A critical force constant of the structural phase transition in quartz

Long wavelength optical phonons of quartz were analyzed by a Born-Von Karman model not previously used. It was found that only one force constant associated with the turning of the Si-O bonds has a critical effect on the soft-mode frequency and the α-β transition in quartz. The square of the soft-mode frequency was found to depend linearly on this force constant which has the temperature dependence K(T)= -5.33+225.3x10-4(851-T)2/3 in units of 104 dyn/cm2.