Coarsening of bicontinuous microstructures is observed in a variety of systems, such as nanoporous metals and mixtures that have undergone spinodal decomposition. To better understand the morphological evolution of these structures during coarsening, we compare the morphologies resulting from two different coarsening mechanisms, surface and bulk diffusion. We perform phase-field simulations of coarsening via each mechanism in a two-phase mixture at nominal volume fractions of 50%-50% and 36%-64%, and the simulated structures are characterized in terms of topology (genus density), the interfacial shape distribution, structure factor, and autocorrelations of phase and mean curvature. We observe self-similar evolution of morphology and topology and agreement with the expected power laws for dynamic scaling, in which the characteristic length scale increases over time proportionally to $t^{1/4}$ for surface diffusion and $t^{1/3}$ for bulk diffusion. While we observe the expected difference in the coarsening kinetics, we find that differences in self-similar morphology due to coarsening mechanism are relatively small, although typically they are larger at 36% volume fraction than at 50% volume fraction. In particular, we find that bicontinuous structures coarsened via surface diffusion have lower scaled genus densities than structures coarsened via bulk diffusion. We also compare the self-similar morphologies to those in literature and to two model bicontinuous structures, namely, constant-mean-curvature surfaces based on the Schoen G minimal surface and random leveled-wave structures. The average scaled mean curvatures of these model structures agree reasonably with those of the coarsened structures at both 36% and 50%, but we find substantial disagreements in the scaled genus densities and the standard deviations of mean curvature.

中文翻译：

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传输机理对双连续结构粗化的影响：体扩散和表面扩散的比较

在各种系统中观察到双连续微观结构的粗化，例如纳米多孔金属和经历了旋节线分解的混合物。为了更好地了解这些结构在粗化过程中的形态演变，我们比较了两种不同的粗化机制（表面扩散和体扩散）产生的形态。我们通过每种机理在标称体积分数分别为50％-50％和36％-64％的两相混合物中执行粗化的相场模拟，并根据拓扑（属密度），界面形状分布，结构因子以及相位和平均曲率的自相关。我们观察到了形态和拓扑的自相似演化，并且与动态缩放的预期幂律一致，${Ť}^{\mathrm{1个}/4}$ 用于表面扩散和 ${Ť}^{\mathrm{1个}/3}$大量扩散。虽然我们观察到了粗化动力学的预期差异，但我们发现，由于粗化机理，自相似形态的差异相对较小，尽管通常它们在体积分数为36％时大于在体积分数为50％时更大。特别是，我们发现通过表面扩散粗化的双连续结构比通过整体扩散粗化的结构具有更低的缩放属密度。我们还将自相似形态与文献和两种模型双连续结构进行比较，即基于Schoen G最小曲面的恒定均值曲率曲面和随机水平波结构。这些模型结构的平均缩放平均曲率在36％和50％时均与粗化结构的平均曲率合理一致，