Infrared eigen frequency and debye θ of ionic crystals

Using a simplified Born-Mayer Potential, u=-∝e2z2/r +Mbe-σ(r/r0) an expression for the lattice frequency of ionic crystals in terms of cohesive energy, E has been obtained: ν= 1/2π(E/r02NMμ)½ [2σ(σ-2)/(σ-1)]½ A relation, very similar to one given by Blackman from lattice theory of specific heat, connecting Debye characteristic temperature, θ and compressibility, χ has also been derived: θ=h/k 1/2π (6r0/Xμ) ½ for NaCl type crystals and θ=h/k 1/2π (3.465r0/Xμ )½ for CsCl type crystals