# Nonlinear electron-density distribution around point defects in simple metals. I. Formulation

## Abstract

Modification, which is exact in the limit of long wavelength, of the nonlinear theory of Sjoelander and Stott of electron distribution around point defects is given. This modification consists in writing a nonlinear integral equations for the Fourier transform ..gamma../sub 12/ (q) of the induced charge density surrounding the point defect, which includes a term involving the density derivative of ..gamma../sub 12/ (q). A generalization of the Pauli-Feynman coupling-constant-integration method, together with the Kohn-Sham formalism, is used to exactly determine the coefficient of this derivative term in the long-wavelength limit. The theory is then used to calculate electron-density profiles around a vacancy, an eight-atom void, and a point ion. The results are compared with those of (i) a linear theory, (ii) Sjoelander-Stott theory, and (iii) a fully self-consistent calculation based on the density-functional formalism of Kohn and Sham. It is found that in the case of a vacancy, the results of the present theory are in very good agreement with those based on Kohn-Sham formalism, whereas in the case of a singular attractive potential of a proton, the results are quite poor in the vicinity of the proton, but much better for larger distances. A critical discussion of the theorymore »

- Authors:

- Publication Date:

- Research Org.:
- Physics Department and Materials Research Center, Northwestern University, Evanston, Illinois 60201

- OSTI Identifier:
- 6694662

- Resource Type:
- Journal Article

- Journal Name:
- Phys. Rev., B; (United States)

- Additional Journal Information:
- Journal Volume: 18:6

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; METALS; VACANCIES; ELECTRON DENSITY; IMPURITIES; COUPLING CONSTANTS; EXCHANGE INTERACTIONS; FOURIER TRANSFORMATION; NONLINEAR PROBLEMS; CRYSTAL DEFECTS; CRYSTAL STRUCTURE; ELEMENTS; INTEGRAL TRANSFORMATIONS; INTERACTIONS; POINT DEFECTS; TRANSFORMATIONS; 360104* - Metals & Alloys- Physical Properties

### Citation Formats

```
Gupta, A K, Jena, P, and Singwi, K S.
```*Nonlinear electron-density distribution around point defects in simple metals. I. Formulation*. United States: N. p., 1978.
Web. doi:10.1103/PhysRevB.18.2712.

```
Gupta, A K, Jena, P, & Singwi, K S.
```*Nonlinear electron-density distribution around point defects in simple metals. I. Formulation*. United States. doi:10.1103/PhysRevB.18.2712.

```
Gupta, A K, Jena, P, and Singwi, K S. Fri .
"Nonlinear electron-density distribution around point defects in simple metals. I. Formulation". United States. doi:10.1103/PhysRevB.18.2712.
```

```
@article{osti_6694662,
```

title = {Nonlinear electron-density distribution around point defects in simple metals. I. Formulation},

author = {Gupta, A K and Jena, P and Singwi, K S},

abstractNote = {Modification, which is exact in the limit of long wavelength, of the nonlinear theory of Sjoelander and Stott of electron distribution around point defects is given. This modification consists in writing a nonlinear integral equations for the Fourier transform ..gamma../sub 12/ (q) of the induced charge density surrounding the point defect, which includes a term involving the density derivative of ..gamma../sub 12/ (q). A generalization of the Pauli-Feynman coupling-constant-integration method, together with the Kohn-Sham formalism, is used to exactly determine the coefficient of this derivative term in the long-wavelength limit. The theory is then used to calculate electron-density profiles around a vacancy, an eight-atom void, and a point ion. The results are compared with those of (i) a linear theory, (ii) Sjoelander-Stott theory, and (iii) a fully self-consistent calculation based on the density-functional formalism of Kohn and Sham. It is found that in the case of a vacancy, the results of the present theory are in very good agreement with those based on Kohn-Sham formalism, whereas in the case of a singular attractive potential of a proton, the results are quite poor in the vicinity of the proton, but much better for larger distances. A critical discussion of the theory vis a vis the Kohn-Sham formalism is also given. Some applications of the theory are pointed out.},

doi = {10.1103/PhysRevB.18.2712},

journal = {Phys. Rev., B; (United States)},

number = ,

volume = 18:6,

place = {United States},

year = {1978},

month = {9}

}