Third-order elastic constants and acoustic mode vibrational anharmonicity of bismuth

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Abstract
The third-order elastic constants of single-crystal rhombohedral bismuth obtained at room temperature are found from measurements of the hydrostatic and uniaxial pressure dependences of ultrasonic wave velocities to be : C 111 = − 7·14, C 112,= 1·16. C 112=−l·78, C 114=−3·77, C 123,= −l·27, C 124=−0·70, C 132=−l·62, C 134 = 0·43, C 144=−0·50, C 155=−40·6, C 222= −5·77, C 233= −4·03, C 244=−0·95 and C 444=l·77, in units of 1011 Nm-2. Using the generalized Grüneisen theory in the quasiharmonic approximation, the high- and low-temperature limiting values of the mean Grüneisen gammas have been computed and together with the thermal expansion, are discussed in terms of the double-layer model for the A 7 structure. The pressure dependences of the second-order elastic constants indicate that the Bi1→Bi11 transition is unlikely to be a purely elastic one associated with acoustic-mode softening.