104 Materials Science and Engineering, AI33 ( 1991 ) 104-106

D-wave phase shift of Cu-Zr metallic glass system under pressure

S. H. Han* Department of Solid State Physics, The Royal Institute of Technology, S-100 44 Stockholm (Sweden)

R. Y. Jin, H. Han and B.-G. Shen Institute of Physics, Chinese Academy of Sciences, Beijing 100080 (China)

Abstract

The pressure dependence of the electrical resistance of metallic glass Cu-Zr alloys is measured at room temperature up to 8 kbar and analyzed by the extended Ziman model. From the measurements and a calculation of the pressure dependence of the structure factor, it is concluded that the pressure depen- dence of the d-wave phase shift is significant and of the same order of magnitude as the pressure coeffi- cient of resistance.

1. Introduction

Although the electrical resistivity of many metallic glasses has been measured as a function of temperature, the mechanism behind its behav- ior in the various temperature ranges is not well understood. Measurements of the resistivity as a function of pressure at constant temperature pro* vide a sensitive test of presumed scattering mechanisms.

Much work has been reported on the resis- tance-pressure behavior of amorphous metals [1-7] and several explanations have been pro- posed. However, the emended Ziman model was most frequently employed, because it has been more successful than other models in explaining the magnitude and temperature dependence of the resistivity and also, particularly, of the thermopower. Some authors suggested that the emended Ziman model might explain their ex- perimental data on the pressure dependence [1-3], but some [4-6] suggested that the simple formulation of the Ziman theory is inadequate to account for the observed pressure dependence of the resistivity. In some work where the Ziman model was used to explain experimental data, the effect of pressure on the d-wave phase shift at Fermi surface, ~72(Ev) was suggested to be so

*Permanent address: Institute of Physics, Chinese Academy of Sciences, Beijing 100080, P.R. China.

small that it might be neglected [1, 3]. Lazarus [1] has reported that for Pd82_xWxSi18 , the pressure coefficient of resistance of all the glasses is iden- tically zero to one part in 104, indicating that the pressure derivative of the logarithm of the resis- tivity is exactly equal to the negative of the linear compressibility. The implication of this result with respect to theoretical models was discussed; and only the Ziman model was found to provide a consistent explanation. In this discussion, it was expficitly assumed that the contribution of drh/ dP and dSr(2k F )/dP to p should be small, and they were neglected.

S. H. Han et al. [3] calculated the effect of pres- sure on the structure factor of metallic glasses of F e l 0 0 _ x B x - and obtained results consistent with the Ziman model. In this work the effect of pres- sure on d-wave shift could also be neglected. However, from reported work [8-12], the d-electron conduction, coupled with lattice vibra- tions, is significant in the electron transport pro- perties of nonmagnetic metallic glasses containing an appreciable number of d-electrons at EF, e.g. Cu-Ti [9], Cu-Zr [9], Y-A1 [10], L-X (X = A1, Si and Au)[10], Ni-Ti [11] and Ni -Zr -X (X=H, B, Si and A1) [12]. Therefore, in these systems, attention should be paid to the effect of pressure on the d-wave phase shift. In this paper, the change of r/2(Er) under pressure for glassy Cu-Zr alloys is discussed on the basis of the cal- culation of the pressure effect on the structure

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factor, ST(2kv ), and on the measured pressure coefficient of resistance.

2. Experimental details

CUl00_~Zr~ (x=75 and 70) alloys were pre- pared by arc-melting, and amorphous ribbons were produced of approximate thickness 30-40 /zm and width 1.5 nun, by the centrifugal melt- spinning technique. All samples were found to be amorphous by X-ray diffraction.

For measuring the pressure dependence of electrical resistance at room temperature the specimens were cut into strips 0.8 mm in width and 8 mm in length. Sample leads were attached by soldering, and resistance was measured using the standard four-probe technique. The sensi- tivity of the measurement was 2 x 10-8 V. Pres- sure up to 8 kbar was applied to the specimen by using a piston-cylinder type device in a Teflon pressure cell filled with a 50:50 mixture of kerosene and diffusion-pump-oil as the pres- sure-transmitting medium. The pressure was measured by means of a calibrated manganin gauge. The temperature of samples was con- tinuously checked by means of a copper - constantan thermocouple to ensure that the resistance changes were measured at 290 + 0.1 K.

3. Results and discussion

For all our samples, we found a decrease in resistance with increasing pressure. The relative variation R(P,290)/R(O,290) as a function of pressure P(kbar) for CUl00_xZr x ( x = 7 5 and 70) metallic glasses is shown in Fig. 1. The pres- sure coefficient of resistance ap is defined as d lnR/dP[r. The results are obtained with the least-squares fit. They are ap = - 1 . 5 7 x 1 0 -3 and - 1 . 7 0 x 1 0 -3 kbar -1 for Cu25Zr75 and Cu30Zr70 respectively. These values are in agree- ment with those of ref. 13. The results for the temperature coefficient of resistance a 7-( = d lnR/ dT) are -1 .11 x 10 -4 K -1 for Cu25Zr75 and - 1.34 × 10-4 K- 1 for Cua0Zr70.

Following Nagel [14], for a transition-metal system the resistivity as a function of temperature can be expressed as

p ( r ) = C kF2Evy sin2[~h(EF)]Sr(2kv) (1)

where C is a constant, V is the volume, k F is the Fermi wavevector, E F is the Fermi energy, r/2(E F )

o3 t"M

rr"

0 Ob 0,1

r r

105

1.000

0.995

0.990

0.985 • Cu25Zr7s

Cu30Zr70

0.980 I t I 0 2 4 6 8

P (kbar) Fig. 1. Relative resistance R(P,290)/R(O,290) as a function of pressure P(kbar) at 290 K for Cu25Zr75 and Cu30Zr70 metallic glasses.

is the d-wave phase shift of the t-matrix describ- ing scattering of the conduction electrons by the ion cores, and ST(2kF) is the static structure factor at T K.

The logarithmic derivative of the resistivity with pressure is therefore:

d lnp= din[kF2EFV] + dlns in2[r l2(EF)]

dP d P dP

dlnST(2kF) ( 2 )

d P

The first term in eqn. (2) can be obtained from a nearly-flee-electron model:

d ln ( kvZ Er V ) - - ( 3 )

d P

where fl is the linear compressibility. The second term in eqn. (2), dlnsinE(rl2(Ev )/

dP, could in principle be calculated from the band theory of crystalline transition metals. How- ever, it is so complex that there is no model theory for crystalline transition alloys. We may only propose some discussion and analyses.

The third term in eqn. (2), dlnSr(2k F )/dP, was calculated by Han et al. [3]. Starting from eqn. (1), they arrived at the following expression:

dlnSr(2kv) 1 dP --~arfl[8T(1--37)+O(2-37)] (4)

where a 7- is the temperature coefficient of resis- tivity, y is the Griineisen constant - d In 0/d In V, and 0 is Debye temperature.

106

TABLE 1

The values of the parameters of eqn. (4) for Cu-Zr metallic glasses

Samples Parameters

a r (this work) fl [15] ~, [16] 0 o [17] T (K ') (GPa-') (K) (K)

Cu25Zr75 - 1.11 x 10 4 2.3 x 10 -3 1.2 182 290 Cu30ZrT0 - 1.34 x 10 4 2.7 x 10 -3 1.2 184 290

The values of the parameters in eqn. (4) for Cu-Zr metallic glasses are given in Table 1. From eqn. (4) we then obtain the a'esults for dlnSz(2kF)/dP of 0 . 4 2 x 1 0 -4 kbar -1 and 0 . 5 9 x 10 . 4 kbar -I for Cu25Zr75 a n d Cu30ZrT0 respectively.

We can now calculate the pressure dependence of the d-wave phase shift from the observed pres- sure coefficient of resistance and the results from eqn. (4),

d In R _ d lnp a e - d P dP

= d In sinZ[r/z(EF)] d l n S r ( 2 k F ) (5)

d P dP

where the last member is obtained from eqns. (2) and (3). The results for dlnsinZrh(EF)/dP are - 1.61 x 10 -3 kbar -1 for Cu25Zr75 and - 1.76 x 10- 3 kbar- 1 for Cu30Zr70.

It is thus found that the order of magnitude of the change of sin 2 rI2(E v ) under pressure is similar to the pressure coefficient of resistance a e. Clearly the d-wave phase shift plays a significant role in the pressure effect and cannot be neglected. This result is consistent with the importance of d-electrons in the transport pro- perties of nonmagnetic metallic glasses with an appreciable number of d-electrons at E F [8].

Summarizing, we have shown that within the extended Ziman model one can use experimental results for ae and calculations of din Sr(2k v )/dP to estimate the pressure dependence of the d-wave phase shifts. When this method is applied to Cu-Zr metallic glasses it is found that the d-wave phase shifts have a pressure dependence which is similar to that of the resistance.

Acknowledgments

We would like to thank O. Rapp for comments on the manuscript. This work has been supported by the Swedish Natural Science Foundation and by the Chinese Natural Science Foundation.

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