Abstract This paper presents an extension of a classical model of the crystal growth, the Burton–Cabrera–Frank (BCF) model, to a system that includes impurity molecules and discusses the formulation of the amount of the impurity uptake into the crystal as a partition coefficient. The BCF model considers the following surface processes of host molecules: adsorption from a solution to a terrace, desorption from the terrace to the solution, surface diffusion on the terrace, incorporation at a step edge, and release from the step edge to the terrace. The above-mentioned processes have been formulated not only for the host molecules but also for the impurity molecules (Miura, 2020). In this paper, the author analytically solves the previous model and derives an analytic formula for the partition coefficient as a ratio of the uptake of the impurity molecule to that of the host molecule into the crystal. The dependence of the partition coefficient on supersaturation is systematically investigated. The analytic formula is applied to the data obtained in the experiments of protein crystal growth to discuss the behavior of impurity molecules on the growing crystal surface. This model provides a theoretical framework for eliciting quantitative data from the crystal growth experiments on impurity partitioning.

中文翻译：

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基于 Burton-Cabrera-Frank 模型的生长晶体中杂质分配系数的公式化

摘要 本文将晶体生长的经典模型 Burton-Cabrera-Frank (BCF) 模型扩展到包含杂质分子的系统，并讨论了作为分区的晶体吸收杂质量的公式。系数。BCF模型考虑了主体分子的以下表面过程：从溶液到平台的吸附，从平台到溶液的解吸，平台上的表面扩散，台阶边缘的结合，以及从台阶边缘到平台的释放。上述过程不仅适用于主体分子，还适用于杂质分子（Miura，2020）。在本文中，作者对之前的模型进行了解析求解，并推导出了分配系数的解析公式，即杂质分子与主体分子进入晶体的吸收率之比。系统地研究了分配系数对过饱和度的依赖性。将解析公式应用于蛋白质晶体生长实验中获得的数据，讨论杂质分子在生长晶体表面的行为。该模型提供了一个理论框架，用于从杂质分配的晶体生长实验中得出定量数据。将解析公式应用于蛋白质晶体生长实验中获得的数据，讨论杂质分子在生长晶体表面的行为。该模型提供了一个理论框架，用于从杂质分配的晶体生长实验中得出定量数据。将解析公式应用于蛋白质晶体生长实验中获得的数据，讨论杂质分子在生长晶体表面的行为。该模型提供了一个理论框架，用于从杂质分配的晶体生长实验中得出定量数据。