结晶与玻璃化理论
Theory of Crystallization versus Vitrification
AI总结：
本文提出Arrow-Potts模型结合统一理论，解释玻璃材料中结晶与玻璃化竞争导致的非单调TTT图，并通过普适指数公式准确预测结晶时间尺度。
摘要：
在玻璃形成材料中，结晶与玻璃化之间的竞争表现为时间-温度转变（TTT）图中的非单调行为，该图量化了结晶时间尺度随温度的变化。我们开发了一个粗粒化晶格模型——Arrow-Potts模型，以探索这一竞争背后的物理机制。通过蒙特卡洛模拟，该模型展示了导致多晶结构的非单调TTT图，其中存在两个由晶体成核或生长分别限制的不同区域。在高温下，结晶受成核限制，导致致密晶粒的生长。在低温下，晶体生长受玻璃态动力学影响，并通过动态异质和层级弛豫路径进行，产生分形和枝状晶体。为解释这些现象，我们将Kolmogorov-Johnson-Mehl-Avrami理论与成核场论、晶体生长的随机游走理论以及玻璃态动力学的动态促进理论相结合。这一统一理论得出了一个解析公式，通过控制模型玻璃态动力学的普适指数，将结晶时间尺度与成核和生长速率联系起来。我们表明，具有普适指数的公式与蒙特卡洛模拟数据高度吻合，因此它也解释了模型产生的非单调TTT图。该模型和理论均可用于理解各种玻璃态系统中的结构有序化，包括块体金属玻璃合金、有机分子和胶体悬浮液。
英文摘要：
The competition between crystallization and vitrification in glass-forming materials manifests as a non-monotonic behavior in the time-temperature transformation (TTT) diagrams, which quantify the time scales for crystallization as a function of temperature. We develop a coarse-grained lattice model, the Arrow-Potts model, to explore the physics behind this competition. Using Monte Carlo simulations, the model showcases non-monotonic TTT diagrams resulting in polycrystalline structures, with two distinct regimes limited by either crystal nucleation or growth. At high temperatures, crystallization is limited by nucleation and results in the growth of compact crystal grains. At low temperatures, crystal growth is influenced by glassy dynamics, and proceeds through dynamically heterogeneous and hierarchical relaxation pathways producing fractal and ramified crystals. To explain these phenomena, we combine the Kolmogorov-Johnson-Mehl-Avrami theory with the field theory of nucleation, a random walk theory for crystal growth, and the dynamical facilitation theory for glassy dynamics. The unified theory yields an analytical formula relating crystallization timescale to the nucleation and growth rates through universal exponents governing glassy dynamics of the model. We show that the formula with the universal exponents yields excellent agreement with the Monte Carlo simulation data and thus, it also accounts for the non-monotonic TTT diagrams produced by the model. Both the model and theory can be used to understand structural ordering in various glassy systems including bulk metallic glass alloys, organic molecules, and colloidal suspensions.
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