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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Peierls transition ： ウィキペディア英語版 Peierls transition A Peierls transition or Peierls distortion is a distortion of the periodic lattice of a one-dimensional crystal. Atomic positions oscillate, so that the perfect order of the 1-D crystal is broken. == Peierls’ theorem == Peierls' theorem states that ''a one-dimensional equally spaced chain with one electron per ion is unstable''. It was asserted in the 1930s by Rudolf Peierls. It can be proven using a simple model of the potential for an electron in a 1-D crystal with lattice spacing ''a''. The periodicity of the crystal creates energy band gaps in the ''E''–''k'' diagram at multiples of the value ''k'' = π/''a'' (similar to the result of the Kronig–Penney model, which helps to explain the origin of band gaps in semiconductors). If the ions each contribute one electron, then the band will be half-filled, up to values of ''k'' = ±π/2''a'' in the ground state. Imagine a lattice distortion where every other ion moves closer to one neighbor and further away from the other, the unfavourable energy of the long bond between ions is outweighed by the energy gain of the short bond. The period has just doubled from ''a'' to 2''a''. In essence, the proof relies on the fact that doubling the period would introduce new band gaps located at multiples of ''k'' = π/2''a''. This would cause small energy savings, based on the distortion of the bands in the vicinity of the new gaps. Approaching ''k'' = π/2''a'' from the left, the distortion due to the introduction of the new band gap will cause the electrons to be at a lower energy than they would be in the perfect crystal. Therefore, this lattice distortion becomes energetically favorable when the energy savings due to the new band gaps outweighs the elastic energy cost of rearranging the ions. Of course, this effect will be noticeable only when the electrons are arranged close to their ground state – in other words, thermal excitation should be minimized. Therefore, the Peierls transition should be seen at low temperature. This is the basic argument for the occurrence of the Peierls transition, sometimes called dimerization. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Peierls transition」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.