Zentropy theory for accurate prediction of free energy, volume, and thermal expansion without fitting parameters

Abstract

Based on statistical mechanics, a macroscopically homogeneous system, i.e., a single phase in the present context, is composed of many independent configurations that the system embraces. The macroscopical properties of the system are determined by the properties and statistical probabilities of those configurations with respect to external conditions. The volume of a single phase is thus the weighted sum of the volumes of all configurations. Consequently, the derivative of the volume to temperature of a single phase depends on both the derivatives of the volumes of every configuration to temperature and the derivatives of their statistical probabilities to temperature, with the latter introducing nonlinear emergent behaviors. It is shown that the derivative of the volume to the temperature of the single phase can be negative, i.e., negative thermal expansion, due to the symmetry-breaking non-ground-state configurations with smaller volumes than that of the ground-state configuration and the rapid increase of the statistical probabilities of the former, and negative thermal expansion can be predicted without fitting parameters from the zentropy theory that combines quantum mechanics and statistical mechanics with the free energy of each configuration predicted from quantum mechanics and the partition function of each configuration calculated from its free energy.

Quantitative predictive theories through integrating quantum, statistical, equilibrium, and nonequilibrium thermodynamics

“…The positive divergency of thermal expansion was predicted at the critical point, attributing to the larger volumes of the AFM and FM nonground-state configurations than that of the NM ground-state configuration. This can be seen from the following volume and thermal expansion equations of a system based on the zentropy theory [140]…”