| On the base of the studies of Kawamura [3-5], Du Yi-jin et al[6-13] and Yi You-min et al[14-15], we introduce the Lennard-Jones potential and the molecular fraction into the two-dimensional Collins model. We deduced the free energies and the Gibbs functions of this system. Because of the existence of the holes in the system, the molecular fraction Q should considered into the free energies and the Gibbs functions. When there are few holes or none existing in the system, i.e., , it corresponds to the liquid state or solid state; when there are lots of holes and a few atoms existing in the system, i.e., , it corresponding to the gas state. Our paper is just on the base of this theoretical physical model to describe the phase transition between solid, liquid and gas. According to the thermodynamic conditions describing the equilibrium state, we use the free energies and the Gibbs functions to study the phase transitions and the phase diagrams of the 2D monatomic L-J system and the 2D binary alternative L-J system respectively. The paper include three parts as follows:1. The 2D monatomic L-J systemOn the base of reference [15], the holes were considered into the 2D monatomic L-J system, we gave the free energies and the Gibbs functions of this system. Using the thermodynamic conditions describing the coexistence of two phases and the stability conditions of Equilibrium State, we have calculated the normalized temperature and the normalized pressure of the triple point (t1, p1), the melting curve, vapouring curve and the sublimation curve. The whole phase diagram of the 2D monatomic L-J system is obtained. Further more, we also calculated the normalized temperature and the normalized pressure of the critical point (tc, pc) in the 2D monatomic system. And we gave some discussions about the qualities around the critical point. Both the triple point and the critical point we obtained are quite close to the experimental results and the computer simulation(38).2. The 2D alternative binary L-J systemWe generalized above results to the two-dimensional alternative binary system. Suppose there are two components a and b in the system. We gave the free energies and the Gibbs functions of the 2D alternative binary L-J system. Then, we use the Largrange indeterminate multiplier Method. According to the thermodynamic conditions describing the coexistence of two phases and the stability conditions of Equilibrium State, the equations describing the solid-liquidphase diagram equilibrium curves of the 2D alternative binary system are obtained. When we determined a group of the attractive interactions' values, we can get some typical phase diagrams between the solid and the liquid. Further, considering the molecular fraction Q, we can also get some typical phase diagrams of this system between the liquid and the gas. These entire typical phase diagram mainly include: the infinite soluble with each other phase diagram, i.e., the "cigar-type" phase diagram and the phase diagram with a maximum or a minimum. The infinite solid insoluble phase diagram, i.e., the phase diagram with a eutectic point. The infinite liquid insoluble phase diagram, i.e., the phase diagram with a shared boiling point. All the phase diagrams we obtained are quite analogous to the behavior of the three-dimensional substances.3. The influence on the phase diagram by the parametersThe normalized pressure and the attractive interactions between atoms are very important parameters. For further researching the influence on the phase transition curve by these parameters, we first present discussions on the "cigar type" phase diagram by the normalized pressure or the ratio of the mixed energies. We fixed the other parameters and changed the normalized pressure or the ratio of the mixed energies only. The results show that the lattice structure, the phase transition normalized temperature and the coexistence area of the phase diagram changed with the variety of the given parameters in certain regularity. Second, we further discussed the inf...
|
PDF Full Text Request