STUDY OF THE hcp-fcc PHASE TRANSITION IN COBALT BY INTERNAL FRICTION AND ELASTIC MODULUS MEASUREMENTS IN THE kHZ FREQUENCY RANGE

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STUDY OF THE hcp-fcc PHASE TRANSITION IN COBALT BY INTERNAL FRICTION AND ELASTIC

MODULUS MEASUREMENTS IN THE kHZ FREQUENCY RANGE

J.-E. Bidaux, R. Schaller, W. Benoit

To cite this version:

J.-E. Bidaux, R. Schaller, W. Benoit. STUDY OF THE hcp-fcc PHASE TRANSITION IN COBALT BY INTERNAL FRICTION AND ELASTIC MODULUS MEASUREMENTS IN THE kHZ FREQUENCY RANGE. Journal de Physique Colloques, 1987, 48 (C8), pp.C8-477-C8-482.

�10.1051/jphyscol:1987874�. �jpa-00227178�

JOURNAL DE PHYSIQUE

Colloque C8, supplement au n 0 1 2 , Tome 48, dkcembre 1987

STUDY OF THE hcp-fcc PHASE TRANSITION IN COBALT BY INTERNAL FRICTION AND ELASTIC MODULUS MEASUREMENTS IN THE kHz FREQUENCY RANGE

J.-E. BIDAUX, R. SCHALLER and W. BENOIT

Institut de GBnie Atomique, Ecole Polytechnique FBdBrale de Lausanne, CH-1015 Lausanne, Switzerland

Des mesures de frottement intbrieur et de module elastique dynamique ont kt& effectubes au voisinage de la transition hc-cfc du cobalt. La frdquence de vibration de 1 '6chantillon est suffisamment &levee (KHz) pour que le frottement interieur transitoire soit BliminB. Un pic de frottement interieur accompagne d'une anomalie du module klastique sont observ.6~.

On montre par le moyen de cycles thermiques effectues au voisinage de la temperature de transition que cette anomalie est la superposition de deux effets : a) un saut db au changement de constantes elastiques hc-cfc; b) une chute d'origine anblastique.

La chute de module est li6e au pic de frottement interieur.

Aucun effet pretransitionnel n 'est observe. L 'anomalie de module est clairement associt5e d la presence simultanee des phases hc et cfc. On en deduit que l'anomalie de module et le pic de frottement intbrieur pourraient Stre dus aux interfaces hc-cfc.

Abstract

Internal friction and dynamic elastic modulus measurements were carried out in the vicinity of the hcp-fcc phase transition in pure cobalt. The vibration frequency was high enough (KHz) to eliminate the transitory internal friction. A peak of internal friction accompanied by an anomaly of the elastic modulus was observed.

It is shown using thermal cycling near the transition temperature that the modulus anomaly is the superposition of the two effects : a) a step-like decrease due to the change of elastic constants hcp-fcc. b) a dip of anelastic origin. The dip is associated with the internal friction peak.

No pretransitional effect was observed. The anomaly of the modulus is clearly related to the simultaneous presence of the two phases hcp and fcc. This suggests that the anomaly of the modulus and the internal friction peak can be associated with the hcp-fcc interfaces.

I N T R O D U C T I O N

The Internal friction ( I F ) observed in the vicinity of a first order phase transition is composed of the three terms : IF*, (Transitory I F ) ,

1 F p ~ (Phase Transition IF), IFcl (Classical IF) [I, 2,3,4 I

.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987874

C8-478 JOURNAL DE PHYSIQUE

The f i r s t t e r m , IFT,, i s a t r a n s i t o r y t e r m . I t a p p e a r s o n l y d u r i n g h e a t i n g o r c o o l i n g ( h e a t i n g o r c o o l i n g r a t e T # o ) . I n D e l o r m e ' s , model IFT, i s p r o p o r t i o n a l t o t h e amount o f t r a n s f o r m e d p h a s e d u r i n g one c y c l e o f v i b r a t i o n .

C o n s e q u e n t l y :

IFTr =

- _a~ r

where m i s t h e amount o f p h a s e t r a n s f o r m e d , T t h e h e a t i n g r a t e and f t h e f r e q u e n c y o f v i b r a t i o n [ I ]

.

The s e c o n d t e r m , I F P T I a c c o u n t s f o r t h e p e a k w h i c h i s anyway o b s e r v e d when t h e t r a n s i t o r y I F i s a b s e n t , t h a t i s a t c o n s t a n t t e m p e r a t u r e (T=O) o r h i g h f r e q u e n c y . D i f f e r e n t m o d e l s h a v e b e e n d e v e l o p e d w h i c h c a n e x p l a i n t h i s i n t e r n a l f r i c t i o n . They i n v o l v e e i t h e r i n t e r f a c e m o t i o n [ 5 ] , d i s l o c a t i o n m o t i o n [ 6 , 7 ] , o r l o c a l i z e d s o f t modes [81

.

t h e s e m o d e l s c o n c e r n m a i n l y t h e p r e t r a n s i t i o n a l domain ( s o f t modes) w h i l e o t h e r a p p l y t o t h e p h a s e t r a n s i t i o n i t s e l f ( i n t e r f a c e s ) . A s p o i n t e d o u t b y K o s h i m i z u [ 7 ] , 1 F p ~ s h o u l d p r o v i d e v e r y u s e f u l i n f o r m a t i o n s on t h e mechanism b y which t h e t r a n s f o r m a t i o n p r o c e e d s . The t h i r d t e r m , I F c l , a c c o u n t s f o r t h e background i n t h e two p h a s e s . I n t h e p r e s e n t s t u d y , we show t h a t 1 F p ~ i s f o u n d i n c o b a l t a n d i s a s s o c i a t e d w i t h a n e l a s t i c modulus anomaly. Then, we p r e s e n t t h e r m a l c y c l i n g e x p e r i m e n t s . These e x p e r i m e n t s were made t o d e t e r m i n e i f 1 F p ~ i s a p r e t r a n s i t i o n a l e f f e c t o r r a t h e r a n e f f e c t o c c u r r i n g d u r i n g t h e t r a n s f o r m a t i o n p r o c e s s . By means o f t h e r m a l c y c l i n g , w e d e t e c t t h e t e m p e r a t u r e a t which t h e h c p - f c c h y s t e r e s i s a p p e a r s . Assuming t h a t t h i s t e m p e r a t u r e i s t h e p h a s e t r a n s i t i o n t e m p e r a t u r e , i t i s p o s s i b l e t o d i s t i n g u i s h between p r e t r a n s i t i o n a l e f f e c t s and t r a n s i t i o n a l e f f e c t s . EXPERIMENTAL

The c o b a l t u s e d i n t h e s e e x p e r i m e n t s was a 9 9 . 9 8 % Co p o l y c r y s t a l p r o v i d e d by Johnson Matthey ( i m p u r i t i e s : Cu 200 ppm, Fe 2 ppm, o t h e r s <

1 p p m ) . The a v e r a g e g r a i n s i z e was 1 mm. The s a m p l e was s p a r k - c u t t o a p p r o x i m a t e d i m e n s i o n s 40*4*1.4 mm. Then, t h e i n t e r n a l f r i c t i o n and t h e e l a s t i c modulus were measured u s i n g a f r e e - f r e e b a r a p p a r a t u s working a t t h e f r e q u e n c y o f t h e f u n d a m e n t a l f l e x u r a l mode ( 3 KHz) [ 9 ] . A s w i l l b e shown, t h i s f r e q u e n c y i s h i g h e n o u g h t o e l i m i n a t e t h e t r a n s i t o r y i n t e r n a l f r i c t i o n .

RESULTS

A t y p i c a l r e s u l t o b t a i n e d a t t h e v i b r a t i o n f r e q u e n c y o f n e a r l y 4 KHz is shown on F i g 1.

I n t h e v i c i n i t y o f 700 K , t h e h c p ( l o w t e m p e r a t u r e p h a s e ) t o f c c ( h i g h t e m p e r a t u r e p h a s e ) t r a n s i t i o n g i v e s r i s e t o i m p o r t a n t m o d i f i c a t i o n s o f t h e i n t e r n a l f r i c t i o n a n d f r e q u e n c y

.

f r e q u e n c y ( r e l a t e d t o t h e e l a s t i c m o d u l u s k by t h e r e l a t i o n E = f 2 ) d e c r e a s e s s u d d e n l y w h e n t h e h c p j f c c p h a s e t r a n s i t i o n o c c u r s . The c u r v e g o e s t h r o u g h a d i p (A, F i g 1) a n d t h e n f o l l o w s a g a i n a n o r m a l l i n e a r d e p e n d e n c e . On c o o l i n g , t h e c u r v e i s l i n e a r i n t e m p e r a t u r e down t o 670 K , t h e n it d r o p s , g o e s t h r o u g h a minimum ( B ) , and a f t e r w a r d s i n c r e a s e s s l o w l y t o r e a c h a v a l u e c o r r e s p o n d i n g t o t h e hcp e l a s t i c modulus.

F i g 1 . Co 9 9 . 9 8 % , temperature dependence of i n t e r n a l f r i c t i o n ( I F ) and frequency

(f), s t r a i n amplitude & = l o - 6 , ?=1.2 K/min.

On h e a t i n g , t h e i n t e r n a l f r i c t i o n c u r v e e x h i b i t s a p e a k ( C )

.

i n c r e a s e o f t h e i n t e r n a l f r i c t i o n c o r r e s p o n d s t o t h e f r e q u e n c y d r o p . By c o n t r a s t , n o pronounced peak was found on c o o l i n g b u t r a t h e r a n i n c r e a s e o f i n t e r n a l f r i c t i o n .

his

The h e i g h t o f t h e p e a k d o e s n o t d e p e n d on h e a t i n g o r c o o l i n g r a t e

'i'.

T h e r e f o r e , i n t e r n a l f r i c t i o n c a n n o t b e r e l a t e d t o t h e t r a n s i t o r y e f f e c t s a s it was t h e c a s e a t low f r e q u e n c y [ 4 ] . T h i s i s i n a c c o r d a n c e w i t h e q u a t i o n (1) which p r e d i c t s a 1000 t i m e s l o w e r i n t e r n a l f r i c t i o n a t t h e KHz f r e q u e n c y t h a n a t t h e Hz f r e q u e n c y . As t h e p e a k h e i g h t i s r o u g h l y 50*10-3 a t 1 Hz, t h e t r a n s i t o r y I F must b e n e g l i g i b l e a t f r e q u e n c i e s h i g h e r t h a n t h e KHz. T h i s c o n f i r m s t h a t t h e KHz f r e q u e n c y r a n g e i s s u i t a b l e f o r s t u d y i n g t h e t e r m 1 F p ~ .

Between 500 a n d 600 K , a n anomalous d e c r e a s e i n f r e q u e n c y i s o b s e r v e d (El F i g I ) , t h e c u r v e g o i n g t h r o u g h two m i n i m a . T h i s a n o m a l y o f f r e q u e n c y i s c o r r e l a t e d w i t h a s m a l l i n c r e a s e o f I F ( F ) . I t h a s b e e n shown t h a t t h e s e e f f e c t s a r e d u e t o a c h a n g e o f t h e e a s y a x i s o f m a g n e t i z a t i o n from p a r a l l e l t o p e r p e n d i c u l a r t o t h e C h e x a g o n a l a x i s

[ l o ] .

C8-480 J O U R N A L DE PHYSIQUE

In order to interpret the internal friction peak and the frequency drop appearing at the hcp-fcc phase transition, it is essential to know what must be attributed to pretransitional effects in the parent phase and what deals with the transformation itself. This means that we have to determine the transition temperature (Cooling : Ms, heating : As). To do that, we will use thermal cyclings and we will detect the temperature at which hysteresis appears for the first time on the frequency curve. We will assume this temperature as the transition temperature. The pretransitional effects should not produce thermal hysteresis, unlike the transitional effects.

Thermal cycling near Ms :

Series of thermal cycling were made in the vicinity of the fcc4hcp phase transition temperature (Ms) (Fig 2). During these cyclings, the resonant frequency of the sample was measured.

Fig. 2. Co 99.98%, t h e m 1 cyclisg near the f d c p t r a n s i t i o n tenperature (m), strain anplitude

&=5*10-6, dashed line : canplete t r a n s f o m t i o n . 3.45

3.40 G I

-

-

3.L5 340-

The first cycle was made entirely in the fcc phase so that no hysteresis appeared. Since the second cycle, the temperature was lowered enough to induce the transformation of a little amount of hcp phase. An hysteresis loop was observed on the frequency curve which became larger at every subsequent cycle in proportion to the amount of phase transformed. In

,,----_

1) TM,,, >> Ms ?a%> -

;

I I I

-

3.35-- '

I , I

> I I

3) TMinEMs 8 1 " l ' ? e 8 4 0 & ~ e ~ ~ I ; 4 ~ w a a a +

[ I

I , I I

\ I ;

$q.g..2 I

- ^r= I '

y..,

4) TMin < Ms

*A

, 1 1 1 , I ,, , I I

. .

600 6 50 700

the third cycle, the frequency drop occurring at the beginning of the transition (B) was not recovered immediately on heating. The frequency remained low until the temperature of the reverse transformation was

,345 3.40 3.35

3.45 -3.40 3.35

750 600 6 50 700 750

reached (near point A). This suggests that the frequency drop ( B ) does not correspond to some catastrophic break away related to the creation of the hcp phase. It should be more likely associated with an anelastic effect in the stable state of the two-phased material. The reverse transformation gives rise to a dip ( A ) . This dip is less pronounced on subsequent cycles because a step-like change of frequency is

superimposed on the dip when a larger amount of material transforms.

This step-like change of frequency is naturally explained by the fact that the fcc elastic modulus is lower than the hcp elastic modulus.

It is now clear that the frequency drop (B) occurring at the beginning of the cooling phase transition results from the transformation and not from a pretransitional phenomenon. As shown on fig ₃ the Ms temperature must be placed just prior to the frequency drop.

Fig 3. Co 99.98%, -rat- dependence of i n t e n d f r i c t i m (IF) and frecpenw

(f) showing tte position of M s and As, strain anplitude elO-6, G1.2 K/min.

Fig 4. co 99.98%, thmml cycling near the h-cc t r a n s i t i o n tenperat- (As) s t r a i n anplitude &lo+, dashed line : caplete t r a n s f o m t i o n

.

T h e r m a l c y c l i n g n e a r As :

Similar experiments were made near the hcpjfcc transition temperature (Fig 4). A first cycle was performed entirely in the hcp phase. Though the cooling curve is not superimposed on the heating curve, the characteristic phase transition hysteresis loop was not observed. In contrast, in the next cycles, the temperature was raised beyond the temperature (A) of the frequency drop. An hysteresis appears which indicates that the phase transition has already occurred.

Here also, the frequency drop is not a precursor effect for the phase transition. The As temperature has to be placed before the frequency drop (see Fig 3 ) .

JOURNAL DE PHYSIQUE

D I S C U S S I O N

The experimental results show that thermal hysteresis is present since the beginning of the frequency drop. Therefore, this anomaly and the internal friction increase are connected with the phase transition and more precisely with the state when the two phases coexist. The internal friction could be attributed to the hcp-fcc interfaces. IF could be produced by the motion of the interfaces taken as a whole or by the individual partial dislocations which constitute the interface.

The step-like change of the elastic modulus is most likely due to the change of the elastic constants. This is in agreement with the neutron scattering measurements of Frey et a1 [ll] which have found a drop of 25% in the hexagonal elastic constant C 4 4 at the hcp+fcc phase transition.

CONCLUSION

An internal friction peak associated with an elastic modulus anomaly was found at the hcp-fcc phase transition in cobalt which is not of transitory nature.

By means of thermal cycling near the phase transition temperature, it was shown that this internal friction was associated with the transformation rather than with pretransitional effects.

This suggests that the internal friction can be associated with the interphase boundaries.

ACKNOWLEDGEMENT

This work was partially supported by the Swiss National Science Fondation.

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[9] A.S. Nowick and B.S. Berry, "Anelastic Relaxation in Crystallin Solids", (Wckmic Press, New York, 1972)

.

[lo] W. Wallace, Internal Friction and Ultrasonic Attenuation in Solids, D. Lenz and K. Iuck, S p r w Vexlag, B e r l i n 1, 16 (1975)

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