First-principles models and computation of thermodynamic functions in crystalline, quasicrystalline and liquid systems

Phase diagrams have been studied over centuries and applied to explain a variety of phenomena. In metallurgy, a phase diagram is an encyclopedia of an alloy which includes information about structure transformation, liquid-liquid phase separation, solid-solid phase separation, peritectic transition, eutectic transition, order-disorder transition, magnetic-paramagnetic phase transition and so on. Calculating a phase diagram is challenging which requires the knowledge of the Gibbs free energy of all phases at all conditions. From a macro point of view, the Gibbs free energy is related to enthalpy and entropy. From a micro point of view, these thermodynamic functions are reflections of micro particles or quasi-particles like molecules, atoms, ions, electrons, phonons etc. 

In solids, atoms are glued to a crystalline lattice. For an alloy, the way that chemical species are organized in the lattice determines the free energy of this phase which is called the configurational free energy. At finite temperature, atoms move away and vibrate around their site. These motions involve a collection of atoms and become intense at higher temperature. In liquids, atoms are free from the crystalline lattice, diffuse over time, and after reach equilibrium, form a uniform and isotropic system. It is also seen that atoms in a liquid have a non-uniform local structure and favor a certain type of species in the present of their neighborhood. All these contribute to the Gibbs free energy and it would be interesting to solve real world problems from these underlying fundamental physics. 

In this thesis, a systematic framework is presented to calculate the Gibbs free energy using first-principles methods and explain phase behaviors from a micro perspective. We will 1) predict Al-Co, Al-Ni binary phase diagrams and Al-Co-Cu ternary phase diagram; 2) calculate vibrational free energy from covariance matrices, compare with experimental measurements and explain BCC-HCP structure transformation; 3) study liquid-liquid phase separation in Li-Na and eutectic transition in K-Na; 4) examine information entropy model in LJ liquids and seek for a empirical rule for general liquid systems; 5) study the tiling pattern and tile decoration of decagonal quasicrystal and explain the stability at finite temperature.