Oblique acoustic axes in trigonal crystals

A general analysis on the subject of acoustic axes for bulk acoustic waves in trigonal crystals is presented. It is shown that the effect of piezoelectricity increases the maximum allowable number of acoustic axes in the plane of elastic symmetry from three to five for trigonal crystals of class 3m, and from 3 to 7 for trigonal crystals of class 32. The theory of acoustic axes of general orientation developed by Khatkevich (1962) is revised. A new, simpler and more general derivation of the conditions for the occurrence of acoustic axes of general orientation in crystals is presented. It is found that the previous analytical results and conclusions stating the absence of such axes in trigonal crystals are incorrect. New correct equations for acoustic axes of general orientation in trigonal nonpiezoelectric crystals are derived and confirmed by independent numerical calculations. Acoustic axes of general orientation oblique to the elastic symmetry planes are found to exist in berlinite (class 32) and in nonpiezoelectric lithium niobate (class 3m), however piezoelectricity eliminates these axes in the latter crystal. Some illustrative examples of the relationship between leaky surface acoustic wave branches and acoustic axes in trigonal crystals axe given.