On the Hill and Kolmogorov statistics and the K-function representation of judiciously modified Avrami kinetics

This study concerns the phase transformation kinetics and pertains to the processes of crystallisation of amorphous polymers, ceramics, and bulk metallic glasses (BMG), as well as solid state transformations by the nucleation and growth mechanism. It is also likely to be relevant to the description of dissolution and precipitation processes, and more generally chemical reaction kinetics, as well as biochemical processes such as ligand binding, haemoglobin oxygenation, etc. The mathematical framework is examined of the of the ‘knee’ function, or K-function, and its implications are explored.