Electron transport properties of amorphous Mg80.4Cu19.6 alloy

~

Solid State Co~nunications, Vol.44,No.2,

pp.145-149,

1982.

Printed in Great Britain.

0038-1098/82/380145-05503.00/0 Pergamon Press Ltd.

ELECTRON TRANSPORTPROPERTIES OF AMORPHOUSMg80.4CUl9.6ALLOY Takeshi Matsuda and Uichiro Mizutani* Department Kariya-shi, *Department Chikusa-ku,

of Physics, Faculty of Education, Aichi University of Education, Aichi 448, Japan. of Crystalline Materials Science, Nagoya University, Furo-cho, Nagoya 464, Japan. (Received 5 July 1982 by W. Sasaki)

The Hall coefficient, thermoelectric power and electrical resistivity of the liquid quenched amorphous Mg80.4Cu19.6 alloy have been measured over a wide temperature range below room temperature. The 2k F value deduced from the observed Hall coefficient agrees well with the free electron value. The thermoelectric power is positive and increases linearly with increasing temperature above approximately 180 K. The downward deviation is evident in the lower temperature range. This behaviour is in sharp contrast with the negative thermoelectric power observed in the amorphous Mg-Zn alloy. Nevertheless, the overall temperature variation of the electrical resistivity resembles the previously reported data of the amorphous Mg72.5Zn27.5 alloy in various aspects; (I) the room temperature resistivity value, (2) the negative TCR and its magnitude, (3) the appearance of a broad maximum at about 50 K and a minimum at about i0 K and (4) T2-dependence in the range of 10%30 K and -(T-Tmax) 3/2-dependence in the range of 50~220 K. The results are discussed in connection with 2 k F / ~ criterion and Mooij correlation.

taining transition metals. Fig.l is schematically drawn, based on the data of the amorphous Mg-Zn 8 and Ag-Cu-Ge 7 alloys. It illustrates the characteristic features of the temperature dependence of p for SMGs with a variety of p values. At high temperatures, more or less linear temperature dependence is observed, irrespective of the p value. The TCR defined as (i/p) (dp/dT) changes from a positive to negative value as the resistivity increases. The behaviour of TCR in SMGs has been discussed in comparison with the similar simple liquid alloys. In spite of a number of similarities in the electron transport properties of liquid and amorphous alloy systems, a distinctive difference is found in the TCR versus 2 k F / ~ plot 8, where ~ is the wave number corresponding to the first peak of the structure factor. At temperatures well below the Debye characteristic temperature, there appears a small and broad maximum (cases(b)%(c)) at T=Tmax, which is apparently reduced in magnitude and shifted to a lower temperature with increasing resistivity. The resistivity varies as T 2 at low temperatures below Tma x and as -(T-Tmax )3/2 in the range above Tma x. In addition to the maximum, p exhibits a very shallow minimum at about i0 K. It is not clear at this moment whether it is due to the structural origin or the residual magnetic impurities. Such fine structures seem to become less prominent as the resistivity increases. In fact, neither maximum nor minimum in p is found in a high-p alloy (f), in which p = I-BT 2 (B>0) at low temperatures as found in the amorphous Ag-Cu-Ge alloys 7.

Metallic glasses consisting of only simple metals or simple metal-noble metal combinations have been referred to as simple metallic glasses (SMGs) because of the ease in the evaluation of a well-defined Fermi momentum and electron concentration. They certainly deserve the fundamental study on the behaviour of conduction electrons in a disordered system. However, the electron transport properties of SMGs have been less extensively studied than those of non-simple metallic glasses involving transition metals and rare earths. The liquid quenched SMGs have been so far available in the alloy systems such as Mg-Zn I, Mg-Ga 2, Mg-Cu 3. Ca-Mg 4, Ca-Zn 4, Ca-A14, Mg-Zn-X 5 and Ag-Cu-X6,7(X stands for the polyvalent element). The following electron transport properties have been found in most of these SMGs; (i) The Hall coefficient R H is negative and almost temperature independent. The value of the Fermi diameter 2k F deduced from the measured R H is generally in good agreement with the corresponding free electron value. (2) The thermoelecric power S has a relatively small negative or positive value. S is proportional to the temperature down to a characteristic temperature Ts, below which it shows a non= linear behaviour against temperature. In the amorphous Mg-Zn alloy system-~, S is found to be negative and its temperature dependence can be well fitted to a straight line passing through the origin for the data above T s. The value of S below T s deviates towards more negative direction. (3) The electrical resistivity p is rather low, as compared with that of the glassy alloys con-

145

146

ELECTRON TRANSPORT PROPERTIES OF AMORPHOUS Mg80.4Cul9.6ALLOY

Vol. 44, Nd. 2

-6

(a)

f

-7

I F

%

(c)

-8

x C~ _c I

I

I

I00

i

20O

I

3O0

J

T, Fig.2

Fig.1

: Schematic illustrations of the general trends in the Q vs T curves found for some SMGs below room temperature.

The present paper, which is a continuation of our studies of the electron transport phenomena in SMGs, reports the results obtained on the amorphous Mg80.4Cu19.6 alloy. The Mg-Cu glassy alloy has been first discovered by Sommer et al~ as one of the metalloid-free metallic glasses. The present amorphous alloy was fabricated in the form of ribbons by rapid quenching from the melt using the melt-spinning technique. The purities of source materials Mg and Cu were 99.99 and 99.998%, respectively. The amorphous state was confirmed by X-ray diffraction each time before and after the measurement of the electron transport properties. All numerical data relevant to the electron transport properties are summarized in Table i.

K

: Hall coefficient for Mg80.4CUl9.6 alloy as a function of temperature; the amorphous (A) and crystallized (C) states, and F denotes the free electron value.

Measurements of the thermoelectric power S were carried out down to 78 K using a differential method with 99.998% pure Cu wire as reference. The reference Cu wire was calibrated against 99.9999% pure Pb using the scale given by Roberts 9. The thermoelectric power S and S/T are shown in Fig.3 as a function of temperature. Contrary to the amorphous Mg-Zn alloy, S is found to be positive and has a positive slope against temperature. The deviation from the linear temperature dependence occurs below 180 K. It has been suggested by Gallagher I0 that the deviation of S from a linear relation at low temperatures could be explained as arising from the electron= phonon enhancement effect. Studying a series of amorphous transition metal alloys, he showed that there is a good agreement between the electron-phonon enhancement factor deduced from

Table i: Data relevant to the electron transport properties for the amorphous Mg80.4CUl9.6 alloy.

Q300K (~.cm) 56.0±1.3

(RH) 293K

$297K

(10-11m3/As) -6.73±0.1

(~V/K) 4.13±0.15

5.226(e/a)i/3(d/WA)I/3

TCR

2k F

Kp

(10-4K-I)

(A-1)

(A-1)

2.80±0.01

2.67±0.02

2.73±0.06

The Hall coefficient R H was measured as a function of temperature using the ordinary DC method in the range from 78 to 300 K. More than five specimens were employed to determine the average value of R H at room temperature. Fig.2 shows the temperature variation of R H, the value being always negative and completely independent of temperature down to about 120 K. The 2k F value is deduced as 2.80 A -I from the room temperature value. This agrees well with the value of 2.80 A -1 calculated from the free electron formula; 2k F =

d293K (g/cm 3)

A -1,

by inserting the measured mass density d, the e/a value (=1.804) and atomic weight W A (=31.92). Therefore, we believe the amorphous Mg80.4Cu19.6 alloy to be one of typical SMGs, the electronic structure of which can be well described by the free electron model.

-1.70±0.1

the thermoelectric power data and that calculated from superconductivity data. His explanation seems to be further substantiated by the temperature dependence of S in the amorphous Mg-Zn alloys 8. As can be seen in Fig.3, however, the direct application of his model to the present data would lead to a negative electron-phonon coupling constant. Similar difficulty has been encountered by Gallagher for amorphous Ni36Zr64 alloy I0. In order to resolve this difficulty, he assumed an additional scattering mechanism associated with the cluster of Ni atoms. However, it is highly unlikely to assume the magnetic contribution in the amorphous Mg-Cu alloy. The different behaviour observed in the thermoelectric power between Mg-Zn and Mg-Cu alloys is quite interesting in view of the similarities of the electrical resistivity behaviour discussed below.

Vol. 44, No. 2

147

ELECTRON TRANSPORT PROPERTIES OF AMORPHOUS Mg80.4Cu]9.6ALLOY I

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AS shown in Figs.4 and 5, the temperature dependence of p in the amorphous M g 8 0 . 4 C U l 9 6 alloy is very similar to that of the amorpn6us Mg-Zn alloy. A very shallow m i n i m u m is again observed at about l0 K. The value of (i/Pmi n )Idp/dTIT<10K is found to be of the order 10 -5. A b o v e about i0 K, p increases as T 2 with increasing temperature. The quadratic dependence is more clearly d e p i c t e d in Fig.5(a). The T 2 - d e p e n d e n c e has been theoretically p r e d i c t e d by O h k a w a II and Cote and Meise112 for the amorphous alloy system at low temperatures. Following the T2-dependence, p shews a small m a x i m u m at Tma x of 46 K. F u r t h e r increase of temperature causes the resistivity to decrease m o n o t o n i c a l l y all the way up to 300 K. Fig°5 (b) shows the variation of 0 above Tma x as a function of (T-Tmax) 3/2. The data are well fitted over a wide temperature range to equation;

I

I

r

"~',~..:~.... ~... .~.~::'i.f'~ " ~

Tm0x

57 95

Tm~.

K

: Thermoelectric power S and S/T as a function of temperature for the amorphous Mg80.4CUl9.6alloy-

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: Electrical resistivity for the amorphous Mg80.4 Cu19.6 alloy in the temperature range from 1.5 to 30OK (a) and that on an expanded scale at low temperature range (b). I

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p = Omax - A(T-Tmax) 3/2, with A = 5.2 x l0 -4 ~ . c m - K - 3 / 2 . This type of temperature v a r i a t i o n has been, for the first time, r e v e a l e d by M a t s u d a and Mizutani 8 for the amorphous M g - Z n alloy. A T3/2-dependence ceases at a temperature T2, w h i c h is 224 K for the present alloy. In the temperature range above T2, p starts decreasing approximately linearly with temperature. The value of TCR is determined from the slope in this temperature range. The behaviour of T C R of liquid and amorphous alloys has been frequently argued in terms of 2 k F / ~ criterion. A s p o i n t e d by us 8, when the TCR is p l o t t e d as a function of 2kF/Kp, a distinctive difference emerges in the T C R trend as 2km/K n exceeds unity. The p r e s e n t results (TCR = -1.7 x i0-~ K- and 2 k F / ~ = 1.05) fall on a master curve drawn through the large number of data points for SMGs and further strengthens this argument. All detailed structures found in the temper-

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: Electrical T 2 (a), and

resistivity (T-T

)3/2

max amorphous Mg80.4Cu19.6

as a function of (b) for the alloy.

148

Vol. 44, No% 2

ELECTRON TRANSPORT PROPERTIES OF AMORPHOUS Mg80.4CuI9.6ALLOY

ature dependence of p have been also observed in the series of the amorphous Mg-Zn alloys. The present authors 8 suggested that these features are strongly dependent on the room temperature resistivity. Table 2 compares the values of characteristic parameters for the amorphous Mg80.4Cu_ 19.6 alloy with the corresponding values for the amorphous Mg72.5Zn27.5 alloy, which happens to possess P300K close to that of the present alloy.

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0

•

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T m •

Table 2: Characteristic parameters derived from the temperature dependence of electrical resistivity.

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° ----O

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£0 Mg80.4CUl9.6

Mg72.5Zn27.5

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~56 %10 ~31 ~46 ~224 ~6.9xi0 -4

~55 ~9 ~30 ~42 ~200 ~7.0x10 -4

A ( ~ ' c m - K -3/2)

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I

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300

P3OOK' ~Q,.

It can be seen that both sets of values agree surprisingly well one another. It seems that the room temperature resistivity value plays some important role in determining the resistivity behaviour at low temperatures. Another approach to discuss the TCR behaviour may rely on the well known "Mooij correlation". Mooij 13 empirically revealed that the TCR correlates well with the magnitude of resistivity in transition metal alloys, which include a wide variety of both crystalline and amorphous alloys. Most transition metal alloys with resistivities exceeding 1 5 0 ~ . c m have negative TCR irrespective of their components• In these high resistivity alloys, p seems to be little affected by the details of the electronic structure 14. The correlation between TCR and p for amorphous transition metal alloys is shown by closed symbols in Fig.6. The results of SMGs are also incorporated by open symbols. It is clear that the data for SMGs form a separate group from those for transition metal alloys, although TCR looks correlating with the magnitude of the resistivity. A negative TCR occurs for SMGs whose resistivity exceeds only about 4 0 ~ - c m • Hence, the physical origin to which the occurrence of a negative TCR is ascribed should be different between these two groups• In the case of transition metal alloys, the effect may be closely related to the fact that the electron mean free path approaches the interatomic distance. Cote and Meise114 called for the saturation effect and proposed that the temperature dependence of the Debye-Waller factor, which gives rise to a negative TCR, dominates under

Fig.6

400

cm

: The TCR vs p plot for various amorphous 8 15 Mg-Cu, v ; Mg-Zn , O; Ag-Cu-Mg ,

alloys: ~ ;

D; Ag-Cu-A115, 0; Ni-P 17,

~; Ag-Cu-Ge 15,

A; Ni-Pt-P 18,

+; Cu-Zr 20 and

m; Pd-Si 16,

• Pd-Ni-P 19,

W; Pd-Cu-P 21.

such extreme conditions, regardless of the 2 k F / ~ condition. Alternatively, Jonson and Girvin 22 showed that the breakdown of the adiabatic-phonon approximation in the high resistivity regime produces a negative TCR. Such theories based on the very short mean free path cannot be directly applied to SMGs having p as low as 4 0 ~ . c m . Mizutani and Yoshida 15 recently ascertained that both TCR and p behaviour in the Hume-Rothery type SMGs can be surprisingly well described in terms of 2kF/K p irrespective of the atomic species involved. Therefore, the different mechanisms are responsible for the observed negative TCR in SMGs and transition metal alloys with p > 1 5 0 ~ . c m . The present results for the amorphous Mg80.4CUl9.6 alloy confirmed that the Mg-Cu alloy system is indeed in the realm of SMGs.

Ackn0wledgement - The authors wish to thank Miss M.Katoh, Messrs. H.Fukuzumi, K.Yoshino and Y.Hoshino for their assistance with the sample preparation and measurements.

REFERENCES i) A.Calka, M.Madhava, D.E.Polk, B.C.Giessen, H.Matyja and J.B.Vander Sande, Scripta Met. l_~_l, 65 (1977). 2) B.Predel and K.Hulse, J.Less-Common Metals 6=~3, 45 (1979). 3) F.Sommer, G.Bucher and B.Predel, J.Phys. Colloq. C-8 supplement 4=~i, 563 (1980). 4) R.St.Amand and B.C.Giessen, Scripta Met. i_~_2,1021 (1978). 5) A.Calka and H.Matyja, Amorphous Metallic Materials; Proc. of the Conf., Smolenice, Phys. and Application8 vol.5 Ed P.Duhaj and P.Mrafko p.71 VEDA Publishing House of the Slovak Academy of Science, Bratislava (1978).

Vol. 44, No. 2

ELECTRON TRANSPORT PROPERTIES OF AMORPHOUS Mg80.4CuI9.6ALLOYS

6) U.Mizutani and Y.Yazawa, Scripta Met. 1 4 637 (1980). 7) U.Mizutani, Pro~. 4th Int. Conf. on R~pid~y Quenched Metals, Ed T.Masumoto and K.Suzuki, p.1279 JIM, Japan (1981). 8) T.Matsuda and U.Mizutani, J.Phys. FI2, (1982); Proc. 4th Int. Conf. on Rapidly Quenched Metals, Ed T.Masumoto and K.Suzuki p.1315 JIM, Japan (1981). 9) R.B.Roberts, Phil.Mag. 36, 91 (1977). io) B.L.Gallagher, J.Phys. FII, L207 (1981); Phys.Rev. B, in pre88. ii) F.J.Ohkawa, J.Phys.Soc.Jpn. 44, 1105 (1978). 12) P.J.Cote and L.V.Meisel, Phys.Rev.Letters 40, 1586 (1978). 13) J.H.Mooij, Phys. Status Solidi (a) 17, 521 (1973). 14) P.J.Cote and L.V.Meisel, Topic8 in Applied Physic8 4=~6 Gla88y Metal8 I, Ed H-J Guntherodt and Beck, p.141 Springer Verlag, Berlin (1981). 15) U.Mizutani and T.Yoshida, J.Phys. F, in pr~88. 16) U.Mizutani, to be published. 17) P.J.cote, Solid State Comm. i8, 1311 (1976). 18) A.K.Sinha, Phys.Rev. B~, 4541 (1970). 19) B.Y.Boucher, J.Non-Cryst. Solids ~, 277 (1972). 2o) F.R.Szofran, G.R.Gruzalski, J.W.Weymouth, D.J.Sellmyer and B.C.Giessen, Phys. Rev. B14, 2160 (1976). 21) G.L.Tangonan, Phys.Lett. 54===A,307 (1975). 22) M.Jonson and S.M.Girvin, Phys.Bev.Letters 4=~3, 1447 (1979); S.M.Girvin and M.Jonson, Phys. Rev. B2=~2, 3583 (1980).

149