Theory for the Electrical Resistivity of Liquid Metals

The electrical resistivities of the liquid metals Li, Na, K, Be, Mg, Cd, Al and In are calculated using mass-renormalized form factors obtained from optimized model potentials and the modified perturbation theory of Shaw (1969). It is found that renormalizing the form factors leads to marginally better agreement with experimental resistivities for the alkali metals Na and K, but has little effect on the calculated resistivities of polyvalent metals. The effect of renormalizing the prefactors in the Ziman expression for resistivity is also investigated.

Applicability of the T-matrix unitary condition for the electrical resistivity of liquid metals

A rotating sample technique for measuring the electrical resistivity of liquid metals is developed in some detail and is checked for accuracy and dependability by making measurements of the resistivity of indium-mercury alloys of different compositions. End corrections have been made to the rotating sample method. This method has several advantages over the rotating magnetic field technique that is currently in use. Use of the null technique in this method has allowed us to measure the balancing current in a more precise and reliable way as compared to measuring the deflection of the sample in the rotating magnetic field method.

An expression for the resistivity of a liquid metal is described, which is exactly of the form proposed by Ziman. The advantage over the usual derivation of this formula is that a unique definition of the pseudopotential is possible.

New calculations of resistivities of liquid metals, Na, K, Rb, and alloys, Na-K, Na-Rb, K-Rb, were carried out by using a variant of the Kubo formula that explicitly contains the temperature T. The results come closer to the experiment than the previous ones that use the Ziman formula of resistivity.

Using the force-force correlation function formula for electrical resistivity, plus an approximate result of Bardeen for the effect of scattering on the off-diagonal elements of the density matrix, a self-consistent method of calculating the electronic mean free path in liquid metals is proposed.

Two facilities for the complete noninvasive measurement of the electrical resistivity of liquid metals above the melting temperature and in the undercooled liquid state below the melting temperature are presented: a ground-based facility that was built up in our laboratory and the microgravity facility TEMPUS. Both facilities are unique in combining the containerless positioning method of electromagnetic levitation with the contactless, inductive resistivity measurement technique, thereby enabling for the first time measurements in the undercooled liquid state of a metal. The principles and technical realizations of the levitation and measurement technique of both facilities are presented. Furthermore, experimental resistivity data for Cu60Ni40 as well as Co80Pd20 alloy are presented which indicate atomic ordering effects in the undercooled melt.

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The Ziman-type theory of the electrical resistivity of liquid metals is extended to disordered crystalline alloys by means of a prescription given by Baym. The formulae for calculating the resistivity of these systems are presented and the temperature dependence of the resistivity in both low and high temperature range is discussed in some detail. By using the Debye model for lattice vibration, we can express the resisti-vity of a disordered system as ρ=ρ0+ρd(T/Θ)2+ρi(T/Θ)5 at temperatures well below Debye temperature,Θ , this behavior is compatible with experiments. On account of the Debye-Waller factor and multi-phonon effects, the resistivity approaches saturation at high temperature instead of the exhibiting a linear T-dependence predicted by onephonon approximation. A comparison between experimental data and a simple expression derived on the basis of the approximation of independent vibration of atom shows that the deviation from linearity of the high temperature resistivity similar to that of Nb can be understood with the present model.

A strong correlation is found between the strength of the scattering potential for the electrons and the deviation of the calculated electrical resistivity from the experimental value. The values found for rho calc/ rho expt are 1.03, 1.04, 0.96, 1.12, 2.4, and 5.3 for Na, K, Al, Pb, Zn and Cd, respectively. These values of rho calc/ rho expt are correlated with the corresponding values for the strength of the scattering potential relative to the kinetic energy of the electron being scattered: 0.04, 0.05, 0.07, 0.15, 0.24, and 0.32. An explanation of this correlation is presented in terms of the criterion for the validity of the Born approximation.

Electrical resistivity of liquid metals in the vicinity of the critical point

Is the Born Approximation Valid for Calculating the Electrical Resistivity of Liquid Metals?

Ion-ion repulsion in a liquid metal is regarded as the principal factor determining the ionic arrangement. This interaction is idealized in a hard-sphere model; the known solution of the Percus-Yevick equation for this model gives a simple closed form for $a(K)$ (the liquid structure factor) which depends only on the effective packing density of the fluid. This fact enables us to make an estimate for the resistivities of most liquid metals for which model potentials are available. Agreement with experiment is generally good, particularly when the potential is known to be accurate. The sensitivity of the resistivity to the depth of the model potential well is indicated.

Calculations of the resistivity of liquid metals are performed basing on the structure factor α(q) which can be measured experimentally or calculated theoretically from tle hard sphere model. The calculations are carried out by using the Ashcroft empty core pseudopotential in the framework of Ziman's formula along with different forms of the screening function due to Hartree, Geldart and Vosko, Hubbard, Overhauser, random phase approximation and self-consistent screening. Tle investigation is useful because it throws light on the importance of exchange and correlation effects in developing an appropriate description of the screening of ions by conduction electrons for calculating the resistivity of liquid metals. PACS numbers: 72.15.Cz

The temperature coefficient of the resistivity, $\ensuremath{\alpha}$, of metallic glasses is calculated starting from the same formalism which has been used to calculate the resistivity in liquid transition metals. An explicit equation is derived for the temperature dependence which includes both effects due to the decrease in the static structure factor as well as those due to phonons. The magnitude as well as the explicit temperature dependence of $\ensuremath{\alpha}$ is in good agreement with experiment.