IR spectroscopy of alkali halides at very high pressures: Calculation of equations of state and of the response of bulk moduli to theB1−B2phase transition

Abstract

New infrared (IR) data on NaF, NaCl, KCl, KBr, and KI were obtained at pressures of up to 42 GPa. The large $(\ensuremath{\sim}20%)$ drops in vibrational frequencies of alkali halides upon transformation of the $B1$ phase to $B2$ are due to the decrease in bond strength as ionic separation increases, and strongly suggest that the bulk modulus ${K}_{T}$ generally decreases during the transition, rather than increases, as commonly accepted. Bulk moduli and equations of state for $B1$ phases are obtained from one initial volume ${V}_{0}$ and our vibrational frequencies ${\ensuremath{\nu}}_{i}(P)$ using a semiempirical model (previous IR data are used for Rb halides). For substances with a cation radius that is greater than 0.6 times the anion radius, initial values ${K}_{0}$ are within 0.4 to 5% of ultrasonic determinations: thus, this model is accurate for cases where quantum mechanical calculations falter. The converse holds for relatively small cations. Curvature of ${K}_{T}$ with pressure matches the previous determinations even if ${K}_{0}$ is not precisely predicted, which allows determination not only of ${K}_{0}^{\ensuremath{'}},$ but also of ${K}_{0}^{\ensuremath{''}},$ which is generally poorly constrained. Care must be taken in specifying the equation of state, as values for both ${K}_{0}^{\ensuremath{'}}$ and ${K}_{0}^{\ensuremath{''}}$ are affected by the format chosen. For the $B2$ phases, $V(P)$ and ${K}_{T}(P)$ are constrained through similar calculations which utilize the volume at the transition as the starting point. Our results are unaffected by shear stress, in contrast to previous x-ray determinations for $B2.$ After transformation at 32 GPa, ${K}_{T}$ of NaCl-$B2$ is $119\ifmmode\pm\else\textpm\fi{}4\mathrm{GPa},$ $16\ifmmode\pm\else\textpm\fi{}3%$ below that of $B1.$ ${K}_{T}(P)$ of $B2$ rises steadily (${K}^{\ensuremath{'}}$ is fairly large, $4.7\ifmmode\pm\else\textpm\fi{}0.3$) resulting in a \ensuremath{\lambda} curve. Results derived for KCl, KBr, and KI are similar such that $K(P)$ of their $B2$ phases are better constrained than those of $B1$ due to larger stability fields. For the Rb halides, ${K}_{T}$ is roughly constant across the phase change. The compositional dependence of the changes in frequency, ${K}_{T},$ and $V$ for alkali halides are compatible with a simple ball-and-spring model. The calculated $B2$ phase volumes of the Na halide are infinite at 1 atm, consistent with instability below 8 GPa, which suggests that theoretical calculations should avoid use of 1 atm starting points for the high-pressure $B2$ phases.