Equation of State of Alkali Halides (NaCl)

Abstract

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 $A{e}^{-Br}$. The Grüneisen parameter ${\gamma }_i=-\frac{d\ln {\nu }_i}{d\ln V}$, where ${\nu }_i$ 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 ${\gamma }_i\text{'}\mathrm{s}$ are used in finding these quantities rather than the approximations made previously of utilizing the elastic constants and the moment expansion $\gamma \mathrm{}\left(S\right)=\frac{\Sigma i^{}{\gamma }_i{{\nu }_i}^s}{\Sigma i^{}{{\nu }_i}^s}=-\frac{\left(\frac{1}{S}\right)d\ln 〈{{\nu }_i}^s〉}{d\ln V}$, where $〈{{\nu }_i}^s〉$ is the $S\mathrm{th}$ moment of the frequency distribution. To check previous work by Barron and Blackman $\gamma \mathrm{}\left(0\right)\mathrm{}$, $\gamma \mathrm{}\left(2\right)\mathrm{}$, $\gamma \mathrm{}\left(1\right)\mathrm{}$, and $\gamma \mathrm{}(-3\mathrm{})\mathrm{}$ were calculated where $\gamma \mathrm{}\left(0\right)={\gamma }_{\infty }$, the high-temperature $\gamma$, and $\gamma \mathrm{}(-3\mathrm{})={\gamma }_0$, the low temperature $\gamma$. Fair agreement is found for $\gamma \mathrm{}(-3\mathrm{})\mathrm{}$, whereas the deviation in $\gamma \mathrm{}\left(2\right)\mathrm{}$ is high.