Real and extended volumes in simultaneous transformations

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Abstract
The relationship between real and extended volumes is expanded to an indefinite number of simultaneous transformation processes. The assumption used in the present study is that the growth and nucleation of each product phase occurs randomly throughout the transforming region. The real volume of each phase is given in the form of an integral, using the extended volumes. Once the extended volumes of different product phases are related, the real volume of each product phase can be analytically or numerically calculated, and analytical solutions for cases where the extended volumes are related linearly or parabolically are given.