AN X-RAY DIFFRACTION STUDY OF A MARTENSITIC TRANSFORMATION IN URANIUM ALLOYS

HAL Id: jpa-00222174

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Submitted on 1 Jan 1982

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AN X-RAY DIFFRACTION STUDY OF A

MARTENSITIC TRANSFORMATION IN URANIUM ALLOYS

D. Carpenter, R. Vandermeer

To cite this version:

D. Carpenter, R. Vandermeer. AN X-RAY DIFFRACTION STUDY OF A MARTENSITIC TRANS-

FORMATION IN URANIUM ALLOYS. Journal de Physique Colloques, 1982, 43 (C4), pp.C4-395-

C4-400. �10.1051/jphyscol:1982458�. �jpa-00222174�

A N X-RAY D I F F R A C T I O N S T U D Y O F A M A R T E N S I T I C T R A N S F O R M A T I O N I N U R A N I U M

ALLOYSO

D.A. c a r p e n t e r X and R.A. vandermeerCI

he

U n i v e r s i t y of Tennessee, KnoxviZZe, TN 37916, U. S . A .

*Union C a r b i d e Corp., N u c l e a r Div., Oak Ridge, TN 37830,

U.

S. A.

(Accepted 9 August 1982)

A b s t r a c t . - The m a r t e n s i t i c b e e (y) t o orthorhombic (a') c r y s t a l s t r u c t u r e change i n uranium a l l o y s is s i m i l a r t o t h e b e e t o hep t r a n s f o r m a t i o n i n T i and Z r . One c h a r a c t e r i s t i c i s t h a t t h e change c a n b e u n d e r s t o o d i n t e r m s of a B u r g e r ' s s h e a r mechanism. I t h a s been proposed t h e o r e t i c a l l y and w i t h some e x p e r i m e n t a l s u p p o r t t h a t by p r o g r e s s i v e l y r e s t r i c t i n g t h e magnitude of t h e s h e a r (by a l l o y i n g , f o r example) a c o n t i n u o u s s e r i e s of d i s p l a c i v e l y - produced t r a n s i t i o n s t a t e s c o u l d b e developed a s f o l l o w s :

y -t yo -t a" + a '

where yo and a" a r e t e t r a g o n a l and m o n o c l i n i c d i s t o r t i o n s of t h e c u b i c and orthorhombic p h a s e s , r e s p e c t i v e l y . P r e v i o u s s t u d i e s have n o t been c l e a r a s t o whether t h e i n t e r m e d i a t e t r a n s f o r m a t i o n i s c o n t i n u o u s o r d i s c o n t i n u o u s . I n t h i s work a n a l l o y c o n t a i n i n g 6.4 wt% niobium i n uranium was p r e p a r e d and h e a t t r e a t e d s o t h a t t h e yo t o a" t r a n s f o r m a t i o n c o u l d b e induced a t room t e m p e r a t u r e by a n a p p l i e d s t r e s s . The s t r u c t u r e change was d e t e c t e d by i n s i t u x-ray d i f f r a c t i o n a n a l y s i s . L a t t i c e p a r a m e t e r measurements i n d i c a t e d t h a t t h e t r a n s f o r m a t i o n was r n a r t e n s i t i c i n v o l v i n g a s i g n i f i c a n t d e v i a t o r i c component of t h e l a t t i c e d i s t o r t i o n , a volume change, and a d i s c o n t i n u o u s r a t h e r t h a n con- t i n u o u s change i n s t r u c t u r e .

I n t r o d u c t i o n . - I n t h e s o l i d s t a t e u n a l l o y e d uranium c a n e x i s t i n t h r e e a l l o t r o p i c forms. These a r e y ( b e e ) , 6 (complex t e t r a g o n a l ) , and a (orthorhombic) l i s t e d ac- c o r d i n g t o s t a b i l i t y w i t h d e c r e a s i n g t e m p e r a t u r e . T r a n s f o r m a t i o n s from one p h a s e t o a n o t h e r d u r i n g c o o l i n g a p p e a r t o b e i n s u p p r e s s i b l e ( 1 ) . S u i t a b l e a l l o y i n g a d d i t i o n s , however, c a n c a u s e t h e f3 phase t o b e s k i p p e d a l l o w i n g t h e y phase t o t r a n s f o r m on r a p i d c o o l i n g d i r e c t l y t o a s u p e r s a t u r a t e d , orthorhombic m o d i f i c a t i o n ( 2 ) . The phase i s c a l l e d a ' b e c a u s e i t s l a t t i c e p a r a m e t e r s d i f f e r from t h o s e of u n a l l o y e d uranium due t o t h e p r e s e n c e of s o l u t e .

The y t o a' t r a n s f o r m a t i o n i s t h o u g h t t o b e m a r t e n s i t i c . H a t t ( 3 ) determined t h e o r i e n t a t i o n r e l a t i o n s h i p between t h e s e p h a s e s i n uranium-zirconium a l l o y s and n o t e d s e v e r a l p a r a l l e l i s m s w i t h t h e b e e t o hep t r a n s f o r m a t i o n i n Z r . A m o d i f i e d Burgers mechanism (4) was s u g g e s t e d f o r t h e t r a n s f o r m a t i o n p a t h . A s h e a r on {112) c u b i c p l a n e s i n a < I l l > c u b i c d i r e c t i o n was c o n s i d e r e d t h e p r i m a r y d i s t o r t i o n w i t h secondary s h u f f l i n g of some of t h e atoms needed t o complete t h e c r y s t a l s t r u c t u r e change. F i g 1, which r e p r e s e n t s a p r o j e c t i o n of t h e b e e l a t t i c e on t h e (011) p l a n e w i l l b e u s e f u l i n d i s c u s s i n g t h e t r a n s f o r m a t i o n . The s t a n d a r d b e e u n i t c e l l w i t h a n a, l a t t i c e p a r a m e t e r i s o u t l i n e d w i t h d o t t e d l i n e s . Open c i r c l e s r e p r e s e n t l a t t i c e p o i n t s from a p a r a l l e l p l a n e d i s p l a c e d J 2 / 2 a. normal t o t h e page. V i s u a l i z a t i o n of t h e t r a n s f o r m a t i o n i s e a s i e r , however, by f o c u s i n g a t t e n t i o n on t h e m o n o c l i n i c u n i t c e l l drawn w i t h s o l i d l i n e s . T h i s c e l l is c h a r a c t e r i z e d by t h e p a r a m e t e r s 2,

>,

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a n g l e between them and a parameter

5,

p e r p e n d i c u l a r t o t h e page. For t h e bee l a t - t i c e e q u a l s 100.02 deg. The m o d i f i e d Burgers mechanism proposed by H a t t would O ~ o r k s u p p o r t e d by t h e U. S . Dept. of Energy under C o n t r a c t W-7405-eng-26.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982458

JOURNAL DE PHYSIQUE

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T h i s d e s c r i p t i o n d i f f e r s from a n e a r l i e r s u g g e s t i o n t h a t t h e correspondence was e q u i v a l e n t t o t h a t a s s o c i a t e d w i t h t h e well-known c u b i c t o orthorhombic t r a n s f o r m a - t i o n i n Au-Cd a l l o y s ( 5 ) . Crocker and Ross ( 5 ) argued t h a t t h e correspondence i n d i c a t e d by F i g . 1 is l i k e l y t o b e f a v o r e d on t h e o r e t i c a l grounds b e c a u s e b o t h t h e magnitudes of t h e p r i n c i p a l s t r a i n s and of t h e s e c o n d a r y s h u f f l e s a r e s m a l l e r .

A number of s t u d i e s ( 6 ) ( 7 ) (8) found t h a t f o r c e r t a i n uranium a l l o y compo- s i t i o n s , o c h e r d i s p l a c i v e l y - g e n e r a t e d t r a n s i t i o n p h a s e s c o u l d b e produced from a y phase p a r e n t . These a r e t h e y o ( t e t r a g o n a l ) and a" (monoclinic) p h a s e s which a r e s l i g h t l a t t i c e d i s t o r t i o n s of y and a ' , r e s p e c t i v e l y . It h a s been proposed (7) (8) (9) (6) t h a t by p r o g r e s s i v e l y r e s t r i c t i n g t h e magnitude of t h e s h e a r , i . e . r e s t r i c t - i n g t h e amount of t h e d e c r e a s e of t h e

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t r a n s f o r m a t i o n i s c o n t i n u o u s o r d i s c o n t i n u o u s . The d i f f i c u l t y i n d e c i d i n g a r i s e s b e c a u s e t h e r e i s i n s u f f i c i e n t d a t a a v a i l a b l e t o i d e n t i f y a narrow, a t most, r a n g e where c o e x i s t e n c e may b e p r e s e n t . The a n g l e seems t o undergo a n a b r u p t change

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The p u r p o s e of t h i s i n v e s t i g a t i o n was t o d e t e r m i n e i n more d e t a i l t h e n a t u r e of t h e l a t t i c e p a r a m e t e r changes d u r i n g t h e y o t o a" t r a n s f o r m a t i o n . By a s u i t a b l e combination of c o m p o s i t i o n and h e a t t r e a t m e n t , a two p h a s e y o

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^a" a l l o y was p r e - pared s u c h t h a t a t room t e m p e r a t u r e a" was t h e minor phase. On s t r a i n i n g t h i s m a t e r i a l i n a d e v i c e mounted o n a n x-ray d i f f r a c t o m e t e r , i t was found t h a t a" c o u l d b e s t r e s s - i n d u c e d from ye. I n s i t u x-ray d i f f r a c t i o n d a t a were measured a t v a r i o u s s t a g e s d u r i n g t r a n s f o r m a t i o n .

Experimental Procedures.- The uranium a l l o y specimens used i n t h i s work came from m a t e r i a l p r e p a r e d f o r a n e a r l i e r i n v e s t i g a t i o n (12) and c o n t a i n e d n o m i n a l l y 6.4 wt%

niobium. Four f l a t t e n s i l e specimens were machined from t h e c e n t e r of a 9.4 mm t h i c k p l a t e t h a t p r e v i o u s l y had been s o l u t i o n h e a t t r e a t e d f o r 7200 s e c a t 1075K i n vacuum, water-quenched t o room t e m p e r a t u r e and aged f o r 14,400 s e c a t 475 K. The gauge c r o s s - s e c t i o n of t h e t e n s i l e specimens was 0.62 mm t h i c k by 1 8 mm wide and t h e gauge l e n g t h was 25 mm. E l e c t r o p o l i s h i n g was u s e d t o remove d e f o r m a t i o n caused by machining. One of t h e specimens was r e - s o l u t i o n h e a t t r e a t e d , w a t e r quenched and aged a s b e f o r e and e l e c t r o p o l i s h e d t o remove t h e o x i d e f i l m . T h i s added p r o c e s s i n g d i d s i g n i f i c a n t l y a l t e r t h e r e s u l t s c a u s i n g t h e y o and a" p h a s e s t o e x i s t i n a b o u t e q u a l p r o p o r t i o n s .

The e l e c t r o p o l i s h e d specimens were p o s i t i o n e d on a s p e c i a l l y d e s i g n e d t e n s i l e s t r a i n i n g d e v i c e t h a t was mounted on a n automated Siemens x-ray d i f f r a c t o m e t e r . To a s s u r e p r o p e r f o c u s s i n g of t h e s p e c t r o m e t e r f o r each t e s t , a p u r e n i c k e l powder was d u s t e d on t h e specimen s u r f a c e and u s e d a s a s t a n d a r d f o r a l i g n m e n t p u r p o s e s . Copper K a r a d i a t i o n was used t o o b t a i n d i f f r a c t i o n p a t t e r n s from t h e f l a t l o n g i t u d i n a l s u r - f a c e o f t h e t e n s i l e specimens. P a t t e r n s were measured i n t h e u n s t r e s s e d c o n d i t i o n and i n s i t u w h i l e t h e specimens were under s t r e s s a t d i f f e r e n t s m a l l s t r a i n i n c r e m e n t s up t o a t o t a l s t r a i n of a s much a s 4%. O c c a s i o n a l l y a t i n t e r m e d i a t e s t r a i n l e v e l s t h e specimens were i n c r e m e n t a l l y unloaded and r e l o a d e d . A d d i t i o n a l x-ray p a t t e r n s were g e n e r a t e d d u r i n g t h e s e s t e p s . Each x-ray p a t t e r n covered a 28 r a n g e from 30 t o 90 deg. and was step-scanned i n 0.02 deg. i n c r e m e n t s . A t each s t e p t h e s i g n a l was

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JOURNAL DE PHYSIQUE

counted f o r 4 s e c . The Bragg peak p o s i t i o n s were c a l c u l a t e d from t h e d a t a by f i t t i n g each o b s e r v e d i n t e n s i t y peak t o a m o d i f i e d L o r e n t z i a n f u n c t i o n u s i n g a n o n - l i n e a r l e a s t - s q u a r e s computer r o u t i n e . T h i s method proved p a r t i c u l a r l y h e l p f u l i n r e g i o n s of peak o v e r l a p . A f t e r a s s i g n i n g t h e p e a k s t o e i t h e r t h e y o o r a" p h a s e s , l a t t i c e p a r a m e t e r s were computed from a l e a s t - s q u a r e s a n a l y s i s of t h e peak p o s i t i o n s . F i n a l - l y , t h e volume f r a c t i o n of t h e a" phase was e s t i m a t e d by a c o m p a r a t i v e a n a l y s i s of t h e peak i n t e n s i t i e s a s s o c i a t e d w i t h each p h a s e , t a k i n g i n t o a c c o u n t p o s s i b l e pre- f e r r e d o r i e n t a t i o n . S t r a i n s were d e t e r m i n e d by measuring t h e d i s t a n c e s between s c r i b e marks on t h e specimens w i t h a n expansometer.

R e s u l t s and D i s c u s s i o n . - The x-ray d i f f r a c t i o n p a t t e r n s v e r i f i e d t h a t f o r t h e p a r t i - c u l a r a l l o y c o m p o s i t i o n chosen, t h e a g i n g h e a t t r e a t m e n t produced a m a t e r i a l a t room t e m p e r a t u r e comprised p r i m a r i l y of t h e y o phase. Small amounts of t h e a" phase of from a t r a c e t o 50% were p r e s e n t and from t h i s i t was concluded t h a t t h e Ms tempera- t u r e was s l i g h t l y above room t e m p e r a t u r e . I n a d d i t i o n t o t h e p r o c e s s i n g d i f f e r e n c e noted e a r l i e r , v a r i a b i l i t y c a n a r i s e b e c a u s e of macro-segregation i n t h e a l l o y t h a t cannot b e e l i m i n a t e d by a homogenization h e a t t r e a t m e n t .

An example of t h e x-ray p a t t e r n changes caused by a p p l i c a t i o n of stress is p r e s e n t e d i n Fig. 4 where t h e d i f f r a c t e d i n t e n s i t y i s p l o t t e d v e r s u s t h e d i f f r a c t i o n a n g l e , 29, o v e r t h e i n t e r v a l 30 t o 42 deg f o r s t r a i n l e v e l s o f 0 , 1, 2 , and 3 % . I n t h e u n s t r e s s e d c o n d i t i o n , i . e . 0% s t r a i n , o n l y a t r a c e amount of t h e a" was d e t e c t e d i n t h i s specimen and yo was t h e predominant phase. I n t h e s t r e s s e d c o n d i t i o n a f t e r 3% s t r a i n , o n t h e o t h e r hand, t h e r e v e r s e was t r u e . As t h e f i g u r e shows, t h e (011) and (111) y o peaks d i s a p p e a r e d w i t h i n c r e a s i n g s t r a i n w h i l e t h e (110) and (111) a"

peaks emerged and grew. At 1% s t r a i n t h e two p h a s e s c o e x i s t e d i n amounts t h a t were n o t t o o d i s s i m i l a r . It was concluded t h a t under s u i t a b l e c o n d i t i o n s c o e x i s t e n c e i s p o s s i b l e and t h a t t h e a" phase c a n grow a t t h e expense of t h e y o p h a s e when stress i s a p p l i e d . The e v i d e n c e a l s o s u g g e s t e d a d i s c r e t e c r y s t a l s t r u c t u r e change a s opposed t o t h e p o s t u l a t e d c o n t i n u o u s change d i s c u s s e d e a r l i e r .

When l a t t i c e p a r a m e t e r s were c a l c u l a t e d , t h e d i s c r e t e n a t u r e of t h e change was more a p p a r e n t . I n F i g . 5 t h e a n g l e l a t t i c e p a r a m e t e r i s p l o t t e d v e r s u s s t r a i n f o r two specimens s t r e s s e d up t o 2 and 4% s t r a i n r e s p e c t i v e l y . Each specimen began t h e e x p e r i m e n t w i t h a t r a c e of a" p r e s e n t . The upper b r a n c h c o r r e s p o n d s t o r e s u l t s from peaks indexed a s y o w h i l e t h e lower c u r v e r e p r e s e n t s t h e r e s u l t s from peaks analyzed a s a". The open p o i n t s came from d a t a o b t a i n e d d u r i n g l o a d i n g w h i l e t h e f i l l e d p o i n t s p e r t a i n t o d a t a o b t a i n e d upon u n l o a d i n g . The v e r t i c a l d o t t e d l i n e i n d i c a t e s where t h e a" peaks f i r s t c o u l d b e s u f f i c i e n t l y r e s o l v e d s o a s t o d e t e r - mine r e a s o n a b l y a c c u r a t e l a t t i c e p a r a m e t e r s . T h i s d a t a c o n f i r m s t h e r e s u l t e v i d e n t i n F i g . 2 t h a t a n g l e s between a b o u t 94 and 97 deg. a r e n o t observed i n uranium- niobium a l l o y s .

When a" i s s t r e s s - i n d u c e d some of t h e e x p e c t e d x-ray peaks were n o t o b s e r v e d . I n F i g . 4 t h i s was t r u e of t h e (110) and (111) peaks. The observed p a t t e r n w i t h t h e m i s s i n g peaks d i d , however, r e s e m b l e t h e p a t t e r n o f a n a t h e r m a l l y t r a n s f o r m e d a"

s u b j e c t e d t o stress i n t h e a" c o n d i t i o n where t h e s t r e s s developed p r e f e r r e d o r i e n - t a t i o n s . Thus, i t was concluded t h a t o n l y c e r t a i n f a v o r e d v a r i a n t s of a" were a c t i - v a t e d d u r i n g s t r e s s - i n d u c e d t r a n s f o r m a t i o n and t h e m i s s i n g peaks r e f l e c t e d t h e de- velopment o f p r e f e r r e d o r i e n t a t i o n s . The f a v o r e d v a r i a n t s a r e presumed t o b e t h o s e whose s h a p e s t r a i n g i v e s r i s e t o maximum e x t e n s i o n i n t h e s t r e s s d i r e c t i o n ( 1 3 ) .

L i k e t h e

y

a n g l e , t h e l a t t i c e p a r a m e t e r s 5 and

b

e x h i b i t e d d i s c r e t e changes d u r i n g s t r e s s - i n d u c e d p h a s e t r a n s f o r m a t i o n . The 5 p a r a m e t e r d e c r e a s e d by 2.1% w h i l e b i n c r e a s e d by 3 . 4 % . To a f i r s t a p p r o x i m a t i o n , t h e 2 p a r a m e t e r remained unchanged - by t h e t r a n s f o r m a t i o n i n c o n f i r m a t i o n of t h e e a r l i e r s u s p i c i o n ( F i g . 3 ) . From t h i s

d a t a a n e t volume e x p a n s i o n of 1.85% was c a l c u l a t e d f o r t h e y o t o a" t r a n s f o r m a t i o n i n d i c a t i n g t h a t i t i s a f i r s t o r d e r phase change.

F i g . 6 summarizes t h e n a t u r e of t h e l a t t i c e d i s t o r t i o n i n v o l v e d i n t h e y o t o a" t r a n s f o r m a t i o n . Only t h e g r o s s l a t t i c e change i s d e p i c t e d h e r e ; t h e s m a l l s h u f - f l e s r e q u i r e d of some of t h e atoms a r e n o t shown. C l e a r l y t h e r e i s a s i g n i f i c a n t d e v i a t o r i c component t o t h e l a t t i c e d i s t o r t i o n .

t e r n s o b t a i n e d . The r e s u l t s of t h i s experiment a r e shown i n F i g . 7 where t h e volume f r a c t i o n of a" i s p l o t t e d v e r s u s t o t a l s t r a i n i n t h e specimen. T h i s specimen con- t a i n e d about 50% of t h e a" phase i n i t i a l l y . The f i g u r e i n d i c a t e s t h a t a s t h e s t r e s s i n c r e a s e d t h e amount of a" i n c r e a s e d ( u n f i l l e d p o i n t s ) a p p r o a c h i n g a s a t u r a t i o n v a l u e of a b o u t 95%. At t o t a l s t r a i n s of 0 . 7 5 , 1 . 5 , 2.25, 3.0, and 3.75%, t h e s t r e s s was removed. The remnant volume f r a c t i o n of a" i n t h e unloaded s t a t e i s a l s o p l o t t e d v e r s u s s t r a i n i n F i g . 7 ( f i l l e d p o i n t s ) . The two s e t s o f p o i n t s n e a r l y d e s c r i b e a s i n g l e c u r v e . The d a t a s u g g e s t e d t h a t t h e t r a n s f o r m a t i o n was p a r t i a l l y r e v e r s i b l e w i t h s t r e s s , and t h a t a s t h e amount of d e f o r m a t i o n i n c r e a s e d , t h e a" p h a s e tended t o b e i n c r e a s i n g l y s t a b i l i z e d .

I n summary, t h e r e s u l t s of t h i s i n v e s t i g a t i o n p r o v i d e d s u b s t a n t i a l e v i d e n c e t h a t t h e y o t o a" p h a s e t r a n s f o r m a t i o n i n uranium-niobium a l l o y s i s indeed a mar- t e n s i t i c p h a s e t r a n s f o r m a t i o n . F u t u r e e x p e r i m e n t a l work w i l l s e e k t o d e t e r m i n e t h e n a t u r e of t h e i n t e r p h a s e i n t e r f a c e , i d e n t i f y t h e l a t t i c e i n v a r i a n t d e f o r m a t i o n mode, and t e s t t h e t r a n s f o r m a t i o n c r y s t a l l o g r a p h y w i t h t h e i n v a r i a n t p l a n e s t r a i n t h e o r y of m a r t e n s i t i c t r a n s f o r m a t i o n .

References.- 1. DUWEZ, P . , J . of Appl. Phys.

24

(1953) 152.

2. GOLDBERG, A. and MASSALSKI, T. B., Nucl. M e t a l l .

17

(w. N. Miner, e d . ) , TMS-AIME, New York (1970).

3. HATT, B. A., J . of Nuclear M a t ' l s .

19

(1966) 133.

4. BURGERS, W. G . , P h y s i c a L ( 1 9 3 4 ) 561.

5. CROCKER, A. G . , and ROSS, N. D. H., The Mechanism of Phase T r a n s f o r m a t i o n s i n C r y s t a l l i n e S o l i d s ; I n s t . of M e t a l s Monograph No. 33 (1969) 129.

6 . ANAGNOSTIDES, M., COLUMBIE, M . , and MONTI, H . , J . of Nucl. ~ a t ' l s .

2

(1964) 67.

7. TANGRI, K. and WILLIAMS, G . I . , J . of Nucl. M a t ' l s .

4

(1961) 226.

8 . JACKSON, R. J . and LARSEN, W. L., J . of Nucl. M a t ' l s . G ( 1 9 6 7 ) 263.

9. JACKSON, R. J . , Dow Chemical Co., Rocky F l a t s Div., Golden, Colo. R e p o r t No.

REP-996 (1970).

1 0 . BLAKE, D. and HEHEMAN, R.F., The P h y s i c a l M e t a l l u r g y of Uranium A l l o y s ; J . Burke, e t a l . e d s . , B r o o k h i l l , C h e s t n u t H i l l , Mass. (1976) 189.

11. YAKEL, H. L., J. o f Nucl. M a t ' l s .

22

(1969) 286.

12. VANDERMEER, R, A . , OGLE, J . C. and NORTHCUTT, W. G . , Met. T r a n s . (1981) 733.

13. TAS, H . , DELAEY, L. and DERUYTTERE, A

.,

^Z M e t a l l k d e

64

(1973) 855.

F i g . 4 . A group of p a r t i a l x-ray

d i f f r a c t o m e t e r s c a n s d e p i c t i n g t h e e f f e c t of d e f o r m a t i o n on t h e t r a n s f o r m a t i o n of y o t o a".

DIFFRACTION ANGLE. 28 l o )

JOURNAL DE PHYSIQUE

STRAIN (%)

F i g . 5. The e f f e c t of s t r a i n on t h e

y

a n g l e d u r i n g t h e s t r e s s - a s s i s t e d y o t o a" t r a n s f o r m a t i o n .

F i g . 6 . The s h a p e change i n v o l v e d i n t h e y o t o a" phase change based on t h e new l a t t i c e p a r a m e t e r measure- m e n t s , i s shown i n t e r m s of t h e u n i t c e l l change. The c i r c l e p o i n t s r e p r e s e n t a p r o j e c t i o n of t h e y o l a t t i c e a l o n g a [010] d i r e c t i o n which i s p a r a l l e l t o 2. The s q u a r e p o i n t s c o r r e s p o n d t o t h e a" l a t t i c e .

(The s m a l l s h u f f l e s r e q u i r e d of t h e atoms i n t h e i n t e r m e d i a t e l a y e r s a r e n o t shown).

F i g . 7 . A p l o t of volume f r a c t i o n of a" v e r s u s s t r a i n . Open p o i n t s r e f e r t o t h e s t r e s s e d c o n d i t i o n w h i l e t h e f i l l e d p o i n t s i n d i c a t e

t h e unloaded s t a t e s .

0 1 2 3 4

STRAIN (%)