Resonant frequency shifts related to the elastic constants near the alpha-beta transition in quartz

The resonant frequency shifts of vibrational modes are related to the elastic constants at various temperatures for the alpha-beta transition in quartz (T-c = 573.0 degrees C for alpha-quartz and 574.3 degrees C for beta-quartz). This correlation is constructed on the basis of the spectroscopic modifications of the Pippard relations near the alpha-beta transition in quartz by using the observed data from the literature