Structural Aspects

Abstract

Building blocks in ordinary non-magnetic metals are atoms. Electrons of s or p character contribute to the quasiparticle states at the Fermi surface which support the transport of charges through the crystal. In relatively simple metallic compounds like sodium or potassium, the constituent atoms each provide an outer-shell s-electron, which, in turn, becomes the conduction electron,and can be considered as a gas of nearly free carriers. Free electrons are described by the simple Drude model where the dc-conductivity (inverse resistivity) is expressed as

$$ \sigma = \rho ^{ - 1} = \frac{{ne^2 \tau }} {m} = ne\mu . $$

(3.1)

Here n denotes the free carrier density, e the electronic charge, τ the relax- ation time, and m the electron mass. μ=eτ/m is the carrier mobility which is a measure of how easily the charge carriers can be accelerated by an ap- plied electrical field. Equation (3.1) is applicable to conduction electrons also, when σ denotes the conductivity tensor and n the electron number density de- pending on the shape of the Fermi surface and direction of acceleration. The electron mass m then has to be replaced by m^*, the effective carrier mass which is inversely proportional to the curvature of the energy band E(k), m^*∞[∂²E(k/∂k²)]⁻¹. In simple metals the Fermi surface — reflecting the anisotropy of the crystal structure — is of spherical shape. This results in a more or less isotropic electrical conductivity.