GRAIN BOUNDARY DIFFUSION - STRUCTURAL EFFECTS AND MECHANISMS

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GRAIN BOUNDARY DIFFUSION - STRUCTURAL EFFECTS AND MECHANISMS

A. Atkinson

To cite this version:

A. Atkinson. GRAIN BOUNDARY DIFFUSION - STRUCTURAL EFFECTS AND MECHANISMS.

Journal de Physique Colloques, 1985, 46 (C4), pp.C4-379-C4-391. �10.1051/jphyscol:1985441�. �jpa- 00224692�

JOURNAL DE PHYSIQUE

Colloque C*, supplement au n"it, Tome *6, avril 1985 page C4-379

GRAIN BOUNDARY DIFFUSION - STRUCTURAL EFFECTS AND MECHANISMS

A. Atkinson

Materials, Development Division, Building 552, AERB Harwell, Didaot, Oxfordshire 0X11 ORA, U.K.

Résumé - Cet article prend en compte les différentes justifications obtenues quant aux relations existant entre la structure des joints de grains et la diffusion. Pour tout matériau la structure des joints est fonction de la géométrie, de la ségrégation du soluté, et dans le cas de certains composés - tels les oxydes - de la non-stoechiométrie. On étudiera l'influence de ces paramètres sur la diffusion aux joints de grains de quelques matériaux cfc, comparera des matériaux bicristallins et polycristallins de même que des métaux et des céramiques.

Toutes les expériences desquelles on a pu déduire quelquechose concernant le mécanisme de la diffusion aux joints de grains suggèrent qu'elle résulte d'une concentration particulièrement élevée de défauts ponctuels qui se dirigent de façon préférentielle vers le coeur du joint où leur mobilité est encore plus élevée que dans le réseau.

Abstract - This paper considers the available evidence for relationships between grain boundary structure and diffusion. In any one material the boundary structure is a function of geometry, solute segregation and, in the case of compounds (e.g. oxides), non-stoichiometry. The effect of these parameters on boundary diffusion in some fee materials is examined and comparisons made between bicrystal and polycrstalline material and between metals and ceramics.

All experiments from which inferences can be made concerning the mechanism of grain boundary diffusion suggest that it takes place by an enhanced concentration of point defects segregated preferentially to the boundary core where they are also more mobile than in the lattice.

INTRODUCTION

There is now in existence a large body of data concerning diffusion in crystalline solids and a corresponding understanding of the atomistic mechanisms which are involved. Thus, for bulk diffusion, the relationships between structure and diffusion are described by the energies required to form and move point defects, such as vacancies or interstitials, and their mutual interactions. A similar situation has not yet been reached for diffusion along grain boundaries despite the fact that such diffusion often controls many technologically important processes, particularly at 'low' temperatures. The data which do exist for grain boundary

diffusion are relatively sparse and of lower quality and poorer reproducibility than the corresponding data for lattice diffusion because of experimental difficulties. Nevertheless, in recent years there have been considerable improvements in understanding and observing the structures of grain boundaries.

Can these lead to a link between grain boundary structure and diffusion?

In this paper we first consider the phenomenological description of grain boundary diffusion and then survey the evidence for variation of diffusion properties with

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985441

C4-380 JOURNAL DE PHYSIQUE

m i s o r i e n t a t i o n a c r o s s t h e boundary. We then c o n s i d e r the r e l a t i o n s h i p between d i f f u s i o n i n i n d i v i d u a l b i c r y s t a l boundaries and d i f f u s i o n i n a p o l y c r y s t a l l i n e mass and the i n f l u e n c e of s e g r e g a t i o n on boundary d i f f u s i o n . The d i f f e r e n c e s i n behaviour between m e t a l s and ceramic m a t e r i a l s a r e then explored and f i n a l l y t h e i m p l i c a t i o n s concerning l i k e l y d i f f u s i o n mechanisms a r e d i s c u s s e d . Many of t h e experimental d a t a considered here a r e not new and have been discussed i n s e v e r a l e a r l i e r reviews [I-41. In t h i s paper the emphasis i s on what new d a t a a r e a v a i l a b l e and looking a t t h e o l d e r r e s u l t s i n a s l i g h t l y d i f f e r e n t way.

1. GRAIN BOUNDARY DIFFUSION EXPERIMENTS

The usual phenomenological d e s c r i p t i o n of g r a i n boundary d i f f u s i o n r e p r e s e n t s t h e boundary a s a s l a b of width 6 i n which t h e d i f f u s i o n c o e f f i c i e n t D ' i s g r e a t e r than D i n t h e surrounding l a t t i c e . Thus t h e f i r s t s t r u c t u r a l a s p e c t of a boundary t h a t we must c o n s i d e r i s i t s width. A l l evidence from c a l c u l a t i o n s , d i r e c t o b s e r v a t i o n s

and t h e d i f f u s i o n experiments themselves now i n d i c a t e s t h a t 6 5 1 nm (wherever a value f o r 6 i s r e q u i r e d i n t h e subsequent d i s c u s s i o n it w i l l be assumed t o be

1 nm). Since 6 i s so small t h e 3-dimensional s l a b model is r a t h e r q u e s t i o n a b l e . N e v e r t h e l e s s , t h e model does allow a l l observable f e a t u r e s of d i f f u s i o n experiments t o be described ( e - g . p r o f i l e s of t r a c e r c o n c e n t r a t i o n v e r s u s depth) and is

t h e r e f o r e a convenient way i n which t o summarise t h e experiments.

The experiments themselves may be c a r r i e d o u t i n d i f f e r e n t k i n e t i c regimes and use a va i e t y of techniques. In t h e regime of n e g l i g i b l e l a t t i c e d i f f u s i o n ,

(Dt)$ << 6 and named type C by Harrison [ 5 ] , t h e boundary d i f f u s i o n c o e f f i c i e n t , D ' , may be measured d i r e c t l y . To o p e r a t e i n t h i s regime low t e p e r a t u r e s and s h o r t anneal times, t , a r e r e q u i r e d because 6 i s so small. When (Dt)? >> 6, which i s more usual and named type B, then experiments y i e l d t h e d i f f u s i o n parameter P = D'6. In a s o l i d s o l u t i o n f o r which t h e r e i s s e g r e g a t i o n t o t h e s l a b with a s e g r g a t i o n c o e f f i c i e n t a , then P = aD'6 and t h e c o n d i t i o n f o r type C d i f f u s i o n i s (Dt): << a6.

The b e s t d a t a come from those experiments i n which a t r a c e r depth p r o f i l e i s measured s i n c e i n t h i s case P i s p r a c t i c a l l y independent of t h e e f f e c t i v e boundary c o n d i t i o n a t t h e specimen s u r f a c e [61. I n some experiments, only t h a t depth of p e n e t r a t i o n a t which t h e t r a c e r can j u s t be d e t e c t e d i s measured (e.g. by autoradiography). This i s not an a c c u r a t e method, but probably g i v e s r e a s o n a b l e comparative values. The r e s u l t s of e a r l y experiments were analysed using F i s h e r ' s approximate s o l u t i o n of t h e d i f f u s i o n e q u a t i o n s r a t h e r than t h e more a c c u r a t e s o l u t i o n s of Suzuoka ( t h i n f i l m boundary c o n d i t i o n ) and Whipple ( c o n s t a n t s u r f a c e c o n c e n t r a t i o n ) . LeClaire [6] compared t h e t h r e e s o l u t i o n s and e s t i m a t e d t h e l i k e l y e r r o r s t h a t could a r i s e from using F i s h e r ' s s o l u t i o n . He concluded t h a t i n

s e c t i o n i n g experiments t h e l i k e l y e r r o r s i n P a r e t y p i c a l l y a f a c t o r of 4 and i n a c t i v a t i o n energy, Q ' , 0.2 t o 0.3 eV.

2. INFLUENCE OF MISORIENTATION ACROSS THE BOUNDARY

This . t o p i c has been l i t t l e s t u d i e d i n r e c e n t y e a r s and t h e o n l y new d a t a a r e t h o s e of Osenbach and Stubican [ 7 ] f o r C r d i f f u s i o n i n [I001 t i l t boundaries i n MgO. In t h i s s e c t i o n t h e e a r l i e r work is summarised and compared with t h e s e more r e c e n t r e s u l t s .

2.1 P a s a f u n c t i o n of m i s o r i e n t a t i o n

The key q u e s t i o n s t o be answered h e r e a r e "do a l l workers observe s i m i l a r e f f e c t s ? "

and " i s t h e r e any evidence f o r low v a l u e s of P a t some m i s o r i e n t a t i o n s ? " I n o r d e r to address these q u e s t i o n s t h e a v a i l a b l e d a t a f o r a v a r i e t y of systems with f c c s t r u c t u r e s , and f o r both [I001 and [I101 t i l t boundaries i n b i c r y s t a l specimens, have been assembled i n Figures 1 and 2. In some experiments [8,9,141 t h e d a t a a r e o n l y a v a i l a b l e a s p e n e t r a t i o n d e p t h , y , of d i f f u s a n t a s a f u n c t i o n of t i l t a n g l e , 0. Since under most c o n d i t i o n s t h e c o n c e n t r a t i o n i n t h e boundary i s a f u n c t i o n of p l y 2 [ 6 ] , r e l a t i v e v a l u e s of P were obtained by assuming them p r o p o r t i o n a l t o y2.

F u r t h e r m o r e , i n o r d e r t o make t h e comparison between d i f f e r e n t systems e a s i e r , e a c h d a t a s e t h a s been n o r m a l i s e d w i t h r e s p e c t t o P a t a t i l t a n g l e of 30' ( o r t h e maximum v a l u e of O i f t h i s i s l e s s t h a n 30').

F i g u r e 1 shows t h a t f o r d i f f u s i o n p a r a l l e l t o t h e [I001 t i l t a x i s t h e g e n e r a l t e n e d e n c y i s f o r P t o i n c r e a s e w i t h O t o a maximum v a l u e a t a p p r o x i m a t e l y 45' and t h e n t o d e c r e a s e . P must be z e r o a t 0 and 90' and t h e r e i s no e v i d e n c e of low v a l u e s of P a t i n t e r m e d i a t e m i s o r i e n t a t i o n s . The s t r u c t u r e s of some of t h e s e h o u n d a r i e s i n Cu have heen c a l c u l a t e d by S u t t o n ad V i t e k [I51 and r a t i o n a l i s e d i n t e r m s of s t r u c t u r a l u n i t s i n t h e boundary c o r e .

The c a l c u l a t i o n s i n d i c a t e t h a t c e r t a i n b o u n d a r i e s a r e s t r u c t u r a l l y ' f a v o u r e d ' and a r e composed e n t i r e l y of a b a s i c c o r e s t r u c t u r a l u n i t . At m i s o r i e n t a t i o n s between two f a v o u r e d o n e s t h e boundary s t r u c t u r e i s a m i x t u r e o f t h e two favoured u n i t s . According t o S u t t o n and V i t e k t h e f a v o u r e d b o u n d a r i e s should show up i n g r a i n boundary d i f f u s i o n a s d i s c o n t i n u i t i e s i n dD'/dO w i t h dD'/dO b e i n g n e a r l y c o n s t a n t f o r i n t e r m e d i a t e v a l u e s of O. (They a l s o p o i n t o u t t h a t t h e same b o u n d a r i e s a r e n o t n e c e s s a r i l y f a v o u r e d i n d i f f e r e n t m e t a l s h a v i n g t h e same c r y s t a l s t r u c t u r e and t h e r e f o r e g e n e r a l i s a t i o n can b e m i s l e a d i n g . ) Whether D' i s l a r g e o r s m a l l a t t h e f a v o u r e d boundary depends on t h e a c t u a l c o r e s t r u c t u r e . I n m e t a l s i t i s r e a s o n a b l e t o assume t h a t t h e d e n s e r t h e c o r e t h e lower i s D ' , b u t t h i s i s n o t n e c e s s a r i l y s o f o r i o n i c m a t e r i a l s . For Cu t h e c a l c u l a t i o n s i n d i c a t e t h a t t h e E = 5 c o i n c i d e n c e b o u n d a r i e s ( 0 = 36.9 and 53.1°) a r e f a v o u r e d and t h a t t h e s t r u c t u r a l u n i t s a r e l a t t i c e d i s l o c a t i o n c o r e s . The e x p e r i m e n t a l r e s u l t s i n F i g u r e 1 f o r t h e f c c m e t a l s a r e r e a s o n a b l y i n a c c o r d w i t h t h e s e p r e d i c t i o n s and t h e r e a r e no m i s o r i e n t a t i o n s i n t h e s e b o u n d a r i e s ( o t h e r t h a n t h e p e r f e c t l a t t i c e ) which show low d i f f u s i v i t y . The d a t a f o r Zn i n Al [ 9 ] a r e v e r y d i f f e r e n t from t h e o t h e r s y s t e m s i n t h a t t h e most r a p i d d i f f u s i o n was observed a t t h e s m a l l e s t m i s o r i e n t a t i o n , 0 =9'. T h i s i s n o t c o n s i s t e n t w i t h t h e d a t a f o r Cu i n Al [ 8 ] n o r w i t h t h e d i s l o c a t i o n p i p e model o f low a n g l e b o u n d a r i e s .

For a s y m m e t r i c a l t i l t boundary w i t h O < 313.9~ t h e boundary may he approximated by a n a r r a y of i n d i v i d u a l l a t t i c e d i s l o c a t i o n s ( B u r g e r s v e c t o r b ) w i t h a s p a c i n g R = b / ( 2 s i n 012) and r a d i u s a . I f we assume t h a t f a s t d i f f u s i o n i s r e s t r i c t e d t o t h e c o r e , P i s r e l a t e 6 t o t h e d i s l o c a t i o n d i f f u s i o n c o e f f i c i e n t , Dd, by

The d a t a i n F i g u r e 1 show t h a t t h e p r o p o r t i o n a l i t y between P and O h o l d s

a p p r o x i m a t e l y , even up t o much h i g h e r a n g l e s t h a n might i n i t i a l l y be e x p e c t e d i.e.

when t h e c o r e s a r e no l o n g e r w e l l s e p a r a t e d . The dependence of P on O f o r Cr d i f f u s i n g i n MgO i s s e e n t o b e somewhat d i f f e r e n t from t h a t o b s e r v e d i n t h e m e t a l s i n t h a t P(O)/P(30) i s l a r g e r a t low v a l u e s of O. C a l c u l a t i o n s of [lo01 t i l t boundary s t r u c t u r e s i n N i O [ I 6 1 (which i s i s o s t r u c t u r a l w i t h MgO) i n d i c a t e i n common w i t h m e t a l s a s i m i l a r b a s i s o f s t r u c t u r a l u n i t s c o m p r i s i n g d i s l o c a t i o n c o r e c o n f i g u r a t i o n s . However, i n i o n i c m a t e r i a l s t h e c o r e c o n f i g u r a t i o n s a r e v e r y d i f f e r e n t b e c a u s e of t h e r e q u i r e m e n t t o p r e v e n t i o n s of l i k e c h a r g e b e i n g t o o c l o s e t o g e t h e r . F u r t h e r m o r e , a l l d i f f u s i o n i n MgO i s t h o u g h t t o be dominated by i m p u r i t y e f f e c t s and t h e r e f o r e d i f f e r e n t b e h a v i o u r may b e e x p e c t e d f o r e i t h e r r e a s o n . F i g u r e 2 shows d a t a f o r [ l o o ] t i l t h o u n d a r i e s i n t h e same f o r m a t a s i n F i g u r e 1.

For t h e s e b o u n d a r i e s a l l t h e d a t a a g r e e i n f i n d i n g a smooth i n c r e a s e of P w i t h 0 up t o about 30°. C a l c u l a t i o n s f o r A l [15] i n d i c a t e t h a t E = 27 (0 = 31.6') i s t h e f a v o u r e d boundary w i t h l o w e s t O and h a s a n open s t r u c t u r e i n which D' i s l i k e l y t o b e l a r g e which i s c o n s i s t e n t w i t h t h e e x p e r i m e n t a l d a t a . T h e r e a f t e r t h e r e s u l t s d i v e r g e and a t 40° a r e i n wide d i s a g r e e m e n t . The d a t a s e t s do t e n d t o c o n v e r g e i n t h e r e g i o n 70-80' and t h i s i s c l o s e t o t h e E = 3 c o h e r e n t t w i n boundary (O = 70.5') a l o n g which f a s t d i f f u s i o n i s e x p e c t e d t o be u n l i k e l y . At h i g h e r a n g l e s t h e d a t a a r e v e r y s p a r s e , b u t t h e r e i s an i n d i c a t i o n of a n o t h e r r e g i o n of s i o w d i f f u s i o n c l o s e t o t h e Z = 11 (O = 129.5O) m i s o r i e n t a t i o n which i s a l s o a Pavoured boundary.

C4-382 JOURNAL DE PHYSIQUE

I 1 0 0 1 t l I t I1

0 A g In A g I T H I V P b i n P b ISUI

N i i n N i IUSl

A = Cu i n A l I P I

A Zn i n Al IHBGl C r in M g O 10s)

F i g u r e 1 - Grain boundary d i f f u s i o n (P =

a D ' 6 ) i n [I001 b i c r y s t a l t i l t b o u n d a r i e s p a r a l l e l t o t h e t i l t a x i s a s a f u n c t i o n o f m i s o r i e n t a t i o n and normalised w i t h r e s p e c t t o P a t O = 30' (Refs. 7-12).

Data i s i d e n t i f i e d by a u t h o r s ' i n i t i a l s e.g. HBG r e f . 9).

F i g u r e 2 - As F i g u r e 1 b u t i n [I101 b i c r y s t a l tilt boundaries.

(Refs. 9, 13, 14).

I";+++;+

^{, +} 1

0 0 20 L O 60 80 100 120 140 160 180

100 = ^{T i l t} a n q l e . 8 l d e g l

r

1 ^.;°

? " , 1

11001 t i l t b o u n d a r i e s

1. 27 1 1 3

F i g u r e 3 - Anisotropy of d i f f u s i o n - i n [loo] t i l t b o u n d a r i e s i n MgO and Ag.

(Refs. 7 and 17).

T i l t a n g l e . 8 l d e g l

O + y f 1 ) 1 1 . 5 I I I 3 I 1 1 I 27 I

0 2 0 L O 60 80 100

e [ d o g ) K e y ⁰ ? i n A l I L J )

A A Zn in A l [ H B G )

However, t h e o n l y boundary f o r which t h e r e i s g e n e r a l agreement on i t s having a low d i f f u s i v i t y i s t h e C = 3 coherent t w i n boundary.

2.2 A n i s o t r o p y a s a f u n c t i o n of m i s o r i e n t a t i o n

Anisotropy i n D' i s t o be expected i n g e n e r a l and t o be u a r t i c u l a r l y e v i d e n t i n low a n g l e t i l t boundaries s i n c e d i f f u s i o n p a r a l l e l t o t h e d i s l o c a t i o n c o r e s ( t i l t a x i s ) d e s c r i b e d by e q u a t i o n (1) w i l l be much e a s i e r t h a n p e r p e n d i c u l a r t o them. A s 0 i n c r e a s e s and t h e c o r e s become c l o s e r t o g e t h e r t h e a n i s o t r o p y would be expected t o d e c r e a s e . This g e n e r a l behaviour has been observed f o r [ l o o ] t i l t b o u n d a r i e s i n b o t h Ag and MgO b i c r y s t a l s ( F i g u r e 3). Again, t h e r e i s a s i g n i f i c a n t q u a n t i t a t i v e d i f f e r e n c e between t h e oxide and t h e m e t a l .

2.3 A c t i v a t i o n energy as a f u n c t i o n of m i s o r i e n t a t i o n

I n t h e i r o r i g i n a l work Upthegrove and S i n n o t t , [ l o ] claimed t o observe a d e c r e a s e i n a c t i v a t i o n energy, Q ' , a s O i n c r e a s e d , f o r N i d i f f u s i o n p a r a l l e l t o t h e t i l t a x i s i n [I001 N i t i l t boundaries. This was s u b s e q u e n t l y shown t o be e r r o n e o u s and an a r t e f a c t of u s i n g F i s h e r ' s approximate s o l u t i o n f o r a n a l y s i n g t h e experiments.

Re-analysis [18] i n d i c a t e s t h a t Q ' i s a p p r o x i m a t e l y independent of 8 i n t h e s e boundaries. Q ' i s a l s o approximately independent of 0 f o r s e l f d i f f u s i o n of Ag i n

[ l o o ] tilt b o u n d a r i e s [ l l ] f o r O up t o 16O, but Q' i s s l i g h t l y g r e a t e r f o r O = 28O which i s r a t h e r s u r p r i s i n g . The analogous e x p e r i m e n t s f o r Cr d i f f u s i o n i n MgO [ 7 ] a l s o show Q' t o be independent of O over t h e r a n g e of t h e measurements i . e . up t o

zoo.

There i s t h u s no r e a l evidence of a s y s t e m a t i c v a r i a t i o n of Q' w i t h m i s o r i e n t a t i o n i n any system. A l l t h e r e s u l t s j u s t c i t e d a r e c o n s i s t e n t w i t h t h e l a t t i c e

d i s l o c a t i o n model of low a n g l e b o u n d a r i e s and t h e r e f o r e Q' i s t o he i d e n t i f i e d w i t h t h e a c t i v a t i o n energy f o r d i s l o c a t i o n p i p e d i f f u s i o n .

3. DIFFUSION I N POLYCRYSTALLINE MATERIALS

Boundaries of t h e t y p e c o n s i d e r e d t h u s f a r a r e r a r e l y encountered i n p o l y c r y s t a l l i n e m a t e r i a l . It i s t h e r e f o r e i n s t r u c t i v e t o compare d a t a f o r d i f f u s i o n i n t h e s e simple b i c r y s t a l boundaries w i t h d a t a f o r d i f f u s i o n i n

p o l y c r y s t a l l i n e ' g e n e r a l ' boundaries i n systems where b o t h t y p e s of experiment have been c a r r i e d out. This i s p o s s i b l e f o r s e l f d i f f u s i o n i n N i , Ag and Pb and t h e d a t a a r e shown i n F i g u r e 4. The d a t a i n d i c a t e t h a t , i n terms of a b s o l u t e v a l u e s , t h e disagreement between b i c r y s t a l and p o l y c r y s t a l l i n e specimens i s u s u a l l y l e s s t h a n a f a c t o r of 5 and much of t h i s may r e s u l t from t h e poor p r e c i s i o n of t h e a u t o r a d i o g r a p h i c technique used i n some o f t h e experiments w i t h b i c r y s t a l s . However, t h e r e i s one q u a l i t a t i v e t r e n d which i s d i f f i c u l t t o understand and t h a t i s a tendency f o r Q' measured i n p o l y c r y s t a l l i n e specimens t o he g r e a t e r than Q ' f o r [I001 t i l t b o u n d a r i e s , ( t h i s is p a r t i c u l a r l y e v i d e n t i n t h e c a s e of Pb). S i n c e Q' f o r t h e [ l o o ] t i l t b o u n d a r i e s i s t h e a c t i v a t i o n energy f o r d i s l o c a t i o n d i f f u s i o n t h i s i m p l i e s t h a t d i s l o c a t i o n d i f f u s i o n h a s a lower a c t i v a t i o n energy t h a n 'random' b o u n d a r i e s . T h i s does n o t seem c o n s i s t e n t a t f i r s t s i g h t w i t h o t h e r experiments i n which d i f f u s i o n along low a n g l e b o u n d a r i e s has been measured i n ' s i n g l e c r y s t a l ' specimens f o r Au i n Au 1251 and N i i n N i O [261. The r a t i o Q' ( h i g h a n g l e ) / Q V (low a n g l e ) was 0.76 f o r Au and 0.89 f o r N i O . This may be because lt8w a n g l e b o u n d a r i e s formed by r e c r y s t a l l i s a t i o n of c o l d work c o n t a i n d i s l o c a t i o n s having t h e Burgers v e c t o r of i s o l a t e d l a t t i c e d i s l o c a t i o n s ( o r may be d i s s o c i a t e d ) , whereas t h o s e grown i n t o b i c r y s t a l s w i l l be c o n s t r a i n e d by t h e boundary geometry.

4. SEGREGATION AND DIFFUSION

I n r e c e n t y e a r s s e v e r a l s t u d i e s of t h i s phenomenon i n p o l y c r y s t a l l i n e m e t a l s have been r e p o r t e d and a wide range of e f f e c t s h a s been observed [27]. These i n c l u d e a l l combinations of enhancing o r r e t a r d i n g g r a i n boundary d i f f u s i o n of t h e s o l v e n t o r s o l u t e and t h e e f f e c t can b e b o t h s t r o n g and weak.

JOURNAL DE PHYSIQUE

P o l y c r y s t a l

B i c r y s t a l [ I 0 0 1 t i l t B i c r y s t a l ' h i g h a n g l e '

F i g u r e 4 - Comparison between s e l f d i f f u s i o n i n b i c r y s t a l and p o l y c r y s t a l l i n e specimens of N i , Ag and Pb. (Refs. 10-12 and 19-24).

Sband Fe i n Fe ( S b l a t 550°C

F i g u r e 5 - The i n f l u e n c e of Sb s e g r e g a t i o n F i g u r e 6 - Comparison between l a t t i c e t o Fe boundaries on t h e boundary d i f f u s i o n and g r a i n boundary d i f f u s i o n f o r some of Fe and Sb and t h e coverage of t h e f c c m e t a l s and oxides (Refs. 7,

boundary by Sb (Ref. 28). 19-22 and 33).

F i g u r e 5 [28] i s an example of a r e t a r d i n g e f f e c t i n which a bulk c o n c e n t r a t i o n of 3 x atom f r a c t i o n of Sb i n Fe i s seen to reduce D ' f o r both Fe and Sb

d i f f u s i o n by a f a c t o r of 70 w i t h r e s p e c t t o i t s value i n pure Fe. In F i g u r e 5 i s a l s o shown t h e f r a c t i o n a l coverage of t h e boundary p l a n e by Sb. The form of t h i s isotherm i n d i c a t e s s t r o n g a t t r a c t i v e f o r c e s between Sb atoms i n t h e boundary.

It has been suggested [27] t h a t i n such c a s e s t h e decrease i n atomic m o b i l i t y i n t h e boundary i s because the segregant p r e f e r e n t i a l l y occupies t h o s e s i t e s which would otherwise have high m o b i l i t y and t h a t t h e s t r o n g i n t e r a c t i o n s between s e g r e g a n t atoms produce a r e l a t i v e l y immobile two-dimensional s t r u c t u r e .

I n o t h e r c a s e s , such a s Ag(Ni) 1291, even a s t r o n g s e g r e g a t i o n of s o l u t e has v e r y l i t t l e e f f e c t on boundary d i f f u s i o n (and boundary energy) and t h i s i s presumably because d i f f e r e n t boundary s i t e s and i n t e r a c t i o n s a r e involved.

The only s t u d i e s of doping on boundary d i f f u s i o n i n a ceramic m a t e i r a l a r e f o r C r d i f f u s i o n i n MgO(Cr) b i c r y s t a l s [ 7 ] and U i n UC p o l y c r s t a l s [30]. I n MgO(Cr) P i n c r e a s e s j$nearly with bulk C r c o n c e n t r a t i o n a s does t h e bulk d i f f u s i v i t y of C r (due t o C r doping c r e a t i n g charge-compensating Mg v a c a n c i e s ) . S t u d i e s of C r s e g r e g a t i o n i n p o l y c r y s t a l l i n e MgO [31] i n d i c a t e t h a t t h e s e g r e g a t i o n of C r i s r e l a t i v e l y weak ( a

-

5. DIFFUSION I N CERAMICS

We have a l r e a d y drawn a t t e n t i o n t o some s i m i l a r i t i e s and d i f f e r e n c e s between metals and t h e ceramics MgO and N i O and t h e s e a r e explored f u r t h e r i n t h i s s e c t i o n . Grain boundary d i f f u s i o n i n a range of ceramic m a t e r i a l s has a l s o been t h e s u b j e c t o f a r e c e n t review [32].

5.1 Comparison w i t h m e t a l s

The l a c k of a l a r g e c o n c e n t r a t i o n of h i g h l y mobile e l e c t r o n s i n i o n i c compounds emphasises t h e importance of t h e charge on d e f e c t s and t h e p o s s i b i l i t y of 1

i n t e r a c t i o n s v i a long range e l e c t r i c f i e l d s . Thus i n such m a t e r i a l s g r a i n boundaries w i l l i n g e n e r a l be charged and a compensating space charge w i l l extend i n t o t h e c r y s t a l s on each s i d e of t h e houndary. There then e x i s t s t h e p o s s i b i l i t y of 6 being c o n s i d e r a b l y l a r g e r than 1 nm, a s normally assumed f o r metals.

D i f f u s i o n experiments i n both type B and C c o n d i t i o n s , from which 6 can be deduced, have been c a r r i e d out f o r N i i n both low and high a n g l e boundaries i n Ni0 [26,27]

and f o r C r i n low angle boundaries i n C r 203 [34 J. They i n d i c a t e t h a t 6' i s a l s o approximately 1 nm i n t h e s e m a t e r i a l s and t h a t any enhanced d i f f u s i o n i n t h e space- c h a r g e r e g i o n i s n e g l i g i b l e compared t o t h a t i n the boundary core.

In Figure 6 both D ( f o r t h e l a t t i c e ) and P ( f o r high angle boundaries) have been p l o t t e d a s a f u n c t i o n of Tm/T f o r some f c c m e t a l s and oxides (Tm = melting temperature). This shows t h a t g r a i n houndary d i f f u s i o n of N i i n N i O i s very s i m i l a r t o t h a t i n p o l y c r s t a l l i n e m e t a l s a t an e q u i v a l e n t temperature. (The r e l a t i v e s c a l e s of P and D have been chosen so t h a t i f 6 i s assumed t o be 1 nm, D ' can be read on t h e D s c a l e . ) However, i t i s a l s o e v i d e n t t h a t , a s a f u n c t i o n of Tm/T, D i s g r e a t e r f o r N i i n N i O than i n t h e metals. This r e s u l t s i n some p r a c t i c a l problems i n measuring P i n an o x i d e such a s N i O s i n c e e x p e r i m e n t a l l y we r e q u i r e good d i f f e e n t i a t i o n between l a t t i c e and g r a i n boundary d i f f u s i o n . For example, D 1 / D = 10 f o r N i a t Tm/T f = 1.5, u t f o r N i i n N i O a t Tm/T = 2.25. The corresponding D ' i n N i i s approximately LOq t h a t i n N i O and t h e p r a c t i c a l consequence i s t h a t N i g r a i n boundary d i f f u s i o n i n N i O can o n l y be a c c u r a t e l y measured a t r e l a t i v e l y low temperatures and small d i f f u s i o n depths.

Another p r a c t i c a l problem when working with ceramic m a t e r i a l s i s t h a t t h e i r d i f f u s i o n p r o p e r t i e s a r e very s e n s i t i v e t o i m p u r i t i e s and t h e m a t e r i a l s themselves a r e g e n e r a l l y l e s s pure than metals. Impurity prohlems a r e so s e v e r e i n t h e a l k a l i

C4-386 JOURNAL DE PHYSIQUE

h a l i d e s t h a t t h e r e a r e no r e l i a b l e d a t a f o r t h e s e m a t e r i a l s [ 3 5 ] . The d a t a f o r C r d i f f u s i o n i n MgO quoted e x t e n s i v e l y i n t h i s paper a r e n o t c h a r a c t e r i s t i c of p u r e MgO s i n c e even D i n MgO i s known t o h e always c o n t r o l l e d by i m p u r i t i e s . T h i s may account f o r t h e high v a l u e s of P f o r C r i n MgO when compared w i t h o t h e r m a t e r i a l s . The d a t a i n F i g u r e 6 i n d i c a t e t h a t D' f o r Cr i n MgO i s of a magnitude

c h a r a c t e r i s t i c o f a l i q u i d a t o n l y h a l f t h e m e l t i n g t e m p e r a t u r e of MgO. On t h e o t h e r hand t h e r e a r e good r e a s o n s t o conclude t h a t t h e d a t a f o r N i O (and some t o be r e f e r r e d t o l a t e r f o r Cr203) a r e c h a r a c t e r i s t i c of t h e p u r e m a t e r i a l .

Being compounds, c e r a m i c s d i f f e r from m e t a l s i n t h a t b o t h components o f t h e compound may have enhanced d i f f u s i o n i n g r a i n boundaries. The o n l y m a t e r i a l i n which b o t h components have b e e n s t u d i e d i s N i O and F i g u r e 7 summarises d i f f u s i o n d a t a f o r b o t h N i and 0 i n t h i s o x i d e . (Again t h e s c a l e s a r e o f f s e t s o t h a t D' i s g i v e n by t h e D s c a l e when' 6 = 1 nm.) The more mobile ion i n t h e l a t t i c e (Ni) i s a l s o t h e more mobile i n t h e g r a i n b o u n d a r i e s and D' f o r oxygen boundary d i f f u s i o n i s a p p r o x i m a t e l y e q u a l t o D f o r n i c k e l l a t t i c e d i f f u s i o n .

The importance o f i o n i c charge i n d e t e r m i n i n g m o b i l i t y i n o x i d e h o u n d a r i e s i s i l l u s t r a t e d i n F i g u r e 8, which shows D' f o r some s o l u t e t r a c e r i o n s i n h i g h a n g l e N i O boundaries. The more h i g h l y charged i o n s have t h e lower d i f f u s i o n c o e f f i c i e n t s whereas i n metal boundaries i t i s t h e atoms of l a r g e r r a d i u s which have t h e lower d i f f u s i o n c o e f f i c i e n t s

.

5.2 E f f e c t of d e v i a t i o n from s t o i c h i o m e t r y

Ceramic compounds a r e i n g e n e r a l n o t of e x a c t s t o i c h i o m e t r i c composition and t h e e x t e n t of non-stoichiometry can v a r y widely. I n t h e c a s e of o x i d e s t h e c o m p o s i t i o n can b e c o n t r o l l e d by t h e oxygen a c t i v i t y i n t h e g a s phase, a ( 0 2 ) , and c o n s e q u e n t l y D and P a r e f u n c t i o n s of a ( 0 2 ) . Moreover, f o r l a t t i c e d i f f u s i o n D a a ( ~and n ~ ) ~ i s c h a r a c t e r i s t i c of t h e p o i n t d e f e c t which i s r e s p o n s i b l e f o r d i f f u s i o n . Thus f o r l a t t i c e d i f f u s i o n of N i i n NiO a t h i g h t e m p e r a t u r e s n = 1/5 which i n d i c a t e s

d i f f u s i o n by a m i x t u r e of doubly and s i n g l y charged N i v a c a n c i e s .

I n F i g u r e 9 D and D'6, f o r b o t h h i g h and low a n g l e b o u n d a r i e s , a r e shown a s a f u n c t i o n of a ( 0 2 ) f o r N i d i f f u s i n g i n N i O a t r e l a t i v e l y low t e m p e r a t u r e s . A t t h e s e t e m p e r a t u r e s i t i s n o t p o s s i b l e t o deduce a v a l u e f o r n, but t h e i n c r e a s e of D w i t h i n c r e a s i n g a ( 0 2 ) a t t h e h i g h e r oxygen a c t i v i t i e s i n d i c a t e s t h a t D a t t h e s e

t e m p e r a t u r e s i s s t i l l c h a r a c t e r i s t i c of p u r e N i O and t h a t N i i s d i f f u s i n g v i a N i v a c a n c i e s . A s i m i l a r dependence on a ( 0 2 ) i s a l s o observed f o r D'6, which s u g g e s t s a s i m i l a r mechanism f o r g r a i n boundary d i f f u s i o n .

This s i m i l a r i t y between D'6 and D a s a f u n c t i o n of composition has been observed i n o t h e r systems. T h i s i s i l l u s t r a t e d i n F i g u r e 10 where b o t h D and D'6 f o r C r d i f f u s i o n i n Cr203 a r e p l o t t e d a s a f u n c t i o n of a(02). I n t h i s c a s e d i f f u s i o n i n t h e l a t t i c e a t h i g h a(Og) i s hy C r v a c a n c i e s and a t low a ( 0 2 ) perhaps by C r i n t e r s t i t i a l s . Furthermore, i n UC Routbort and Matzke [40] observed t h a t f o r U d i f f u s i o n b o t h D and D'6 were g r e a t e r i n UCl, t h a n a t t h e s t o i c h i o m e t r i c composition.

6. MECHANISM OF GRAIN BOUNDARY DIFFUSION

The e x p e r i m e n t a l evidence which g i v e s i n f o r m a t i o n concerning t h e mechanism of g r a i n boundary d i f f u s i o n i n m e t a l s h a s been d i s c u s s e d a t l e n g t h i n o t h e r reviews [1,21 and i s o n l y b r i e f l y summarised here. The f a c t t h a t mass t r a n s p o r t a l o n g b o u n d a r i e s t a k e s p l a c e i n such p r o c e s s e s a s s i n t e r i n g and c r e e p shows t h a t a p l a c e exchange mechanism i s n o t involved s i n c e t h i s i s i n c a p a b l e of g i v i n g a n e t t r a n s p o r t of m a t t e r . The i n f l u e n c e of a h y d r o s t a t i c p r e s s u r e on D'6 f o r Ag s e l f d i f f u s i o n has been measured by Martin e t a l . [24]. From t h e s e experiments t h e y deduced an a c t i v t i o n volume f o r boundary d i f f u s i o n of a p p r o x i m a t e l y 1 atomic volume which i s c l o s e t o t h e v a l u e of 0.9 f o r l a t t i c e d i f f u s i o n by a vacancy mechanism (0.1 would be expected f o r an i n t e r s t i t i a l ) . Again f o r Ag s e l f d i f f u s i o n , Robinson and

- 2 5 - 2 0 -15 - 1 0 - 5 0 5 log,, ( a (0,))

-1 8

5 6 7 8 9 10 11 1 2 13

1 0 i T / K - ' )

F i g u r e 7 - L a t t i c e and g r a i n boundary d i f f u s i o n of N i and 0 i n NiO. a ( 0 2 ) = 1 f o r N i and 0.2 f o r 0 ( r e f s . 26, 33, 36 and 37).

N i i n N i O

F i g u r e 9

-

-

F i g u r e 8 - S o l u t e t r a c e r d i f f u s i o n i n N i O g r a i n boundaries ( r e f s . 33, 38, 39 and, f o r Cr, t o be published).

I I I I I

-16-

- Lattice diffusion

*

.. .

6 . '

.

-

.

slope =-),IS

- ^{-18- -,,}

.-'

3

Oiffus~on in low angle boundaries

0'6 1

d

- l L

Log,, 1010,1l

-

Figure 10 - The i n f l u e n c e of oxygen a c t i v i t y on d i f f u s i o n of C r i n the l a t t i c e and low a n g l e boundaries i n Cr703 ( r e f . 34).

0

C4-388 JOURNAL DE _PHYSIQUE

P e t e r s o n [ 2 0 ] measured the i s o t o p e e f f e c t f o r D'6 and found i t to be o n l y s l i g h t l y d i f f e r e n t from t h a t observed f o r D. From t h i s t h e y concluded t h a t t r a c e r motion i n t h e boundary i s n o t h i g h l y c o r r e l a t e d ( i - e . a s i n g l e row of atoms i s n o t i n v o l v e d ) and t h a t t h e atomic jump i t s e l f o n l y i n v o l v e s a small number of atoms. A l l t h e s e o b s e r v a t i o n s s u p p o r t t h e concept of g r a i n boundary d i f f u s i o n i n Ag t a k i n g p l a c e v i a

' v a c a n c i e s ' which a r e more e a s i l y formed i n t h e boundary and a r e more mobile t h a n i n t h e l a t t i c e .

The experiments on ceramic m a t e r i a l s d e s c r i b e d i n S e c t i o n 5.2 l e n d f u r t h e r s u p p o r t t o t h i s mechanism. They a l s o s u g g e s t i n a d d i t i o n t h a t the ' d e f e c t ' r e s p o n s i b l e f o r boundary d i f f u s i o n may be an i n t e r s t i t i a l when l a t t i c e d i f f u s i o n o c c u r s by an i n t e r s t i t i a l , and m e c h a n i s t i c experiments i n such a system would be worthwhile.

I n c o n c l u s i o n i t would appear t h a t t h e l i n k between g r a i n boundary s t r u c t u r e and d i f f u s i o n w i l l probably be made t h r o u g h computer s i m u l a t i o n s and c a l c u l a t i o n s of t h e formation and m i g r a t i o n e n t h a l p i e s of t h e s e g r a i n boundary ' p o i n t d e f e c t s ' . An a t t e m p t along t h e s e l i n e s was r e c e n t l y r e p o r t e d by Riscondi [41] f o r t i l t and twist b o u n d a r i e s i n Al. The approach used was t o e s t i m a t e t h e mean r e c i p r o c a l jump f r e q u e n c i e s a l o n g ' e a s y ' pathways through t h e c o r e s t r u c t u r e s . The r e s u l t s f o r D ' b o t h p a r a l l e l and p e r p e n d i c u l a r t o t h e t i l t a x i s of [ l o o ] and [110] t i l t b o u n d a r i e s a r e shown i n F i g u r e s 11 and 12 and may be compared w i t h t h e e x p e r i m e n t a l d a t a i n F i g u r e s 1 and 2. I n n e i t h e r c a s e do t h e c a l c u l a t i o n s p r e d i c t a l l t h e g e n e r a l f e a t u r e s d i s c u s s e d i n S e c t i o n 2.1. They do s u c c e s s f u l l y p r e d i c t l a r g e a n i s o t r o p y a t low 0 and low d i f f u s i v i t y i n t h e C=3 and C = l l [110] boundaries. However, t h e y a r e not s u c c e s s f u l i n p r e d i c t i n g t h e p r o p o r t i o n a l i t y between D' and 0 ( * 45O) i n

[ l o o ] b o u n d a r i e s , o r t h e g r a d u a l rise t o a maximum a t about 30° i n [110]

boundaries.

ACKNOWLEDGEMENT

The a u t h o r wishes t o thank A.D. L e C l a i r e , A.T. Chadwick and P.W. Tasker f o r u s e f u l , d i s c u s s i o n s .

I

I

A : I1 to <110> t i l t a x i s I 8 : 1 to <110> t i l t a x i s - 8

-

E -10

\

b m -12

- 0 ⁰

Bd6,

e

F i g u r e 11 - C a l c u l a t e d s e l f d i f f u s i o n F i g u r e 12 - A s F i g u r e 11 b u t f o r (1101 c o e f f i c i e n t s f o r [ l o o ] t i l t b o u n d a r i e s t i l t b o u n d a r i e s ( r e f . 41).

i n Al a t 250°C a s a f u n c t i o n of m i s o r i e n t a t i o n ( r e f . 41).

REFERENCES

[ l ] BALLUFFI, R.W., M e t a l l . T r a n s . A., (1982) 2069.

[ 2 ] PETERSON, N.L., i n ' G r a i n Boundary S t r u c t u r e and K i n e t i c s ' , ASM, M e t a l s P a r k , Ohio (1980) pp. 209-238.

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DISCUSSION

A.P. Sutton: I n t h e case of impurity i o n s d i f f u s i n g i n boundaries i n N i O how can one know t h e charge s t a t e o f t h e impurity?

A. Atkinson: There is experimental evidence from bulk d i f f u s i o n s t u d i e s t h a t cr3+