INFLUENCE OF IMPURITIES AND DISLOCATIONS ON ULTRASONIC ATTENUATION IN COPPER AND DILUTE COPPER ALLOYS AT LOW TEMPERATURES

JOURNAL DE PHYSIQUE

CoZZoque C 5 , suppZ6rnent au nO1O, Tome 4 2 , octobre 1081 page C5-671

INFLUENCE OF IMPURITIES AND DISLOCATIONS ON ULTRASONIC ATTENUATION IN COPPER AND DILUTE COPPER ALLOYS AT LOW TEMPERATURES

P . Schrey, J. Schulz, H. Schmidt and D. Lenz

I n s t i t u t fiir AZZgemeine MetaZZkunde und MetaZZphysik der RWTY Aachen und Sonderforschmgsbereich 125, Aachen - JuZich - KSZn, F.H.G.

Abstract.- We have measured the phonon-electron attenuation a (10<f<200 MHz, long. wave in <Ill>) in Cu single crystals of wl- PF

dely different purity (20<RRR<20.000) after suppression of dislo- cation damping by y-irradiation. The apg-data are in agreement with Pippard's theory. The measurements on crystals doped with pa- ramagnetic impurities (Fe,Mn) show an "ultrasonic Kondo-effect".

1. Introduction.- At T<100K the ultrasonic attenuation (UA) in pure Cu (impurity content typically <I 02 ppm) is determined by dislocations (dis- location resonance attenuation aGL) and electrons (phonon-electronatten- uation apE /I/). Both effects are superimposed on a comparatively small background attenuation ag (being mainly caused by the thermoelastic effect, sample- and sound field geometry /2/). Fig.1 (upper curve) shows as an example the attenuation of high

purity Cu (RRR - 1000, sandwich buffer

I

crystal /3/ to avoid quartz sample de- -.

formation / 4 / ) which strongly increa-

f0[L ^;% -7

ses below 100K due to aPE. (The sample =

?

was slightly y-irradiated (@ _Y = 102@~h) 4

to demonstrate the advantages of the ^...-.

\.-

--_.--l"B-

buffer technique). However, by a heavy

Y-irradiation which causes strong p m g

of the mobile dislocation loops the dis- - FIG 1

location attenuation aGL can be comple- Temperature dependence of dislocation attenu- tely suppressed and the (apE+aB)-contri- ation a G , background

aB and pkonon-electron butions remain (lower curve). Since aB attenuation a p ~

- -

is only slightly temperature dependent

between 300 and 100 K the a(T)-behaviour after irradiation can be extra- polated to 4.2K (dashed dotted curve) in order to separate apE. Subtrac- tion of apE+ag finally yields the wanted dislocation attenuation aGL

(dashed curve in fig. 1 ) .

The presentpaper reports on apE measurements on a wide variety of Cu crystals used for studies of dislocation damping effects. It compares measured apE with theoretical predictions by using residual resistivity

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19815103

C5-672 JOURNAL DE PHYSIQUE

ratios RRR measured on the ultrasonic samples. The resulting Pippard factor /5/ then allows calculation of apE(T) and thus evaluation of a

GL from the a(T) measurement and knowledge of RRR without resort to irra- diation (i.e. the second u(T)-run on the irradiated sample is not needed).

2. Experiment.- We measured longitudinal UA (10<f<200 MHz) in <Ill>- oriented Cu single crystals between 4.2 and 300K. Sample preparation is described elsewhere / 9 / . The residual resistivity ratios of the indivi- dual samples (20<RRR<20.000) were measured by the eddy current technique

/ 6 / . The y-irradiation was produced by a Van de Graaff electron genera-

tor in an Au-target (Frenkel defect (FD) production rate 5 . 5 ~ 1 0 9 FD/cm2s /g/. The total irradiation induced defect concentration needed for com- plete dislocation pinning is < 1 0 - ~ ~ ~ m . This low concentration does not influence the RRR and thus apE to any measurable extend.

3. Theory of phonon-electron absorption.- According to Pippard (free electron gas assumed / 5 / ) the attenuation apE of longitudinal sound in a metal is determined by a=q- R with q= 1; ^{(1 1 1 )} 1 = 2nf /vL the wave number, R the mean free path length of the electrons and vL the sound velocity (5.16-10 5 cm/s)

6 a arc tan a ) - 1

a~~ = A~~ 7 '3(a - arc tan a a (1) 2

AFE = n with N = electron concentration, m = electron mass, VF = Fermi-velocity, p,, = density of Cu. For comparison with experimen- tal results the limits of equ.(l) are useful

ql! > > 1 ("pure limit"): apE/AFE.f = 1 (2)

qc

1 ("impure limit"): apE/AFE.f = 0.5 qR ( 3 ) The"impure limit" refers to doped crystals (having small Q (i.e. low RRR or high T) or to measurements at low E). The "pure limit" refers to high purity crystals at lowest T measured at high frequencies.

4. Results and discussion.- Fig.2 shows apE(T)-curves for samples of different purity levels (e.g. RRR=20.000 refers to < 0.1 at ppm total impurity (Fe)). The strong upE increase between 6 0 and 20 K is due to increasing .t. The maximum GpE measured at 4.2K is determined by t the residual !L for the "impure" case (qL<l, e.g. samples 4 , 6 , 7 ) where apE OA -

(lo - RRR. In the "pure limit" ( q R > > I , ^sample 1 ) aPE=AFEf, i.e. the naxjm-m attenuation is given by the Pippard factor AFE (equ. (2) ) . For compari- son of magnitude the dashed curve in fig.2 shows the dislocation attenu- ation -aGL measured on sample 2: at T > 50K apE << aGL; however, at

T < 10K we find apEzlOaa. This shows that the knowledge of apE is of

fundamental importance for the evaluation of dislocation damping at

these low T ,

Temperature

T [K]

FIG 2 Temperature dependence

Of ~ P E

RRR 20000 @ +

2 5 5 0 @

w 11

200 @

Frequency f

[MHz]

FIG 3 Frequency dependence of a~~

Fig.3 shows apE(f) for three samples of widely different RRR. Whe- reas the impure samples exhibit curved apE behaviour (equ.(3)) the high- est puriiy sample 1 shows a linear apE(f)-dependence (equ.(2)). From its slope we obtain the Pippard factor A _FE = 0.045 + ^0.005.

Fig.4 shows the T-dependence of the electronic mean free path L(T) de-

' 0 2 ~ ~ - - -

rived with help of equ. (3) and %=0.045 (left scale). It can be seen that for

the low sample purities shown the ^-

2

"

a - f dependence is fulfilled

PE

within experimental accuracy (right

scale) . The data can be compared with Z

RIDEAL (T) the "ideal" (lattice-) mean free path length. As to be expected the measured L ( T ) (i.e. apE(T)) is

I R R R '590-377 199 7 0 u?il

h

1 0 - 0 A

5 4 ' '

9 0 . ' A

.

determined by LIDEAL at T > 50K where- L-,----d

^zw

rsmpnoturc 1 (61

as it becomes impurity controlled at

lower T. For T -* 4.2K individual L FIG 4 0

values are measured which scale T-dependence of electron

mean free path length

with the samples RRR values (id RRR) . _R compared with LIdeal

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Fig.5 depicting apE(f) for the sa- me samples as in fig.4 shows more di- rectly the apE - f behaviour (which is 2 seen to break down for the purer sample at hiqhest f). Since apE - ^{E (equ.(3))}

the slope 2-lines scale with RRR. The dashed line of slope 1 depicts the upper limit of applicability of equ.(3) defi- ned by apE/f = 0.02 (see below). From this limiting condition we obtain the experimentally more useful form fLIMIMHz]=

2 - 10 /RRR which limits the (apE 4 - ^{f 2 ) -}

range to frequencies f 5 f LIM. For expe- riments outside this range (f > f

4 LIM Or

RRR > 2 - 1 0 /5MHZ = 4.000, f = 5MHZ be-

ing the lowest f for the present pulse echo technique) instead of equ. (3) the complete Pippard formula (equ. (I)) must be used for calculation of aPE.

Fig.6 shows our apE/f data (left

Frequency

[MHz]

FIG 5

apg(f) in the q . L < ¹ limit defined by

a p ~ 5 0.02 f (dashed line) scale) fitted to the theoretical

apE/AFES f behaviour (equ. (I ) , right

scale). The fit yields AFE = 0.045 the same value as already derived from the data in the pure limit (dashed line). Pippards equation ( 1 ) describes the present data over almost three decades in qR within narrow limits (10%). Thus it can be used for calculation of the apE contribu- tion and separation of the wanted dislocation resonance damping. Up to apE/f = 0.02 (i.e. qR < ^0.9) the "impure limit" equ. (3) can be used with sufficient accuracy.

0,045r I

- -

- 1 1

- 2 I I

5 I I < FIG 6 Present apE da-

- ;

^{0.01~ I Sample l 5} ta fitted to

-. I ^No. a " Pippard equa-

0

RRR 590 = 6' tion (equ. ( I ) )

377 1 1 7 ' to obtain

" 20000 1

+ 0 -

Pippard factor

.

^{2550 2 900 3 I AFE ( 2 0.045).}

. ^{.' 200 4}

I

0,001L --- ₀₁ ^{- -} ₁

^{- -.-} ₁₀

^{- -} - ₁₀₀

q.

5. Ultrasonic Kondo-Effect.- Our results on crystals doped with paramagnetic im- purities (Fe, Mn) exhibit on "anomalous"

apE(T) dependence (attenuation maximum) at T < 30X (c.f. fig. I, sample 7). Fiq.7 shows this for a Cu+50ppmFe and a Cu+6OppmMn crystal. We plot the inverse attenuation vs T since according to equ.(3) f /aPE 2 - 1/R is directly pro- portional to the electrical resistivity

( p - ? / a ) . Both results in fig.7 are in

2 3 < ~ 5 6 7 8 5 1 0 15 20 2 5 3 0

accordance with measured p(T)-curves

Temperature T [K]

/7,8/ on dilute CuFe, CuMn which show _-

Kondo behaviour. Table 1 (comparing our T-de~endence Of

nically measured resisti- results with the resistivity-data)shows vity - ^{f2/a,, showing}

close agreement between the observed ond do-minim%.

temperature T KMIN (Kondo-minimum tempe-

rature) and Kondo-slope SLK = [ I / x ( 4 . 2 ) ] .dx/dloqT with x = Ap(T)/c

( C =impurity concentration) for the electrical resistivity data and x = f /apE(T) for the present ultrasonic attenuation data. 2

TAB. 1

The close agreement between TK and SLK (measured by attenuation and resistivity) indicates that the same phenomenon is observed. To our knowledge this is the first ultrasonic measurement of Kondo scatte- ring.

Electrical Resistivity

21 / 7 /

0.153 /7/

16.2 /8/

0.178 /8/

Ultrasonic pttenuation

2 2 0.149

17 0.176 CuFe

-

CuMn

-

-

T~~~~ rK1

s L ~

T~~~~ LK3

S L ~

JOURNAL DE PHYSIQUE

References

/I/ J.A. Rayne: Proc. kith ICIFUA, Vol. I, p.13, Springer Berlin 1975 /2/ R. Truell, C. Ellbaum, B.~.Chick: "Ultrasonic Methods in Solid

State Physics", Academic Press, New York 1969

/3/ D. Lenz, H. Schmidt: to be published in "Zeitschrift fur Physik B"

41, 1981

-

/4/ J. Schulz, D . Lenz: this volume

/ 5 / A.B. Pippard; Phil. Mag. 46, 1104 (1955)

/6/ P. Bean, R.W. De Blois, L.S. Nesbitt: J. Appl. Phys. 30, 1976 (1959) /7/ G. Holfelder: Dissertation RWTH Aachen (1 977)

/ 8 / P. Monod: Phys. Rev. Lett. 2, 1113 (1967)

/ 9 / P. Winterhager, K. Liicke: J. Appl. Phys. 44, 4855 (1973)