A Determination of the Adiabatic Elastic Constants of Quartz

If the elastic constants of a homogeneous, anisotropic material are known, it is possible to calculate the theoretical frequencies of the different modes of vibration between the faces of an infinite plate of the material. Conversely, knowing the frequencies of sufficient modes of vibration, it is possible to calculate the elastic constants. The frequencies of vibration of higher harmonics of finite plates, divided by the order of the harmonic, should approach very close to the frequency of the theoretical infinite plate. Plates of quartz were accurately oriented and cut from well-developed, flaw-free quartz crystals and the frequencies of higher harmonic piezo-electric vibrations were accurately determined. With this information, the six adiabatic elastic constants of quartz were evaluated