Impurity-impurity interactions in Cu, Ni, Ag, and Pd.

Abstract

We present systematic ab initio calcultions for the interaction energies of impurity pairs in Cu, Ni, Ag, and Pd. The calculations are based on local-density theory and apply the Korring-Kohn-Rostoker Green's-function method for spherical potentials. The full nonspherical charge density is used to calculate the double-counting contributions to the total energy. In particular, we calculate the nearest- and next-nearest-neighbor interaction energies of impurity pairs of the 3d and 4sp elements in Cu and Ni as well as of similar pairs of the 4d and 5sp elements in Ag and Pd: these interactions determine the ordering or segregation behavior of the alloys at finite temperatures. Comparisons are drawn with experimental phase diagrams, solid solubilities of the impurities, and also with the available information about the interaction from diffuse-scattering experiments. The physical mechanisms determining the nearest-neighbor interactions of the impurity pairs are discussed using simple model calculations based on the tight-binding method and the jellium approach: (1) The 4d-4d interactions in Ag and Pd, being repulsive at the beginning in the 4d series and attractive around the middle, can be understood by considering both the changes of the d bond and the repulsive energies between different atomic rearrangement of isolated impurities and impurity pairs. For 3d impurity pairs with the large local moments (Cr to Co) in Cu and Ni, magnetic effects also become important. (2) The repulsive interactions of 4sp-4sp in Cu as well as of 5sp-5sp in Ag can be understood by the electrostatic interaction between the excess ionic charges of the impurities, being screened by the conduction electrons of the host, while the stronger repulsive interactions of 4sp-4sp in Ni as well as of 5sp-5sp in Pd mainly arise from the breakup of the sp-d bonds between the sp impurities and the transition-metal hosts.