What are the interface acoustic modes of twins in quartz?

Interface acoustic waves (IAWs) at the boundaries of Dauphine and Brazil twins in quartz are studied using numerical and analytical techniques. It is assumed that the boundary is coincident with the YZ mirror plane of quartz. The numerical solution of the problem for Dauphine twins reveals that non-leaky waves exist only for the propagation directions within 0.02-degree deviations from the Y-axis. For the Y-propagation direction, the depth of wave localization is about 25 wavelengths, and the predominant displacement component at the boundary is shear-vertical, although all displacement components are present and they are comparable. For Brazil twins, the conditions of the existence of interface modes are less restricted but the depth of wave localization in the case of propagation along the Y-axis is about two times more than that for Dauphine twins. A possibility to derive the secular equation of the problem in explicit form by direct integrating the equations of motion is demonstrated in a particular case of IAW propagation along the Y-axis at the boundary of Dauphine twins, ignoring piezoelectricity. The analysis of this equation allows one to separate qualitatively the contributions of different elastic constants to the occurrence of IAWs