A Microscopic Theory of a SingleHydrogen Centre in Niobium

Abstract

A microscopic theory of a single hydrogen centre embedded in a Niobium crystal lattice is given. The electronic structure is investigated on the basis of a special energy difference procedure devel­oped by Wahl et al. This procedure, here applied in its lowest approximation, yields the change in the electronic energy and electronic density distribution due to the embedded hydrogen atom. From these quantities, the dipole force tensor, the displacement of the ions close to the interstitial (nearest and next nearest neighbours) and the heat of solution are calculated. The computed results show good agreement with experimental data.

On the Effective Interaction of two Hydrogen Centres in Niobium

“…In our calculations external perturbative forces and ionic displacements are confined to the nearest neighbours of the impurities. We justify this approximation by the encouraging results of our previous investigations [11] and certain experiments [19] which show the displacement of the next nearest ions to be considerably smaller to that of the nearest neighbours. We further assume the perturbative forces to be additive central forces depending only on the distance between the impurities and the host ions.…”

“…Employing this theory we have recently treated a single hydrogen center in an infinite bcc-crystal as a model for dilute H in niobium. We calculated the lattice relaxation, the dipole force tensor, the relative change of volume and the heat of solution [11] as well as local excitation energies of the H-impurity [12]. The results of these calculations are in good agreement with the experimental data.…”

“…As with our preceeding papers on the static properties of metal hydrides [9,11] we consider both the protons and the ions of the infinite Nb host lattice as classical pointlike charged particles. This approximation is justified by a twofold adiabatic decoupling: first of the electronic from the protonic and ionic subsystems and secondly the protonic from the ionic subsystem in both the hydrided and the unloaded crystal.…”

“…Within this range we fit the parameter to the experimentally obtained heat of solution and fix it to y = 0.45 [11]. This effective ion potential is split into two parts, This yields the embedding energy of an excess electron into the unperturbed crystal , 47T _ 1 -n(k) ., v^' -X) = Ze ä 0 z -w 2 * (21) The second term accounts for the displacements of the next neighbouring ions.…”

“…As the solution of the one-particle problem is known [11], it is natural to make a separation ansatz to solve (13). For this purpose we expand the two-particle function \fi) into Slater-determinants of the oneelectron functions.…”