### Abstract

The original coherent potential approximation (CPA) used for calculating the electronic states in substitutional solid-solution alloys contains the implicit assumption that the alloy is isomorphous. That is, all of the atoms of a given chemical type are assumed to be identical. The extension of the CPA philosophy to treat an alloy model in which all of the atoms are allowed to have distinct charges and potentials is called the polymorphous CPA (PCPA). This extension requires some interesting changes in the mathematical formalism that is used to develop the CPA equations. Aspects of the mathematical formalism of the PCPA will be discussed. In particular, the ergodic theorem from measure theory will be invoked to justify the new equations for the average Green's function.

Original language | English |
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Pages (from-to) | 8573-8585 |

Number of pages | 13 |

Journal | Journal of Physics Condensed Matter |

Volume | 13 |

Issue number | 38 |

DOIs | |

Publication status | Published - Sep 24 2001 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Electronic, Optical and Magnetic Materials

### Cite this

*Journal of Physics Condensed Matter*,

*13*(38), 8573-8585. https://doi.org/10.1088/0953-8984/13/38/304

**The mathematics of the polymorphous coherent potential approximation.** / Faulkner, J. S.; Újfalussy, B.; Moghadam, Nassrin; Stocks, G. M.; Wang, Yang.

Research output: Contribution to journal › Article

*Journal of Physics Condensed Matter*, vol. 13, no. 38, pp. 8573-8585. https://doi.org/10.1088/0953-8984/13/38/304

}

TY - JOUR

T1 - The mathematics of the polymorphous coherent potential approximation

AU - Faulkner, J. S.

AU - Újfalussy, B.

AU - Moghadam, Nassrin

AU - Stocks, G. M.

AU - Wang, Yang

PY - 2001/9/24

Y1 - 2001/9/24

N2 - The original coherent potential approximation (CPA) used for calculating the electronic states in substitutional solid-solution alloys contains the implicit assumption that the alloy is isomorphous. That is, all of the atoms of a given chemical type are assumed to be identical. The extension of the CPA philosophy to treat an alloy model in which all of the atoms are allowed to have distinct charges and potentials is called the polymorphous CPA (PCPA). This extension requires some interesting changes in the mathematical formalism that is used to develop the CPA equations. Aspects of the mathematical formalism of the PCPA will be discussed. In particular, the ergodic theorem from measure theory will be invoked to justify the new equations for the average Green's function.

AB - The original coherent potential approximation (CPA) used for calculating the electronic states in substitutional solid-solution alloys contains the implicit assumption that the alloy is isomorphous. That is, all of the atoms of a given chemical type are assumed to be identical. The extension of the CPA philosophy to treat an alloy model in which all of the atoms are allowed to have distinct charges and potentials is called the polymorphous CPA (PCPA). This extension requires some interesting changes in the mathematical formalism that is used to develop the CPA equations. Aspects of the mathematical formalism of the PCPA will be discussed. In particular, the ergodic theorem from measure theory will be invoked to justify the new equations for the average Green's function.

UR - http://www.scopus.com/inward/record.url?scp=0035943772&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035943772&partnerID=8YFLogxK

U2 - 10.1088/0953-8984/13/38/304

DO - 10.1088/0953-8984/13/38/304

M3 - Article

VL - 13

SP - 8573

EP - 8585

JO - Journal of Physics Condensed Matter

JF - Journal of Physics Condensed Matter

SN - 0953-8984

IS - 38

ER -