Theory of Formation Energy of the External and the Internal Surface for Free Electron Metals

概要

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The formula for the surface energy σ_S = k_F^4/160π is proved to be nearly valid for any self-consistent surface barrier, independently both of the surface shape and of the potential form. 1) On the basis of Friedel theorem and the extended expression N(k)⋍k^3V/3π^2-k^2S/8π of Weyl-Laue theorem, it is proved that the formula σ_S = k_F^4/160π holds not only for the plane surface but also for the surface of any shape, provided the surface potential barrier is infinitely high. 2) As the Friedel sum rule for the plane surface potential, the charge neutrality condition in the interior is obtained as [numerical formula] in terms of the phase shift η(kx). Then the formula σ = β_<σS> for the surface energy is derived, where [numerical formula]. By these formulae, we can prove the approximate validity of σ_S (or β⋍1) for any self-consistent potential on the plane surface. 3) The surface energy of a small spherical cavity is calculated as a function of the radius, assuming the quasi self-consistent infinite barrier for the cavity surface. 4) The formation energy of an atomic vacancy and that of a vacancy pair are discussed as special cases of small volume cavities. The analysis shows the approximate validity of σ_S for any potential form.
社団法人日本物理学会の論文
1960-06-05