温度依赖的多阱相变自由能谱：以PbTiO3为原型
Temperature-dependent Multi-well Free-energy Landscape for Phase Transitions: PbTiO3 as a Prototype
摘要：
在描述相变和相关临界现象的序参量空间上，解析地构建定量的温度依赖的多阱自由能景观是一个长期的挑战。在这里，我们提出了一个简单的分析模型的自由能景观的基础上的先验概念的玻尔兹曼热混合之间的多个抛物线电位代表不同的能量退化的基态在流行的朗道理论使用高温无序状态作为参考。该模型恢复了Weiss分子场论和二阶Landau系数的温度依赖行为。值得注意的是，这样一个简单的解析表达式可以描述各种各样的性质跨越铁电相变在PbTiO 3，包括自发极化的温度依赖性，热容量，介电常数张量，和晶格参数。该方法还允许参数化的自由能函数直接基于0 K热力学数据，可以从DFT计算得到的相变。我们预计，这种方法可以同样适用于其他类型的关键现象，例如，超导相变、金属-绝缘体转变和磁转变。
英文摘要：
It has been a long challenge to analytically construct the quantitative temperature-dependent multi-well free-energy landscape over the space of order parameters describing phase transitions and associated critical phenomena. Here we propose a simple analytical model for the free energy landscape based on a priori concept of Boltzmann thermal mixing among multiple parabolic potentials representing different energetically degenerated ground states in contrast to the popular Landau theory using the high-temperature disordered state as a reference. The model recovers both the Weiss molecular field theory and the temperature dependent behaviors of the second order Landau coefficient. It is rather remarkable that such a simple analytical expression can describe a wide variety of properties across the ferroelectric phase transition in PbTiO3, including the temperature dependences of the spontaneous polarization, the heat capacities, the permittivity tensor, and the lattice parameters. The approach also allows parametrization of the free energy function across phase transitions based directly on the 0 K thermodynamics data that can be obtained from DFT calculations. We anticipate that the approach can be equally applied to other types of critical phenomena, e.g., the superconducting phase transition, the metal-insulator transition, and the magnetic transitions.
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