A theoretical basis for the Rabin-Klick criterion in terms of off-centre self-trapped-exciton relaxation

Rabin and Klick showed empirically that low-temperature F-centre formation in alkali halides is easy or hard depending on whether the value of a geometric ratio S/D is greater or less than 0.45. The authors show that a similar correlation holds between the ease of F-centre formation at low temperature and the value of a parameter Delta E 2 /( Delta E 1 + Delta E 2 ), where Delta E 1 and Delta E 2 are the calculated energies of odd-parity relaxation of the self-trapped exciton (STE) in modes that do not involve halogen pair translation and do involve halogen pair translation, respectively. These are the local relaxation modes used previously in calculation of the potential curves for on-centre-off-centre motion of the STE, and the values of Delta E 1 and Delta E 2 are obtained directly from such calculations for 12 alkali halides in the present work. The energy barrier that inhibits low-temperature F-centre formation is found to be comparable to the barrier already associated with thermally activated defect formation. That is, the barrier height against defect production does not change greatly from one side of the Rabin-Klick diagram to the other, in contrast to what was held to be the case in previous interpretations of the S/D parameter. What changes is the division of available STE relaxation energy between the productive and non-productive modes. This picture provides a unifying account of both thermally activated and low-temperature defect production in the alkali halides. Furthermore, this description of the Rabin-Klick diagram is based on a model in which low-temperature as well as high-temperature F-centre formation occurs on the lowest adiabatic potential surface connecting the STE pi -luminescent state and the F-H pair.