# Statistical mechanics treatment of the evolution of dislocation distributions in single crystals

## Abstract

A statistical mechanics framework for the evolution of the distribution of dislocations in a single crystal is established. Dislocations on various slip systems are represented by a set of phase-space distributions each of which depends on an angular phase space coordinate that represents the line sense of dislocations. The invariance of the integral of the dislocation density tensor over the crystal volume is proved. From the invariance of this integral, a set of Liouville-type kinetic equations for the phase-space distributions is developed. The classically known continuity equation for the dislocation density tensor is established as a macroscopic transport equation, showing that the geometric and crystallographic notions of dislocations are unified. A detailed account for the short-range reactions and cross slip of dislocations is presented. In addition to the nonlinear coupling arising from the long-range interaction between dislocations, the kinetic equations are quadratically coupled via the short-range reactions and linearly coupled via cross slip. The framework developed here can be used to derive macroscopic transport-reaction models, which is shown for a special case of single-slip configuration. The boundary value problem of dislocation dynamics is summarized, and the prospects of development of physical plasticity models for single crystals are discussed. (c) 2000more »

- Authors:

- Pacific Northwest National Laboratory, MSIN: K1-83, 902 Battelle Boulevard, P.O. Box 999, Richland, Washington 99352 (United States)

- Publication Date:

- OSTI Identifier:
- 20216412

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. B, Condensed Matter and Materials Physics

- Additional Journal Information:
- Journal Volume: 61; Journal Issue: 18; Other Information: PBD: 1 May 2000; Journal ID: ISSN 1098-0121

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; STATISTICAL MECHANICS; CRYSTALS; DISLOCATIONS; KINETIC EQUATIONS; SLIP; PLASTICITY; THEORETICAL DATA

### Citation Formats

```
El-Azab, A.
```*Statistical mechanics treatment of the evolution of dislocation distributions in single crystals*. United States: N. p., 2000.
Web. doi:10.1103/PhysRevB.61.11956.

```
El-Azab, A.
```*Statistical mechanics treatment of the evolution of dislocation distributions in single crystals*. United States. doi:10.1103/PhysRevB.61.11956.

```
El-Azab, A. Mon .
"Statistical mechanics treatment of the evolution of dislocation distributions in single crystals". United States. doi:10.1103/PhysRevB.61.11956.
```

```
@article{osti_20216412,
```

title = {Statistical mechanics treatment of the evolution of dislocation distributions in single crystals},

author = {El-Azab, A.},

abstractNote = {A statistical mechanics framework for the evolution of the distribution of dislocations in a single crystal is established. Dislocations on various slip systems are represented by a set of phase-space distributions each of which depends on an angular phase space coordinate that represents the line sense of dislocations. The invariance of the integral of the dislocation density tensor over the crystal volume is proved. From the invariance of this integral, a set of Liouville-type kinetic equations for the phase-space distributions is developed. The classically known continuity equation for the dislocation density tensor is established as a macroscopic transport equation, showing that the geometric and crystallographic notions of dislocations are unified. A detailed account for the short-range reactions and cross slip of dislocations is presented. In addition to the nonlinear coupling arising from the long-range interaction between dislocations, the kinetic equations are quadratically coupled via the short-range reactions and linearly coupled via cross slip. The framework developed here can be used to derive macroscopic transport-reaction models, which is shown for a special case of single-slip configuration. The boundary value problem of dislocation dynamics is summarized, and the prospects of development of physical plasticity models for single crystals are discussed. (c) 2000 The American Physical Society.},

doi = {10.1103/PhysRevB.61.11956},

journal = {Physical Review. B, Condensed Matter and Materials Physics},

issn = {1098-0121},

number = 18,

volume = 61,

place = {United States},

year = {2000},

month = {5}

}