Thermodynamics, formation dynamics, and structural correlations in the bulk amorphous phase of the phase-field crystal model.

Thermodynamics, formation dynamics, and structural correlations in the bulk amorphous phase of the phase-field crystal model.

We investigate bulk thermodynamic and microscopic structural properties of amorphous solids in the framework of the phase-field crystal (PFC) model. These are metastable states with a non-uniform density distribution, having no long-range order. From extensive numerical simulations, we determine the distribution of free energy density values in varying size amorphous systems and also the point-to-set correlation length, which is the radius of the largest volume of amorphous one can take while still having the particle arrangements within the volume determined by the particle ordering at the surface of the chosen volume. We find that in the thermodynamic limit, the free energy density of the amorphous tends toward a value that has a slight dependence on the initial state from which it was formed-i.e., it has a formation history dependence. The amorphous phase is observed to form on both sides of the liquid linear-stability limit, showing that the liquid to amorphous transition is first order, with an associated finite free energy barrier when the liquid is metastable. In our simulations, this is demonstrated when the noise in the initial density distribution is used to induce nucleation events from the metastable liquid. Depending on the strength of the initial noise, we observe a variety of nucleation pathways, in agreement with previous results for the PFC model, which show that amorphous precursor mediated multi-step crystal nucleation can occur in colloidal systems.

我们在相场晶体（PFC）模型的框架内研究非晶固体的体热力学和微观结构性质。这些是具有非均匀密度分布的亚稳态，没有长程有序性。通过大量的数值模拟，我们确定了不同尺寸的非晶系统中自由能密度值的分布以及点到集关联长度，点到集关联长度是指在所选体积表面的粒子排列所决定的体积内，人们可以选取的最大非晶体积的半径，同时该体积内的粒子排列由所选体积表面的粒子排序决定。我们发现，在热力学极限下，非晶的自由能密度趋向于一个对其形成的初始状态有轻微依赖的值，即它具有形成历史依赖性。观察到非晶相在液体线性稳定性极限的两侧形成，这表明液体到非晶的转变是一级相变，当液体处于亚稳态时，存在相关的有限自由能垒。在我们的模拟中，当利用初始密度分布中的噪声来诱导亚稳态液体中的成核事件时，就证明了这一点。根据初始噪声的强度，我们观察到多种成核途径，这与PFC模型先前的结果一致，先前的结果表明在胶体系统中可能发生非晶前驱体介导的多步晶体成核。