THERMOELECTRIC POWER OF LIQUID ALLOYS OF TRANSITION METALS

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THERMOELECTRIC POWER OF LIQUID ALLOYS OF TRANSITION METALS

A. Zimmermann

To cite this version:

A. Zimmermann. THERMOELECTRIC POWER OF LIQUID ALLOYS OF TRANSITION MET- ALS. Journal de Physique Colloques, 1974, 35 (C4), pp.C4-343-C4-344. �10.1051/jphyscol:1974466�.

�jpa-00215657�

JOURNAL DE PHYSIQUE

Colloque C4, supplkment au

5, Tome 35, Mai 1974, page C4-343

THERMOELECTRIC POWER OF LIQUID ALLOYS OF TRANSITION METALS

A. ZIMMERMANN

Laboratoriurn fiir Festkorperphysik ETH, Honggerberg CH-8049 Ziirich, Switzerland

RCsumB. - La tension thermoBlectrique des alliages liquides du Ge avec le Cu et avec les mktaux de transition Fe, Co et Ni a Bte mesuree par la methode des petits

Les influences des etats 3d non occupBs sur la tension thermoelectrique de ces alliages sont discutkes.

Abstract. -

The thermoelectric power of liquid alloys of Ge with Cu and with the transition metals Fe, Co, Ni has been measured by the small AT-method. The influence of the filled and unfilled 3d-states on the thermoelectric power of liquid alloys is discussed.

1 .

In the last years the main interest on the electronic properties of liquid metals has been focused on liquid transition metals and their alloys. The detailed investigations of the electrical resistivity, the Hall coefficient [I] and of the magnetic susceptibility [2] have shown very interesting results.

The aim of these measurements on the thermoelectric power was to complete these experimental data of liquid alloys of Ge with Fe, Co and Ni and to prove the simple model which has been suggested f z these alloys [3].

2.

The thermoelectric power of liquid alloys of Ge with Cu, Fe, Co and Ni has been measured by using the small AT-method.

Experimental details will be published elsewhere [dl.

The thermopower of these liquid alloys has been measured against Pt [5] with an accuracy of

+ 0.2 pV/deg. Thus the absolute error of the thermo- power of these liquid alloys amounts to

0.5 ,uV/deg.

The concentration dependence of the thermopower of liquid alloys of Ge with Cu, Fe, Ni and Co is shown in figure 1. The thermopower of liquid Ge is zero within the experimental error. The therrnopower of liquid Cu-Ge alloys shows a small minimum at about 20 at. % Cu and increases to the positive value of liquid Cu

This behavior is nearly the same as the one that has been observed for liquid Cu-Sn alloys. On the other hand, the thermopower decreases on alloying with the transition metals and goes for Ge-Fe alloys through a minimum at about 30 at. % Fe.

The extrapolated value of the thermopower of liquid Fe from the solid state lies close to the value of liquid Co [7], indicated in the figure. Liquid Ge-Co

(*)

On

Annamarie Zimmermann, age

in

accident while climbing

mountains.

FIG. 1.

- Thermoelectric power of liquid alloys

Ge

Fe, Co and Ni.

alloys tend to show a minimum of the thermopower in the middle of the concentration range. The thermo- power of liquid Ge-Ni alloys varies nearly linearly up to 50 at. % Ni. The value of the thermopower of pure liquid Ni [7] lies out of the scale of figure

at

- 39 pV/deg.

It should be noted that the systematic variation of the thermopower for liquid Sn alloys with Fe, Co and Ni [8] differs from that observed in'Ge alloys.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1974466

C4-344 A. ZIMMERMANN

For Ge-rich alloys an increase in the thermopower

has been observed from Co to Fe to Ni, whereas in Sn-rich alloys the thermopower increases from Fe to Co to Ni.

3. Discussion.

In general, the thermopower of pure liquid transition metals [9] and their alloys

can be explained by the extended Ziman or Faber- Ziman theory in terms of resonant scattering.

Numerical values of the electrical resistivity and the thermopower of liquid Fe and Ni 19, 111 and of the electrical resistivity of liquid alloys of transition metals, such as Ni-Au, Fe-Au, Ni-Sn and Fe-Ge, are in reasonable agreement with the experimental data [12]. Thus, the explanation of the thermo- power of liquid alloys of Ge with Fe, Co and Ni is suggested by using the following formulas

The thermopower S is given by the usual relation

where

The resistivity is given by

where

( ~ ( k ) l2

I t . 12(1 -

+

+

+

I

12(1

+

+

+ ^tA

^{(aAB - 1)} .

(4)

The resistivity derivative appearing in eq. (2) contains different contributions to the thermopower.

The resonant scattering contribution is clearly domi- nant and therefore the actual calculations are quite sensitive to the actual position and width of the resonance and its position relative to the Fermi

energy. Therefore, very careful calculations are needed to obtain useful values of the thermopower in liquid alloys of transition metals.

Until such calculations are available the results can be discussed in a qualitative manner by comparison with the thermopower of liquid Cu-Ce alloys.

For liquid Cu-Sn alloys [13]

detailed comparison between the Faber-Ziman theory of the thermopower and the experimental data is possible because the three partial structure factors [I41 are reasonably well known. The achieved agreement between theory and experiment by assuming local pseudopotentials and by using the measured partial structure factors is very satisfactory. Therefore, the same calculation should also explain the thermopower of liquid Cu-Ge alloys because of nearly the same behavior as a function of concentration.

It is known from more recent calculations [15] that the thermopower of liquid mercury is extremely sensitive to the choice made for the pseudopotential.

Only an energy-dependent (non-local) model potential of liquid Hg predicts the observed high value of the thermopower of liquid Hg. This typical potential of Hg is due to the d-states at the bottom of the conduc- tion band.

is therefore concluded that the non-locality of the t-matrices becomes even more important for transition metals and their alloys. Thus, the quite different behavior of liquid Ge-Cu and Ge-Fe, Ge-Co, Ge-Ni alloys reflects the different influence of filled and unfilled 3d-bands on the thermopower.

4. Conclusion. - The observed variation of the thermopower of liquid alloys of Ge with Fe, Co and Ni as a function of concentration cannot be explained in a simple qualitative way. Only detailed calculations by using the Faber-Ziman formula and by taking into account t-matrices and partial structure factors may provide a reasonable understanding.

Ackwnowledgment. -Financial support of this work by the

Schweizerische Nationalfonds zur Forderung der wissenschaftlichen Forschung

is gratefully acknowledged.

References

[I] GUENTHERODT, H. J. and KUENZI H, U., Phys. Kond. [8] TAMAKI et al., to be published.

Mater. 16 (1973) 117. [9] EVANS, R., GREENWOOD, D. A. and LLOYD, P., Phys. Lett.

[2] GUENTHERODT, H. J. and MEIER, H. A. Phys. Kond. 35A (1971) 57. _{> ,}

Mater. 16 (1973) 25. [lo] EVANS, R., GUENTHERODT, H. J., KUENZI, H. U. and [3] B u s c ~ G. and GUENTHERODT H. J. Solid State Physics, ZIMMERMANN, A., Phys. Lett. 38A (1973) 151.

to be published.

[4] ZIMMERMANN A. to be published. ^{[ l l ]} BROWN, J. S., J. Phys. F(Meta1 Phys.) 3 (1973) 1003.

[51 CUsAcK N. E. and K E N D A ~ ~ P. W. PYoC. SoC. 72 [I21 DREIRACH, O., EVANS, R., GUENTHERODT,

H.

(1958) 898. KUENZI, H. U., J. Phys. F (Metal Phys.) 2 (1972) 709.

[6] There are several values. The figure shows the value of ^[I31 ENDERBY, J. E. and HOWE, R. A., ~ h i l . ~ a18 (1968) 923. ~ . reference 13. [14] NORTH, D. M., ENDERBY, J. E. and EGELSTAFE, P. A., [7] HOWE R. A. and ENDERBY, J. E., J. Phys. F(Meta1 Phys.) Adv. Phys. 16 (1967) 171.

3 (1973) L 12. [15] EVANS, R., J. Phys. C (Metal Phys.) Suppl. 2 (1970) 5137.