Applicability of the coherent-potential approximation in the theory of random alloys

Abstract

The applicability of the coherent-potential approximation ͑CPA͒ for the description of electronic properties of completely random alloys is investigated. This is done by calculating the density of states and the total energy for different systems and by comparing the results with those obtained for large supercells consisting of up to 320 atoms in the framework of the order-N locally self-consistent Green's function method. Thereby it is found that in the framework of the CPA one obtains a reliable description of the electronic structure of random alloys. The total energy of a completely disordered alloy can also be reliably estimated provided an appropriate account is given for the electrostatic contribution to the one-electron potential and energy. Therefore, we conclude that the CPA can be safely applied to study the influence of disorder on various properties of metallic alloys for which the muffin-tin or atomic sphere approximation is sufficient and the chemical contribution to the total energy dominates. ͓S0163-1829͑98͒03122-1͔

High temperature phase decomposition in TixZryAlzN

“…Though CPA treats substitutional disorder at a mean-field level, it is proven to be effective and reliable for completely disordered alloy systems. 5,26 Exchange-correlation effects are treated within the Generalized Gradient Approximation according to Perdew, Burke and Ernzerhof. 27 We restrict ourselves solely to the study of isostructural decomposition of the cubic B1, or rock-salt, structure of Ti x Zr y Al z N. Within this structure one of the fcc sublattices holds all the N atoms and has no compositional degrees of freedom, the other holds the metal atoms and is treated as a solid solution phase.…”

Surface segregation energies in transition-metal alloys

“…45 Preliminary results from super-cell calculations for surfaces of random CuPt alloys 48 show that this empirical coefficient also works well at surfaces. We emphasize that this approach ensures a correct concentration dependence of the total energies and a correct renormalization of the electronic structure of the host atoms around the impurities.…”

Charge Distributions in Metallic Alloys: A Charge Excess Functional Theory Approach

“…As noticed in [7] this uniqueness is due to the mathematical simplicity of the CPA projectors and, therefore, probably does not hold for more exact approaches, where some residual dependence on the site nearest neighbours environment is expected for. Nevertheless, the fact that the CPA theory accurately accounts for the spectral properties of metallic alloys [15] and the quantitative agreement with LSMS calculations found in Refs. [7,14] suggest that the errors introduced by neglecting the nearest neighbours influence are probably not much larger than numerical errors in order N electronic structure calculations.…”