Theory of melting based on lattice instability

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Abstract
The various instability-based theories of melting are reviewed with special emphasis on a particular type of instability which is both thermodynamic and elastic in nature. This “thermoelastic” instability originates from a decrease in resistance to shear stress, an idea developed by Born, and is characterized by divergent coefficients of thermal expansion (α) and isothermal compressibility at the melting temperature (T m), an ideal first proposed by Herzfeld and Goeppert-Mayer (1934). Evidence is presented from the results of parameter-free equation-of- state calculations for alkali halides and from published thermal expansion results for a variety of materials, which suggests that melting in many materials may be caused by a thermoelastic instability. A study of the potential energy surface for NaF suggests a type of disorder for the liquid phase which is consistent with recent results of molecular dynamics calculations. If α diverges at Tm then the slope of the melting curve can be deduced from the properties of the solid, a result which is tested for rare gas solids, alkali halides, and a number of metals, and found to work very well in most cases. In addition, a divergent a implies a vanishing thermal diffusivity. Results of thermal diffusion calculations are presented for two different models of a hypothetical continuous melting transition in NaCl with a divergent α at T m. The effect of the divergent α is to make the otherwise continuous transition appear discontinuous: the concept of latent heat and Clapeyron's equation are retained, but in an approximate way. Many of the seemingly diverse ideas which have been thought to be important in understanding melting are, or can be, included within the framework of a thermoelastic instability theory of melting. Moreover, this view of the melting transition fits into a broader picture for the origins of displacive and superionic transitions as well.

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