Mathematical Model
Numerical analysis of X-ray diffraction patterns from natural fibres employs a mathematical approximation that combines Gaussian and Lorentzian profile shapes. This mathematical equation is the pseudo-Voigt function, which is utilized to model the complex shape of diffraction peaks.
Peak Profile
Applying this curve-fitting method to cellulose diffraction data allows the separation of overlapping peaks and the calculation of crystalline parameters. Within the analysis software, the pseudo-Voigt function adjusts its shape parameters to match the experimental data points of the 200 reflection. This fitting process is required because bast fibres present highly asymmetric profiles due to their complex semicrystalline nature.
The calculated peak widths are recorded in the laboratory database to track differences in fibre crystallinity across various batches of raw flax.
Analytical Outcome
Accurate peak fitting is necessary to ensure that the crystallinity index calculations are repeatable across different laboratories and spinning mills. When using the pseudo-Voigt function, the software can isolate the amorphous background from the crystalline scattering with high precision. This limits the errors caused by manual baseline selection and provides the mill with a reliable measure of fibre quality.
The resulting data helps the technical team optimize the bleaching process to avoid degrading the crystalline regions of the cellulose.