The nucleation of crystals from liquid melt is often characterized by a competition between different crystalline structures or polymorphs and can result in nuclei with heterogeneous compositions. These mixed-phase nuclei can display nontrivial spatial arrangements, such as layered and onionlike structures, whose composition varies according to the radial distance, and which so far have been explained on the basis of bulk and surface free-energy differences between the competing phases. Here we extend the generality of these nonclassical nucleation processes, showing that layered and onionlike structures can emerge solely based on structural fluctuations even in the absence of free-energy differences. We consider two examples of competing crystalline structures, hcp and fcc forming in hard spheres relevant for repulsive colloids and dense liquids, and the cubic and hexagonal diamond forming in water relevant also for other group 14 elements such as carbon and silicon. We introduce a novel structural order parameter that combined with a neural-network classification scheme allows us to study the properties of the growing nucleus from the early stages of nucleation. We find that small nuclei have distinct size fluctuations and compositions from the nuclei that emerge from the growth stage. The transition between these two regimes is characterized by the formation of onionlike structures, in which the composition changes with the distance from the center of the nucleus, similar to what is seen in the two-step nucleation process.

中文翻译：

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堆积无序晶体中的非经典成核途径

来自液态熔体的晶体成核通常以不同晶体结构或多晶型物之间的竞争为特征，并可能导致具有异质成分的晶核。这些混合相核可以显示出非平凡的空间排列，例如层状和洋葱状结构，其组成根据径向距离而变化，并且迄今为止已根据竞争相之间的体积和表面自由能差异进行了解释。在这里，我们扩展了这些非经典成核过程的一般性，表明即使在没有自由能差异的情况下，分层和洋葱状结构也可以仅基于结构波动而出现。我们考虑两个竞争晶体结构的例子，hcp 和 fcc 在与排斥胶体和稠密液体相关的硬球中形成，在水中形成的立方体和六角形金刚石也与其他 14 族元素（如碳和硅）有关。我们引入了一种新的结构顺序参数，该参数与神经网络分类方案相结合，使我们能够从成核的早期阶段研究生长核的特性。我们发现小核与从生长阶段出现的核具有明显的大小波动和组成。这两种状态之间的过渡以形成洋葱状结构为特征，其中成分随着距核中心的距离而变化，类似于两步成核过程中所见。我们引入了一种新的结构顺序参数，该参数与神经网络分类方案相结合，使我们能够从成核的早期阶段研究生长核的特性。我们发现小核与从生长阶段出现的核具有明显的大小波动和组成。这两种状态之间的过渡以形成洋葱状结构为特征，其中成分随着距核中心的距离而变化，类似于两步成核过程中所见。我们引入了一种新的结构顺序参数，该参数与神经网络分类方案相结合，使我们能够从成核的早期阶段研究生长核的特性。我们发现小核与从生长阶段出现的核具有明显的大小波动和组成。这两种状态之间的过渡以形成洋葱状结构为特征，其中成分随着距核中心的距离而变化，类似于两步成核过程中所见。