There has long been a question concerning the existence of a single vs. multiple asymptotic grain size distributions in normal grain growth. The goal of this study has been to address this topic by investigating the underlying mechanisms by which grain face and volume distributions evolve from transient to asymptotic states during grain growth. This investigation employs 3D Monte Carlo simulations to quantify the topological mechanisms of this transition, i.e., grain separation, encounter and loss, and examine their mutual evolution with the distributions from a wide range of initial states towards their multiple final asymptotic states. In the initial transient growth stage, the topological event rates fluctuate markedly, seeking balance among themselves and with the face/volume distributions. In the asymptotic stage this balance is indicated by asymptotic behavior of the ratios of the rates, as well the mean face class 〈, and normalized widths, , of the face and size distributions. It was found that a moderate range of initial distributions evolved through relatively short transient periods towards asymptotic states less spread from each other but with those same relative orders of width. Initial distributions much wider or narrower than these evolved through longer transient periods with trajectories crossing the paths of the more moderate ones, with the widest initial distributions becoming the narrowest and the initially narrowest becoming the widest. These behaviors are explained by their interactive evolution with the topological event rates.

中文翻译：

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晶粒生长过程中多个渐近晶面和体积分布的演化-与拓扑事件率的初始分布和渐近稳定的联系

长期以来，人们一直对正常晶粒生长中是否存在单一渐近晶粒尺寸分布和多重渐近晶粒尺寸分布存在疑问。本研究的目的是通过研究晶粒生长过程中晶粒面和体积分布从瞬态演化到渐近态的基本机制来解决这个主题。本研究采用 3D 蒙特卡罗模拟来量化这种转变的拓扑机制，即晶粒分离、相遇和损失，并检查它们从各种初始状态到多个最终渐近状态的分布的相互演化。在最初的瞬态生长阶段，拓扑事件率波动显着，寻求自身之间以及面/体积分布的平衡。在渐进阶段，这种平衡由比率比率的渐近行为以及平均面部类别 < 以及面部和尺寸分布的归一化宽度 表示。研究发现，中等范围的初始分布通过相对较短的瞬态周期演化为渐近状态，彼此之间的扩散较小，但具有相同的相对宽度顺序。初始分布比这些分布更宽或更窄，是通过更长的瞬态周期演变而来的，轨迹与更温和的分布相交，最宽的初始分布变得最窄，最初最窄的变成最宽。这些行为可以通过它们与拓扑事件率的交互演化来解释。