Measurements of the dynamic piezoelectric properties of bone as a function of temperature and humidity

Abstract

The utilization of piezoelectricity as a clinical or diagnostic tool in medicine and dentistry is dependent upon an adequate quantitative description of the piezoelectric coefficients. Here, measurements of the dynamic piezoelectric d constant, d ∗ = d′ − id″ , for bovine bone are presented as a function of temperature (20–60°C), relative humidity (r.h.) (33–98%), frequency of applied stress (10 −2–10 2 Hz). and sample orientation. The anisotropic character of cortical bone requires that d be expressed as a matrix containing 18 coefficients. Dispersion phenomena, i.e. d″ ≠ 0, are present in these coefficients for our frequency-temperature-r.h. range. At low r.h. (≤75%), d 12 and d 13 show little or no dispersion ( d″ = 0), whereas varying degrees of relaxation are observed in the other coefficients. The d 14 shear term is notable for a large dispersion at f = 40 Hz, T = 38.6°C and 55% r.h., for which d″ 14 is negative. The negative imaginary coefficient means that energy is being gained in the 14 coefficient. The change in d 14, with a change in temperature and/or r.h., is attributed to a change in sample water content. For 98% r.h., the low frequency data ( f < 10 Hz) are dominated by a polarization which varies as the reciprocal of the frequency. This polarization is attributed to an interfacial or Maxwell-Wagner polarization which occurs as a result of ionic conduction under the influence of the piezoelectric polarization field.