On the Effective Interaction of two Hydrogen Centres in Niobium

Abstract

We derive an effective interaction between hydrogen impurities in Niobium using a microscopic theory of hydrogen in metals. Our model consists of an infinite bcc-crystal with two hydrogen centres occupying tetrahedral interstitial sites, neighbouring on the first to the fourth coordination shell. The elastic interactions are assumed to obey the classical harmonic approximation. The electronic interactions due to both the coulomb potentials and the overlap of the impurity induced electron densities in the vicinity of the interstitials also play an important role. These latter interactions are treated as two-body interactions in a zeroth order approximation of the New Tamm-Dancoffmethod. A separation ansatz results in an effective interaction which depends on the distance between the interstitials and upon the spin states of their excess electrons. We propose some improvements on our model, and to test our calculations, we construct the grand partition function of an appropriate lattice gas model.