High pressure equations of state and planetary interiors

Developments in the theory of strong compression of solids in the last decade, especially some results based on thermodynamic principles, have not yet been digested by the geophysics and high pressure physics communities. They are reviewed here with emphasis on analytical representations that readily accommodate the thermodynamic constraints. Molecular dynamics calculations, made possible by large, fast computers, offer an alternative approach that can handle complex crystal structures and may reveal effects missed by analytical methods but can give unsatisfactory values of properties that depend on high derivatives of the potential functions and, like many of the analytical equations, have difficulty with thermodynamic constraints. Both analytical and numerical methods are simpler in the classical, high temperature regime, well above the Debye temperature, and for most purposes this is a reasonable approximation in applications to planetary interiors. Seismological observations yield data for equation of state studies that are far more reliable than laboratory data at pressures exceeding about 30 GPa and can be used to calibrate laboratory pressure scales. Equations developed for the Earth's mantle and core are applied to the other terrestrial planets and the Moon, yielding estimates of the radii of their metallic cores and deep interior densities and compositions.