Piezoelectric Constants of Alpha- and Beta-Quartz at Various Temperatures

摘要: The adiabatic piezoelectric constants ${d}_{11}$ and ${d}_{14}$ of alpha-quartz have been measured between room temperature 571.5\ifmmode^\circ\else\textdegree\fi{}C. At the latter temperature, is about one-half its value, whereas has increased by a factor almost three. 573\ifmmode^\circ\else\textdegree\fi{}C (the inversion temperature) crystal structure changes to that beta-quartz, vanishes. constant for beta-quartz 584\ifmmode^\circ\else\textdegree\fi{}C 626\ifmmode^\circ\else\textdegree\fi{}C. appears be substantially over this short range differs from at 570\ifmmode^\circ\else\textdegree\fi{}C only few percent. were deduced measurements (with $Q$-meter technique) equivalent circuits long thin bars driven electrically frequencies near resonance.