Temperature dependence of the Brillouin frequency shift in crystals

In order to find a theoretical expression which most faithfully reproduces the temperature dependence of the Brillouin frequency shift in crystals, we have performed stimulated Brillouin spectroscopy in two crystals of TeO2 and PbMoO4 as test crystals by using a high precision Brillouin spectrometer with the frequency resolution of 20 kHz. In general, the temperature dependence of a Brillouin shift in crystals not undergoing phase transitions exhibits a linear negative slope at high temperatures and an asymptotic approach with zero slopes at low temperatures. We have experimentally confirmed that this temperature dependence stems from the temperature change of the elastic constant rather than the thermal changes of the refractive index and the volume expansion coefficient. It has been found that the Lakkad function based on Debye model and the Varshni function based on the Einstein model both reproduce quite well the temperature dependence of the Brillouin frequency shift in crystals.