THE BORDONI PEAK IN ALUMINIUM SINGLE CRYSTALS AT MHz FREQUENCIES

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THE BORDONI PEAK IN ALUMINIUM SINGLE CRYSTALS AT MHz FREQUENCIES

M. Zein

To cite this version:

M. Zein. THE BORDONI PEAK IN ALUMINIUM SINGLE CRYSTALS AT MHz FREQUENCIES.

Journal de Physique Colloques, 1987, 48 (C8), pp.C8-131-C8-135. �10.1051/jphyscol:1987816�. �jpa-

00227120�

THE BORDONI PEAK IN ALUMINIUM SINGLE CRYSTALS AT MHz FREQUENCIES

M. ZEIN

Physics Department, University of Bahrain, College of Arts, Science and Education, PO Box 1082. Bahrain

ABSTRACT

The Bordoni peak i n h i g h p u r i t y aluminium s i n g l e c r y s t a l s has been i n v e s t i - gated by measuring t h e a t t e n u a t i o n o f l o n g i t u d i n a l waves a t 10 MHz, using a conventional u l t r a s o n i c pulse echo technique w i t h a s i n g l e quartz transducer.

The c r y s t a l s , o f (100>, <110) and <111> o r i e n t a t i o n , were deformed by

compression, and t h e temperature dependence o f t h e u l t r a s o n i c a t t e n u a t i o n was measured a f t e r applying resolved shear stresses ranging up t o 60 ~ r r m - ~ . The r e s u l t s l e a d t o t h e f o l l o w i n g conclusions: ( i ) t h e temperature o f t h e Bordoni peak i n aluminium s i n g l e c r y s t a l s i s e s s e n t i a l l y independent o f t h e o r i e n - t a t i o n ; ( i i ) t h e temperature o f the peak decreases considerably as t h e p r i o r deformation was increased up t o a resolved shear s t r e s s near 28 ~ m n - ~ , and then increases s l i g h t l y f o r higher p r i o r stresses, ( i i i ) t h e peak h e i g h t increases w i t h i n c r e a s i n g deformation and, ( i v ) t h e s u b s i d i a r y peak appears o n l y a t low deformation.

INTRODUCTION

The i n t e r p r e t a t i o n o f t h e r m a l l y a c t i v a t e d i n t e r n a l f r i c t i o n peaks observed i n f.c.c. metals a t low t e i p e r a t u r e a f t e r p l a s t i c deformation, necessitates a d e t a i l e d study o f t h e i n f l u e n c e o f t h e amount o f cold-work and o r i e n t a t i o n on t h e h e i g h t and temperature o f t h e peaks.

The e a r l y measurements on p o l y c r y s t a l l i n e copper /1/ showed t h a t , f o r a given frequency, t h e Bordoni peak always occurred a t t h e same temperature, apart from v a r i a t i o n s o f a few degrees f o r specimens given d i f f e r e n t mechanical and thermal treatments. However, Mongy e t a1

121

found a s t r o n g dependence o f t h e temperature o f t h e peak on t h e o r i e n t a t i o n o f an aluminium c r y s t a l w i t h respect t o t h e d i r e c t i o n o f propagation o f t h e u l t r a s o n i c pulses. For

example, a t 10 MHz t h e peak occurred a t 139,153 and 196K r e s p e c t i v e l y when t h e a t t e n u a t i o n was measured along the

Ull.,

(100) and (1102 d i r e c t i o n s ; they a l s o found s i m i l a r r e s u l t s f o r copper, s i l v e r and g o l d s i n g l e c r y s t a l s . It would be expected t h a t any such a n i s o t r o p i c e f f e c t s o c c u r r i n g a t megahertz frequencies would a1 so manifest themselves i n measurements on s i n g l e c r y s t a l s a t KHz frequences 131. However, measurements on copper s i n g l e c r y s t a l s a t KHz and MHz frequencies /4/,

151

and /6/ showed t h a t t h e peak occurred a t approxi- mately t h e same temperature. Measurements on s i l v e r and g o l d i n KHz ranges /7/ and /8/ do not show any such a n i s o t r o p i c e f f e c t o c c u r r i n g a t these ranges o f frequenci es.

This apparent absence o f o r i e n t a t i o n dependence o f t h e temperature o f t h e peak a t KHz frequencies suggests t h e need f o r f u r t h e r measurements a t MHz frequen- cies. Apart from t h a t i n v e s t i g a t i o n , t h e v a r i a t i o n o f t h e peak h e i g h t and p o s i t i o n has been s t u d i e d as a f u n c t i o n o f various amounts o f deformation.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987816

JOURNAL DE PHYSIQUE

EXPERIMENTAL PROCEDURE

The specimens used i n t h i s i n v e s t i g a t i o n were h i g h p u r i t y 5N aluminium s i n g l e c r y s t a l s , supplied by Metal Research L i m i t e d i n t h e form o f c y l i n d e r s approxi- mately 10.5mm long and 13mn diameter. The c r y s t a l s were deformed by

compression along t h e a x i s o f t h e c y l i n d e r i n a Monsanto tensometer a t room temperature.

The o r i e n t a t i o n o f each c r y s t a l was checked a f t e r each deformation by t h e Laue b a c k - r e f l e c t i o n x-ray method; i n each case t h e o r i e n t a t i o n was w i t h i n t h r e e degrees o f the a p p r o p r i a t e axis. The u l t r a s o n i c a t t e n u a t i o n was measured d i r e c t l y a f t e r t h e deformation. The measurement technique was s i m i l a r t o t h a t described by N i b l e t t and Zein /6/. Measurements were made i n t h e temperature range from 120 t o 300K, the temperature being measured w i t h two platinum sen- sors placed close t o t h e specimen and connected t o a Lakeshore d i g i t a l t h e r - mometer and c o n t r o l l e r . The temperature was h e l d constant w h i l e each a t t e n u a t i o n measurement was made.

RESULTS

The p r i n c i p a l measurements were c a r r i e d out on t h r e e s i n g l e c r y s t a l s w i t h o r i e n t a t i o n s c l o s e t o t h e 419, <Ill> and <100>directions. The temperature dependence o f t h e u l t r a s o n i c a t t e n u a t i o n o f each c r y s t a l was measured a f t e r each o f a s e r i e s o f compressions f o r resolved shear stresses ranging up t o 60 ~ m n - ~ .

The r e s u l t s o f measurements a t lOMHz f o r t h e t h r e e c r y s t a l s a f t e r compressions w i t h i n t h e range o f 3 t o 42 ~ m n - ~ are shown i n f i g u r e s 1, 2 and 3.

The u l t r a s o n i c a t t e n u a t i o n of a O O > A1 s i n g l e c r y s t a l as a f u n c t i o n o f

temperature 6 ~ m n - ~

F i g (1) The u l t r a s o n i c a t t e n u a t i o n 8 .

.

of 311) A1 s i n g l e c r y s t a l as a f u n c t i o n o f

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s i n g l e c r y s t a l as a f u n c t i o n of

temperature

A l l t h e measurements a t 10 MHz show t h e Bordoni peak o c c u r r i n g i n t h e range between 193 and 225K. The measurements showed t h a t t h e h e i g h t o f t h e peak increases by i n c r e a s i n g t h e deformation.

Table 1 l i s t s the peak h e i g h t and temperature a f t e r each stage o f deformation.

:Resolved

I

Peak Temperature Tm K

I

Peak h e i g h t 1 1 ~ ~ 1 0 '

I

:shear s t r e s s :

Table ( 1 )

i

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<111> (llo>

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i

JOURNAL DE _PHYSIQUE

DISCUSSION

The r e s u l t s described here do not show any degree of anisotropy. The tem- perature o f the Bordoni peak i s e s s e n t i a l l y independent o f the o r i e n t a t i o n o f t h e c r y s t a l s . This i s c o n s i s t e n t w i t h those measurements obtained by Sack /3/

f o r aluminium s i n g l e c r y s t a l s a t KHz frequency which g i v e temperatures o f t h e peak t h a t correspond f a i r l y w e l l t o those observed i n p o l y c r y s t a l l i n e A1 by Fantozzi e t a1 /9/ and Hassan and N i b l e t t /lo/. The temperature o f the Bordoni peak observed here corresponds t o those obtained f o r p l y c r y s t a l l i n e aluminium a t MHz frequency by Zein Ill/.

These r e s u l t s a r e c o n s i s t e n t w i t h those obtained by N i b l e t t and Zein /6/ i n copper s i n g l e c r y s t a l s .

The temperature a t which t h e peak occurs i s p l o t t e d against the resolved shear s t r e s s f o r the t h r e e c r y s t a l s i n Fig. 4. The temperature o f t h e peak gra- d u a l l y increases w i t h i n c r e a s i n g p r i o r s t r e s s u n t i l about 2 8 ~ m - ~ . Further deformation caused t h e temperature o f t h e peak t o increase. The temperature of t h e Bordoni p a k v a r i e s i n t h e same way f o r a l l t h r e e o r i e n t a t i o n s , which confirms t h a t the resolved shear s t r e s s and n o t t h e s t r a i n i s t h e appropriate

parameter t o be used t o describe t h e p l a s t i c deformation.

The shape o f t h e graph i s r a t h e r s i m i l a r t o t h a t found i n A1 by Hassan and N i b l e t t /lo/, Zein /11/. and t h a t found f o r copper by N i b l e t t and Zein 161.

and Farman and N i b l e t t /12/, b u t t h e magnitude of t h e s h i f t i s g r e a t e r i n the case o f Al. This l a r g e s h i f t i s comparable t o t h a t found i n n i c k e l by

Venkatesan and Beshers 1131. This l a r g e s h i f t can be a t t r i b u t e d t o t h e higher s t a c k i n g f a u l t energy i n A1 and Ni.

240- F i g (4) V a r i a t i o n o f t h e Bordoni

peak temperature f o r t h e t h r e e A1 s i n g l e c r y s t a l s w i t h resolved shear

s t r e s s _200-

( v ) <Ill>

( 0 ) <110>

(

.

<loo>

The v a r i a t i o n o f the Bordoni peak h e i g h t w i t h deformation i s shown i n Fig. 5.

The peak h e i g h t grows w i t h deformation i n agreement w i t h t h e work done by Zein

I l l / ,

Hassan and N i b l e t t /ID/ and Deterre e t a1 141. A s i m i l a r observation was found i n copper by Farman and N i b l e t t /12/.

8 v v

= a 0 . " :

Bee 8

L ,

^{1 I I}

F i g ( 5 ) V a r i a t i o n o f the Bordoni peak h e i g h t f o r t h e t h r e e A1 s i n g l e c r y s t a l s w i t h r e s o l v e d shear s t r e s s

1 0 30 t&,,,,-2 5 0 7 0

qua1 i t a t i v e agreement w i t h Seeger's t h e o r y of double-kink generation, as m o d i f i e d by Par6 /15/, and Engelke /16/ t o take i n t o account t h e i n t e r n a l s t r e s s e s and t h e d i s l o c a t i o n l o o p l e n g t h s present a t d i f f e r e n t deformations.

The higher peak temperature observed i n t h e l i g h t l y deformed c r y s t a l s i s b e l i e v e d t o be due t o t h e longer d i s l o c a t i o n loops o c c u r r i n g a t these defor- mations, w h i l e the s l i g h t increase i n peak temperature a t high deformations i s a t t r i b u t e d t o a r e d u c t i o n i n t h e i n t e r n a l s t r e s s caused by t h e formation o f a c e l l s t r u c t u r e i n which t h e m a j o r i t y o f t h e d i s l o c a t i o n s are l o c a t e d i n t h e c e l l walls. An i n t e r p r e t a t i o n o f how the height o f t h e Bordoni peak v a r i e s w i t h p l a s t i c deformation r e q u i r e s a knowledge of how t h e d i s l o c a t i o n d e n s i t y and t h e i n t e r n a l s t r e s s and l o o p l e n g t h d i s t r i b u t i o n s vary w i t h p r i o r s t r e s s o r s t r a i n . The s u b s i d i a r y peak appears o n l y i n t h e s l i g h t l y deformed specimen as has been observed by Kamigaki and Hirone /17/, and Alnaser /18/. This c o u l d be due t o t h e predominancy o f edge d i s l o c a t i o n s a t high deformations.

REFERENCES

/1/ N i b l e t t , D.H. and Wilks, J. P h i l . Mag 2. 1427-44, 1957.

/2/ Mongy, M., Salama, K. and Beckman, O., S o l i d s t a t e communication vol .l, pp 234-236, 1963.

/3/ Sack, H.S. Acta Metal. 10. 455, 1962.

/4/ Brown, G.R. and N i b l e t t , D.H. 1973. J. Phys. D:Appl. Phys. 6. 809-18.

/5/ N i b l e t t , D.H., Brown, G.R. and Zein, M. 1975. I n t e r n a l F r i c t i o n and U l t r a s o n i c a t t e n u a t i o n i n c r y s t a l l i n e s o l i d s vol

.

^11, ed. D. Lenz and K Lucke (Ber1in:Springer-Verlag) pp. 306-13.

/6/ N i b l e t t , D.H. and Zein, M. J.Phys. F:Metal Phys., 10 pp.773-80, 1980.

/7/ Brown, G.R. and N i b l e t t , D.H. J. Phys.D:Appl. Phys. 6 1560-5, 1973.

/8/ Grandchamp, P.A. J.Physique Co11.32, C-2, 229-41, 1971.

/9/ Fatnozzi, G., Fouquet, F. and Gobin, P.F., Mem-Sci, Rev,Met 69.64, 1973.

/ l o /

Hassan, R.A.R., and N i b l e t t , D.H. J.De.Phys. Colloque 44, C9.569,

1983.

/11/ Zein, M. J.De.Phys. Colloque, 46.C10, 297-300, 1985.

/12/ Farman, H. and N i b l e t t , D.H. I n t e r n a l F r i c t i o n and U l t r a s o n i c a t t e - n u a t i o n i n s o l i d s (ed.Smith, C.C.) 7, 1980.

/13/ Venkatesan, P.S. and Beshers, D.M. J.Appl.Phys. 41.42, 1970.

/14/ Deterre, Ph., Esnouf, G., Fantozzi, G., Peguin, P., Perez, J., R i t c h i e , I., Vanoni, F. and Vincent, A., Acta.Met, 27, 1779, 1979.

/15/ par;, V.K. J.Appl .Phys. 28.332-40, 1961.

/16/ Engelke, H. Phys.Stat.Solidi 36,231-59, 1961.

/17/ Kamigaki, K. and Hirone, T. J.Phys.Soc. Japan, 16,2077, 1961.

/18/ Alnaser, W.E. Thesis, U n i v e r s i t y o f Kent a t Canterbury, 1986.