In melt crystallization, how the cooling rate and initial concentration affect metastable zone width (MSZW), thus altering the impurity distribution coefficient, remains elusive. To explore the above problem, the layered melting crystallization of 4,5-dimethyl-1,3-dioxol-2-one is taken as a research case here. In this work, first, we show that when the composition decreases or the cooling rate increases, the value of interfacial energy (γ) increases and the pre-exponential factor (A) decreases, leading to a wider MSZW. Second, the faster the cooling rate or the higher the impurity content of the raw material, more impurity will be entrapped in the crystal layer, leading to a larger impurity distribution coefficient. More interestingly, we found that the relationship between K_BS and K_AS is linear for K_AS = 0.422 to 0.875 within the cooling rate 1–40 K/h, which increases with the increase of cooling rate and tends to be consistent. Finally, we highlight that the essential relationship between the impurity distribution coefficient before and after sweating is a straight line and unless the impurity distribution in the cooling stage reaches 0.377, it is impossible to obtain the product that approaches 100% purity through sweating.

中文翻译：

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层状熔融结晶中成核和杂质迁移行为的关键作用：4,5-二甲基-1,3-二氧杂环戊醇-2-酮的案例研究

在熔体结晶中，​​冷却速率和初始浓度如何影响亚稳区宽度（MSZW），从而改变杂质分布系数，仍然是一个难以捉摸的问题。为了探讨上述问题，本文以4,5-二甲基-1,3-间二氧杂环己烷-2-酮的分层熔融结晶作为研究案例。在这项工作中，首先，我们表明，当成分减少或冷却速率增加时，界面能（γ）值增加，指前因子（A）减小，导致更宽的MSZW。其次，冷却速度越快或原料的杂质含量越高，就会有更多的杂质被截留在晶层中，从而导致杂质分配系数越大。更有趣的是，我们发现，在冷却速率1-40 K/h内， K _BS和K _{AS之间的关系在}K _AS = 0.422 至0.875之间呈线性关系，并且随着冷却速率的增加而增加，并且趋于一致。最后我们强调，发汗前后的杂质分布系数本质上是一条直线关系，除非冷却阶段的杂质分布达到0.377，否则不可能通过发汗获得接近100%纯度的产品。