File: SUMARY.WM of Tape: Various/ETH/s10-diss

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VI. SUMMARY.
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We have shown in this work that the concept of anisotropic

relaxation times of the conduction electrons can be used to

explain experimental results on the resistivity and the Hall

effect in pure and alloyed specimens of indium and aluminum.
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The introduction of small quantities of various impurities has

a profound influence on the low field Hall coefficient of both

In and Al. In the specific case of In, we showed that these

effects could not be explained by considering changes in the

Fermi surface brought about by the introduction or removal of

extra electrons.
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The only way we can explain these results is in assuming that

these various impurities each have their own particular

scattering properties, leading to an anisotropy of the

relaxation time of the various electronic states on the Fermi

surface.
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In the framework of pseudopotential and OPW band structure

calculations, we have extended the model potential formalism of

Shaw to the description of the proper potential of in impurity

in a foreign host crystal and given the parameters to be used

in calculating various impurity effects. By extracting the non

periodic part of these potentials we then specify a set of

characteristic phase shifts for both In and Al.
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These phase shifts were then used to define local relaxation

times with the help of the approximate methods developed by

Sorbello giving the averaged character of the wavefunctions

over specific parts of the Fermi surface.
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The fact that we had to discuss effects depending on a magnetic

field demands a reconsideration of Sorbello's conduction

relaxation time. We have extended his treatment in zero field

to the case of the non-quantum field regime. Our result is an

exact expression of the conductivity tensor which will be of

use in forthcoming numerical calculations.
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In this work we have expanded this tensor in powers of the

magnetic field and applied the resulting three first terms to a

3-band model representing the topologically different parts of

the Fermi surface. The theoretical results of this model,

applied to the resistivity and the low field Hall effect are

shown to be in reasonable agreement with data obtained from our

experiments and from other sources.
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In the same framework we also give a simplified discussion of

the influence of temperature on the Hall coefficient and show

that, when Umklapp processes are ignored, a rather good

agreement between theory and experiment can be obtained.
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