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N A T I O N A L R E S E A R C H C O U N C I L O F CANADA O t t a w a , C a n a d a T r a n s l a t i o n T T - 1 4 3 ON T H E MECHANISM O F D I F F U S I O N I N S O L I D S O L U T I O N S O F S U B S T I T U T I O N ( 0 M e k h a n f zme D f f f u z f f v Tverdykh R a s t v o r a k h Z a m e shchenf y a ) by T o A , Lebedev T r a n s l a t e d by
E o
R a b k f n OTTAWA 1950T i t l e :
NATIONAL RESEARCH COUNCIL OF CANADA
Ottawa, Canada
T r a n s l a t i o n TT-143
On t h e Mechanism of D i f f u s i o n i n S o l i d S o l u t i o n s of S u b s t i t u t i o n ,
By: T , A , Lebedev.
R e f e r e n c e : Doklady AkaderniP Nauk, U .S . S .R ,
,
Vol, 6 5 , No, 2 , 1949, p o 162j0T r a n s l a t e d byr E s t h e r Rabkfn
Doklady Akademif Nauk, U.S,S,R,, Vol, 65, No, 2 , 1949 Chemistry S e c t i o n
ON THE hECHANISM OF DIFFUSION I N SOLID SOLUTIONS OF SUBSTITUTION by
T ,
A o Lebedev [ P r e s e n t e d by I ,P o
Bardin, J a n u a r y 15, 1949) T r a n s l a t e d by E s t h e r Rabkin The phenomenon of d i f f u s f on Pn s o l i d s o l u t i o n s p r e s e n t san important f a c t o r from t h e vfewpofnt of t h e h e a t t r e a t m e n t of
a l l o y s . However, up t o t h e p r e s e n t time, t h e r e i s no c l e a r con-
c e p t i o n on t h e mechani sm of t h e m i m a t i o n of t h e d i f f u s i n g atoms
f n t h e c r y s t a l l f n e l a t t i c e , T h i s i s e s p e c i a l l y t r u e of s o l i d
s o l u t i ons of s u b s t i t u t i o n , The e x i s t i n g c o n c e p t i o n s of t h e mecha-
nism of d i f f u s i o n i n s o l i d s o l u t f o n s of s u b s t i t u t i o n a r e e s s e n - t i a l l y deduced from t h e f o l l o w f n g t h r e e a t t e m p t s t o e x p l a i n t h i s phenomenon: ( 1 ) By means of t h e m i g r a t i o n of hole^'^, (2) By means of t h e m f g r a t i o n of t h e so-cabled d i s l o c a t e d atoms ( t h e m i p a t i o n of d i s s o l v e d p a r t f c l e s i n t h e i n t e r s t i c e s of t h e l a t t i c e ) ,
( 3 ) By means of a d i r e c t p l a c e change between two nefgh-
b o u r i n g atoms,
I t may b e c o n s i d e r e d t h a t i n s o l i d c r y s t a l l i n e l a t t i c e s
t h e l a s t two mechanf sms of d i f f u s i o n c a n n o t b e r e a l 1 zed, s i n c e
d i s t o r t i o n of t h e s o l v e n t d u r i n g t h e m i g r a t i o n of t h e d i s - s o l v e d p a r t i c l e s , The f i r s t p r o c e s s may occur, b u t i t i s q u i t e i n s u f f i c i e n t f o r t h e e x p l a n a t i o n of t h e e x i s t i n g d i f - f u s i o n r a t e i n s o l i d s o l u t i o n s of s u b s t i t u t i o n ,
A p a r t i c u l a r l y d i f f f c u l t problem a r i s e s when t r y i n g t o e x p l a i n t h e mechanism of d i f f u s i o n i n s o - c a l l e d molecular s o l i d s o l u t i o n s ( f o r example, i n s o l u t i o n s Cu-A1, Fe-A1,
Ni-SI, and o t h e r s ) , I n f a c t , t h i s problem was n o t even p r e - s e n t e d f o r s o l u t i o n
-
s o e v i d e n t a r e t h e d i f f i c u l t i e s whf ch would be encountered by t h e i n v e s t i g a t o r s d e s i r i n g t o e x p l a f n t h e mechanism of m i g r a t i o n of whole atomic complexes ( f o r example, molecules CuA12, FeSi, FeAl and s o o n ) i n a dense c r y s t a l l i n e l a t t i c e , However, we b e l i e v e t h a t t h e mechanism of d i f f u s i o n f n s o l i d s o l u t i o n s of s u b s t f t u t f on, i n c l u d i n g a l s o m o l e c u l a r s o l i d s o l u t f o n s , may b e s o l v e d i f t h e d i f f u s i o n of d i s s o l v e d p a r t i c l e s i s n o t assumed t o b e due t o a l t e r n a t i n g m i g r a t i o n , b u t t o t h e t r a n s f e r by r o t a t i o n of c e r t a i n atomic groups, The p o s s i b i l i t y of a s i m i l a r m i g r a t i o n of p a r t i c l e s h a s been s u g g e s t e d p r e v i o u s l y '394), b u t i t h a s n o t been deve-l o p e d , However, f f we r e a n a l y s e t h e contemporary s t a t e of t h e problem of t h e mechanism of d i f f u s i o n i n s o l i d s o l u t i o n s of s u b s t i t u t i o n , t h e n i t i s obvious t h a t t h e g r e a t e s t a t t e n - t i o n must be given t o t h e mechanism of d i f f u s i on by means of r o t a t i n g complexes,
A s an example, i n F i g , 1 a r e shown some groups of atoms, which by s i m u l t a n e o u s r o t a t i o n t h r o u g h a c e r t a i n a n g l e , may f r e e l y t r a n s f e r from one p l a c e t o a n o t h e r n o t o n l y p a r t i c l e s such a s atoms, b u t a l s o p a r t i c l e s such a s molecules.
I n a c r y s t a l l i n e s u b s t a n c e e a c h p a r t i c l e i s o b l i g e d t o commensurate i t s k i n e t i c energy w i t h i t s n e i g h b o u r s , t h e r e - f o r e i n a c r y s t a l l i n e l a t t i c e t h e maxima and minima of t h e h e a t e,nergy must n o t have any s h a r p peaks: t h e f l u c t u a t i o n
of t h i s e n e r g y must n o t i n t h i s c a s e f a v o u r n e i t h e r t h e ap- pearance of d i s l o c a t e d atoms, n o r t h e exchange of p l a c e s by
two neighbourfng p a r t i c l e s , I n a c r y s t a l l i n e l a t t i c e t h e i n d i v i d u a l waves ( " ~ p l a s h e s ' ~ ) of h e a t energy must b e s u f f i c i e n t l y v o l u m e t r i c , and, t h e r e f o r e t h e y must d f s t r f b u t e t h e i r e f f e c t on t h e volume of t h e l a t t i c e , It i s n o t d i f f i c u l t t o imagine, t h a t t h e nwnerous and nonunfform c o u n t e r a c t f n g e a c h o t h e r i n one p l a c e and adding i n a n o t h e r s e c t i o n of t h e c r y s t a l l i n e l a t t i c e h e a t energy waves a t any g i v e n moment, e i t h e r compressing o r s t r e t c h i n g i n v a r i o u s d i r e c t i o n s t h e numerous e l e m e n t s of t h e c r y s t a l l f n e l a t t i c e , c o u l d of t e n c r e a t e such s u i t a b l e p a i r s of f o r c e s which would j u s t a s o f t e n b r i n g about r o t a -
t i o n s of i n d l v i d u a l atomic groups around i t s a x i s ( i n v a r i o u s p l a n e s w l t h v a r i o u s i n t e n s i t i e s , q u i t e by a c c i d e n t ) , It i s
e a s y t o d e t e r m i n e t h a t t h e df s t o r t f o n of t h e l a t t i c e durEng
t h e r o t a t i o n of t h e complexes wf 11 prove t o b e s e v e r a l t f m e s s m a l l e r t h a n t h a t f o r t h e above mentianed mechanf sms of
d i f f u s i o n ,
During t h e r o t a t i o n of complexes, shown i n Ff g. 1,
t h e l a t t i c e i s d i s t o r t e d by 10-12 tfmes l e s s t h a n d u r i n g t h e
m f g r a t f o n of d i s l o c a t e d atoms, Elementary c a l c u l a t f o n s show
t h a t t h e a c t f v a t i o n energy f o r t h e r o t a t i o n of atoniic com-
p l e x e s must b e s h a r p l y d e c r e a s e d , if "packagestt having a
t h i c k n e s s of s e v e r a l atomic d l a m e t e r s p a r t i c i p a t e i n t h e r o t a -
t i o n s i n s t e a d of p l a n e complexes w i t h a t h i c k n e s s of one
atomic d i a m e t e r , Thus, from t h e energy p o i n t of view, t h e
d i f f u s i o n mechanism of p a r t i c l e s b y means of r o t a t i o n of
atomic complexes a p p e a r s t o be q u i t e p r o b a b l e and j u s t f f f a b l e ,
On t h e o t h e r hand, many problems connected w i t h t h e
m i g r a t i o n of atoms, and p a r t E c u l e r l y of molecules i n a medium w i t h a dense c r y s t a l l f n e l a t t i c e , a c q u i r e a m i t a b l e explana-
t i o n and c l a ~ ~ f f c a t f o n ,
I n p a r t i c u l a r , G o G e r t s r i k e n and E, Dekhtyas ( 5 )
determined from t h e f r c a l c u l a t i c n s chat t h e d i f f u u f ~ g aeorne
sometfmes exchange p l a c e s a t such d i s t a n c e s which may be
ef t h e r s m a l l e r than o r l a r g e r than t h e normal parameter of
t h e l a t t i c e , From t h e viewpoint of the proposed mechanism of d i f f u s i o n such behavfour of' t h e d f f f u s i n g p a r t i c l e s may be
f u l l y j u s t i f i e d ( t h e r o t a t i o n o r a complex z h r o u g t ~ a l a r g e r o r s m a l l e r a n g l e , see F i g , lj,
How can i t now b e e x p l a i n e d t h a t i n a heteroc- geneous s o l i d s o l u t f o n with a chaot,lz r o t a t i o n of complexes ( a n g l e of r o t a t i o n , magni t u d e , shape and p l a c e of t h e appear- ance of each complex a r e dependent on t h e momentary combina-
t i o n s of t h e i n t e r a c t i n g nonuniform t e m p e r a t u r e atomic v i b r a t i o n s i n t h e a l l o y s ) t h e r e s t i l l must a r t s e a c e r t a i n d i r e c t a d r o t a t i o n of complexes, c a p a b l e of s t r a i g h t e n i n g o u t
t h e c o n c e n t r a t i o n of a g i v e n s o l u t i o n ,
I n F f g , 2 a r e shown t h e complexes 1 and 2 whl.oh, s h a r f n g atom b , can t r a n s f e r I t e i t h e r t o t h e l e f t or t o t h e r f ght
.
The n a t u r e of a s o l i d s o l u t i o n , h e t e r o g e n e o u s a c c o r d f n g t o i t s c o n c e n t r a t i o n , p r o v i d e s d e f i n i t e advantages f o r t h e clockwfse r o t a t i o n of complex 2 , i , e , i t f a c i l i t a t e s t h e m i g r a t i o n of atom b i n a d i r e c t i o n of lower c o n c e n t r a - t i o n s , The f a c t i s , t h a t t h e h i g h e r t h e c o n c e n t r a t i o n of t h e s o l i d s o l u t i o n , t h e more s t r o n g l y d i s t o r t e d i s i t s c ~ y s t a l l l n e l a t t i c e , t h e r e f o r e , each a d d f t f o n a l d i f f u s i o n of new p a r t i c l e s i n t h i s l a t t i c e all e n c o u n t e r from t h e coneentlaated s o l i d s o l u t i o n a c o r r e s p o n d i n g counteract$on,4+ 5 t It i s known t h a t f n o r d e r t o overcorne t h i s c o u n t e r a c t i o n i n some c a s e s i t f s n e c e s s a r y t o i n c r e a s e t h e t e m p e r a t u r e of t h e s o l i d s o l u t i o n so a s t o i n c r e a s e i t s ' t d i s s o l v f n g l ~ p r o p e r t y ,T h e r e f o r e , a t c o m p l e t e l y u n i f o r m s t a t i s t i c a l p o s s i -
b i l i t i e s t h e clockwise r o t a t i o n of complex 2 w i l l be more
p r o b a b l e t h a n t h e r o t a t i o n of complex 1, sincei t h i s r o t a t i o n
may be accompli shed a t l e s s e x p e n d i t u r e of e n e r g y , A l l t h i s l e a d s t o t h e f a c t t h a t d i s s o l v e d p a r t i c l e s i n g e n e r a l w i l l
m i g r a t e from p l a c e s of h i g h e r c o n c e n t r a t i o n t o p l a c e s of lower
c o n c e n t r a t i o n ,
Due t o t h e f a c t t h a t d u r i n g the r o t a t i o n of com-
p l e x e s t h e s u r r o u n d i n g l a t t i c e always e x p e r i e n c e s a def i n i t e
p r e s s u r e due t o t h e s e complexes, which becomes g r e a t e r a s t h e
l a t t i c e i t s e l f becomes more d e n s e , i n a c o l d worked a l l o y t h e
r o t a t i o n of complexes w i l l be l e s s c o n s t r a i n e d and t h e d i f f u -
s i o n r a t e w i l l be h i g h e r , ( 1 n f a c t , e x p e r i m e n t s have l o n g
ago e s t a b l i s h e d a h i g h e r d i f f u s i o n r a t e i n c o l d worked mate-
r i a l s a s w e l l a s a l o n g t h e boundary of t h e p a i n * )
The d i f f u s i o n mechanism by means of t h e r o t a t i o n of
atomic complexes q u i t e c l e a r l y e x p l a i ~ l s t h e s o - c a l l e d c o u n t e r
d i f f u s i o n , Let u s s a y t h a t s i l i c o n d i f f u s e s i n t o I r o n from
p l a c e s of h i g h e r c o n c e n t r a t i o n , t h e n t h e Fe atoms should go
over t o t h e Sf p l a c e s , During the r o t a t i o n of complexes b o t h
t h e s e c o n d i t i o n s a r e s a t i s f i e d : atoms of one element a r e
brought o u t from a g i v e n volume, and atoms of t h e o t h e r element
a r r i v e i n t h e i r p l a c e s ,
I n a d d i t i o n , a s h a s a l r e a d y been s t a t e d , by means
m o l e c u l e s f n t h e c r y s t a l l i n e l a t t i c e ( i n m o l e c u l a r s o l i d s o l u t f o n s ) ,
The t h e o r y of a l l o y s , n o t knowing how t o e x p l a i n
t h e d i f f u s i o n of m o l e c u l e s i n 3015. d s o l u t i o n s p r o c e e d e d a l o n g t h e p a t h of d e n y i n g t h e e x i s t e n c e of m o l e c u l a r s o l i d s o l u t i o n s ( 2 ) , However, t h i s d e s i r e t o a v o i d t h e d i f f i - c u l t i e s of e x p l a i n i n g a gf ven p r o c e s s ( d i f f u s i o n mechanism i n m o l e c u l a r s o l u t i o n ) i s n o t a way o u t , s i n c e r e c e n t l y t h e e x i s t e n c e of m o l e c u l a r s o l i d s o l u t i o n s h a s b e e n f u l l y sub- s t a n t i a t e d ( 6 - 7 ) , T h e r e f o r e , i t i s n e c e s s a r y t o p r o p o s e and d i s c u s s more p r o b a b l e c o u r s e s a l o n g which p r o c e e d t h e
m i g r a t i o n of atoms and m o l e c u l e s I n s o l i d sol-cltiaons of
s u b s t f t u t i o n ,
S e n t t o t h e E d i t o r
L i t e r a t u r e
1, Y a , E o F r e n k e l , Kine t i c T h e o r y of L i q u i d s , p u b l i s h e d b y t h e Academy of S c i e n c e s , USSR, 1945,
2 ,
Z,
J e f f r i e s , T r a n s , A , S o ~ l o E o , 7 0 , 3 0 3 ( 1 9 2 4 ) ~ 3, R , Mehl, M e t a l s Technology, August ( 1 9 3 6 ) -4 . T o A , Lebedev, Theory of A l l o y s , P a r t I , 1934.
5 , C. G e r t s r i k e n and E, D e k h t y a r , Z h u r n a l T e k h n i c h e s k o i F i z i k f , 1 7 , 8 , 8 7 1 ( 1 9 4 7 1 ,
6 ,
F,
~ b r b e r , S t . u , E i s , , 4 8 , 1 4 0 1 ( 1 9 3 6 ) .7 , N o V. Ageev, Nature of t h e Chemical Bond i n M e t a l l i c A l l o y s , M , 1947,
F i g . 1. a
-
one of the possible a t o m i c complexes in plane (001); the rotation of the complex by 90O clock- w i s e .6
-
one of the possible a t o m i c complexes in plane ( 1 11); rotation of the 'complex by 1 8 0 ~ .G e n e r a l Direction of Diffusion ( 0 - 1
-
2F i g . 2 . 1
