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STRUCTURAL DESCRIPTION OF TRANSITION METAL-METALLOID GLASSES
Jessica Dubois, Gérard Le Caër
To cite this version:
Jessica Dubois, Gérard Le Caër. STRUCTURAL DESCRIPTION OF TRANSITION METAL- METALLOID GLASSES. Journal de Physique Colloques, 1982, 43 (C9), pp.C9-67-C9-74.
�10.1051/jphyscol:1982912�. �jpa-00222425�
Colloque C9, supplément au n12, Tome 43, décembre 1982 page C9-67
STRUCTURAL DESCRIPTION OF TRANSITION METAL-METALLOID GLASSES
J.M. Dubois and G. Le Caer
Laboratoire de Métallurgie (L.A. 159) ENSMIM, Para de Saurupt, 64042 Nancy Cedex, France
Résumé - On propose une d e s c r i p t i o n s t r u c t u r a l e des v e r r e s métal de t r a n s i t i o n - m é t a l - l o ï d e qui s ' a p p u i e sur l e s opérations s t r u c t u r a l e s qui permettent de générer l e s com- posés c r i s t a l l i n s . Une démixtion à l ' é c h e l l e microscopique s ' i n t r o d u i t naturellement et ses conséquences sur l a s t r u c t u r e sont d i s c u t é e s . On apporte des arguments e x p é r i - mentaux en faveur d'une t e l l e d e s c r i p t i o n qui p o u r r a i t fournir un moyen de prévoir c e r t a i n e s p r o p r i é t é s des v e r r e s m é t a l l i q u e s .
Abstract - A s t r u c t u r a l d e s c r i p t i o n of t r a n s i t i o n metal-metalloid g l a s s e s i s proposed.
I t i s based on the s t r u c t u r a l operations which allow generating the c r y s t a l l i n e coun- t e r p a r t s . A demixion a t a microscopic l e v e l i s n a t u r a l l y introduced whose consequences on the s t r u c t u r e are d i s c u s s e d . Experimental arguments in favour of such a d e s c r i p t i o n a r e given which should provide a b a s i s for the p r e v i s i o n of some p r o p e r t i e s of m e t a l - l i c g l a s s e s .
1. Introduction
The notion of stereochemically defined amorphous structures has recently emerged from the field of models devoted to the structural description of metallic glasses (1). As emphasized by GASKELL (1), numerous experimental evidences demonstrate that one atomic species is embedded in a definite polyhedron formed from the other species.
For energetical reasons, this cluster may be the most stable of all the possible configurations and thus be the basic structural unit of both the glassy and crystal- line states.
Metallic glasses formed from transition metals M (Mn, Fe, Co, Ni, Pd) and from metalloids X (B, C, P, Si) have been extensively studied in recent years. Many struc-
tures of M-X crystalline compounds can be built with the help of metallic trigonal prisms centered by the metalloid atom. Only the way they are interconnected is to be changed to account for the different structures. Therefore, the trigonal prism seems to be the best candidate as a basic structural unit of this type of metallic glasses.
GASKELL (2) indeed succeeded by using it iti a structural model of a - Pd Si . ou zO The purpose of this paper is thus to extent the "hand building" algorithm of this model (2) by proposing a general description of the arrangements of trigonal prisms which should be suited for all M, X glasses (0.1 < x < 0.3). After justi- fying the choice of this polyedron as a structural unit on the basis of experimental data, we will describe the structures of the M-X compounds in terms of chemically twinned close packed structures. From this systematics, a description of the amorphous structure will be given leading to the definition of two noteworthy compositions. Experimental chesks of their existence will then be reported. Finally, as a matter of conclusion, a prospective account of some characteristic features of this description will be given.
2. Physical properties of M _ X glasses and crystalline compounds
Numerous experimental studies have demonstrated that the local properties mea- sured in M-X glasses are quite similar to those of the crystalline counterparts. The most informative data were obtained from techniques using the X element as a local probe. PANISSOD et al. (3) have shown by NMR that the quadrupole splittings at
11B nuclei in M07.0B30 and NiysPitBsglasses are nearly identical to those measured in Mo B and Ni3B respectively. The average hyperfine field transfered from the iron neighbours to boron in a - Fe82B18is identical to the transfered field measured in Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982912
C9-68 JOURNAL DE PHYSIQUE
c - Fes BE] ( 4 ) . T h e s e r e s u l t s a l l o w a s s u m i n g t h e m e t a l p o l y e d r o n s u r r o u n d i n g t h e m e t a l l o i d i s s i m i l a r i n b o t h s t r u c t u r e s . Taking t h e i r o n atom a s a l o c a l p r o b e , t h e Mgssbauer s p e c t r o s c o p y h a s e v i d e n c e d a l o t of s i m i l a r i t i e s i n i r o n b a s e d g l a s s e s and c r y s t a l l i n e compounds. For example, t h e h y p e r f i n e f i e l d d i s t r i b u t i o n c a l c u l a t e d from t h e s p e c t r u m a o f a-Fe75B25(T=4K)argues i n f a v o u r o f s i m i l a r m e t a l l o i d d i s t r i - b u t i o n s around t h e m e t a l atom i n t h e two g l a s s y and c r y s t a l l i n e s t a t e s ( f i g u r e 1 ) . I n f a c t , n o t o n l y t h i s d i s t r i b u t i o n a t g i v e n c o n c e n t r a t i o n b u t a l s o i t s e v o l u t i o n w i t h t h e m e t a l c o n t e n t i s s i m i l a r i n b o t h s t a t e s . C o n c l u s i v e r e s u l t s seem t o b e i n d e e d p r o v i d e d by t h e non random s u b s t i t u t i o n of i r o n i n Co R g l a s s e s a s i t o c -
1-y x
c u r s i n t h e Co3B b o r i d e ( 5 ) and by t h e e v o l u t i o n of t h e h y p e r f ~ n e p a r a m e t e r s i n (Fel-zNiz)-B g l a s s e s w h i c h e x h i b i t t h e c h a n g e s a t z = 0 . 4 c h a r a c t e r i s t i c of t h e
t e t r a g o n a l t o o r t h o h o m b i c t r a n s i t i o n of t h e ( F e N i ) B b o r i d e s ( 6 ) . 1-2 z 3
S t r o n g s i m i l a r i t i e s o f t h e d b a n d s a r e o b s e r v e d by XPS i n g l a s s y a l l o y s and 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 while t h e c r y s t a l l i n e p u r e m e t a l d band i s d i f f e r e n t ( 7 ) . F i n a l l y , some o t h e r p h y s i c a l p r o p e r t i e s a r e c l o s e l y r e l a t e d i n b u l k amorphous and c r y s t a l l i n e m a t e r i a l s . T h i s i s t h e c a s e i n t h e F e n ( P , B)21 g l a s s e s and Fe3(P,B) p h o s p h o b o r i d e s which e x i b i t t h e same s l o p e c h a n g e o f t h e T - c o m p o s i t i o n r e l a t i o n a t z = P/B = 0.5 ( 8 ) . The g l a s s e s a r e l e s s d e n s e t h a n t h e c r y s t a l l i n e compounds by o n l y few p e r c e n t s . Moreover, t h e p a c k i n g f r a c t i o n q o f t h e m e t a l atoms v a r i e s w i t h t h e r a d i i r a t i o p = r / r M i n c l o s e s i m i l a r i t y w i t h t h e c h a n g e of
r!
i n M3X compounds ( 9 ) .Thus, i n d i r e c t methods of p r o b i n g t h e l o c a l o r d e r l e a d s u s t o c o n c l u d e t h a t , a t a v e r y f i n e s c a l e , t h e g l a s s y s t r u c t u r e i s formed from t h e same u n i t s a s t h e c r y s t a l l i n e compounds. A s i m i l a r c o n c l u s i o n c a n be drawn from t h e d i r e c t s t u d y o f t h e s t r u c t u r e by d i f f r a c t i o n methods. The f i r s t c o n c l u s i v e remark is t h a t t h e X atoms a r e i s o l a t e d from o t h e r X atoms by a M s h e l l a s shown by n e u t r o n d i f f r a c t i o n i n i n a l o t of M-X g l a s s e s - S e c o n d l y , t h e mean number of M f i r s t n e i g h b o u r s of t h e X e l e m e n t i s found t o b e Z 2 9 by d i f f e r e n t t e c h n i q u e s ( t a b l e 1 ) . T h i s v a l u e of Z , which i s a l s o o b t a i n e d by ~ a s s b a u e r s p e c t r o s c o p y i n Fe B g l a s s e s
( Z = 9
2
1 . 5 f o r x 2 0.2 ( 1 5 ) ) i s e x a c t l y e q u a l t o c o o r d i n a t i o n number o f m e t a l l o i d i n t h e E43X compounds.TABLE 1
F i g u r e 1
H y p e r f i n e f i e l d d i s t r i b u t i c i ~ o f a Fe 75B2 h ~ ~ v e r f i n e f i e l d s i n E'e 6s ( T = 4 R)
3 1
Referent?
( 1 0 ) ( 1 1 ) (12) (13) ( 1 4 )
Moreover, t h e d i s t o r t i o n of t h e m e t a l l i c s h e l l around t h e m e t a l l o i d r e s e m b l e s t h a t e n c o u n t e r e d i n M 3 X compounds : d i s t o r d e d i n a - P d s 4 S i 1 6 a s i n P d s S i ( I ) , s h a r p l y d e f i n e d i n a-FeaQBzo(lO) a s i n Fe3 B ~ l ( 1 6 ) . F i n a l l y , M-M and M-2 nn X d i s t a n c e s i n t h e amorphous s t a t e a r e a l s o c o m p a t i b l e w i t h t h e 2 n n d i s t a n c e s i n M 3 X compounds ( I ) .
Method
R.X.and n e u t r o n d i f . R . X . d i f .
R.X.and n e u t r o n d i f .
EXAFS Composition
FesoB20 Fe75Pz5 Co~l 1 P19
Pd8,,Si16 Pd7,Ge2,
The b e s t s u i t e d s t r u c t u r a l u n i t f o r l i q u i d quenched Ml-xXx g l a s s e s ( i . e . x
<
0 . 3 ) i s t h e s o - c a l l e d t e t r a k a i d e c a h e d r o n c e n t e r e d on t h e m e t a l l o i d and formed from a t r i g o n a l p r i s m w i t h s i x m e t a l atoms a t e a c h v e r t e x and t h r e e f u r t h e r m e t a l s c a p p i n g t h e r e c t a n g u l a r f a c e s . T h i s i n t e r s t i t i a l s i t e o p t i m i z e s t h e p a c k i n g e f f i c i e n c y of t h e m e t a l l i c atoms and t h e s p a c e needed by t h e m e t a l l o i d atom F i n a l l y , i t may be r e a s o n a b l y assumed t h a t t h e c o r r e l a t i o n s between u n i t s i n t h e c r y s t a l l i n e c o u n t e r p a r t r e m a i n s i m i l a r i n t h e g l a s s . T h e r e f o r e , a d e s c r i p t i o n of t h e amorphous s t r u c t u r e grounded o n t h e c r y s t a l l i n e s h o r t r a n g e o r d e r and which a v o i d s t h e s e t t l i n g o f a l o n g r a n g e o r d e r s h o u l d be a d a p t e d t o Ml-xXx g l a s s e s .- Z
8.64 8.1 8 . 9
5
0.5 9.0 - + 0 - 9 8.6- +
0.5HYDE,ANDERSON and coworkers ( 1 7 ) have shown t h a t t h e a p p a r e n t l y complex s t r u c - t u r e s of t h e M-X compounds c a n be simply g e n e r a t e d from c l o s e packed s t r u c t u r e s (hcp of f c c ) by p e r i o d i c a l l y t w i n n i n g t h e s e s t r u c t u r e s on t h e u n i t c e l l l e v e l . The p r i s m a t i c i n t e r s t i c e s a r e c r e a t e d i n t h e twinning p l a n e c a l l e d t h e composition p l a n e . The p e r i o d i c i t y and t h e t w i n p l a n e t y p e ( h e r e a f t e r termed t h e s t r u c t u r a l o p e r a t i o n ) depend on t h e a c t u a l s t r u c t u r e and a r e l a b e l l e d i n r e f e r e n c e (17) a s chemical twin- n i n g , t r i l i n g , f o u r l i n g , swinging t w i n n i n g , e t c . For t h e s a k e of b r e v i t y , we o n l y d e s c r i b e t h e g e n e r a t i o n of t h e Fe C and Fe5C2 t y p e s t r u c t u r e s by c h e m i c a l twinning
( 1 8 ) . 3
The c o m p o s i t i o n p l a n e i s t h e (113-2) p l a n e of t h e hcp s t r u c t u r e and t h e twinning i s r e p e a t e d e v e r y f o u r p l a n e i n Fe C o r i n t h e ( 3 , 4 , 3 , 4 . .
. I
sequence i n Fe C ( f i g u r e 2 ) . Between two twinning p?anes, t h e M atoms remain v e r y c l o s e t o t h e 5 2 o r i g i n a l hcp p o s i t i o n s t h u s forming a l m o s t p e r f e c t hcp b l o c k s . I n Fe3C t y p e s t r u c t u r e s , e v e r y second b l o c k i s r o t a t e d 180" around t h e twing a x i s and j o i n e d e x a c t l y t o t h e a d j a c e n t b l o c k s accross t h e twin p l a n e s . Two a d j a c e n t p r i s m s s h a r e a t r i g o n a l edge forming c h a i n s of t r i g o n a l p r i s m s . The c h a i n s a r e c o n n e c t e d i n t h e twinning p l a n e by s h a r i n g v e r t i c e s of t r i g o n a l p r i s m s .I t i s o b v i o u s l y t h e n a t u r e of t h e s t r u c t u r a l o p e r a t i o n and i t s p e r i o d i c i t y , t h a t means t h e c o n n e c t i v i t y r u l e s between s t r u c t u r a l u n i t s , which a c c o u n t s f o r t h e s t o i c h i o m e t r y w i t h o u t i n t r o d u c i n g p o i n t d e f e c t s . PARTHE and MOREAU (19) have d e f i n e d a l i n k a g e c o e f f i c i e n t LC which r e p r e s e n t s t h e number of prisms t o which a m e t a l atom b e l o n g s . On t h e a v e r a g e , LC = 6 x / ( l - x ) v a r i e s between 1 and 12 i f a l l m e t a l atoms b e l o n g t o t r i g o n a l p r i s m s . The former v a l u e c o r r e s p o n d s t o i s o l a t e d p r i s m s w h i l e f o r
t h e l a t t e r t h e s p a c e i s t i l e d o n l y w i t h p r i s m s . F i n a l l y , when LC < 1 , some o L t h e m e t a l atoms do n o t b e l o n g t o any prism. The O 2 LC 2 12
I
A1
r a n g e a l l o w s t h u s s c a n n i n g t h e 0 5 x 2 0.67 composition r a n g e .4 . S t r u c t u r a l d e s c r i p t i o n of M X g l a s s e s 1-x x
We propose t o g e n e r a t e t h e g l a s s l i k e t h e c r y s t a l l i n e compound of same composition w i t h t h e h e l p of t h e same s t r u c t u r a l o p e r a t i o n , i..e. chemical twinning i n Pd75 S i 2 5,
Co75B25, c h e m i c a l f o u r l i n g i n Fe75 B25, e t c . The l a c k of
F l g u r e 2
S c h e m a t i c d r a w ~ n g o f t h e s t r u c t u r e o f Fe C and Fe5C2 (ten-
t e r ) and projections o n the ( 1 0 0 ) p l a n e 3 0 f the Fe C strut-
,
$ b t u r e ( b e l o w ) and on the ( 0 1 0 ) p l a n e o f t h e Fe,C, s g r u c t u r e
1
1 I I I( a b o v e ) . T h e t r a c e s o f t h e t w i A i n g p l a n e s a r z 6 a r k e d b y a r r o w s ( a f t e r ( 1 8 ) ) .
l o n g r a n g e p e r i o d i c i t y can simply a r i s e from t h e l i m i t e d s p a t i a l e x t e n t of t h e s t r u c t u r a l o p e r a t i o n . Above a g i v e n c o h e r e n t l e n g t h 1
,
t h e c o m p o s i t i o n p l a n e i s randomly changed f o r a n o t g e r p l a n e c r y s t a l l o g r a p h i c a l l y e q u i ~ a l e n t . For example, i n Pd S i t h e r e a r e t h r e e e q u i v a l e n t (1122) p l a n e s which can b e randomly chosen a s composition p l a n e s . 3 Both t h e u n i t s and c h a i n s c o n n e c t i o n s a r e t h u s d e f i n e d by t h e s t r u c t u r a l o p e r a t i o n .The m e t a l l o i d c o n t e n t is simply accounted f o r by chan- g i n g t h e c o n n e c t i v i t y between t h e p r i s m a t i c u n i t s , t h a t means by v a r y i n g t h e p e r i o d i c i t y a n d / o r t h e s t r u c t u r a l o p e r a t i o n . T h i s a l l o w s f o r example k e e p i n g c o n s t a n t t h e number n of m e t a l l o i d n e a r e s t n e i g h b o u r s of a m e t a l atom when x d e c r e a s e s , because a m e t a l atom may belong t o LC p r i s m s and c a p s t h e r e c t a n g u l a r f a c e s of ( n -LC) o t h e r p r i s m s . T h i s f e a t u r e a c c o u n t s f o r t h e s t r i k i n g independen- c y on x of t h e s t a n d a r d d e v i a t i o n of t h e h y p e r f i n e f i e l d A Jn,
1
d i s t r i b u t i o n s i n Fe-B g l a s s e s ( 1 5 ) .C9-70 JOURNAL DE PHYSIQUE
The f o r m a t i o n of m i c r o c r y s t a l s i s f o r b i d d e n on one hand by t h e magnitude of 1 which i s assumed t o be of t h e o r d e r of t h e l a t t i c e p a r a m e t e r s of t h e M-X compounds a and on t h e o t h e r hand by t h e f a c t t h a t two a d j a c e n t domains can b e j o i n e d t o g e t h e r by a hcp p l a n e w i t h o n l y s l i g h t d i s t o r s i o n s . T h i s l e a d s of c o u r s e t o t h e f o r m a t i o n of l i n e a r d e f e c t s c l o s i n g t h e c o m p o s i t i o n p l a n e s whose l e n g t h i s c r u d e l y approxima- t e d by ?r l a . We i d e n t i f y 1 w i t h t h e c r o s s dimension of t h e i n t e r f e r e n c e f r i n g e s p a t t e r n s observed by h i g E r e s o l u t i o n e l e c t r o n microscopy i n a - P d 8 0 S i 2 0 ( 2 0 ) , i . e . 1
-
151;.
T h i s v a l u e i s i n agreement w i t h t h e e x t e n t of l o c a l d e f e c t s shown by a NOLD e t a l . i n a-
Fe8o Bzo(21)A s a l r e a d y emphasized, t h e r e i s a m e t a l l o i d c o n c e n t r a t i o n xl below which metal atoms do n o t b e l o n g t o s t r u c t u r a l u n i t s , namely - :
@ h e r e Z is t h e number of f a c e s of t h e Voronoi polyedron of X and
n
t h e ave- r a g e number of M-X p a i r s . I n t h e c a s e of t e t r a k a i d e k a h e d r a , t h i s c o n c e n t % a t i o n l i m i t i s a t l e a s t xl = 1 / 1 0 b u t may b e h i g h e r i f m e t a l atom t e n d t o b e s u r r o u n d e d by more than one X n e i g h b o u r .Below t h i s c o n c e n t r a t i o n l i m i t x
,
a demixion o c c u r s a t a v e r y f i n e s c a l e (' 1 ) and t h e s t r u c t u r e may b e d e s c r i 6 e d a s b e i n g formed from two k i n d s of m e t a l l i cenvi?onments :
1 - Metal atoms which b e l o n g t o t e t r a k a i d e k a e d r a w i t h a n a v e r a g e number of X n e i g h b o u r s n 2 1 . The mean composition of t h i s r e g i o n i s t h u s M X ( h e r e a f t e r
c a l l e d AX envi?onment)
.
1-x 1 1 x2
-
Dense random packed m e t a l atoms w i t h no m e t a l l o i d neighbour which f i l l t h e s p a c e between t h e A r e g i o n s ( h e r e a f t e r c a l l e dAM
e n v i r o n m e n t ) .X
The r e l a t i v e f r a c t i o n of m e t a l atoms i n t h e AM r e g i o n s i s simply : 1 - x
a = 1 -A-
1-x x / 2 /
1 and i s r e p o r t e d on f i g u r e 3 f o r d i f f e r e n t v a l u e s of x
1'
On p r i n c i p l e , t h e m e t a l l o i d atoms l i e i n t h e composition p l a n e a s i n t r o d u c e d above and t h e r e f o r e i t i s r e a s o n a b l e t o assume t h a t t h e c o h e r e n c e l e n g t h 1 o n l y s l i g h t l y depends on x when x 5 xl. Thus, a c o n n e c t i v i t y p e r c o l a t i o n t h r e s g o l d x i s a s s o c i a t e d t o t h e demixion below x When x < x
,
t h i s c o n n e c t i v i t y p e r c o l a t i &problem e x p r e s s e s t h e e x i s t e n c e of a n l i n f i n i t e walg from
%
t oAM
s i t e s w i t h o u t s e e i n g any X atom a s f i r s t n e i g h b o u r . I n o t h e r words, above x t h e AX r e g l o n s form an i n - f i n i t e c l u s t e r c o n t a i n i n g s m a l l AM a g g r e g a t e s . T h e demi-zed g l a s s shows t h u s con- c e n t r a t i o n f l u c t u a t i o n s of wave l e n g t h A which can b e i d e n t i f i e d w i t h 1 f o r x = x .P
Two c r u d e e s t i m a t e s of x can b e g i v e n . I f we c o n s i d e r f i r s t t h a t t h e Ax r e - g i o n s have a n a l m o s t s p h e r i c a l p s h a p e , t h e p e r c o l a t i o n t h r e s h o l d w i l l c o r r e s p o n d t o t h e c o m p o s i t i o n a t which they remain j u s t i n c o n t a c t and form a d e n s e packing o f s p h e r e s , t h u s o c c u p y i n g a f r a c t i o n (1- f ) = ~ / 2 / 6 of t h e t o t a l volume. f i s
r e l a t e d t o x by : P P
P
-
where fiJ i s t h e a c t u a l mean atomic volume i n r e g i o n A
.
I t i s a l s o p o s s i b l e t o c o n s i - d e r o n l y t h e m e t a l l i c network and f i l l t h e M s i t e s wigh m e t a l atoms w i t h and w i t h o u t X atoms a s n e a r e s t n e i g h b o u r s . By n e g l e c t i n g a s a f i r s t a p p r o x i m a t i o n t h e packing d i f f e r e n c e s which a r i s e from t h e a c t u a l p r e s e n c e o r a b s e n c e of t h e m e t a l l o i d , t h i s p e r c o l a t i o n problem i s q u i t e s i m i l a r t o a s i t e p e r c o l a t i o n problem i n a random n e t - work. S o l u t i o n s a r e p r o v i d e d from computer s i m u l a t i o n s ( 2 2 , 23) and l e a d t o0.21 5 a 5 0.26 i f t h e a v e r a g e c o o r d i n a t i o n number of t h e network i s assumed t o b e 9 @ Y 5 12. T h i s c o o r d i n a t i o n number r a n g e i s t y p i c a l l y deduced from t h e d i f - f r a c t i o n measurements i n M-X g l a s s e s . The second e s t i m a t e of x i s t h u s g i v e n by :
P
fluctuation wavelength
A
i n c r e a s e s due t o t h e d e c r e a s e of t h e number of AX zones w h i l e t h e a v e r a g e s i z e of t h e s e zones remains c l o s e t o 1.
However, i n t h e u s u a l composition r a n g e of t h e l i q u i d quenched g l a s s e s ( 0 . 1 <ax < 0 , 3 ) ,A
c a n n o t s i g n i - f i c a n t l y d i f f e r from 1 0 - 20A .
T h i s r a n g e c l e a r l y d i s t i n g u i s h e s t h i s demixion phe- nomenon from t h e l o n g wavelength f l u c t u a t i o n s (1000A)
a l r e a d y p u b l i s h e d i n t h e li-t e r a t u r e .
F i g u r e 3 F i g u r e 4
F r a c t i o n a o f m e t a l l i c a t o m s embedded i n t h e A re- P i c t u r e o f t h e s t r u c t u r e f o r g i o n s f o r d i f f e r e n t v a l u e s o f x l . E x p e r i m e n t a l d a t a M x > x l , xp < x < x l and x < x
i n Fe-B g l a s s e s from r e f e r e n c e s m ( 1 5 ) , A ( 2 4 ) , ( 2 5 1 , P
0 ( 2 6 1 , X ( 2 7 ) .
5 . E x p e r i m e n t a l check o f t h e proposed d e s c r i p t i o n
The Fe B g l a s s e s e x h i b i t some w e l l known changes i n t h e i r p h y s i c a l proper- ties-compos$t??o% r e l a t i o n s h i p s . They seem t h e r e f o r e t o b e good c a n d i d a t e s f o r che- c k i n g t h e above d e s c r i p t i o n . E s p e c i a l l y , t h e y c r y s t a l l i z e i n m u l t i p l e s t e p s a t low boron c o n t e n t ( x < 0.17) ( t h e f i r s t one c o r r e s p o n d s t o t h e f o r m a t i o n of p u r e bcc F e ) . Assuming t h a t t h i s bcc Fe r e s u l t s from t h e c r y s t a l l i z a t i o n of A zones embedded i n
zones of c o m p o s i t i o n Fe B d i f f e r e n t i a l e n t h a l p i c a n a l y s i s (24) and r e s i s - Fe k v i t y d u r i n g ~ r ~ s t a ~ i i z a t ! ~ ~ ~ X 1 y ( 2 5 ) measurements a l l o w d e t e r m i n i n g t h e experimen- t a l f r a c t i o n a r e p o r t e d on f i g u r e 3 . A s i m i l a r d e f e r m i n a t i o n of a i n p a r t i a l l y c r y s - t a l l i z e d g l a s s e s b y Mossbauer s p e c t r o s c o p y ( x = 0 . 1 4 ) ( 2 6 ) and r e s i s t i v i t y ( x = 0.17) (27) i s a l s o r e p o r t e d i n f i g u r e 3 . F i n a l l y t h e h y p e r f i n e f i e l d d i s t r i b u t i o n s c a l c u - l a t e d from t h e Mijssbauer s p e c t r a of-as-quenched g l a s s e s a l s o f u r n i s h v a l u e s of a by comparing t h e measured v a l u e of Z t o t h e expected one Z = 9 ( 1 5 ) . As a good agreement between a v a l u e s from a s quenched and h e a t t r e a t e d g l a s s e s i s o b s e r v e d , a r e l i a b l e c o m p o s i t i o n l i m i t c a n be l e a s t s q u a r e f i t t e d t o t h e d a t a of f i g u r e 3 , i . e ( f o r Fe-B g l a s s e s ) :
JOURNAL DE PHYSIQUE
which a g r e e s w i t h t h e change s l o p e of t h e d e n s i t y .
From e q . 3 and 4 , t h e p e r c o l a t i o n t h r e s h o l d i s e s t i m a t e d t o l i e i n t h e r a n g e 0.15 C x 2 0 . 1 6 . T h i s c o n c e n t r a t i o n r a n g e k o r r e s p o n d s t o t h e c o m p o s i t i o n of t h e INVAR Fee 3B 17 g l a s s and a l l o w s u s t o s u g g e s t t h a t t h e INVAR b e h a v i o u r of t h e g l a s s e s i s t h e r e s u l t o f t h e p e r c o l a t i o n of two m a g n e t i c a l l y d i f f e r e n t r e g i o n s of t h e s t r u c t u r e . T h i s s u g g e s t i o n i s a l s o i n agreement w i t h t h e s l o p e change n e a r x = 0.15 of t h e m a g n e t i c moment a t 4 K and t h e d e s c r i p t i o n of t h e h y p e r f i n e f i e l d d i s t r i b u t i o n s g i v e n i n r e f . ( 1 5 ) .
The s m a l l a n g l e s c a t t e r i n g t e c h n i q u 2 s s h o u l d b e s e n s i t i v e t o t h e demixion.
SAXS i n Fee3B17 (27) i n f a c t g i v e s
X
= 12 A, i n q u i t e s a t i s f a c t o r y agreement w i t h o u r e s t i m a t e A 5 1 n e a r x.
C o n c e n t r a t i o n d e p e n d e n t f l u c t u a t i o n s of t h e d i f f u s e n e u t r o n s c a t t e r i n g c r o z s s e c t i B n s were a l s o r e c e n t l y o b s e r v e d i n Fe B g l a s s e s f o rx 2 0.19 ( 2 8 ) . F i n a l l y , t h e demixion e n t a i l s s p e c i f i c f e a t u l ~ 2 a s t h e l i e n a r vai-ia- t i o n s of t h e e x t e n s i v e thermodynamical v a r i a b l e s when x < xl s u c h a s t h e volume p a r atom gram o r t h e c r y s t a l l i z a t i o n e n t h a l p y ( 2 4 ) .
Q u a n t i t a t i v e c h e c k s o f t h e s t r u c t u r e of boron r i c h g l a s s e s ( x > x ) a p p e a r t o b e more d i f f i c u l t t o o b t a i n . However, t h e d b v i o u s agreement between t h e assumed e x i s t e n c e of c o h e r e n t domains and t h e o b s e r v e d o n e s ( 2 0 ) was a l r e a d y mentionned.
I t i s a l s o c o n s i s t e n t w i t h t h e B-B medium r a n g e c o r r e l a t i o n s shown by LAMPARTER e t a l . (29) i n a - N i s l B 1 9 . The f i r s t m e t a s t a b l e b o r i d e which a p p e a r s d u r i n g t h e c r y s - t a l l i z a t i o n c a s c a d e o f a-Fe7sB2sis Fe B w h i l e d i f f e r e n t a u t h o r s have g i v e n some e v i d e n c e t h a t a n o t h e r b o r i d e forms
ii
a-FesoBno ( 3 0 ) . T h i s o b s e r v a t i o n i s cohe- r e n t w i t h t h e a s s u m p t i o n t h a t t h e w n n e c t e i t y between p r i s m s e v o l v e s when x d e c r e a s e s . For x = 0 . 2 5 , L C = 2 a s i n Fe3BE1 w h i l e LC = 1 . 5 f o r x = 0 . 2 . T h e r e f o r e , a b o r i d e w i t h a n a c t u a l LC = 1.5 v a l u e may form f i r s t . I n low boron c o n t e n t g l a s s e s ( x < x ), l o n g r a n g e d i f f u s i o n o f boron i s h i n t e r e d d u r i n g t h e second c r y s t a l l i z a t i o n s t e p P by t h e bcc Fe z o n e s a l r e a d y formed. The a g g r e g a t e s g i v e s t h u s a f i r s t m e t a s t a b l e b o r i d e which i s o b v i o u s l y d i f f e r e n t frooPf)e3B'El a s r e c e n t l y shown b y J. WELFRINCER( 3 1 ) .
T i l l now, t h e r e i s no c l e a r e v i d e n c e t h a t a demixion p r e v a i l s i n o t h e r b i n a r y g l a s s e s . I n p a r t i c u l a r , t h e d e n s i t y v a r i e s l i n e a r l y w i t h x i n a l l t h e o t h e r g l a s s e s
( 9 ) . The s l o p e change of t h e d e n s i t y i n Fe-B g l a s s e s seems t h e r e f o r e t o b e a s p e c i - f i c f e a t u r e of t h i s system. However, it i s w o r t h n o t i c i n g t h a t t h e o t h e r c o n s i d e r e d g l a s s e s a r e formed form t r a n s i t i o n m e t a l s whose c r y s t a l l i n e s t r u c t u r e i s close-packed u n l i k e bcc Fe. F o r s u c h g l a s s e s , no s i g n i f i c a n t change of t h e d e n s i t y is t o b e expec- t e d below x ( p r o v i d e d x l i s h i g h e r t h a n t h e l o w e r l i m i t of t h e amorphous composi- t i o n r a n g e ) ' i f t h e
&
s t r u c t u r e r e s e m b l e s t h a t of t h e p u r e m e t a l . N e v e r t h e l e s s , some p r o p e r t i e s l i k e t r a n s p o r t p r o p e r t i e s s h o u l d b e s e n s i t i v e t o t h e e x i s t e n c e of a demixion and p r o v i d e f u r t h e r c h e c k s of o u r d e s c r i p t i o n .F i n a l l y , t h e Fe-(X, X') g l a s s e s a r e a l s o r e l e v a n t t o t h i s d e s c r i p t i o n . For example, S i B g l a s s e s (x < xl) e x h i b i t d r a s t i c changes of a l l t h e i r p h y s i c a l
:::~::LBs~oY
l i l i c o n c o n c e n t r a t i o n s yl depending of x . I n t h e framework of t h e above d e s c r i p t i o n , i t i s p o s s i b l e t o c a l c u l a t e yl b y assuming t h a t , due t o s t r o n g r e p u l s i o n s between m e t a l l o i d s p e c i e s which a v o i d forming S i - S i , B-B and B-Si p a i r s , s i l i c o n e n t e r s f i r s t t h e A zones s u b s t i t u t i n g f o r Fe atoms u n t i l t h e AFe.order i s maximum. Assuming t h a t xlF%oes n o t depend on t h e s i l i c o n c o n t e n t , y1 i s d e f i n e d by :where
B1
= 0.29 c o r r e s p o n d s t o t h e maximum c h e m i c a l o r d e r i n a random network of c o m p o s i t i o n M ( 3 2 ) . E x p e r i m e n t a l v a l u e s of yl t a k e n from t h e s l o p e changes of d e n s i t y, ' m i c r o h a r d n e s s , q u a d r u p o l e splitting ( 3 3 ) and i n i t i a l permeabjli- t y (343 measurements i n Fe-Si-B g l a s s e s a r e s a t i s f a c t o r i l y a c c o u n t e d f o r by e q u a t i o n
161
a s shown i n figure 5 ( s o l i d l i n e ) . The agreement i s improved b y t a k i n g = 0.25 (dashed l i n e ) which s u g g e s t s t b a t the mean F e - & c o o r d i n a t i o n i n t h e A zones i s c l o s e t o 8 a s i n bcc i r o n . The packing f r a c t i o n qM = 0 . 6 9 c a l c u l a t e d from t h e d e n s i t y Fe measurements o f HASEGAWA and RANJAN RAY (35) a l s o s u p p o r t s t h i s a s s u m p t i o n .c r i p t i o n o f M-X g l a s s e s w h i c h a p p e a r s w e l l s u T t e d t o a c c o u n t f o r t h e p e e u l a r i t i e s o f i r o n b a s e d g l a s s e s . However, we b e l i e v e t h a t t h i s d e s c r i p t i o n may a l s o p r o v i d e so- me u n d e r s t a n d i n g o f t h e s t r u c t u r e o f o t h e r s t e r e o c h e m i c a l l y d e f i n e d g l a s s e s ( f o r i n s - t a n c e r a r e e a r t h - t r a n s i t i o n m e t a l g l a s s e s ) .
B e s i d e s t h e n e e d o f a d i r e c t c h e c k o f t h i s d e s c r i p t i o n b y c o m p u t e r m o d e l l i n g M-X n e t w o r k s f o r d i f f e r e n t c o m p o s i t i o n s , i t s h o u l d b e i n t e r e s t i n g t o f u r t h e r s t u d y t h e Cwo f o l l o w i n g a s p e c t s . On t h e o n e h a n d , t h e l i m i t e d e x t e n t o f t h e c o m p o s i t i o n p l a - n e s i n t r o d u c e s l i n e a r d e f e c t s a s a n a t u - r a l c o n s e q u e n c e o f t h e e x i s t e n c e o f t h e
0.12 0.16 0.20 X g l a s s y s t a t e . T h e d e f e c t d e n s i t y may b e
c r u d e l y e s t i m a t e d f o r a { 4 , 4 , 4$ twin- n i n g s e q u e n c e a s d "J n 1-2 w h e r e
F i g u r e 5 n 1 5 i s t h e mean numberaof t w i n n i n g p l a - S i l i c o n c o n c e n t r a t i o n yl i n F e Si n e s p e r c o h e r e n t d o m a i n , l e a d i n g t h u s t o g l a s s e s . The s o l i d l l n e was 1-x-y y x d c 1014
-
1015 cm cm-3* w h i c h s h o u l d b e c a l c u l a t e d w i t h e q / 6 / b y u s i n g (3 = 0 . 2 9 u s e f u l i n t h e i n t e r p r e t a t i o n o f t h e o u t - and the line fiy using51 s t a n d i n g m e c h a n i c a l p r o p e r t i e s of t h e g l a s -( 0 f r o m ( 3 3 ) , B from ( 3 4 ) ) . s e s . I n t h e r e c e n t m o d e l s o f SADOC ( 3 6 ) , t h e c l o s i n e . o f d e n s e domains bv sets of
-
d e f e c t s a n d L o c a l d i s t o r s i o n s a r e a l s o n a t u r a l c o n s e q u e n c e s o f t h e mapping a non eu- c l i d i a n s p a c e o n t o t h e c a r t e s i a n s p a c e .
On t h e o t h e r hand, t h e d e s c r i p t i o n seems t o b e a b l e t o p r o v i d e a g u i d e f o r c a l c u - l a t i n g t h e r m o d y n a m i c a l d a t a ( 2 4 ) . As t h e s t r u c t ~ t r a l o p e r a t i o n s c a n t a k e p l a c e a t t h e u n d e r c o o l e d l i q u i d - g l a s s i n t e r f a c e ( 1 9 ) , t h e e x i s t e n c e of c l u s t e r s d e f i n i n g i n t e r - n a l s u r f a c e s l e a d s t h e M-X g l a s s e s t o b e a l s o r e l e v a n t t o t h e k i n e t i c " f l a k i n g 1 ' model of PHILIPS f o r t h e g l a s s t r a n s i t i o n ( 3 7 ) w h i l e i t h a s a l r e a d y b e e n e m p h a s i z e d b y t h i s a u t h o r t h a t t h e m e t a l l i c p r i s m w e l l c o r r e s p o n d s t o h i s g l a s s f o r m i n g c o n d i - t i o n ( 3 8 ) . A c c o r d i n g t o him, t h e maximum g l a s s f o r m i n g t e r d e n c y may b e e x p e c t e d when t h e d e m i x i o n b e g i n s a n d t h u s c r e a t e s t h e b e s t d e f i n e d i n t e r n a l s u r f a c e s w h i c h a c t a s b a r r i e r s a g a i n s t c r y s t a l l i z a t i o n , i . e . a r o u n d x < x < xl as i t is i n d e e d o b s e r v e d . Acknowledgements
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E n l i g h t e n i n g d i s c u s s i o n s w i t h Dr. P.H. GASKELL a r e g r a t e f u l l y ack- nowledged. We t h a n k D r . J . P . SENATEUR f o r t h e c e n t r a l p a r t o f f i g u r e 2 t a k e n f o r m h i s t h e s i s ( P a r i s 1 9 6 7 ) .BIBLIOGRAPHY
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( 1 9 7 9 ) 4 6 5 . ( 2 1 ) E . NOLD, S . STEEB, P . LAMPARTER, Z. N a t u r f o r s c h .35
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21-8
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