The porosity dependence of the dielectric constant for sintered hydroxyapatite

Hydroxyapatite (HAp) is the major mineral constituent of bone, and as such, the dielectric properties of HAp are of interest because electromagnetic fields have been shown to accelerate healing in bone fractures. In addition, an interest in the dielectric properties of HAp stems from the suggestion that electrically insulating HAp coatings might be used on implantable devices. In this study, the dielectric constant of polycrystalline hexagonal HAp was measured at nine different frequencies, from 45 kHz to 7.3 MHz for relative porosities ranging from 0.05 to 0.42. At a fixed frequency, the decrease in k as a function of increasing porosity is described well by an exponential function of porosity such that k = k(0)exp(-bP), where k(0) is the dielectric constant at zero porosity and b is a constant. In addition, the entire data set of 108 data points (representing the 12 specimens of differing porosity measured at each of the nine frequencies) was fit to a candidate function formed from the product k(0)exp(-bP) and a simple expression relating frequency to the dielectric constant. The candidate function fit the data relatively well, with a coefficient of determination of 0.91.