Infrared eigen frequency and debye θ of ionic crystals

Abstract

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/r_0²NMμ)^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.