Anisotropy visualisation from X-ray diffraction of biological apatite in mixed phase calcified tissue samples

Abstract

X-ray diffraction is widely used to characterise the mineral component of calcified tissue. Broadening of the diffraction peaks yields valuable information on the size of coherently diffracting domains, sometimes loosely described as crystallite size or crystallinity. These domains are markedly anisotropic, hence a single number describing their size is misleading. We present a novel variation on a method for visualising crystallographic anisotropy in X-ray diffraction data. This provides an intuitively interpretable depiction of crystalline domain size and anisotropy. The new method involves creating a polar plot of calculated domain thickness for peaks in a diffractogram versus crystallographic direction. Points with the least error are emphasised. Anisotropic domain dimensions are calculated by refining an ellipsoidal model in a whole pattern fit. These dimensions are then used to overlay an ellipse on the peak broadening plot. This is illustrated by application of the method to calcifications in breast tissue with suspected cancer, which frequently contain whitlockite as well as nanocrystalline apatite. Like most biogenic apatite, this exhibits markedly anisotropic peak broadening. The nature of this anisotropy offers potentially useful information on normal function and pathology of calcified tissue and is a frequently neglected crystallographic feature of these materials.

Keywords: Anisotropy; Apatite; Hydroxyapatite; Whitlockite; X-ray diffraction.

Fig. 1

Diffractograms after background subtraction, showing the measured intensity in black, and the fitted pattern as a dashed red line. This is composed of 24 fitted apatite peaks individually refined for intensity, width and Lorentzian mixing factor, shown in blue.

Fig. 2

Diffractogram of a calcification containing 20 wt% whitlockite. The inset view of the 002 apatite peak and the 1 0 10 whitlockite peak shows the potential for confounding if the whitlockite peak is not included in the fit.

Fig. 3

Polar plot showing calculated domain thickness for each of 24 apatite peaks as a function of crystallographic direction, overlaid with an ellipse representing the domain dimensions calculated from an ellipsoidal whole pattern fit. The diameter of the plotted points is inversely proportional to the calculated error in peak width measurement. FWHM values used to calculate both the point positions and the ellipsoidal fit were corrected for instrumental broadening.

Fig. 4

2D kernel-density plot of ellipsoidal domain dimensions for 4125 diffractograms measured from taken from 259 calcifications.

Fig. 5

Polar plot similar to Fig. 3, showing the fit for calcifications close to the extremes of aspect ratio for these specimens.