Abstract Equations for the transformed volume fraction of a spherical particle with nucleation on its surface, both nonisothermal and isothermal, are derived in the framework of Kolmogorov method adapted for this problem. Characteristic parameters governing the transformation kinetics are determined; the latter is studied with particular emphasis on the Avrami exponent temporal behavior. It is shown that the surface-nucleated transformation qualitatively differs from the bulk-nucleated one at large values of the characteristic parameters due to the one-dimensional radial growth of a new phase occurring after the complete transformation of the surface itself at the early stage of the process. This effect also manifests itself in the considered ensemble of size-distributed particles and in grain-boundary nucleated transformations. The logarithmic normal distribution inherent for the particles obtained by grinding is employed for numerical calculations and shown to stretch temporally the volume-fraction and Avrami-exponent dependences for the ensemble of identical particles. A new model for grain-boundary nucleated transformations alternative to the Cahn model of random planes is offered; it is based on the ensemble of size-distributed spherical particles with the possibility for a growing nucleus to cross grain boundaries. Transformation kinetics in the present model qualitatively differs from that of the Cahn model. In particular, the double-logarithmic volume-fraction plot at large values of the governing parameter ends by a characteristic bend observed on experimental curves for the crystallization of bulk metallic glasses. Originating from the closed geometry of grain boundaries and the one-dimensional radial growth of a new phase, this bend together with the form of the plot as a whole directly indicates to the grain (polycluster) structure of metallic glasses and nucleation at intercluster boundaries.

中文翻译：

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球形粒子表面成核转变的动力学和晶界成核转变的新模型

摘要 在适用于该问题的 Kolmogorov 方法的框架内，导出了表面成核的球形粒子的转换体积分数方程，包括非等温和等温的。确定控制转化动力学的特征参数；后者的研究重点是 Avrami 指数时间行为。结果表明，表面形核转变在特征参数值较大时与体形核转变在性质上不同，这是由于在表面本身在早期阶段完全转变后发生的新相的一维径向生长。过程。这种效应也体现在所考虑的尺寸分布粒子的整体和晶界成核转变中。通过研磨获得的颗粒固有的对数正态分布用于数值计算，并显示出在时间上拉伸相同颗粒集合的体积分数和 Avrami 指数依赖性。提供了一种新的晶界成核变换模型，可替代随机平面的 Cahn 模型；它基于尺寸分布的球形颗粒的集合，并且有可能使生长的核跨越晶界。本模型中的转化动力学与 Cahn 模型的转化动力学性质不同。特别是，大控制参数值下的双对数体积分数图以在块状金属玻璃结晶的实验曲线上观察到的特征弯曲结束。