Sources of errors in nonlinear constants of crystals and their assessment

Abstract

Standard errors of third-order nonlinear material constants of a crystal, obtained by the least-squares fit, reflect only the errors from a single source. The source is the random errors in the experimental data used to determine the nonlinear constants. Other, hitherto disregarded, sources of errors are pointed out, namely the linear material constants of the crystal and the orientations of the crystal specimens used to produce the experimental data, and a method to assess their effect is suggested. The case investigated numerically concerns the third-order nonlinear electromechanical constants of α-quartz determined by the transit-time method. To minimize the effect of the errors mentioned, attention must be focused on the linear elastic constants. Standard errors of 1%–2% in the linear constants produce nontrivial errors in the nonlinear constants comparable in size to those due to experimental errors. The standard errors increase the traditionally calculated errors of the nonlinear constants by about 10%–40%, respectively. The errors caused by the remaining linear constants and by the orientation angles seem to be substantially less important.