Dependence of KCl:Li+and KBr:Li+Off-Center Behavior on Lattice Parameter

Abstract

Minimum-energy configurations for impurity displacements along the $〈111〉$ crystal axis in KBr:${\mathrm{Li}}^{+}$ and KCl:${\mathrm{Li}}^{+}$ systems were calculated over a range of lattice-parameter (LP) values: 3.200 to 3.315 Å for KBr:${\mathrm{Li}}^{+}$, and 3.070 to 3.180 Å for KCl:${\mathrm{Li}}^{+}$. The nearest-neighbor Born-Mayer model previously applied by the authors was utilized. The minimum-energy curves and configurations were found to be rather sensitive to the lattice parameter. Thus, in contrast to the room-temperature LP (3.293 Å) results for KBr:${\mathrm{Li}}^{+}$, where the $〈111〉$ off-center well was 0.015-eV deep, the depth for the liquid-helium LP (3.26 Å) was only 0.002 eV. The latter depth is comparable to the zero-point energy for ${\mathrm{Li}}^{+}$ vibration, indicating that the ${\mathrm{Li}}^{+}$ ion should not be localized at an off-center site at liquid-helium temperatures. This agrees with current experimental evidence at this temperature, which indicates that ${\mathrm{Li}}^{+}$ is on center in KBr; it also supports the low-barrier interpretation due to Bowen, Gomez, and Krumhansl for this system. Estimates are made of the dependence of the $〈111〉$ motional frequencies on lattice parameter and show that the frequencies are quite sensitive, in agreement with results due to Clayman, Nolt, and Sievers. For KCl:${\mathrm{Li}}^{+}$, the off-center configuration is found to persist for the liquid-helium-temperature KCl lattice parameter (3.117 Å). An applied hydrostatic pressure of 7 kbar is found to be sufficient to restore an on-center configuration. The electric field gradient at the ${\mathrm{Li}}^7$ nucleus was calculated over the entire range of KCl lattice parameter considered.