Acoustic symmetry and vibrational anharmonicity of rhombohedral ${\mathrm{Pb}}_5$${\mathrm{Ge}}_3$${\mathrm{O}}_{11}$ and ${\mathrm{Pb}}_{4.7}$${\mathrm{Ba}}_{0.3}$${\mathrm{Ge}}_3$${\mathrm{O}}_{11}$

Acoustic symmetry in crystals belonging to the rhombohedral 3¯ Laue group is discussed with special reference to the ultrasonic properties of ${\mathrm{Pb}}_5$ ${\mathrm{Ge}}_3$ ${\mathrm{O}}_{11}$. In this material the acoustic symmetry axes are so close to the crystallographic axes that its elastic behavior is essentially that of a 3¯m Laue group crystal. Ultrasonic wave velocities in single crystals of ${\mathrm{Pb}}_5$ ${\mathrm{Ge}}_3$ ${\mathrm{O}}_{11}$ and ${\mathrm{Pb}}_{4.7}$ ${\mathrm{Ba}}_{0.3}$ ${\mathrm{Ge}}_3$ ${\mathrm{O}}_{11}$ have been measured at room temperature as a function of hydrostatic pressure and uniaxial stress. Results have been used to obtain the second-order elastic constants and their hydrostatic pressure derivatives. By treating the materials as if they had 3¯m Laue symmetry, the 14 third-order elastic constants describing the third-order elasticity of crystals have also been determined. To quantify the vibrational anharmonicities of the long-wavelength acoustic modes, the mode Grüneisen parameters have been computed and are found to be positive. This finding indicates that there is no significant acoustic mode softening induced by incipient ferroelectric optic-phonon–acoustic-phonon interactions in these materials at room temperature, which is substantially below that at which the soft optic mode, ferroelectric phase transition takes place.