Pseudopotential calculation of the residual resistance of dilute solid solutions based on normal metals
Abstract
The well known nonlocal pseudopotentials of Animalu, Appapillai, Shaw, and Shyu as well as the Ashcroft local one-parameter pseudopotential have been used to calculate the residual resistance (Δρ/c) of some ISO one-percent metal alloys based on II normal metals: Li, Mg, Zn, Cd, Hg, AI, Ga, In, TI, Sn, and Pb. For comparison with theory, experimental values of Δρ/c for the same alloys were selected critically (by a “reliability criterion" for the evaluation of experimental data) from a large number of published experimental papers. The computations were performed on a computer both without and with account taken of the foreign environmennt of an impurity atom in the alloy (by introducing a renormalization of the impurity form factor). To begin with, only changes in the atomic volume V0 of the impurity during alloying were considered (local approximation) and then changes in the electronic density in the neighborhood of the impurity atom during the transition from the pure impurity metal to the alloy were included. It is shown that the foreign environment of the impurity atom plays an important role (in calculations of the resistance of alloys) and that it is best taken into account right at the very outset of the calculation of the impurity form factor Wi(q). This must be done through the nonlocal renormalization of Wi(q) to the atomic volume if tabulated values of the form factors are used . A suitable quantitative evaluation is suggested for the degree of fit of the calculated to the experimental Δρ/c values for an arbitrary number of impurities in any of the matrices considered. The Δρ/c values calculated with the various pseudopotentials by using the same fitting coefficient nef (equivalent to the number of conduction electrons per atom) proved to be in good agreement (the mean difference for all the impurities in the Li matrix was less than20%) or satisfactory agreement (by a factor or less than 2) with the experimental values, apart from alloys based on mercury (divergence by a factor of 2 to 2.5) and gallium (divergence by a factor of more than 4). The nef alloy values found for alloys based on Li, Zn, Al, Ga, In, Sn, and Pb are consistent with the values nlit from the literature, found from other experiments with pure metals, although for Mg, Cd, Hg, and T1 the values on nef and nlit differ by a factor of 2 to 3. On the basis of an analysis of the calculated results and comparison with experiment we suggest that the influence of the band structure of the matrix metal must be taken into account in calculations of Δρ/c in order to reduce the discrepancy. It is shown that the values of (Δρ/c)calc are 20-60% higher if the manyelectron effects are taken into account by the Singwi–Shyu procedure. Solving the inverse problem of finding the parameter rc (ionic core radius) within the framework of the Ashcroft one-parameter “empty core” model with known experimental values of Δρ/c, we show that some optimal values or rc found for 17 elements are in good agreement with rc values given in the literature obtained from other physical investigations.