Modeling the attenuated total reflectance infrared (ATR-FTIR) spectrum of apatite

Attenuated total reflectance (ATR) infrared spectra were measured on a synthetic and a natural fluorapatite sample. A modeling approach based on the computation of the Fresnel reflection coefficient between the ATR crystal and the powder sample was used to analyze the line shape of the spectra. The dielectric properties of the samples were related to those of pure fluorapatite using an effective medium approach, based on Maxwell-Garnett and Bruggeman models. The Bruggeman effective medium model leads to a very good agreement with the experimental data recorded on the synthetic fluorapatite sample. The poorer agreement observed on the natural sample suggests a more significant heterogeneity of the sample at a characteristic length scale larger than the mid-infrared characteristic wavelength, i.e., about 10 micrometers. The results demonstrate the prominent role of macroscopic electrostatic effects over fine details of the microscopic structure in determining the line shape of strong ATR bands.