Coherent Potential Approximation
Encyclopedia
The coherent potential approximation (or CPA) is a method, in physics
, of finding the Green's function
of an effective medium. It is a useful concept in understanding how waves scatter in a material which displays spatial inhomogeneity.
One version of the CPA is an extension to random materials of the muffin-tin approximation
used to calculate electronic band structure
in solids. A variational implementation of the muffin-tin approximation to crystalline solids using Green's function
s was suggested by Korringa and by Kohn
and Rostocker, and is often referred to as the KKR method. For random materials, the theory is applied by the introduction of an ordered lattice of effective potentials to replace the varying potentials in the random material. This approach is called the KKR coherent potential approximation.
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, of finding the Green's function
Green's function
In mathematics, a Green's function is a type of function used to solve inhomogeneous differential equations subject to specific initial conditions or boundary conditions...
of an effective medium. It is a useful concept in understanding how waves scatter in a material which displays spatial inhomogeneity.
One version of the CPA is an extension to random materials of the muffin-tin approximation
Muffin-tin approximation
The muffin-tin approximation is a shape approximation of the potential field in an atomistic environment. It is most commonly employed in quantum mechanical simulations of electronic band structure in solids. The approximation was proposed by John C. Slater. Many modern electronic structure methods...
used to calculate electronic band structure
Electronic band structure
In solid-state physics, the electronic band structure of a solid describes those ranges of energy an electron is "forbidden" or "allowed" to have. Band structure derives from the diffraction of the quantum mechanical electron waves in a periodic crystal lattice with a specific crystal system and...
in solids. A variational implementation of the muffin-tin approximation to crystalline solids using Green's function
Green's function
In mathematics, a Green's function is a type of function used to solve inhomogeneous differential equations subject to specific initial conditions or boundary conditions...
s was suggested by Korringa and by Kohn
Walter Kohn
Walter Kohn is an Austrian-born American theoretical physicist.He was awarded, with John Pople, the Nobel Prize in chemistry in 1998. The award recognized their contributions to the understandings of the electronic properties of materials...
and Rostocker, and is often referred to as the KKR method. For random materials, the theory is applied by the introduction of an ordered lattice of effective potentials to replace the varying potentials in the random material. This approach is called the KKR coherent potential approximation.