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The Determination of Direction-Dependent Crystallite Size and Strain by X-Ray Whole-Powder-Pattern Fitting

Abstract The procedure of whole-powder-pattern fitting without reference to a structural model has been applied to the determination of direction-dependent crystallite size and strain. The fitting function used is defined as the sum of (1) background intensity and (2) contributions from individual reflections given as the convolution of the observed instrumental function with the true data function in analytical form. Crystallite size and strain parameters are adjustable, together with unit-cell parameters and the integrated intensities of all reflections, during the whole-powder-pattern fitting. The procedure requires neither structural parameters nor intensity correction for preferred orientation in calculating profile intensity. The two models are incorporated for line broadening, one for isotropic size and strain effects and the other for the anisotropic size effect of cylindrical shape. The procedure has been tested for these two models using the observed data of 4 mole % Y2O3-doped tetragonal ZrO2 and hydroxyapatite, Ca5(PO4)3OH, respectively, and been shown to be effective for determining crystallite size and strain from the powder pattern with a relatively high peak density.