Extended theoretical analysis of crystallisation kinetics being studied by in situ XRD

Abstract

Theoretical simulations were used to study the consequences of simplifying the replacement of the step-wise in situ X-ray diffraction (XRD) temperature programme by simple linear heating (at corresponding effective heating rate) during the kinetic calculations based on the multivariate kinetic analysis. The simulations were performed for a large variety of step-wise non-isothermal in situ XRD temperature programmes, covering most practically used combinations of the temperature step magnitude Delta T, rate of heating, and duration of the isothermal hold Delta t. To achieve the universal interpretation of the obtained results, the behaviour of the majority of crystallisation processes with commonly encountered kinetic profiles was explored: simulations were performed for single-process transformations with highly negative, symmetric and highly positive asymmetries; complex multi-process reactions with different degrees of sub-process overlaps and variable activation energy were analysed. It was found that the asymmetry and shape of the crystallisation peaks do not significantly influence the level of distortion of kinetic parameters. The main factors that increase the errors of in situ XRD kinetic evaluations are high Delta t, high Delta T and high activation energy (with the latter two being most important). Findings were discussed for the accuracy of the corresponding kinetic predictions. Generalisation of the present conclusions towards their universal utilisation for optimisation of in situ XRD experiments was suggested.