Efficient approaches to solutions of partition function for condensed matters.

The key problem of statistical physics standing over one hundred years is how to exactly calculate the partition function (or free energy), which severely hinders the theory to be applied to predict the thermodynamic properties of condensed matters. Very recently, we developed a direct integral approach (DIA) to the solutions and achieved ultrahigh computational efficiency and precision. In the present work, the background and the limitations of DIA were examined in details, and another method with the same efficiency was established to overcome the shortage of DIA for condensed system with lower density. The two methods were demonstrated with empirical potentials for solid and liquid cooper, solid argon and C60 molecules by comparing the derived internal energy or pressure with the results of vast molecular dynamics simulations, showing that the precision is about ten times higher than previous methods in a temperature range up to melting point. The ultrahigh efficiency enables the two methods to be performed with ab initio calculations and the experimental equation of state of solid copper up to ∼600 GPa was well reproduced, for the first time, from the partition function via density functional theory implemented.

How accurate for phonon models to predict the thermodynamics properties of crystals.

Previous work has shown that thermodynamics properties calculated by phonon model with quasi-harmonic approximation (QHA) may differ badly from experiment in some cases. The inaccuracy was examined in the present work by comparing the results of QHA for argon and copper crystal with the ones of molecular dynamics simulations, partition functions obtained by a new method or experiment. It is shown that QHA works well for the systems of atomic volume smaller than 22 Å3/atom and the accuracy gets lower and lower gradually with increasing of the atomic volume. Based on this fact, the disagreement (or agreement) between the thermodynamics properties of MgO, Si, CaO, ZrO2 calculated in previous work by QHA and the experiments can be well understood.

A New Model to Predict Optimum Conditions for Growth of 2D Materials on a Substrate.

Deposition of atoms or molecules on a solid surface is a flexible way to prepare various novel two-dimensional materials if the growth conditions, such as suitable surface and optimum temperature, could be predicted theoretically. However, prediction challenges modern theory of material design because the free energy criteria can hardly be applied to this issue due to the long-standing problem in statistical physics of the calculations of the free energy. Herein, we present an approach to the problem by the demonstrations of graphene and γ-graphyne on the surface of copper crystal, as well as silicene on a silver substrate. Compared with previous state-of-the-art algorithms for calculations of the free energy, our approach is capable of achieving computational precisions at least 10-times higher, which was confirmed by molecular dynamics simulations, and working at least four orders of magnitude faster, which enables us to obtain free energy based on ab initio calculations of the interaction potential instead of the empirical one. The approach was applied to predict the optimum conditions for silicene growth on different surfaces of solid silver based on density functional theory, and the results are in good agreement with previous experimental observations.