Crystallization is fundamental to materials science and is central to a variety of applications, ranging from the fabrication of silicon wafers for microelectronics to the determination of protein structures. The basic picture is that a crystal nucleates from a homogeneous fluid by a spontaneous fluctuation that kicks the system over a single free-energy barrier. However, it is becoming apparent that nucleation is often more complicated than this simple picture and, instead, can proceed via multiple transformations of metastable structures along the pathway to the thermodynamic minimum. In this article, we observe, characterize, and model crystallization pathways using DNA-coated colloids. We use optical microscopy to investigate the crystallization of a binary colloidal mixture with single-particle resolution. We observe classical one-step pathways and nonclassical two-step pathways that proceed via a solid–solid transformation of a crystal intermediate. We also use enhanced sampling to compute the free-energy landscapes corresponding to our experiments and show that both one- and two-step pathways are driven by thermodynamics alone. Specifically, the two-step solid–solid transition is governed by a competition between two different crystal phases with free energies that depend on the crystal size. These results extend our understanding of available pathways to crystallization, by showing that size-dependent thermodynamic forces can produce pathways with multiple crystal phases that interconvert without free-energy barriers and could provide approaches to controlling the self-assembly of materials made from colloids.

结晶是材料科学的基础，也是各种应用（从微电子硅晶片的制造到蛋白质结构的确定）的核心。基本情况是晶体通过自发波动从均质流体中形核，从而使系统在单个自由能垒上受力。然而，很明显的是，成核通常比这个简单的图更为复杂，取而代之的是，它可以通过亚稳结构的多次转化沿着热力学最小值进行。在本文中，我们使用涂有DNA的胶体观察，表征和建模结晶途径。我们使用光学显微镜研究具有单颗粒分辨率的二元胶体混合物的结晶。我们观察到经典的一步式路径和非经典的两步式路径，它们通过晶体中间体的固-固转化而进行。我们还使用增强的采样来计算与我们的实验相对应的自由能态势，并表明一步和两步路径均受热力学驱动。具体来说，两步固-固转变由两个不同晶体相之间的竞争所决定，自由能取决于晶体尺寸，这两个晶体相之间存在竞争。这些结果通过显示尺寸依赖的热力学力可以产生具有多个晶相的通道，这些相互变而没有自由能垒，并且可以提供控制由胶体制成的材料的自组装的方法，从而扩展了我们对可用的结晶途径的理解。