Reexamination of the Basic Theoretical Model for the Kinetics of Solid-State Reactions

The equations properly describing the diffusion–controlled reaction of a spherical particle to form a concentric spherical shell of product are set up then solved numerically and their predictions compared with those of the commonly used approximate models due to jander, Ginstling and Brounshtein, and Valensi or Carter. It is shown that the quasi‐steady‐state Ginstling and Brounshtein model correctly describes the kinetics of the process when the solute is of low solubility but becomes increasingly inaccurate as solubility increases; the Jander model gives almost identical predictions up to about 60% degree of converison. There is thus a range of problems of practical interst for which either the Jander or Ginstling and Brounshtein model gives an acceptable description of the shape of at least the early stages of the degree of reaction versus time curve, but these simple models do not then give the correct values of, for example, diffusivity from such curve fitting. The simple models are nevertheless suitable for determining whether a reaction is controlled by diffusion through the product layer or by reaction at the interface, provided that some important assumptions are satisfied.