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<pre><b> File: SECT01.WM of Tape: Various/ETH/s10-diss</b></pre>
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I. INTRODUCTION.
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This work will be primarily concerned with the anisotropy of

the conduction electron relaxation times, in the context of

conduction phenomena, i.e. resistivity and Hall effect. Our

main effort will be to explain the influence of impurities

introduced, substitutionally, in an otherwise ideal metal. We

shall now briefly discuss the developments leading toward the

concept of anisotropic relaxation times and the reasons why we

only discuss the simple trivalent metals.
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1). Historical background.
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The concept of relaxation times was introduced by Drude(1902)

and Lorentz(1909) shortly after the discovery of the electron.

They developed simple phenomenological theories based on the

kinetic arguments of the theory of gases, where the relaxation

time was a parameter describing the time between collisions of

the conduction electrons. Amongst other problems, this relax-

ation time, or in other words, the mean free path, turned out

to be much longer than the interatomic distance when the theory

was applied to low temperature, or even to room temperature

phenomena. At that time it was difficult to explain how an

electron could move over several thousand atoms before it was

removed, by succesive scattering events, from the conduction

process.
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The advent of quantum mechanics solved most of the problems.

Sommerfeld(1928) used Fermi-Dirac statistics to show that it

was necessary to consider only a small part of all the avail-

able electrons in order to explain the conduction process. The

ideas of Bloch(1928) about periodic potentials led to the fact

that, in a first order theory, the electrons should experience

no resistance whatsoever in a perfect lattice at zero tempera-

ture. These advances in the theoretical description of the

conduction mechanism reversed the situation: one had to show

why metals have a resistance at all. (i.e. why they are not all

&quot;superconductors&quot;!). This led to refinements of the models

which now had to include imperfections of the perfect lattice.
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The problem can be roughly separated into two types of dis-

turbing effects of the ideal lattice; the first has to do with

displacements of host atoms from their equilibrium positions,

the second with the replacement of host atoms by other atoms.

Naturally this division is rather artificial, but it seems that

the two subjects were often treated separately. The first part

was mainly concerned with the intrinsic resistance of the pure

metal attributed to the thermal motion of lattice. The first

theory adequate for a large temperature range and explaining

experimental results rather well was proposed by Grueneisen

(1933). The second aspect dealt with the deviations of the

periodicity of the lattice due to the change in atomic poten-

tials themselves and was mainly used to explain the resis-

tivities due to foreign atoms, vacancies, etc.
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For a long time it was assumed that the relaxation times were

isotropic, i.e. independent of the location in wave number

space of the electronic wave packet being scattered from one

place of the Fermi surface to another. At a relativily early

date (see Wilson(1953)) two- band models were introduced, but

these models had no direct connection with anisotropic relax-

ation times; they were phenomenological theories used mainly to

separate contributions, with different effective masses, from

different parts of the Fermi surface.
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In this same period of time the influence of the boundaries

(size effects) was investigated. A review by Sondheimer(1952)

showed that these size effects were usually applied in a free

electron model and that they were assumed to modify the mean

free paths by direct geometric effects rather than by an

influence of the boundary on the intrinsic bulk properties of

the crystal.
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Anisotropic relaxation times definitely became fashionable when

the ideas of Ziman (1960,1961) explained most of the conflict-

ing experimental results in the bulk noble metals. He proposed

a model incorporating the main features of the Fermi surface

and the anisotropies of the electronic relaxation times, which

explained many of the difficulties. After this, the subject of

anisotropic relaxation times became an active research topic

and the first conference dealing specifically with this topic

took place in Zuerich. (Chambers,Olsen,Ziman(1968)).
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In considering the reasons for preferring investigations in

trivalent simple metals, we may note that experimental work

relating to conduction phenomena has been the most intensive

in the noble metals group. (see for instance Alderson;Hurd

(1970)) Although very many experimental facts are known about

these metals, it remains that the theoretical treatment is

complicated by the fact that their Fermi surfaces are rather

strongly influenced by the vicinity of the d-bands and have to

be described by augmented plane wave methods.
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The advantage of the trivalent metals aluminum and indium is

that they satisfy the small core approximation needed for the

pseudopotential theories. Their Fermi surface is accurately

described by the orthogonalized plane wave formalism which uses

matrix elements derived from pseudopotentials. We think that

such a description is much better suited for discussions in

terms of the standard text book methods of electronic conduc-

tion. We will treat these two metals from this view point and

develop simple models to describe the Hall effect and the

resistivity, in a way closely related to the work of Sorbello.

(for a recent review see Sorbello (1975))
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2). Organization.
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In Sect.II we first give an introduction to the characteristics

of these two metals, which we used in our calculations of the

Fermi surface properties. As our main concern is in measuring

relaxation time effects in alloys of these two metals, we

further discuss the range of solutes available and the reasons

why some solutes should be better suited than others for our

kind of measurements. Some collected data is also presented

concerning lattice distortions, which will come to use in later

sections.
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The next section III handles the problem of scattering centers.

It starts off with a presentation of newly compiled free

elctron data of the two metals in question and of their solute

candidates. This data was also given for future reference,

because we found that the constants used in low temperature

calculations were often erroneous.
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In Sect.III.2, two pseudopotential formalisms are discussed.

The first is the simple Ashcroft empty core pseudopotential and

we give our new values of it&#039;s single parameter. It was found

that this potential was not realistic enough for scattering

calculations and we also present the Shaw potential as modified

by us for the case of solutes in solution in some other metal.

We give our re-evaluated parameters for the pure metal case and

for the solute case.
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Sect.III.3 shows how to construct a scattering potential from

the last mentioned pseudo potentials and includes a discussion

of lattice distortion effects. A new series of phase shifts,

parametrizing the scattering properties of solutes in Al and In

are the main result of Section III.
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For dealing with the resistivity and the Hall effect, we recap-

itulate the theory of Sorbello and add some extra features con-

cerning the character of the wave functions of Al and In on

certain parts of the Fermi surface, in Sect.IV.1. Our extension

of this theory to the situation in a magnetic field is given in

Sect.IV.2. The result is given by a general expression for the

conductivity tensor in a magnetic field and also an expansion

in powers of H is given for the treatment of low field effects.

Finally a simple 3-band model is proposed which, we hope,

should describe the main features of the Fermi surfaces.
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In Sect.V our experimental results on the Hall effect and the

resistivity in dilute Indium alloys is presented. We show that

the important sign reversals in the Hall effect cannot be due

to rigid band effects. At the end of this section our exper-

imental results are discussed in a quantitative manner, using

the theoretical results obtained in the earlier sections,

concerning scattering potentials, phase shifts, character of

the wave functions, etc., in the context of a 3-band model.
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We also give some results for the resistivity of Al based

alloys in connection with our de Haas- van Alphen (dHvA)

experiments as discussed by Wejgaard (1975) and compare some

experimental Hall effect data by Boening et al. (1975).
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