INFLUENCE OF PLASTIC DEFORMATION ON THE TEMPERATURE DEPENDENCE OF ULTRASONIC ATTENUATION IN COPPER SINGLE CRYSTALS

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INFLUENCE OF PLASTIC DEFORMATION ON THE

TEMPERATURE DEPENDENCE OF ULTRASONIC

ATTENUATION IN COPPER SINGLE CRYSTALS

J. Schulz, D. Lenz

To cite this version:

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JOURNAL DE PHYSIQUE

ColZoque C5, suppZ6ment au nOIO, Tome 4 2 , octobre 1981 page C5- 15 1

INFLUENCE OF P L A S T I C DEFORMATION ON THE TEMPERATURE DEPENDENCE OF

ULTRASONIC A T T E N U A T I O N I N COPPER S I N G L E CRYSTALS

J. Schulz and D. Lenz

I n s t i h i t fur AZZgemeine MetaZZkzcnde wzd MetaZZphysik, RWTH Aachen, F.R.G.

Abstract.- The influence of plastic deformation (O<&<10%) on the

MHz-ultrasonic attenuation a in single crystals of pure Cu, Cu50ppmAu and Cul30ppmAu has been measured over the temperature range 4<T<300K. The major contributions to the total attenuation originate from dislocation resonance, double-kink relaxation, phonon-electron interaction (at T<50K) and non-dislocation effects which are discussed especially with respect to the separation of dislocation resonance and dislocation relaxation contributions. For the activation quantities of Bordini relaxation we obtain

0

= 0.105

+

0.005 eV,

To

= (1.2

+

0.4) x 10-I2s.

1. Introduction.- Ultrasonic attenuation in well annealed pure (typi-

cally

<

lo2 ppm impurities) fcc single crystals is governed by wver-

damped dislocation resonance (DR) as described by the Granato-I.ticke (GL)

theory /I/. At frequencies f below the resonance frequency fmX (about

100 MHz for the present samples) this damping is given by

4

6GL = 0.11 5 aGL[dB/ps]/f[MHz]

-

BhL f (1)

(6GL = DR decrement, aGL = DR attenuation, B = damping force factor,

A = dislocation density, L = loop length between pinning points). Since

B decreases linear with temperature T at T > - 50K, becoming constantat

T < 50K /2/ and fmX

-

1/B equ.(I) holds for low temperatures and a

linear decrease of aGL with decreasing T is observed / 3 / . Since plastic

deformation E increases A (A-E /4/) resonance damping is expected to

increase (a GL-~). However, any decrease of loop length L (e.g. due to

mutual intersection of dislocations or pinning of dislocation by deformation induced pinning points) will counteract the effect of increasing

A on aGL. Furthermore deformation results in dislocation Bordoni rela-

xation (BR) attributed to thermally activated double-kink generation

/5,6/ bB0

-

A L ~ D ( U T ) ₍₂₎

with 15x52 /7/ and D(uT) a Debeye type function depending on frequency

and relaxation time T = T, exp (Q/kT). Present knowledge about BR main-

ly results from Hz- and kHz experiments, i.e. from frequencies well be-

low the typical DR-range. Accordingly AGL contributions are usually not

considered (see however /8/). There is only a relatively small number

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C5-152 JOURNAL DE PHYSIQUE

the linear aB (T) -dependence measured

by Kaufmann /14/. The apE(T) contribution is calculated from the RRR of our samples with help of Pippards theory /15/ (the dashed curve infig.1

at T < 70K is obtained after subtraction of apE(T) /17/.~he a (T) (solid

curves, irreversible for cooling and warming) was measured with the

Nonaq bond. The (dashed dotted) a (T) which is reversible and less steep

below 200K was measured with the 3MP bond. The difference a between

QSD

these a(T)-curves is due to guartz-sample deformation (QSD) which results from different thermal expansion of transducer and sample /14/:

At T<Tq (Tq = solidification temperature of Nonaq

=

200K) the bond trans-

mits QSD stresses into the sample which (due to dislocation break-away) cause irreversible L-changes and the aQSD-effects. QSD is avoided with

3MP (Tq ; 120K); however, the bonding can only be done with considerable

effort at 240K. Also with the 3MP bond a peaked a (T) is measured (fig.1)

showing two maxima tigoI (at

-

150K),

GBoII

(at

-

60K) which indicatethe

Bordini (BoI) and Niblett-Wilks (BoII) peaks. With Nonaq BoI is seen erroneously at slightly higher T. The ago(T) contributions are superim- of MHz-investigations of BR in Cu/9,10,11,16/. To our knowledge the contributions of BR and DR respectively to the total dislocation damping have not yet been clarified quantitatively.

2. Experimental.- We measured attenuation a (1 0 to 50 MHz) in <I 1 1 >-

oriented crystals of pure Cu ( 5 5 ppm impurities), Cu+5OpprnAu1 and

Cu+l30ppmAu by the pulse-echo technique between 4.2 and 300K after compressional deformations of O < ~ < 1 0 % along < I l l > . After deformation the samples were annealed Ih at 363K to eliminate the deformation produced

point defects. The residual resistivity ratio RRR was measured on each

sample by the eddy current technique /12/. The x-cut quartz transducers (0.25"@) were bonded to the specimens by Nonaq (and in several cases by

3-methyl-pentan (3MP) )

.

25

3. Results and evaluation.- Fig.1 intro-

duces the observed phenomena: Point A

-

w

01

..

9.

c=ng9a

-

.

lhoo'c k n a q

- - -

3

3 MP

shows a before, point B after 0.99%

deformation and 1 h 90°C. The a(T)

curves are to be separated into three

dislocation contributions aD =

"GL+

a ~ o +and the non-dislocation a ~ ~ ~

background aB (plus the phonon-elec-

Temperature Tw]

tron effect apE at low T). The back-

ground-is measured after complete dis- FIG 1

a (T) measured with diffe-

location pinning by y-irradiation at _{rent transducer bonds}

RT. We use the ag(c)-values obtained (Nonaq, 3MP) separated in-

to the different a-contri-

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posed on the dislocation resonance con- 20

Cu SOppmAu -21"

tribution aGL (T) given by the straight line. How do we derive aGL(T)?

Fig. 2 shows a (T) for Cu+5OppmAu

measured with Nonaq immediately (45 min)

after 0.3% deformation. The strongly increased aD is seen again (c.f.fig.1)

Temperature T[K]

however, there are no peaks indicating

Bordini or QSD contributions. Thus the

-

FIG 2

observed aD (T) is completely due to dis- a (T) after 0.3% deforma-

location resonance: a- (apE+aB)

= aGL.

tion (unannealed sample) The nearly linear aGL (T) behaviour is

in agreement with B-T in equ. (I). For

further evaluation we assume the linear aGL(T) for all experiments. Avoiding the QSD disturbance we observed ago contributions only for

E > 0.3% (c.f. figs. 1,3,4).

After E = 9.3% (fig.3) ago is very pronounced. Assuming ago t 0 at

4.2K subtraction of apE yields crGL at 4.2K and the dashed curve at high-

er T. To find the correct slope for N ~ ~ ( T ) we consider high temperatu-

res (T>TBoI) where LOT < < I . For variing slopes we logarithmically fit

BO

the resulting normalized BR contribution ao: Z ago(T)/GBo =

[a(T)-(aGL(T) + aB)] / MAX{[a(T)-(aGL(T) + aB)l 1 to the slope of the

- -

high temperature asymptote of D ( L O T ~ ~ ) , (c.£. equ.(2)), determined by

the activation energy Q for double kink generation. Using Q = 0.11 eV

/16/ the best fit obtained yields ao: (300K) = 0.2 (for 50 MHz, verti-

cal bar at 300K in fig.3). Since aio

-

f the BR contributions for 30

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C5- 154 JOURNAL DE PHYSIQUE

and 10 MHz i n f i g . 3 a r e r e a d i l y o b t a i n -

ed. D i s r e g a r d i n g s m a l l v a r i a t i o n s found $E%~ :;>&= c ~ s o ~n ~

.

~ A ~

we u s e t h i s a i o (300) - r a t i o f o r a l l de- f o r m a t i o n s . The v a l i d i t y o f t h i s ago++aGL s e p a r a t i o n i s d e m o n s t r a t e d by f i g . 5 a . The o b t a i n e d

2

- f dependence

Bo P 0.2

means t h a t t h e peak h e i g h t gm-GBo/f

i s i n d e p e n d e n t o f £ , a s must be t h e ca- Frequency f [MHz] io-JIr[~-lI

se f o r a r e l a x a t i o n p r o c e s s . The sepa- r a t i o n i s f u r t h e r s u p p o r t e d by t h e f a c t

_{- -}

2 FIG 5a

t h a t aGL i s n e a r l y

-

f a s e x p e c t e d f o r

----

FIG 5b

Frequency dependence o f Bordoni DR a t f < < f M A X ( e q u - ( 1 ) 1. F i g - 5 b shows peak h e i g h t ( a ) and A r r h e n i u s A r r h e n i u s p l o t s which f o r t h e doped p l o t o f peak t e m p e r a t u r e ( b )

samples y i e l d Q = 0.11

+

0.005 eV, T = ( 9 . 4

+

0 . 5 ) 1 0 - ~ ~ s i n d e p e n d e n t of

0

E . S l i g h t l y d i f f e r e n t v a l u e s ( Q =

0.10 2 0.005 eV, r o = ( 1 . 6

+

0 . 5 ) 1 0 - I 2 s ) a r e d e r i v e d f o r t h e p u r e samp- l e s . Comparison w i t h a s i n g l e Debeye peak shows t h a t t h e measured BoI peak i s broadened by t h e f a c t o r 2 2.

4 . D i s c u s s i o n . - R e c e n t l y N i b b l e t t r e p o r t e d on BR measured a s f u n c t i o n o f E and c r y s t a l o r i e n t a t i o n / 1 1 / . N i b l e t t mentions a l a r g e background

damping ( n o t t o b e c o n f u s e d w i t h t h e p r e s e n t ag and n o t f u r t h e r d i s - c u s s e d i n / 1 1 / ) and o b s e r v e d ( i n c o n t r a s t t o t h e p r e s e n t r e s u l t s ) effects a l r e a d y a f t e r E 2 0.1% d e f o r m a t i o n . However, h i s deformed samples w e r e s t o r e d a t RT f o r 3 d a y s and t h e n measured w i t h Nonaq bonding. Under s u c h c o n d i t i o n s we a l s o o b s e r v e peaked a ( T ) c u r v e s which we, however, a t t r i b u t e t o QSD e f f e c t s : i . e . d u r i n g RT " a n n e a l i n g " t h e f r e s h d i s l o - c a t i o n s a r e s l i g h t l y pinned by d e f o r m a t i o n produced d e f e c t s which a n n e a l o u t a t t k d i s l o c a t i o n s . Cooling below 200K r e s u l t s i n QSD induced break- away of t h e d i s l o c a t i o n s from t h e s e p i n n i n g p o i n t s . T h i s l e a d s t o a a ( T ) maximum a t t e m p e r a t u r e s i n t h e r a n g e of t h e BoI peak /14/ ( C . f . a l s o f i g . 1 ) . Such QSD e f f e c t s a r e observed a f t e r a n n e a l i n g ( o r l o n g e r RT s t o r a g e ) r e d u c i n g L compared w i t h t h e l o o p l e n g t h immediately a f t e r d e f o r m a t i o n . T h e r e f o r e aQSD i s a b s e n t i n f r e s h l y deformed samples (fig.2). Under t h e p r e s e n t a n n e a l i n g c o n d i t i o n ( l h , 9 0 ° C ) QSD e f f e c t s a r e compa- r a t i v e l y u n i m p o r t a n t a t h i g h e r d e f o r m a t i o n s where ago i s d o m i n a t i n g

( f i g . 3 , 4 ) e s p e c i a l l y i n doped c r y s t a l s . We have c a r e f u l l y c o n s i d e r e d QSD a f t e r s m a l l E ( < I % ) i n p u r e Cu and r e p e a t e d d o u b t f u l e x p e r i m e n t s

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-3

Plastic Dekumatimn EN]

FIG 6 Influence of impurity content and plastic deformation on dislocation resonance atte nuation aGL, Bordoni relaxation ago and non-dislocatxon background aB at T=131K.

Fig.6 collects our results showing the influence of E and impurity con-

tent on the main MHz attenuation contributions aGL,aBo and ag (atf=IOMHz,

T=TBoI=131K). The non-dislocation aB-surface is unaffected by doping and

small deformations (E <2%). For c>.2% the aB values increase due to sound

wave scattering caused by deformation induced lattice inhomogeneities / 1 3 / . The shape of the dislocation resonance aGL-surface is the same as measured by Drescher et a1 /13/ on pure Cu at RT. The aGL increase up to

~ ~ 0 . 2 % (pure Cu) and E-0.4% (130ppmAu) is due to increasing dislocation

density (A-~)/4/. The aGL-levelling-off and -decrease at higher E is cm-

sed by loop-length shortening /13/. We point out that the background dam

ping mentioned by Niblett /11/ also exhibits a maximum as function of

deformation. The Bordani relaxation ago-surface emerges at ~ = l to 2%

from the background due to aGL+aB. Since Bordoni relaxation is known to be brought out by internal stresses /6/ we attribute the observed aGL reduction in this €-range (at least partly) to dislocation/dbslocation strainfield interaction in e.g. tangles or dipols.

Compressional deformation and the aB increase at high E prohibited

the investigation of ago(E) beyond ~210%. Nevertheless, the resultsclear-

ly show that ago increases less than proportional to E indicating L-short-

ening effects (as observed for aGL at ~b0.2 to 0.4%). Since it can be

assumed that L - l / n and A - & the value x=2 in equ.(2) would lead to satu-

ration of ago at high E; but x=l would result in a ago-&dependence. Experiments with €>lo% are needed for final conclukions. In comparison

with E the impurity influence on the different a-contributions in fig.6

is minor. (We attribute the pronounced BR at €=lo% in the 13OppmAu doped

sample to enhanced easy glide which is known to occur in solution harde-

ned crystals). Both aGL and aBo decrease with increasing impurity level in accordance with theory (equ.(l) and (2)): The effect is stronger on

4

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C5- 156 JOURNAL DE PHYSIQUE

Bordoni experiments on still higher concentrated alloy crystals as well as on strongly irradiation pinned pure material.

We thankfully acknowledge financial support by the Deutsche Forschungs-

gemeinschaft (SFB 125)

.

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