X-ray powder diffraction patterns of calcium phosphates analyzed by the Rietveld method.

Least-square refinement of x-ray powder diffraction patterns analyzed by the Rietveld method can yield structural information which had been unattainable or at least elaborate to obtain by conventional pattern analysis. The Rietveld method calculates a powder pattern on the basis of a structural model as well as the characteristics of the instrument used, and minimizes the differences between the intensities observed and the intensities calculated. The method is applied on patterns produced powders or polycrystalline solids on conventional powder diffractometers. For materials containing more than one crystalline phase with known structures such as hydroxyapatite (HA) and whitlockite (beta-TCP), pattern analysis yields phase quantification without internal or external standards. Refinement of the lattice parameters a0 and c0 determines the degree of dehydroxylation in plasma-sprayed HA coatings. The presence of amorphous Ca phosphates in HA coatings is detected by background modeling. The calculation of entire powder patterns allows discrimination of small concentrations of poorly crystallized Ca phosphate phases against the background, and prevents gross aberrations in estimating secondary phases. Even detect structures such as an OH-deficient HA lattice can be detected through slight differences in diffracted intensity by which the pattern calculated deviates from the pattern observed.