A geometrically generalized model of isothermal peritectic transformation

A geometrically generalized analysis of isothermal peritectic transformation based on the linearized concentration gradient approximation has been presented. The predictions of the present model, as compared with those by the earlier proposed ones, show a better agreement with the kinetic data from the Cd-Ag system. However, the computed kinetics differ from the observed rates beyond a certain limit, perhaps due to the variation in the shape and size of beta particles and/or depletion of the liquid phase under the experimental conditions. For an equivalent size (diameter or thickness) of the beta particles, the kinetics are progressively faster as the geometry of the particles changes from planar to cylindrical or spherical with the related solute flux assuming a 1-, 2- and 3-dimensional nature, respectively. A detailed parametric study reveals that the product (alpha) and alpha + beta field widths exert appreciable influence on the rate of beta consumption. Finally, a dimensionless parameter has been proposed to rationalize the process parameters and predict the lower limit of the time required for completion of the transformation for hyper-peritectic alloys without resorting to any lengthy calculation.