Kanzaki Forces and Electron Theory of Displaced Charge in Relaxed Defect Lattices
Almost all work concerned with the electron theory of point defects in metals has dealt with the displaced charge under the assumption that lattice relaxation is neglected.
Appropriate response functions for the perfect crystal. These, inevitably, can be found only approximately, and a procedure is adopted whereby direct use is made of the intensities of X-ray scattering at Bragg reflections for the perfect crystal.
A defect potential. This defect potential is defined as follows. We first strain the perfect lattice so that all the atomic positions, except for those at which the point defects reside, are as in the final equilibrium position of the defect lattice. Let the density in this strained but otherwise perfect lattice (Kanzaki lattice) be the sum of the perfectly periodic lattice density ρo(r) and a perturbation ρ1(r). The defect potential Vd(r) is then, by definition, that scattering potential required to convert the density ρo(r) + ρ1(r) in the Kanzaki lattice into the final state density ρf(r) = ρo(r) + ρ1(r) + ρd(r) with the defect introduced.
The displaced charge due to the potential Vd(r) introduced into the perfect lattice, but with the nuclei held fast.
A term correcting this, which is shown to be rather closely related to ρ1(r) above, but involves also the defect potential Vd(r) It is also shown how a first approximation to this term presented here can be systematically refined.
Some preliminary numerical results for ρ 1(r) for a vacancy in copper are presented.
KeywordsDensity Matrix Bragg Reflection Perfect Crystal Reciprocal Lattice Vector Electron Theory
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