Kinetics and microstructure of a transformation on a sphere

The evolution of a first-order phase transition in a non-Euclidean space, namely the surface of a sphere, is examined to highlight the role of geometry and spatial confinement on transition kinetics and the associated product microstructure. This is accomplished by investigating spatio-temporal correlations in the transforming system and geometrical features in the transformed microstructure via the calculation of non-equilibrium correlation functions and microstructural descriptors (i.e., moments of the grain-area distribution). From this analysis, the usual Kolmogorov-Johnson-Mehl-Avrami (KJMA) analysis of transformation kinetics and the resulting microstructural tessellation are generalized to this spherical geometry. Computer simulations of nucleation and growth processes are also employed to validate the theoretical description. Finally, our results are extended to characterize more complex nucleation conditions and geometries.