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 to 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 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, and which show that amorphous precursor mediated multi-step crystal nucleation can occur in colloidal systems.

中文翻译：

---

相场晶体模型的块状非晶相的热力学、形成动力学和结构相关性

我们在相场晶体 (PFC) 模型的框架内研究了无定形固体的整体热力学和微观结构特性。这些是具有不均匀密度分布的亚稳态，没有长程有序。从广泛的数值模拟中，我们确定了不同尺寸无定形系统中自由能密度值的分布，以及点到集的相关长度，这是在粒子排列仍然在体积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，非晶态的自由能密度趋向于一个对它形成的初始状态有轻微依赖性的值——即它具有形成历史的依赖性。观察到无定形相在液体线性稳定性极限的两侧形成，表明液体到无定形的转变是一级的，当液体亚稳态时具有相关的有限自由能垒。在我们的模拟中，当使用初始密度分布中的噪声来诱导亚稳态液体的成核事件时，这一点得到了证明。根据初始噪声的强度，我们观察到各种成核途径，与 PFC 模型的先前结果一致，这表明无定形前体介导的多步晶体成核可能发生在胶体系统中。当液体是亚稳态时，具有相关的有限自由能垒。在我们的模拟中，当使用初始密度分布中的噪声来诱导亚稳态液体的成核事件时，这一点得到了证明。根据初始噪声的强度，我们观察到各种成核途径，与 PFC 模型的先前结果一致，这表明无定形前体介导的多步晶体成核可能发生在胶体系统中。当液体是亚稳态时，具有相关的有限自由能垒。在我们的模拟中，当使用初始密度分布中的噪声来诱导亚稳态液体的成核事件时，这一点得到了证明。根据初始噪声的强度，我们观察到各种成核途径，与 PFC 模型的先前结果一致，这表明无定形前体介导的多步晶体成核可能发生在胶体系统中。