Hancock-Sharp equation

The most reliable way to find n is to use the method of Sharp and Hancock. This consists of taking logarithms of the Avrami-Erofe ev equation, to give... 

The gradient of this graph therefore permits the determination of n, and the intercept allows k to be calculated. The advantage of using a Sharp-Hancock plot rather than a least squares fitting process with the Avrami equation is that if Avrami kinetics are not applicable, this can be seen in the former plot, and hence other kinetic models may be investigated. Purely diffusion controlled processes can be identified using a Sharp-Hancock plot n is foimd to be 0.5 in such cases. 

The above equations summarize the three (3) diffusion mechanisms, one of which usually predominates in any given case (see 3.1.74.). But these equations contain quantities that are hard to measure, or even estimate. A much better way is to follow the method of Hancock and Sharp ( 1938). If one can measure x, the amount of reactant formed in time, t, then the following equation applies ... 

BaTiOj Kinetic Analysis. Utilization of the Hancock and Sharp modification of the Johnson-Mehl-Avrami analysis permits formation mechanism evaluation of an otherwise closed hydrothermal system(7,79). Through application of the following equation,... 

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