tem determination of incoherent twin-boundary …

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TEM DETERMINATION OF INCOHERENTTWIN-BOUNDARY STRUCTURE IN L12 ORDERED

ALLOYSF. Tichelaar, F. Schapink

To cite this version:F. Tichelaar, F. Schapink. TEM DETERMINATION OF INCOHERENT TWIN-BOUNDARYSTRUCTURE 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 Col loque C5, suppl6ment a u n o l O , Tome 49, o c t o b r e 1988

TEM DETERMINATION OF INCOHERENT TWIN-BOUNDARY STRUCTURE IN L12 ORDERED ALLOYS

F.D. TICHELAAR and 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 Technology, Rotterdamseweg 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 incoheren t z=3 twin boundar ies i n t h e L12 o rdered a l l o y Cu3Au i s i n v e s t i g a t e d employing TEM. The boundary planes a r e found t o va ry about t e n degrees from a {112) 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 used f o r de te rmin ing t h e r ig id-body 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 boundary. No d i l a t a t i o n has been found a t a (753) i n c o h e r e n t twin boundary w i t h i n exper imenta l e r r o r . Four g r a i n boundary areas having 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 demonstra ted, s e p a r a t e d from each o t h e r by an a n t i p h a s e boundary on one s i d e of 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 boundary 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 impor tan t r o l e i n de te rmin ing mechanical p r o p e r t i e s [ I ] , and consequen t ly t h i s s u b j e c t h a s been 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 . Ana lys i s was made of co inc idence g r a i n boundar ies i n L20 ( C s C 1 ) and L 1 2 (Cu3Au) o r d e r e d a l l o y s , based on t h e geomet r i ca l coincidence-site-lattice (CSL) model [ 2 , 3 , 4 ] . A l s o s p a c e group t h e o r e t i c a l a n a l y s i s [5,61 and computer s i m u l a t i o n of g r a i n boundar ies i n N i 3 A 1 171 have been c a r r i e d o u t . However, v e r y few exper imenta l i n v e s t i g a t i o n s have been r e p o r t e d s o f a r . T i c h e l a a r and Schapink [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 and found two s t r u c t u r e s : one symmetric and t h e o t h e r asymmetric, 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 with Burgers v e c t o r <112>/6 o r by an APB t e r m i n a t i n g i n t h e t w i n boundary which c a u s e s a <110>/2 t r a n s l a t i o n of t h e two c r y s t a l s r e l a t i v e t o each o t h e r .

I n t h i s paper we r e p o r t t h e r e s u l t s of 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 of 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 rdered Cu3Au.

E x ~ e r i m e n t a l Drocedure. Cu3Au specimens were made from a mel t , having a composi t ion of 25,02 % Au, by a rc -mel t ing u s i n g s p e c t r o g r a p h i c a l l y pure Cu and h igh-pur i ty go ld (99.99 % ) . This 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 minutes , 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 12 h i n vacuum

T o r r ) , s l o w l y c o o l e d t o 375 OC i n 50 h , and s u b s e q u e n t l y annea led a t 375 OC f o r 25 days i n o r d e r t o o b t a i n an average domain s i z e of abou t 0 .5 Fm. Discs from 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 je t -po l i sh ing , us ing an 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 and 85 % a c e t i c a c i d . Some d e p o s i t i o n of go ld 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 and l o c a l e t c h i n g cou ld n o t be avoided; t h i s u n f o r t u n a t e l y l e d t o an 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 . Specimens were examined i n a P h i l i p s 400T e l e c t r o n microscope.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988535

JOURNAL DE PHYSIQUE

$;I: p2'mm' A I a : p2'm b' A1b:p l A I c : p l

SII: p2'mm' ~Ila:p2'mb' Al l b: p'l AIIc: pl

Figure 1 : [old -projection of symmetric *B-atom in the plane of paper and asymmetric configurations of a <=3 PA-a tom a / E above the plane of paper (217) twin boundary in a Cu Au ordered

3 alloy, with their bicrystal layer *B-atom a / 2 G below the plane of paper

groups. EA-a tom a / 2 n above the plane of paper

(112) twin boundary 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 of t h e unre laxed { I121 twin boundary i n o rdered Cu3Au w i l l be cons ide red 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 of t h e Cu3Au a l l o y changes from f . c . c . t o s . c . ; t h e space group 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 atoms can occupy any of 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. Antiphase boundar ies (APBs) between domains a r e c h a r a c t e r i z e d by 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=<110>/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 symmetr ical 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 asymmet r ic s t r u c t u r e s (AIa, AIIa, e t c . ) can be g e n e r a t e d from S I and S I I by an APB t e r m i n a t i n g i n t h e g r a i n boundary, which c a u s e s a <110>/2-type t r a n s l a t i o n of t h e two c r y s t a l s r e l a t i v e t o each o t h e r . Not ice t h a t a - p=[110]/2- type APB changes S I i n t o AIb o r AIIb i f t h e atoms 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 boundary wi th Burgers v e c t o r 1 /3 [171] , a s s o c i a t e d wi th a 1 / 1 2 [ 2 1 i ] s t e p i n t h e boundary plane, a l s o changes a symmetrical s t r u c t u r e i n t o an asymmetrical one ( S I i n t o AIIa o r S I I i n t o A I a ) . The two symmetric s t r u c t u r e s can be t ransformed i n t o each o t h e r by an APB i n each 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

3 area using different common superlattice reflections. Bright-field micrograph (c) 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.

having 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 composi t ion 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 and AIIa 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 (excess of Au) and A I I b ( excess of Cu) . However, t h e s e two s t r u c t u r e s can be t r ans formed i n t o each o t h e r by changing o n l y t h e atoms i n t h e boundary plane, which c a u s e s a change i n c o m p o s i t i o n . Also, an i s o l a t e d 1 /4 [211] s t e p i n t h e boundary p lane changes AIb i n t o AI Ic .

The s t r u c t u r e s AIb and AIc (and a l s o AIIb and AIIc ) a r e mutua l ly 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 ; consequent ly 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 groups 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 of 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 and d i s c u s s i o n . F igures 2 ( a ) and (b) a r e two micrographs of an i n c o h e r e n t t w i n boundary and some APBs, employ ing 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 gc . From t h e s e mic rographs , t h e domain s t r u c t u r e has been ana lysed 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 bo th s i d e s of 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 boundary i s shown. I n t h i s micrograph t h r e e <l lO>-type 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 , and consequen t ly a l l APBs show c o n t r a s t .

The t w i n boundary 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 ncoheren t %3 twin 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 {211) , which probably i n d i c a t e s t h a t t h e t211) p l a n e i s unfavourable , a s opposed t o s i m i l a r twin boundar ies i n some f . c . c . me ta l s [ l o ] . -

I n o r d e r t o de te rmine 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 each o t h e r , t h e TEM method of a - f r i n g e s i s

C5-296 JOURNAL DE PHYSIQUE

employed [ 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 used. For t h r e e non-coplanar qC1s 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 which gC.5 i s known, r e s u l t i n g i n a unique 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 lement of t h e displacement-shif t -complete (DSC)- la t t i ce a s s o c i a t e d w i t h t h e ordered 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[121] and 1 / 3 [ l ' i l ] [ 1 2 ] . Likewise 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 [2111 , 1 /6[1211 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 and G c ~ ~ ~ ~ O ( t h e l a t t i c e of 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 ) , because 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 developed by Blom [ 1 3 ] , employing t h e many-beam dynamical 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 . For each 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 used, and a b s o r p t i o n w a s i nc luded .

The r e s u l t s o f t h e match ing p r o c e d u r e employing 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 of t h e boundary s e p a r a t e d by APBl ( s e e f i g . 2 ) , Ges igna ted 3 q / l t and 3m/3t. The unce_r ta in ty 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 0.15 f o r ~ c = [ l l O ] , 0 . 1 f o r 4c=[311] and 0 .85 f o r gc=[O1l] . 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 poor q u a l i t y o f t h e specimen 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 specimen t h i c k n e s s (measured a s 850 A ) and i n t h e d e v i a t i o n pa ramete 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 might b e d i f f e r e n t from 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 matching p rocedure was a l s o carr>ed_ o u t f o r gc=[202], gc=[022] anti gc=[220L. The r e s u l t i n g v a l u e s of g c . t a r e shown i n t a b l e 1. ~ l l v a l u e s of g t _are c o n s i s t e n t , which reduces 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 of 'ic. t g i v e n i n f i g . 3 . For e a c h gc t h e matching procedure WisS c a r r i e d o u t f o r +pc-and -qc, i n bo th BF and DF.

Fur thermore, f o r ?jc=[O1l], ?jc.t f o r 3m/3t a lmost 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 lmos t symmetr ical 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 contrasf i s symmetrical w i t h r e s p e c t t o t h e middle 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 . Also t h e v a l u e gc . f=0.95 ( 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 wi th t h e low c o n t r a s t i n t h i s boundary a r e a .

For ?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 wi th r e s p e c t t o t h e middle of -the 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 fo l lowing 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 /It) (mod I ) , g c . t ( 3 /3 t )=gC.t (3,/lt) +0.5 (mod 1) . The s o l u t i o ~ ~ i s Qc.y (3m/3t) =0.25 (mod 1?2), whlch i s c o n s i s t e n t wi th [ 2 2 0 ] . t = 0 . 5 (mod 1 ) . - - Using v a l u e s of gc . t f o r ? jc=[Ol l ] , ?jc=[iiO] and ?jc=[311] ( f i g u r e 3 ) t fo l lows f o r t h e boundary a r e a 3m/3t ( c f . f i g u r e 2) :

Other t rans:Lat ions , d e r i v e d from t (3m/3t) by add ing e lements of DSCO

a r e conside1:ed improbable, 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 spacings 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 , :follow by 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 an e lement of DSC'. F i g u r e 4 shows t h e e f f e c t of 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

Table 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)

. . . .

\-- ..... . . . .

. . . . . . . . . . . . . .

... '..:

--v. . . . . . , . '.. . . . . . . . . . . . . . .

. . . . . . .

0.25

5;: 3,/It..

Ec.F - 0.75

. . . .

.., .. . . . . . . . . . . . . . . . . .

. . . . . .

. . . . . . ....... . . . . : . . . . . . . ... ... . . . . . . . . . .

JOURNAL DE PHYSIQUE

A I b S I1 A IIc AIIa S II A I b

Figure 4: P r o j e c t i o n a long [OI 1] of a ( 2 1 i ) tw in boundary and APBs t e rmina t ing i n t h i s boundary i n o rde red Cu3Au ( c f . f i g . 2 ) . Ma t r ix M has been t r a n s l a t e d wi th r e s p e c t t o twin T. S t r u c t u r e t ypes 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 ro j e c t i o n ; domain numbers a r e c o n s i s t e n t wi th 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 , AIIa , AIb and A I I c can be d e r i v e d from 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 ig id-body t r a n s l a t i o n f g i v e n by e q u a t i o n (1). However, it should b e emphasized t h a t t h e s t r u c t u r e g iven 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 . For example, i n twin boundary a r e a 3,/ l t , the Au atoms i n t h e boundary p l a n e can be r e p l a c e d by Cu atoms, wi thout changing t h e r ig id-body 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 boundary a r e a s i n f i g . 4 show t h e expec ted 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 and 3 ) i f t h e APBs t e r m i n a t i n g a t t h e boundary a r e t a k e n i n t o accoun t . For example, t h e c o n t r a s t i n 2m/3t i s equa l t o t h a t i n 3m/ l t r which i s c o n s i s t e n t wi th g c . [ C (Zm/3,;) -E (3 , / l t ) ] =gc. [Ij (APB5) +p(APB3) ] = 1 f o r g c = [ l l O l . This i m p l i e s that: a l l twin boundary a r e a s have 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 have n o t been found i n t h e ana lysed twin boundary.

I t i s cqpcluded t h a t no d i l a t a t i o n o r compression has been found f o r t h e (754) twin boundary w i t h i n exper imenta 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 boundary 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 twin boundary a r e a c l o s e t o n e a r e s t neighbour d i s t a n c e s ( f i g . 4 ) , a s oppos_ed t o atom spac ings i n t h e unrelaxed stru-ctures ( f i g . 1 ) . S ince t h e (754) boundary p l a n e d e v i a t e s zz 8O from- (211) , t h e r e a l s t r u c t u r e may wel l be s l i g h t l y d i f f e r e n t from t h e (211) s t r u c t u r e g iven i n f i g . 4 .

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