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QUANTIFICATION OF INTERCONNECTED MICROSTRUCTURES BY FIM
P. Camus, W. Soffa, S. Brenner, M. Miller
To cite this version:
P. Camus, W. Soffa, S. Brenner, M. Miller. QUANTIFICATION OF INTERCONNECTED MI- CROSTRUCTURES BY FIM. Journal de Physique Colloques, 1984, 45 (C9), pp.C9-265-C6-268.
�10.1051/jphyscol:1984945�. �jpa-00224426�
JOURNAL DE PHYSIQUE
Colloque C9, supplément au n°12, Tome »5, décembre 1984 page C9-265
QUANTIFICATION OF INTERCONNECTED MICROSTRUCTURES BY FIM
P . P . Camus, W.A. S o f f a , S . S . Brenner and M.K. M i l l e r * University of Pittsburgh, Pittsburgh, PA 1S236, U.S.A.
*Oak Ridge National Laboratory, Oak Ridge, TN 37831, U.S.A.
RESUME - Les propriétés physiques des matériaux biphasés sont en grande partie déterminées par la morphologie de la microstructure. Pour les matériaux contenant des précipités isolés, la microstructure pourra être entièrement définie par la taille, la forme et la densité des par- ticules. Néanmoins, pour les systèmes dont les deux phases sont inter- connectées, la morphologie est beaucoup plus difficile à décrire quan- titativement. Cet article fait le point sur quelques approches possi- bles permettant par microscopie ionique de champ, d'obtenir les para- mètres quantitatifs pour décrire des morphologies plus complexes.
ABSTRACT - The physical properties .of two-phase materials are largely determined by the morphology of the microstructure. With materials containing isolated precipitates, the microstructure can be fully defined by the size, shape, and number density of the particles.
However, in systems in which both phases are interconnected, a quantitative description of the morphology is much more difficult to make. This paper points out some possible approaches to obtaining quantitative parameters to describe these more complex morphologies using field ion microscopy.
I. INTRODUCTION
P r e v i o u s APFIM s t u d i e s have c l e a r l y demonstrated for t h e f i r s t time t h a t t h e m o r p h o l o g y of t h e m i c r o s t r u c t u r e t h a t forms by s p i n o d a l decomposition i n t h e iron-chromium and i r o n - c h r o m i u m - c o b a l t systems i s i s o t r o p i c and h i g h l y i n t e r c o n n e c t e d o r p e r c o l a t e d i n t h r e e d i m e n s i o n s [ 1 , 2 ] . The observed m i c r o s t r u c t u r e c o a r s e n s v e r y s l o w l y and i t has been proposed t h a t t h i s i s c l o s e l y r e l a t e d t o t h e morphology of t h e h i g h l y i n t e r c o n n e c t e d two p h a s e m i c r o s t r u c t u r e [ 1 ] . To d e t e r m i n e t h e e f f e c t of m o r p h o l o g y on c o a r s e n i n g , i t i s n e c e s s a r y t o h a v e a q u a n t i t a t i v e parameter of t h e morphology.
The f i e l d - i o n m i c r o s c o p e may be t h e i d e a l i n s t r u m e n t t o p r o v i d e t h e r e q u i r e d m o r p h o l o g i c a l p a r a m e t e r b e c a u s e of i t s u n i q u e s e c t i o n i n g c a p a b i l i t y with which a t h r e e - d i m e n s i o n a l view of t h e m a t e r i a l can be g e n e r a t e d . T h i s p a p e r o u t l i n e s p o s s i b l e a p p r o a c h e s t o t h e q u a n t i f i c a t i o n of t h e morphology of i n t e r c o n n e c t e d m i c r o s t r u c t u r e s and p o i n t s o u t some Of t h e d i f f i c u l t i e s .
II. PERCOLATION
P e r c o l a t i o n t h e o r y p r e d i c t s t h a t i s o l a t e d p a r t i c l e s w i l l e x i s t i n any s t r u c t u r e where t h e volume f r a c t i o n i s l e s s than a c r i t i c a l v a l u e [ 3 ] , At v o l u m e f r a c t i o n s g r e a t e r t h a n t h i s c r i t i c a l v a l u e i n i s o t r o p i c systems, t h e t h e o r y p r e d i c t s t h a t t h e r e w i l l be a f i n i t e p r o b a b i l i t y of an i n f i n i t e l y s i z e d c l u s t e r . The c r i t i c a l volume f r a c t i o n , known a s t h e p e r c o l a t i o n l i m i t , i s 50 % i n two dimensional systems and o n l y 15 % i n t h r e e d i m e n s i o n a l s y s t e m s . I n a m a t e r i a l a b o v e t h e p e r c o l a t i o n l i m i t , an i n t e r c o n n e c t e d m i c r o s t r u c t u r e may e x i s t w i t h l o o p s or c i r c u i t s of one phase e n v e l o p i n g t h e o t h e r phase.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984945
C9-266 JOURNAL DE PHYSIQUE
I n m a t e r i a l s b e l o w t h e p e r c o l a t i o n 1 i m i t t h e m i c r o s t r u c t u r e o f i s o l a t e d p a r t i c l e s , a s shown i n t h e e v a p o r a t i o n s e q u e n c e o f f i e l d - i o n m i c r o g r a p h s i n f i g u r e 1, c a n b e f u l l y d e s c r i b e d by p a r a m e t e r s s u c h a s
s i z e , s h a p e , a n d number d e n s i t y . H o w e v e r , i n m a t e r i a l s a b o v e t h e p e r c o l a t i o n l i m i t b e c a u s e o f t h e p o s s i b i l i t y o f i n f i n i t e s i z e d p a r t i c l e s , t h e s e p a r a m e t e r s a r e n o t n e c e s s a r i l y a p p l i c a b l e a n d d o n o t f u l l y d e s c r i b e t h e m i c r o s t r u c t u r e . The a v e r a g e s p a c i n g a n d mean i n t e r c e p t o f o n e p h a s e , t h a t h a v e b e e n p r e v i o u s l y u s e d t o d e s c r i b e p e r c o l a t e d m i c r o s t r u c t u r e s , a r e a m e a s u r e o f t h e s c a l e o f t h e m i c r o s t r u c t u r e b u t t h e y d o n o t d e s c r i b e i t f u l l y , i n p a r t i c u l a r t h e d e g r e e o f i n t e r c o n n e c t i v i t y .
111. TOPOLOGY
The m o r p h o l o g y may a l s o b e d e s c r i b e d b y t h e m e a s u r e m e n t o f t h e t o p o l o g i c a l p r o p e r t i e s . T h e s e t y p e o f m e a s u r e m e n t s d e s c r i b e t h e c o n n e c t i v i t y o f t h e s t r u c t u r e b u t i g n o r e t h e d e t a i l s of t h e s i z e and s h a p e [ 4 ] . I n t h i s a p p r o a c h t h e s t r u c t u r e i s s e c t i o n e d a n d r e c o n s t r u c t e d t o p r o d u c e a r e d u c e d n e t w o r k o f n o d e s t h a t a r e c o n n e c t e d by b r a n c h e s a s shown i n f i g u r e 2. The s t r u c t u r e i s t h e n c h a r a c t e r i z e d by t h e t o p o l o g i c a l i n v a r i a n t s g i v e n by
where Po and P1 a r e t h e z e r o t h and f i r s t B e t t i number, b and n a r e t h e number o f b r a n c h e s a n d n o d e s r e s p e c t i v e l y . P1 i s t h e n u m b e r o f t h e b r a n c h e s which may b e removed w i t h o u t c r e a t i n g new s e p a r a t e p a r t s and Po i s t h e number of s e p a r a t e p a r t s . The g e n u s o r t h e number of c l o s e d l o o p s p e r u n i t v o l u m e may a l s o b e c a l c u l a t e d f r o m t h i s d a t a .
The most s e r i o u s p r o b l e m a s s o c i a t e d w i t h t h i s t y p e of a n a l y s i s i s t h e l a r g e number of s e c t i o n s t h a t must b e r e c o r d e d s o t h a t a s i g n i f i c a n t number o f n o d e s a n d b r a n c h e s a r e r e c o r d e d . T h i s t y p e o f a n a l y s i s i s a l s o r e s t r i c t e d t o t h e f i n e r s t r u c t u r e s s o t h a t t h e f u l l e x t e n t o f t h e l o o p s i s i n t e r s e c t e d w i t h i n t h e l a t e r a l f i e l d of view.
I V . FRACTALS
A r e l a t i v e l y new a p p r o a c h t o d e s c r i b e t h e g e o m e t r i c a l f e a t u r e s o f c o m p l e x , i r r e g u l a r l y s h a p e d s t r u c t u r e s i s u s i n g t h e c o n c e p t o f f r a c t a l s d e v e l o p e d by M a n d e l b r o t [ 5 1. F r a c t a l s r e p r e s e n t o b j e c t s o r p a t t e r n s t h a t a p p e a r s e l f - s i m i l a r i n d e p e n d e n t o f s c a l e . D e t a i l e d m e a s u r e m e n t o f t h e p a t t e r n s l e a d s t o a f r a c t a l d i m e n s i o n w h i c h i s a m e a s u r e o f t h e d e n s i t y w i t h w h i c h a c u r v e f i l l s a s p a c e . F r a c t a l a n a l y s i s h a s b e e n f o u n d t o b e u s e f u l i n a n a l y z i n g p e r c o l a t e d s t r u c t u r e s . H o w e v e r , a t t h i s s t a g e o f d e v e l o p m e n t , t h e f r a c t a l a n a l y s i s of e x p e r i m e n t a l d a t a i n g e n e r a l and f i e l d - i o n m i c r o g r a p h s i n p a r t i c u l a r i s e x t r e m e 1 y d i f f i c u l t a n d t i m e c o n s u m i n g b e c a u s e o f t h e p o i n t - w i s e c a l c u l a t i o n which must b e performed.
ACKNOWLEDGMENTS
R e s e a r c h s p o n s o r e d by t h e N a t i o n a l S c i e n c e F o u n d a t i o n u n d e r a I n d u s t r y / U n i v e r s i t y c o o p e r a t i v e g r a n t DMR-8022225. A d d i t i o n a l s u p p o r t p r o v i d e d b y t h e D i v i s i o n o f M a t e r i a l s S c i e n c e s , U.S. D e p a r t m e n t o f Energy, u n d e r c o n t r a c t DE-AC05-840R21400 w i t h M a r t i n M a r i e t t a Energy S y s t e m s , I n c .
FIGURE 1. Series of field ion micrographs showing the appearance a n d disappearance of an isolated particle. Amount of material remov'ed between each microqraph is 4.0 nm.
JOURNAL DE PHYSIQUE
F i g u r e 2 . S t a g e s of t o p o l o g i c a l a n a l y s i s of a f i e l d i o n m i c r o g r a p h : ( a ) F i e l d i o n m i c r o g r a p h showing b r i g h t l y i m a g i n g and
i n t e r c o n n e c t e d d a r k l y i m a g i n g p h a s e s
( b ) R e p r e s e n t a t i v e n e t w o r k o f d a r k l y imaginq p h a s e
( c ) Reduced node and b r a n c h n e t w o r k o f t h e m i c r o s t r u c t u r e
REFERENCES
1. S.S. B r e n n e r , M.K. M i l l e r , a n d W.A. S o f f a , S c r i p t a Met., 1 6 , 8 3 1 , 1982
2. S.S. B r e n n e r , P.P. Camus, M.K. M i l l e r , a n d W.A. S o f f a , A c t a M e t . , i n P r e s s
3 . J . T . Edwards,and R . I . S a u n d e r s o n , S c r i p t a Met., 1 0 , 1 0 8 7 , 1976 4. R.T. DeHoff and F.N. R h i n e s , " Q u a n t i t a t i v e Microscopy",
McGraw-Hi 11, N Y , 1968
5. B.B. Mandelbrot,!'The F r a c t a l Geometry o f N a t u r e " , W.H. Freeman and Co., N Y , 1 9 8 2
