Properties of a harmonic lattice

Physics

Scientific paper

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Scientific paper

Elastic and thermal properties of crystals depend upon anharmonic behaviour of the atomic bonds that hold them together. In extrapolating these properties to pressures of the Earth's deep interior, an idealized reference material, a harmonic crystal, is often referred to. However, the discussions are often clouded by misunderstanding of what the properties of such a crystal would be. It is shown here that the initial pressure dependence of incompressibility is K'0 = 1. Thermal expansion is negative, with a low pressure Grüneisen parameter γ0 = -0.45 for a close-packed lattice (and more negative for open lattice) with a density dependence (d ln γ/d ln ρ)0 = 1.23. Adiabatic incompressibility is greater than the isothermal value, as for a crystal with positive expansion coefficient.

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