Sensitivity analysis for extraction of material constants for trigonal crystal classes

There have been a number of published results of the material constants of quartz and more recently, of langasite (LGS), langanite (LGN) and langatate (LGT). Many of the constants reported to date do not discuss the approach or inherent accuracies of their measurements. The stiffness parameter extraction can be obtained using well-known equations given velocity and density data. Assuming the known material density, four of the stiffness constants can be obtained directly from single mode velocity data in a given cut direction using time-echo measurement techniques and are only a function of the mode time delay measurement accuracy. However, c₁₄ and c₁₃ extraction are more complicated and must be obtained from multiple mode velocity measurements and calculations. In addition, there are several equations using different longitudinal and shear mode velocities that can be used for the parameter extraction of the stiffness constant. This indicates that the extraction is a function of the time delay measurement accuracy and the sensitivity to the velocities used in the calculations. Based on a sensitivity analysis, it is shown that it is best to use the equations using shear mode velocities, rather than longitudinal velocities, in calculations to reduce sensitivity to measurement inaccuracies