An Phase in the Cu-16.5 At. Pct Sn Alloy

W. VANDERMEULEN AND A. DERUYTTERE

In many z i r c o n i u m - and t i t a n i u m - b a s e a l loys a p r e c i p i t a t e of an r phase is found a f t e r quenching f r o m the high t e m p e r a t u r e / 3 phase reg ion . In a Cu-16.5 at . pc t Sn a l loy the s a m e phase is p r e s e n t a f t e r quenching f rom the y - p h a s e r eg ion to r o o m t e m p e r a t u r e . The quenched Cu-Sn a l l oy shows e l e c t r o n d i f f r ac t ion e f fec t s which a r e v e r y s i m i l a r to those of the z i r c o n i u m - and t i t a n i u m - b a s e a l loys , i.e., diffuse s c a t t e r i n g and shif t of the co r e f l e x i o n s . In o r d e r to expla in th is shi f t a model , b a s e d on the p r e s e n c e of c e r t a i n faul t s in the 6o s t r u c t u r e , i s p r e s e n t e d . Af ter aging at 100 ~ and 130~ the ~0 phase i s r e p l a c e d by a phase which c l o s e l y r e s e m b l e s the s t ab le Cu-Sn ~ phase . Nuclei of th is phase a r e thought to be at l e a s t p a r t i a l l y r e s p o n s i b l e for the dif fuse s c a t t e r i n g o b s e r v e d .

IN s e v e r a l z i r c o n i u m - and t i t a n i u m - b a s e a l loys a p r e - c ip i t a t e of an w phase i s p r e s e n t a f t e r quenching f rom the high t e m p e r a t u r e / 3 phase r eg ion to r o o m t e m p e r a - t u r e I r . t . ) . x'4 This w phase i s t r i gona l o r hexagonal and can f o r m a l l y be d e r i v e d f rom the/3 bcc s t r u c t u r e through s m a l l a t omic sh i f t s . 5 The ~ ce l l can take four d i f f e ren t pos i t i ons r e l a t i v e to the bcc m a t r i x a c c o r d i n g to the o r i - en ta t ion r e l a t i onsh ip :s

(0001)c o n (111)/3 [ 2 i i 0 ] ~ II [110]/3

The w phase a p p e a r s a s rows o r c l u s t e r s of rows of v e r y s m a l l p a r t i c l e s , the rows be ing p a r a l l e l to the [0001] d i r e c t i o n of the w v a r i a n t involved, s,e

As the s t r u c t u r e of the high t e m p e r a t u r e Cu-Sn y phase i s bec , with a DOs type s u p e r l a t t t c e , x2 i t has in p r i n c i p l e a l so the p o s s i b i l i t y to t r a n s f o r m to the w s t r u c t u r e . In the p r e s e n t s tudy i t is shown that th is ac tua l l y o c c u r s when the y phase is quenched in wa te r a t r . t .

EXPERIMENTAL TECHNIQUES

An a l loy conta in ing 16.5 a t . pc t Sn was p r e p a r e d by vacuum mel t ing e l ec t r o l y t i c copper and 99.99 pc t pu re t in. P l a t e s of 0.03 to 1 m m thick were hea ted for 10 min at 570~ (y r eg ion ) tn a n i t rogen a t m o s p h e r e and quenched in wa te r at r . t . Af ter e l e c t r o l y t i c thinning in a m ix tu r e of one p a r t c o n c e n t r a t e d HNOs and two p a r t s pu re CHsOH ( -70~ ~ 10 V), the fo i l s were ex - amined in a JEM 7A-120 kV e l e c t r o n m i c r o s c o p e .

EXPERIMENTAL RESULTS

Figs . 1, 2, and 3 show some e l e c t r o n d i f f r ac t ion pa t - t e r n s of the quenched T phase . Four t ypes of spo ts a r e p r e s e n t :

i) y m a t r i x fundamenta l and s u p e r l a t t i c e spo ts . i i) spots f o r m i n g a p a t t e r n which is p r a c t i c a l l y iden-

t i c a l with the d i f f r ac t ion p a t t e r n of the w phase in t i t a - n ium and z i r c o n i u m a l loys . The phase c o r r e s p o n d i n g with th is p a t t e r n wil l in ana logy be des igna t ed as ~o phase .

W. VANDERMEULEN formerly Assistant, Katholieke Universiteit Leuven, Leuven, Belgium, is now with Studiecentrum voor Kernenergie, Mol, Belgium. A. DERUYTFERE is Professor of Metallurgy, Katholieke Universiteit Leuven.

Manuscript submitted October 30, 1972.

11t) s t r e a k s , Fig . 2, which a r e due to the a ' phase which a lways f o r m s on quenching the Y phase to t e m - p e r a t u r e s be tween r . t . and about 350~ Its f o r m a t i o n at the h igher t e m p e r a t u r e s has been s tud ied p r e v i - ous ly . %e

Iv) weak spo ts due to a phase ca l l ed b' which v e r y much r e s e m b l e s the Cu-Sn 8' phase . This phase wi l l be d i s c u s s e d below.

Be s ide s these spo ts (t) to (iv) s e v e r a l r e f l e x tons whtch can be exp la ined by double d i f f r ac t ion a r e p r e s - ent . The d e t a i l s of the d i f f r ac t ion p a t t e r n of the Cu-Sn r phase a r e v e r y s t r i k i n g l y the s a m e as those of e e r - ta tn t i t an ium and z i r c o n i u m a l l oys . In p a r t i c u l a r , the Cu-Sn w spots a r e r e l a t i v e l y s h a r p , they have an e l l l p - so lda l shape and they a r e somewha t sh i f ted f rom the i r Ideal pos i t i on (see the d i agona l s d rawn on Fig . 4). F r o m th is poin t of v iew the compos i t i on Cu-16.5 a t . pe t Sn c o r r e s p o n d s b e s t with Tt-25 at. pe t V s or z r - 1 5 wt pe t Nb. e The p r e s e n c e of the I100 co and 2200 co spo t s In the l i 1 T o r 0001co r e c i p r o c a l l a t t i c e sec t ion p r o v e s that t he se spo ts a r e r e a l and not due to doubie d i f f r a c - t ion. s This means that e i t he r the w phase is o r d e r e d o r that the a toms within the ce l l a r e shi f ted p a r a l l e l with the b a s a l p lane f rom the i r idea l pos i t ion .

Dark f ie ld Images were taken us ing s e v e r a l w r e - f l ex ions . Only in one ea se the image qual i ty was good enough to r e s o l v e p a r t i c l e r ows which were m o r e o r l e s s p a r a l l e l to the [001]co d i r e c t i on . These rows were un i fo rmly d i s t r i b u t e d , no c l u s t e r i n g was o b s e r v e d .

The d i f f r ac t ion p a t t e r n s of the quenched Cu-Sn a l l oy show a l so diffuse s c a t t e r i n g , aga in in s i m i l a r i t y with the t i t an ium and z i r c o n i u m a l loys . One reg ion of d i f - fuse In tens i ty ex tends be tween the fundamenta l m a t r i x spo ts a long (110)7 d i r e c t i o n s with the excep t ion of those ly ing in a {110} T p lane through the o r ig in . A second reg ion of dif fuse In tens i ty extends be tween the e ight co spo ts su r round ing the 2h, 2k, 21 type Y s u p e r - l a t t i c e spo ts . The In tens i ty of the diffuse s c a t t e r i n g zones is not un i form but shows ma x ima . Cool ing to l iquid n i t rogen t e m p e r a t u r e does not a l t e r the in ten- s i ty of the diffuse s c a t t e r i n g . After aging the quenched s p e c i m e n s at 100 ~ o r 130~ new spots a ppe a r . Some of them eoinctde with the diffuse m a x i m a on the <l l0>T d i r e c t i o n s . The spo ts in { l l 0 } T p lanes through the o r i - gin fo rm m o r e s lowly . All t he se new spo t s and a l so the w spo t s can be indexed In t e r m s of the Cu-Sn 5 phase . However , a c a r e fu l examina t ion of t he i r pos i t i ons shows

METALLURGICAL TRANSACTIONS VOLUME 4, JULY 1973-1659

444 r 00.3~

00.1~ 111r

22o r

Fig. 1--112 Rec ip roca l la t t ice sec t ion of the - / p h a s e . One o~ va r i an t g ives r i s e to e x t r a r e f l ex ions . The r e f l ex ions of the t h r ee o the r w v a r i a n t s coincide with the fundamenta l y r e - f lexions . The spo t s due to double d i f f rac t ion and to the 5' phase and the diffuse s c a t t e r i n g zones a r e not indicated on the drawing,

(~ ), fundamental reflexions

�9 r superlattice reflexions w re|lexion$ (one variant)

~:u I

22.0z

242 Y

23.II

01.0;

000 iO.i~ 22o 1.0.I z

,On

Fig. 2--113 Reciprocal lattice section of the ), phase. Two variants give rise to extra reflexions. The reflexions of the (~) ~" two other co variants coincide with the ~ reflexions. The spots due to doub]e diffraction and to the 5' and ~' phases and the diffuse s c a t t e r i n g zones a r e not indicated on the drawing . C~ o~

1660-VOLUME4, JULY 1973

03.0 zz

fundamental rellexions

reflexions (two var;ants)

METALLURGICAL TRANSACTIONS

o}}r

%

Fig. 3--111 Reciprocal lattice section of the y phase. One w variant gives r ise to extra reflexions. The reflexions of the three other a) variants coincide with the , /reflexions. The spots due to the 6' and ct' phases are not indicated on the drawing.

| r

0 cu

fundamental reflex;ons

rellexions (one var;ant)

Fig. 4--1i0 Reciprocal lattice section of the y phase. Two co variants give r ise to extra reflexions. The reflexions of the two other w variants coincide with the fundamental y ref lex- ions. The spots due to double diffraction and to the 6' and ~ ' phases are not indicated on the drawing.

that t hese spots a r e s l igh t ly shi f ted f r o m the ideal 5 po- s i t ion. All sh i f t s a r e d i r e c t e d to the n e a r e s t y funda- men ta l o r s u p e r l a t t i c e point . T h e r e f o r e , these spots a r e a t t r ibu ted to a phase ca l l ed 6 ' . In s o m e c a s e s they a r e a l r e ady p r e s e n t a f t e r a r e l a t i v e l y s low quench (see the spots on the <110> d i r ec t i ons of the y la t t i ce i n Fig . 3), in a g r e e m e n t with an o b s e r v a t i o n by Morikawa et al. who a lso noted t he i r shift . ~

F r o m these obse rva t i ons it fol lows that the above ment ioned diffuse m a x i m a along <l l0>T may be caused by v e r y s m a l l p a r t i c l e s o r by c l u s t e r s of a toms p r e - ceding the 5' fo rma t ion . In the s a m e way the diffuse in tens i ty be tween the w spots may a l so be due to some

30.On 004),

7.0.0~" o . y% 10.0,,

0

i 0.] m

30.01 ?

�9 o~ O.Oz

lO.Oze % 1 222Y

s ]'10.1i

00.irr ~ "o %* oO 0.1z

(~) r tundamenlal reflexions �9 r superlaltice retlexions c~ w retlexions

f ine p r e c i p i t a t e . Indeed, in a thin foi l obtained by spla t cool ing and aged at r . t . , t h r e e sharp spots w e r e found be tween the w spots . The s t r u c t u r e of the phase(s ) they belong to has not yet been d e t e r m i n e d but is d i f - f e r en t f r o m that of any known phase in the Cu-Sn s y s - t em.

DISC USSION

Only the ~) and 8' phases will be considered here as the ~' phase has been discussed in previous work. %s

Sass s and de Fontaine z~ have attributed the occur- rence of the w phase in the bcc lattice to mechanical

METALLURGICAL TRANSACTIONS VOLUME 4, JULY 1973-1661

i n s t a b i l i t i e s . A s s u m i n g some hypo the t i ca l va lues for the e l a s t i c i n t e r a c t i o n cons tan t s , de Fonta ine c a l c u - l a t ed the waves fo r which the i n s t a b i l i t i e s o c c u r and he could show that t h e s e waves give the a t o m s the r i gh t d i s p l a c e m e n t to p roduce the w s t r u c t u r e . In the ca se of Cu-Sn a l l oys ev idence for the ex i s t ence of such waves s e e m s to be p rov ided by the work of N i sh iyama et al. who examined thin fo i l s of a Cu- 14.8 a t . pc t Sn a l l oy in a hot s tage e l e c t r o n m i c r o - scope , n The i r d i f f r ac t ion p a t t e r n s taken in the /3 - phase r eg ion a l l show s t rong diffuse s c a t t e r i n g . This s c a t t e r i n g ex tends in the {111}3, p l anes and in the r e - gions where the co spo t s n o r m a l l y occu r . These a r e exac t ly the r e g i o n s of i n s t ab i l i t y c a l c u l a t e d by de Fon - ta ine . The waves p r e d i c t e d by de Fonta ine thus r e a l l y s e e m to e x i s t a t l e a s t a t high t e m p e r a t u r e s in Cu-Sn a l l oys and p r o b a b l y con t r ibu te to the w fo rma t ion .

In a quenched Z r - 3 0 wt. pc t Nb a l loy v e r y diffuse w r e f l e x i o n s we re obta ined . 6 It is not exc luded that t he se a r e due to l a t t i c e v i b r a t i o n s i n s t ead of w p a r t i c l e s . This s i tua t ion would be equiva len t to the s t ab le high t e m p e r a t u r e s t a t e of a l l oys with lower so lu te content . In the quenched Cu-Sn a l loy the diffuse s c a t t e r i n g is a t l e a s t p a r t i a l l y due to v e r y s m a l l p r e c i p i t a t e p a r t i - c l e s . However some con t r ibu t ion f r o m t h e r m a l s c a t - t e r i n g r e m a i n s p o s s i b l e .

The shif t of the 60 spo t s o c c u r r i n g for some a l loy c ompos i t i ons is d i f f icul t to expla in by the v i b r a t i o n a l waves in the m a t r i x a s f o r m e r l y s u g g e s t e d by Dawson and Sass . 6 Indeed, d a r k f i e ld i m a g e s us ing the w r e - f l ex ions c l e a r l y show the w p a r t i c l e s . T h e r e f o r e it is thought that the o r ig in of the shif t of the w spo ts is to be found in the co phase i t se l f .

As Sass po in ted out, the w phase can be d e s c r i b e d as a modula t ion of the ( l l l ) f l p l anes caused by a s inu - so ida l longi tudina l d i s p l a c e m e n t wave. As a r e s u l t of th i s modula t ion the /3 m a t r i x spo ts get s a t e l l i t e s at a d i s t a n c e of -~ 1/A in the [111]/3 ct irect ion, A be ing the modula t ion wavelength . F o r the idea l w s t r u c t u r e A = - ~ d m = cr and the s a t e l l i t e s co inc ide with the un- sh i f ted pos i t i ons of the co spo t s . This means that the d e s c r i p t i o n s of w a s a phase by i t s e l f o r a s a modu- l a t ed bcc phase a r e equiva len t . In o r d e r to expla in the shi f t of the w spo ts i t mus t be a s s u m e d that the modula t ing wavelength is somewha t s m a l l e r than cw. In ana logy with non in teger p e r i o d s in p e r i o d i c a l an t i - phase s t r u c t u r e s , th is can be ob ta ined b y in t roduc ing

--2 c some modula t ions with wavelength ff c~o o r s co, so that the mean wavelength is s m a l l e r than c6o. As the shi f t of the co r e f l e x i o n s is v e r y s m a l l , the extent of

2 the r e g i o n s with modula t ion wavelength ~ coj or -xcw mus t be s m a l l . F o r a p r e l i m i n a r y ca l cu l a t i on r e g ions only one wavelength long a r e now c o n s i d e r e d . Fig. 5(a) shows the d i s p l a c e m e n t function which d e s c r i b e s the modula t ion of the bcc s t r u c t u r e l ead ing to the f o r m a - t ion of the w s t r u c t u r e . The v e r t i c a l l ines r e p r e s e n t a se t of (111) bcc p l anes . The magni tude of the s ine function at any pos i t ion g ives the d i s t ance ove r which the a t o m s in that pos i t ion have to be sh i f ted a long the [111] d i r e c t i o n in o r d e r to f o r m the 60 phase (see a l so Ref. 5). The s ign d e t e r m i n e s whether the shif t is in the pos i t i ve o r nega t ive [111] d i r ec t i on . Fig. 5(b) shows the 60 phase f o r m e d : the ful l v e r t i c a l l ines r e p r e s e n t the b a s a l p l anes of the r ce l l , they a r e the unshif ted bcc p l anes . The da shed l ines r e p r e s e n t the p l anes at half height of the w c e l l ; they a r e f o r m e d by sh i f t ing t o -

-- c~ 3

fay /c) r

', ' ',, , i"kl,, 'l'l,, ,, /b) /d) If)

Fig . 5 - - F o r m a t i o n of the w s t r u c t u r e by m o d u l a t i o n o f the bcc s t r u c t u r e (a) (111) bcc p l a n e s wi th m o d u l a t i o n func t ion of w a v e l e n g t h c w (b) p e r f e c t w s t r u c t u r e (c) m o d u l a t i o n func t ion wi th one p e r i o d of w a v e l e n g t h cw/3 i n s e r t e d (d) 6o s t r u c t u r e wi th type 1 f au l t (e) m o d u l a t i o n func t ion with one p e r i o d of w a v e l e n g t h 2cw/3 i n s e r t e d (f) w s t r u c t u r e wi th type 2 fau l t .

ge ther two bee p l a n e s . Now, if one pe r i od , Fig . 5(c), of a d i s p l a c e m e n t funct ion with wavelen.gth ~ cw is in - s e r t e d in the n o r m a l d i s p l a c e m e n t funct ion, the r e g u - l a r sequence of co c e l l s is d i s t u rbe d , Fig . 5(d). The conf igura t ion so c r e a t e d wil l be ca l l ed a type 1 faul t . It can be shown that a c r o s s th is faul t the r e l a t i v e shif t of the w l a t t i ce is R-= ~ ( - a + b + c), a, b, c be ing the axes of the co unit ce l l . If one p e r i o d of a d i s p l a c e m e n t funct ion with wavelength ~ co~ i s i n s e r t e d , Fig. 5(e), the conf igura t ion d rawn on Fig. 5 ( f ) i s obta ined . This wi l l be ca l l ed a type 2 faul t . In th is c a se the r e l a t i v e shif t of the co l a t t i c e a c r o s s the faul t is 2/~. In addi t ion one (111) bcc p lane has been i n s e r t e d in the r e g u l a r s t ack ing of w c e l l s . It can e a s i l y be s een that the in - t roduc t ion of one p e r i o d ~ coj i s equiva len t to the i n - t roduc t ion of two p e r i o d s x ~CW.

In o r d e r to a l low the ca lcu la t ion of the d i f f r ac t ed in tens i ty , the fau l t s we re supposed to occu r a t equal d i s t a n c e s . The ca l cu l a t i ons were made for an w p a r - t i e l e c ons i s t i ng of M . N c e l l s in i t s [0001] d i r ec t i on , only the in t ens i ty d i s t r i bu t i on a long this d i r e c t i o n wi l l be c o n s i d e r e d .

In the e a s e of r e g u l a r l y d i s t r i b u t e d type 1 faul t s , Fig . 6(a), the i n t ens i ty d i s t r i b u t i o n a long the [0001]~o d i r e c t i o n of the r e c i p r o c a l l a t t i c e is given by :

I(1) = IFo~{ z s inz 7rN1 s in z lrM(N + 1/3)1 [1] s in ~-Trl " s in z l r ( N + l / 3 ) 1

where

Fw : s t r u c t u r e f ac to r of one w ce l l N : number of w c e l l s be tween two fau l t s in

the [0001] d i r e c t i o n M - 1 : number of fau l t s in the co p a r t i c l e 1 : coo rd ina t e a long the [0001]oj r e c i p r o c a l

l a t t i c e d i r e c t i o n

Fig . 7(a), (b), and (c) show th is function r e s p e c t i v e l y in the v i c in i t y of the w r e f l e x ions 0001, 1 = 1; 0002, 1 = 2; 0003, 1 = 3. F o r 1 = I and 1 = 2, two peaks of unequal i n t ens i ty o c c u r . In the f i r s t c a s e the l a r g e r peak i s sh i f ted to the o r ig in a s c o m p a r e d to the idea l pos i t ion of the 0001w re f l ex ion . In the second ca se the l a r g e r peak is sh i f ted away f rom the o r ig in as c o m p a r e d to the idea l 0002 w pos i t ion . The o c c u r r e n c e of two peaks can be a s c r i b e d to the r e g u l a r d i s t r i bu t i on of the fau l t s . With r a n d o m l y d i s t r i b u t e d faul t s p r o b a b l y only one sh i f ted peak would be found. The r e s u l t obta ined with r e g u l a r l y d i s t r i b u t e d fau l t s i nd ica t e s that t he se faul t s a r e ab le to p roduc e a peak shif t . In the ca se of the type 1 fau l t s the sh i f t s a r e in the oppos i te d i r e c t i o n

1662-VOLUME 4, JULY 1973 METALLURGICAL TRANSACTIONS

J _ E f e l l ~___ �9

o o N-I , i t . ~ ~.,,

(a)

[ ~ IOJ ce l l - - - #

o . . . .

o o N-I

o ; M:, (b)

Fig. 6--Model for the calculation of the influence of type 1, Fig. 6(a) and type 2, Fig. 6(b), faults on the diffracted inten- sity. The co particle is supposed to consist of M "packets" of 5I oJ unit cells separated by a fault.

/Tx\

/

/

I:1

,T', / /

I \ / I \\ / I x i/

A,__,s N

(0)

I \\

[~ \ \ . .

t :2

l " \\ I/' I / l/ ~\\

/ J \\ 2 = t:3

(b) It) Fig. 7--Calculated intensity distribution for type 1 faults in the vicinity of the ~o reflexions 0001, 1 = 1, Fig. 7(a); 0002, 1 = 2, Fig. 7(b), and 0003, I = 3, Fig. 7(c). M and N have been taken equal to 4. The dashed line represents the function sin2~ffVl/sin 27rl from Eq. [1].

of the expe r imen ta l l y obse rved shif ts . For r e g u l a r l y d i s t r ibu ted type 2 faul ts , Fig. 6(b), the

in tens i ty d i s t r ibu t ion is :

It(i) = [(5 + 4 cos ITI)S a + 2S cos ,r (N + 1 + 2 /3 ) I

+ 4 S c o s ~ ( N + 2 / 3 ) I + I ] G

where

[2]

s in ITNI S -

s in ~i

s in z ~M (N + 2/3) I G =

s in z w (N + 2/3)1

I = coordinate along the [00011o ~ r e c i p r o c a l la t t ice d i rec t ion

N = n u m b e r of co ce l l s between two faults in the [0001] d i rec t ion

M - 1 = n u m b e r of faul ts in the co pa r t i c l e

For the purpose of ca lcu la t ion the s t r u c t u r e of the co phase is supposed to be hexagonal a n d d i s o r d e r e d . The s ca t t e r i ng factor of the a toms is put equal to unity.

Fig. 8(a), (b), and (c) show the ca lcula ted in tens i ty d i s t r ibu t ion r e spec t i ve ly for the co re f lex ions 0001,

x

c;-" "~. t o~ A 1 1oo t~

Ii I

/

ill I 11 ~ It~

~/t'~ / B hZO0 A 2~ 2 75 t:alX+ (b,* ( cJ

+,

i / ,( ," , , I \ i \

�9 / l q \ / \

A, 3Z5

Fig. 8--Calculated intensity distribution for type 2 faults in the vicinity of the co reflexions 0001, 1 = 1, Fig. 8(a); 0002, 1 = 2, Fig. 8(b) and 0003, 1 = 3, Fig. 8(c). M and N have been taken equal to 4. The dashed line (I~) represents the function between square brackets in Eq. [2].

I = I ; 0002, I = 2; 0003, 1 = 3. Again two unequal peaks occur nea r the pos i t ions 1 = 1 and 1 = 2, whereas for 1 = 3 th ree peaks a re found. Once more the appearance of two or th ree peaks may be a t t r ibu ted to the r egu l a r d i s t r ibu t ion of the faul ts . In this case the l a rge r peak is shifted away f rom the o r ig in r e l a t ive to the ideal pos i t ion of the 0001~o ref lexion, whereas it is shifted towards the o r ig in r e l a t ive to the ideal 0002co posi t ion. As in the case of the type 1 faul ts there is no peak shift at the 0003 posi t ion. For r e g u l a r l y d i s t r ibu ted type 2 faul ts the shift d i r ec t ion of the l a r g e r peaks there fore co r re sponds with the obse rved shift of the co re f lex ions .

F r o m these f i r s t r e s u l t s it follows that the obse rved shift of the co re f lex ions may be a t t r ibu ted to the o c c u r - r ence of type 2 faul ts in the co pa r t i c l e s . Type 1 faults may also occur but in s m a l l e r amounts so that the ef- fect of the type 2 faul ts p redomina te s . The r e a s o n for the ex is tence of such faul ts can be sought e .g : , in t r a n s - fo rmat ion s t r e s s e s or in some wel l -def ined t r a n s f o r m a - t ion mechan i sm. The la t te r cause would explain why a p a r t i c u l a r type of faul t is p r e f e r r e d . Indeed, if the faul ts were fo rmed randomly , one would expect them to occur in equal amounts and probably no peak shift would occur .

If in the modulat ion function reg ions of more than two per iods of wavelength cco/3 are in se r t ed , co r e - gions sepa ra t ed by sma l l bcc reg ions a re formed. This can lead to the fo rmat ion of the rows of pa r t i c l e s which a re obse rved expe r imen ta l l y in many cases . If it is a s s u m e d that a l l the p a r t i c l e s a r e ident ica l and conta in an in teger n u m b e r of co ce l l s along the [0001] d i rec t ion , the p reced ing ca lcula t ions also hold for the ideal case where the pa r t i c l e s a r e equidis tant . Three cases can be cons ide red :

i) The d is tance between the pa r t i c l e s is of type 1:

R =(3n + I ) cco. 3

In this case the in tens i ty d i s t r ibu t ion along the [0001] d i r ec t ion in the r e c i p r o c a l la t t ice is the s ame as for type I faul ts .

i i) The d is tance between the pa r t i c l e s is of type 2:

c R = (3n - 1) co

3 This gives an in tens i ty d i s t r ibu t ion as for type 2 faul ts .

i i i ) The d i s tance between the p a r t i c l e s is of type 3:

co) R = 3 n - -

3

METALLU RGICAL TRANSACTIONS VOLUME 4. JU LY 1973-1663

In th is c a s e a l l the w p a r t i c l e s s c a t t e r in phase . The in t ens i ty d i s t r i b u t i o n is the s a m e as for an ~o p a r t i c l e conta in ing no fau l t s . F r o m th is i t can be concluded that an a l t e r n a t i v e explana t ion for the sh i f t of the co r e f l e x - ions i s the o c c u r r e n c e o r p r e d o m i n a n c e of the type 2 d i s t a n c e be tween w p a r t i c l e s in a row. However , a s the o b s e r v e d d i s t a n c e be tween the ~o p a r t i c l e s is of the o r d e r of 10.~ (this i s about 6dl l l (bcc) o r 4cco), i t is d i f - f icu l t to imag ine a t r a n s f o r m a t i o n m e c h a n i s m which could make one type of d i s t ance p r e d o m i n a t e ove r the two o the r types .

The 6' phase , which f o r m s a f t e r aging, can be con- s i d e r e d a s an i n t e r m e d i a t e s t ep be tween 3/ o r co and 5. Whether 5 ' n u c l e a t e s f r o m co o r not could not be o b s e r v e d . If i t does , i t would be unde r s t andab l e tha t the faul t s in ~o, i . e . , the l ack of un i fo rmi ty of the modula t ion w a v e - length, a r e t r a n s f e r r e d to 5 ' . This would exp la in the sh i f t of the 5' spo t s . At any r a t e , th i s sh i f t poin ts to a non in teger mean p e r i o d for the 5' s t r u c t u r e . A mode l for th i s has ye t to be found.

CONC LUSIONS

a) In the 3/ phase of a Cu-16.5 at . pc t Sn a l l o y a phase , s i m i l a r to the co phase in t i t a n i u m - and z i r c o - n i u n - b a s e a l l oys , is f o r m e d on quenching.

b) The diffuse e l e c t r o n s c a t t e r i n g ob ta ined f rom the

quenched 3 / phase i s m a i n l y due to the f i r s t s t a g e s of the 5' p r e c i p i t a t i o n al though t h e r e m a y a l so be a con- t r ibu t ion f r o m t h e r m a l s c a t t e r i n g .

c) The o b s e r v e d shif t of the co r e f l e x i o n s m a y be e x - p l a ined by the o c c u r r e n c e of a g iven type of fau l t s in the co p a r t i c l e s o r by the co p a r t i c l e s be ing a r r a n g e d in r o w s in which the spac ing i s of the type ( 3 n - 1 ) C ~ / 3 .

d) Aging the quenched 3/ phase at low t e m p e r a t u r e s c a u s e s p r e c i p i t a t i o n of the 5' phase which c l o s e l y r e - s e m b l e s the e q u i l i b r i u m Cu-Sn 5 -phase .

RE FERENCES

1. A. J. Perkins, P. E. Yaffe, and R. F. Hehemann: Met. Trans., 1970, vol. 1, p. 2785.

2. B. A. Hatt .and J. A. Roberts: Acta Met, 1960, vol. 8, p. 575. 3. A. T. Balcerzak, C. W. Dawson, K. K. McCabe, and S. L. Sass: 7me Congrbs

Int. de Microscopie Electronique, p. 483, Grenoble, 1970. 4. W. A. Jackson, A. J. Perkins, and R. F. Hehemann: Met. Trans., 1970, vol. 1,

p. 2014. 5. S. L. Sass:ActaMet., 1969, vol. 17, p. 813. 6. C. W. Dawson and S. L. Sass: Met.Trans., 1970, vol. 1, p. 2225. 7. A. Deruyttere: Mdr~ Sci. Rev. Mdt., 1963, vol. 60, p. 359. 8. M. De Bondt and A. Deruyttere: ActaMet., 1967, vol. 15, p. 993. 9. M. Morikawa, K. Shimizu, and Z. Nishiyama: Trans. Jap. Inst. Metals, 1967,

vol. 8, p. 145. 10. D. de Fontaine: ActaMet., 1970, vol. 18, p. 275. 11. Z. Nishiyama, H. Morikawa, and K. Shimizu: Jap. J. Appl. Phys., 1967, voL 6,

p. 815. 12. H. Kn6dler: Acta Cryst., 1956, vol. 9, p. 1036.

1664-VOLUME 4, JULY 1973 METALLURGICAL TRANSACTIONS