The Effect of Initial Pressure on Two and Three Dimensional Solids

The elastic properties of two and three-dimensional Cauchy solids subject to initial pressure are examined and shown to require only experimental isotherm information for application. In two and three dimensions the sound speeds, Poisson's ratio, and the Debye temperatures depend upon a dimensionless parameter given by the product of pressure and compressibility. It is shown that the pressure-compressibility product has a maximum value of 0.5, independent of dimensionality, and that this maximum corresponds to a vanishing shear modulus and the concommitant disappearance of transverse sound modes. For a given value of the pressure-compressibility product, the effect of initial pressure on the elastically derived properties is always greater in two dimensions than in three. The model is compared to direct experimental information for bulk helium and neon, and to the two-dimensional solid case of helium adsorbed on graphite.