Real and extended volumes in simultaneous transformations

The relationship between real and extended volumes is expanded to an indefi nite number of simultaneous transformation processes. The assumption used i n the present study is that the growth and nucleation of each product phase occurs randomly throughout the transforming region. The real volume of eac h phase is given in the form of an integral, using the extended volumes. On ce the extended volumes of different product phases ale related the real vo lume of each product phase cart be analytically or numerically calculated, and analytical solutions for cases where the extended volumes are related l inearly or parabolically are given.