  The overall solid-to-solid phase transformation kinetics under non-isothermal
conditions has been modeled by means of a differential equation method. The
method requires provisions for expressions of the fraction of the transformed
phase in equilibrium condition and the relaxation time for transition as
functions of temperature. The thermal history is an input to the model. We have
used the method to calculate the time/temperature variation of the volume
fraction of the favored phase in the alpha-to-beta transition in a zirconium
alloy under heating and cooling, in agreement with experimental results. We
also present a formulation that accounts for both additive and non-additive
phase transformation processes. Moreover, a method based on the concept of path
integral, which considers all the possible paths in thermal histories to reach
the final state, is suggested.
