A fitting method for the determination of crystallinity by means of X-ray diffraction

A best-fitting version of the X-ray diffraction method of Gehrke & Zachmann [Makromol. Chem. (1981). 182, 627–635] for crystallinity determination, which is a modification of the method developed by Ruland [Acta Cryst. (1961). 14, 1180–1185], is presented. The data, corrected and normalized to electron units (e.u.), are plotted as I(s)s² vs s and fitted by pseudo-Voigt functions for the crystalline peaks added to a background scattering I_B(s)s², with I_B(s) = (1 − X_c)I_am(s) + X_c〈f(s)²〉[1 − exp(−ks²)], where I_am is the experimental intensity of a completely amorphous sample (also corrected and normalized to e.u.), 〈f(s)²〉 is the mean square atomic scattering factor in the material, X_c is the degree of crystallinity and k is a factor which includes either thermal or lattice disorder, where s = 2(sin θ)/λ. The use of the scattering of the amorphous sample in this non-integral form of the Ruland equations overcomes the problem, encountered with other procedures, of locating the continuous (background) scattering with accuracy. The degree of crystallinity and the disorder factor are supplied directly by the optimization process. Furthermore, the line broadening analysis which allows the determination of crystallite size is automatically obtained as a by product. Samples of polyethylene terephthalate (PET) with different degrees of crystallinity are investigated. The results are compared with those obtained by other methods which do not use fitting techniques.