Temperature-compensated cuts for vibrating beam resonators of gallium orthophosphate GaPO4

A theoretical investigation of rectangular cross-section GaPO₄ vibrating beam resonators is proposed. Flexural modes are the basic vibrating mode of tuning forks used in quartz wrist watches, and can also be used as sensors. Very little work, if any, has been done for vibrating beam resonators in GaPO₄. The goal is then to investigate the possibility of temperature-compensated cuts for all three kinds of vibrations in GaPO₄: extensional, flexural, and torsional modes by analytical methods. Modeling temperature effects is achieved by the approximate but classical method of varying effective elastic constants, beam dimensions and crystal mass density versus temperature. Temperature-compensated cuts are found in GaPO₄ for length extensional modes and flexural modes. For vibrating beams, some of temperature-compensated cuts of GaPO₄ exhibit inversion points at high temperatures.