Group-theoretical calculation of the diffusion coefficient via the vacancy-assisted mechanism

Ryuichi Okamoto, Youhei Fujitani

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Lower vacancy-density in a crystalline solid slows down the tracer diffusion via the vacancy-assisted mechanism, which can be modeled by means of particles hopping to their respective nearest-neighbor lattice-sites stochastically with double occupancy prohibited. The explicit expressions of the diffusion coefficient were previously obtained for various lattices in terms of Nakazato and Kitahara's method [Prog. Theor. Phys. 64 (1980) 2261]. This method yields a set of linear simultaneous algebraic equations as many as the number of lattice sites, which is reduced to a simple equation with respect to the diffusion coefficient in the final step of the method. We here give a systematic way of the reduction in terms of the group theory.

Original languageEnglish
Pages (from-to)2510-2516
Number of pages7
JournalJournal of the Physical Society of Japan
Volume74
Issue number9
DOIs
Publication statusPublished - 2005 Sep

Fingerprint

diffusion coefficient
simultaneous equations
group theory
tracers

Keywords

  • Correlation factor
  • Projection operator
  • Self-diffusion

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Group-theoretical calculation of the diffusion coefficient via the vacancy-assisted mechanism. / Okamoto, Ryuichi; Fujitani, Youhei.

In: Journal of the Physical Society of Japan, Vol. 74, No. 9, 09.2005, p. 2510-2516.

Research output: Contribution to journalArticle

@article{835bd44217ee4a5fa5c1c8febaf6d50f,
title = "Group-theoretical calculation of the diffusion coefficient via the vacancy-assisted mechanism",
abstract = "Lower vacancy-density in a crystalline solid slows down the tracer diffusion via the vacancy-assisted mechanism, which can be modeled by means of particles hopping to their respective nearest-neighbor lattice-sites stochastically with double occupancy prohibited. The explicit expressions of the diffusion coefficient were previously obtained for various lattices in terms of Nakazato and Kitahara's method [Prog. Theor. Phys. 64 (1980) 2261]. This method yields a set of linear simultaneous algebraic equations as many as the number of lattice sites, which is reduced to a simple equation with respect to the diffusion coefficient in the final step of the method. We here give a systematic way of the reduction in terms of the group theory.",
keywords = "Correlation factor, Projection operator, Self-diffusion",
author = "Ryuichi Okamoto and Youhei Fujitani",
year = "2005",
month = "9",
doi = "10.1143/JPSJ.74.2510",
language = "English",
volume = "74",
pages = "2510--2516",
journal = "Journal of the Physical Society of Japan",
issn = "0031-9015",
publisher = "Physical Society of Japan",
number = "9",

}

TY - JOUR

T1 - Group-theoretical calculation of the diffusion coefficient via the vacancy-assisted mechanism

AU - Okamoto, Ryuichi

AU - Fujitani, Youhei

PY - 2005/9

Y1 - 2005/9

N2 - Lower vacancy-density in a crystalline solid slows down the tracer diffusion via the vacancy-assisted mechanism, which can be modeled by means of particles hopping to their respective nearest-neighbor lattice-sites stochastically with double occupancy prohibited. The explicit expressions of the diffusion coefficient were previously obtained for various lattices in terms of Nakazato and Kitahara's method [Prog. Theor. Phys. 64 (1980) 2261]. This method yields a set of linear simultaneous algebraic equations as many as the number of lattice sites, which is reduced to a simple equation with respect to the diffusion coefficient in the final step of the method. We here give a systematic way of the reduction in terms of the group theory.

AB - Lower vacancy-density in a crystalline solid slows down the tracer diffusion via the vacancy-assisted mechanism, which can be modeled by means of particles hopping to their respective nearest-neighbor lattice-sites stochastically with double occupancy prohibited. The explicit expressions of the diffusion coefficient were previously obtained for various lattices in terms of Nakazato and Kitahara's method [Prog. Theor. Phys. 64 (1980) 2261]. This method yields a set of linear simultaneous algebraic equations as many as the number of lattice sites, which is reduced to a simple equation with respect to the diffusion coefficient in the final step of the method. We here give a systematic way of the reduction in terms of the group theory.

KW - Correlation factor

KW - Projection operator

KW - Self-diffusion

UR - http://www.scopus.com/inward/record.url?scp=25144515941&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=25144515941&partnerID=8YFLogxK

U2 - 10.1143/JPSJ.74.2510

DO - 10.1143/JPSJ.74.2510

M3 - Article

VL - 74

SP - 2510

EP - 2516

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 9

ER -