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 METALMETALLOID GLASSES. Journal de Physique Colloques, 1982, 43 (C9), pp.C9-67-C9-74. .
HAL Id: jpa-00222425
https://hal.archives-ouvertes.fr/jpa-00222425
Submitted on 1 Jan 1982
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
JOURNAL DE PHYSIQUE
Colloque
C9, supplément
au n012,
Tome 43, décembre
1982
page
C9-67
STRUCTURAL DESCRIPTION OF TRANSITION METAL-METALLOID GLASSES
J.M. Dubois and G. Le Caer
Laboratoire
de Métallurgie
64042 Nancy Cedex,
France
(L.A. 159) ENSMIM, Para de
Saurupt,
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'appuie sur l e s opérations s t r u c t u r a l e s qui permettent de générer l e s composés 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 verres 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 glasses 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 count 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 discussed. Experimental arguments in favour of such a d e s c r i p t i o n
are given which should provide a b a s i s for the prevision of some p r o p e r t i e s of m e t a l lic glasses.
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 crystalline 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 structures 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 justifying 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 measured 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
11
B 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 - Fe 82 B 18 is 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 ) . These r e s u l t s a l l o w assuming t h e m e t a l polyedron 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 evidenced a l o t of s i m i l a r i t i e s i n i r o n based 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 spectrum a o f a-Fe75B25(T=4K)argues i n f a v o u r of 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 only t h i s d i s t r i b u t i o n a t given concentration but a l s o i t s evolution
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
indeed 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 oc1-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 ep 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 changes 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 orthohombic t r a n s i t i o n of t h e (Fe
N i ) B borides ( 6 ) .
1-2 z 3
S t r o n g s i m i l a r i t i e s of t h e d bands a r e observed 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 is 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)
phosphoborides which e x i b i t t h e same s l o p e change of t h e T -composition 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 packing f r a c t i o n q of 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 change 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 of
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 - Secondly, 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
element 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 rs p e c t r o s c o p y i n Fe
B glasses
( 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
of m e t a l l o i d i n t h e E43X compounds.
-
Composition
Method
Z
FesoB20
Fe75Pz5
8.64
R.X.and
8.1
R.X.
5
0.5
Co~l1 P19
8.9
Pd8,,Si16
9.0 + 0-9
Pd7,Ge2,
8.6
+ 0.5
-
neutron d i f .
dif.
R.X.and
neutron d i f .
Referent?
(10)
(11)
(12)
(13)
EXAFS
TABLE 1
(14)
Figure 1
Hyperfine f i e l d d i s t r i b u t i c i ~
o f a Fe 75B2
h~~verfine
f i e l d s i n E'e 6s ( T = 4 R)
3
1
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 ) .
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
glasses
(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
metalloid
and formed from a t r i g o n a l prism 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 metals capping t h e rectangular faces. This i n t e r s t i t i a l s i t e optimizes the
packing 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 remain 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 on 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 of 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
glasses.
<
3. The M-X compounds a s chemically twinned CP s t r u c t u r e s
HYDE,ANDERSON and coworkers (17) 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 can 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 periodically twinning 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 twin p l a n e type ( 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 twinn i n g , t r i l i n g , f o u r l i n g , swinging twinning, e t c . For t h e s a k e of b r e v i t y , we only
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 chemical twinning
3
(18).
The composition 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 every 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 5C 2
( 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
o r i g i n a l hcp p o s i t i o n s t h u s forming almost p e r f e c t hcp b l o c k s . I n Fe3C type 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 prisms 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 prisms. The c h a i n s a r e connected 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 prisms.
I t i s obviously 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
belongs. 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
belong t o t r i g o n a l prisms. The former v a l u e corresponds t o i s o l a t e d prisms 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 prisms. F i n a l l y , when LC < 1 , some o L t h e
metal atoms do n o t belong t o any prism. The O 2 LC 2 12
1 range a l l o w s t h u s scanning t h e 0 5 x 2 0.67 composition
range.
I
A
4 . S t r u c t u r a l d e s c r i p t i o n of M
1
1
I
I
A
X glasses
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, chemical f o u r l i n g i n Fe75 B25, e t c . The l a c k of
long range 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 given
c o h e r e n t l e n g t h 1 , t h e composition 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)
3
p l a n e s which can b e randomly chosen a s composition p l a n e s .
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
the s t r u c t u r a l operation.
I
1
Jn,
,
$
b
The m e t a l l o i d c o n t e n t is simply accounted f o r by chang 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 keeping 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 neighbours 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 prisms 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
prisms. This 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 independency 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
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 ) .
Flgure 2
S c h e m a t i c d r a w ~ n go f t h e s t r u c t u r e o f Fe C and Fe5C2 (tent e r ) and projections o n the ( 1 0 0 ) p l a n e 3 0 f the Fe C strutt 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
( a b o v e ) . The 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 6arked by
arrows ( a f t e r ( 1 8 ) ) .
C9-70
JOURNAL DE PHYSIQUE
The formation 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 parameters 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 composition p l a n e s whose l e n g t h i s c r u d e l y approximat e d by ?r la. 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
patterns
observed by higE 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
15 1;. This 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
a NOLD e t a l . i n a - Fe8o Bzo(21)
by
-
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 belong t o s t r u c t u r a l u n i t s , namely :
-
n
@ 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
t h e aver 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 concent%ation 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 surrounded by more
neighbour.
than one X
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 c
envi?onments :
('
1 - Metal atoms which belong t o t e t r a k a i d e k a e d r a w i t h an average number of
X neighbours 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 (hereafter
1-x x
c a l l e d AX envi?onment)
1 1
.
2 - 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 d
environment).
X
AM
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/2/
1-x
x
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 coherence 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
to
s i t e s without seeing
any X atom a s f i r s t neighbour. 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 aggregates.The demi-zed
g l a s s shows t h u s conc 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 an almost 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 correspond t o
t h e composition a t which they remain j u s t i n c o n t a c t and form a dense packing of
s p h e r e s , t h u s occupying 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
P
r e l a t e d t o x by :
P
P
%
-
.
AM
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 consid 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 neighbours. By n e g l e c t i n g a s a f i r s t approximation 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 presence o r absence 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 provided from computer s i m u l a t i o n s (22, 23) and l e a d t o
0.21 5 a 5 0.26 i f t h e average 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. This c o o r d i n a t i o n number range 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
F i g u r e 4 p i c t u r e s t h i s d e s c r i p t i o n f o r t h e t h r e e c o n c e n t r a t i o n ranges
x > xl,
< x < x1 and x < xp. I n t h e l a t t e r c o n c e n t r a t i o n r a n g e , t h e c o n c e n t r a t i o n
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 range of t h e l i q u i d quenched g l a s s e s ( 0 . 1 <ax < 0 , 3 ) , A cannot s i g n i f i c a n t l y d i f f e r from 10 - 20 A . This range 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 phenomenon from t h e long wavelength f l u c t u a t i o n s (1000 A) a l r e a d y p u b l i s h e d i n t h e literature.
X~
.
Figure 3
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 reM
gions f o r d i f f e r e n t v a l u e s o f xl. Experimental data
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 ) ,
(251,
0 (261, X ( 2 7 ) .
Figure 4
Picture o f t h e structure for
x > x l , xp < x < x l and x < x
P
5. Experimental check of 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 properties-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 chec 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 corresponds t o t h e f o r m a t i o n of pure 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
Fe
zones of composition 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 k v i t y d u r i n g ~ r ~ s t a ~ i i z aX 1
t y! ( ~
2 5~) measurements
~
a l l o w d e t e r m i n i n g t h e experiment 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 cryst 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 = 0.14) ( 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 observed,
a r e l i a b l e composition 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 eq. 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 range
0.15 C x 2 0.16. T h i s c o n c e n t r a t i o n range korresponds t o t h e composition of t h e
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 behaviour of t h e
INVAR
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 magnetic 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 given i n r e f . (15).
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 should 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
C o n c e n t r a t i o n dependent 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
estimate A 5 1 near x
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 observed i n Fe
B glasses for
x 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-iat 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 such 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 (24).
.
Q u a n t i t a t i v e checks 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 ) appear
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 dbvious 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 observed 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 range c o r r e l a t i o n s shown by LAMPARTER e t
a l . (29) i n a - NislB19. 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 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
t a l l i z a t i o n c a s c a d e o f a-Fe7sB2sis Fe B
a-FesoBno ( 3 0 ) . T h i s o b s e r v a t i o n i s cohee 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
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 prisms e v o l v e s when x d e c r e a s e s .
For x = 0.25, 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 is 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
aggregates gives thus a f i r s t metastable
by t h e bcc Fe zones a l r e a d y formed. The
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 by J. WELFRINCER
(31).
ii
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
glasses. I n p a r t i c u l a r , the density v a r i e s l i n e a r l y with x i n a l l the other glasses
( 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 worth 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. For 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 expect e d below x (provided x l i s h i g h e r t h a n t h e lower l i m i t of t h e amorphous composis t r u c t u r e resembles t h a t of t h e pure m e t a l . N e v e r t h e l e s s ,
t i o n range)'if t h e
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 our 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
physical
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 by 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 :
:::~::LBs~oY
'
where B1 = 0.29 c o r r e s p o n d s t o t h e maximum chemical o r d e r i n a random network of
composition M
( 3 2 ) . Experimental 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,
microhardness, quadrupole splitting ( 3 3 ) and i n i t i a l permeabjlit 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 accounted 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 by 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 Fe-&coordination i n t h e A
zones i s c l o s e
Fe
t o 8 a s i n bcc i r o n . The packing f r a c t i o n qM = 0.69 c a l c u l a t e d from t h e d e n s i t y
measurements o f HASEGAWA and RANJAN RAY (35)
a l s o s u p p o r t s t h i s assumption.
6 . C o n c l u s i o n and p e r s p e c t i v e s
We have p r o p o s e d a s t r u c t u r a l desc r i p t i o n of M-X g l a s s e s which 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 of
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 some 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
stereochemically defined glasses (for instance r a r e earth-transition metal glasses).
B e s i d e s t h e need of a d i r e c t c h e c k
of t h i s d e s c r i p t i o n b y computer 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 ,
it should be 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 of t h e composition planes introduces l i n e a r d e f e c t s a s a natur a l consequence of t h e e x i s t e n c e of 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$ twinn i n g s e q u e n c e a s d "J n 1-2where
Figure 5
n 1 5 i s t h e mean numberaof t w i n n i n g p l a n e s p e r c o h e r e n t domain, l e a d i n g t h u s t o
S i l i c o n c o n c e n t r a t i o n yl i n Fe
Si
1-x-y
y x
d c 1014 - 1015 cm cm-3* which s h o u l d b e
g l a s s e s . The s o l i d l l n e was
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 of t h e o u t 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 = 0.29
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 and the
line fiy using51
s e s . I n t h e r e c e n t models o f SADOC ( 3 6 ) ,
( 0 f r o m ( 3 3 ) , B from ( 3 4 ) ) .
t h e c l o s i n e . of d e n s e domains bv sets of
d e f e c t s and 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 euc l i d i a n space onto t h e c a r t e s i a n space.
-
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 thermodynamical d a t a ( 2 4 ) . As t h e s t r u c t ~ t r a lo 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 (37) w h i l e i t h a s a l r e a d y been emphasized
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 forming c o n d i t i o n ( 3 8 ) . According 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 demixion b e g i n s and 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 which 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 - 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 acknowledged. 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 form
h i s t h e s i s ( P a r i s 1967).
BIBLIOGRAPHY
L (1982)
P.H.
GASKELL, P r o c . 4 t h I m t . Conf. R.Q.M.
(2)
P.H.
GASKELL, J . Non C r y s t . S o l .
(3)
P . PANISSOD, D. ALLIIAGA-GERRA,A. AMAMOU, J . DURAND, W.L.
S.J. POON, Phys. Rev. L e t t . 44-22 ( 1 9 8 0 ) , 1465.
(1)
32
Sendai
247
( 1 9 7 9 ) , 207.
JOHNSON, N.L.
CARTER,
(4)
V.S.
POKATILOV, Sov. Phys. Dokl. 26 (3.),(1981),
(5)
J.M.
DUBOIS, G. LE CAER, S o l . S t a t e Comm. i n p r e s s .
(6)
T. KEMENY, I . VINCZE, J . BALOGH, L. GRANASY, B. FOGARASSY, F. HAJDV, E . SVAB,
I n t . Conf. Met. G l a s s e s : S c i e n c e a n d Technology B u d a p e s t (1980).
(7)
M. MATSUURA, T. NOMOTO, F. ITOH, K . SUZUKI, S o l . S t a t e Comm.
(8)
J . DURAND IEEE T r a n s . Mag. MAG 12 (1976) 945.
(9)
P.H.
*
and n o t
GASKELL, Acta M e t .
2
l o f 7 - lo1* a n a n -3 as
(1981) 1203.
given
in ( 1 5 ) .
327.
C9-74
JOURNAL DE PHYSIQUE
( 1 0 ) E. NOLD, P . LAMPARTER, H. OLBRICH, G. RAINER-HARBACH,
3 6 a (1981) 1032.
-
( 1 1 ) Y. WASEDA, RQM 111, B r i g h t o n
2
S . STEEB, Z. N a t u r f o r s c h .
(1978) 352.
(12) J.F.
SADOC, J . DIXMIER, Mat. S c . E n g . 2 ( 1 9 7 6 )
(13) J.F.
SADOC, T h e s i s O r s a y ( 1 9 7 6 ) .
( 1 4 ) T.M. HAYES, J . W . ALLEN, T . TAUC, B.B.
40-9 ( 1 9 7 8 ) 1 2 8 2 .
187.
GIESSEN, J . J . HAUSER, P h y s . R e v . - L e t t .
-
( 1 5 ) J.M.
I n s t r . Methods, i n p r e s s .
DUBOIS, G. LE CAER, N u c l .
( 1 6 ) S . RUNDQVIST, A c t a Chem. S c a n d .
16, ( 1 9 6 2 )
( 1 7 ) B.G. HYDE, S . ANDERSON, M. BAKKER, C.M.
(1979), 273.
Chem.
12,
1.
PLUG, M. OrKEEFFE, P r o g . S o l i d . S t .
( 1 8 ) S . ANDERSON, G. B. HYDE, 3. S o l . S t t a t . Chem.
( 1 9 ) E. PARTHE, J.M.
( 2 0 ) P.H.
9
GASKELL, D . J .
SMITH, C.J.D.
CATTO, J.R.A.
POWELL, P h y s . Rev. B
( 2 3 ) M. AHMADZADEH, A.W.
21-8
1
CLEAVER, N a t u r e
( 2 1 ) E . NOLD, S . STEEB, P . LAMPARTER, Z. N a t u r f o r s c h .
( 2 2 ) M.J.
(1974) 92.
MOREAU, J . L e s s Common M e t a l s x , ( 1 9 7 7 )
35 ( 1 9 8 0 )
281 ( 1 9 7 9 )
465.
610.
(1980) 3725.
SIMPSON, P h y s . Rev. B 25-7 ( 1 9 8 2 ) 4 6 3 3 .
( 2 4 ) C. CUNAT, M. NOTTIN, J . HERTZ, J.M. DUBOIS, C. LE CAER, J. Non C r y s t . S o l . s u b mitted
C. CUNAT, J . HERTZ, J.M. DUBOIS, G. LE CAER, T h i s C o n f e r e n c e .
( 2 5 ) K. DEHGHAN, J.M.
Sol.
DUBOIS, G. LE CAER,C.
TETE, t o b e s u b m i t t e d t o J . Non C r y s t .
( 2 6 ) J.M. DUBOIS, G. LE CAER, S t r u c t u r e o f Non C r y s t a l l i n e M a t e r i a l s 11, C a m b r i d g e
(1982) t o b e p u b l i s h e d .
( 2 7 ) K. OSAMURA, K. SHIBUE, R. SUZUKI, Y. MURAKAMI, S . TAKAYAMA, J . M a t . S c .
(1981) 957.
16
( 2 8 ) L . CSER,I. KOVACS, A. LOVAS, E. SVAB, G . ZSIGMONT, N u c l . I n s t . M e t . i n p r e s s .
( 2 9 ) P . L M A R T E R , W. SPERL, E . NOLD, E. MINER-HARBACH,S.
C o n f . RQM, S e n d a i ( 1 9 8 2 )
STEEB, P r o c . 4 t h I n t .
( 3 0 ) P. DUHAJ, F. HANIC, P h y s . P h y s . S t a t . S o l . ( a ) 62, ( 1 9 8 0 ) 7 1 9 ;
K.P. MIZGALSKI, O.T. INAL, F.G. YOST, M.M. KARNOWSKY, J . M a t . Sc..
16 ( 1 9 8 1 )
3357.
( 3 1 ) J . WELFRINGER, t o b e p u b l i s h e d .
( 3 2 ) J. BLETRY, 7.. N a t u r f o r s c h . a
s (1978)
327.
( 3 3 ) J.M. DUBOIS,G. LE CAER, Mem. S c . R e v u e M e t a l . t o b e p u b l i s h e d
S . AL BIJAT,R. IRALDI, J.M. DUBOIS, G. LE CAER,C. TETE, P r o c . 4 t h I n t . C o n f .
RQM S e n d a i L ( 1 9 8 2 ) 3 7 5 .
( 3 4 ) N.NARITA,
H. FUKUNAGA, 3. YAMASAKI, K . HAM, S u p p . S c i . Rep. RITU
( 3 5 ) R. HASEGAWA, RANJAN RAY. J . A p p l . P h y s . 4 9 - 7
(36) J.F.
A
(1.980) 251
(1978) 4174.
SADOC, J . d e P h y s . 3 ( 1 9 8 0 ) C8-326.
(37) J.C.
PHILIPS " K i n e t i c m o d e l o f t h e g l a s s T r a n s i t i o n " t o b e p u b l i s h e d .
(38) J.C.
PHILIPS, P h y s . S t a t . S o l . ( b )
101 ( 1 9 8 0 )
473.