Equation of State of Certain Ideal Lattices

The equation of state of a face-centered cubic lattice and a two-dimensional diatomic square lattice considering nearest and next nearest neighbors is given as well as a preliminary investigation of a simple cubic lattice. The Gr\"uneisen parameter γᵢ=-dlnνᵢdlnV, where νᵢ is the normal mode frequency and V is the volume, is derived and used to determine the thermal expansion coefficient for these crystals assuming different forms of the interatomic potential energy. Negative thermal expansion at low temperatures is found for the two-dimensional model when the ratio of the next nearest neighbor interaction is negative and for the simple cubic lattice with positive ratio of next nearest to nearest neighbor interaction.