On the equation of state for solids
On the equation of state for solids
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DOI：
10.1098/rspa.1944.0023
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发表时间：
1944-08
期刊：
影响因子：
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通讯作者：
R. Fürth
中科院分区：
文献类型：
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作者：
R. Fürth
最近玻恩及其合作者的一系列论文用严格的方法处理了晶格热力学问题。特别是，布拉德伯恩成功地推导出了固体立方晶体的状态方程，由相同的原子组成，假设一对原子的相互势能满足一个定律的形式，即π = - ar-m+br-n。在本文中，开发的方法，使它能够确定的指数m和n的力的法律为一个给定的元素从测量的升华能，压缩性，热膨胀系数，以及这些量的压力和温度的依赖性。该方法适用于大量的元素，它表明，这些物质的压缩和热膨胀，如理论所预测的，是在令人满意的协议与这些量的测量值非常高的压力和温度附近的熔点。熔化是否是由晶格的机械不稳定性引起的问题也进行了调查，并发现了一定的规则连接这两种现象是密切相关的林德曼定律。
The problem of the thermodynamics of crystal lattices has been treated by rigorous methods recently in a series of papers by Born and collaborators. In particular, Bradburn succeeded in deriving the equation of state for a solid cubic crystal, consisting of identical atoms, under the assumption that the mutual potential energy of a pair of atoms satisfies a law of the form ɸ = — ar-m+br-n. In the present paper a method is developed which makes it possible to determine the exponents m and n in the force law for a given element from measurements of the sublimation energy, the compressibility, the thermal expansion coefficient, and the dependence of these quantities on pressure and temperature. The method is applied to a large number of elements, and it is shown that the compression and the thermal expansion of these substances, as predicted by the theory, are in satisfactory agreement with the measured values of these quantities up to very high pressure and up to temperatures near the melting-point. The question whether melting is caused by the mechanical instability of the lattice is also investigated, and a certain rule connecting the two phenomena is found which is closely related to Lindemann’s law.