An analytical model for the evolution of the boundary of the new phase in transformations ruled by nucleation and growth is presented. Both homogeneous and heterogeneous nucleation have been considered: The former includes transformations in 2D and 3D space and the latter nucleation and growth on flat solid substrate. The theory is formulated for the general case of spatially correlated nuclei, arbitrary nucleation rate and power growth law of nuclei. In the case of heterogeneous nucleation, spheroidal nuclei have been assumed and the dependence of the kinetics on contact angle investigated. The validity of the present approach is deemed through comparison with experimental data from literature which also comprise oxide growth by ALD (Atomic Layer Deposition) metal electrodeposition at solid substrate and alloy recrystallization.

提出了一个新模型的边界演化的解析模型，该模型由成核和生长决定。已经考虑了均相和异相成核：前者包括在2D和3D空间中的转换，而后者包括在平坦的固体基底上的成核和生长。该理论是针对空间相关核，任意成核速率和核的功率增长定律的一般情况制定的。在异质成核的情况下，假设为球状核，并研究了动力学对接触角的依赖性。通过与文献中的实验数据进行比较，可以认为本方法的有效性，这些文献还包括在固体基材上通过ALD（原子层沉积）金属电沉积进行氧化物生长以及合金重结晶。