INTERNAL FRICTION IN DEFORMED CuAl SOLID SOLUTIONS

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INTERNAL FRICTION IN DEFORMED CuAl SOLID SOLUTIONS

G. Tonn, P. Haasen, H. Möller

To cite this version:

G. Tonn, P. Haasen, H. Möller. INTERNAL FRICTION IN DEFORMED CuAl SOLID SOLUTIONS.

Journal de Physique Colloques, 1983, 44 (C9), pp.C9-587-C9-591. �10.1051/jphyscol:1983987�. �jpa-

00223437�

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JOURNAL DE PHYSIQUE

Colloque C9, suppl6ment au n012, Tome 44, d k e m b r e 1983 page C9-587

INTERNAL FRICTION I N DEFORMED C u A l SOLID SOLUTIONS

G. Tonn, P. Haasen and H.J. ~ G l l e r *

I n s t i t u t ^f2trMetaZZphysik, UniversitZt Gb'ttinqen, F.R.G.

REsumg -Nous avons etudi6 le frottement interieur (90 K H ~ ) de monocristaux CuAl (0,07 B 0 , 8 % at. Al) deform6 plastiquement (E < 2,5 X ) dans le domaine de temp&

rature 1 0 0

-

6 5 0 K.

Deux petits maximas et un plus important sont observes en-dessous et juste au- dessus de la temperature ambiante : les temperatures de ces pics dependent essen- tiellement de la teneur en Al. La hauteur des petits pics est fortement influen- cee par le traitement thermique des echantillons. Ces effets stexpliquent dans le cadre de la theorie de LABUSCH-HAASEN en considerant une interaction dislocations - A 1 et dislocations-complexes-Al-lacunes pour les petits pics. Dans le premier cas nous avons obtenu une Pnergiedtinteraction de 0,6 eV.

A b s t r a c t

-

The i n t e r n a l f r i c t i o n of deformed ^{( E}s 2.5 %) CuAl s i n g l e c r y s t a l s 0.8 a t % A l ) was i n v e s t i g a t e d i n t h e temperature-range 100

-

650 K a t 90 Kc.

Two small peaks and a l a r g e r one were observed below and j u s t above room temperature. T h e i r peak temperatures depended s y s t e m a t i c a l l y on t h e A1 content and s l i g h t l y on t h e degree o f deformation. The h e i g h t o f the s m a l l e r peaks was very s e n s i t i v e t o t h e thermal treatment o f t h e specimens.

These dependencies can be explained w i t h i n t h e frameworkof t h e Labusch- Haasen t h e o r y i f one assumes an i n t e r a c t i o n between d i s l o c a t i o n s and A l - atoms and Al-vacancy complexes, r e s p e c t i v e l y , f o r t h e small peaks. An i n t e r a c t i o n energy o f about 0.6 eV i s d e r i v e d i n t h e former case.

1. INTRODUCTION

I n a number of papers /1,2,3/ Labusch and Haasen have developed a s t a t i s t i c a l theory o f t h e s o l i d s o l u t i o n hardening o f d i l u t e a l l o y s . An important aspect i n t h e i r model i s t h e i n t e r a c t i o n between d i s l o c a t i o n s and t h e p o i n t d e f e c t s . The authors have shown i n a r e c e n t paper /4/ t h a t i t may e v e n t u a l l y be p o s s i b l e t o study t h i s e f f e c t s e p a r a t e l y by i n t e r n a l f r i c t i o n measurements. The t h e o r y p r e d i c t s t h a t a d i s l o c a t i o n i n t h e v i c i n i t y o f an o b f i t a ~ l e due t o the r e p u l s i v e i n t e r a c t i o n can assume two e q u i l i b r i u m p o s i t i o n s ( y ,y ) ( s . F i g , 1 ) .

F i g . 1

-

Thehtw$ e q u i l i b r i u m p o s i t i o n s ( y ,y ) o f a d i s - l o c a t i o n near a r e p u l s i v e o b s t a c l e

*present Address : Technical University Hamburg-Harburg, Arbeitsbereich Halbleitertechnologie, F.R.G.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983987

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C9-588 JOURNAL DE PHYSIQUE

Thermally a c t i v a t e d jumps between these two p o s i t i o n s can be t r e a t e d as a r e l a x a t i o n process and should l e a d t o an i n t e r n a l f r i c t i o n maximum a t low temperatures i n t h e k i l o c y c l e range. An i m p o r t a n t p r e d i c t i o n o f t h e model i s a dependency o f t h e a c t i - v a t i o n energy on t h e d e f e c t concentration.

To c o n f i r m t h e i r model i n t e r n a l f r i c t i o n measurements i n deformed &A1 s o l i d s o l u t i o n s were c a r r i e d o u t i n t h e kc range.

2. EXPERIMENTAL PROCEDURE

For t h e i n t e r n a l f r i c t i o n measurement i n t h e kc range a technique was employed o r i g i n a l l y developed by Schwarz /5,6,7/. Rod-1 i ke SPeclmens w i t h a square cross s e c t i o n a r e glued t o a s i n g l e q u a r t z transducer w i t h a matching frequency o f approximately 90 kc. T h i s two conlponent o s c i l l a t o r i s hung between two t h i n copper w i r e s and e x c i t e d t o v i b r a t i o n s by an e l e c t r o n i c feedback c i r c u i t . The measurements a r e c a r r i e d o u t a t a constant amplitude and a l l o w a low background damoing (Fig.2).

The CuAl s i n g l e c r y s t a l s were grown by t h e Bridgman technique w i t h a

<loo>

d i r e c t i o n p a r a n e l t o the l o n g a x i s and t h e i r exact l e n g t h was c u t by spark erosion. The c r y s t a l s w i t h an Al-content v a r y i n g between 0.07 and 0.8 a t % were deformed under pressure a t room temperature t o a maximum s t r a i n E 2 2 . 5 % and then glued t o t h e q u a r t z c r y s t a l . The i n t e r n a l f r i c t i o n was measured i n t h e temperature range 100 - 650 K. The background damping m a i n l y due t o t h e g l u e and t h e f r i c t i o n between the q u a r t z c r y s t a l and t h e supporting w i r e s i s shown i n F i g . 2. Samples showing an i n t e r n a l f r i c t i o n peak were successively deformed again t o g e t h e r w i t h t h e quartz c r y s t a l i n order t o study the dependency o f t h e peaks on t h e degree o f deformation.

3. EXPERIMENTAL RESULTS

I t i s an e s s e n t i a l f e a t u r e o f t h e measurements t h a t t h e speciments behave q u i t e d i f f e r e n t below and above room temperature, t h e r e f o r e t h e r e s u l t s s h a l l be d i s - cussed separately. The i n t e r n a l f r i c t i o n o f t h e specimens which were deformed a t room temperature and then heated t o a temperature above room temperature decreased approximately exponential 1 ~ w i t h time. Therefore d u r i n q one heatinq c v c l e t h e

Fig. 2

-

I n t e r n a l f r i c t i o n measurement of a deformed CuAl sample (11.3 MP$

0.8 a t %) whicTshows a peak a t 80 C

(P

) . Cementing two quartzes t o g e t h e r ( 9 8 and 96 kc) t h e underground ( g l u e ) was measured.

F i g . 3

-

Second measurement o f t h e peak. Frequency curve w i t h a small s t e p and t h e numeric d i f f e r e n t i a t e d

frequency curve w i t h a maximum a t t h e same temperature.

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d a m p ~ n p was u s u ~ l l y much l o w e r c o o l i n g down t h e specimens ( F i g . 2 ) . Keeping t h e samples a t 150 C f o r a b o u t one h o u r was u s u a l l y s u f f i c i e n t t o r e a c h t h e s a t u r a t i o n l e v e l o f t h e i n t e r n a l f r i c t i o n . It i s assumed t h a t some p o i n t d e f e c t s may be c r e a t e d d u r i n g t h e d e f o r m a t i o n p r o c e d u r e m i g r a t e t o w a r d t h e d i s l o c a t i o n s and d e c r e a s e t h e a v e r a g e d i s l o c a t i o n s l e n g t h L.

A p a r t f r o m t h i s t i m e dependent decrease o f t h e damping a n i n t e r n a l f r i c t i o n maximum ( P , ) i s observed b o t h d u r i n g h e a t i n g - u p and c o o l i n g - d o w n . A t y p i c a l measurement o f a t'tewly deformed specimen w i t h an A l - c o n t e n t c = 0 . 8 a t i i s g i v e n i n F i g . 2.

A f t e r a h e a t t r e a t m e n t a t 150 ^OCt h e peak shape i s g i v e n i n F i g . 3 . The c o r r e s p o n d i n g f r e q u e n c y v e r s u s t e m p e r a t u r e c u r v e shows a s m a l l s t e p a t t h e same t e m p e r a t u r e t y p i c a l f o r a s i n g l e r e l a x a t i o n s p r o c e s s .

Below room t e m p e r a t u r e s t w o sm l l e r peaks ( P I , P ) c a n be o b s e r v e d w i t h peak h e i g h t s v a r y i n g between (1 - 50)

-

^lo'$. They w e r e n o t v a r y r e p r o d u c i b l e and t h e i r

o c c u r r e n c e and h e i g h t was s e n s i t i v e t o t h e t h e r m a l t r e a t m e n t o f t h e samples b e f o r e and a f t e r t h e d e f o r m a t i o n ( h o l d i n g t h e s p e c i m e n a b o v e r o o m t e m p e r a t u r e ) . A t y p i c a l measurement i s shown i n F i g u r e 4.

F i g . 4

-

The two s m a l l peaks P1 and P2 F i g . 5 - Dependency on t h e peak h e i g h t from d e f o r m a t i o n

The t e m p e r a t u r e s a t w h i c h a l l t h e peaks ( P I , P ) a p p e a r a r e o n l y s l i g h t l y and t h e peak h e i g h t s , however, s t r o n g l y dependlngP& t a e d e g r e e o f d e f o r m a t i o n ( F i g . 5 ) . S i n c e w i t h i n c r e a s i n g d e f o r m a t i o n t h e d i s l o c a t i o n d e n s i t y

N

i n c r e a s e s , t h e a v e r a g e d i s l o c a t i o n

1

o l e n g t h L, however, d e c r e a s e s . One may e x p l a i n t h e o b s e r v e d maximum i f Q

'

P f o l l o w s t h e f r e q u e n t l y d e r i v e d r e l a t i o n /4,6/.

max

-

^NL2

Qmax

A q u a n t i t a t i v e c o m p a r i s o n i n v o l v i n g t h e d e t e r m i n a t i o n o f b o t h N and L has n o t been t r i e d .

The m o s t i m p o r t a n t f e a t u r e of each peak i s , however, t h a t t h e maximum t e m p e r a t u r e i s depending on t h e c o n c e n t r a t i o n o f Al-atoms. Some t y p i c a l r e s u l t s a r e g i v e n i n F i g . 6 f o r t h e peaks P I , P 2 , P3.

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JOURNAL DE PHYSIQUE

F i g . 6 - Peak t e m p e r a t u r e v e r s u s c o n c e n t r a t i o n f o r a l l t h r e e peaks P P P a t 15.2 MPa flow s t r e s s .

FI;

o f ' t h s t h e o r e t i c a l f u n c t i o n T ( C a t ) (equ. 3 ) t o t h e measured v a l u e s

4. DISCUSSION

The dependence of t h e peak temperatures and h e i g h t s on t h e d e g r e e of deformation and t h e Al-content s u g g e s t s t h a t t h e u n d e r l y i n g p r o c e s s i s t h e i n t e r a c t i o n of d i s - l o c a t i o n s with some p o i n t d e f e c t s involving t h e aluminium s u b s t i t u t i o n a l atoms. The dependence of t h e peak temperature on t h e Al-content i s i n accordance with t h e p r e d i c t i o n s of t h e Labusch-Haasen theory which i s approximately given by /4,6/

E i s t h e a c t i v a t i o n energy of t h e r e l a x a t i o n process w i t h a jump frequency v = 2dn exp (-EYkT). E i s depending on t h e o b s t a c l e c o n c e n t r a t i o n c

with qo t h e normalized o b s t a c l e width p w3 1 / 2

no

= ( 4 / 3 c )

WW

E

maximal i n t e r a c t i o n energy, s h e a r modulus, w o b s t a c l e width. S and So a r e d#ined in. t h e Labusch-Haasen t h e o r y /4/ a s f o l l o w s ( b Burgers v e c t o r )

2 E C

so

⁼b b / L and S = 0.816

3

^{q o}

^'I2

(l.68-% l / 3 ) 1 / 2

S i n c e o u r o b s e r v a t i o n s prove t h a t t h e l a r g e peak

P

i s v e r y r e p r o d u c i b l e we assume t h a t i t . i s t h i s one which i s due t o t h e i n t e r a c t i o a w i t h t h e aluminium atoms.

Equation ( l ) . w a s t h e r e f o r e f i t t e d t o a l l experimental d a t a y i e l d i n g t h r e e parameters E

,

w, v ( F i g . 6 ) . The maxima P , P were very s e n s i t i v e t o t h e thermal t r e a t m e n t o p t h e spgcimens t h e r e f o r e one ma4 c8ncl ude t h a t t h e i n t e r a c t i o n of d i s l o c a t i o n s with an aluminium

-

vacancy complex i s r e s p o n s i b l e f o r t h e i r occurrence. Given t h a t t h i s i n t e r a c t i o n can s t i l l be d e s c r i b e d by t h e Labusch and Haasen t h e o r y one can a g a i n apply equation /1/ t o d e s c r i b e t h e d a t a . All r e s u l t i n g parameters a r e given i n Table 1 f o r d i f f e r e n t degrees of deformation and a g r e e q u i t e r e a s o n a b l e with each o t h e r . The derived i n t e r a c t i o n e n e r g i e s E a r e on t h e o r d e r on h a l f of an e l e c t r o n v o l t and small e r f o r t h e d i s l o c a t i o n i n t e M c t i o n w i t h an aluminium-vacancy complex.

One may s p e c u l a t e whether t h e two peaks P

,

P a r i s e because of two t y p e s of

d i s l o c a t i o n s (screw and edge) o r two d i f f & r e n ? aluminium complexes, however, t h a t p o i 4 s h a l l not be discussed f u r t h e r .

Onemayadd t h a t e q u a t i o n /1/ y i e l d s a s l i g h t dependence on t h e d e g r e e of deformation

7 i f L

-

^{J / T}

^as

has a c t u a l l y been observed/6,7/.

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Summarizing t h e r e s u l t s we have demonstrated occurrence o f an i n t e r n a l f r i c t i o n peak i n t h e Kc range which shows a l l f e a t u r e s o f a d i s l o c a t i o n p o i n t d e f e c t i n t e r a c t i o n process as p r e d i c t e d by t h e Labusch-Haasen t h e o r y .

E 1 % )

0.1

1.1

2 . 5

REFERENCES

/1/ Labusch, Grange, Ahearn and Haasen (1975) i n Rate Processes i n P l a s t i c Deformation o f M a t e r i a l s (ASM, O h i o ) , p. 26

T IMPa)

1.8

1 1 . 4

1 5 . 2

/ 2 / Haasen, P . , (1979) i n Nabarro, F.R.N., ed. D i s l o c a t i o n s i n S o l i d s , v o l . 4 (North-Holland, Amsterdam) p. 155

/3/ Schwarz, R. B. and Labusch, R., (1978) J. Appl. Phys. 49, 5174 /4/ Labusch, Haasen, Pi-oceed. ICSMA 4, (1976) p. 246

P a r a m e t e r

E - l e V ) w ( b )

V o ( H z )

-

/5/ Schwarz, R. B., (1977) ev. S c i . I n s t r . , 48, 111 /6/ Tonn, G., (1981) D i p l o ~ a t h e s i s , U n i v e r s i t y o f Gottingen / 7 / A1 ber, H. U., (1981) Diploma t h e s i s , U n i v e r s i t y o f Gottingen

P 1

5 . 3 6 1 . 7 2 . 0 1 ~ 1 0 ~

0 . 3 6

0 . 5 0 2.0

0 . 5 0

1.9 2 . O

7.00x?09 9 . 5 9 ~ 1 0 '

-- --- 0 . 5 3 0 . 6 4

1.7 1 . R

6.50x109 9 . 5 5 ~ 1 0 ~ -.

0.51 0 . 6 2