The determination of crystal size and disorder from the X-ray diffraction photograph of polymer fibres. 2. Modelling intensity profiles

Abstract

The intensity profile of the X-ray reflection from a crystalline material is related to the lattice disorder and the distribution of crystal sizes through its Fourier cosine coefficients. However, existing methods of obtaining these structural parameters from the coefficients require more than one order of reflection and this is seldom available with polymer fibres. They also rely heavily on the low-order harmonics which are those determined with least accuracy. The development and testing of a method which overcomes this weakness and which is suitable for use with a single order is described. The coefficients are calculated for a model with paracrystalline disorder and an assumed distribution of crystal sizes and the parameters describing this model are refined to minimize the discrepancy between the calculated and experimental values of the coefficients. Provided the distribution of lengths is asymmetric this discrepancy is no greater than would be expected from experimental error and so the assumed model cannot be rejected on the evidence available. Since a range of model parameters all gave equally good agreement with experiment, it was not possible with a single order to obtain a well defined set of values. Diffraction patterns displaying two orders had been chosen and results from the second order were consistent with the first, only a narrow range satisfying both simultaneously. The method was further developed by calculating the intensity profile from the harmonics and using this in the refinement. There was no advantage over using harmonics; indeed, on occasions the refinement algorithm was unstable producing unreliable results.

Crystallite size and shape in Twaron fibers heat treated at different temperatures using WAXS

“…For a paracrystalline material like Twaron fiber, A d (n) turns out to be a Gaussian strain distribution 13,14 :…”

PVA/NaCl/MgO nanocomposites-microstructural analysis by whole pattern fitting method

“…Incidentally, most of the methods depend upon multiple-order approach [13]. A multitude of these modelling designs enunciate the significance of line profile analysis [14].These studies embark on use of single-order method for analysis of microstructure [15]. The whole pattern fitting gives us more reliable microstructural parameters compared to other methods [16].…”

Crystal structure and elastic constants of Dharwar cotton fibre using WAXS data

“…We have used single order method (Hall and Somashekar 1991;Pope and Balzar 2002;Balzar 2004) to obtain crystal size and lattice strain, using an analytical function for the probability distribution, P(i). For this reason, we have chosen an asymmetric function (exponential distribution) to find out the finer details of the microstructural parameters of Dharwar cotton fibres (Somashekar and Somashekarappa 1997).…”