INTERNAL FRICTION ASSOCIATED WITH THE ALLOTROPIC TRANSFORMATION OF COBALT

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INTERNAL FRICTION ASSOCIATED WITH THE

ALLOTROPIC TRANSFORMATION OF COBALT

J. Bidaux, R. Schaller, W. Benoit

To cite this version:

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

INTERNAL FRICTION ASSOCIATED WITH THE

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INTERNAL FRICTION ASSOCIATED WITH THE

ALLOTROP'IC

TRANSFORMATION OF COBALT

J.E. BIDAUX, R. SCHALLER AND W. BENOIT

Institut de GBnie Atomique, Institut federal Suisse de

Technologic , PHB-Ecublens, CH-1015 Lausanne, Switzerland

Resume

-

Des mesures de f r o t t e m e n t i n t e r i e u r ont 6 t @ effectuees dans du co- b a l t de haute purete au voisinage de l a t r a n s f o r m a t i o n a l l o t r o p i q u e hc-cfc.

A basse frequence (% 1 Hz), on observe un p i c important q u i e s t do

a

un e f -

f e t t r a n s i t o i r e . En e f f e t , ce p i c d i s p a r a i t en c o n d i t i o n s isothermes. A haute frequence ( s 5 kHz), l e terme t r a n s i t o i r e e s t absent. Le f r o t t e m e n t i n t e r i e u r v a r i e de f a ~ o n d i s c o n t i n u e au cours de l a t r a n s f o r m a t i o n de phase. De plus, au chauffage, apparaissent un p e t i t p i c de f r o t t e m e n t i n t e r i e u r e t une chute de l a frequence, q u i sont probablement r e l i e s

a

l a transformation de phase.

Ces c a r a c t e r i s t i q u e s sont analogues c e l l e s observees dans d ' a u t r e s transformations martensitiques.

A b s t r a c t

-

Measurements o f i n t e r n a l f r i c t i o n have been performed i n high- p u r i t y c o b a l t i n t h e temperature range o f the a l l o t r o p i c hcp-fcc t r a n s f o r - mation.

A t low frequency ( a 1 Hz), an important peak i s observed which i s due t o a t r a n s i t o r y e f f e c t . This peak, a c t u a l l y , disappears under isothermal condi- t i o n s .

A t h i g h frequency ( s 5 kHz), t h e t r a n s i t o r y term i s absent and a d i s c o n t i - nuous change o f i n t e r n a l f r i c t i o n occurs d u r i n g the transformation. Moreover d u r i n g heating, a l i t t l e i n t e r n a l f r i c t i o n peak and a frequency d i p a r e observed, which are probably connected w i t h the phase transformation.

These features a r e s i m i l a r t o those observed f o r o t h e r m a r t e n s i t i c t r a n s f o r - mati ons.

I. INTRODUCTION

The i n t e r n a l f r i c t i o n spectrum associated w i t h f i r s t order phase t r a n s i t i o n s (spe- c i a l l y m a r t e n s i t i c transformations) can be decomposed i n t o t h r e e terms :

Q;

:,

:

Q

,

and

Q;;.

The

first,^;;,

i s a t r a n s i t o r y term which appears o n l y d u r i n g h e a t i n g o r cooling. I t has been shown [I, 2, 31 t h a t

Q&

i s p r o p o r t i o n a l t o t h e amount o f m a t e r i a l t r a n s - formed per cycle, and as a consequence

where a i s a constant, f i s t h e frequency o f t h e a p p l i e d s t r e s s and

?

i s t h e heat- i n g o r c o o l i n g r a t e . The second ferm,

Qp;,

i s a l s o associated w i t h the phase t r a n s i - t i o n , b u t i t does n o t depend on T. I t i s , on t h e contrary, c o r r e l a t e d w i t h t h e chan-

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C10-602 JOURNAL DE PHYSIQUE

ge o f t h e e q u i l i b r i u m s t a t e induced by t h e a p p l i e d s t r e s s near the phase t r a n s i t i o n . Dejonghe e t a l . [3] and Koshimizu [ 4 ] have shown t h a t

Q2T

can depend on the frequency and/or the amplitude o f the a p p l i e d s t r e s s . As p o i n t e d o u t by Koshimizu [41

,

t h i s t e r m should g i v e important i n f o r m a t i o n on t h e dynamical p r o p e r t i e s o f the phase t r a n s i t i o n .

The t h i r d term, Q-' i s a c l a s s i c a l term, which i s n o t d i r e c t l y associated w i t h the phase t r a n s i t i o n , " b u t which corresponds t o t h e appropriate i n t e r n a l f r i c t i o n due e i t h e r t o t h e low temperature (Qi;) o r h i g h temperature (9;;) phase. Thus

a,;

= m

Qi;

+

( 1

-

m) QH; (2)

where m = m(T) i s the p r o p o r t i o n o f t h e low temperature phase and can change more o r l e s s suddenly d u r i n g t h e phase t r a n s i t i o n .

Since the microscopical mechanisms and, more p r e c i s e l y , the r o l e o f t h e d i s l o c a t i o n s are w e l l known f o r t h e a l l o t r o p i c t r a n s f o r m a t i o n o f c o b a l t [5, 6 1 , i n t e r n a l f r i c t i o n measurements were performed on t h i s metal. I n order t o show the r e s p e c t i v e importan- ce o f t h e t h r e e terms, measurements were c a r r i e d o u t i n two frequency ranges (1 Hz and 5 kHz) and a t T d i f f e r e n t o r equal t o zero.

EXPERIMENTAL METHODS

The c o b a l t used was provided by tlohnson-Matthey i n t h e shape o f a 2 mm t h i c k poly- c r y s t a l l i n e sheet. The nominal p u r i t y o f t h e m a t e r i a l was 99.99 % Co. The average g r a i n di-ameter was about 0.1 mm.

From t h i s m a t e r i a l a 40 x 4 x 2 mm sample was c u t by e l e c t r o e r o s i o n , and then annea- l e d 4 hours a t 800 OC. Measurements were c a r r i e d o u t i n t h e h i g h frequency range (5 kHz) u s i n g a f r e e - f r e e b a r apparatus.

10.0

RESISTANCE t d d

300 400 500 600 700 BOO 900

TEMPERATURE (K)

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frequency c l o s e t o 1 Hz. The t o r s i o n a l pendulum apparatus allowed simultaneous measurements of i n t e r n a l f r i c t i o n , frequency and e l e c t r i c a l r e s i s t i v i t y t o be made a s a function of temperature.

Low frequency experiments

Fig. 1 shows t y p i c a l r e s u l t s obtained during heating and cooling a t

f

= 1 K/min. In

t h e v i c i n i t y of t h e transformation (a 700 K ) , anomalies of t h e measured q u a n t i t i e s

a r e observed L6, 71. On heating, a sudden decrease o f t h e e l e c t r i c a l r e s i s t a n c e i s observed (A, f i g . l ( a ) ) due t o t h e transformation. The reverse e f f e c t appears on

cooling ( 8 , f i g . 1 ( a ) ) with a temperature h y s t e r e s i s of about 50 degrees.

Similar e f f e c t s occur f o r t h e frequency, except t h a t t h e jump (C, f i g . l ( b ) ) i s pre-

ceded by a d i p (D, f i g . l ( b ) ) . This dip i s o f t e n observed during s t r u c t u r a l phase

t r a n s i t i o n s and i s g e n e r a l l y a t t r i b u t e d t o a s o f t e n i n g of t h e shear modulus L81. As i s t h e case f o r many m a r t e n s i t i c transformations, t h e i n t e r n a l f r i c t i o n e x h i b i t s an important peak near t h e transformation temperature [g]. In o r d e r t o d i s p l a y t h e t r a n s i t o r y component ( Q - I ) , measurements were c a r r i e d out a l s o under isothermal conditions. The internaTr f r i c t i o n peak, which appears when t h e temperature i s va- r i e d ( f i g . 2, f u l l c u r v e ) , i s no more present under isothermal conditions ( f i g . 2, dashed curve). As a consequence, t h i s peak i s due t o a t r a n s i t o r y e f f e c t ( Q T ~ ) .

Since no maximum of i n t e r n a l f r i c t i o n is observed i n t h e isothermal c o n d i t i o n s , i t

seems t h a t t h e second term

Qp;

i s small o r i n any case d i f f i c u l t t o be observed i n

the low frequency range. The c o r r e l a t i o n between this curve and t h e r e s i s t i v i t y measurements shows t h a t t h e change of i n t e r n a l f r i c t i o n observed during t h e t r a n s -

formation i s due t o t h e c l a s s i c a l component

QC;.

As f o r t h e i n t e r n a l f r i c t i o ? , t h e frequency d i p which i s present when

f

# 0 a l s o

disappears completely when T = 0. This means t h a t t h i s e f f e c t is s t r i c t l y c o r r e l a -

ted with t h e e f f e c t responsirb'le f o r t h e i n t e r n a l f r i c t i o n peak and should not be a t t r i b u t e d t o a s o f t e n i n g of t h e shear modulus. The same behaviour was observed du- r i n g heating.

In the 500 K t o 600 K temperature range, t h e frequency shows an anomalous decrease,

t h e curve going through two minima (E, f i g . 1 ( b ) ) . This e f f e c t i s probably r e l a t e d

t o t h e drop of e l a s t i c constants observed by Wallace [ l o ] i n t h e v i c i n i t y of 2500C, t h e o r i g i n of which i s a t t r i b u t e d t o a change of t h e easy a x i s of magnetization.

High frequency experiments ( 5 KHz)

Fig 3. shows r e s u l t s obtained i n t h e kHz frequency range during heating and cooling.

Fig. 2

-

Co 4N, Effect of

7

on t h e Fig. 3

-

Co

4N,

Temperature dependance

i n t e r n a l f r i c t i o n spectrum on cooling. of i n t e r n a l f r i c t i o n and frequency measu-

red a t high frequency (- 5 kHz).

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C10-604 JOURNAL DE PHYSIQUE

t e r n a l f r i c t i o n and frequency curves. Measurem$nts done a t d i f f e r e n t heating and

cooling r a t e s o r under isothermal conditions (T = 0) show no e f f e c t on t h e i n t e r n a l

f r i c t i o n spectrum. This r e s u l t i s i n accordance with equation 1 and shows t h a t t h e

t r a n s i t o r y term i s completely absent i n t h i s frequency range. As a consequence,

t h i s frequency range i s more s u i t a b l e f o r studying t h e two o t h e r terms,

Qp;

and

Q - I . I t i s not easy, b u t n e v e r t h e l e s s important, t o show t h e i n f l u e n c e of each of

t h e s e two terms. C e r t a i n l y ? t h e big drop (F t o G , f i g . 3 ) observed on t h e i n t e r n a l

f r i c t y o n curve

7s

due t o t h e c l a s s i c a l term Q-; and should be a t t r i b u t e d To t h e ap-

p r o p r i a t e i n t e r n a l f r i c t i o n o f t h e low o r high temperature phase (eq. 2 ) . B u t , dur-

ing heating t h e d i p observed on t h e frequency curve (H, f i g . 3) i s c e r t a i n l y corre- l a t e d with a small peak appearing on t h e i n t e r n a l f r i c t i o n curve ( J , f i g . 3 ) . These f e a t u r e s should be s y s t e m a t i c a l l y s t u d i e d i n o r d e r t o understand b e t t e r how they a r e a s s o c i a t e d with t h e phase t r a n s i t i o n ( Q - ' term). Note t h a t during cooling, t h e s e f e a t u r e s a r e not obsetved on t h e i n t e r n i l f r i c t i o n and t h e frequency curves.

F i n a l l y , f i g u r e 4 shows a comparison between t h e behaviors of t h e l a s t term

_Qi;

i n

t h e low and high frequency ranges. S i g n i f i c a n t d i f f e r e n c e s a r e observed :

-

The i n t e r n a l f r i c t i o n i s much smaller

f o r high frequency measurements than f o r 1 ow frequency measurements.

-

The jump of i n t e r n a l f r i c t i o n appear-

ing during t h e phase t r a n s i t i o n occurs i n an opposite s e n s e , i . e . f o r low f r e - quency measurements on h e a t i n g , t h e in- t e r n a l f r i c t i o n i n c r e a s e s a t t h e phase t r a n s i t i o n , whereas f o r high frequency

measurements, i t decreases. As a conse-

quence t h e physical mechanisms responsi- b l e f o r t h e i n t e r n a l f r i c t i o n should be

Fig. 4

-

Co 4N. ( a ) low frequency i n t e r n a l d i f f e r e n t f o r t h e two frequency ranges.

f r i c t i o n ( a 1 HZ) under isothermal conditions

(7

= 0 ) . ( b ) High frequency i n t e r n a l

f r i c t i o n ( a 5 k ~ ; ) . 111. CONCLUSION

From a general point o f view, t h e i n t e r n a l f r i c t i o n measured during t h e a l l o t r o p i c transformation of high-purity c o b a l t shows q u i t e s i m i l a r e f f e c t s a s f o r o t h e r mar-

t e n s i t i c transformations. In t h e low frequency range, t h e t r a n s i t o r y term Q-' i s

predominant and masks Q-' completely. On t h e o t h e r hand, i n t h e kHz range, {he t r a n -

s i t o r y t e r n d i s a p p e a r r . P T ~ h e change i n t h e c l a s s i c a l term

Q;;

i s t h e most important

e f f e c t , but during heating a frequency d i p (H, f i g . 3) and an i n t e r n a l f r i c t i o n peak ( J , f i g . 3) occur, which i s probably r e l a t e d t o t h e phase transformation (Qp;).

REFERENCES

[ I ] V . N. Belko, B.M. Darinsky, V . S. Postnikov and I . M. Sharshakov, Phys. of

Metals and Metallurgy

7

(1969) 140

[2] J . F. Delorme and P. F. Gobin, Metaux, no. 573 (1973) 185, no. 574 (1973) 209

[3] W. Dejonghe, R. De B a t i s t and L . Delaey, S c r i p t a Met.

10

(1976) 1125

[41 S. Koshimizu, Ph. D. Thesis Lausanne EPFL (1981), t h & s e no. 416

[5] F. S e b i l l e a u and H . Bibring "The mechanisms of phase transformations i n metals I n s t . of Metals, London (1955)

[6] J . T . Plewes and K. J . Bachmann, Met. Trans. vol

.

4 (1973) 1729

[71 J.-E. S e l l e , Cobalt

45

(1969) 186

[81 A . S. Nowick and B . S. Berry, "Anelastic Relaxation i n c r y s t a l l i n e S o l i d s " ,

Academic P r e s s , New York (1972)

[9] K. Sugimoto, Proc. ICIFUAS-7, J . de Physique

9

(1981) C5-971

!I01 W. D. Wallace, I n t e r n a l F r i c t i o n and Ultrasonic Attenuation i n Solids. D . Lenz