Low-temperature thermoelastic effects in glasses

Abstract

Thermoeiastic effects have been studied in vitreous silica and in polymethyl methacrylate (PMMA) by measuring the temperature response of a sample subjected to strain. Both ramp and sinusoidal strains were used, the latter covering the frequency range 0·01 to 10 Hz, in the temperature range 0·5 to 10 K.

The temperature changes induced by applying and removing the strain over a time interval Δt, typically 0·1 s (the ramp strains), were analysed into sunn and difference terms, representing the symmetric and antisymmetric responses respectively. Antisymmetric changes give values of the Gruneisen function y which agree well with values derived from thermal-expansion experiments in silica above 4 K and in PMMA above 2 K. At lower temperatures, the antisymmetric response is swamped by the symmetric term which measures irreversible processes. The magnitude of the losses increases with decreasing Δt, but, by assuming a microscopic model based on two-level states, this behaviour can be explained, and leads to values of Q ⁻¹ which are in good agreement with existing theory.

Sinusoidal strains give not only a steady increase of sample temperature from which an alternative and consistent value of Q ⁻¹ can be found, but also a periodic temperature response at the fundamental and second harmonic frequencies. The fundamental component gives a value for γ which agrees with thermal measurements above 1 K but increases in magnitude more rapidly with decreasing temperature below 1 K, reaching a value of - 80 at 0·5 K. γ shows a marked strain dependence, decreasing in magnitude when a steady-bias tension is applied, and reversing its sign below 1 K at strains greater than 10⁻⁴. The second harmonic arises as a result of irreversibility, and the amplitude is consistent with the other measurements of Q ⁻¹.

The results for Q ⁻¹ can be interpreted in terms of the tunnelling model of glasses to give, estimates for the magnitude of the coupling between tunnelling states and phonons which are in good agreement with high-frequency acoustic measurements. In contrast, the results for γ are not completely understood.