Phase Growth with Heat Diffusion in a Stochastic Lattice Model
Phase Growth with Heat Diffusion in a Stochastic Lattice Model
复制标题
随机晶格模型中热扩散的相生长
DOI：
10.1007/s10955-022-02990-8
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发表时间：
2022
影响因子：
1.6
通讯作者：
Sasa Shin-ichi
中科院分区：
文献类型：
--
作者：
Hiraizumi Mao;Ohta Hiroki;Sasa Shin-ichi
当稳定相与具有平面界面的亚稳定相相邻时，稳定相会生长。我们提出了一个随机晶格模型来描述伴随热扩散的相生长。该模型基于能量守恒 Potts 模型，其动能项定义在二维晶格上，其中每个位点在一个方向上稀疏随机连接，在另一个方向上局部连接。对于该模型，我们使用统计力学精确计算稳定相和亚稳定相。通过数值模拟，我们测量了界面的位移 R(t)。我们观察比例关系，其中 是热扩散常数， 是两个热浴之间的系统尺寸。缩放函数显示 for 和 for，其中交叉值和指数取决于浴的温度，和。然后我们确认确定性相场模型表现出相同的比例关系。此外，相场模型的数值模拟表明，当稳定相变为中性时，交叉值接近于零。
When a stable phase is adjacent to a metastable phase with a planar interface, the stable phase grows. We propose a stochastic lattice model describing the phase growth accompanying heat diffusion. The model is based on an energy-conserving Potts model with a kinetic energy term defined on a two-dimensional lattice, where each site is sparse-randomly connected in one direction and local in the other direction. For this model, we calculate the stable and metastable phases exactly using statistical mechanics. Performing numerical simulations, we measure the displacement of the interfaceR(t). We observe the scaling relation, whereDis the thermal diffusion constant andis the system size between the two heat baths. The scaling functionshowsforandfor, where the cross-over valueand exponentdepend on the temperatures of the baths, and. We then confirm that a deterministic phase-field model exhibits the same scaling relation. Moreover, numerical simulations of the phase-field model show that the cross-over valueapproaches zero when the stable phase becomes neutral.