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Submitted on 1 Jan 1980
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MODELLING OF THE SHORT-RANGE ORDER IN
GLASSY METALLIC ALLOYS
M. Popescu
To cite this version:
JOUBNAL DE PHYSIQUE Colloque C8, suppl&nen& au n08, Tome 4 1 , aoct 2980, page Cg-309
MODELLING O F THE SHORT-RANGE ORDER IN GLASSY NETALLIC ALLOYS
M.A. Popescu
I n s t i t u t e of Physics and TechnoZogy of Materials, Bucharest, P.O. Box MG.7, Romania
Abstract.- A new model for the structure of the metallic glasses M4Me was developed. DRPSU model (dense random packing of structural units) is based on the predominant metal-metalloid interaction. The calculated data from the relaxed model are in good agreement with the experimental data. The glass annealing process was successfully simulated.
1 . f n t r o d u c t i o n .
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The s t r u c t u r e o f g l a s s y m e t a l l i c a l l o y s h a s been t h e sub- j e c t of a l o t of p a p e r s d u r i n g l a s t y e a r s b u t up t o day no d e f i n i t e c o n c l u s i o n s were r e ached. The g l a s s y m a t e r i a l s i n t h e s y s t e m t r a n - s i t i o n m e t a l CM)- m e t a l l o i d (Me) a r e found o n l y i n a f a i r l y narrow composition r a n g e , u s u a l l y l e s s t h a n 1 0 a t . % w i d e , c e n t r e d on % 78-80 a t . % M ( i . e . a t Q, M4Iie c o m p o s i t i o n ) . A l l t h e s e g l a s s e s show almost t h e same d i f - f r a c t i o n p a t t e r n . The f i r s t narrow i n t e n s e peak is f o l l o w e d by l a r g e r ones w i t h de-c r e a s i n g i n t e n s i t y . The second peak h a s a p e c u l i a r s h a p e : on i t s high a n g l e s i d e t h e r e i s a s h o u l d e r which i s more o r l e s s p r o m i n e n t , depending on t h e t y p e of a l l o y .
Various s t r u c t u r a l models were d e v i s e d
i n o r d e r t o e x p l a i n t h e e x p e r i m e n t a l r e - s u l t s on M-Me g l a s s e s . The m o d e l l i n g re-
s u l t s have shown t h a t t h e dense random pack- i n g of h a r d s p h e r e s (DRPHS) r e p r o d u c e s , q u a l i t a t i v e l y , t h e main s t r u c t u r a l f e a t u r e s o f t h e g l a s s e s
/I/.
The DRPHS models o r i g i -its h o l e s . P o l k found t h a t t h e composition of t h e g l a s s c o r r e s p o n d i n g t o t h e f i l l i n g of a l l h o l e s i s 7 9 . 1 a t
%
!4-
2 0 . 9 a t .%
Me i n agreement w i t h t h e g l a s s y c o m p o s i t i o n p r e p a r e d by quenching t h e m e l t s .The q u a l i t a t i v e agreement between DRPHS
models and experiment i s f a r from p e r f e c t ( e . g . t h e s p l i t second peak i n t h e r a d i a l d i s t r i b u t i o n f u n c t i o n (RDP) is n o t c o r r e c t - l y r e p r o d u c e d ; t h e c a l c u l a t e d d e n s i t y is much lower t h a n t h e e x p e r i m e n t a l o n e ) . An Amportant improvement o f t h e model was a c h i e v e d u s i n g s o f t r e p u l s i v e p o t e n t i a l s 1 4 1 - C a r g i l l 1 1 1 / 5 / h a s found t h a t r e l a x e d random p a c k i n g o f s p h e r e s w i t h p r e s c r i b e d " t e t r a h e d r o n p e r f e c t i o n " g i v e s much b e t t e r models t h a n s i m p l e DRP, f o r m e t a l l i c g l a s - s e s . I n o r d e r t o e x p l a i n t h e deepening 0-f t h e e u t e c t i c i n t h e p h a s e diagram o f g l a s s f orming a l l o y s , r e c e n t l y Boudreaux sug- g e s t e d t h a t t h e g l a s s s t r u c t u r e may con- sist o f some r e l a t i v e l y w e l l d e f i n e d mole- n a t e s from t h e w i d e l y a c c e p t e d s u g g e s t i o n c u l a r u n i t s / 6 / .
given by P o l k / 2 / a c c o r d i n g t o which t h e Based on t h e above i d e a we developed a m e t a l atoms a r e p o s i t i o n e d a s i n a DRPHS new model f o r t h e M4Me g l a s s , c o n s i s t i n g assembly d e r i v e d from t h e B e r n a l model /3/, o f a random assembly o f s p e c i a l b u i l d i n g
t h e s m a l l e r metialloid atoms b e i n g p l a c e d i n u n i t s .
c8-3 10 JOURNAL DE PHYSIQUE
2 . D R P S U Cdense random p a c k i n g o f s f r u c t u r a l u n i t s ) model
The p a r t i a l c o v a l e n c y o f t h e M-Me bond l e a k u s t o t a k e a s a b a s i c s t r u c t u r a l u n i t f o r t h e M4Me g l a s s , a m e t a l l o i d atom s u r - rounded by a number o f m e t a l atoms which v a r i e d i n a n a r r o w r a n g e (10-13 atoms a s s u g g e s t e d by some e x p e r i m e n t a l d a t a ) . Such s t r u c t u r a l u n i t s were b u i l t by i n t e r c o n - n e c t i n g s p e c i a l n y l o n dodecapodes ( f o r me- t a l atoms) a n d t e t r a p o d e s ( f o r m e t a l l o i d a t o m s ) . A s p a t i a l model was d e v i s e d by pack-
i n g t o g e t h e r 1 0 s u c h u n i t s . The h o l e s de- f i n e d by t h e i n t e r c o n n e c t e d u n i t s were f i l - l e d by t e t r a p o d e s ( m e t a l l o i d ) and t h u s new s t r u c t u r a l u n i t s were formed, s i d i l a r s t o t h e above d e s c r i b e d o n e s . The f i n a l s t r u c - t u r e emerged a t a n a t u r a l d e n s e p a c k i n g o f s 80 a t . % M and 20 a t
.%
M e . The model s i z e was 1 6 0 atoms (33 M e and 1 2 7 M). The c o o r - d i n a t e s o f t h e atoms were r o u g h l y measured.3 . R e l a x a t i o n .
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I n o r d e r t o b e r e a l i s - t i c t h e model must b e e n e r g e t i c a l l y r e l a x e d . The main p r o b l e m is t h e c h o i c e o f t h e ade- q u a t e i n t e r a c t i o n p o t e n t i a l . F o r t h e M-Me c o v a l e n t f o r c e which a c t s w i t h i n t h e s t r u c - t u r a l u n i t i t i s n a t u r a l t o u s e t h e w e l l - known bond s t r e t c h i n g p o t e n t i a l-
: where ro i s t h e e q u i l i b r i u m d i s t a n c e M-Me and a is a c o n s t a n t . A s f o r t h e M-M i n - t e r a c t i o n , a Lennard-Jones p o t e n t i a l (VLJ) can be u s e d b u t t h e r e a r e d i f f i c u l t i e s o f c o r r e c t c h o i c e of t h e c o n s t a n t s o f V1 and V m , Moreover, a s s t a t e d i n o t h e r s i m u l a - t i o n e x p e r i m e n t s , Lennard-Jones p o t e n t i a l p r o v e d t o b e u n a b l e t o g i v e a n a r r o w f i r s t a t o m i c c o o r d i n a t i o n . That Is why we u s e d a l s o a V1 t y p e M-M i n t e r a c t i o n . The M-Me bonds a r e a v o i d e d i n t h e model; t h u s a che- m i c a l bond p r e f e r e n c e was i n t r o d u c e d .The e n e r g e t i c a l r e l a x a t i o n was p e r f o r m e d u s i n g a Monte-Carlo method /7/. Every atom t a k e n a t random was s h i f t e d by a s m a l l a l e - a t o r y d i s t a n c e , t h e i n t e r a c t i o n e n e r g y w i t h i t s n e i g h b o u r s was computed b e f o r e and a f t e r t h i s s h i f t i n g a n d t h e new p o s i t i o n o f t h e atom was r e t a i n e d o n l y when t h e t o t a l e n e r g y d e c r e a s e d . The IBM 370/135 computer o f t h e C e n t r a l I n s t i t u t e o f P h y s i c s
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B u c h a r e s t was u s e d i n c a l c u l a t i o n s .4 . R e s u l t s .
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The bond d i s t a n c e s were s c a l e d t o t h o s e o f a Fe-P a l l o y . The ra- d i u s of Fe and P atom was t a k e n a sA f t e r c 1000 r e l a x a t i o n s t e p s f a t o m t h e minimum e n e r g y c o n f i g u r a t i o n was a t t a i n e d . The RDF and t h e i n t e n s i t y p a t t e r n I ( s ) o f t h e model was computed. The i n t e n s i t y c u r v e ( f i g . 1 ) i s i n e x c e l l e n t agreement w i t h t h e b e s t c u r v e of i n t e n s i t y f o r a Fe-P g l a s s w i t h s i m i l a r composition / 8 / . The shape of t h e second peak i s p e r f e c t l y reproduced a s o p p o s i t e t o t h e o l d DRPS models. As con- c e r n e d t h e RDF ( f i g . 2 ) o n l y t h e peak s i t u - a t e d a t 4 . 8 i s a l i t t l e b i t lower t h a n e x p e c t e d . A f t e r
an
a n a l y s i s o f t h e s t r u c t u r e o f t h e r e l a x e d model we concluded t h a t t h e f i r s t c o o r d i n a t i o n s p h e r e i s t o o much s p r e d and it is p o s s i b l e t o reduce t h e d i s t r i b u --
quenched..-..
anneo/ed F i g . 2-
The RDF h i s t o g r a m o f t h e DRPSU model f o r Fe4P g l a s s < i n s e t : e x p e r i m e n t a1 DRDF o f Fe75P25 g l a s s ) t i o n o f t h e f i r s t n e i g h b o u r s b r e a k i n g some bonds and i n t r o d u c i n g new o t h e r f o l l o w i n g t h e tendency towards bonding e x h i b i t e d by some atoms. A f t e r t r a n s f o r m i n g t h e bonds a r e l a x a t i o n p r o c e s s was c a r r i e d o u t , f i n a l l y a new bond arrangement was i n t r o d u c e d and t h e p r o c e s s was r e p e a t e d u n t i l no more b r e a k i n g of bonds was n e c e s s a r y . So, t h e F i g . 1-
I n t e n s i t y p a t t e r n computed from a n n e a l i n g of t h e g l a s s was s i m u l a t e d . TheDRPlU model f o r Fe4P g l a s s f i n a l model was a n a l y s e d and f i g u r e 1 shows
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q u e n c h e d ;....
a n n e a l e d .c 8 - 3 12 JOURNAL DE PHYSIQUE
h i g h e r and n a r r o w e r . The second s p l i t peak same model a p p l i e d t o Pd4Si g i v e s a d e n s i t y behaves abnormally : w h i l e t h e l e f t - s i d e - component i n c r e a s e s . t h e s h o u l d e r on t h e o f 10.5+0.3 g/cm3 i n e x c e l l e n t agreement 3 w i t h t h e experiment (10.25210.50 gjcm ) . r i g h t s i d e d e c r e a s e s . The o t h e r p e a k s a l s o The d i s t r i b u t i o n s o f t h e c o o r d i n a t i o n
numbers i n t h e model a r e compared w i t h t h a t show an i n c r e a s e d h e i g h t .
of t h e DRPHS model of B e r n a l ( f i g . 3 ) and No i n t e n s i t y d a t a a r e a v a i l a b l e f o r a s -
quenched and a n n e a l e d Fe4P samples b u t w i t h same e x p e r i m e n t a l d a t a . The mean coor- d i n a t i o n number (6c) of t h e m e t a l is 1 3 . 1 , f o r t u n a t e l y t h e r e a r e c a r e f u l measurements
i n good agreement w i t h t h e experiment and on Pd4Si ( t h i s g l a s s h a s t h e same r a d i u s
more l a r g e r t h a n t h a t o f B e r n a l model. The r a t i o a s Fe4P) / 9 / . A remarkable agreement
m e t a l l a i d mean c o o r d i n a t i o n i s . l l , 8 , lower between t h e I ( s ) c u r v e s of t h e model and
t h a n t h e e x p e r i m e n t a l v a l u e (920.9 f o r t h o s e from Pd4Si ( t h e i n s e t i n f i g . 2 ) i s
Pdg4Si16 / 1 1 / ) . The mean number o f Me s u r - r e v e a l e d . The s t r u c t u r a l s e n s i t i v e compo-
rounding a M atom i s 3 . 8 a s compared t o t h e n e n t s of t h e second peak a r e w e l l r e p r o - e x p e r i m e n t a l v a l u e s s i t u a t e d i n t h e range duced. O t h e r s t r u c t u r a l f e a t u r e s of t h e mo- d e l f i t t h e e x p e r i m e n t a l d a t a q u i t e w e l l . The d e n s i t y of t h e Fe4P g l a s s i s 7.09
