Disorder-induced piezoelectric and piezo-optic effects. I. The theory of the piezoelectric properties and its application to ice

Abstract

When a macroscopic elastic strain is applied to an isotropic disordered solid a dipole moment may be generated, but it is usually very small and averages to zero over an ensemble of similar samples. Disordered solids are, therefore, not usually considered as piezoelectric. However, each small volume element has no symmetry, and so a dipole moment is generated in it by an applied stress, but its effect is often not noticeable on a macroscopic scale, and a suitable probe is needed to detect it. Sound waves in typical solids have speeds of several kilometers per second, and sound waves having wavelengths of, say, 50 Å have frequencies of about 1 THz. The dipole moments generated in disordered solids by the spontaneously fluctuating stresses should, therefore, cause absorption of light in the far infrared, and the absorption allows these disorder-induced piezoelectric properties to be measured. The purpose of this paper is to develop the theory of the absorption of far-infrared light by the sound waves of disordered solids in terms of suitable disorder-induced piezoelectric moduli. The theory has been applied to the sound waves of ice and yields the value 50.4×10−6 D2 μm−3 bar−2 (cm s−1)−1 for the quantity d″2l/cl+2d″2t/ct, where d″2l and d″2t are the squared scalar moduli of the disorder-induced piezoelectric effect for longitudinal and transverse waves, respectively, and cl and ct are the speeds of longitudinal and transverse sound, respectively. If the absorption by the transverse waves is assumed to be negligible, the coefficient d″2l has the value 19.5 D2 μm−3 bar−2. A similar disorder-induced piezomagnetic effect should in principle cause a similar absorption, and a related disorder-induced piezo-optic effect should cause the sound waves in disordered solids to be Raman active.