POSITIONAL (DIS)ORDER AND COMPOSITIONAL (NON-)HOMOGENEITY IN METALLIC GLASSES

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POSITIONAL (DIS)ORDER AND COMPOSITIONAL

(NON-)HOMOGENEITY IN METALLIC GLASSES

Jessica Dubois

To cite this version:

JOURNAL DE PHYSIQUE

Colloque C8, suppl6ment a u n012, Tome 46, d6cembt-e 1985 page C8-335

POS

I T I O N A L

(DI

S)ORDER A N D

C O M P O S I T I O N A L

(NON-1

H O M O G E N E I

TY

I N M E T A L L I C

GLASSES

J . M . Dubois

Laboratoire de Me'taZZurgie, U.A. 159, Pare de Saurupt, 54042 Nancy Ceder, France

RQsumQ

-

Dans l e s modkles de s t r u c t u r e des v e r r e s m 6 t a l l i q u e s q u i r e p o s e n t s u r un empilement c o r r Q l 6 d l u n i t Q s s t r u c t u r a l e s , il e s t assez f a c i l e d ' e x p l o r e r l e s l i e n s q u i e x i s t e n t e n t r e l ' o r d r e de p o s i t i o n e t l a c o n c e n t r a t i o n . Cet a r t i c l e s 1 i n t 6 r e s s e B ce probleme e t a t t i r e l ' a t t e n t i o n s u r d l Q v e n t u e l l e s sources de d Q s o r d r e q u i p r o v i e n d r a i e n t ou e n t r a i n e r a i e n t des f l u c t u a t i o n s de c o n c e n t r a t i o n l o c a l e . On examine b r i e v e m e n t l e u r r e l a t i o n avec l a f o r m a t i o n e t l a s t a b i l i t 6 des v e r r e s . A b s t r a c t

-

I n models f o r t h e s t r u c t u r e o f m e t a l l i c g l a s s e s based on a c o r r e l a t e d p a c k i n g o f s t r u c t u r a l u n i t s , i t i s r e l a t i v e l y easy t o e x p l o r e t h e c o u p l i n g between p o s i t i o n a l o r d e r and c o m p o s i t i o n . T h i s paper d e a l s w i t h t h i s problem and focuses on some ( p o s s i b l e ) sources o f d i s o r d e r a r i s i n g f r o m o r i n v o l v i n g l o c a l c o n c e n t r a t i o n f l u c t u a t i o n s . T h e i r r e l e v a n c e t o g l a s s f o r m a t i o n and s t a b i l i t y i s b r i e f l y examined.

I

-

INTRODUCTION

The n o t i o n t h a t p o s i t i o n a l o r d e r - t h e s p a t i a l ( s t a t i c ) d i s t r i b u t i o n o f t h e c e n t r e s o f g r a v i t y o f t h e p a r t i c l e s - and chemical o r d e r - t h e occupancy d i s t r i b u t i o n o f t h e s e p o i n t s b y t h e d i f f e r e n t s p e c i e s - a r e u s u a l l y n o t independent q u a n t i t i e s i n amorphous a l l o y s can be r a i s e d e x p e r i m e n t a l l y b y i n s p e c t i o n o f BHATIA-THORNTON

111 p a r t i a l p a i r f u n c t i o n s . An e q u i v a l e n t p o i n t o f v i e w can o f c o u r s e be g i v e n b y t h e same f u n c t i o n s c a l c u l a t e d f o r a l i s t o f a t o m i c c o o r d i n a t e s i n a s t r u c t u r a l model b u t d e t a i l e d knowledge a b o u t t h e c o u p l i n g between p o s i t i o n a l and chemical o r d e r s i s i n h e r e n t l y much more d i f f i c u l t t o a c h i e v e w i t h o u t any a p r i o r i i n f o r m a t i o n on t h e p a c k i n g a l g o r i t h m o f t h e model.

I n dense random p a c k i n g models o f i n d i v i d u a l atoms, no such a b - i n i t i o i n f o r m a t i o n i s a v a i l a b l e b u t may be c o n t a i n e d i n t h e f i n a l l i s t o f c o o r d i n a t e s as a r e s u l t o f t h e subsequent energy m i n i m i z a t i o n p r o c e d u r e under s u i t a b l e i n t e r a t o m i c p o t e n t i a l s . A t c o n t r a s t , t h i s c o u p l i n g i s an i n - b u i l t i n g r e d i e n t o f n o n - c r y s t a l l o g r a p h i c c u r v e d space models o r o f models based on t h e l o c a l s t r u c t u r e o f c r y s t a l l i n e compounds. I n n o n - c r y s t a l l o g r a p h i c " v i t r o n s " , l i k e t h o s e p r e s e n t e d b y GASKELL i n a r e c e n t paper 121, a c o u p l i n g between a t o m i c p o s i t i o n s and l o c a l c o n c e n t r a t i o n i s induced v i a t h e l i n k a g e o f s t r u c t u r a l u n i t s b y r e g u l a r p o l y h e d r a and imposes t h e c u r v a t u r e o f t h e e l l i p t i c space. I n models w i t h i c o s a h e d r a l s h o r t range o r d e r , a s i m i l a r c o u p l i n g s h o u l d a l s o be c o n s i d e r e d i f e.g. t h e i n t e r a c t i o n between u n l i k e s p e c i e s i s l a r g e and l e a d s t o a s t r o n g chemical o r d e r , i . e . t o t h e e x i s t e n c e o f i d e n t i f i a b l e c e l l s o f one element s u r r o u n d i n g a n o t h e r (as i n Frank-Kasper phases).

I 1

-

STRUCTURAL UNIT AND POSITIONAL (D1S)ORDER

The r e l a t i o n s h i p between g e o m e t r i c a l and chemical d i s o r d e r s i s e a s i e r t o assess i f any s u i t a b l e s t u c t u r a l u n i t may be d e f i n e d around one o f t h e species. I n a l a r g e number o f t r a n s i t i o n m e t a l - m e t a l l o i d c r y s t a l l i n e compounds ( b u t a l s o i n

C8-336 JOURNAL

DE

PHYSIQUE

many r a r e e a r t h - t r a n s i t i o n metal o r e a r l y - l a t e t r a n s i t i o n metal c r y s t a l s ) , such

a u n i t i s r e a d i l y i d e n t i f i a b l e . I t i s a t r i a n g u l a r prism of s i x l a r g e atoms

M

(e:g. t r a n s i t i o n metal atoms) centred by a small atom

X

(e.g. a m e t a l l o i d ) . This

u n i t

i s common t o a wealth of d i f f e r e n t compounds with compositions ranging from

MGX

( o r even poorer i n

X

s p e c i e s ) t o MX2 and what d i f f e r e n t i a t e s t h e d i v e r s e s t r u c -

t u r a l types i s t h e way t h e u n i t s a r e interconnected o r , i n o t h e r words, t h e under-

lying s t r u c t u r a l operation which couples p o s i t i o n and l o c a l concentration.

I t t u r n s out t h a t i n m e t a l l i c g l a s s e s of s i m i l a r n a t u r e ,

some convincing

experimental evidence t h a t t h i s type of l o c a l u n i t e x i s t s i s now a v a i l a b l e 131.

Furthermore, some r e s u l t s i n d i c a t e t h a t s t r u c t u r a l organization may extend up

t o several atomic diameters. There i s , however, no d i r e c t proof t h a t t h e medium

range o r d e r in an amorphous m a t e r i a l

i s

of t h e same n a t u r e (nor i s i n t r i n s i c a l l y

d i f f e r e n t ) than i n i t s c r y s t a l l i n e c o u n t e r p a r t on t h e one hand and i s compatible

o r not with t r a n s l a t i o n a l symetry on t h e o t h e r hand. The claim 141 t h a t t h e atomic

c o o r d i n a t e s

i n

an amorphous s t r u c t u r e model may be accounted f o r by a s e t of r u l e s

defined with r e s p e c t (but not n e c e s s a r i l y i d e n t i c a l ) t o t h e r u l e s which apply

i n t h e c r y s t a l l i n e s t a t e

i s

t h u s supported by nothing e l s e but t h e assumption

of t h e e x i s t e n c e of l o c a l arrangements a b l e t o break t h e t r a n s l a t i o n a l symetry

of t h e c r y s t a l while being compatible with t h e global homogeneity of t h e s t r u c t u r e

imposed by t h e i n t e r a t o m i c p o t e n t i a l s .

The very important point here i s t h a t t h e number of d i f f e r e n t connections which

a

-

f u l f i l t h e above space f i l l i n g requirements and b

-

account f o r t h e s t o i c h i o -

metry i s i n f a c t small. To i l l u s t r a t e t h i s p o i n t , consider a

M i - ,

Xx network with

f i x e d stoichiometry x

=

0.25 and assume t h a t each

X

atom l i e s i n t h e c e n t r e of

a prism.

As a consequence of t h e mean composition, the

M

atoms belong t o I

=

2

prisms on an average and accordingly, t h e r e a r e several connections between u n i t s

a b l e t o achieve t h i s mean value. However, s u i t a b l e connections a r e . r e s t r i c t e d

t o packing c o n f i g u r a t i o n s which do not involve i

-

highly constrained bonds o r

i i

-

l a r g e empty i n t e r s t i c e s . Adequate s o l u t i o n s can be found by t r i a l and e r r o r

and t h e most adequate - c h a r a c t e r i s t i c of t h e Re3B, Fe3C and Ti3P c r y s t a l types-

a r e depicted i n f i g u r e

1.

Because of t h e composition, each prism v e r t e x

i s

a l s o

a capping atom f o r another prism and t h e r e f o r e , t h e t r i a n g u l a r prisms w i l l f i t

t o g e t h e r with only l i t t l e degrees of freedom i n t h e choice of t h e i r r e s p e c t i v e

arrangements. For t h e c o n f i g u r a t i o n s

C =

-

1

and

C =

+

1

shown i n f i g u r e

1,

t h e

prisms w i l l be found on t o p of each o t h e r . Depending on t h e

r x / r ~ ra t i o or/and

t h e s t r e n g t h of t h e

X-M

i n t e r a c t i o n , they w i l l occur i n Fe3C i s o t y p e s (C

=

+1)

o r

i n

Ti3P i s o t y p e s (C

=

-1) with t h e p o s s i b i l i t y of polymorphism (e.g. Fe3B)

f o r couples of elements i n between.

111

-

AMORPHOUS

STRUCTURE

AND

STRUCTURAL OPERATIONS

Figute

7 :

Edge c o n n e d o n can be uckieved

i n two di66ehent wayh do t h a t /roAation

More s y s t e m a t i c a l l y , each type of connection i s expressed i n terms of

a

s t r u c t u r a l

operation 151 which may be viewed a s a s p e c i f i c one t o one correspondence from

an i d e a l s t r e s s

-

r e l i e v e d c l o s e packed a r r a y (of two o r more components) towards

t h e e u c l i d i a n 3D space. This correspondence involves an a n i s o t r o p y of t h e r e a l

space and i s c h a r a c t e r i z e d by a s e t

o f

a few r u l e s d e s c r i b i n g a l l t h e p o s s i b l e

r e l a t i o n s h i p s from one u n i t t o another which a r e e q u i v a l e n t t o t h e l o c a l configu-

r a t i o n s a c t u a l l y found i n t h e c r y s t a l l i n e s t a t e . (For a t y p i c a l example, see 161).

c z o e=.l c = - 1

mound t k i n edge ~up&pohes

t h e hedehence

As f a r as s h o r t range p a i r p o t e n t i a l s are concerned, t h i s d e f i n e s atomic environments e i t h e r i d e n t i c a l t o ( c r y s t a l l o g r a p h i c ) o r v e r y s i m i l a r (though non- c r y s t a l lo g r a p h i c ) t o t h e c r y s t a l 1 i n e ones. Occurence o f such n o n - c r y s t a l l o g r a p h i c c o n f i g u r a t i o n s i s t h e r e f o r e e n e r g e t i c a l l y t o l e r a b l e and i s a b l e t o change t h e d i r e c t i o n o f a p p l i c a t i o n o f t h e s t r u c t u r a l operation. This breaks t h e c r y s t a l l i n e sequence b u t n o t the o v e r a l l homogeneity o f the m a t e r i a l i n t h e sense t h a t the s t r u c t u r a l o p e r a t i o n s t i l l assigns t h e connections between every two u n i t s .

A model was b u i l t f o r t h e NigoB20 glass according t o the above p r i n c i p l e 161. It i s an example o f an amorphous s t r u c t u r e generated by a s i n g l e s t r u c t u r a l o p e r a t i o n i n t o which d i s o r d e r a r i s e s from d i r e c t i o n changes. They a r e however o t h e r ways t o d i s o r d e r such networks e i t h e r by m i x i n g d i f f e r e n t s t r u c t u r a l o p e r a t i o n s o r by m i x i n g d i f f e r e n t p e r i o d i c i t i e s o f a s t r u c t u r a l operation. I n f a c t , a l o t o f s i m i l a r o r even more s o p h i s t i c a t e d examples i s known i n the c r y s t a l l i n e s t a t e 171 which a r e worth c o n s i d e r i n g t o understand t h e amorphous s t r u c t u r e . Therefore,the purpose o f t h e n e x t s e c t i o n i s j u s t t o i l l u s t r a t e -among a l l o t h e r p o s s i b i l i t i e s - how d i s o r d e r may a r i s e from t h e a p p l i c a t i o n o f i

-

one s i n g l e s t r u c t u r a l operation,

ii

-

a m i x t u r e o f two s t r u c t u r a l o p e r a t i o n s and iii

-

a change i n the p e r i o d i c i t y o f t h e operation.

I V

-

POSITIONAL DISORDER AND COMPOSITIONAL NON-HOMOGENEITY

Figure 2a presents a schematic i l l u s t r a t i o n o f several prisms arranged i n an ( i d e a l y p e r f e c t ) a r r a y generated by a s t r u c t u r a l o p e r a t i o n corresponding t o t h e s t o i c h i o - metry MgoX20. By v i r t u r e o f t h i s operation, such a long range ordered network y ~ e l d s M atoms belonging t o

L

= 2 prisms and t o

L

= 0 prism ( f o r more d e t a i l s , see 161). I t i s p o s s i b l e t o induce d i s o r d e r by stopping t h e c r y s t a l growth a t t h e l e v e l o f t h e shaded t r i a n g u l a r faces and c o n t i n u i n g t h e network w i t h prisms arranged as i n b. These new u n i t s a r e connected t o t h e p r e v i o u s ones according t o a few simple r u l e s c h a r a c t e r i s t i c o f t h e former o p e r a t i o n (as a c t i n g i n a ) and are themselves c o r r e l a t e d by the same s t r u c t u r a l operation. However, some o f t h e atoms which ought t o belong t o

L

= 0 o r

L

= 2 prisms, now belong t o one u n i t . The number o f u n i t s found i n the v i c i n i t y o f a given M atom i s thus n o t (always) r e t a i n e d w i t h respect t o t h e same number d e f i n e d by a s i n g l e d i r e c t i o n o f the s t r u c t u r a l operation.

a

:

phinmb cvlhanged acconding t o a bLucAwLae

o p u d o n od

btoickiom&y

MgoX20.

M o m

tubelled L

= 2

and L

= 0

o u g k t o belong

t o .duo and z m o

unitn,

xebpective&,

i d

cnybtc& gxowth wo~Led have continued.

6

: T k i d

bequence

A

LivLtmupted

by

a change

od

dineotion

06

t h e bRnuotwtcLe o p m d o n .

Note t h d t h e connection b m e e n a q .duo

phinm

h a

not changed i n n a h t e but

tm

home atomh belong now t o one u n i t

( L = l )

.

(3-338 JOURNAL DE PHYSIQUE

f i g u r e 3 ) . There a r e several p o s s i b i l i t i e s t o change t h e propagation d i r e c t i o n of t h e s t r u c t u r a l operation but t h e most obvious i s t o place another s e t of prisms in a p o s i t i o n enanthiomorphous t o t h e former one w i t h u n i t s i n c o n t a c t sharing a r e c t a n g u l a r f a c e a s shown i n t h e upper p a r t of t h e f i g u r e . The c r y s t a l l i n e sequence

i s

broken accordingly but not t h e c h a r a c t e r i s t i c connection between any two u n i t s .

F i g a t 3 :

P d m b (phojected

a,

L?ngLea) m a n g e d accohding t o

SCT

w&h 3 1 3 , IboMom Le6x Cohneh) O h { 3 , .

. .

[bo.ttom

n i g k t

cohnm) p&adiCitieb. RoXaLLon by IJ

06

Rhe diheotion 06 ,the o X ~ . ~ o t w l a e o p e h d o n phaducea t h e uppeh paht

ad

t h e digme (b&ch

c i m ~ e a

m e ~ h i d t e d with neapeot i o whcte c i ~ ~ c L e a by hold a phinm Lengxh nomallg t o t h e p&ne 06 xhe d i g m e ) .

i

C l u s t e r s of f o u r face-sharing u n i t s appears then and a r e linked t o g e t h e r by capping atoms o r by edge and vertex connections ( n o t v i s i b l e i n t h e f i g u r e ) a s elsewhere i n t h e network between t h e o t h e r prisms. This r e s u l t s a l s o i n an i n c r e a s e of t h e l o c a l number d e n s i t y of

X

atoms which t r u l l y r e p r e s e n t s a concentration f l u c t u a t i o n with r e s p e c t t o t h e average stoichiometry of t h e s t r u c t u r a l o p e r a t i o n . To balance t h i s e f f e c t , an i n c r e a s e of t h e operation p e r i o d i c i t y may be introduced elsewhere i n such a way t h a t an average over t h e whole network brings t h e composition back t o M2X. The most n a t u r a l change

is

t o transform t h e s t r u c t u r a l operation from {3,1,3,1,

...

) t o I 3 , 3 ,

...

) a s schematised i n t h e r i g h t hand s i d e p a r t of f i g u r e

3. A t y p i c a l arrangement of t h e s e u n i t s i s t h a t i n f i g u r e 1 with C = + 1 which has again t h e same edge and v e r t e x connections than i n t h e c e n t r a l p a r t of f i g u r e

3 (with prism v e r t i c e s a s capping atoms of neighbouring prisms a s w e l l ) . In t h i s region, t h e composition i s M3X. I t s t u r n s out t h a t t h e Y2Ni g l a s s has no c r y s t a l l i n e c o u n t e r p a r t of i d e n t i c a l composition but l e a d s t o t h e formation of t h e Y3Ni and Y3Ni2 compounds 181. The cementi te-type Y3Ni compound i s generated by {3,3,.

. .

)

SCT. The Y3Ni2 c r y s t a l has a more complicated s t r u c t u r e b u i l t up by 4-prisms c l u s t e r s i d e n t i c a l t o those i n f i g u r e 3 ( b u t a l t e r n a t i n g l y r o t a t e d by IT/^ from one l a y e r t o a n o t h e r ) . Note t h a t t h e s o l e s t r u c t u r a l operation with t h e {3,1,3,1) p e r i o d i c i t y a l r e a d y e n t a i l s t h e most s a l i e n t f e a t u r e s e x h i b i t e d by t h e experimental p a i r c o r r e l a t i o n f u n c t i o n s published by MARET e t a1 181 :a c l o s e c o n t a c t Ni-Ni d i s t a n c e (through f a c e s h a r i n g ) and a well defined f i r s t peak of t h e N i - Y f u n c t i o n followed by two subpeaks which correspond i n t h i s model t o d i s t a n c e s from N i t o t h e prism v e r t i c e s and t o t h e two d i f f e r e n t types of capping atoms. A s u i t a b l e guide t o t h e modelling of t h e Y2Ni g l a s s may thus be found i n f i g u r e 3 and corresponding work

i s

i n progress.

Figuhe 4 :

ExampLe 06 SCT w d h wcuying p d o -

d i c i t y XunLtcLting t h e change i n R o d c o m p o n ~ o n ccnnociated w d h t h e p o n i L i o d dinofiden. X

domb ( n o t dtLuwn) m e i n t h e centtre

06

each pninm.

On@

one h d 6

06

t h e pninmn m e dtLclwn

M i x i n g s t r u c t u r a l o p e r a t i o n s i s an a t t r a c t i v e p o s s i b i l i t y e i t h e r i n b i n a r y systems w h i c h may e x h i b i t polymorphism as mentioned i n s e c t i o n 2 (e.g. Fe-B) o r i n m u l t i - component systems (e.g. t e r n a r y Fe-B-C) i n w h i c h each s o l u t e s p e c i e s may be a s s o c i a t e d w i t h one t y p e o f s t r u c t u r a l o p e r a t i o n . However, under usual p r e p a r a t i o n c o n d i t i o n s , t h e s e g l a s s e s behave as homogeneous media, s u g g e s t i n g e i g h e r t h a t t h e c o r r e l a t i o n s o p e r a t e i n t o o s m a l l volumes t o be d i s t i n g u i s h e d o r t h a t B and C b e l o n g t o t h e same s t r u c t u r a l o p e r a t i o n . F i g u r e 5 i s a s p e c u l a t i v e d e s c r i p t i o n o f a s i n g l e s t r u c t u r a l o p e r a t i o n r e l a t e d t o SCT b u t m i x i n g t h e c o n n e c t i o n s w i t h C =

-

1 ( i . e . Fe3B) and C = + 1 ( i . e . Fe3C). P e r i o d i c i n t e r m i x i n g o f C =

0

and C =

-

1 c o n n e c t i o n s i s known t o o p e r a t e i n c r y s t a l l i n e compounds 191 b u t i n t h i s example, n o p e r i o d i c r e p e t i t i o n i s considered. Here, p r i s m s f o r m s w i n g i n g c h a i n s a r r a n g e d i n p l a n a r l a y e r s and, i f occupied b y a s m a l l X atom, may c o n t i n u e t h e n e t w o r k w i t h a C = + 1 c o n n e c t i o n o r , i f X i s l a r g e r , w i t h a C =

-

1 connection. Again, t h i s example emphasizes a coup1 i n g between p o s i t i o n a l d i s o r d e r and c o m p o s i t i o n non-homogeneity. Moreover, t h e l i n k a g e d e f i c i t i n t h e C = -1 c o n n e c t i o n

( L = 1 i n s t e a d o f & = 2 o r 3 as i n f i g u r e 1) a l s o l e a d s t o a v a r i a t i o n i n t h e X-number d e n s i t y which, c o n v e r s e l y , i s a b l e t o accomodate l o c a l f l u c t u a t i o n s .

Figuhe 5 :

S p e c u L d v e n h & u h e o p e n d o n mixing t h e C = - I and C = + I connectiovln nhvwn

i n 6iguhe I buR cvrnanged i n pdanm LyetL.J

w d h lwo .di66ene& fiepehition pehiodi- c i t i e ~ . Note t h e c h a i ~ n

06

t&ahedlLaR and ootuhedrrd n d e ~ wkich n e p m d e t h e h o didde/re& AequenCtb and t h e a d d e d appeuiance oh

L

= 1 d u r n .

F i n a l l y , i t i s w o r t h c o n s i d e r i n g a M1-xXx amorphous s t r u c t u r e i n t h e l o w - x l i m i t as then, p a r t o f t h e M atoms w i l l n o t c o n t r i b u t e t o any u n i t e i t h e r as p r i s m v e r t e x o r as capping atom, i . e . w i l l n o t i n t e r a c t d i r e c t l y w i t h X atoms. I n o r d e r t o accomodate such atoms, t h e system has t h e p o s s i b i l i t y t o " b r e a k " t h e g e n e r a t i v e symetry o f t h e s t r u c t u r a l o p e r a t i o n i n such a way t h a t t h e s t r u c t u r e i s d i v i d e d i n two components : r e g i o n s Ax where a s t r u c t u r a l o p e r a t i o n a p p l i e s and o f average c o m p o s i t i o n MI-~L X x ~ and r e g i o n s AM o f p u r e M element where no more c o r r e l a t i o n o p e r a t e s .

C8-340 J O U R N A L D E PHYSIQUE

quoted i n references 13,41. The question t o know what a c t u a l l y i s t h e s t r u c t u r e o f t h e -presumably mono-atomic- AM regions i s open as t h e r e are several candidate models f o r t h i s purpose : d i s o r d e r e d m i c r o - c r y s t a l s , dense random packed o r

icosohedral bond o r i e n t e d c l u s t e r s . V

-

WHAT ABOUT REAL GLASSES ?

A s t r i c k i n g d u a l i t y o f these m e t a l l i c glasses i s r e l a t e d t o t h e i r ( u s u a l l y ) broad composition range : a t t h e macroscopic l e v e l , they behave as continuous s o l i d s o l u t i o n s while, a t t h e microscopic l e v e l , t h e i r s i m i l a r i t y w i t h c r y s t a l l i n e com- pounds w i t h narrow s t o i c h i o m e t r y ranges seems t o be i n c o n t r a d i c t i o n w i t h t h e i r macroscopic homogeneity. The c h i e f m e r i t o f t h e model developped i n t h e previous s e c t i o n s appears thus t o be a b l e -by i n t e r c o n n e c t i n g a unique type o f u n i t - t o account f o r a l a r g e domain o f amorphous compositions o r f o r t h e c o n c e n t r a t i o n v a r i a t i o n s t h a t a r e known t o occur w i t h i n a specimen d u r i n g p r e p a r a t i o n .

The i n t e r e s t i n g p o i n t here, however, i s a t an even more microscopic scale as i t shows

how

minute s h i f t s o f t h e c o n s t i t u e n t s p r o f i l e w i t h respect t o t h a t o f an i d e a l - p o s s i b l y metastable- c r y s t a l l i n e s t a t e may induce p o s i t i o n a l d i s o r d e r ( w i t h o u t r e q u i r i n g p o i n t defects, i . e . empty prisms, which o f course may a l s o appear). Conversely, i t a l s o p o i n t s towards why such disordered m a t e r i a l s may form.

I n s e c t i o n 4, use was made o f o n l y f o u r examples t h a t can be c l a s s i f i e d as :

1

-

change o f d i r e c t i o n o f t h e s t r u c t u r a l o p e r a t i o n 2

-

change o f p e r i o d i c i t y o f t h e s t r u c t u r a l o p e r a t i o n 3

-

i n t e r m i x i n g o f s t r u c t u r a l operations

4

-

r e s t r i c t i o n o f t h e domain o f a p p l i c a t i o n o f t h e s t r u c t u r a l operation.

The author i s nonetheless convinced t h a t many o t h e r p o s s i b i l i t i e s can be imagined from t h e c r y s t a l l i n e c o n f i g u r a t i o n s shown i n 17

1 .

Obviously, several o f these e f f e c t s may operate simultaneously. Case 1 i s t h e most " e f f i c i e n t 1 ' i n i n t r o d u c i n g d i s o r d e r and case 2 i n changing t h e composition. I t must be noted t h a t i n t h e p i c t o r i a l d e s c r i p t i o n s o f t h i s paper, the r e g u l a r i t y o f the s t r u c t u r e i s over- emphasized f o r t h e sake o f c l a r i t y . I n f a c t , an average c o r r e l a t i o n l e n g t h i s associated w i t h t h e s t r u c t u r a l o p e r a t i o n and accounts f o r t h e l i n e a r dimension o f t h e volume over which i t a p p l i e s w i t h o u t changing i t s d i r e c t i o n or/and p e r i o d i - c i t y . It i s j u s t a few times l a r g e r than a u n i t l e n g t h which smoothes o u t t h e " p l a n a r " p i c t u r e suggested i n t h e f i g u r e s and -more s e r i o u s l y - d e f i n e s e s s e n t i a l l y 20 r e g i o n s where angular d e f i c i t s ( d i r e c t i o n change) or/and v a r i a t i o n s i n t h e X-number d e n s i t y are concentrated.

E l i m i n a t i o n o f one o r both e f f e c t s t o recover c r y s t a l l i n i t y r e q u i r e s atomic t r a n s - p o r t and d e f e c t m o b i l i t y because t h e X atoms i s supposed t o f o r c e always t h e forma- t i o n o f

a

u n i t and t h e r e f o r e t r a n s p o r t s a l s o i t s own connection. The reason why c l u s t e r s o f atoms, organized according t o a s i n g l e d i r e c t i o n o f t h e s t r u c t u r a l operation, do n o t grow f u r t h e r d u r i n g the glass t r a n s i t i o n and form a glass may thus be understood i f t h e time constants associated w i t h these d i f f u s i o n e f f e c t s are l a r g e r than t h e time b a s i s imposed by t h e quenching process. I n t h e l i q u i d a l l o y s considered here, d i f f u s i o n i s l i k e l y t o be slowed down by i

-

the s t r o n g i n t e r a c t i o n between X and M species and ii

-

by t h e tendency t o form c l u s t e r s ( a s s o c i a t e s ) which enhances t h e l o c a l c o n c e n t r a t i o n f l u c t u a t i o n s , e s p e c i a l l y i n a l i q u i d w i t h a mean composition i n between t h a t o f t h e associates ( o r of t h e c r y s t a l l i n e phases). Note t h a t i n case 4, t h e formation o f pure M regions works opposite t o t h i s as t h e absence o f X atoms r a p i d l y balances t h e s t a b i l i z i n g e f f e c t due t o t h e i n t e r f a c e w i t h t h e surrounding amorphous phase.

Acknowledgements : The a u t h o r wishes t o express h i s g r a t i t u d e toward Drs G. Le Caer e t P.H. G a s k e l l f o r t h e i r k i n d h e l p o v e r p a s t and r e c e n t years. Thanks a r e a l s o due t o S. E b a l a r d f o r i n t e r e s t i n g d i s c u s s i o n s and t o Dr. M. Maret who s u p p l i e d h e r Y2Ni d a t a p r i o r t o p u b l i c a t i o n . P a r t o f t h i s work was a c h i e v e d a t t h e Cavendish L a b o r a t o r y , Cambridge (U.K.) and s u p p o r t e d b y a g r a n t o f t h e Commission X I 1 o f t h e E.E.C.

.

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