tight-binding coherent potential approximation embedded cluster method Monte Carlo approach and approximations to the quadratic Korringa-Kohn-Rostoker method

The coherent potential approximation (CPA) can yield information about the long-range characteristics of an alloy. However, since it is a single-site theory, the effect of the local environment cannot be taken into account. The CPA can be extended to more than one site using the embedded cluster method, thereby including short-range order effects. The tight-binding coherent-potential approximation embedded cluster method can be used to generate the densities of states corresponding to all possible configurations of any cluster, but in particular a cluster consisting of an atom and its nearest neighbors. It is then demonstrated that the interaction energies can be calculated and used in conjunction with the Monte Carlo approach to generate the phase diagram of an alloy. In addition, the formalism for two new approximations to the Quadratic Korringa-Kohn-Rostoker method is developed and is applied to a system consisting of one metal.