 CPA: Coherent Potential Approximation 
Definition:  Quantummechanical
meanfield 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
selfconsistently.
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 MuffinTin
Orbitals (→EMTO)
method) [3].
The CPA is a
singlesite
approximation (in
contrast to the
Special Quasirandom
Structures
(→SQS)
approach where a
random alloy is
described by
supercells). The
effect of
shortrange 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
FeMn), 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 FeMn
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) 

