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- W2082719673 startingPage "965" @default.
- W2082719673 abstract "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 3 V /3π 2 - k 2 S /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 begin{aligned} int_{0}^{k_{F}}eta(k_{x})k_{x}dk_{x}{=}frac{pi{k_{F}}^{2}}{8} end{aligned} in terms of the phase shift η( k x ). Then the formula σ=βσ S for the surface energy is derived, where begin{aligned} beta{=}frac{80}{pi}frac{1}{{k_{F}}^{4}}int_{0}^{k_{F}}eta(k_{x}){k_{x}}^{3}dk_{x}-5. end{aligned} 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." @default.
- W2082719673 created "2016-06-24" @default.
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- W2082719673 date "1960-06-01" @default.
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- W2082719673 title "Theory of Formation Energy of the External and the Internal Surface for Free Electron Metals" @default.
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