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This paper proves a locality principle for a wave-mechanical particle governed by the Schr6dinger equation. It is shown that p(r,,4), the Laplace transform of the local density of states n(r,E), depends significantly only on the potential V(r') at points r' near r. The effect of changes of V(r') at distant points r' (lxi'-xil > a) on p(r,,8) decay in a Gaussian fashion with a. This result sheds some light on the locality of physical properties of extended systems and provides general support for various local methods of calculation.Z(3) = p(rd)dr = E e-,.

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The electronic contribution to the effective, indirect, vacancy-vacancy interaction in the bulk and on the surface of a simple-cubic' tight-binding solid is evaluated. The analysis is performed within a one-electron picture using a Green's-function technique. The intervacancy interaction is shown to be significant up to about fourth-nearest neighbors, and to have an oscillatory dependence on their separation. The nearest-neighbor interaction is found to be negative for both bulk and surface vacancies. The behavior of surface vacancies appears qualitatively similar to those in the bulk, although their interaction is found to be stronger in most cases. It is shown that vacancies, both in the bulk and on the surface, have the thermodynamic tendency of forming nearest-neighbor dimers, and that the diffusion process leading to the formation of these dimers occurs along preferred routes. These preferred routes should, in principle, be observable for surface vacancies.