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CXVI. Vacancies in Monovalent Metals

机译：CXVI。单价金属中的空位

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The aim of this paper is to give a simplified calculation of the energy required to form a vacancy in a metal, which is applied to the noble and alkali metals. Although all such calculations are subject to considerable error unless many refinements are introduced, it is felt that such a calculation will give a useful indication of the various factors "which determine the energy and the variation from metal to metal. An outline of the method is as follows. The metal is represented as a large spherical box in which the positive charge of the ions is uniformly distributed and the electrons are free to move. When an ion is removed from the centre of the sphere and spread over its surface, the energy of the free electrons changes by DELTA E_(el), because the electron waves undergo phase shifts in order to screen the vacancy and the volume of the metal box changes. DELTA E_(el) is proportional to the Fermi energy of the metal E_F, and is estimated to be about 1/6E_F. For the noble metals another relevant contribution to the energy needed to create a vacancy is that of the closed-shell repulsion between ions: for Cu this is about -0.3 ev. The energy to move a vacancy is also discussed: the electronic contribution is fairly small and in noble metals the term due to the closed-shell repulsion predominates. This is probably somewhat underestimated if one uses repulsive potentials valid in the neighbourhood of the equilibrium interatomic distance. The general agreement between the theoretical results and the experimental values for the energies to form and to move a thermal defect in the alkali and noble metals is satisfactory and suggests that vacancies are responsible for the transport of matter also in the alkalis.
机译：本文的目的是对在贵金属和碱金属中形成金属空位所需的能量进行简化计算。尽管除非进行许多改进，否则所有这些计算都会有相当大的误差，但可以认为，这种计算将为“确定能量和金属之间的变化的各种因素提供有用的指示。该方法的概述是金属被表示为一个大的球形盒子，其中离子的正电荷均匀分布，电子自由移动，当离子从球心中移出并散布在其表面时，能量自由电子的变化量为DELTA E_（el），因为电子波经过相移以屏蔽空位和金属盒的体积变化。DELTAE_（el）与金属E_F的费米能成比例，对于贵金属，产生空位所需的能量的另一个相关贡献是离子之间的闭壳排斥力：对于Cu，大约为-0.3 ev。能量，并且估计约为1 / 6E_F。还讨论了移动空缺的问题：电子贡献相当小，在贵金属中，由于闭壳斥力而占主导地位。如果人们使用在平衡原子间距离附近有效的排斥势，这可能被低估了。在碱金属和贵金属中形成和移动热缺陷的能量的理论结果和实验值之间的一般共识是令人满意的，并且表明空位也负责物质在碱中的传输。

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