DEPENDENCE OF DIFFUSION-INDUCED GRAIN BOUNDARY MIGRATION ON GRAIN BOUNDARY STRUCTURE

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DEPENDENCE OF DIFFUSION-INDUCED GRAIN BOUNDARY MIGRATION ON GRAIN BOUNDARY

STRUCTURE

A. King, F.-S. Chen, R.-J. Jahn

To cite this version:

A. King, F.-S. Chen, R.-J. Jahn. DEPENDENCE OF DIFFUSION-INDUCED GRAIN BOUNDARY

MIGRATION ON GRAIN BOUNDARY STRUCTURE. Journal de Physique Colloques, 1988, 49

(C5), pp.C5-617-C5-622. �10.1051/jphyscol:1988578�. �jpa-00228075�

DEPENDENCE OF DIFFUSION-INDUCED GRAIN BOUNDARY MIGRATION ON GRAIN BOUNDARY STRUCTURE

A.H. KING, F.-S. CHEN and R.-J. JAHN

Department o f Materials Science and Engineering, S t a t e U n i v e r s i t y of New York a t Stony Brook, Stony Brook, NY 1 1 7 9 4 - 2 2 7 5 , U.S.A.

/ / /

Resume: D e nombreuses e t u d e s o n t ete e f f e c t & s u r l e c o m p o r t e m e n t d e s j o i n t s d e g r a i ? a u c o u r s d e l a d i f f u s i o n d u z i n c d a n s l e c u i v r e . P o u r l e s j o i n t s d e flexion symetriques il a p p a r a i t que l e s vitesses d e migration s o n t minimales lorsque l e s d e u x g r a i n s s o n t e n position d e coincidence. La p&ne'tration du solute' e s t m a x i m a l e pour c e s joints ainsi q u e l a c o n c e n t r a t i o n d e r r i s r e l e joint a u c o u r s d e s a migration. D e m s m e o n ob- s e r v e un d6veloppement prononc6 d e f a c e t t e s . Les observations effectue's p a r MET in- diquant q u e d e s m6canisms c o m p l e x e s i n t e r v i e n m e n t d u r a n t DIGM: e n p a r t i c u l i e r l e joint e m e t d e s dislocations e t laisse d e r r i k r e lui u n e s u r s a t u r a t i o n s i g n i f i c a t i v e ,en l a c u n ~ s a u c o u r s d e s a m i g r a t i o n . T o u s c e s r 6 s u l t a t s soulignent I'importance d e s d e f a u t s p r e s e n t s d a n s l e joint s u r l a migration elle-mgme.

Abstract: An e x t e n s i v e s e r i e s of e x p e r i m e n t s on t h e behavior of grain boundaries during t h e diffusion o f z i n c i n t o c o p p e r h a s b e e n performed. In s y m m e t r i c a l t i l t bicrystals, i t is found t h a t t h e migration v e l o c i t i e s a r e minimised f o r coincidence-related boundaries, and t h a t t h e s e b o u n d a r i e s a l s o exhibit t h e g r e a t e s t d e p t h p e n e t r a t i o n of solute, t h e highest c o n c e n t r a t i o n o f s o l u t e behind t h e moving boundary a n d t h e m o s t p r o n o u n c e d f a c e t i n g . T r a n s m i s s i o n e l e c t r o n m i c r o s c o p e investigations i n d i c a t e t h a t t h e r e a r e complex d e f e c t p r o c e s s e s o c c u r r i n g during DIGM: notably, i t is f o u n d t h a t s i g n i f i c a n t v a c a n c y s u p e r - s a t u r a t i o n s e x i s t in t h e m a t e r i a l behind t h e moving boundary a n d t h a t dislocations a r e e j e c t e d by t h e boundary. These results a l l s u g g e s t t h e i m p o r t a n c e o f g r a i n b o u n d a r y d e f e c t s in t h e DIGM prpcess itself.

1. Introduction.

D i f f u s i o n i n d u c e d g r a i n b o u n d a r y m i g r a t i o n ( D I C M ) i s n o w a w e l l r e c o g n i z e d phenomenon in which t h e sideways migration of grain boundaries a c c o m o p a n i e s t h e diffu- sion of s o l u t e a l o n g t h e m . T h e r e h a v e b e e n s e v e r a l models proposed t o explain DICM.

S m l t h a n d King (1) a n d a l s o Balluffi a n d Cahn (2) proposed t h e f i r s t mechanism in whlch a n e t v a c a n c y p r o d u c t i o n d u e t o unbalanced fluxes of s o l u t e a n d s o l v e n t along a grain boundary c a n d r i v e t h e c l i m b of dislocations which a r e a s s o c i a t e d w i t h g r a i n b o u n d a r y steps. However, t h e g e n e r a l i t y of t h i s model w a s questioned by Hiilert (31, who a s s e r t e d t h a t t h e observed u n i f o r m i t y o f DIGM w a s inconsistent w i t h a s t r u c t u r e - d e p e n d e n t model.

In a n e w m o d e l , h e p r o p o s e d t h a t t h e d r i v i n g f o r c e f o r DIGM might b e t h e c h e m i c a l p o t e n t i a l g r a d i e n t c a u s e d by c o h e r e n t l y s t r a i n e d l a y e r s l y ~ n g o n d i f f e r e n t s i d e s of a boundary. Although t h i s model has d e m o n s t r a t e d i t s validity in liquid f i l m migration in at l e a s t t w o s y s t e m s (4,5) i t h a s n o t been c o n f i r m e d in d e t a i l for t h e solid s t a t e process of DIGM.

In t h i s paper w e s u m m a r i z e t h e r e s u l t s o f investigations i n t o t h e e f f e c t s of g r a i n boundary s t r u c t u r e o n DIGM, a n d conversely o f t h e e f f e c t s o f DIGM upon g r a i n boundary s t r u c t u r e .

2. Experimental.

A s e r i e s of s y m m e t r i c a l t i l t t y p e p u r e copper bicrystals w i t h a r a n g e of misorienta- t i o n s a b o u t t h e a x i s [001] w e r e grown by t h e Bridgman t e c h n i q u e . T h e m i s o r i e n t a t i o n w e r e r e c h e c k e d a f t e r g r o w t h by m e a n s of t h e L a u e technique. Individual DIGM s p e c i m e n s w e r e c u t f r o m t h e bulk bicrystals in t h e f o r m of s l i c e s a p p r o x i m a t e l y 2 m m thick, with t h e i r planes e i t h e r perpendicular of parallel t o t h e t i l t axis. Each s p e c i m e n w a s rnechani-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988578

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caliy polished by silicon carbide grinding paper as well a s chemically etched in a mixture of equal parts of phosphoric, acetic, and nitric acids for 10 minutes before being encapsu- lated under vacuum with 10 grams of fine brass chips (70% Cu, 30% Zn). The specimens w e r e annealed a t temperatures in t h e DIGM range in order t o investigate t h e e f f e c t s of misorientation upon DIGM. Transmission electron microscopy specimens were prepared by thinning polycrystalline copper, and then annealing under conditions identical t o those used for t h e "bulk" bicrystal experiments. TEM specimens w e r e also prepared from t h e bulk bicrystals by thinning them a f t e r t h e annealing treatment.

3. Results

Migration r a t e variation with misorientat$on.

The mean migration distance was obtained by measuring t h e a r e a of t h e alloyed zone on t h e specimen surface and dividing by t h e original boundary length. The mean migra- tion distance a s a function of misorientation for four annealing t i m e s a r e shown in Fig. I.

No DIGM was observed t o occur for low-angle grain boundaries (<15O), and t h e r e a r e sig- nificant and reproducible variations in t h e migration r a t e among t h e high angle boundaries.

Relatively low migration r a t e s a r e observed for misorientation close t o high coincidence boundaries :jpecifically 5 , 17, 25. These observations d o not change a s t h e boundary r o t a t e 900' t o give another symmetrical t i l t boundary structure.

The forms of t h e migrating boundaries w e r e o b s e r v e d t o t a k e f e w d i s t i n c t t y p e s depending upon t h e misorientation, a s reported elsewhere (6). Notably, faceting of t h e migrating inl.erface was observed only for boundaries within t w o degrees of a coincidence misorientation.

Penetration depth variation with misorientation

In order t o d e t e r m i n e whether or n o t t h e low migration r a t e s of coincidence-related boundaries w e r e associated with low grain boundary diffusivity, t h e specimens were sec- t i o n e d in o r d e r t o m e a s u r e t h e p e n e t r a t i o n depth, which was measured a s t h e largest depth a t which DIGM was observable. The penetration depth showed uniform values for cases where t h e migration was uniform on t h e specimen surface, while t h e results may b e less reliable if a specimen was sectioned near t o a region where DIGM changed directions.

C a r e was therefore taken t o choose t h e cross section in order t o prevent this t y p e of e r - ror. The measured penetration depths a r e normalized by t h e surface migration distance, and plotted versus misorientation in Fit.2. It c a n b e seen t h a t t h e slow-moving bound- a r i e s e x h i b i t l a r g e p e n e t r a t i o n d e p t h s , a n d a r e therefore not associated with low dif- fusivity.

Chemical analysis

The zinc contents of our s?ecimens were determined by means of energy dispersive x-ray spectrometry in a scanning electron microscope, in order t o determine t h e surface and cross-section distributions of solute behind t h e moving boundaries. Our results show fluctuations in t h e solute concentration behind t h e migrating boundaries a s seen in Fig.3, consistent with other works (7). The a v e r a g e z i n c c o n c e n t r a t i o n b e h i n d a n i n d i v i d u a l boundary was d e t e r mined by c a l c u l a t i n g t h e a r e a below t h e concentration profile a n d dividing by t h e a v e r a g e width of t h e alloyed z o n e . T h e m e a n z i n c c o n c e n t r a t i o n vs.

misorientation i s plotted in Fig.4.

It i s noteworthy t h a t t h e slow-moving coincidence boundaries deposited higher solute concentrations than t h e faster "general" boundaries did. The solute concentration distribu- t i o n a l o n g f a c e t s ( a s i l l u s t r a t e d in Fig.3) is also somewhat interesting, since i t is dis- tinctly non-uniform in spite of t h e sharply defined planarity o f t h e facet.

Transmission Electron Microscopy

The TEM results a r e not a s systematic a s t h e results on bulk bicrystals, b u t they d o s e r v e t o illustrate several very important points. A common occurrence i s t h e obser- vation of point d e f e c t clusters in t h e material which is alloyed by DIGM, a s shhown in Fig.5 and Fig.6. In Fig. 5, t h e clusters a r e in t h e form of unresolved c e n t e r s of dilata- tion and some resolvable dislocation loops; and in Fig.6 t h e c l u s t e r s t a k e t h e f o r m o f stacking fau1.t tetrahedra, a s previously reported (8). The difference presumably arises be- cause of differences in t h e r a t e s of migration of t h e g r a i n b o u n d a r i e s i n v o l v e d i n t h e DIGEA, a n d t h e c o n s e q u e n t v a r i a t i o n s in t h e z i n c c o n c e n t r a t i o n l e f t behind them, a s demonstrated above. In copper-zinc, t h e stacking fault e n e r s y i s strongly dependent upon t h e zinc concentration and this will a f f e c t t h e form of t h e clusters. The observation of

d i s t a n c e , a s m e a s u r e d o n t h e s p e c i m e n s u r f a c e , w i t h m i s o r i e n t a t i o n f o r v a r i o u s annealing times.

F i 2 . 2 . T h e r a t i o o f p e n e t r a t i o n d e p t h t o m i g r a - t i o n d i s t a n c e as a function o f misorientation.

Fig.3. T h e s o l u t e d i s t r i b u - t i o n g e n e r a t e d by D I G M u s i n g a C 5 b i c r y s t a l specimen. T h e t o p d i a g r a m i n d i c a t e s t h e o u t l i n e o f t h e a l l o y e d z o n e a n d t h e t w o c u r v e s below a r e c o n c e n t r a - t i o n profiles along t h e lines A C a n d BC, a s d e t e r m i n e d by E D X a n a l y s i s o n t h e s p e c i m e n surface.

t h e s e c l u s t e r s is t a k e n a s s t r o n g e v i d e n c e of t h e emission of point d e f e c t s by t h e moving g r a i n boundaries.

In addition t o t h e e f f e c t s o f t h e moving boundary upon t h e c r y s t a l m a t r i x , s o m e i m p o r t a n t e f f e c t s of DIGM upon t h e moving boundary h a v e been observed. In Fig.5, a f a c e t e d b o u n d a r y i s s e e n w i t h i n a n a l l o y e d region of t h e m a t e r i a l , a n d t h i s would b e presumed t o b e a r e l a t i v e l y immobile boundary. I t is strongly f a c e t e d , a s l o w mobility boundaries a r e commonly observed t o b e in t h e bulk bicrystal studies. In t h i s c a s e , o n e s e t of f a c e t s shows a very c l e a n s t r u c t u r e , w i t h very f e w dislocations, e i t h e r intrinsic o r extrinsic. T h e o t h e r s e t of f a c e t s , however, is s o densely populated w i t h e x t r i n s i c d e f e c t s t h a t i t i s impossible t o resolve t h e m a s individuals. I t would a p p e a r t h a t t h e diffusion

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Fig.4. T h e v a r i a t i o n o f m e a n s o l u t e c o n c e n t r a t i o n behind t h e moving b o u n d a r y w i t h i n i t i a l b o u n d a r y misorientation.

Misorientation, degrees

process drives d e f e c t s a w a y f r o m o n e s e t of f a c e t s a n d f o r c e s t h e m t o c o l l e c t i n t h e o t h e r , o r t h a t t h e e x t r i n s i c d e f e c t s only f o r m o n o n e set of f a c e t s . Figure 7 is a n i m a g e of a DIGM i n t e r f a c e which is e m i t t i n g dislocations into t h e m a t r i x a h e a d of it. This dis- l o c a t i o n emission i s a p p a r e n t l y a c h i e v e d b y t h e r e a c t i o n of grain boundary dislocations t o f o r m t h e m a t r i x d e f e c t s , in a m a n n e r essentially opposite t o t h a t of dislocation absorption by a g r a i n b o u n d a r y . This w o u l d a p p e a r t o b e f a c i l i t a t e d by t h e e x i s t e n c e of ir- r e g u l a r i t i e s in t h e distribution o f dislocations in t h e boundary plane.

Fig.5. T r a n s m i s s i o n e l e c t r o n microscope i m a g e of a f a c e t e d , low mobility boundary in a n a l - loyed region of a copper s a m p l e e x p o s e d t o z i n c v a p o r . N o t e t h e e x i s t e n c e of p o i n t d e f e c t c l u s t e r s i n t h e m a t r i x , in t h e f o r m o f u n r e s o l v e d c e n t e r s o f dilatation. Also n o t e t h a t o n e o f t h e f a c e t s i s relatively f r e e of d e f e c t s , while t h e o t h e r o n e i s a p p a r e n t l y densely populated w i t h t h e m .

showing s t a c k i n g f a u l t t e t r a h e d r a in a n a l - l o y e d r e g i o n o f a c o p p e r s p e c i m e n e x - posed to z i n c vapor.

Fig.7. Transmission e l e c t r o n micrograph i l l u s t r a t i n g t h e e m i s s i o n of dislocations a h e a d of a moving boundary. N o t e t h e c u r v a t u r e of t h e boundary plane, a n d t h e f a c t t h a t t h e d i s l o c a t i o n s w i t h i n t h e b o u n d a r y i t s e l f show c h a n g e s of s p a c i n g a n d o r i e n t a t i o n a t t h e point of emission.

4. Discussion

T h e r e s u l t s in t h i s p a p e r a l l sug- g e s t t h e i m p o r t a n c e of t h e d e t a i l e d d e f e c t processes o c c u r r i n g d u r i n g DIG M.

I t h a s b e e n s h o w n t h a t t h e p r e v i o u s l y d e m o n s t r a t e d l o w m o b i l i t y o f c e r t a i n b o u n d a r i e s i s n o t simply r e l a t e d t o l o w diffusivity in t h o s e boundaries, s i n c e t h a t w o u l d y i e l d a c o n s t a n t r a t i o of d e p t h p e n e t r a t i o n t o migration d i s t a n c e , a n d a c o n s t a n t v a l u e of m e a n s o l u t e c o n c e n t r a - tion i n t h e alloyed zone, i r r e s p e c t i v e o f misorientation. We find, r a t h e r , t h a t t h e low mobility boundaries e x h i b i t relatively l a r g e p e n e t r a t i o n d e p t h s a n d d e p o s i t higher c o n c e n t r a t i o n s o f s o l u t e b e h i n d t h e m t h a n d o t h e m o r e "general" bound- a r i e s . I t i s t h e r e f o r e c l e a r t h a t t h e a m o u n t of m i g r a t i o n t h a t o c c u r s p e r m o l e of s o l u t e passing down t h e boundary varies w i t h t h e misorientation, a n d t h e r e - f o r e w i t h t h e boundary s t r u c t u r e .

T h e p e n e t r a t i o n d e p t h a n d t h e d e p o s i t e d s o l u t e c o n c e n t r a t i o n m a y b e s e e n a s d e p e n d i n g u p o n t h e c o r n p e t i n ; <

processes of diffusion a n d g r a i n boundary migration, since diffusion t r a n s p o r t s t h e s o l u t e d o w n t h e g r a i n b o u n d a r y , while migration t r a n s p o r t s t h e b o u n d a r y a w a y f r o m t h e s o l u t e , d e p o s i t i n g i t i n t h e rriatrix. F o r f a s t m o v i n g b o u n d a r i e s , t h e n , i t w o u l d b e e x p e c t e d t h a t t h e

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p e n e t r a t i o n d e p t h s would b e shallow, a n d t h e s o l u t e c o n c e n t r a t i o n s would b e small, a s w e o b s e r v e . W e n o t e t h a t t h e s o l u t e c o n c e n t r a t i o n behind t h e moving boundary is n o t i n t h e r m o d y n a m i c equilibrium with t h e z i n c vapor p r e s s u r e o v e r t h e s p e c i m e n , b e c a u s e i t would t h e n t a k e a c o n s t a n t value i r r e s p e c t i v e of misorientation.

T h e variation of s o l u t e c o n c e n t r a t i o n along a well defined f a c e t , a s shown in Fig.3 a l s o provides e v i d e n c e o f t h e n a t u r e of t h e e f f e c t s o f grain boundary s t r u c t u r e o n DIGM response. F a c e t planes a r e generally believed t o b e t h e s l o w e s t moving planes if t h e y develop during a migration process, a n d t h e plane shown i n Fig.3 would a p p e a r t o f i t t h i s c h a r a c t e r i z a t i o n . However, t h e c o n c e n t r a t i o n of s o l u t e i s v e r y variable a l o n g t h i s plane a n d t h i s would a p p e a r t o i n d i c a t e a wide variation of driving f o r c e for migration, if i t is in a n y w a y r e l a t e d t o t h e s o l u t e c o n c e n t r a t i o n . It would t h u s a p p e a r t h a t if t h e v e l o c i t y o f migration r ~ o r m a l t o t h i s plane i s c o n s t a n t , t h e mobility of t h e boundary plane m u s t b e t h e controlling f a c t o r , r a t h e r t h a n t h e driving force. In t h e dislocation c l i m b mechanism, t h e mobility o f a boundary p l a n e depends upon t h e d e t a i l s o f t h e dislocations a n d t h e i r a s s o c i a t e d s t e p s within t h a t plane (1,2) s o t h e mobility c a n b e z e r o for c e r t a i n planes, a n d t h i s m a y well b e t h e c a s e here.

P o i n t d e f e c t c l u s t e r s observed in t h e alloyed z o n e s i n d i c a t e t h e p r e s e n c e o f s i g - n i f i c a n t super:;aturations of t h e m i n t h e moving boundaries, a s might b e e x p e c t e d if dis- location c l i m b i s involved in DIGM. The n a t u r e of t h e c l u s t e r s varies f r o m boundary t o boundary, being dislocation loops i n s o m e c a s e s a n d s t a c k i n g f a u l t t e t r a h e d r a i n others.

This would a p p e a r t o result f r o m variations in s t a c k i n g f a u l t energy, which is strongly d e - p e n d e n t o n z i n c c o n c e n t r a t i o n in alpha-brass, a n d also upon t h e deposited s u p e r s a t u r a t i o n which will depend upon t h e g r a i n boundary velocity, m u c h a s t h e z i n c c o n t e n t itself does.

We n o t e t h a t t h e s e c l u s t e r s a r e only observed f o r c e r t a i n c a s e s , which would a p p e a r t o correspond t o boundary migration v e l o c i t i e s within a c e r t a i n r a n g e (7).

Finally, t h e e j e c t i o n of dislocations f r o m a grain boundary is t h e i n v e r s e process o f dislocation absorption, a n d i t is e x p e c t e d t o result in a n i n c r e a s e in t o t a l energy. E j e c - t i o n would only b e e x p e c t e d t o o c c u r if a higher e n e r g y configuration e x i s t e d within t h e grain boundary, a n d t h i s might result f r o m t h e c l u s t e r i n g of dislocations i n t h e i n t e r f a c e , caused by variations in t h e c l i m b velocity of t h e d e f e c t s . Our dislocation e j e c t i o n obser- vations a r e a s s o c i a t e d w i t h inhomogeneous dislocation distributions in t h e g r a i n boundaries.

5. Conc1usion:j

T h e d e t a i l s of t h e phenomena a s s o c i a t e d w i t h DIGM a r e s t r o n g l y d e p e n d e n t u p o n t h e s t r u c t u r e o f t h e m i g r a t i n g b o u n d a r y . M i g r a t i o n v e l o c i t y , p e n e t r a t i o n d e p t h a n d deposited s o l u t e c o n c e n t r a t i o n a r e a l l functions of boundary misorientation. O t h e r d e f e c t processes such a s point d e f e c t deposition a n d dislocation e j e c t i o n a l s o a p p e a r t o depend upoh t h e d e t a i l s of t h e grain boundary s t r u c t u r e .

Acknowledgment

This work w a s supported by t h e National S c i e n c e F o u n d a t i o n u n d e r g r a n t n u m b e r DMR 8601433.

R e f e r e n c e s

1. D.A. S m i t h a n d A.H. King: Philos. Mag. A, 44 (1981) 333.

2. K.W. Balluffi and J.W. Cahn: A c t a Met., ~ T 9 8 1 ) 493.

3. M. Hillert: S c r i p t a Met.,

11

4. Y.-J. Baik a n d D.N. Yoon: A c t a Met.,

2

5. W.-H. Rhee, Y.-D. Song a n d D.N. Yoon: A c t a Met., 3 5 (1987) 57.

6. Fu-Sen C h e n a n d A.H. King: S c r i p t a Met.,

20

7. T.J. P i c c o n e , D.B. B u t r y m o w i c z , D.E. N e w b u r y , J.R. M a n n i n g a n d J.W. Cahn:

S c r i p t a Met.,

16

8. R.J. J a h n a n d A.H. King: Philos. Mag. A,

54