HAL Id: jpa-00222146
https://hal.archives-ouvertes.fr/jpa-00222146
Submitted on 1 Jan 1982
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
MARTENSITIC TRANSFORMATIONS IN A TiNi THIN FOIL
P. Moine, E. Goo, R. Sinclair
To cite this version:
P. Moine, E. Goo, R. Sinclair. MARTENSITIC TRANSFORMATIONS IN A TiNi THIN FOIL.
Journal de Physique Colloques, 1982, 43 (C4), pp.C4-243-C4-248. �10.1051/jphyscol:1982432�. �jpa-
00222146�
MARTENSITIC TRANSFORMATIONS I N A TiNi THIN FOIL
P . Moine, E. GOO* and R. s i n e l a i r *
l h i v e r s i t e ' de P o i t i e r s , Laboratoire de Me'taZZurgie Physique, 86022 P o i t i e r s , France
*&oxford University, Department o f Materials Science, Stanford University, Stanford, CaZifornia 94305, U.S.A.
(Accepted 9 August 1982)
A b s t r a c t . - The i n t e r m e t a l l i c compound TiNi h a s l o n g been known t o e x h i b i t "ano- m a l i e s " above t h e M t e m p e r a t u r e
-
t h e s o - c a l l e dre-martensitic
phenomena.I n p a r t i c u l a r e l e c t g o n d i f f r a c t i o n p a t t e r n s show e x t r a r e f l e c t i o n s and t h e Trans- m i s s i o n E l e c t r o n Microscopy (TEM) images some m o t t l i n g , "tweed-like" s t r u c t u r e . . . However, i t i s s u s p e c t e d t h a t some of t h e s e e f f e c t s a r e n o t p r e m o n i t o r y f o r t h e 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 t h e b u l k m a t e r i a l . R e c e n t l y i t was p o i n t e d o u t
t h a t e x t r a r e f l e c t i o n s o b s e r v e d i n Cu-%n-A1 e l e c t r o n d i f f r a c t i o n p a t t e r n s were due t o a s u r f a c e e f f e c t . To c l a r i f y a l l t h e s e p r e t r a n s i t i o n phenomena i n TEM s p e c i m e n s , we have c a r r i e d o u t an i n v e s t i g a t i o n on p h a s e t r a n s f o r m a t i o n s i n a Ti-50.5 a t % N i t h i n f o i l . I n o r d e r t o know t h e i n f l u e n c e o f t h e i n i t i a l s t a t e a t Room Temperature (RT) on t h e r r a r t e n s i t i c f o r m a t i o n i n a t h i n f o i l d u r i n g a n
" i n s i t u " c o o l i n g p r o c e s s , d i f f e r e n t t h e r m a l t r e a t m e n t s were performed i n t h e microscope. TEM samples h e a t e d up t o 400°C and c o o l e d down t o RT e x h i b i t i n t h e i r e l e c t r o n d i f f r a c t i o n p a t t e r n s s t r o n g 112 100 and 114 210 t y p e e x t r a r e f l e c t i o n s , and do n o t t r a n s f o r m i n t o m a r t e n s i t e when t h e y a r e c o o l e d down t o L i q u i d N i t r o g e n
(LN) t e m p e r a t u r e . The same t h e r m a l t r e a t m e n t performed on t h e b u l k d o e s n o t g i v e r i s e t o t h e s e e x t r a r e f l e c t i o n s and does n o t s u p ? r e s s t h e m a r t e n s i t i c t r a n s f o r - mation when t h e specimen i s c o o l e d d o , . t o LM t e m p e r a t u r e . I t i s t h o u g h t t h a t t h i s t h i n f o i l b e h a v i o r i s due t o c o n t a m i n a t i o n d u r i n g t h e " i n s i t u " t h e r m a l t r e a t m e n t . I n t e r s t i t i a l o r d e r i n g of atoms ( ~ o s s i b l y oxygen), which would adequa- t e l y a c c o u n t f o r t h e e x p e r i m e n t a l o b s e r v a t i o n s , i s s u g g e s t e d .
I n t r o d u c t i o n . - E l e c t r o n d i f f r a c t i o n p a t t e r n s of t h e B2 TiNi phase c o n t a i n , i n a d d i t i o n t o t h e B2 s p o t s , many e x t r a r e f l e c t i o n s and some s t r e a k i n g e f f e c t s (1-6). These phenomena have been a t t r i b u t e d t o new o r d e r e d p h a s e s (7-9) o r t o a l a t t i c e dynamical i n s t a b i l i t y o r s o - c a l l e d s o f t phonon mode (1-6) and have o f t e n been t h o u g h t t o a r i s e from p r e m a r t e n s i t i c o r p r e m o n i t o r y e f f e c t s . I I o w e v e r , t h i s b e h a v i o r i s n o t y e t w e l l u n d e r s t o o d and i s q u i t e complex. Moreover, t h i n f o i l e f f e c c s must be t a k e n i n t o a c c o u n t , when T r a n s m i s s i o n E l e c t r o n Microscopy (TEM) e x p e r i m e n t s a r e performed.
I n a ~ r e v i o u s p a p e r (4) we n o t i c e d t h a t some e x t r a r e f l e c t i o n s which we a n a l y z e d a s L a t t i c e Displacement Waves (LDIJ) a r e u n r e l a t e d t o t h e major p h a s e t r a n s f o r m a t i o n and s o c o u l d n o t b e rem monitory phenomena ( v i z . 112 100, 114 210 and p o s s i b l y 113 110 t y p e r e f l e c t i o n s ) . I n t h i s p a p e r , we a t t e m p t t o d e t e r m i n e t h e o r i g i n o f t h e s e l a t t e r supplementary s p o t s d u r i n g a s t u d y of phase t r a n s f o r - mations i n a TiNi t h i n f o i l . H e a t i n g and c o o l i n g e x p e r i m e n t s a r e performed
1 1 .
I n s i t u " i n t h e microscope. Some comparison w i t h t h e b u l k m a t e r i a l i s a l s o pre- s e n t e d .
E x p e r i m e n t a l p r o c e d u r e .
Ti-50.5 a t % N i s t r i ~ s were ? r o v i d e d by Qaychem Co (:?e1110 P a r k , U.S.A.).
They were a n n e a l e d a t 9 0 0 t f o r 10 m i n u t e s and water-quenched. The l a y e r o f o x i d e was c h e m i c a l l y removed. D i s c s 3 m i n d i a m e t e r f o r TEM o b s e r v a t i o n s were s p a r k
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982432
C4-244 JOURNAL DE PHYSIQUE
c u t , then mechanically thinned and e l e c t r o p o l i s h e d a t room temperature using a p e r c h l o r i c - a c e t i c a c i d s o l u t i o n . The TEM experiments were performed with a P h i l i p s EM 400, 120 kv microscope equipped with c o o l i n g and h e a t i n g s t a , ~ e s .
R e s u l t s and d i s c u s s i o n .
"In s i t u " h e a t i n g experiments : A t Room Temperature (RT), t h e a l l o y i s mainly m a r t e n s i t i c with some a u s t e n i t i c g r a i n s . Figure 1 i s t y p i c a l of t h e micro-struc- t u r e a t RT. When a TEM sample i s h e a t e d t h e m a r t e n s i t e d i s a p p e a r s around 100°C and l e a v e s "ghost m a r t e n s i t e " (10) (Fig. 2 ) .
Pig. 1 : Typical f e a t u r e s of T i M i micro- Fig. 2 : Bright F i e l d (BF) and SAD s t r u c t u r e a t RT showing i n the t o p l e f t p a t t e r n showing "ghost m a r t e n s i t e "
hand c o m e r a g r a i n of o x i d e and i n t h e ( i n a specimen heated up t o 219OC) low l e f t hand corner m a r t e n s i t e ~ l a t e s and e x t r a r e f l e c t i o n s among t h e B2 and i n s e t d i f f r a c t i o n p a t t e r n r e l a t e d r e f l e c t i o n s
.
t o t h e l a t t e r .
When t h e temperature reaches 3 0 0 " ~ , theTTp,host m a r t e n s i t e " has d i s a p p e a r e d , t h e sample becomes f u l l y a u s t e n i t i c and t h e S e l e c t i o n Area D i f f r a c t i o n p a t t e r n s show e x t r a r e f l e c t i o n s t o g e t h e r with B2 r e f l e c t i o n s (Fig. 3 ) . These e x t r a re- f l e c t i o n s a r e d i f f u s e and elongated along < l o o > o r <110> d i r e c t i o n s . We can no- t i c e e x t r a r e f l e c t i o n s l o c a t e d a t h a l f of t h e < l o o > fundamental spacings ( c a l - l e d 112 100 r e f l e c t i o n s ) a t 114 of t h e <210> fundamental spacings ( c a l l e d
114 210 r e f l e c t i o n s ) and a t 113 and 1/2 of t h e <110> fundamental s p a c i n g s ( c a l l e d
Fig. 3 : B.F. and SAD p a t t e r n i n a specimen heated up t o 3 2 3 ' ~ showing small i s o l a t e d r e g i o n s and 112 100, 114 210 e x t r a r e f l e c t i o n s r e s p e c t i - v e l y .
( o r 112 010) r e f l e c t i o n i n support of t h i s c o n t e n t i o n . The 112 100 r e f l e c t i o n s a r e l o c a t e d s l i g h t l y away from r a t i o n n a l p o s i t i o n s . The 113 110 r e f l e c t i o n s a r e observed when t h e specimen i s s l i g h t l y t i l t e d from a p e r f e c t Bragg o r i e n t a t i o n
d
Fig. 4 : a) P e r f e c t 111 zone a x i s o r i e n t a t i o n SAD p a t t e r n - b) t i l t e d
-
6' - c) t i l t e d + 6"-
d) r e l a t e d B.F. from a specimen heated up t o 323OC.I n o r d e r t o answer t h e q u e s t i o n : " a r e t h e regions which give r i s e t o t h e s e e x t r a r e f l e c t i o n s , s u r f a c e e f f e c t s ?"Centered Dark f i e l d s t e r e o - p a i r images have been taken (1 l o a p a r t ) u s i n g t h e s t r o n g e x t r a r e f l e c t i o n 312 100 and t h e super- l a t t i c e r e f l e c t i o n 100. The s m a l l p a r t i c l e s r e l a t e d t o t h e 312 100 r e f l e c t i o n ( a s e s t a b l i s h e d by a 2 112 D experiment ( 5 ) ) a r e seen a t d i f f e r e n t h e i g h t s when examined i n a s t e r e o viewer, and i t i s concluded t h e r e f o r e t h a t they a r e n o t s u r f a c e phenomena.
Cken t h e temperature reaches 400°C ( i n t h e microscope) t h e i n t e n s i t y of t h e 112 100 type r e f l e c t i o n s and 114 210 type r e f l e c t i o n s i n c r e a s e s ( F i g . 5 ) ; they become s h a r p e r b u t t h e i r p o s i t i o n s remain t h e same. A t t h e same time, t h e number of small p a r t i c l e s a s s o c i a t e d with t h e s e r e f l e c t i o n s i n c r e a s e s considera- b l y . When t h e sample i s cooled down t o R.T. t h i s new s t r u c t u r e remains p r e s e n t and 113 (110) r e f l e c t i o n s appear. I f t h e i n i t i a l s t a t e of t h e specimen a t R.T. i s f u l l y a u s t e n i t i c (depending on the thermal h i s t o r y ) , t h e behavior i s t h e same e x c e p t , of course, a t t h e beginning of t h e h e a t i n g p r o c e s s .
Fi5.5 : B.F. and SAD p a t t e r n i n a W s p e c i m e n heated up t o 398OC
showing a l o t of small p a r t i c l e s and s t r o n g e x t r a r e f l e c t i o n s . Several v a r i a n t s of l a t t i c e displacement wa- ves a r e p r e s e n t : 112 <100><100>,
112 <010><010> and f o u r v a r i a n t s of 115 <210> waves.
C4-246 JOURNAL DE PHYSIQUE
" ~ n s i t u " c o o l i n g e x p e r i m e n t s : The s p e c i m e n , h e a t e d up t o 400°C and c o o l e d down t o R.T.,does n o t t r a n s f o r m t o m a r t e n s i t e when it i s cooled down t o L i q u i d N i t r o g e n
(LN2) t e m p e r a t u r e . But i n a sample n o t h e a t e d b e f o r e t h e c o o l i n g p r o c e s s a u s t e n i - t i c g r a i n s surrounded by m a r t e n s i t i c g r a i n s w i l l t r a n s f o r m t o "wavy m a r t e n s i t e "
( F i n . 6 a . b ) .
k'lg. b : a) B.F. showing an a u s t e n i t e F i g . 7 : T.E.M. TiNi specimen h e a t e d g r a i n s u r r o u n d e d by m a r t e n s i t e a t R.T. and =2oo0c and c o o l e d down t o LN r e l a t e d SAD p a t t e r n . b) B.F. showing wavy t e m p e r a t u r e : a ) B.F. showing d e n d r i - m a r t e n s i t e a t LN t e m p e r a t u r e and r e l a t e d t i c s t r u c t u r e s and r e l a t e d SAD p a t - SAD p a t t e r n . c )
it
R.T. t h e wavy m a r t e n s i t e t e r n . b ) B.F. showing " ~ a t c h w o r k h a s d i s a p p e a r e d i n t h e i n i t i a l a u s t e n i t e q u i l t " s t r u c t u r e and r e l a t e d SAD p a t -g r a i n . t e r n . c ) B.F. showing d e n d r i t i c s t r u c -
t u r e s ; t h e r e l a t e d SAD p a t t e r n s show s t r o n g 113 110 r e f l e c t i o n s .
These s t r u c t u r e s d i s a p p e a r a t R.T. This behavior i s d i f f e r e n t from t h a t of t h e bulk m a t e r i a l because r e g a r d l e s s of t h e thermal h i s t o r y , Ti-50.5 % a t N i a l l o y transforms t o m a r t e n s i t e upon c o o l i n g t h e b u l k m a t e r i a l down t o LN temperature.
I n o r d e r t o know i f t h e small r e g i o n s r e l a t e d t o 112 100 and 112 2?0 r e f l e c t i o n s could be r e s p o n s i b l e f o r t h e s u p p r e s s i o n of t h e 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 , bulk m a t e r i a l was heated up t o 4 0 0 ' ~ f o r 112 hour and cooled down t o R.T. A f t e r e l e c - t r o p o l i s h i n n f o r T.E.M., we d i d n o t n o t i c e 112 100 and 114 210 type r e f l e c t i o n s b u t 113 110 t y p e r e f l e c t i o n s a r e p r e s e n t i n a[001]zone a x i s o r i e n t a t i o n S e l e c t i o n Area D i f f r a c t i o n (S.A.D.) p a t t e r n . So it appears t h a t t h e 112 100 and 114 210 r e f l e c t i o n s a r e due t o a t h i n f o i l e f f e c t b u t n o t t h e 113 110 r e f l e c t i o n s . I t can be thought t h a t t h e r e i s a contamination of t h e whole t h i n f o i l which a f f e c t s t h e subsequent 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 t h e bulk m a t e r i a l t h i s contamina- t i o n w i l l occur only on t h e s u r f a c e and s o , w i l l n o t a f f e c t t h e m a r t e n s i t e forma- t i o n . I n f a c t , T.E.M. samples l e f t a t R.T. f o r s e v e r a l months show i n t e n s e 112 100 and 1/4 2 1 3 type r e f l e c t i o n s . This contamination i s a p p a r e n t l y due t o t h e ambient atmosphere of t h e specimen and s o could be due t o oxygen, n i t r o g e n
...
atoms. Wasilewski (11) h a s demonstrated t h a t i n c r e a s i n g t h e oxynen contamina- t i o n l e v e l can lower t h e M temperature of TiNi. I n t e r s t i t i a l atom o r d e r i n g ( p o s s i b l y oxygen) could prgduce s t a t i c l o n g i t u d i n a l displacement waves which would adequately account f o r t h e experimental o b s e r v a t i o n s . For i n s t a n c e , f i g u r e 8 a , we show i n a diagram how atoms i n o c t a h e d r a l i n t e r s t i c e s of BCC TiNi can g i v e r i s e t o a 112 [loo] [loo] LDW and so e x p l a i n why t h e 112 100 s p o t i n t e n s i t y i s lower t h a n t h e 312 100 s p o t i n t e n s i t y . P e r i o d i c p l a n e f a u l t s i n t h i s s t r u ~ t u - r e , l y i n g i n every o t h e r (010) p l a n e (Fig. 8 b) g i v e r i s e t o LDrJ's, with a q v e c t o r 114 <210> which could accnimt f o r 114 210 e x t r a r e f l e c t i o n s . W e t h e r o r n o t t h i s model f u l l y accounts f o r a l l t h e observed r e f l e c t i o n s i n 3-D r e c i p r o c a l s?a- c e remains t o be seen. 113 110 type r e f l e c t i o n s which appear i n[ o o ~ ]
,[I 111and[ll0] zone a x i s o r i e n t a t i o n S.A.D. p a t t e r n a t room temperature occur i n T.E.M.
specimens thermally t r e a t e d i n t h e microscope a s w e l l a s i n t h e bulk m a t e r i a l . Chandra e t Purdy ( 6 ) have a l r e a d y observed t h e s e e x t r a r e f l e c t i o n s , assuming t h a t they appear a s a r e s u l t of i n t e r s e c t i o n s of s p i k e s o r s t x e a k s with t h e Ewald s?he- r e and i n t e r p r e t i n g them i n terms of " s o f t phonon"<321><111>. These e x t r a r e f l e c - t i o n s , a l s o , o f t e n p r e s e n t a t R.T. a r e n o t premonitory f o r t h e m a r t e n s i t i c t r a n s - formation ( 4 , 5 ) , b u t r a t h e r c h a r a c t e r i s t i c of a n o t h e r n e t a s t a b l e phase which may compete with t h e 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 .
When t h e T.E.M. specimen i s only heated up t o 200°c-250°C, we can assume t h a t t h e contamination i s l e s s r a p i d : t h e 112 100 and 114 210 supplementary re- f l e c t i o n s a r e n o t very s t r o n g (FiG.7 c ) .
4-1 pool
7 2
,
+
\I2
001~ i g . 8 a : Diagram showing how i n t e r s - Fig. 8 b : Diagram showing how p e r i o d i c t i t i a l o r d e r i n g of atoms can c r e a t e a p l a n e d e f e c t (010) (period = 2a) can L.D.W. 112 100 100
.
c r e a t e i n t h e s t r u c t u r e of t h e f i g u r e114 210
.
JOURNAL DE PHYSIQUE
However, d u r i n g t h e c o o l i n g p r o c e s s t h e u s u a l wavy m a r t e n s i t e does n o t form even a t LN2temperature, b u t a d e n d r i t i c and a "patchwork q u i l t " s t r u c t u r e a p p e a r . These s t r u c t u r e s d i s a p p e a r when t h e specimen i s h e a t e d up a g a i n t o R.T. T h i s b e h a v i o r s u g g e s t s t h e f o r m a t i o n of a new m a r t e n s i t e whose s t r u c t u r e p r e s e n t s some s i m i l a r i t i e s w i t h t h e 3R m a r t e n s i t e d e s c r i b e d by Gupta and a l . ( 1 2 ) . We do n o t know i f t h i s new s t r u c t u r e competes w i t h t h e u s u a l m a r t e n s i t e , o r i s premoni- t o r y f o r t h e m a r t e n s i t e f o r m a t i o n below LN7 t e m T e r a t u r e , o r s u p p r e s s e s t h e u s u a l 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 t i s w o r t h n o f i c i n g t h a t t h e s t r o n g 113 110 t y p e e x t r a r e f l e c t i o n s a s s o c i a t e d w i t h t h e d e n d r i t i c s t r u c t u r e s observed t o g e t h e r w i t h t h e fundamental B2 s p o t s , a p p e a r i n p e r f e c t Bragg o r i e n t a t i o n SAD p a t t e r n s which i s t h e o p p o s i t e of t h e ! / 3 110 e x t r a r e f l e c t i o n s when t h e specimen i s a t R.T. o r above. I t may a l s o be n o t i c e d t h a t 113 112 r e f l e c t i o n s appear i n [ l 1 1 1 zone a x i s o r i e n t a t i o n SAD p a t t e r n s .
Conclusion.
T.E.M. phenomena observed above M t e m p e r a t u r e i n a TiNi t h i n f o i l have t o b e a n a l y z e d v e r y c a r e f u l l y ; varkoious phe:omena o c c u r c o n c u r r e n t l y s p e c i a l l y i n T.E.M. specimens. We ~ o i n t o u t , f o r i n s t a n c e , t h a t 112 100 and 114 210 t y p e ex- t r a r e f l e c t i o n s o b s e r v e d i n a <001> zone a x i s o r i e n t a t i o n SAD p a t t e r n a f t e r hea- t i n g t h e specimen " i n s i t u " up t o 400°C a r e n o t observed i n t h e b u l k m a t e r i a l a f t e r t h e same t h e r m a l t r e a t m e n t . I t i s t h o u g h t t h a t t h e s e e f f e c t s may a r i s e from c o n t a m i n a t i o n o f t h e whole t h i n f o i l ( p o s s i b l y i n t e r s t i t i a l o r d e r i n g o f oxygen atoms) which w i l l s u p p r e s s t h e m a r t e n s i t e f o r m a t i o n d u r i n g a s u b s e q u e n t c o o l i n g p r o c e s s down t o LN t e m p e r a t u r e ( o r d e p r e s s t h e Ms t e m p e r a t u r e below LN2 t e m p e r a t u r e ) . Conversely, $he 113 110 t y p e e x t r a r e f l e c t i o n s a r e o b s e r v e d i n T.E.M. specimens and b u l k m a t e r i a l a t room t e m p e r a t u r e . We do n o t know y e t what r o l e t h i s i n t e r m e d i a t e s t a t e p l a y s i n t h e 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 a t h i n f o i l a s opposed t o t h e b u l k m a t e r i a l t h e m a r t e n s i t e f o r m a t i o n i s v e r y s e n s i t i v e t o i t s t h e r m a l h i s t o r y . It i s t h o u g h t t h a t t h i s i s due t o a t h i n f o i l c o n t a m i n a t i o n d u r i n g t h e " i n s i t u " t h e r m a l t r e a t m e n t s . Depending on t h e c o n t a m i n a t i o n l e v e l new m a r t e n s i t i c s t r u c t u r e s can a p p e a r d u r i n g t h e c o o l i n g p r o c e s s o r t h e r e may b e no t r a n s f o r m a t i o n a t a l l .
Acknowledgements: F i n a n c i a l s u p p o r t f o r t h i s work was p r o v i d e d by t h e NSF-MRL program through t h e C e n t e r o f M a t e r i a l s Research, S t a n f o r d U n i v e r s i t y . A s s i s t a n - c e from Raychem Co was g r e a t l y a p p r e c i a t e d . One o f us (PM1) i s v e r y g r a t e f u l t o P r o f e s s o r R. S i n c l a i r f o r h i s s u p p o r t w h i l e d o i n g r e s e a r c h i n h i s l a b o r a t o r y a t S t a n f o r d U n i v e r s i t y .
1
-
G.D. S a n d r 0 ~ k ~ A . J . P e r k i n s and R.F. Hehemann. i 4 e t a l l . T r a n s . 2 (1971), 2769.2
-
S.R. Z i j l s t r a , J. B e i j e r and J . A . Klostermann. J. Mater. S c i . (1374),145.3
-
D.P. Dautovich and G.R. Purdy. Can M e t a l l . 94
(1965), 129.4 - G.M. Michal, P. Moine and R. S i n c l a i r . Acta M e t a l l .
2
(1982), 125.5
-
P.Moine, G.M. Michal and R. S i n c l a i r . Acta M e t a l l . 30 (1982), 109.6 - K. Chandra and G.R. Purdy. J . Appl. Phys. 39, ( 1 9 6 8 z 2176.
7
-
A, Nagasawa. J. Phys. Soc. o f J a p a n2
(1970), 1386.8
-
F . E . Wang, W.J. Buehler and S.J. P i c ~ a r t . J . of Appl. Phys.2
(1965), 3232.9
-
H.A. Ffohamed. Ph. D. T h e s i s U.C. B e r k e l e y , Berkeley C a l i f o r n i a (1976).10 - R.H. B r i c k n e l l and K.N. Melton. M e t a l l . T r a n s . 11 a , (1980), 1541.
11