Valensi, Carter

Valensi C ) earlier developed the same solid-state reaction model mathematically from a different starting point. Thus Eq. (9) is referred to as the Valensi-Carter equation. 

This formula is a generahzation of the Valensi-Carter law [VAL 31] (see section 10.2.2), with a stoichiometry ratio of the mixture other than 1, and in the cases in which grains C can have any size and position with respect to grains A. 

Hulbert [77] discusses the consequences of the relatively large concentrations of lattice imperfections, including, perhaps, metastable phases and structural deformations, which may be present at the commencement of reaction but later diminish in concentration and importance. If it is assumed [475] that the rate of defect removal is inversely proportional to time (the Tammann treatment) and this effect is incorporated in the Valensi [470]—Carter [474] approach it is found that eqn. (12) is modified by replacement of t by In t. This equation is obeyed [77] by many spinel formation reactions. Zuravlev et al. [476] introduced the postulate that the rate of interface advance under diffusion control was also proportional to the amount of unreacted substance present and, assuming a contracting sphere (radius r) model... 

The Carter-Valensi equation was not used in analyzing the data, due... 

Some laws result from the preceding ones by sinqjle modification of the geometiy of the sample hence, Valensi and Carter (see section 10.2.2) switched from plane samples to cylinders and spheres and introduced the coefficient of... 

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