Microstructural paths of shape-preserved nucleation and growth transformations

Microstructural Path Analysis of Martensite Dimensions in FeNiC and FeC Alloys

“…DeHoff introduced the concept of microstructural path to characterize the sequence of states that a system goes through during a phase transformation. His idea was subsequently developed into a fully-fledged analytical methodology, the microstructural path method, MPM, by Vandermeer and co-workers 17 . The microstructural path method has been employed in recrystallization as well as in diffusional transformation studies.…”

On the Specific Area of Inhomogeneous Boolean Models. Existence Results and Applications

“…Many real phenomena as crystallization processes (Vandermeer et al, 1991;Capasso, 2003, and references therein), tumor growth (Anderson, 2003), etc., may be modelled as evolving random closed sets, that is as full dimensional time dependent random closed sets. In particular, any real situation in which nuclei are born in time and are located in space randomly, and each nucleus generates a grain evolving in time according to a given growth law, may be modelled as space-time structured stochastic birthand-growth processes.…”

“…Notice that such a model may be used to describe real situations in which the growth model is assumed to be such that the shape of the grains is preserved during the process (e.g., prolates and spheroids in Vandermeer et al, 1991). Clearly, the particular case of spherical growth (which corresponds to the previous growth model with G = G(t)), can be described also by means of the present model with Z 0 (T n ) = B R(T n ,t) (0), where R(T n ,t) = t T n G(s) ds.…”

Simulation of recrystallization in iron single crystals

“…Moreover, JMAK's theory was subsequently extended by DeHoff and Gokhale [9][10][11][12] , who proposed the use of an additional microstructural measure, namely, the interfacial area per unit of volume between transformed and untransformed regions, S V , and the associated kinetic concept of microstructural path. Vandermeer and coworkers 13 extended that concept in a theoretical treatment covering variable nucleation and growth rates, as well as inclusion of non-spherical regions. They called their extended analysis the microstructural path method (MPM).…”