atom

micro

macro

A

B

C
CPA

CPA: Coherent Potential Approximation
Definition:Quantum-mechanical mean-field approach for the description of substitutionally disordered alloys
Explanation:The CPA is based on the assumption that an alloy may be replaced by an ordered effective (coherent) medium, the parameters of which are determined self-consistently. The method is based on the following assumptions:
(i) the local potentials around a certain type of atom in the alloy are the same;
(ii) the alloy is replaced by a monoatomic structure and described by a site independent coherent potential, which, being placed on every site of the alloy lattice, mimics the electronic properties of the actual material (see the figure below);
(iii) the real Green’s function of the alloy is approximated by a coherent Green’s function, which is calculated using an electronic structure method (e.g. the Exact Muffin-Tin Orbitals (→EMTO) method) [3].

The CPA is a single-site approximation (in contrast to the Special Quasi-random Structures (→SQS) approach where a random alloy is described by supercells). The effect of short-range order cannot be taken into account within the CPA. The CPA is mainly used for alloys in which the size mismatch between atoms is small (such as Fe-Mn), because the effects of local lattice relaxations can not be attained within the approach.

The CPA can also be applied to paramagnetic systems, where the local magnetic moments are disordered. The performance of the CPA is compared with that of supercell approaches for the phase stability of Fe-Mn based alloys in [4].
Picture /
Figure /
Diagram:

References:[1] B. L. Györffy. Physical Review B 5, 2382 (1972)
[2] P. Soven. Physical Review 156, 809 (1967)
[3] L. Vitos. Computational Quantum Mechanics for Materials Engineers: The EMTO Method and Applications. Engineering Materials and Processes, Springer London (2007)
[4] T. Gebhardt, D. Music, M. Ekholm, I.A. Abrikosov, L. Vitos, A. Dick, T. Hickel, J. Neugebauer, J.M. Schneider, J. Phys: Condens. Matter 23, 246003 (2011)