Phase Diagram Study Of The Two-dimensional Ternary Lennard-Jones System

Phase Diagram Study is an important branch in the field of the basic and the applied science. The main study of the Phase Diagram is the relationships between the matter's components and its phases with the outside conditions. Obtaining a phase diagram of a matter, the relationships between the matter's components, structure and capabilities can be easily got, which is just the place where Phase Diagram Study shows very important meaning. This paper entirely uses a theoretical model –Collins model–to calculate and study phase diagrams, which has some theoretical meaning to the practice.The first chapter gives some basic conceptions and theories according to phase diagrams, introduces the current progresses of the calculation of phase diagrams, and discusses the probabilities of the existing phase transitions in the two dimensions (2D), and then introduces the establishment of the Collins model as well as its development and study trends. The second chapter supposes three components a,b and c in the 2D system ,writes out the expressions of the free energy and the Gibbs functions of the 2D alternative ternary L-J system. Firstly, by using the Largrange indeterminate multiplier method, and according to the thermodynamic conditions describing the coexistence of two phases and the stability conditions of Equilibrium State, the equations describing the solid-liquid phase diagram equilibrium curves of the 2D alternative ternary system are obtained. Given a group of the attractive interactions' values, the isothermal sectional diagrams and the vertical sectional diagrams of the typical phase diagram of the ternary system (e.g. the "even crystal" type) are obtained. Then using the similar method , the equations describing the three phases (e.g. one liquid phase and two solid phases) equilibrium curves of the 2D alternative ternary system are obtained. Given a group of the attractive interactions' values, the phase diagrams that representing the equilibrium of one liquid phase and two solid phases, i.e. the knot triangles, are got, which are similar to the practice.The third chapter. There are three kinds of parameters that influence phase diagram, i.e., the temperature, the normalized pressure and the attractive interactions between atoms. For further researching the influence on the phase transition curves by these parameters, the first discussions are made about the normalized pressure's influence (fixing the temperature and the attractive interactions parameters) on the isothermal sectional and vertical sectional diagrams of the "even crystal" type ternary system, as well as on the knot triangles representing the equilibrium of one liquid phase and two solid phases. Then another discussion is made about the influence (fixing the temperature and the normalized pressure) of the changed attractive interactions parameters on the isothermal sectional diagrams of the "even crystal" type ternary system.The results show that the lattice structure, the normalized temperature of the phase transition and the coexistence area of the phase diagram changed with the variety of the given parameters in certain regularity.In the end, we make a summary of our work and give the prospects for the 2D Collins model. We believe that the Collins model is a simple but visual model, which can enlighten people well on the understandings of the matter's intetior structure and the phase diagram' theorectical calculation.