Revisiting nonequilibrium characterization of glass: History dependence in solids

Koun Shirai
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Abstract

Glass has long been considered a nonequilibrium material. The primary reason is its history-dependent properties: the obtained properties are not uniquely determined by two state variables alone, namely, temperature and volume, but are affected by the process parameters, such as cooling rates. However, closer observations show that this history dependence is common in solid; in crystal growth, the properties of an obtained crystal are affected by the preparation conditions through defect structures and metallurgical structures. The problem with the previous reasoning of history dependence lies in the lack of appropriate specification of state variables. Without knowledge of the latter, describing thermodynamic states is impossible. The guiding principle to find state variables is provided by the first law of thermodynamics. The state variables of solids have been searched by requiring that the internal energy $U$ is a state function. Detailed information about the abovementioned microstructures is needed to describe the state function $U$. This can be accomplished by specifying the time-averaged positions R_{j} of all atoms comprising the solids. Therefore, R_{j} is a state variable for solids. Defect states, being metastable states, represent equilibrium states within a finite time (relaxation time). However, eternal equilibrium is nonexistent: the perfect crystal is thermodynamically unstable. Equilibrium states can only be considered at the local level. Glass is thus in equilibrium as long as its structure does not change. The relaxation time is controlled by the energy barriers by which a structure is sustained, and this time restriction is intimately related to the definition of state variables. The most important property of state variables is their invariance to time averaging. The time-averaged quantity R_{j} meets this invariance property.
重新审视玻璃的非平衡特性:固体的历史依赖性
长期以来,玻璃一直被认为是一种非平衡材料。其主要原因是玻璃具有与历史相关的特性:所获得的特性并非仅由温度和体积这两个状态变量决定,而是受到冷却速率等工艺参数的影响。然而,仔细观察会发现,这种历史依赖性在固体中很常见;在晶体生长过程中,所获得晶体的特性会通过缺陷结构和冶金结构受到制备条件的影响。前面关于历史依赖性推理的问题在于缺乏对状态变量的适当说明。如果不了解后者,就无法描述热力学状态。热力学第一定律提供了寻找状态变量的指导原则。固体的状态变量是通过要求内能 U$ 是一个状态函数来寻找的。要描述状态函数 $U$,需要有关上述微结构的详细信息。这可以通过指定构成固体的所有原子的时间平均位置 R_{j} 来实现。因此,R_{j} 是固体的状态变量。缺陷态作为一种可转移状态,代表了有限时间(弛豫时间)内的平衡态。然而,永恒的平衡是不存在的:完美晶体在热力学上是不稳定的。平衡状态只能在局部层面上考虑。因此,只要玻璃的结构不发生变化,它就处于平衡状态。弛豫时间由维持结构的能量屏障控制,而这种时间限制与状态变量的定义密切相关。状态变量最重要的特性是对时间平均的不变性。时间平均量 R_{j} 符合这一不变性。
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