i b l e r e l a x a t i o n ( 6 0 ) , b u t it i s t r u e t h a t n e i t h e r he nor anyone e l s e h a s demonstrated r e v e r s i b l e changes i n x-ray d i f f r a c t i o n p a t t e r n s , though Radelaar and h i s c o l l a b o r a t o r s (61) a r e making p r o g r e s s towards t h i s important o b j e c t i v e . I t i s agreed by many t h a t changes i n TSRO neces- s a r i l y i n v o l v e some changes i n CSRO, and v i c e v e r s a . Yet t h e d i s t i n c - t i o n i s c o n c e p t u a l l y c l e a r and o p e r a t i o n a l l y u s e f u l , and it i s i n p r i n c i p l e p o s s i b l e t o d i s t i n g u i s h between them by combining d i f f r a c - t i o n and d e n s i t y measurements. T h i s i s t h e main reason why I r e g a r d measurements of changes, b o t h i r r e v e r s i b l e and r e v e r s i b l e , i n d e n s i t y

( o r l e n g t h ) a s being p a r t i c u l a r l y v a l u a b l e i n a f f o r d i n g i n s i g h t i n t o changes i n o r d e r d u r i n g r e l a x a t i o n ; it i s a p i t y t h a t t h i s kind of measurement h a s been s o n e g l e c t e d h i t h e r t o .

I t appears t o be widely agreed among magneticians t h a t t h e magnetic Curie temperature i s e s p e c i a l l y s e n s i t i v e t o n e a r e s t neighbour i d e n t i t y (and t o a l e s s e r e x t e n t , n e a r e s t neighbour

s e p a r a t i o n ) , and t h i s would account f o r t h e high R / I r a t i o f o r t h i s p r o p e r t y . E l a s t i c modulus i s known t o be s e n s i t i v e t o chemical

(long-range) order i n c r y s t a l l i n e a l l o y s ( 6 2 ) and it i s t h u s n o t s u r p r i z i n g t h a t t h e same

4 s

t r u e f o r m e t a l l i c g l a s s e s . However, t h e m a t t e r h a s n o t been examined t h e o r e t i c a l l y . Induced u n i a x i a l magnetic a n i s o t r o p y i s known (from ~ 6 e l ' s d e c i s i v e experiments many y e a r s ago on c r y s t a l l i n e s o l i d s o l u t i o n s ) t o be d i r e c t l y due t o an a n i s o t r o p i c arrangement of t h e frequency of A - B atom p a i r s p a r a l l e l and normal t o t h e d i r e c t i o n of t h e magnetic i n d u c t i o n v e c t o r a p p l i e d d u r i n g t h e anneal. The f a c t t h a t t h i s p r o p e r t y does n o t behave i n a who11 r e v e r s i b l e manner ( a s t h e i n d u c t i o n v e c t o r i s r o t a t e d b e t w e e n k s - s i v e a n n e a l s ) i m p l i e s t h a t i r r e v e r s i b l e s t r u c t u r a l changes reduce t h e number of atom p a i r s which a r e a v a i l a b l e f o r f r e e r e o r i e n t a t i o n , but why t h i s should be s o h a s n o t been analysed.

R e s i s t i v i t y i s much more a c o l l e c t i v e p r o p e r t y , e s p e c i a l l y s e n s i t i v e t o e l e c t r o n i c band s t r u c t u r e , and t h e r e f o r e t o i n t e r a t o m i c d i s t a n c e s and TSRO g e n e r a l l y ( t h i s i s q u i t e c l e a r from t h e s u c c e s s of t h e s t a n d a r d Ziman t h e o r y of r e s i s t i v i t y of l i q u i d s and g l a s s e s ) ; t h u s one e x p e c t s i r r e v e r s i b l e changes t o predominate,

found. The French work ( 5 5 ) shows a f a i r l y s u b s t a n t i a l

component i n Fe40NigOP14B6 (and t h e r e v e r s i b l e component i s e s p e c ~ a l l y l a r g e (55) i n Cu5g~, O , which a s we have seen has v e r y s u b s t a n t i a l CSRO), but Kelton an2 Spaepen ( 6 3 ) f i n d only a s a l l r e v e r s i b l e compo- n e n t i n r e s i s t i v i t y changes i n Pd

-

S i g l a s s e s while Cost and S t a n l e y

T

( 6 4 ) f i n d no r e v e r s i b l e component a t a l l i n Fe80B20. T h i s l a s t f a c t i s i n t r i g u i n g , because t h e peak magnitude of r e v e r s i b l e Curie tempe- r a t u r e changes a r e much smaller i n FegOB t h a n i n a g l a s s l i k e Fe N i OP14BZ0 ( 6 5 ) ; only t h e l a t t e r

kina

of g l a s s can have changes i n 4 @ s ~ 8 between metal atoms. I t seems t h e n t h a t changes i n CSRO i n v o l v i n g only metal-metalloid atom p a i r s ( a s opposed t o metal-metal p a i r s ) can produce some, r e v e r s i b l e , changes i n C u r i e temperature (and a l s o i n induced a n i s o t r o p y ) b u t h a s n e g l i g i b l e e f f e c t on e l e c t r i c a l r e s i s t i v i t y , and t h e r e f o r e g l a s s e s l i k e Fe80B20 have no measurable r e v e r s i b l e changes i n r e s i s t i v i t y .

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C9-64 JOURNAL DE PHYSIQUE

Nothing s p e c i f i c h a s been s a i d y e t about d e n s i t y changes

-

o r l e n g t h changes, which a r e e q u i v a l e n t i n an i s o t r o p i c m a t e r i a l . These a r e very d i f f i c u l t t o measure a c c u r a t e l y . With t h e most e l a b o r a t e p r e c a u t i o n s , d e n s i t y of m e t a l l i c g l a s s specimens can only be measured t o about 0.05% p r e c i s i o n , and t h i s i s only marginally s u f f i c i e n t f o r measurements of i r r e v e r s i b l e changes ( P r a t t e n , S c o t t and Cahn, t o be published) and i n s u f f i c i e n t t o observe r e v e r s i b l e changes. Length changes a r e t h u s a b e t t e r q u a n t i t y t o measure. I r r e v e r s i b l e l e n g t h changes have been measured by ~ u r s u m o v i 6 e t a l . ( 6 6 ) , ~ i e t z and

filler ( 6 7 ) and r e c e n t l y by S i n n i n g , Cizeron and Cahn ( t o be published).

The l a s t two groups used p r e c i s i o n i s o t h e r m a l d i l a t o m e t r y , a technique f u l l of p i t f a l l s . S i n n i n g , Cizeron and Cahn have t e n t a t i v e observa- t i o n s of what appear t o be small r e v e r s i b l e components of l e n g t h change i n Fe40Ni40B20 g l a s s , but t h i s component i s l e s s t h a n 0.01 % and t h e R / I r a t i o i s small. E f f o r t s a r e under way t o confirm t h e s e preliminary r e s u l t s . Such r e v e r s i b l e changes should indeed be found i f CSRO i s r e s p o n s i b l e , s i n c e h i g h e r CSRO i m p l i e s more e f f i c i e n t packing of atoms and t h e r e f o r e a s l i g h t c o n t r a c t i o n . One p o s s i b i l i t y of confirming a l i n k between changes i n CSRO and l e n g t h changes i n g l a s s e s i s t o u s e i r r a d i a t i o n t o enhance atomic m o b i l i t y s o t h a t e q u i l i b r i u m CSRO can be a t t a i n e d a t low t e m p e r a t u r e s where under normal circumstances it i s never a t t a i n e d ( t h i s h a s r e p e a t e d l y been

s u c c e s s f u l l y done with c r y s t a l l i n e a l l o y s ) ; i n t h a t c a s e , l a r g e changes i n CSRO might l e a d t o r e a d i l y measurable l e n g t h changes.

Some d i l a t o m e t r i c r e s u l t s r e c e n t l y obtained by Cahn e t a l . ( 6 8 ) have been i n t e r p r e t e d a s due t o an i n c r e a s e i n CSRO, b u t t o c a r r y convic- t i o n t h e y need t o complemented by d i f f r a c t i o n s t u d i e s , which a r e n o t easy when a m a t e r i a l i s h i g h l y r a d i o a c t i v e !

-

D i f f i c u l t though t h e problem i s i n experimental t e r m s , r e v e r s i b l e l e n g t h changes should be sought i n a number of d i f f e r e n t g l a s s e s .

The k i n e t i c s of r e l a x a t i o n , both r e v e r s i b l e and i r r e v e r s i b l e , have been i n c r e a s i n g l y s t u d i e d . G e n e r a l l y , i r r e v e r s i b l e d e n s i f i c a t i o n l e a d s t o a slowing down of subsequent changes ( t h i s i n c l u d e s superimposed r e v e r s i b l e changes a l s o ( 5 5 ) ) , b u t t h e o b s e r v a t i o n s of Chambron and Chamberod (51) t h a t k i n e t i c s can change r e v e r s i b l y a s a g l a s s i s quenched s u c c e s s i v e l y from d i f f e r e n t h i g h temperatures and a f t e r each quench, annealed a t a f i x e d lower temperature, h a s c r e a t e d a new mystery, because it i m p l i e s t h a t k i n e t i c s themselves a r e t o some e x t e n t r e v e r s i b l e . This mystery i s f u r t h e r compounded by some i n t r i g u i n g measurements due t o H i l z i n g e r and Warlimont ( 6 9 ) , of k i n e t i c s of r e l a x a t i o n of m a g n e t o s t r i c i t o n and induced a n i sotropy

,

which i n d i c a t e t h e e x i s t e n c e of two q u i t e d i s t i n c t k i n d s of k i n e t i c s , according t o t h e quenching and a n n e a l i n g t e m p e r a t u r e s used.

Superimposed on t h e s e new experimental c o m p l i c a t i o n s concerning r e l a x a t i o n k i n e t i c s i s a c o n f l i c t of opinion on t h e q u e s t i o n whether r e l a x a t i o n , r e v e r s i b l e o r i r r e v e r s i b l e , i s governed by one, two o r a whole spectrum of a c t i v a t i o n e n e r g i e s . Gibbs e t a 1 ( 7 0 ) marshal an impressive range of evidence i n favour of t h e e x i s t e n c e of a spectrum of a c t i v a t i o n e n e r g i e s , whereas van den Beukel and Radelaar (71) marshal e q u a l l y impressive evidence from t h e i r q u a n t i t a t i v e k i n e t i c a n a l y s i s 3f m i c r o c a l o r i m e t r i c measurements of r e l a x a t i o n ( i n t h i s c o n n e c t i o n , s e e a l s o t h e r e c e n t work of Duddek e t alfz)on m i c r o c a l o r i - metry of r e l a x a t i o n ) , t h a t a reasonably good though n o t p e r f e c t accord w i t h observed r e l a x a t i o n k i n e t i c s of both kinds can be obtained by assuming only a s i n g l e a c t i v a t i o n energy. B a t t l e must now be joined between t h e s e two i r r e c o n c i l a b l e approaches.

There i s one t y p e of experiment which makes it unambiguously c l e a r t h a t a t l e a s t two r e l a x a t i o n t i m e s must govern r e v e r s i b l e k i n e t i c s , which i m p l i e s a t l e a s t two d i f f e r e n t a c t i v a t i o n e n e r g i e s

and two p h y s i c a l l y d i s t i n c t c o n t r i b u t o r y p r o c e s s e s . T h i s i s t h e c r o s s o v e r

experiment,

which h a s now been done f o r Curie temperature ( 7 3 ) and e l a s t i c modulus ( 5 4 ) i n m e t a l l i c g l a s s e s and a l s o f o r

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r e f r a c t i v e i n d e x i n an o x i d e g l a s s ( 7 4 ) . For d e t a i l s , t h e r e a d e r must r e f e r t o t h e o r i g i n a l papers: i n o u t l i n e , t h e sample i s annealed a t a t e m p e r a t u r e T1 till r e v e r s i b l e e q u i l i b r i u m i s r e a c h e d , t h e n a t T3 f o r a t i m e t * when t h e p r o p e r t y , n o t y e t i n e q u i l i b r i u m a t T3, h a s reached a l e v e l L known t o be c h a r a c t e r i s t i c of e q u i l i b r i u m a t an i n t e r m e d i a t e t e m p e r a t u r e T2 ( T I > T 2 > T 3 ) ; from t h i s moment t h e sample is h e l d a t T2. I t h a s been found I n a l l t h e e x p e r i m e n t s t h a t t h e p r o p e r t y goes t h r o u g h f u r t h e r changes b e f o r e r e t u r n i n g t o and remaining a t t h e v a l u e L . I f t h e r e were o n l y a s i n g l e r e l a x a t i o n t i m e , t h i s would b e i m p o s s i b l e , an2 t h e sample, when brought t o t e m p e r a t u r e T

,

would n o t change f u r t h e r ; t h e r e must t h e r e f o r e be e i t h e r two r e l a x a t i o n t i m e s , o r a spectrum.

I n c o n c l u s i o n , t h e c r o s s o v e r experiment t a k e s u s back t o S e c t i o n 2 and SRO i n c r y s t a l l i n e a l l o y s . W e have s e e n t h a t CSRO i s prime c a n d i d a t e f o r t h e c e n t r a l p r o c e s s i n r e v e r s i b l e r e l a c a t i o n i n m e t a l l i c g l a s s e s , and t h a t r e l a t e d p r o p e r t y c h a n g e s , a s a f u n c t i o n of r e l a x a t i o n t e m p e r a t u r e , r e a c h a peak v a l u e (below which e q u i l i b r i u m cannot be a t t a i n e d i n t h e a v a i l a b l e t i m e ) , his i s j u s t what i s found i n c r y s t a l - l i n e a l l o y s a l s o ( e . g . 3 2 ) . T r i e b and V e i t h ( 7 5 ) h a v e done a c r o s s o v e r experiment on c r y s t a l l i n e 16 a t . % Cu

-

A 1 a l l o y , u s i n g v e r y p r e c i s e r e s i s t i v i t y e x p e r i m e n t s . They found r e s u l t s s i m i l a r t o t h o s e o b t a i n e d on g l a s s e s , and t h e y p o s t u l a t e d t h a t t h e two r e l a x a t i o n t i m e s w e r e a s s o c i a t e d w i t h a change i n CSRO and a m i c r o s e g r e g a t i o n p r o c e s s . T h i s i n t e r p r e t a t i o n (which i s h o t l y c o n t e s t e d ! ) i s v e r y s i m i l a r t o t h a t advanced by Sommer e t a l . (4-7) f o r g l a s s e s

-

h i s w a s s o c i a t i o n " model.

I t may w e l l prove t h a t t h i s model, implying b o t h s e g r e g a t i o n and changis i n CSRO, w i l l s e r v e t o i n t e r p r e t some of t h e anomalies i n r e v e r s i b l e r e l a x a t i o n behaviour i n m e t a l l i c g l a s s e s . I n any c a s e , it i s i m p o r t a n t t h a t s t u d e n t s of m e t a l l i c g l a s s e s l e a r n from t h e e x p e r i e n c e of c r y s t a l - l o g r a p h e r s 20 y e a r s ago, and make proper s t u d i e s of CSRO i n m e t a l l i c g l a s s e s a s f u n c t i o n b o t h of a n n e a l i n g t e m p e r a t u r e and of c o m p o s i t i o n , Without t h i s , t h e u n d e r s t a n d i n g of r e l a x a t i o n , which i s of b o t h funda- m e n t a l and p r a c t i c a l c o n c e r n , w i l l h a r d l y make much p r o g r e s s .

R e f e r e n c e s

1 . MASUMOTO T.

,

Proc. 4 t h I n t . Conf. on R a p i d l y Quenched M e t a l s , 1981 (Japan I n s t . of M e t a l s , S e n d a i , 1 9 8 2 ) , Vol. 1 , p. 5.

2. GICSSEN B

.

^C

. ^,

a s Ref. 1

,

Vol

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