ACOUSTIC EMISSION DURING MARTENSITIC TRANSFORMATION OF Cu-Zn-Al

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Submitted on 1 Jan 1982

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ACOUSTIC EMISSION DURING MARTENSITIC TRANSFORMATION OF Cu-Zn-Al

D. Maeder, P. Ryser, B. Sanderson, A. Sillou, A. Steiner

To cite this version:

D. Maeder, P. Ryser, B. Sanderson, A. Sillou, A. Steiner. ACOUSTIC EMISSION DURING

MARTENSITIC TRANSFORMATION OF Cu-Zn-Al. Journal de Physique Colloques, 1982, 43 (C4),

pp.C4-609-C4-614. �10.1051/jphyscol:1982496�. �jpa-00222216�

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ACOUSTIC EMISSION DURING MARTENSITIC TRANSFORMATION OF Cu-Zn-A1

D . Maeder, P. Ryser, B. Sanderson, A. S i l l o u and A . S t e i n e r

~&artement de Physique Nucle'aire e t CorpuseuZaire, Universite' de GenBve, Svitzer Land

(Revised t e x t accepted 24 September 1982)

A b s t r a c t . - The c h a r a c t e r i s t i c t r a n s f o r m a t i o n temperatures of s m a l l samples of a CuZnAl a l l o y were determined by r e s i s t i v i t y measurements.

Ring-down counting measurements of a c o u s t i c emission d u r i n g tFmperature c y c l i n g o f t h e s e samples show d i s t i n c t i v e maxima o c c u r r i n g n e a r Ms(T < 0 ) and Af(T > 0 ) . Counting r a t e s depend s t r o n g l y on mechanical/thermal sample h i s t o r y b u t a r e always p r o p o r t i o n a l t o temperature v a r i a t i o n r a t e . D e t a i l e d e v e n t r e c o r d i n g s r e v e a l b u r s t - l i k e s i g n a l s of widely f l u c t u a t i n g amplitudes g e n e r a t e d by s o u r c e p r o c e s s e s of very s h o r t d u r a t i o n . T h e i r c h a r a c t e r i s t i c s a r e l i t t l e a f f e c t e d by d i f f e r e n t r a t e s of temperature v a r i a t i o n .

I n t r o d u c t i o n . - CuZnAl belongs t o t h e shape-memory a l l o y s which undergo a r e v e r s i b l 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 induced by v a r i a t i o n of temperature and/or s t r e s s .

The c r y s t a l s t r u c t u r e s of i t s 5 ⁽⁼m a t r l x ) and ^M(= M a r t e n s i t i c ) phases have been w e l l established ( r e f . 1) whereas t h e n u c l e a t i o n and growth o f M - p l a t e l e t s and subsequent i n t e r n a l s t r e s s accommodation p r o c e s s e s a r e s u b j e c t s o f c u r r e n t r e s e a r c h , based mainly on o p t i c a l - and electron-microscopic o b s e r v a t i o n s ( r e f . 2 ) . X-ray d i f f r a c t i o n measurements ( r e f . 3 ) have r e v e a l e d r e o r i e n t a t i o n and l a t t i c e s t r u c t u r e changes d u r i n g t h e t r a n s f o r m a t i o n . Macroscopic methods such a s r e s i s t i v i t y , i n t e r n a l f r i c t i o n , c a l o r i m e t r y , and ultrasonic a t t e n u a t i o n measurements a r e used t o d e t e r - mine t h e c h a r a c t e r i s t i c temperatures and t o s t u d y a s s o c i a t e d d i s s i p a t i v e phenomena

( r e f . 4,5).

I n p r i n c i p l e , AE (= a c o u s t i c emission) experiments may provide i n f o r m a t i o n on t h e k i n e t i c s of t h e t r a n s f o r m a t i o n , i n s o f a r a s t h e g l o b a l e f f e c t can b e r e s o l v e d i n t o d i s c r e t e , w e l l - s e p a r a t e d b u r s t s o r "events". AE techniques have been a p p l i e d t o CuZnAl by s e v e r a l groups ( r e f . 6,7,8); i n p a r t i c u l a r , a s t r o n g c o r r e l a t i o n be- tween AE and enthalpy changes was e s t a b l i s h e d . Baram and Rosen ( r e f . 9) made d e t a i l e d AE measurements on AuCd where t h e observable e v e n t s seem t o v a r y consider- a b l y i n number, amplitude and d u r a t i o n between t h e forward and r e v e r s e transform- a t i o n s , and a l s o a s a f u n c t i o n of h e a t i n g / c o o l i n g r a t e s .

Our f i r s t AE s t u d i e s on CuZnAl ( r e f . 1 0 , l l ) i n d i c a t e d l i t t l e v a r i a t i o n of e v e n t c h a r a c t e r i s t i c s n e i t h e r f o r d i f f e r e n t t r a n s f o r m a t i o n r a t e s , nor between t h e forward/reverse d i r e c t i o n s . We now r e p o r t o n . a d d i t i o n a 1 experiments u s i n g samples w i t h v a r i o u s thermal and/or mechanical t r e a t m e n t s , where we f i n d s i g n i f i c a n t d i f f e r e n c e s i n counting r a t e s .

Experimental procedure.- Two p o l y c r i s t a l l i n e m e l t s of s i m i l a r compositions, approximately given by (weight % ) , have been p r e p a r e d from 3 N p u r i t y a l l o y i n g elements and c a s t i n t o a Cu mould a t room temperature. I n t a b l e 1, A0 and BO d e s i g n a t e t h e raw i n g o t s from which s m a l l e r samples were machined, o r c u t by

spark e r o s i o n i n o r d e r t o minimize mechanical s t r e s s e s t h a t could l o c a l l y modify

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982496

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t h e t r a n s f o r m a t i o n c h a r a c t e r i s t i c s . Annealing of mechanically worked samples a t 8 0 0 ~ ~ d u r i n g 5 minutes was followed by an argon j e t quench a t

l o 3

^{O / s} ^{t o room}

temperature (A2, B4). A2 was k e p t i n a m a r t e n s i t i c s t a t e between quenching and t h e beginning o f AE r e c o r d i n g s . The s t a r t and f i n i s h temperatures of t h e

B

+ M and M +

B

t r a n s f o r m a t i o n s given i n t h e l a s t f o u r columns o f t h e t a b l e were d e r i v e d from e l e c t r i c r e s i s t i v i t y measurements, u s i n g a c o n t a c t l e s s d i f f e r e n t i a l method devel- oped t o f i t our sample geometry ( t o be p u b l i s h e d e l s e w h e r e ) . I n g e n e r a l , Ms, Af and t h e i r d i f f e r e n c e Af-Ms a r e well-defined (t-

1°c)

whereas Mf and As a r e more u n c e r t a i n (+ ~ O C ) .

Metallographic examination of t h e B-samples confirmed t h e appearance/disap- pearance of m a r t e n s i t i c p l a t e l e t s i n a temperature range compatible with t h e r e s i s - t i v i t y d a t a of Table I . No p r e c i p i t a t e s were observed, and it was a s c e r t a i n e d t h a t t h e whole s u r f a c e had transformed a t M f .

Sample h i s t o r y Sample

type

Average g r a i r diameter Sample dim?

(mm) d i a t h i c k

C h a r a c t e r i s t i c temp. ( 0 C) (from r e s i s t i v i t y )

Ms Mf As Af

quenched by c a s t i n g from melt

machined from AO, aged by %

l o 2

thermal c y c l e s a s A l , ann.

+

quenched

- -

0.5

. . .

¹

0.5

...

¹

7.5 50

7.5 1

5 1

5 2

5 1

*

A:, A2, B2, B4 r e p r e s e n t our " s t a n d a r d s i z e " (19,4 mm 3 ) Table I - Sample c h a r a c t e r i s t i c s

Piezoceramic t r a n s d u c e r d i s k s of high conversion e f f i c i e n c y ( P h i l i p s PXE-5,

K

=

0 . 7 , diameter 5 mm) were bonded t o both sample f a c e s a s i n d i c a t e d i n F i g . 1 with e l e c t r i c a l l y conductive epoxy (TRA-CON 2902). Simultaneous AE d e t e c t i o n a t two r e s o n a n t f r e q u e n c i e s i s p o s s i b l e i n a range from about 0.5 MHz t o 12 MHz, w i t h d e c r e a s i n g s e n s i t i v i t y f o r t h e h i g h e r f r e q u e n c i e s . E l e c t r i c a l connections t o t h e two a m p l i f i e r c h a i n s a r e made v i a f l e x i b l e w i r e s i n s i d e t h e sample h o l d e r , t o a s s u r e a c o u s t i c insulation from t h e dewar. Holder temperature i s d i g i t i z e d every 10 s, and compared i n t h e T4051 g r a p h i c s console w i t h t h e programmed temperature.

Via a sample h e a t e r , s l o p e s w i t h i n t h e l i m i t s of - 6O/min and

+

12O/min can b e r e a l i z e d t o

+

O.loc/min. Bandpass f i l t e r s ( Q 10) c e n t e r e d a t t h e r e s p e c t i v e r e s o n a n t f r e q u e n c i e s a r e i n s e r t e d i n t o t h e 80 dB a m p l i f i e r c h a i n s . The e l e c t r o n i c c h a i n a l o n e would have a r e s o l v i n g time ro Q / i r f , o r 0.6 u s a t 5 MHz. The o v e r a l l r e s o l v i n g time f o r a t h e r m o e l a s t i c impulse i s much l a r g e r , due t o m u l t i p l e r e - f l e x i o n s and v i b r a t i o n mode conversions i n t h e sample-transducer assembly. I t was determined e x p e r i m e n t a l l y using 1 n s , 50

uJ

l a s e r p u l s e focused on t h e sample s u r f a c e a s a s i m u l a t o r of elementary a c o u s t i c emission " e v e n t s " having minimum d u r a t i o n . The half-wldth o f . l a s e r generated p u l s e s was -rq ( L a s e r ) = 8

u s

a t 5 MHz, and 2.5

u s

a t 12 MHz. We found t h a t t r u e AE s i g n a l s had s i m i l a r waveforms whose d u r a t i o n r a r e l y exceeded 30 us; even a t t h e h i g h e s t counting r a t e s , AE s i g n a l s were always s e p a r a t e d by q u i e t i n t e r v a l s which allowed t o d e f i n e i n d i v i d u a l e v e n t s .

a s A0

c u t by s p a r k e r o s i o n machined from BO a s B2, e t c h e d % 1 p a s B2, ann.+quenched

-

0 . 1

. . .

^{0 - 2}

0 . 1

...

^0.2

0.1

. . .

^0.2

0.5

...

1

- - -

-

23 1 6 24

31 - 5 1 35

29

-

20 - 5 34

-

- -

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7.5 pV ( r e f e r r e d t o i n p u t ) t o reduce background counting t o < 3/sec. A l a s e r - g e n e r a t e d p u l s e of 30 pV peak amplitude would t h u s r i n g down i n 2 ^T$²1 6 p s , g i v i n g 2 80 counts. To r e c o r d t h e d e t a i l s of an e v e n t a t 5

( o r even 12) MHz on o u r 5 MHz t r a n - s i e n t r e c o r d e r , t h e envelope of t h e a m p l i f i e r o u t p u t was generated i n an a n a l o g c i r c u i t . The t r a n s i e n t r e - corder t r i g g e r was u s u a l l y s e t t o 50 pV ( o c c a s i o n a l l y 30 uV) t o l i m i t t h e amount of d a t a t h a t had t o be 2C s t o r e d . Temporary s t o r a g e i n a Z80

microprocessor allowed a c q u i s i t i o n r a t e peaks up t o 6 e v e n t s / s e c .

R e s u l t s

Common f e a t u r e s i n ring-down counting.-

...

A l l counter experiments-have been done r e p e a t e d l y a t d i f f e r e n t c o o l i n g / h e a t i n g r a t e s , mostly w i t h i n

/ T I

⁼^1.5

...

6OC/min, b u t o c c a s i o n n a l l y down t o 0.3O/min. A t l e a s t one f u l l 6 + M -t 6 c y c l e ( t y p i c a l l y

1 0 0 ~ ~ + OOC + ~ O I ? ~ C ) was completed a t each r a t e v a l u e , i n o r d e r t o check t h e r e - l a t i o n between IT/ and t h e counting r a t e s , N. Except f o r t h e f i r s t two cycles of quenched samples (A2, B4), we never found s i g n i f i c a n t d e v i a t i o n s from p r o p o r t i o n - a l i t y

-

i n o t h e r words, t h e cumulative counts were independent o f t h e transform- a t i o n r a t e s ( w i t h i n

+

10 % ) . A l l curves p r e s e n t e d i n t h i s a r t i c l e were o b t a i n e d a t

+

3OC/min, and were reduced t o t h e s t a n d a r d sample volume ( s e e Table I ) i n t h e c a s e s of B1 and B3 c o u n t i n g r a t e peaks a r e g e n e r a l l y l o c a t e d close t o Ms ( f o r

6

⁺M) and Af ( f o r M -t 8 1 . I t i s p a r t i c u l a r l y e v i d e n t from a l o g a r i t h m i c

fi

v e r s u s T p l o t ( a s m F l g . 2) t h a t t h e AE a c t i v i t y e x t e n d s f a r beyond t h e r e s p e c t i v e "end p o i n t s "

M f , Af determined from r e s i s t i v i t y measurements. Sample B1 even h a s i t s M +

8

peak l o ° C above A f . The B3** curve shows t h e c l o s e c o r r e l a t i o n between ringdown counting

and e v e n t d e t e c t i o n , w i t h a b o u t one e v e n t p e r 4000 counts.

F i g . 2

Counting r a t e s v e r s u s tempera- t u r e f o r samples B1 and B3.

B1 and B3*:threshold 7.5 pV.

For comparison, B3** d i s p l a y s t h e t r a n s i e n t r e c o r d e r t r i g g e r r a t e ( m u l t i p l i e d by 2 ) w i t h t h r e s h o l d a t 50 pV.

With t h e only e x c e p t i o n of sample A l , t h e M +

8

counting r a t e s a r e u s u a l l y much l a r g e r t h a n t h o s e found i n t h e forward t r a n s f o r m a t i o n , w i t h r a t i o s of t h e peak r a t e s v a r y i n g between 2

...

15, depending on sample t r e a t m e n t (Fig. 3 ) . Simultaneous counting i n two frequency bands ( f o r example 5 and 12 MHz, o r 5 and 1 MHz, e t c . ) g e n e r a l l y produced very s i m i l a r r e s u l t s , a p a r t from t h e lower s e n s i t i v i t y a t t h e h i g h e r f r e q u e n c i e s .

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JOURNAL DE PHYSIQUE

TEMPERATURE

L

O C

I

TEMPERATURE

L

"C

I

F i g . 3 L e f t : I zounting r a t e s v e r s u s temperature f o r t h e Rlght : cumulative counts ) B 1 , 8 2 , B3, B4 samples Notice t h e l i n e a r v e r t i c a l s c a l e .

TEMPERATURE L

^{O C}

1

F i g . 4 Counting r a t e s f o r t h e sample A2. Dotted l i n e shows f i r s t h e a t i n g / c o o l i n g c y c l e a f t e r quench; heavy l i n e s r e p r e s e n t t h e 1 2 t h c y c l e . E f f e c t s o f sample p r e p a r a t i o n on counting r a t e s . - Annealed/quenched samples,

...

compared with t h e i r mechanically worked p r e d e c e s s o r s i n F i g . 3 (B2 ⁺B4), have t h e i r AE peaks n o t i c e a b l y s h i f t e d toward h i g h e r temperatures. However, A2 showed a p a r t i c u l a r i t y which e x i s t e d o n l y d u r i n g t h e f i r s t h e a t i n g procedure a f t e r t h e quench: t h e dashed l i n e i n F i g . 4 i n d i c a t e s a n enormous temporary s h i f t of t h e e f f e c t i v e As, Af p o i n t s ( t h e temperatures given i n t a b l e 1 were measured only a f t e r s e v e r a l c y c l e s ) . The AE peak i n t h e f i r s t h e a t i n g i s a t

+

8 8 O ~ , i . e .

s h i f t e d

+

40°c with r e s p e c t t o t h e s t a b i l i z e d s t a t e . The subsequent f i r s t c o o l i n g a l r e a d y produced a n e a r l y "normal" counting r a t e curve, and t h e second c y c l e e s s e n t i a l l y coincided with t h e heavy l i n e i n F i g . 4.

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appears t o b e q u i t e e f f e c t i v e i n reducing t h e e f f e c t s of p r e v i o u s machining on t h e shape of AE c u r v e s (B2 + B3 i n Fig. 3 ) . Counting r e s u l t s from a l l samples a r e summarized i n t a b l e 2.

Table 2

-

Summary o f 5 MHz ringdown c o u n t i n g r e s u l t s (Bl, B3 d a t a reduced t o s t a n d a r d sample s i z e ) Sample

A2 B 1 B2 B 3 B4

+ r ~ & y ~ & s _ - o _ f _ e _ ~ ~ n ~ - r e c o r d & ~ ~ ~ . - I f ring-down counting r a t e s vary c o n s i d e r a b l y from one sample t o a n o t h e r , and between forward/reverse t r a n s f o r m a t i o n s , such v a r i a t i o n s c o u l d b e caused by changes i n ( a ) number, (b) amplitude, and (c) d u r a t i o n o f events.

( a ) From a c t u a l a c q u i s i t i o n r a t e s , we can e x t r a p o l a t e t h e t r u e number of e v e n t s by a p p l y i n g deadtime c o r r e c t i o n s . With t h e t r i g g e r t h r e s h o l d a t 50 UV ( 5 MHz), t h i s l e a d s t o rough e s t i m a t e s of %

l o 4

e v e n t s d u r i n g a complete t r a n s f o r m a t i o n . ( b ) Amplitudes v a r y much more between c o n s e c u t i v e e v e n t s than do t h e i r averages

from one experiment t o a n o t h e r . For example, A2 produced AE s i g n a l s of 84 VV and 75 pV average amplitude i n t h e M +

6

and

8

+ M h a l f c y c l e s r e s p e c t i v e l y

(average of p u l s e s exceeding t h e 50 pV t h r e s h o l d ) , with s t a n d a r d d e v i a t i o n s o f 35 VV and 26 vV; o t h e r samples showed s i m i l a r l y s m a l l amplitude changes between forward/reverse t r a n s f o r m a t i o n s . I n a d d i t i o n , we found t h a t amplitude d i s t r i b u t i o n s d i d n o t s i g n i f i c a n t l y change from sample t o sample, nor f o r d i f f e r e n t h e a t i n g / c o o l i n g r a t e s .

Cumul. c o u n t s

( l o 4 )

f3+M M+%

9 5 7

15 69

27 54

15 23

9 6 1

R e s i s t i v i t y

Ms Af

65 70

23 24

31 35

29 34

- -

( c ) By a v e r a g i n g t h e envelopes of some

l o 2

c o n s e c u t i v e e v e n t s , a r e g u l a r waveform with a well-defined half-width

T3

i s o b t a i n e d . I n t h e 12 MHz channel,

T+

(AE) was found t o b e < 2.8 ps; comparison with t h e l a s e r r e s u l t , -c4(Laser) 2.5

u s ,

s u g g e s t s t h a t n e a r l y a l l recorded AE e v e n t s a r e from s t e p w i s e p r o c e s s e s o f extremely s h o r t d u r a t i o n (<< 3 p s ) .

Discussion.- ~ r o m ' t h e l a r g e d i f f e r e n c e between AE produced i n t h e f i r s t and l a t e r c y c l e s ( F i g . 4 ) , i t i s e v i d e n t t h a t t h e r e i s no uniquely d e f i n e d m a r t e n s i t i c s t a t e : quenching l e a d s t o a s t a t e which d i f f e r s from t h e one a t t a i n e d i n slow c o o l i n g / h e a t i n g c y c l e s . AE observed i n p a r t i a l temperature c y c l e s ( r e f . 10) s u g g e s t s , i n a d d i t i o n , an i n c r e a s i n g h y s t e r e s i s a s t h e m a r t e n s i t i c phase pro- g r e s s e s . T h i s i s i n c o n t r a s t w i t h r e c e n t r e s u l t s on AuCd ( r e f . 8 ) ; we a l s o f i n d some i n c r e a s e of t h e average AE p u l s e amplitudes d u r i n g M + 8 compared t o

B

+ M b u t t o a much s m a l l e r degree. These d i f f e r e n c e s may be r e l a t e d t o t h e s t a c k i n g f a u l t t y p e of o u r CuZnAl m a r t e n s i t e whereas t h e AuCd t r a n s f o r m s i n t o a twinned s t r u c t u r e . On t h e o t h e r hand, t h e e x t e n s i o n of AE a c t i v i t i e s beyond M ~ / A ~ i s

Temp. o f

i

(OC) max

B-fM M+%

52 57

24 34

2 7 33

26 33

34 49

Value of

iJ

(104s-l)max B-tM M+B

0.3 2 . 5

1 15

1 1.7

0.8 1.7

0.25 1 . 5

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JOURNAL DE PHYSIQUE

g e n e r a l l y confirmed by o t h e r workers.

The e f f e c t o f machining on t h e AE c u r v e s ( F i g . 3) may b e understood i n terms of i n t e r n a l s t s e s s e s w i t h i n a s u r f a c e l a y e r where t h e t r a n s f o r m a t i o n i s s h i f t e d t o h i g h e r temperatures a s confirmed by r e s i s t i v i t y d a t a . Consequently AE from t h i s l a y e r appears a t h i g h e r temperatures while t h e bulk peak i s reduced i n h e i g h t b u t remains a t t h e o r i g i n a l temperature. The a p p a r e n t i n c r e a s e of AE d u r i n g '8 -z M might r e s u l t from reduced sound a t t e n u a t i o n due t o a s i m p l e r m a r t e n s i t e s t r u c t u r e i n t h e s t r e s s e d l a y e r of t h e sample. The e f f e c t of s u r f a c e e t c h i n g seems t o i n d i c a t e t h a t an a p p r e c i a b l e f r a c t i o n of AE s o u r c e s i n t h e 6 + M t r a n s f o r m a t i o n may be due t o s u r f a c e s t r e s s e s . The e f f e c t s of annealing

+

quenching on our samples i s n o t c l e a r y e t ; t h e d i f f e r e n c e s may have t o do w i t h t h e f a c t t h a t t h e quench l e f t A2 i n an almost 100 % m a r t e n s i t i c s t a t e , i n c o n t r a s t t o B4. I n b o t h c a s e s , however, a s t r o n g asymmetry between forward/reverse t r a n s f o r m a t i o n s i s e s t a b l i s h e d a f t e r t h e quench. A comparison o f t h e AE peak temperatures w i t h Ms, Af shows t h a t a n o t i c e - a b l e f r a c t i o n o f t h e AE observed i n t h e t r a n s f o r m a t i o n s i s e m i t t e d b e f o r e t h e m a r t e n s i t e p l a t e l e t s form r e s p e c t i v e l y a f t e r t h e y d i s a p p e a r .

Acknowledgements.- Supply of v a r i o u s samples and v a l u a b l e d i s c u s s i o n s w i t h P r o f . W. Benoit, D r . R. G o t t h a r d t ( L a b o r a t o i r e de Gdnie Atomique EPFL) and P r o f . 0 . Mercier (BBC r e s e a r c h l a b o r a t o r i e s ) a r e acknowledged. A s s i s t a n c e and s u g g e s t i o n s of c o l l e a g u e s from t h e S o l i d S t a t e Department o f our i n s t i t u t e were g r e a t l y a p p r e c i a t e d . Thus work was supported by t h e Swiss N a t i o n a l Research Foundation.

References

1 ) DELAEY L., Report 78R1-1978 U n i v e r s i t B c a t h o l i q u e de Louvain, Belgique 2 ) GOTTEIARDT R. and MERCIER O . , J. Phys.

10

(C5-1981) 995

3 ) BARCELO G., AHLERS M . and RAPACIOLI R., Z . Metallkunde

70

(1979) 732

4 ) MORIN M., GUENIN G . and GOBIN P.F.,

J.

Phys.

10

(C5-1981) 1013

5 ) MACQUERON J . L . and RUB10 A . , JournBes de calorimetric e t d ' a n a l v s e thermique, Barcelona (1977) 140

6 ) PASCUAL R., AHLERS M . , RAPACIOLI R. and ARNEODO W . , S c r i p t a Met. 9 (1975) 79 7) PLANES A., MACQUERON J.L., MORIN M. and GUENIN G . , p h y s . s t a t . s o l . T a ) ~ (1981) 717 8) PLANES A., ROUBY D., MACQUERON J.L., MORIN M. and GUENIN G . , ~ . ~ h y s . D:

Appl. Phys.

15

(1982) 89

9 ) BARAM J. and ROSEN M., Acta M e t a l l .

30

(1982) 655

10) MAEDER D.G., RYSER P . , SANDERSON B.I., SILMU A. and STEINER A., Helv. Phys. Acta

54

(1981) 222

11) MAEDER D.G., RYSER P., SANDERSON B.I., SILLOU A. and STEINER A . , ( i n p r e s s ) Helv. Phys. Acts

55

(1982).