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This study concerns the phase transformation kinetics and pertains to theprocesses of crystallisation of amorphous polymers, ceramics, and bulk metallicglasses (BMG), as well as solid state transformations by the nucleation andgrowth mechanism. It is also likely to be relevant to the description ofdissolution and precipitation processes, and more generally chemical reactionkinetics, as well as biochemical processes such as ligand binding, haemoglobinoxygenation, etc. The mathematical framework is examined of the of the 'knee'function, or K-function, and its implications are explored.

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