Descriptors :
Binary lattice,Configurational entropy,Nearest-neighber,Interaction
Abstract :
The extended sequential construction method, which is newly introduced in this paper, is used for an exact solution to the binary lattice model in the closed form. In section I, this method is applied to one-dimensional model and a two-dimensional, model of a square lattice, for the cases where the fractions of species are not equal (f 0.5), and the special case (f = 0.5) is being considered in section II. Application of this method to other two-dimensional, and all three-dimensional, models seems to be straightforward. In the cases where f 0.5, no first-order phase transition has been found, which is in agreement with the fact that this transition may occur only when f=0.5. However, in the case where f = 0.5, the results of our calculations show that no first-order phase transition occurs in the case of a one-dimensional model, and configurational heat capacity (against temperature) goes through a maximum continuously. For the case of a two-dimensional model (of the square lattice), when f = 0.5, first-order phase-transition phenomenon occurs, and the critical temperature is located roughly at the point x***c = 0.41, where x***c = exp(element/Kt***c). A simple exact expression is also obtained for the heat capacity of the one-dimensional model when f = 0.5.
