Open AccessOn the equation of state for solids
Author(s) -
Reinhold Fürth
Publication year - 1944
Publication title -
proceedings of the royal society of london. series a, mathematical and physical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.814
H-Index - 135
eISSN - 2053-9169
pISSN - 0080-4630
DOI - 10.1098/rspa.1944.0023
Subject(s) - thermodynamics , sublimation (psychology) , thermal expansion , compressibility , melting point , crystal (programming language) , theorem of corresponding states , lattice (music) , equation of state , physics , condensed matter physics , chemistry , materials science , van der waals radius , quantum mechanics , van der waals force , psychology , molecule , computer science , acoustics , psychotherapist , programming language
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 formɸ = —ar-m +br-n . In the present paper a method is developed which makes it possible to determine the exponentsm andn 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.