Nikishina Margarita A, Alexandrov Dmitri V
Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Ekaterinburg, 620000, Russian Federation.
Philos Trans A Math Phys Eng Sci. 2021 Sep 6;379(2205):20200306. doi: 10.1098/rsta.2020.0306. Epub 2021 Jul 19.
When describing the growth of crystal ensembles from metastable solutions or melts, a significant deviation from a spherical shape is often observed. Experimental data show that the shape of growing crystals can often be considered ellipsoidal. The new theoretical models describing the transient nucleation of ellipsoidal particles and their growth with and without fluctuating rates at the intermediate stage of bulk phase transitions in metastable systems are considered. The nonlinear transport (diffusivity) of ellipsoidal crystals in the space of their volumes is taken into account in the Fokker-Planck equation allowing for fluctuating growth rates. The complete analytical solutions of integro-differential models of kinetic and balance equations are found and analysed. Our solutions show that the desupercooling dynamics is several times faster for ellipsoidal crystals as compared to spherical particles. In addition, the crystal-volume distribution function is lower and shifted to larger particle volumes when considering the growth of ellipsoidal crystals. What is more, this function is monotonically increasing to the maximum crystal size in the absence of fluctuations and is a bell-shaped curve when such fluctuations are taken into account. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.
在描述从亚稳溶液或熔体中晶体聚集体的生长时，经常会观察到与球形有显著偏差的情况。实验数据表明，生长晶体的形状通常可视为椭圆形。本文考虑了新的理论模型，该模型描述了亚稳系统中体相转变中间阶段椭圆形颗粒的瞬态成核及其在生长速率有波动和无波动情况下的生长情况。福克 - 普朗克方程考虑了椭圆形晶体在其体积空间中的非线性输运（扩散率），并允许生长速率有波动。找到了并分析了动力学和平衡方程的积分 - 微分模型的完整解析解。我们的解表明，与球形颗粒相比，椭圆形晶体的过冷动力学要快几倍。此外，在考虑椭圆形晶体生长时，晶体体积分布函数更低且向更大颗粒体积偏移。而且，在没有波动的情况下，该函数单调增加至最大晶体尺寸，而在考虑这种波动时则是一条钟形曲线。本文是主题为“复杂系统中的输运现象（第1部分）”的一部分。
