C. - AMORPHOUS METALLIC SYSTEMS.TEMPERATURE DEPENDENCE OF THE ELECTRICAL RESISTIVITY OF AMORPHOUS Ge, Sn AND Bi ALLOYS AND ITS RELATION TO SUPERCONDUCTIVITY

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C. - AMORPHOUS METALLIC

SYSTEMS.TEMPERATURE DEPENDENCE OF THE ELECTRICAL RESISTIVITY OF AMORPHOUS Ge,

Sn AND Bi ALLOYS AND ITS RELATION TO SUPERCONDUCTIVITY

D. Korn, W. Mürer, G. Zibold

To cite this version:

D. Korn, W. Mürer, G. Zibold. C. - AMORPHOUS METALLIC SYSTEMS.TEMPERATURE DE- PENDENCE OF THE ELECTRICAL RESISTIVITY OF AMORPHOUS Ge, Sn AND Bi ALLOYS AND ITS RELATION TO SUPERCONDUCTIVITY. Journal de Physique Colloques, 1974, 35 (C4), pp.C4-257-C4-260. �10.1051/jphyscol:1974448�. �jpa-00215639�

C. - AMORPHOUS METALLIC SYSTEMS.

TEMPERATURE DEPENDENCE OF THE ELECTRICAL RESISTIVITY OF AMORPHOUS Ge, Sn AND Bi ALLOYS AND ITS RELATION TO

SUPERCONDUCTIVITY

D. KORN, W. MURER and G. ZIBOLD Fachbereich Physik der Universitat Konstanz D-775 Konstanz, Postfach 733, West Germany

R6surn6. - Pour produire les alliages en Ctat amorphe ils sont condenses de la phase vapeur sur un substrat 5 4 K. La resistivite Blectrique de Ge

+

+

+

at. % Cu (x = 10 a 80) en Ctat amorphe est mesuree. Une dkpendance lineaire est trouvke avec une pente negative pour les alliages de Ge, Bi et Sn et avec une pente positive pour les alliages de Sn avec Cu d'une concentration moins que 60 at. %. La dkpendance de la resistivite klectrique de la temperature est expliquee par la dispersion des electrons de conduction avec les electrons p.

La temperature de Ia transition a la supraconductivite des alliages amorphes de Sn est trouvee btre proportionnelle a la pente positive de la resistivite en Ltat normal.

Abstract. - The amorphous alloys are quench-condensed from the vapour phase on a substrate at 4 K. The electrical resistivity of amorphous Ge

+

+

The superconducting transition temperature of amorphous Sn alloys is found to be proportional to the positive slope of the normal state resistivity.

1 . Experimental results. - The alloys are prepar- ed by fractionationless deposition of the metal vapour on a substrate at 4 K in vacuum of lo-' torr. All films are annealed to certain temperatures T,. The measurements are done a t temperatures lower than T, to avoid irreversible effects. The relative error is lower than 1 x unless otherwise stated. The absolute error has a value of 10 %.

In a previous paper [I] it has been shown that the electrical resistivity of amorphous Ga, Sn and Pb alloys increases linearly with temperature in the low temperature region. Further measurements on Ge, Sn and Bi alloys show that the electrical resistivity can even decrease linearly with temperature.

Ge can be forced into the metallic amorphous state by adding Cu, as reported by Wiihl and Stritzker [Z]. Figure 1 shows the electrical resistivity of an amorphous Ge-Au alloy as a function of tem- perature. There exists a linear temperature dependence with negative slope at high temperature followed by a deviation from 1inear.t~ at about 90 K. At even lower temperature the resistivity passes through a maximum and then the transition to superconductivity occurs.

Bi is superconducting in the amorphous state, as has been found by Buckel and Hilsch 131.

Temperature

FIG. 1. - Temperature dependence of the electrical resistivity of an amorphous Ge-Au film. Annealing temperature Tt.

Bergmann [4] has observed a maximum in the resis- tivity of pure Bi films. By adding a second component to Bi, Barth [5] has extended the range of stability of the amorphous phase to higher temperature. The

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1974448

resistivity of an amorphous Bi-Ag alloy is plotted in figure 2. The Bi-Ag ailoy is superconducting at low temperature. At temperatures above 30 K exists a linear temperature dependence with negative slope.

Temperature

FIG. 2. - Temperature dependence of the electrical resistivity of an amorphous Bi-Ag film.

,

' ^;i

52'2

/

Temperature

FIG. 3. - Temperature dependence of the electrical resistivity of amorphous Sn-Cu alloys with Cu concentrations varying between 10 and 80 atomic percent. Annealing temperatures are close to 80 K, except Sn

+

to 35 K.

Sn-Cu alloys have been investigated by Fortmann and Buckel [6] with respect to Hall effect and super- conductivity. In figure 3 is shown the temperature dependence of the electrical resistivity of amorphous Sn-Cu alloys. (The error of the electrical resistivity of the Sn

+

With regard to rising Cu concentration one can summarize the following results :

1) The constant positive slope at low temperature decreases.

2) A maximum appears at high temperature shifting to lower temperature.

3) Beyond the maximum the resistivity decreases linearly. (For those alloys which can be annealed up to 160 K, the linearity is observable to nearly 160 K.) The negative slope is growing with concentration.

4) A negative slope appears when there is a high residual resistivity. This is a common feature of the measurements on Ge, Bi and Sn.

The magnitude of the positive and negative slope is plotted in figure 4. The error has a value of

+

C u Concentration In Sn

FIG. 4. - Positive and negative slope of the electrical resistivity of amorphous Sn-Cu alloys. Data taken from figure 3.

In figure 5 there is plotted the transformation temperature from the amorphous to the crystalline state as a function of Cu concentration. It can be seen that the amorphous state becomes instable below 10 at. % Cu in Sn. A Sn alloy with 90 at. % Cu could not be forced into the amorphous phase.

Additional data are summarized in the following Table.

2. Discussion. - Extrapolation of the positive slope (Fig. 4) to zero Cu concentration shows that there would be a positive slope for pure Sn too, if one could force pure Sn into the amorphous state. This proves the linear temperature dependence of resistivity to be no alloying effect. The linear temperature depen- dence at low temperature is a property of the metallic amorphous state.

TEMPERATURE DEPENDENCE OF THE ELECTRICAL RESISTIVITY C4-259

A linear term at low temperature can arise only from an electron-electron process. The disappearance of the positive and negative slope (Fig. 4) at concen- trations other than 0 or 100 at. % suggests the scattering to be caused by collective modes of the electrons.

The linear temperature dependence has been dis- cussed [I] by scattering of s-electrons (conduction electrons) by fluctuations of p-electrons with effective mass m, and density N, :

The s-electrons are wave packets with a broad width of momentum Ak, because in amorphous metals there

0 ~ " " " ' " '

0 2 0 LO 60 8 0 a t % 100 exists only a small mean free path due to the high

residual resistivity p,,,.

c u C o n c e n t r a t ~ o n ~ n Sn The high residual resistivity is caused by the structure FIG. 5. - Transformation temperature from the amorphous of the disordered lattice. Rising pres means

to the crystalline state of amorphous Sn-Cu alloys. coupling of the conduction electrons to the structure

Alloy T ^{P r e s} Pose

e

Sn

+

+

+

+

+

+

+

+

+

+

T, : maximum annealing temperature.

preS : residual electrical resistivity, deduced by extrapolating the linear part of the resistivity curve to zero K. For Ge and Bi alloys the maximum resistivity is taken.

pos. (neg.) - AP : constant positive (negative) slope of the temperature dependent resistivity.

AT

T,,, : temperature of maximum resistivity.

T , : transition temperature of superconductivity.

(") The transition temperature was extrapolated from the shape of the resistivity versus temperature curve.

resulting in an increasing effective mass m, of the conduction electrons.

With growing Cu concentration the rcsidual resistivity rises, thereby increasing m,. Then, according to the above equation, the positive slope becomes smaller. Annealing within the amorphous state diminishes the residual resistivity being accompanied by an increase of the positive slope (Table).

To understand result 2 one has to consider that the p-wave functions are not fixed to certain airections.

This means for p-wave functions of different momen- tum k, that they can correlate in phase and build up wave packets with effective mass m,. The driving force for this correlation can be the spin orbrt inter- action which is strong for single p-electrons as known from atomic properties (jj-coupling) of Ga, Ge, Sn, Pb and Bi. With rising temperature the correlation between different k-values will diminish, resulting in a smaller m,. Hence, the slope decreases and becomes negative.

Extrapolation to pure Cu in figure 4 shows that there exists a finite negative slope if one could force pure Cu into the amorphous state. This suggests p- or d-electrons of Cu to be connected with the amorphous state. The high residual resistivity (Table) agrees with this statement. There is further agreement with the empirical fact that only metals with unfilled p- or d-shells can exist in the metallic amorphous phase [I].

3. Relation to superconductivity. - All amorphous alloys with partly filled p-shells are superconductors with higher transition temperatures than the corres- ponding crystalline modifications. Included are all amorphous alloys for which we found a linear temperature dependence.

In figure 6 there is plotted the transition tempe-

Positive Slope of R e s ~ s t i v t t y

FIG. 6. - Transition temperature of superconductivity of amorphous Sn-Cu alloys as a function of the constant positive

slope of the eIectrical resistivity in the normal state.

rature of superconductivity T, as a function of the positive slope of resistivity for the amorphous Sn-Cu alloys. The transition temperature is proportional to the slope of the resistivity. When the slope is zero, superconductivity vanishes. For the first time here is observed a connexion between the superconducting transition temperature and the temperature dependence of the electrical resistivity in the normal state.

We have added 0.5 at. % Mn to Sn with 14 at. % Cu.

Without magnetic addition this amorphous alloy shows a Tc and a positive slope. With Mn impurities, however, Tc vanishes and the slope is zero.

The linear temperature dependence of the electrical resistivity is explained to be due to p-electrons. In addition, there exists a connexion between the slope of the resistivity in the normal state and the transition temperature of superconductivity. From these results we conclude that p-electrons are of principal impor- tance for superconductivity in amorphous metals.

References

[I] KORN, D., M ~ ~ R E R , W., ZIBOLD, G., 2. P h y ~ . 260 (1973) 351. [4] BERGMANN, G., 2. P h y ~ . 225 (1969) 430.

[2] STRITZKER, B., W ~ ~ H L , H., 2. Phys. 243 (1971) 361. [S] BARTH, N., 2. Phys. 142 (1955) 58.

[3] BUCKEL, W., HILSCH, R., 2. Phys. 138 (1954) 109. [6] FORTMANN, J., BUCKEL, W., 2. Phys. 162 (1961) 93.