Disorderhyphen;induced piezoelectric and piezohyphen;optic effects. I. The theory of the piezoelectric properties and its application to ice

摘要

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 Aring; 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 disorderhyphen;induced piezoelectric properties to be measured. The purpose of this paper is to develop the theory of the absorption of farhyphen;infrared light by the sound waves of disordered solids in terms of suitable disorderhyphen;induced piezoelectric moduli. The theory has been applied to the sound waves of ice and yields the value 50.4times;10minus;6D2thinsp;mgr;mminus;3thinsp;barminus;2(cmthinsp;sminus;1)minus;1for the quantitydPrime;2l/cl+2dPrime;2t/ct, wheredPrime;2landdPrime;2tare the squared scalar moduli of the disorderhyphen;induced piezoelectric effect for longitudinal and transverse waves, respectively, andclandctare the speeds of longitudinal and transverse sound, respectively. If the absorption by the transverse waves is assumed to be negligible, the coefficientdPrime;2lhas the value 19.5 D2thinsp;mgr;mminus;3thinsp;barminus;2. A similar disorderhyphen;induced piezomagnetic effect should in principle cause a similar absorption, and a related disorderhyphen;induced piezohyphen;optic effect should cause the sound waves in disordered solids to be Raman active.