DIFFUSION INDUCED GRAIN BOUNDARY MIGRATION IN Ni(Zn) POLYCRYSTALS

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DIFFUSION INDUCED GRAIN BOUNDARY MIGRATION IN Ni(Zn) POLYCRYSTALS

R. Fournelle, B. Giakupian, W. Gust, B. Predel

To cite this version:

R. Fournelle, B. Giakupian, W. Gust, B. Predel. DIFFUSION INDUCED GRAIN BOUNDARY

MIGRATION IN Ni(Zn) POLYCRYSTALS. Journal de Physique Colloques, 1988, 49 (C5), pp.C5-

593-C5-598. �10.1051/jphyscol:1988574�. �jpa-00228071�

JOURNAL DE PHYSIQUE

Colloque C5, suppl6ment au nO1O, Tome 49, octobre 1988

DIFFUSION INDUCED GRAIN BOUNDARY MIGRATION IN Ni(Zn) POLYCRYSTALS

R.A. FOURNELLE, B. GIAKUPIAN*

,

^W. GUST" and B. PREDEL*

Dept. of Mechanical Engineering, Marquette University, Milwaukee, WI 53233, U.S.A.

ax-~lanck-~nstitut

fiir Metallforschung and Institut fiir Metallkunde, Seestrasse 92, 0-7000 Stuttgart 1, F.R.G.

A b s t r a c t

-

D i f f u s i o n induced g r a i n boundary m i g r a t i o n (DIGM) has been i n v e s t i g a t e d i n t h e Ni(Zn)system f o r t h e f i r s t time by z i n c i f i c a t i o n o f pure Ni p o l y c r y s t a l s . The morphology o f t h e r e a c t i o n has been s t u d i e d on s e c t i o n s p a r a l l e l and perpendicular t o t h e specimen surface. I n a d d i t i o n t o DIGM, d i f f u s i o n induced r e c r y s t a l l i z a t i o n (DIR) has a l s o been observed. The experimental r e s u l t s show t h a t t h e boundary m i g r a t i o n v e l o c i t y d u r i n g DIGM i s s t r o n g l y dependent on t h e annealing temperature. Also, t h e v e l o c i t y depends on t h e depth below t h e n i c k e l surface. The g r e a t e r t h e depth, t h e s m a l l e r t h e v e l o c i t y . Concentration p r o f i l e s have been measured by energy d i s p e r s i v e X-ray a n a l y s i s (EDX). The Zn c o n c e n t r a t i o n depends on both t h e annealing c o n d i t i o n s and t h e depth below t h e surface. The c o n c e n t r a t i o n p r o f i l e s were used as t h e b a s i s f o r c a l c u l a t i n g t h e d r i v i n g force, t h e g r a i n boundary d i f f u s i v i t y and t h e g r a i n boun- dary m o b i l i t y .

1. I n t r o d u c t i o n

-

Under c e r t a i n c o n d i t i o n s t h e d i f f u s i o n o f s o l u t e atoms i n t o a pure metal along a g r a i n boundary (GB) can cause t h e boundary t o m i g r a t e l e a v i n g behind an a l l o y e d zone (AZ). This phenomenon, which i s r e f e r r e d t o as d i f f u s i o n induced g r a i n boundary m i g r a t i o n (DIGM), has a l r e a d y been s t u d i e d i n several b i n a r y systems; e.g., Fe(Zn) C1,21, Cu(Zn) C33, Cu(Au), Ag(Au) C41, W(Cr) C51 and Ag(Pd) [63.

A t t h e s t a r t o f DIGM, a l l o y e d zones (AZs) i n t h e form o f bulges growing i n t o g r a i n i n t e r i o r s a r e observed t o form a t v a r i o u s places along GBs near t o o r a t t h e metal surface. W i t h i n t h e AZs t h e enrichment o f a l l o y element, which i s u s u a l l y t r a n s p o r t e d t o t h e GBs through t h e vapor phase, i s d e t e c t a b l e by means o f c o n c e n t r a t i o n measure- ments. How h i g h t h i s c o n c e n t r a t i o n i s depends on t h e experimental c o n d i t i o n s .

GB m i g r a t i o n d u r i n g DIGM can be d i v i d e d i n t o two types, t h a t i n which o n l y forward m i g r a t i o n occurs and t h a t i n which an o s c i l l a t i n g back and f o r t h motion i s observed [7]. I n a d d i t i o n , t h e phenomenon o f d i f f u s i o n induced r e c r y s t a l l i z a t i o n (DIR), i n which f i n e g r a i n s w i t h a h i g h s o l u t e atom concentration form on t h e metal surface, has been found t o occur. These f i n e g r a i n s grow i n t h e same way as t h e AZs f o r DIGM, exhi b i t i n g both forward and o s c i 1 la t i n g GB motion. The GB m i g r a t i o n v e l o c i t i e s have been measured f o r v a r i o u s systems as a f u n c t i o n o f t h e annealing temperatures and times [I-3,8], and i t has been found t h a t t h e v e l o c i t y increases w i t h i n c r e a s i n g tem- perature. No d e f i n i t e i n f o r m a t i o n on t h e i n f l u e n c e o f t h e depth below t h e metal s u r - f a c e on the GB m i g r a t i o n e x i s t s . This has been s t u d i e d f o r t h e f i r s t time i n t h e pre- s e n t work.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988574

C5-594 JOURNAL DE PHYSIQUE

Concentration p r o f i l e s have been determined f o r t h i n f o i l s as w e l l as f o r t h i c k sam- p l e s . A c l e a r decrease o f t h e s o l u t e atom c o n c e n t r a t i o n w i t h i n c r e a s i n g depth below t h e s u r f a c e has been shown [I-31. The GB d i f f u s i v i t y and m o b i l i t y i n DIGM boundaries have been c a l c u l a t e d using t h e c o n c e n t r a t i o n p r o f i l e s f o r v a r i o u s systems [I-31. Both q u a n t i t i e s increase e x p o n e n t i a l l y w i t h temperature. With reference t o t h e d r i v i n g f o r c e f o r DIGM, no d e f i n i t i v e statements have y e t been made. It has been proposed t h a t t h e d r i v i n g f o r c e f o r GB m i g r a t i o n i s m a i n l y o f chemical n a t u r e [9].

2. Experimental D e t a i l s

-

The p o l y c r y s t a l l i n e Ni (3N7 m e t a l l i c p u r i t y , 3N4 t o t a l p u r i t y ) used was i n t h e form of 9 mm diameter d i s k s about 1 mm t h i c k . The d i s k s were c u t from a Ni r o d by spark erosion, cleaned, ground and polished. They were then annealed f o r 18 h a t 1073 K i n q u a r t z g l a s s capsules evacuated t o 1 x Pa ( 8 x 1 0 ' ~ T o r r ) and subsequently cooled s l o w l y i n a i r . With t h i s treatment t h e g r a i n s a t t a i n e d a s i z e s u i t a b l e f o r DIGM measurements. Powder o f a s i n t e r e d Ni

-

50 a t . % Zn a l l o y served as a Zn source.

The p o l y c r y s t a l l i n e Ni specimens and t h e Zn source were annealed i n evacuated q u a r t z g l a s s capsules a t v a r i o u s temperatures i n t h e range from 721 t o 973 K f o r v a r i g u s l e n g t h s of time. The capsules were quenched i n water w i t h o u t breaking i n o r d e r t o a v o i d p o s s i b l e undesirable influences o f water on t h e specimen surface. For f u r t h e r s t u d i e s t h e samples were c a r e f u l l y p o l i s h e d and subsequently etched ( 7 ml a c e t i c acid, 27 ml 65% n i t r i c acid, 7 ml d i s t i l l e d water

[lo])

f o r examination by l i g h t and scanning e l e c t r o n microscopy (LM, SEM)

.

3. Experimental Results

-

M i g r a t i o n o f GBs c o u l d c l e a r l y be seen on a l l samples w i t h t h e t y p e o f m i g r a t i o n being o f two main types, o r d i n a r y and o s c i l l a t i n g . For o r d i n a r y m i g r a t i o n , t h e GB can m i g r a t e i n e i t h e r one (Fig.1) o r b o t h (Fig.2) d i r e c t i o n s away from i t s o r i g i n a l l o c a t i o n . For t h e l a t t e r case t h e m i g r a t i n g GB o f t e n e x h i b i t e d an

"S" shape (Fig.2). For t h e o s c i l l a t i n g t y p e o f m i g r a t i o n an a l t e r n a t i n g f o r w a r d and backward m i g r a t i o n o f t h e GB occurs.

I n a d d i t i o n t o t h e above two types o f GB m i g r a t i o n , DIR was observed d u r i n g sample p r e p a r a t i o n . The r e g i o n s i n which DIR had occurred c o n s i s t e d o f f i n e Zn r i c h g r a i n s d i s t r i b u t e d over t h e e n t i r e sample s u r f a c e and c o u l d a l r e a d y be seen w i t h t h e l i g h t microscope a f t e r a l i g h t p o l i s h . With f u r t h e r p o l i s h i n g t h e DIGM morphology appeared a b r u p t l y a t a c e r t a i n depth z below t h e sample surface. Some f i n e DIR g r a i n s c o u l d s t i l l be seen i n t h e m i c r o s t r u c t u r e w i t h most o f these b e i n g on t h e GBs (Fig.3). The number o f Zn r i c h DIR g r a i n s became smaller and s m a l l e r w i t h f u r t h e r p o l i s h i n g , and t h e o r i g i n a l GBs c o u l d be more and more c l e a r l y seen. F i n a l l y , none o f t h e o r i g i n a l f i n e g r a i n e d s t r u c t u r e was l e f t , and o n l y t h e o r i g i n a l GBs w i t h t h e i r AZs remained.

For t h e d e t e r m i n a t i o n o f t h e t r u e average AZ w i d t h i ( d i s t a n c e from o r i g i n a l GB l o c a - t i o n t o t h e m i g r a t i n g boundary) t h e method o f Luck [ll] was used. According t o t h i s method

where R 1 i s t h e average o f t h e apparent AZ w i d t h s w'.

The GB m i g r a t i o n v e l o c i t y v was determined from t h e slopes o f t h e i4 versus t graphs (Fig.4), where t i s t h e annealing time. Because d i f f e r e n t average w i d t h s fi a r e ob- served f o r d i f f e r e n t depths z, t h e average AZ w i d t h was f i r s t determined as a f u n c - t i o n o f t h e depth below t h e sample s u r f a c e (Fig.5). Subsequently, t h e GB m i g r a t i o n v e l o c i t y a t v a r i o u s temperatures f o r d i f f e r e n t depths was determined from these curves (Fig.6). For a given temperature t h e v e l o c i t y v decreases w i t h i n c r e a s i n g depth z such t h a t a l i n e a r r e l a t i o n s h i p between v and t h e f u n c t i o n l/(az+b) i s found.

Here a and b a r e a d j u s t a b l e parameters.

F i g . 1 Fig.2 Fig.3

Micrograph showing DIGM i n Micrograph showing t h e DIR. Fine grained s u r f a c e o n l y one d i r e c t i o n from t h e S-mechanism f o r DIGM. 18 h l a y e r along g r a i n bounda- o r i g i n a l g r a i n boundary. a t 775 K, z = 10 vm. r i e s observed a t a depth

195 h a t 721 K, z = 10 vm. z = 5 pm below t h e surface.

AZ = a l l o y e d zone. 1080 min a t 775 K.

Fig.4

Measurements o f t h e m i g r a t i o n d i s t a n c e as a f u n c t i o n of t h e annealing t i m e f o r several d i f f e r e n t depths below t h e specimen s u r f a c e a t 911 K.

t 9 I

Fig.5

Measurements o f t h e m i g r a t i o n d i s t a n c e as a f u n c t i o n o f t h e depth below t h e specimen s u r f a c e a t 911 K.

Concentration p r o f i l e s , which g i v e t h e Zn c o n c e n t r a t i o n i n t h e AZs as a f u n c t i o n o f t h e depth below t h e sample surface, were determined u s i n g energy d i s p e r s i v e X-ray a n a l y s i s (EDX). The p r o f i l e s (Fig.7) show an exponential decrease w i t h i n c r e a s i n g depth. I n each AZ t h r e e measurements, from which i t was hoped t h a t a d d i t i o n a l i n f o r - mation about whether and how t h e Zn c o n c e n t r a t i o n w i t h i n a c e r t a i n a l l o y e d zone changed, were made. However, these measurements d i d n o t p r o v i d e any e x a c t d e t a i l s about whether t h e Zn content w i t h i n an AZ remains constant o r whether i t changes

r e g u l a r l y i n any way.

C5 -5 96 JOURNAL

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Fig.6

M i g r a t i o n v e l o c i t y as a f u n c t i o n o f t h e depth below t h e ~ u r - f a c e a t several annealing tempe- r a t u r e s .

Fig.7

Concentration p r o f i l e s o f specimens z i n c i f i d a t several annealing temperatures and times.

xo Iwt?/~Zn)

973K 2h L6.8

o 911K 5h 5.5

A 858K 10h 9.1 n 721K 195h 19.8

* o A exp.

caIc.

0

0 53 100 150

z (pml

*---I

-

-1co

^I

i --'\--fl=\ 7 ( 3 rn)

I

Fig.8

\'

D r i v i n g f o r c e as a f u n c t i o n o f t h e annealing temperature f o r several d i f f e r e n t depths below t h e sur- f ace.

25 -300

700 800 900 1000

T (Kl

With t h e a i d o f t h e c o n c e n t r a t i o n p r o f i l e s , t h e d r i v i n g force, d i f f u s i v i t y and m o b i l - i t y can be determined. For t h e d e t e r m i n a t i o n of t h e d r i v i n g force AG t h e r e l a t i o n - ship,

was used [2]. Here xzn i s t h e mole f r a c t i o n o f Zn a t v a r i o u s depths. Fig.8 g i v e s t h e dependence of t h i s d r i v i n g force on t h e temperature f o r v a r i o u s depths.

A mass balance equation was used by A. Bogel f o r c a l c u l a t i n g t h e d i f f u s i v i t y as t h e t r i p l e product s6Db [12]. From t h i s equation t h e f o l l o w i n g equation r e s u l t s :

1

l o g x ( z ) = l o g xo

- _mb m

^{. z .}

I n 10

Here x ( z ) i s t h e s o l u t e atom c o n c e n t r a t i o n immediately behind t h e GB a t a depth z,xo i s t h e s o l u t e atom c o n c e n t r a t i o n on t h e surface, v(z! i s t h e m i g r a t i o n v e l o c i t y a t t h e depth z, s i s t h e segregation f a c t o r , 6 i s t h e g r a i n boundary w i d t h and Db i s t h e g r a i n boundary d i f f u s i o n c o e f f i c i e n t . Consequently a l o g x ( z ) versus

z

p l o t should g i v e a s t r a i g h t l i n e from whose slope t h e s6Db values can be determined.

Values o f s6Db obtained i n t h i s way a r e presented i n Fig.9.

The c a l c u l a t i o n o f t h e m o b i l i t y M i s c a r r i e d o u t u s i n g t h e equation,

where Vm i s t h e molar volume [2]. The Arrhenius p l o t (Fig.9) shows t h e temperature dependence o f M.

4. Discussion

-

Consideration o f t h e R versus z diagram (Fig.5) shows unexpectedly t h a t two of t h e curves i n t e r s e c t one another. T h i s i n t e r s e c t i o n may be caused by t h e o s c i l l a t i n g mechanism of GB m i g r a t i o n mentioned p r e v i o u s l y , o r by t h e i n f l u e n c e o f oxygen. When t h e GB m i g r a t i o n o s c i l l a t e s t h e GB f i r s t migrates i n one d i r e c t i o n en- r i c h i n g t h e AZ i n Zn. Then i t pauses, migrates backward, pauses, and then m i g r a t e s forward again, e t c . If t h e time and t h e temperature of t h e f i r s t pause a r e d i f f e r e n t from sample t o sample f o r t h i s process, then i t would be imaginable t h a t t h e R versus z curves c o u l d i n t e r s e c t one another. The presence o f t h e oxygen d u r i n g t h e e x p e r i - ment i s h a r d l y avoidable. I t i s presumed t h q t h e t h i n water s k i n on t h e i n n e r w a l l s o f t h e q u a r t z capsules and t h e oxygen absorbed around each powder p a r t i c l e a c t as.

oxygen sources [13]. Therefore, one c o u l d imagine t h a t v a r i o u s oxygen c o n c e n t r a t i o n s c o u l d e x i s t on t h e m i g r a t i n g GBs and cause them t o m i g r a t e d i f f e r e n t l y , l e a d i n g t o an i n t e r s e c t i o n o f t h e R versus

z

curves.

-

t

a Fig.9

2

Arrhenius p l o t o f t h e g r a i n bound-

VJ a r y d i f f u s i v i t v and t h e a r a i n

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Considerations o f t h e fi versus t graph (Fig.4) shows immediately t h a t t h e b e s t f i t l i n e s do n o t pass through t h e o r i g i n . On t h e c o n t r a r y , t h e y i n t e r s e c t t h e 4 a x i s a t some f i n i t e v a l u e o f t h e AZ w i d t h 4. T h i s c o u l d mean t h a t t h e m i g r a t i o n o f c e r t a i n GBs would have a l r e a d y occurred a t zero time. T h i s , o f course, does n o t correspond t o t h e f a c t s . One p o s s i b l e e x p l a n a t i o n f o r t h i s i s t h a t a t t h e s t a r t o f GB m i g r a t i o n t h e v e l o c i t y v i s h i g h e r than a f t e r t h e GB has m i g r a t e d a d i s t a n c e o f about 1 t o 2 pm and a t t a i n e d a steady s t a t e . Our measurements a r e r e l a t e d t o t h e steady s t a t e case. For an unknown reason t h e GB m i g r a t i o n apparently occurred v e r y r a p i d l y a t t h e s t a r t o f anneal i n g

.

T h i s r a p i d m i g r a t i o n was b a r e l y measureable and, t h e r e f o r e , was n o t con- s i d e r e d i n t h i s study.

I n order t o determine a mathematical expression f o r t h e v versus z curve, which completely d e s e r i bes t h e dependence o f t h e m i g r a t i o n v e l o c i t y on t h e depth, t h e f o l l o w i n g f a c t o r s must be taken i n t o c o n s i d e r a t i o n (A. Bogel [12]):

1. The expression z i s a m o n o t o n i c a l l y i n c r e a s i n g f u n c t i o n . 2. For z

-*

0, X ( Z ) -t x0.

3. For z ^-+ 0 t h e f u n c t i o n v ( z ) must y i e l d a f i n i t e value f o r v.

4. For z - > a , v -t 0.

A f u n c t i o n , which f u l f i l l s t h e above c o n d i t i o n s and agrees w i t h t h e experimental v versus z curve, i s

where a and b a r e a d j u s t a b l e parameters. As a consequence a l / v ( z ) versus z p l o t e x h i b i t s a s t r a i g h t l i n e , from whose slope and i n t e r c e p t a and b can be determined.

By i n t e r p o l a t i o n o f t h e l / v ( z ) versus z diagram f o r equal depths t h e v versus z diagram (Fig.6) can be determined f o r a l l samples.

I n Fig.7 t h e c a l c u l a t e d c o n c e n t r a t i o n p r o f i l e s f o r t h e f o u r d i f f e r e n t temperatures a r e shown. The c a l c u l a t i o n was accomplished by means o f Eqs.(3) and ( 5 ) . Thus, f o r every depth z t h e corresponding Zn c o n t e n t and f o r every temperature t h e correspond-

i n g c o n c e n t r a t i o n p r o f i l e c o u l d be determined. With reference t o t h i s f i g u r e , i t should be mentioned t h a t f o r depths z

<

10 pm, the c a l c u l a t i o n o f t h e Zn concentra- t i o n c o u l d n o t be c a r r i e d out, because Eq.(5) f a i l s i n t h i s range. However, t h e con- c e n t r a t i o n a t xo i s g i v e n by Eq.(3) f o r z = 0, so t h a t t h e p r o f i l e i n t h i s range can a t l e a s t be presented g r a p h i c a l l y .

References

[l] M. H i l l e r t and G.R. Purdy, Acta Met. 26 (1978) 333.

[2] L i Chongmo and M. H i l l e r t , Acta Met. 29 (1981) 1949.

[3] L i Chongnio and M. H i l l e r t , Acta Met. 30 (1982) 1133.

[[I] J.W. Cahn, J.D. Pan and R.W. B a l u f f i , S c r i p t a Met. 1 3 (1979) 503.

[5] F . J . A . den Broeder, Acta Met. 20 (1972) 319.

[6] K.N. Tu, J. Appl. Phys. 48 (1977) 3400.

[7] L i Chongmo, Scand. J. M e t a l l u r g y 11 (1982) 179.

[8] F.J.A. don Broeder, S c r i p t a Met. 17 (1983) 399.

[9] M. H i l l e r t , The Mechanism o f Phase Transformations i n C r y s t a l l i n e S o l i d s , Mono graph and Report Series No. 33, The I n s t i t u t e o f Metals, London (1969) 231.

[lo]

G. Petzow, Metallographisches ~ t z e n , Materialkundlich-Technische Reihe 1, Gebruder Borntraeger, B e r l i n (1976) 81.

[ll] R. Luck, 2 . M e t a l l k . 66 (1975) 488.

[12] 6. Giakupian, Diploma Thesis, U n i v e r s i t y o f S t u t t g a r t (1987) 59.

[ I 3 1 T . J . Picc:one, D.B. Butrymowicz, D.E. Newbury, J.R. Manning and J.W. Cahn, S c r i p t a Plet. 16 (1982) 839.