Intercalated Ion Two-dimensional Order - Disorder Phase Transitions In Computer Simulation

The cluster variation method is applied for studying the order-disorder phase transition, which was first presented by Kikuchi to solve the cooperative phenomena. Broader utilization of the method was hampered due to the slowness of computer in the early times. With the high-speed computers available, this method has been widely used in the computation of phase transition such as alloy, mineral, and ceramics. During the process of solving simultaneous algebraic equations, natural iteration method, rather than Newton-Raphson iteration method, is adopted in order to avoid the complex differentiations and matrix inversion. In the past, the interaction between the same near neighbor is considered equivalent however different the atoms are. In this paper, the interaction between the same near neighbor is separated. Accordingly, phase diagrams with respect to different interactions parameters are also calculated.From the phase diagrams calculated by the cluster variation method, some valuable results have been achieved. Firstly, the stronger the interaction between the intercalated ion and vacancy is, the more likely the ordered structure is to be obtained. Secondly, in the case of 3 a 0×a0 superlattice, the range of temperature, during which the ordered structures exist, is very broad, i.e., these ordered structures are very stable under the room temperature. Thirdly, as far as 3 a 0×3a0superlattice is concerned, it is more likely to form this kind of ordered structure in the case of concentration of M (intercalated ion ) equal to 1/3 than 2/3. Fourthly, from the figure of entropy and probability of intercalated ions with respect to temperature, it can be confirmed that the order-disorder phase transition about 3 a 0×3a0 superlattice is a weakly first-order phase transition. Finally, from the figure of probability of intercalation ion on respective lattices with respect to concentration of intercalation ion, 3 a 0×3a0 ordered structures can exist in the wide range of concentration under certain temperature. However, only in the case of it that ion concentration is equal to 1/3, can the most stable ordered structure be formed.