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TEM DETERMINATION OF INCOHERENT
TWIN-BOUNDARY STRUCTURE IN L12 ORDERED ALLOYS
F. Tichelaar, F. Schapink
To cite this version:
F. Tichelaar, F. Schapink. TEM DETERMINATION OF INCOHERENT TWIN-BOUNDARY
STRUCTURE IN L12 ORDERED ALLOYS. Journal de Physique Colloques, 1988, 49 (C5), pp.C5-
293-C5-298. �10.1051/jphyscol:1988535�. �jpa-00228032�
JOURNAL DE PHYSIQUE
C o l l o q u e C5, s u p p l 6 m e n t a u n o l O , Tome 4 9 , o c t o b r e 1 9 8 8
TEM DETERMINATION OF INCOHERENT TWIN-BOUNDARY STRUCTURE IN L 1 2 ORDERED ALLOYS
F.D. TICHELAAR a n d F.W. SCHAPINK
L a b o r a t o r y of M e t a l l u r g y , D e l f t U n i v e r s i t y of T e c h n o l o g y , R o t t e r d a m s e w e g 137, NL-2628 AL D e l f t , The N e t h e r l a n d s
A b s t r a c t . The s t r u c t u r e of i n c o h e r e n t z = 3 t w i n b o u n d a r i e s i n t h e L12 o r d e r e d a l l o y Cu3Au i s i n v e s t i g a t e d employing TEM. The boundary p l a n e s a r e found t o v a r y a b o u t t e n d e g r e e s from a { 1 1 2 ) p l a n e . Employing t h e TEM method o f a - f r i n g e s common d i f f r a c t i o n v e c t o r s a r e u s e d f o r d e t e r m i n i n g t h e r i g i d - b o d y t r a n s l a t i o n between t h e two c r y s t a l s a t t h e b o u n d a r y . No d i l a t a t i o n h a s b e e n f o u n d a t a ( 7 5 3 ) i n c o h e r e n t t w i n b o u n d a r y w i t h i n e x p e r i m e n t a l e r r o r . Four g r a i n b o u n d a r y areas h a v i n g d i f f e r e n t t r a n s l a t i o n s t h a t p r e s e r v e t h e d e n s i t y i n t h e boundary a r e d e m o n s t r a t e d , s e p a r a t e d from e a c h o t h e r b y a n a n t i p h a s e boundary on one s i d e o f t h e boundary p l a n e .
I n t r o d u c t i o n . I n o r d e r e d a l l o y s g r a i n b o u n d a r y s t r u c t u r e p l a y s a p a r t i c u l a r l y i m p o r t a n t r o l e i n d e t e r m i n i n g m e c h a n i c a l p r o p e r t i e s [ I ] , a n d c o n s e q u e n t l y t h i s s u b j e c t h a s b e e n s t u d i e d i n r e c e n t y e a r s by s e v e r a l a u t h o r s . A n a l y s i s was made o f c o i n c i d e n c e g r a i n b o u n d a r i e s i n L20 ( C s C 1 ) a n d L 1 2 (Cu3Au) o r d e r e d a l l o y s , b a s e d on t h e g e o m e t r i c a l coincidence-site-lattice (CSL) model [ 2 , 3 , 4 ] . A l s o s p a c e g r o u p t h e o r e t i c a l a n a l y s i s [5,61 a n d computer s i m u l a t i o n o f g r a i n b o u n d a r i e s i n N i 3 A 1 171 h a v e b e e n c a r r i e d o u t . However, v e r y few e x p e r i m e n t a l i n v e s t i g a t i o n s have b e e n r e p o r t e d s o f a r . T i c h e l a a r a n d S c h a p i n k [ 8 ] s t u d i e d c o h e r e n t t w i n b o u n d a r i e s i n o r d e r e d Cu3Au a n d f o u n d two s t r u c t u r e s : o n e s y m m e t r i c a n d t h e o t h e r a s y m m e t r i c , s e p a r a t e d by a d i s l o c a t i o n i n t h e g r a i n boundary w i t h B u r g e r s v e c t o r <112>/6 o r by an A P B t e r m i n a t i n g i n t h e t w i n b o u n d a r y w h i c h c a u s e s a <110>/2 t r a n s l a t i o n o f t h e two c r y s t a l s r e l a t i v e t o e a c h o t h e r .
I n t h i s p a p e r we r e p o r t t h e r e s u l t s o f a TEM i n v e s t i g a t i o n on t h e s t r u c t u r e o f i n c o h e r e n t t w i n b o u n d a r i e s o f { I 1 2 1 t y p e i n o r d e r e d Cu3Au.
E x ~ e r i m e n t a l D r o c e d u r e . Cu3Au specimens were made from a m e l t , h a v i n g a c o m p o s i t i o n o f 25,02 % Au, by a r c - m e l t i n g u s i n g s p e c t r o g r a p h i c a l l y p u r e Cu and h i g h - p u r i t y g o l d ( 9 9 . 9 9 % ) . T h i s a l l o y was r o l l e d , with i n t e r m e d i a t e a n n e a l s a t 600 OC f o r 20 m i n u t e s , t o 100 p.m s h e e t . The s h e e t was r e c r y s t a l l i z e d by a n n e a l i n g a t 900 OC f o r 1 2 h i n vacuum T o r r ) , s l o w l y c o o l e d t o 375 O C i n 50 h , a n d s u b s e q u e n t l y a n n e a l e d a t 375 OC f o r 25 d a y s i n o r d e r t o o b t a i n an a v e r a g e domain s i z e o f a b o u t 0 . 5 Fm. D i s c s f r o m t h e s h e e t were e l e c t r o c h e m i c a l l y t h i n n e d f o r TEM by j e t - p o l i s h i n g , u s i n g a n e l e c t r o l y t e c o n t a i n i n g 15 % p e r c h l o r i c a c i d a n d 85 % a c e t i c a c i d . Some d e p o s i t i o n o f g o l d from t h e e l e c t r o l y t e o n t o t h e specimen s u r f a c e a n d l o c a l e t c h i n g c o u l d n o t be a v o i d e d ; t h i s u n f o r t u n a t e l y l e d t o a n i n c r e a s e d background c o n t r a s t i n many c a s e s . S p e c i m e n s were e x a m i n e d i n a P h i l i p s 400T e l e c t r o n m i c r o s c o p e .
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988535
JOURNAL
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PHYSIQUE$;I: p2'mm' A I a : p2'm b' A 1 b : p l A I c : p l
SII: p2'mm' ~Ila:p2'mb' A l l b: p'l A I I c : pl Figure 1 : [ o l d -projection of symmetric *B-atom i n the plane of paper
and asymmetric configurations of a <=3 P A - a t o m a / E above the plane of paper (217) twin boundary i n a Cu Au ordered
a l l o y , with t h e i r b i c r y s t a l layer 3 *B-atom a / 2 G below the plane of paper
groups. E A - a t o m a / 2 n above the plane of paper
( 1 1 2 ) t w i n b o u n d a r y
structures.
D i f f e r e n t p o s s i b l e c o n f i g u r a t i o n s o f t h e u n r e l a x e d { I 1 2 1 t w i n b o u n d a r y i n o r d e r e d Cu3Au w i l l b e c o n s i d e r e d i n t h i s s e c t i o n . Upon o r d e r i n g t h e l a t t i c e o f t h e Cu3Au a l l o y c h a n g e s f r o m f . c . c . t o s . c . ; t h e s p a c e g r o u p t r a n s f o r m s from Fm3m i n t o Pm3m.S i n c e t h e Au a t o m s c a n o c c u p y a n y o f t h e f o u r s u b l a t t i c e s , t h e r e a r e f o u r p o s s i b l e domains. A n t i p h a s e b o u n d a r i e s (APBs) between domains a r e c h a r a c t e r i z e d b y a t r a n s l a t i o n ( a n t i p h a s e v e c t o r ) o f t h e t y p e 3 = < 1 1 0 > / 2 . F i g u r e 1 shows t h e two p o s s i b l e u n r e l a x e d s y m m e t r i c a l c o n f i g u r a t i o n s ( S I a n d S I I ) f o r t h e b o u n d a r y . S i x a s y m m e t r i c s t r u c t u r e s ( A I a , A I I a , e t c . ) c a n b e g e n e r a t e d f r o m S I a n d S I I by a n APB t e r m i n a t i n g i n t h e g r a i n b o u n d a r y , which c a u s e s a < 1 1 0 > / 2 - t y p e t r a n s l a t i o n o f t h e two c r y s t a l s r e l a t i v e t o e a c h o t h e r . N o t i c e t h a t a - p = [ 1 1 0 ] / 2 - t y p e APB c h a n g e s S I i n t o AIb o r A I I b i f t h e a t o m s i n t h e b o u n d a r y p l a n e a r e p a r t o f t h e l o w e r o r t h e u p p e r c r y s t a l r e s p e c t i v e l y . A d i s l o c a t i o n i n t h e g r a i n b o u n d a r y w i t h B u r g e r s v e c t o r 1 / 3 [ 1 7 1 ] , a s s o c i a t e d w i t h a 1 / 1 2 [ 2 1 i ] s t e p i n t h e b o u n d a r y p l a n e , a l s o c h a n g e s a s y m m e t r i c a l s t r u c t u r e i n t o a n a s y m m e t r i c a l o n e ( S I i n t o A I I a o r S I I i n t o A I a ) . The two s y m m e t r i c s t r u c t u r e s c a n b e t r a n s f o r m e d i n t o e a c h o t h e r b y a n APB i n e a c h c r y s t a l t e r m i n a t i n g i n t h e boundary,
(a) DF
%=[iio] -
Figure 2: Electron micrographs showing the incoherent (75z) twin boundary and some APBs in ordered Cu Au. Dark-field micrographs (a) and ( b ) were taken of the same area using different common superlattice reflections. Bright-field micrograph (c) 3 shows all APBs in a larger area. Numbers are assi n e c t o different domains. The scale marker indicates 1000
1.
The foil normal is78 11 21.
Antiphase vectors are[loll /2 for APBI
,
APB3 and APB4; [01 I] /2 for APB5 and [I 101 12 for APB2. All indices refer to the matrix.h a v i n g m i r r o r r e l a t e d
5,
i n c l i n e d t o t h e boundary p l a n e .The l o c a l c o m p o s i t i o n i n t h e boundary a r e a o f t h e s t r u c t u r e s S I , S I I , AIa a n d A I I a i s s t o i c h i o m e t r i c . T h i s i s n o t t h e c a s e f o r AIb ( e x c e s s of Au) and A I I b ( e x c e s s of Cu)
.
However, t h e s e two s t r u c t u r e s c a n b e t r a n s f o r m e d i n t o e a c h o t h e r b y c h a n g i n g o n l y t h e atoms i n t h e b o u n d a r y plane, w h i c h c a u s e s a c h a n g e i n c o m p o s i t i o n . A l s o , ani s o l a t e d 1 / 4 [ 2 1 1 ] s t e p i n t h e boundary p l a n e c h a n g e s AIb i n t o A I I c . The s t r u c t u r e s AIb a n d AIc ( a n d a l s o A I I b and A I I c ) a r e m u t u a l l y r e l a t e d by t h e (011) o r d i n a r y m i r r o r p l a n e ( t h e p l a n e o f p r o j e c t i o n ) e x i s t i n g i n t h e holosymmetric s t r u c t u r e s S I o r S I I ; c o n s e q u e n t l y t h e s e s t r u c t u r e s a r e e q u i v a l e n t . The b i c r y s t a l l a y e r g r o u p s of t h e remaining s i x c o n f i g u r a t i o n s a r e i n d i c a t e d i n f i g . 1 . I f a r i g i d - b o d y t r a n s l a t i o n t h a t d e s t r o y s t h e m i r r o r symmetry i n d i c a t e d above i s p a r t o f a r e l a x a t i o n a t t h e boundary, t h e n t h e above r e l a t i o n between AIb and AIc no l o n g e r e x i s t s .
R e s u l t s a n d d i s c u s s i o n . F i g u r e s 2 ( a ) and ( b ) a r e two m i c r o g r a p h s o f an i n c o h e r e n t t w i n b o u n d a r y a n d some APBs, e m p l o y i n g two common s u p e r l a t t i c e r e f l e c t i o n s
g c .
From t h e s e m i c r o g r a p h s , t h e domain s t r u c t u r e h a s been a n a l y s e d u s i n g t h e i n v i s i b i l i t y c r i t e r i o n f o r APBs 2nCj.p=0 (mod 2n) [ 9 ] . Domain numbers on b o t h s i d e s o f t h e boundary a r e d e s i g n a t e d by a s u b s c r i p t m o r t r e s p e c t i v e l y . I n f i g u r e 2 ( c ) a l a r g e r a r e a of t h e same t w i n b o u n d a r y i s shown. I n t h i s m i c r o g r a p h t h r e e< l l O > - t y p e s u p e r l a t t i c e r e f l e c t i o n s a r e o p e r a t i v e , a n d c o n s e q u e n t l y a l l APBs show c o n t r a s t .
The t w i n b o u n d a r y p l a n e i s ( 7 5 ; ) , d e v i a t i n g from ( 2 1 7 ) . A l l i n c o h e r e n t %3 t w i n boundary p l a n e s i n v e s t i g a t e d s o f a r were found t o d e v i a t e 5O t o
l o 0
from { 2 1 1 ) , which p r o b a b l y i n d i c a t e s t h a t t h e t211) p l a n e i s u n f a v o u r a b l e , a s opposed t o s i m i l a r t w i n b o u n d a r i e s i n somef . c . c . m e t a l s [ l o ] .
-
I n o r d e r t o d e t e r m i n e t h e r i g i d body t r a n s l a t i o n t of t h e two c r y s t a l s r e l a t i v e t o e a c h o t h e r , t h e TEM method of a - f r i n g e s i s
C5-296 JOURNAL
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PHYSIQUEemployed [ I l l , i n which common d i f f r a c t i o n v e c t o r s ?jC a r e u s e d . For t h r e e n o n - c o p l a n a r
q C 1 s
t h e c o n t r a s t i n t h e boundary IS matched t o a c a l c u l a t e d c o n t r a s t f o r whichgC.5
i s known, r e s u l t i n g i n a u n i q u e v a l u e o f (mod a DSCO v e c t o r ) : DSCO r e p r e s e n t s a n e l e m e n t o f t h e d i s p l a c e m e n t - s h i f t - c o m p l e t e ( D S C ) - l a t t i c e a s s o c i a t e d w i t h t h e o r d e r e d s t r u c t u r e . The s h o r t e s t DSCO v e c t o r s f o r %3 a r e 1 / 3 [ 2 1 i ] , 1 / 3 [ 1 2 1 ] a n d 1 / 3 [ l ' i l ] [ 1 2 ] . L i k e w i s e t h e -DScd v e c t o r s a s s o c i a t e d -with t h e d i s o r d e r e d s t r u c t u r e a r e 1 / 6 [ 2 1 1 1 , 1 / 6 [ 1 2 1 1 and* 1 / 3 [ I l l ] . The boundary w i l l show no c o n t r a s t i f ?EDSCO a n dG c ~ ~
( t h e l a t t i c e of~ ~ O
t h e common s u p e r l a t t i c e c e f l e c t i o n s ) , b e c a u s e 4,.t=n (n=O, l r 2 , . . . )
.
The c o n t r a s t was c a l c u l a t e d u s i n g t h e computer program d e v e l o p e d by Blom [ 1 3 ] , e m p l o y i n g t h e many-beam d y n a m i c a l t h e o r y o f e l e c t r o n d i f f r a c t i o n . F o r e a c h c a l c u l a t i o n s i x r e f l e c t i o n s i n a s y s t e m a t i c row were u s e d , a n d a b s o r p t i o n w a s i n c l u d e d .
The r e s u l t s o f t h e m a t c h i n g p r o c e d u r e e m p l o y i n g t h r e e common r e f l e c t i o n s a r e shown i n f i g u r e 3 f o r two p a r t s o f t h e b o u n d a r y s e p a r a t e d b y APBl ( s e e f i g . 2 ) , G e s i g n a t e d 3 q / l t a n d 3 m / 3 t . The u n c e _ r t a i n t y i n t h e v a l u e s f o r ?j . t g i v e n i n f l g u r e 3 i s 0 . 1 5 f o r
~ c = [ l l O ] , 0 . 1 f o r 4c=[311] a n d 0 . 8 5 f o r g c = [ O 1 l ] . The u n s a t i s f a c t o r y match f o r some s u p e r l a t t i c e r e f l e c t i o n s r e s u l t s from t h e p o o r q u a l i t y o f t h e s p e c i m e n s u r f a c e , e s p e c i a l l y when c o n t r a s t i s low; a l s o i n a c c u r a c i e s i n s p e c i m e n t h i c k n e s s ( m e a s u r e d a s 850 A ) a n d i n t h e d e v i a t i o n p a r a m e t e r s (measured a s 0.0
+
0 . 5 . 1 0 - ~ I / & ) p l a y a r o l e . F i n a l l y a b s o r p t i o n m i g h t b e d i f f e r e n t f r o m t h e v a l u e t a k e n - i n t o a c c o u n t . The m a t c h i n g p r o c e d u r e was a l s o carr>ed_ o u t f o r g c = [ 2 0 2 ] , gc=[022] anti gc=[220L. The r e s u l t i n g v a l u e s o f g c . t a r e shown i n t a b l e 1. ~ l l v a l u e s o f g t _are c o n s i s t e n t , which r e d u c e s t h e u n c e r t a i n t i e s i n t h e v a l u e s o f'ic.
t g i v e n i n f i g . 3 . F o r e a c h g c t h e m a t c h i n g p r o c e d u r e WisS c a r r i e d o u t f o r +pc-and-qc,
i n b o t h BF and DF.F u r t h e r m o r e , f o r ?jc=[O1l], ?jc.t f o r 3m/3t a l m o s t e q u a l s 0 . 5 , which i s c o n s i s t e n t w i t h t h e a l m o s t s y m m e t r i c a l DF c o n t r a s t i n t h i s c a s e . Dark- f i e l d c o n t r a s f i s s y m m e t r i c a l w i t h r e s p e c t t o t h e m i d d l e of t h e f o i l o n l y when g c . t = 0 . 5 i n t h e c a s e o f a b s o r p t i o n . A l s o t h e v a l u e g c . f = 0 . 9 5 ( c l o s e t o 1 ) f o r 3,/lt i s c o n s i s t e n t w i t h t h e low c o n t r a s t i n t h i s boundary a r e a .
F o r ?jc=[j.iO] t h e d a r k - f i e l d c o n t r a s t f o r 3,,,/3t i s t h e m i r r o r image of 3,/lt w i t h r e s p e c t t o t h e m i d d l e of - t h e fo11.-Also t h e c o n t r a s t i s r e v e r s e d when
9,
i s i n v e r t e d . S i n c e t (3,/3,=) = t ( 3 , / l t )+c
(APB1) and~ ( A P B 1 ) = 1 / 2 [ 1 0 1 ] , t h e f o l l o w i n g e q u a t i o n s
-
a r e o b t a i n e d :-?jc.? (3m/3t)=gc.€ ( 3 / I t ) (mod I ) , g c . t ( 3 / 3 t ) = g C . t (3,/lt) + 0 . 5 (mod 1)
.
The s o l u t i o ~ ~ i s
Qc.y
(3m/3t) = 0 . 2 5 (mod 1 ? 2 ) , whlch i s c o n s i s t e n t w i t h [ 2 2 0 ] . t = 0 . 5 (mod 1 ) .-
-
Using v a l u e s o fg c . t
f o r ? j c = [ O l l ] , ?jc=[iiO] and ?jc=[311] ( f i g u r e 3 ) t f o l l o w s f o r t h e boundary a r e a 3m/3t ( c f . f i g u r e 2 ) :O t h e r t r a n s : L a t i o n s , d e r i v e d from
t
(3m/3t) by a d d i n g e l e m e n t s of DSCOa r e conside1:ed i m p r o b a b l e , s i n c e t h e y r e s u l t i n u n l i k e l y atom s p a c i n g s i n t h e boundary a r e a . The t r a n s l a t i o n s i n o t h e r boundary a r e a s , shown i n f i g . 2 , : f o l l o w b y a d d i n g t h e a p p r o p r i a t e a n t i p h a s e v e s t o r and p o s s i b l y a n e l e m e n t of DSC'. F i g u r e 4 shows t h e e f f e c t o f t on t h e boundary s t r u c t u r e . D i f f e r e n t a r e a s of t h e boundary, s e p a r a t e d by
T a b l e 1
Figure 3: Bright-field and dark-field electron micrographs employing superlattice reflections in (a) and (b) and a fundamental reflection in (c). Solid and dotted curves represent densitometer plots and calculated intensities (arbitrary units) respectively at different depths of the boundary plane for boundary areas 3 /3 and
m t 3,/lt. The total thickness is t. The scale marker indicates 500 A.
0.45 3m/1 den sit0
'
meter 3 , / 1
-
gc.f= 0.95
G depth t 0 depth t 0 A t h t 0 &th t
-C (a) --C (b)
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JOURNAL DE PHYSIQUE
A I b S
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AIIc
A I I a SII
A I bF i g u r e 4: P r o j e c t i o n a l o n g [OI
1]
of a ( 2 1 i ) t w i n boundary and APBs t e r m i n a t i n g i n t h i s boundary i n o r d e r e d Cu3Au ( c f . f i g . 2 ) . M a t r i x M h a s b e e n t r a n s l a t e d w i t h r e s p e c t t o t w i n T. S t r u c t u r e t y p e s r e f e r t o t h e boundary s t r u c t u r e b e f o r e t h i s t r a n s l a t i o n was a p p l i e d .APBs, a r e shown i n [ O l l l - p r o j e c t i o n ; domain numbers a r e c o n s i s t e n t w i t h t h o s e i n f i g . 2 . The f o u r d i f f e r e n t s t r u c t u r e s S I I , A I I a , AIb and A I I c c a n b e d e r i v e d f r o m t h e c o r r e s p o n d i n g s t r u c t u r e s i n f i g u r e 1 a f t e r a p p l y i n g t h e r i g i d - b o d y t r a n s l a t i o n f g i v e n b y e q u a t i o n ( 1 ) . However, it s h o u l d b e e m p h a s i z e d t h a t t h e s t r u c t u r e g i v e n i n f i g . 4 i s n o t t h e o n l y p o s s i b l e s o l u t i o n . F o r e x a m p l e , i n t w i n b o u n d a r y a r e a 3 , / l t , t h e Au a t o m s i n t h e b o u n d a r y p l a n e c a n b e r e p l a c e d b y Cu atoms, w i t h o u t c h a n g i n g t h e r i g i d - b o d y t r a n s l a t i o n i n t h i s a r e a .
A l l t w i n b o u n d a r y a r e a s i n f i g . 4 show t h e e x p e c t e d c o n t r a s t f o r d i f f e r e n t common s u p e r l a t t i c e r e f l e c t i o n s ( f i g s . 2 a n d 3 ) i f t h e APBs t e r m i n a t i n g a t t h e b o u n d a r y a r e t a k e n i n t o a c c o u n t . F o r example, t h e c o n t r a s t i n 2m/3t i s e q u a l t o t h a t i n 3 m / l t r which i s c o n s i s t e n t w i t h
g c .
[ C (Zm/3,;) -E ( 3 , / l t ) ]=gc.
[Ij (APB5) +p(APB3) ] = 1 f o r g c = [ l l O l.
T h i s i m p l i e s that: a l l t w i n b o u n d a r y a r e a s h a v e t h e same t r a n s l a t i o n f o r t h e d i s o r d e r e d s t r u c t u r e . I n f a c t d i s l o c a t i o n s h a v e n o t b e e n f o u n d i n t h e a n a l y s e d t w i n b o u n d a r y .I t i s c q p c l u d e d t h a t n o d i l a t a t i o n o r c o m p r e s s i o n h a s b e e n f o u n d f o r t h e ( 7 5 4 ) t w i n boundary w i t h i n e x p e r i m e n t a l e r r o r . The t r a n s l a t i o n p a r a l l e l t o t h e b o u n d a r y p l a n e r e s u l t s i n atom s p a c i n g s i n t h e t w i n b o u n d a r y a r e a c l o s e t o n e a r e s t n e i g h b o u r d i s t a n c e s ( f i g . 4 ) , a s oppos_ed t o atom s p a c i n g s i n t h e u n r e l a x e d s t r u - c t u r e s ( f i g . 1 ) . S i n c e t h e (754) b o u n d a r y p l a n e d e v i a t e s zz 8O from- ( 2 1 1 ) , t h e r e a l s t r u c t u r e may w e l l be s l i g h t l y d i f f e r e n t from t h e ( 2 1 1 ) s t r u c t u r e g i v e n i n f i g . 4 .
R e f e r e n c e s
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