Temperature dependences of the third-order elastic constants and acoustic mode vibrational anharmonicity of vitreous silica

Measurements of the effect of uniaxial stress on ultrasonic wave velocities have been used to determine the temperature dependences of the third-order elastic stiffness tensor components (TOEC) of vitreous silica between 77 and 293 K. In the absence of such data previous practice has been to assume that these TOEC are independent of temperature; however a significant temperature dependence has been observed. With the exception of the smallest C 456, each of the TOEC is anomalously positive: a feature consistent with the well established aberrant negative values for the hydrostatic pressure derivatives (∂ C ij /α P) P=0 of the second-order elastic stiffness tensor components (which reveal softening of the long-wave-length acoustic modes under pressure). The TOEC increase as the temperature is reduced showing that the pressure-induced acoustic mode softening becomes enhanced at lower temperatures. The largest TOEC is C 111 which is 46.7 × 10 10 Pa at 293 K and increases to 99.1 × 10 10 Pa at 77 K. The hydrostatic pressure derivatives of the second-order stiffnesses have been calculated from the TOEC; (∂ C 11/∂ P) p=0 is much larger than (∂ C 44/∂ P) P=0 over the whole temperature range: the longitudinal acoustic mode softens more with pressure than the shear mode. This effect is emphasised by the finding that the acoustic mode Grüneisen parameters are negative with |γ L| > |γ S|. As the temperature is reduced the longitudinal acoustic mode Grüneisen parameter, γ L, increases in magnitude considerably, reaching a value of −5.5 at 77 K. The mean acoustic mode Grüneisen parameter, γ el, increases to a larger negative value (−3.1 at 77 K) than previously suspected on the basis of the assumption of temperature-independent third-order elastic constants: the discrepancy between the low-temperature limits of the thermal, γ th L, and mean acoustic mode, γ el L, Grüneisen parameters is not quite so large as had been thought. The vibrational anharmonicity of the acoustic modes plays an important part in causing the thermal expansion of vitreous silica to be negative at low temperatures.