TEM-OBSERVATION AND RELATED O-LATTICE MODEL OF A CLOSE COINCIDENCE BOUNDARY IN ALUMINIUM

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TEM-OBSERVATION AND RELATED O-LATTICE MODEL OF A CLOSE COINCIDENCE BOUNDARY

IN ALUMINIUM

C. Solenthaler, W. Bollmann

To cite this version:

C. Solenthaler, W. Bollmann. TEM-OBSERVATION AND RELATED O-LATTICE MODEL OF A

CLOSE COINCIDENCE BOUNDARY IN ALUMINIUM. Journal de Physique Colloques, 1985, 46

(C4), pp.C4-299-C4-305. �10.1051/jphyscol:1985433�. �jpa-00224683�

JOURNAL DE PHYSIQUE

Colloque CH, supplément au n°4, Tome 46, avril 1985 page C4-299

TEM-OBSERVATION AND RELATED O-LATTICE MODEL OF A CLOSE COINCIDENCE BOUNDARY IN ALUMINIUM

C. Solenthaler and W. Bollmaim

o/o SULZER AG, Abt. 1511, CH-8401 Winterthur, Switzerland

+

22 Chemin Vert, CH-1234 Pinchat, Geneva, Switzerland

Résumé - La structure des joints de grains est représentée, au moyen de la méthode du réseau zéro, sous forme de filets de dislocations. L'idée physique derrière ces considérations est la conservation de certaines structures, c — à-d. d'"états préférés" dans le joint. L'"état préféré primaire" est l'état du monocristal, pendant que des "états préférés secondaires" se forment dans les joints comme motifs périodiques, dues à certaines orientations de coïnci- dence. Pendant que les dislocations représentent des sauts discrets (quanta) de déplacement, les plages entre les dislocations forment l'état préféré, pour- tant quelque peu déformé élastiquement. L'exemple traité est un joint dans de l'aluminium près de l'orientation de coïncidence Z = 59.

Abstract - The structure of grain boundaries can be represented by means of the O-lattice method in terms of dislocation networks. The physical guide-line behind these considerations is that, in the boundary, certain structures, i.e.

"preferred states" are conserved. The "primary preferred state" is the single crystal state, while "secondary preferred states" are periodic patterns in the boundary which are formed in certain coincidence orientations. While the dislo- cations are discrete jumps (quanta) of displacement, the areas within the meshes of the dislocation network are in the preferred state which may, however, be somewhat elastically distorted. The example treated is a boundary in aluminium close to a £ = 59 orientation.

1. Introduction - The O-lattice method, with its mathematical implications, for calculating the dislocation structure of intercrystalline boundaries, is given in [1]. Applications to the study of close coincidence boundaries in aluminium are pre- sented in [2]. The example shown here of a boundary close to £=59 is part of that work.

2. A £=59 Near Coincidence Boundary - TEM-micrographs of the boundary are shown in fig. 1. An ordered set of strong dislocation-contrast lines L. .L is clearly vi- sible. The lines change their direction and spacing in a continuous manner, depen- ding on the orientation and curvature of the interface. The crystallographic para- meters of the boundary have been determined by means of diffraction, tilting experi- ments, and analytical calculation, as follows:

- The relative orientation of crystals 1 and 2, i.e. the transformation A rela- ting crystal lattice 1 to lattice 2 is:

A := R(c

( R )

, e

( R )

) = R([-1.11 -0.95 2.97] 23.81°) (1)

- The approximate interface planes are:

F(n') = (13.89 39.17 90.96) (above e..e, area "A", fig. 1a) F(n

2

) = (31,11 91.11 27.05) (below e..e, area "B", fig. 1a) (coordinates normed to 100)

In order to give an interpretation of the observed dislocation contrast, the

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985433

Fig. 1 TEM-contrast image in dark field. a) - c) have been taken with the (ill)-reflection of crystal 1, d) with the reflection (ill) of crystal 2. The beam direction is [112j. L - L are dislocation contrast lines. D - D marks the trace of a triple line. The line e - e corresponds to the line e - e in fig. 7.

s e c o n d a r y d i s l o c a t i o n s y s t e m was c a l c u l a t e d w i t h r e s p e c t t o t h e r e f e r e n c e s y s t e m :

~ = 5 9 ( [ T i 3 1 24.94')

( 3 )

A l l t h e c a l c u l a t i o n s a r e r e f e r r e d t o t h e c o o r d i n a t e s y s t e m o f c r y s t a l

1.

The a c t u a l d e v i a t i o n o f A ( e q u . 1 ) f r o m E=59, i . e . t h e s e c o n d a r y t r a n s f o r m a t i o n

B

i s :

-

B := !(AC)-' = R ( [ E ^{2 7} 671 ^1.45')

- - ^{! 4 )}

- - S i n c e 5 i s a r o t a t i o n , i t s " r e d u c e d d i s p l a c e m e n t f i e l d " (RDF) i s t h e p l a n e ( 2 7 2 7 6 7 ) n o r m a l t o t h e s e c o n d a r y r o t a t i o n a x i s . The RDF i s c o v e r e d b y t h e s t e p p e d b - n e t ( f i g . 3 ) . The shadowed a r e a s m a r k t h e " b - s t e p s " . The D S C - l a t t i c e u n i t i s g i v e n i n f i g . 2.

W i t h t h e s e c o n d a r y t r a n s f o r m a t i o n B ( e q u . 4 ) a n d t h e b - n e t ( f i g . 3 ) , t h e s o l u - - t i o n o f t h e 0 - l a t t i c e e a u a t i o n i n t h e f o r m :

r e s u l t s i n t h e 0 2 - l a t t i c e c e l l s t r u c t u r e o f f i g . 4 . The l i n e s h e r e h a v e t o be c o n - s i d e r e d a s v e r t i c a l c e l l w a l l s a n d t h e s t r o n g l i n e s m a r k t h e b - s t e p c e l l w a l l s . The s e c o n d a r y d i s l o c a t i o n n e t w o r k w i t h i n t h e b o u n d a r y p l a n e F(nl) ( F ( n z ) r e - s p e c t i v e l y ) i s g i v e n b y t h e c u t t h r o u g h t h e 0 2 - l a t t i c e c e l l s t r u c t u r e o f f i g . 4 . T h e s e n e t w o r k s a r e shown i n f i g s . 5 a n d 6 . The s t r o n g l i n e s show t h e s e q u e n c e s of t h e b - s t e p d i s l o c a t i o n s . The B u r g e r s v e c t o r s a r e a t t r i b u t e d t o t h e d i s l o c a t i o n l i n e s b y means o f t h e d u a l i t y r e l a t i o n s f r o m t h e b - n e t ( f i g . 3 ) .

F i g . 2

D S C - l a t t i c e u n i t c e l l o f C=59 ( [ 1 1 3 ] 24.94')

C4-302 JOURNAL DE PHYSIQUE

k 10 nm

I

Fig.

4

0 2 - l a t t i c e c e l l s t r u c t u r e . C u t p a r a l l e l t o t h e RDF, i . e . normal t o t h e 0 2 - l i n e s

( s m a l l c i r c l e s ) . The s t r o n g l i n e s mark t h e b-step c e l l w a l l s .

Fig. 5 Cut through the 02-lattice cell structure parallel to the interface plane F (%') . Secondary dislocation network within F

(&I)

. The strong lines show the b-step dislocation sequences. Fig. 6 Analogous to fig. 5 but for the interface plane F(2').

JOURNAL DE PHYSIQUE

The c a l c u l a t e d d i s l o c a t i o n s y s t e m i s now p r o j e c t e d i n t o t h e a c t u a l TEM-beam d i r e c t i o n

[112.]

( f i g .

7 )

a n d c o m p a r e d w i t h t h e g i v e n T E i ' 4 - c o n t r a s t i m a g e . We n o t e t h a t t h e c a l c u l a t e d b - s t e p d i s l o c a t i o n s e q u e n c e s r e f l e c t i n a c l o s e l y c o n s i s t e n t way t h e o v e r a l l c o n f i g u r a t i o n o f t h e o b s e r v e d d i s l o c a t i o n - c o n t r a s t l i n e s , a l t h o u g h t h e r e a r e some d i f f e r e n c i e s w i t h r e s p e c t t o l i n e d i r e c t i o n and s p a c i n g , due t o t h e l i m i t e d p r e c i s i o n o f t h e p r i m a r y m e a s u r e m e n t s . I n t h e m i c r o g r a p h s ( f i g s . l c , d ) t h e r e i s e v e n c l e a r e v i d e n c e f o r t h e f i n e - s c a l e d z i g - z a g o f t h e b - s t e p d i s l o c a t i o n se- q u e n c e s .

F i g .

7

P r o j e c t i o n o f t h e c a l c u l a t e d d i s l o c a t i o n s y s t e m a l o n g t h e a c t u a l TEM-beam d i r e c t i o n

[112].

The shadowed a r e a s show t h e a v e r a g e p r o - j e c t e d d i r e c t i o n o f t h e b - s t e p d i s l o c a t i o n s e q u e n c i e s .

3. C o n c l u s i o n s - T E M - o b s e r v a t i o n s o f g r a i n b o u n d a r y d i s l o c a t i o n s y s t e m s , t o g e t h e r w i t h t h o r o u g h t h e o r e t i c a l i n t e r p r e t a t i o n , c a n g i v e i n s i g h t i n t o t h e r e l a x a t i o n p r o - c e s s i n b o u n d a r i e s . The 0 - l a t t i c e c o n c e p t c a n , s t a r t i n g f r o m 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 o f t h e b o u n d a r y , p r e d i c t t h e i m p o r t a n t f e a t u r e s o f

a

r e l a t e d g r a i n boun- d a r y d i s l o c a t i o n s y s t e m i n t o v e r y f i n e d e t a i l s e v e n i n g e o m e t r i c a l l y c o m p l i c a t e d s i t u a t i o n s - d e t a i l s w h i c h a r e c o m p l e t e l y n e g l e c t e d , f o r e x a m p l e , b y t h e " p l a n e m a t c h i n g " a p p r o a c h

[ 3 ] .

A c k n o w l e d g e m e n t - One a u t h o r (C.S.) w o u l d l i k e t o e x p r e s s h i s g r a t i t u d e t o SULZER AG, W i n t e r t h u r , f o r i t s g e n e r o u s s u p p o r t o f t h i s w o r k .

R e f e r e n c e s

[ I ] B o l l m a n n , W . ,

" C r y s t a l L a t t i c e s , I n t e r f a c e s , M a t r i c e s " , p r i v a t e l y p u b l i s h e d

(1982)

[ 2 ] S o l e n t h a l e r , C.,

D o c t o r a l T h e s i s n o .

7235, ETH

Z u r i c h

(1983) [ 3 ] Pumphrey, P . H . ,

S c r i p t a M e t . 6,

107

-

1 1 4 , (1972)