THE SIGNIFICANCE OF THE STRUCTURE OF INTERNAL INTERFACES FOR THE PROPERTIES OF MATERIALS

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THE SIGNIFICANCE OF THE STRUCTURE OF INTERNAL INTERFACES FOR THE PROPERTIES

OF MATERIALS

H. Gleiter

To cite this version:

H. Gleiter. THE SIGNIFICANCE OF THE STRUCTURE OF INTERNAL INTERFACES FOR THE PROPERTIES OF MATERIALS. Journal de Physique Colloques, 1985, 46 (C4), pp.C4-393-C4-404.

�10.1051/jphyscol:1985442�. �jpa-00224693�

JOURNAL DE PHYSIQUE

Colloque C4, suppl6ment au n04, Tome 46, a v r i l 1985 page C4-393

THE SIGNIFICANCE OF THE STRUCTURE OF INTERNAL INTERFACES FOR THE PROPERTIES OF MATERIALS

H . Gleiter

U n i v e r s i t a t des Saar Zandes, Bau 2, 0-6600 Saarbriicken, F. R. G .

A b s t r a c t

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S t u d i e s o f t h e b e h a v i o u r o f g r a i n b o u n d a r i e s by means o f t h e p l a t e / s p h e r e m e t h o d a r e r e p o F t % h T n a i T F t T K g t h a t a f e w b o u n d a r i e s e x h i b i t s p e c i a l p r o p e r t i e s w h i c h w e r e o b s e r v e d f o r a p a r t i c u l a r i n t e r f a c e i n d e p e n d e n t l y o f t h e p r o p e r t y i n v e s t i g a t e d ( e . g . e n e r g y , c o r r o s i o n , e m b r i t t l e m e n t ) . M o s t s p e c i a l b o u n d a r i e s w e r e o f h i g h c o i n c i d e n c e t y p e . B u t n o t a l l h i g h c o i n c i d e n c e b o u n d a r i e s showed s p e c i a l p r o p e r t i e s . I t seems t h e i n t e r a t o m i c i n t e r a c t i o n w h i c h s e l e c t s b e t w e e n s p e c i a l a n d " n o n - s p e c i a l " h i g h c o i n c i d e n c e b o u n d a r i e s . T h e p r o p e r t i e s o f b o u n d a r i e s d e v i a t i n g f r o m s p e c i a l m i s o r i e n t a t i o n s w e r e f o u n d t o be c o n t r o l l e d by t h e p r e s e n c e o f

( s e c o n d a r y ) b o u n d a r y d i s l o c a t i o n s .

s y s t e m a t i c s t u d i e s o f t h e p r o p e r t i e s o f i n t e r p h a s e b o u n d a r i e s b e t w e e n i o n i c c r y s t a l s a n d n o b l e m e t a l s S K o K d d - f h - a E c o i n i r d e t i c e m i s o r i e n t a t i o n s do n o t r e s u l t i n s p e c i a l b e h a v i o u r w h i c h was o b - s e r v e d o n l y i f c l o s e p a c k e d r o w s o f a t o m s a t t h e " s u r f a c e s " o f the m e t a l c r y s t a l s " l o c k e d " i n t o t h e " v a l l e y s " b e t w e e n c l o s e p a c k e d a t o m i c r o w s a t t h e " s u r f a c e s U o f t h e i o n i c c r y s t a l s ( " l o c k - i n "

m o d e l o f i n t e r p h a s e b o u n d a r i e s ) .

The b a s i c i d e a o f n a n o c r y s t a l l i n e m a t e r i a l s i s t o g e n e r a t e a new t y p e o f s o l i d s b y 5 X p T o i f f i ? ~ f f i e - h - i g l r y - d i s t o r t e d a t o m i c s t r u c t u r e e x i s t i n g i n t h e c o r e o f g r a i n ( i n t e r p h a s e ) b o u n d a r i e s . T h i s i s a c h i e v e d b y r e d u c i n g t h e c r y s t a l s i z e o f a p o l y c r y s t a l l i n e m a t e r i a l t o a few n a n o m e t e r s ( n a n o c r y s t a l l i n e m a t e r i a l ) s o t h a t t h e v o l u m e f r a c t i o n o c c u p i e d b y i n t e r f a c e s ( i n t e r f a c i a l c o m p o n e n t ) a n d c r y s t a l s a r e c o m p a r a b l e . The i n t e r f a c i a component o f s u c h a m a t e r i a l c o n s i s t s o f many ( t y p i c a l l y 1 0 1 9 c m ) b o u n d a r i e s . As t h e s t r u c t u r e s o f t h e s e b o u n d a r i e s a r e a l l d i f f e r e n t , t h e i n t e r - f a c i a l c o m p o n e n t ( i . e . t h e sum o f a l l b o u n d a r y s t r u c t u r e s ) r e s e m b l e s a f r o z e n g a s . E x p e r i m e n t a l s t u d i e s o f n a n o c r y s t a l l i n e m a t e r i a l s s u p p o r t t h i s h y p o t h e s i s a n d s u g g e s t t h a t i n t e r f a c e s may be u s e d a s a s t r u c t u r a l c o m p o n e n t f o r g e n e r a t i n g a g a s - l i k e s o l i d s t a t e s t r u c t u r e .

INTRODUCTION

The o b j e c t o f t h i s c o n t r i b u t i o n i s t o a s s e s s some a s p e c t s o f t h e c o r r e l - a t i o n b e t w e e n t h e a t o m i c s t r u c t u r e a n d t h e p r o p e r t i e s o f i n t e r f a c e s . F o r p r e v i o u s r e v i e w s we r e f e r t o t h e p a p e r by Pumphrey ( 1 ) a n d Goodhew ( 2 ) . The m a i n c o n t e n t o f t h i s p r e s e n t a t i o n was s e t f o r t h i n p a p e r s w h i c h h a v e a p p e a r e d o r w i l l a p p e a r e l s e w h e r e . H e r e a summary w i l l b e g i v e n o f t h e p o i n t s w h i c h seem m o s t p e r t i n e n t t o t h i s s y m p o s i u m .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985442

C4-394 JOURNAL DE PHYSIQUE

MICROSCOPIC STATISTICAL EXPERIMENTS VERSUS MACROSCOPIC BICRYSTAL MEASURE- MENTS

S t u d i e s o f t h e c o r r e l a t i o n between boundary s t r u c t u r e and p r o p e r t i e s by means of b i c r y s t a l s a r e c a r r i e d o u t by growing from t h e m e l t a s e r i e s of c r y s t a l l o g r a p h i c a l l y we1 1 c h a r a c t e r i z e d b i c r y s t a l s , t h e p r o p e r t i e s of which a r e measured ( 3 ) a s a f u n c t i o n o f t h e c r y s t a l l o g r a p h i c p a r a m e t e r s A l t h o u g h m e a s u r e m e n t s of t h i s t y p e have made o u t s t a n d i n g c o n t r i b u t i o n s t o o u r p r e s e n t u n d e r s t a n d i n g o f i n t e r f a c e s ( c . f . f o r example i n c l a s s i c a l p a p e r s by A u s t e t a l . ( 4 ) , ( 5 ) ) , t h e method s u f f e r s p r i m a r i l y from t h r e e d i s a d v a n t a g e s . Growth from t h e m e l t i s g e n e r a l l y n o t a p p l i c a b l e t o i n t e r - p h a s e b o u n d a r i e s . As a c o n s e q u e n c e o f t h e s u b s t r u c t u r e p r e s e n t i n t h e c r y s t a l s , a n y b o u n d a r y o f m a c r o s c o p i c d i m e n s i o n s r e p r e s e n t s a m i x t u r e of d i f f e r e n t boundary s t r u c t u r e s . Hence, t h e p r o p e r t i e s m e a s u r e d by u s i n g m a c r o s c o p i c b o u n d a r i e s a r e i n r e a l i t y a v e r a g e v a l u e s . The t i m e consuming g r o w t h p r o c e d u r e of a b i c r y s t a l l i m i t s t h e number o f m e a s u r e m e n t s a n d , t h e r e f o r e , r e d u c e s t h e s t a t i s t i c a l c o n f i d e n c e of t h e p r o p e r t y - s t r u c t u r e c o r r e l a t i o n d e r i v e d . For t h e same r e a s o n , p r a c t i c a l l y a 1 1 m e a s u r e m e n t s a r e biased i n t h e s e n s e t h a t o n l y s p e c i f i c ( e . g . [110] t i l t ) b o u n d a r i e s have been i n v e s t i g a t e d by t h e b i c r y s t a l method. As t h e s e l e c t i o n ofi t h e s e b o u n d a r i e s i s g u i d e d by a s t r u c t u r a l m o d e l , t h e d a n g e r o f c o n f i r m i n g p r e - c o n c e i v e d i d e a s of t h e b o u n d a r y s t r u c t u r e i s n o t u n l i k e l y . I n o r d e r t o remove t h e s e d i s a d v a n t a g e s , a s t a t i s t i c a l method h a s been p r o p o s e d (6), ( 7 ) . A l a r j e number ( 1 0 4

. . .

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Two f u r t h e r a d v a n t a g e s of t h e p l a t e / s p h e r e method a r e t h a t g r a i n bound- a r i e s a s w e l l a s i n t e r p h a s e b o u n d a r i e s may be g e n e r a t e d ( 7 ) and t h a t a l l b o u n d a r i e s a r e t e s t e d s i m u l t a n e o u s l y u n d e r i d e n t i c a l c o n d i t i o n s . C l e a r - ly t h e p l a t e / s p h e r e method i s l i m i t e d t o s y s t e m s t h a t c a n be s i n t e r e d . GRAIN B O U N D A R Y STUDIES

The p l a t e l s p h e r e method h a s been a p p l i e d s o f a r t o s t u d y t h e c o r r e l a t - i o n s between b o u n d a r y s t r u c t u r e and b o u n d a r y e n e r g y (6), ( 8 ) c o r r o s i v i t y (9), embri t t l ement ( l o ) , mobi 1 i t y ( 1 1 ) , p r e s s u r e ( 1 2 ) and t e m p e r a t u r e ( 1 3 ) . The e f f e c t o f t h e a t o m i c s t r u c t u r e on t h e e n e r g y o f a b o u n d a r y was i n v e s t i g a t e d by a n n e a l i n g t h e s p e c i m e n s a t e l e v a t e d t e m p e r a t u r e s . I n o r d e r t o m i n i m i z e t h e f r e e e n e r g y o f t h e s y s t e m , t h e s p h e r e s r o t a t e ( b y a d i f f u s i o n a l a n d / o r g r a i n boundary s l i d i n g p r o c e s s ) i n t o s u c h o r i e n t - a t i o n s which r e s u l t i n b o u n d a r i e s o f minimum e n e r g y ( 1 4 ) ( F i g . 1 ) . Hence, i n a s i n g l e e x p e r i m e n t a l l low e n e r g y b o u n d a r i e s c a n be i d e n t i f - i e d by m e a s u r i n g ( e . g . by means o f a s t a n d a r d X-ray method) t h e o r i e n t - a t i o n s o f t h e s p h e r e s a f t e r l o n g s i n t e r i n g t i m e s . I f t h e p l a t e / s p h e r e method i s s l i g h t l y m o d i f i e d , o t h e r p r o p e r t i e s , s u c h a s b o u n d a r y em- b r i t t l e m e n t , m o b i l i t y o r c o r r o s i v i t y may be i n v e s t i g a t e d and c o r r e l a t e d w i t h t h e boundary s t r u c t u r e . F o r example, b o u n d a r y c o r r o s i o n was s t u d -

* ) S t r u c t u r a l v a r i a t i o n s d u e t o d i f f e r e n t r i g i d body t r a n s l a t i o n s ( 3 1 ) i n d i f f e r e n t a r e a s o f t h e boundary ( 3 2 ) c a n n o t be r u l e d o u t . However, a f t e r l o n g a n n e a l i n g t i m e s , t h e boundary p r o b a b l y a p p r o a c h e s t h e t r a n s - l a t i o n c o r r e s p o n d i n g t h e minimum f r e e e n e r g y . '

i e d by i m m e r s i n g a s p h e r e / p l a t e s p e c i m e n ( F i g . 2 b ) w i t h r a n d o m l y

o r i e n t e d s p h e r e s i n t o a c h e m i c a l s o l u t i o n c a u s i n g g r a i n b o u n d a r y c o r r o s - i o n .

F i g . 1 F i g . 2

F i g . 1: Formation of a g r a i n boundary (AB) d u r i n g s i n t e r i n g o f a s i n g l e c r y s t a l sphere -to a s i n g l e c r y s t a l p l a t e (p). The c r y s t a l l a t t i c e o f b i s t i l t e d 0O w i t h r e s p e c t t o p.A r o t a t i o n o f b may be achieved f o r example by a d i f f u s i v e f l u x o f atoms removing a wedge shaped p i e c e o f m a t e r i a l from t h e l e f t p a r t and i n s e r t i n g i t a t t h e r i g h t p a r t o f t h e boundary.

F i g . 2: Schematic diagram o f t h e specimens used f o r t h e i n v e s t i g a t i o n o f g r a i n bound- a r y p r o p e r t i e s by t h e plate/sphere method (a). b shows t h e process o f removing i n d i v i d - u a l spheres by boundary corrosion.

As t h e c o r r o s i o n p r o c e s s o c c u r s u n d e r i d e n t i c a l c o n d i t i o n s a t a l l b o u n d - a r i e s . ~ i m u l t a n e o ~ s l y , t h e b o u n d a r i e s w i t h h i g h e s t c o r r o s i o n r a t e s w i l l be c o r r o d e d t h r o u g h f i r s t a n d , h e n c e , t h e c o r r e s p o n d i n g s p h e r e s f a l l o f f f i r s t . Then, t h e s p h e r e s ( b o u n d a r i e s ) w i t h t h e n e x t h i g h e r c o r r o s i o n r a t e f o l l o w a n d so o n . I n o t h e r w o r d s , i f o n e m e a s u r e s t h e o r i e n t a t i o n o f t h e s p h e r e s t h a t f a l l o f f f i r s t ( l a s t ) , o n e knows t h e b o u n d a r i e s o f maximum ( m i n i m u m ) c o r r o s i o n r a t e . The e n t i r e b o u n d a r y c o r r o s i o n s p e c t r u m may be o b t a i n e d i n t h e same way i f t h e o r i e n t a t i o n o f t h e s p h e r e s

f a l l i n g o f f i s m o n i t o r e d a s a f u n c t i o n o f t h e c o r r o s i o n t i m e . I n a s i m i l a r f a s h i o n t h e b o u n d a r y e m b r i t t l e m e n t ( 1 0 ) a n d b o u n d a r y m o b i l i t y ( 1 1 ) a s a f u n c t i o n o f b o u n d a r y s t r u c t u r e was m e a s u r e d . I n t h e s e s t u d i e s ( l o ) , ( 1 1 ) t h e s p e c i m e n s w e r e v i b r a t e d t o b r e a k t h e s p h e r e s o f f o r a n n e a l e d t o i n d u c e i n t e r f a c e m i g r a t i o n . The r e s u l t s o b t a i n e d may b e s u m m a r i z e d a s f o l l o w s . ( i ) A c o r r e l a t i o n b e t w e e n b o u n d a r y s t r u c t u r e a n d p r o p e r t i e s e x i s t s . The o r i e n t a t i o n r e l a t i o n s h i p s f o r w h i c h b o u n d a r i e s w i t h s p e c i a l p r o p e r t i e s ( l o w e n e r g y , c o r r o s i v i t y a n d e m b r i t t l e m e n t ) w e r e o b s e r v e d , w e r e t h e same a n d d i d n o t d e p e n d o n t h e p r o p e r t y s t u d i e d . ( i i ) M o s t ( b u t n o t a l l ) s p e c i a l b o u n d a r i e s w e r e o f t h e h i g h c o i n c i d e n c e ( o r s h o r t p e r i o d i c i t y ) t y p e . T h i s r e s u l t i s c o n s i s t e n t w i t h t h e f i n d i n g s o b t a i n e d f r o m b i c r y s t a l e x p e r i m e n t s ( 1 8 ) - ( 2 1 ) . H o w e v e r , t h e p l a t e / s o h e r e e x p e r i m e n t s showed t h a t n o t a l l c o i n c i d e n c e ( s h o r t p e r i o d i c ) b o u n d a r i e s e x h i b i t e d s p e c i a l p r o p e r t i e s . I n f a c t , t h e s e l e c t i o n b e t w e e n h i q h c o i n c i d e n c e b o u n d a r i e s w i t h a n d w i t h o u t s p e c i a l p r o p e r t i e s s e e m s t o d e p e n d o n t h e i n t e r a t o m i c i n t e r a c t i o n ( T a b l e I ) a s c o m p o s i t i o n a l c h a n g e s v a r y t h e o r i e n t a t i o n r e l a t i o n s h i p s f o r w h i c h s p e c i a l b o u n d a r i e s a r e o b - s e r v e d . P a r a l l e l i t y o f c l o s e p a c k e d d i r e c t i o n s ( p l a n e s ) a p p a r e n t l y f a v o u r s s p e c i a l p r o p e r t i e s (19);(cf. p o s t e r A3 o f t h i s s y m p o s i u m a n d a l s o t h e " l o c k - i n " m o d e l o f t h e s u b s e q u e n t s e c t i o n ) .

C4-396 JOURNAL DE PHYSIQUE

T a b l e I: C o m p a r i s o n o f some s p e c i a l b o u n d a r i e s i n d i f f e r e n t m a t e r i a l s ( 8 )

t c o i n c .

I

1

( i i i ) The p r o p e r t i e s o f b o u n d a r i e s d e v i a t i n g f r o m t h e s e s p e c i a l o r i e n t - a t i o n r e l a t i o n s h i p s a r e d e t e r m i n e d b y d e f e c t s i n t h e b o u n d a r y s t r u c t u r e . F o r e x a m p l e , b o u n d a r y c o r r o s i o n (9) was o b s e r v e d t o i n i t i a t e a n d p r o - c e e d a l o n g ( s e c o n d a r y ) b o u n d a r y d i s l o c a t i o n s . I f t h e s e c o r r o s i o n c h a n n e l s o v e r l a p , t h e b o u n d a r y e x h i b i t e d h i g h c o r r o s i v i t y . A s i m i l a r m e c h a n i s m was f o u n d t o c o n t r o l t h e e m b r i t t l e m e n t o f g r a i n b o u n d a r i e s

( 1 0 ) . I n t h e v i c i n i t y o f t h e ( s e c o n d a r y ) b o u n d a r y d i s l o c a t i o n s a c l o u d o f s o l u t e a t o m s ( 1 7 ) i s f o r m e d w h i c h e m b r i t t l e s t h e b o u n d a r y l o c a l l y . H i t h i n c r e a s i n g d e v i a t i o n f r o m a s p e c i a l o r i e n t a t i o n r e l a t i o n s h i p t h e s p a c i n g b e t w e e n t h e s e c l o u d s ( a n d , h e n c e , t h e s p a c i n g b e t w e e n t h e em-

b r i t t l e d a r e a s ) d e c r e a s e s s o t h a t t h e b o u n d a r i e s become m o r e a n d m o r e b r i t t l e . . O b s e r v a t i o n s o f t h i s k i n d w o u l d h a v e b e e n d i f f i c u l t b y u s i n g t h e b i c r y s t a l metho! b e c a u s e a n a c c u r a c y o f t h e o r i e n t a t i o n r e l a t i o n - s h i p o f l e s s t h a n 1 i s r e q u i r e d a n d t h e p r o w t h o f p r e l i m i n a r y u n - known n o n - c o i n c i d e n c e b o u n d a r i e s o f l o w e n e r g y , c o r r o s i v i t y a n d em- b r i t t l e m e n t w o u l d h a v e b e e n n e c e s s a r y .

3 9 11 17b 33

INTERPHASE BOUNDARY STUDIES

The u n d e r s t a n d i n g b e t w e e n a t o m i c s t r u c t u r e a n d p r o p e r t i e s o f i n t e r - p h a s e b o u n d a r i e s i s l e s s d e v e l o p e d t h a n f o r g r a i n b o u n d a r i e s ( 2 2 ) . p r o b a b l y , t h e v a r i o u s t y p e s o f i n t e r p h a s e b o u n d a r i e s w i 1 1 b e h a v e d i f f

-

e r e n t l y d e p e n d i n g o n t h e c h e m i c a l b o n d i n g a n d p h y s i c a l p r o p e r t i e s o f t h e c r y s t a l s i n v o l v e d , s u c h a s p o l a r i z a b i l i t y , c o n d u c t i v i t y , m o l e c u l a r w e i g h t e t c . T h i s makes i t d i f f i c u l t t o c o m p a r e t h e r e s u l t s o b t a i n e d f o r d i f f e r e n t t y p e s o f i n t e r p h a s e s . A f i r s t s y s t e m a t i c s t u d y h a s b e e n c a r r i e d o u t ( 2 3 ) o f t h e c o r r e l a t i o n b e t w e e n b o u n d a r y e n e r g y a n d a t o m i c s t r u c t u r e o f i n t e r p h a s e b o u n d a r i e s f o r m e d b y n o b l e m e t a l s (Au, Ag, Cu) and a v a r i e t y o f i o n i c c r y s t a l s ( L i F , KC1, NaC1, Ng0, A1203, m i c a ) . T h e b o u n d a r i e s w e r e g e n e r a t e d b y t h e p l a t e / s p h e r e m e t h o d u s i n g a b o u t 1 0 7 s p h e r e s w i t h d i a m e t e r s o f 0 . 5 t o 1 urn. T h e r e s u l t s o b t a i n e d l e d t o t h e

f o l l o w i n g c o r r e l a t i o n s b e t w e e n t h e b o u n d a r y s t r u c t u r e a n d p r o p e r t i e s ( ( 2 3 ) , p o s t e r A9 o f t h i s s y m p o s i u m ) . ( i ) I n t e r p h a s e b o u n d a r y m o d e l s b a s e d o n t h e c o i n c i d e n c e c o n c e p t a r e n o t a p p l i c a b l e - t o i n t e r f a c e s b e t - ween n o b l e m e t a l s a n d i o n i c c r y s t a l s b e c a u s e t h e l o w e n e r g y b o u n d a r i e s o b s e r v e d w e r e n o t o f t h e c o i n c i d e n c e t y p e a n d c o n c e i v a b l e c o i n c i d e n c e r e l a t i o n s h i p s d i d n o t r e s u l t i n l o w e n e r g y b o u n d a r i e s . F o r e x a m p l e , F i g . 3 shows t g e s c h e m a t i c c r o s s s e c t i o n t h r o u g h a c = 11 c o i n c i d e n c e b o u n d a r y ( 5 0 . 5 r o t a t i o n a b o u t

[lla

( ~ 4 . 7 ~ [110] r o t a t i o n ) e x h i b i t e d l o w e n e r g y ( F i g , 4 ) .

+

+

+

+

+ + + -

+

+ + + +

-

- + + -

+

+ -

+ I3 s p e c i a l p r o p e r t i e s (low energy) observed L i o t observeu-.

F i g . 3 F i g . 4

Fig. 3: Schematic cross s e c t i o n through a c = 11 coincidence boundary between Au and LiF. The c i r c l e s shown represent t h e atoms and s c a l e w i t h t h e Gold schmidt r a d i i o f t h e i o n s and atoms o f b o t h m a t e r i a l s . The atoms ( i o n s ) a t coincidence s i t e s a r e i n d i c a t e d i n black. This boundary was n o t observed t o be o f l o w energy F i g . 4: Schematic cross s e c t i o n through t h e low energy boundary between Au and L i F n e x t t o t h e c = 11 i n t e r f a c e ( F i g . 3). The o r i e n t a t i o n r g l a t i o n s h i p observed (54.7'

[I101 ) r e s u l t s i n p a r a l l e l i t y o f c l o s e packed planes ((111)

11

11

" l o c k - i n " rows o f the Au c r y s t a l a r e removed.

( i i ) A l l l o w e n e r g y b o u n d a r i e s o b s e r v e d e x p e r i m e n t a l l y may b e d e s c r i b e d b y means o f t h e f o l l o w i n g a t o m i c s t r u c t u r e ( l o c k - i n m o d e l ) . A l o w e n e r g y i n t e r p h a s e b o u n d a r y r e s u l t s , i f c l o s e p a c k e d r o w s o f a t o m s a t t h e " s u r f a c e " o f t h e m e t a l c r y s t a l f i t i n t o t h e l ' v a l l e y s " b e t w e e n t h e c l o s e p a c k e d r o w s o f a t o m s a t t h e s u r f a c e o f t h e i o n i c c r y s t a l .

E x a m p l e s o f t h i s t y p e o f b o u n d a r y s t r u c t u r e a r e shown i n F i g s . 4,5,6

F i g . 5 F i g . 6

F i g . 5: "Lock-in" s t r u c t u r e o f one o f t h e low energy boundaries observed between

Au L i F . Adjacent c l o s e packed rows o f g o l d atoms l o c k i n t o adjacent " v a l l e y s "

between c l o s e packed rows a t t h e (001) "surface" o f LiF. The boundary i s n o t a c o i n - cidence boundary.

F i g . 6 "Lock-in" s t r u c t u r e o f a l o w energy A U L i F i n t e r f a c e .

C4-398 JOURNAL DE PHYSIQUE

T h i s s t r u c t u r a l model n o t o n l y e x p l a i n s ( 2 3 ) t h e e x p e r i m e n t a l l y o b s e r v - ed o r i e n t a t i o n d e p e n d e n c e of t h e boundary e n e r g y b u t a l s o t h e v a r i a t - i o n o f t h e b o u n d a r y e n e r g y a s a f u n c t i o n o f t h e b o u n d a r y i n c l i n a t i o n , t h e l a t t i c e mismatch between t h e two p h a s e s which was v a r i e d i n t h e s e e x p e r i m e n t s from a b o u t 1 % t o 35 %. I t may be of i n t e r e s t t o p o i n t o u t a c o n c e i v a b l e c o r r e l a t i o n between t h e s e r e s u l t s and t h e o b s e r v a t i o n s m e n t i o n e d i n t h e p r e v i o u s p a r a g r a p h . The l o c k - i n s t r u c t u r e r e s u l t s i n p a r a l l e l i t y of c l o s e packed d i r e c t i o n s and @ l a n e s i n b o t h c r y s t a l s ( c f . F i g s . 3 , 4 , 5 and 6 ) . A s i m i l a r p r e f e r e n c e f o r p a r a l l e l i t y of c l o s e p a c k - ed d i r e c t i o n s and p l a n e s was a l s o n o t i c e d i n s p e c i a l g r a i n b o u n d a r i e s ( c f . T a b l e I ) .

NAMOCRYSTALLINE MATERIALS

I f t h e c r y s t a l s i z e o f a p o l y c r y s t a l i s r e d u c e d t o a few n a n o m e t e r s , t h e volume f r a c t i o n o c c u p i e d by t h e i n t e r f a c e s becomes c o m p a r a b l e t o t h e volume f r a c t i o n o f t h e c r y s t a l s . I n o t h e r w o r d s , i n m a t e r i a l s o f t h i s t y p e ( c a l l e d n a n o c r y s t a l l i n e m a t e r i a l s ) , t h e i n t e r f a c e s may no l o n g e r be r e g a r d e d a s p e r t u r b a t i o n s o f t h e c r y s t a l l i n e s t r u c t u r e . The sum o f a l l i n t e r f a c e s ( c a l l e d t h e " i n t e r f a c i a l c o m p o n e n t " ) r e p r e s e n t s a p a r t of t h e m i c r o s t r u c t u r e j u s t l i k e t h e o t h e r more c o n v e n t i o n a l s t r u c t u r a l c o m p o n e n t s , s u c h a s p r e c i p i t a t e s , g r a i n s o f a s e c o n d p h a s e e t c . ( 2 4 ) . One of t h e a t t r a c t i v e f e a t u r e s of s u c h n a n o c r y s t a l l i n e m a t - e r i a l s may be t h a t t h e y p r o v i d e a means o f g e n e r a t i n g s o l i d s h a v i n g an a t o m i c s t r u c t u r e w i t h n e g l i g i b l e s h o r t and l o n g r a n g e o r d e r , i . e . t h e s t r u c t u r e of a f r o z e n g a s ( 2 5 ) , ( 2 6 ) . I f t h i s were s o , n a n o c r y s t - a l l i n e m a t e r i a l s would r e p r e s e n t a s o l i d s t a t e s t r u c t u r e d i f f e r e n t from t h e two known s o l i d s t a t e s ( c r y s t a l l i n e and g l a s s y s t a t e ) t o o n e o f which a l l m a t e r i a l s p r e s e n t l y a v a i l a b l e b e l o n g . The r e a s o n f o r t h e f o r m a t i o n o f a f r o z e n - g a s - l i k e s t r u c t u r e i n n a n o c r y s t a l l i n e s u b s t a n c e s may be r a t i o n a l i z e d a s f o l l o w s . I n m e t a l s , and p r e - sumably a l s o i n many i o n i c and c o v a l e n t l y bonded m a t e r i a l s , g r a i n b o u n d a r i e s a r e p r o b a b l y t w o - d i m e n s i o n a l p e r i o d i c s t r u c t u r e s t h e p e r i o d i c i t y o f which a n d , h e n c e , t h e p o s i t i o n a l c o r r e l a t i o n f u n c t i o n o f t h e i n t e r f a c i a l atoms d e p e n d s on t h e o r i e n t a t i o n r e l a t i o n s h i p b e t - ween a d j a c e n t c r y s t a l s . Hence, i f a p o l y c r y s t a l c o n t a i n s many bound- a r i e s , and i f t h e o r i e n t a t i o n r e l a t i o n s h i p f o r e v e r y boundary i s d i f f - e r e n t , i t c o m p r i s e s many d i f f e r e n t boundary s t r u c t u r e s . F o r e x a m p l e ,

i f we c o n s i d e r a n a n o c r y s t a l l i n e m a t e r i a l of c r y s t a l l o g r a p h i c a l l y

F i g . 7 : S c h e m a t i c s t r u c t u r e o f a n a n o c r y s t a l l i n e m a t e r i a l . For s i m - p l i c i t y , t h e b o u n d a r y ( c r y s t a l ) r e g i o n s a r e i n d i c a t e d by b r o k e n l i n e s . The b o u n d a r y atoms a r e marked i n b l a c k f o r c l a r i t y . T h i s d o e s n o t im- p l y t h a t t h e y a r e c h e m i c a l l y d i f f e r e n t from t h e atoms i n t h e c r y s t a l s .

randomly o r i e n t e d c r y s t a l l i t e s ( t h e d i a m e t e r i s a sumed t o be 5 nm, t h e i n t e r f a c i a l t h i c k n e s s 1 m ) i t c o n t a i n s a b o u t i n t e r f a c e s p e r cm3 which occupy a volume f r a c t i o n o f r o u g h l y 40 % ( F i g . 7 ) . As t h e o r i e n t - a t i o n r e l a t i o n s h i ( a n d , t h e r e f o r e , t h e boundary s t r u c t u r e ) a r e d i f f e r e n t ( a n d u n c o r r e l a t e d ! f o r e v e r y i n t e r f a c e due t o t h e random t e x t u r e , t h e i n t e r f a c i a l component o f g t h e n a n o c r y s t a l l i n e m a t e r i a l c o n s i d e r e d i s t h e sum of many ( r o u g h l y 1 0 ) d i f f e r e n t and u n c o r r e l a t e d boundary s t r u c t - u r e s . The a v e r a g e o v e r s o many u n c o r r e l a t e d s t r u c t u r e s i s u n l i k e l y t o e x h i b i t a n y s i g n i f i c a n t s h o r t o r l o n g r a n g e o r d e r , i . e . t h e a t o m i c a r r a n g e m e n t may be c o m p a r a b l e t o t h a t o f a f r o z e n g a s . I n t h e c a s e of a g a s , i t i s t h e e n t r o p y which f o r c e s t h e s y s t e m s t o form a l a r g e number of a t o m i c c o n f i g u r a t i o n s ; i n t h e c a s e o f a n a n o c r y s t a l l i n e m a t e r i a l , i t i s t h e boundary c o n d i t i o n s ( v a r y i n g from i n t e r f a c e t o i n t e r f a c e ) which f o r c e t h e atoms i n a n y i n t e r f a c e t o form d i f f e r e n t a t o m i c a r r a n g e - ments. The r e s u l t s of s t r u c t u r a l s t u d i e s by X-ray d i f f r a c t i o n , 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 y and Mossbauer s p e c t r o s c o p y seem t o s u p p o r t t h e i d e a t h a t t h e i n t e r f a c i a l component o f a n a n o c r y s t a l l i n e m a t e r i a l has a s t r u c t u r e w i t h l i t t l e s h o r t o r l o n g r a n g e o r d e r .

L 0 L 8

VELOCITY [mrnlsl

F i g . 9

Fig. 8: X-ray d i f f r a c t i o n curve ( l i n e C) of t h e i n t e r f a c i a l component of nano- c r y s t a l l i n e iron with a crystal s i z e of about 6 nm. The l i n e D represents the e l a s t i c X-ray d i f f r a c t i o n of a gas of iron atoms with the same density a s t h e mat- e r i a l of curve C. E i s the measured d i f f r a c t i o n i n t e n s i t y of the iron g l a s s FegO P13C7 (27) which i s similar t o t h a t of molten iron (28).

Fig. 9: ITijssbauer spectrum of the i n t e r f a c i a l (A) and c r y s t a l l i n e component (B) of t h e m e nanocrystalline iron a s in Fig. 8.

For e x a m p l e , F i g s . 8 and 9 show t h e Mossbauer s p e c t r u m and t h e X-ray s c a t t e r i n g c u r v e o f t h e i n t e r f a c i a l component o f 6 nm n a n o c r y s t a l l i n e i r o n . I t may be s e e n ( F i g . 8 ) t h a t p r a c t i c a l l y no i n t e r f e r e n c e e f f e c t s d u e t o s h o r t r a n g e o r d e r a r e n r e s e n t s o t h a t a f r o z e n g a s - l i k e s t r u c t - u r e i s s u g g e s t e d . Measurements o f p r o p e r t i e s t h a t a r e s e n s i t i v e t o s h o r t r a n g e o r d e r ( e . g . s a t u r a t i o n m a g n e t i z a t i o n o f 3d f e r r o m a g n e t s , s p e c i f i c h e a t and p o s i t r o n a n n i h i l a t i o n ) s u g g e s t t h e a t o m i c a r r a n g e - ment i n n a n o c r y s t a l l i n e m a t e r i a l s t o be d i f f e r e n t from g l a s s e s and

r y s t a l s . T h i s r e s u l t a o r e e s w i t h . t h e s t r u c t u r a l . i n v e s t i g a t i o n s

f ~g s . 8 and 9 ) mntioned;For l e x a m p l e , t h e saturation m a g n e t ~ r a t l o n of a - i r o n which d i f f e r s by o n l y a few p e r c e n t between t h e c r y s t a l l i n e and t h e g l a s s y s t a t e ( 2 9 ) but i t chanaes by a factor ~2 i f one goes from t h e c r y s t a l 1 i n e t o t h e n a n o c r y s t a l l i n e s t a t e ( 2 5 The p r o p o s e d i n t e r - p r e t a t i o n o f t h e e f f e c t s r e p o r t e d i n t e r m s o i ' t h e numerous a t o m l c s t r u c t u r e s p r e s e n t i n t h e i n t e r f a c e s i s s u p p o r t e d by t h e f o l l o w i n g two o b s e r v a t i o n s . A n n e a l i n g o f n a n o c r y s t a l l i n e m a t e r i a l s a t e l e v a t e d t e m p e r a t u r e s c o n v e r t s them back i n t o c o n v e n t i o n a l i r o n a s soon a s

C4-400 JOURNAL DE PHYSIQUE

t h e b o u n d a r i e s a r e r e m o v e d b y g r a i n g r o w t h . M e a s u r e m e n t s o n i s o l a t e d 6 nm i r o n c r y s t a l s o u t o f w h i c h t h e n a n o c r y s t a l l i n e m a t e r i a l s w e r e p r o - d u c e d ( c f . n e x t p a r a g r a p h ) d i d n o t r e v e a l a n y o f t h e s e e f f e c t s . I n f a c t , a l l e f f e c t s w e r e o n l y s e e n when a h i g h d e n s i t y o f g r a i n b o u n d - a r i e s was p r e s e n t .

F o r c o n v e n i e n c e , t h e n a n o c r y s t a l l i n e m a t e r i a l s w e r e g e n e r a t e d b y a mod- i f i e d m e t h o d o f p o w d e r m e t a l l u r g y . The s u b s t a n c e , ( e . g . Fe)was e v a p o r a t - ed i n a n i n e r t ( H e ) a t m o s p h e r e ( p r e s s u r e 1

-

C ! e a r l y , n a n o c r y s t a l l i n e s o l i d s a r e n o t r e s t r i c t e d t o p u r e e l e m e n t s . S ~ m u l t a n e o u s o r c o n s e c u t i v e e v a p o r a t i o n o f s e v e r a l c o m p o n e n t s l e a d t o m u l t i p h a s e m a t e r i a l s . One o f t h e a t t r a c t i v e f e a t u r e s o f m u l t i - p h a s e n a n o c r y s t a l l i n e m a t e r i a l s ( n a n o c r y s t a l l i n e " a l l o y s " ) i s t h a t o n e i s n o t l i m i t e d b y m i s c i b i l i t y o f t h e c o m p o n e n t s i n t h e l i q u i d s t a t e

a s i n t h e c a s e o f m e l t s p i n n i n g , f o r e x a m p l e

.

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R B i r r i n e r

m,

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62,

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.,

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M.J. Weins, H. G l e i t e r and B. Chalrners, J n l . of Appl .Phys. - 42, 2639 (1971) P. Pumphrey, T. Malis and H. G l e i t e r , Phil.Mag. - 34, 159 (1976).

DISCUSSION

K.L. Merkle: Would you c a r e t o s p e c u l a t e about t h e p h y s i c s behind t h e g r e a t reduction i n s a t u r a t i o n magnetization o f t h e s i n t e r e d Fe p o l y c r y s t a l s ? What is t h e reduction i n bulk density?

H. . G l e i t e r : The reduction i n t h e macroscopic d e n s i t y o f t h e n a n o c r y s t a l l i n e m a t e r i a l i s about 50%. A t p r e s e n t we do n o t know how much o f t h i s d e n s i t y d e f i c i t is due t o small voids and how much r e s u l t s from t h e presence o f t h e high d e n s i t y o f i n t e r f a c e s . The observed reduction i n s a t u r a t i o n magnetization is assumed t o be due t o t h e d e v i a t i o n o f n e a r e s t neighbour d i s t a n c e s o f t h e i r o n atoms i n t h e boundary regions a s compared t o t h e p e r f e c t l a t t i c e . It h a s been shown t h e o r e t i c a l l y t h a t a change o f a few percent i n t h e spacing between neighbouring i r o n atoms r e s u l t s i n a s t r o n g reduction o f t h e magnetic moment. Perhaps t h e most w e l l known experimental evidence f o r t h i s e f f e c t is t h e change o f t h e magnetic p r o p e r t i e s o f i r o n when grown a s a t h i n f i l m e p i t a x i a l l y on s u i t a b l e s u b s t r a t e s s o t h a t t h e spacing between neighbouring i r o n atoms d e v i a t e s from t h e equilibrium value i n t h e bulk ( c f . a l s o t h e comments Prof. Andersen).

O.K. Andersen: I would l i k e t o remark t h a t t h e magnetization o f i r o n is highly s e n s i t i v e t o t h e l o c a l atomic coordination. For i n s t a n c e , a t a p r e s s u r e o f 100

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k b a r s , which merely d e c r e a s e s t h e l a t t i c e c o n s t a n t and t h e magnetization by a few p e r c e n t , bcc Fe undergoes a first o r d e r phase t r a n s i t i o n and becomes hcp and nonmagnetic, j u s t l i k e Ru and 0 s . This f a c t , t h a t a few p e r c e n t decrease o f t h e magnetization c a u s e s t h e hcp r a t h e r than t h e bcc s t r u c t u r e t o be s t a b l e was explained by u s s e v e r a l y e a r s ago a s t h e b a s i s o f t h e e l e c t r o n i c s t r u c t u r e . If Fe is constrained t o remain i n t h e hcp ( o r f c c ) s t r u c t u r e ( f o r i n s t a n c e , a s an e p i t a x i a l l a y e r grown on a noble-metal s u b s t r a t e ) and t h e l a t t i c e c o n s t a n t i s now i n c r e a s i n g a few p e r c e n t (by changing t h e composition o f t h e s u b s t r a t e a l l o y ) t h e magnetization r i s e s a b r u p t l y from Oh/atom ( o r 0.6 /atom i n t h e f c c s t r u c t u r e )

t o about 3 /atom.

b

r~

H. G l e i t e r : We a r e aware o f t h e s e observations. I n f a c t , they have been used t o i n t e r p r e t t h e low s a t u r a t i o n magnetization observed ( c f . r e f . 25 o f t h e manuscript).

G. K u I would l i k e t o comment on t h e o r i e n t a t i o n r e l a t i o n s h i p observed i n your i n t e r p h a s e boundary experiments. If you were t o c o n s i d e r t h e e n t i r e i n t e r s e c t i o n group (and n o t only its t r a n s l a t i o n a l subgroup, t h e so-called CSL) you would f i n d t h a t o f your o r i e n t a t i o n r e l a t i o n s , a r e d i c t a t e d t o y i e l d extreme i n i n t e r f a c i a l p r o p e r t i e s . S i n c e you have seen them, we know t h e y - a r e minimas. T h i s is a f i n e example where symmetry arguments, when used i n a g e n e r a l i z e d and ' u n r e s t r i c t e d way may y i e l d u s e f u l information about p r o p e r t i e s .

H. G l e i t e r : I f u l l y a g r e e with Prof. K a l o n j i t s comment. Of c o u r s e , t h e prime motivation f o r o u r experiments was t o f i n d t h e p h y s i c a l p r i n c i p l e which s e l e c t s t h e low energy boundaries from t h e e n t i r e s e t o f boundaries which can be expected on t h e b a s i s o f symmetry o p e r a t i o n s t o y i e l d extrema i n t h e i n t e r f a c i a l p r o p e r t i e s . I n f a c t , t h e problem o f p h y s i d a l l y understanding t h e a t o m i s t i c s t r u c t u r e o f i n t e r f a c e s is analogous t o t h e determination o f t h e s t a b l e c r y s t a l s t r u c t u r e o f a p a r t i c u l a r m a t e r i a l . Crystallography provides t h e framework o f t h e conceivable atom arrangements. However, i n o r d e r t o s e l e c t t h e s t a b l e s t r u c t u r e a m n g a l l conceivable s t r u c t u r e s , we have t o understand t h e p h y s i c a l e f f e c t s c o n t r o l l i n g s t r u c t u r a l s t a b i l i t y .

D. A s t : ( i ) Could you c o m e n t on t h e d e n s i t y d e f i c i t o f t h e s i n t e r e d phase? How is t h i s volume d i s t r i b u t e d ? Mostly a s t t l a r g e t t (say nm) voids o r a s atomic s i z e o r subatomic s i z e " f r e e volumett? ( i i ) Is t h e s i n t e r e d phase s t a b i l i z e d by gas? During r e c r y s t a l l i z a t i o n , is g a s desorbing?

H. G l e i t e r : ( i ) Small angle x-ray s c a t t e r i n g experiments i n d i c a t e t h e presence o f voids t h e average s i z e o f which was about 7 nm i n n a n o c r y s t a l l i n e i r o n with an average c r y s t a l s i z e o f 6 nm. The s c a t t e r i n g experiments showed l i t t l e evidence

f o r voids smaller than about 2 nm. On t h e b a s i s o f t h e s e r e s u l t s and TEM observations on t h e d e n s i t y o f voids (defocus c o n t r a s t o b s e r v a t i o n s ) , one i s led t o conclude t h a t a c o n s i d e r a b l e f r a c t i o n o f t h e observed d e n s i t y d e f i c i t between bulk i r o n and n a n o c r y s t a l l i n e i r o n r e s u l t s from t h e presence o f t h e g r a i n boundaries. ( i i ) There is l i t t l e evidence t h a t t h e n a n o c r y s t a l l i n e s t r u c t u r e i s s t a b i l i z e d by g a s . I r o n specimens were heated up t o 1400 K i n a mass-spectrometer, s o t h a t t h e desorption process could be followed. These experiments showed no measurable desorption o f He.

A. R a i t Could you p l e a s e comment on t h e s t a b i l i t y o f your nanometer g r a i n s i z e p o l y c r y s t a l ?

H. G l e i t e r : On t h e b a s i s o f s t a b i l i t y s t u d i e s involving s e v e r a l n a n o c r y s t a l l i n e metals a s w e l l a s n a n o c r y s t a l l i n e s o l i d s with i o n i c and covalent bonding, it appears t h a t t h e thermal s t a b i l i t y o f t h e n a n o c r y s t a l l i n e m i c r o s t r u c t u r e s c a l e s approximately with t h e melting temperature. Roughly speaking, metals w i t h melting p o i n t s h i g h e r than about 5 0 0 ' ~ a r e found t o be s t a b l e a t ambient temperature o r below.

J.M. Gibson: What is t h e impurity c o n t e n t o f t h e n a n o c r y s t a l l i n e i r o n ? Have you done, f o r example, x-ray fluorescence looking f o r oxygen? It seems t h a t t h e massive s u r f a c e a r e a o f t h e powder used t o prepare t h i s m a t e r i a l might absorb c o n s i d e r a b l e amounts o f i m p u r i t i e s .

H. G l e i t e r : The impurity c o n t e n t was 0.5% o r l e s s ( c f . w r i t t e n version o f t h e manuscript). We have analyzed t h e chemical composition o f o u r specimens by mass spectroscopy and atomic absorption spectroscopy ( c f . r e f . 25 i n t h e w r i t t e n v e r s i o n ) . The oxygen c o n t e n t was determined by a s p e c i a l method capable o f r e v e a l i n g an oxygen c o n c e n t r a t i o n o f 1 ppm. Furthermore oxide formation i n annealed specimens was checked by Mossbauer spectroscopy. None o f t h e methods revealed measurable amounts o f gases. It is c o r r e c t t h a t t h e m a t e r i a l might adsorb c o n s i d e r a b l e amounts o f i m p u r i t i e s a t t h e l a r g e f r e e s u r f a c e . I n o r d e r t o avoid t h i s a d s o r p t i o n , t h e m a t e r i a l was produced by a "self-cleaningtt method ( s i m i l a r t o a Wilson chamber) i n a He atmosphere t h e r e a c t i v e i m p u r i t i e s o f which were removed by g e t t e r i n g them with evaporated i r o n . The g e t t e r m a t e r i a l r e s u l t i n g from t h i s procedure was accummulated on a s e p a r a t e cold t r a p s o t h a t it could n o t i n t e r f e r e w i t h t h e i r o n evaporated subsequently i n t o t h e "cleanedv He i n o r d e r t o o b t a i n t h e n a n o c r y s t a l l i n e m a t e r i a l . This p r e c a u t i o n s turned o u t t o be c r u c i a l f o r o b t a i n i n g n a n o c r y s t a l l i n e i r o n w i t h an impurity c o n t e n t o f < 0.5%.

Y. I s h i d a : Comment: Mijssbauer experiment on 1 1 9 m ~ n i n t h e g r a i n boundary o f Fe showed ferromagnetism is l a r g e l y changed by IVB t o VIB elements ( i n c l u d i n g P). It

C4-404 JOURNAL DE PHYSIQUE

appears t h a t your spectrum should t a k e i n t o account t h i s e f f e c t . The argument o f specimen s t r u c t u r e upon s i n t e r i n g t h e f i n e p a r t i c l e s may be c l a r i f i e d e i t h e r by HREM o r by examining s i m i l a r f i n e grained s t r u c t u r e s such a s ~ r + bombarded Fe t h i n f o i l .

H. G l e i t e r : The p o i n t concerning t h e IVB and VIB i m p u r i t i e s is w e l l taken.

However, a s we know from chemical a n a l y s i s t h a t our specimens contain no measurable amount o f i m p u r i t i e s o f t h i s k i n d , we neglected t h e s e e f f e c t s s o f a r . HREM s t u d i e s a s w e l l a s EXAFS (e.g. NMR, low temperature s p e c i f i c h e a t , XPS) a r e a p p l i e d t o c h a r a c t e r i z e t h e new s t r u c t u r e .

H.T. Sawhill: We a l s o f r e q u e n t l y s e e alignment o f low index d i r e c t i o n s i n Ni/NiO i n t e r f a c e s . I n t h i s c a s e t h e geometry would n o t follow such a "lock-in s t r u c t u r e t f . Would you expect t h a t such a model would apply a l s o t o t r a n s i t i o n metal/ionic i n t e r f a c e s o r can you make conclusions only about noble metal/ionic i n t e r f a c e s ?

H. G l e i t e r : On t h e b a s i s o f t h e d a t a p r e s e n t l y a v a i l a b l e we can draw conclusions only about noble metal/ionic i n t e r f a c e s . An attempt t o extend t h e work t o o t h e r metals w i l l be made.

G. Elssner: Would you a g r e e t h a t your locked-in t y p e o f i n t e r f a c e may be r e s t r i c t e d t o combinations o f metal and i o n i c c r y s t a l s o r s a p p h i r e , r e s p e c t i v e l y , with low i n t e r f a c e energy o r low chemical a f f i n i t y ?

H. G l e i t e r : It is d i f f i c u l t t o comment without having measurements on systems with high i n t e r f a c e energy and/or high chemical a f f i n i t y . However, my guess is t h a t such systems may well show d i f f e r e n t behaviour. Additional r e s e a r c h is planned t o check t h e v a l i d i t y o f t h e nlock-inlf model prbposed f o r systems o t h e r than noble metals and i o n i c c r y s t a l s .