Equation of State of Alkali Halides (NaCl)

The equation of state of NaCl is given using the Kellermann model of NaCl as well as a modified model making use of a repulsive potential energy of the Born-Mayer form Ae^-Br. The Gr\"uneisen parameter γᵢ=-dlnνᵢdlnV, where νᵢ is the normal mode frequency and V is the volume, is derived by the development of a perturbation method in the volume. This is then used where needed to calculate all thermodynamic quantities of interest using an IBM 7090. A spectrum of 11 454 frequencies and γᵢ's are used in finding these quantities rather than the approximations made previously of utilizing the elastic constants and the moment expansion ${γ}(S)={{Σ}{i}^{}{{γ}}ᵢ{{{ν}}ᵢ}ˢ}{{Σ}{i}^{}{{{ν}}ᵢ}ˢ}={-}{(1/S)dln〈{{{ν}}ᵢ}ˢ〉}{dlnV}$, where $〈{{{ν}}ᵢ}ˢ〉$ is the $Sth$ moment of the frequency distribution. To check previous work by Barron and Blackman ${γ}(0)$, ${γ}(2)$, ${γ}(1)$, and ${γ}({-}3)$ were calculated where ${γ}(0)={{γ}}_{{∞}}$, the high-temperature ${γ}$, and ${γ}({-}3)={{γ}}₀$, the low temperature ${γ}$. Fair agreement is found for ${γ}({-}3)$, whereas the deviation in ${γ}(2)$ is high.