Continuity of dislocations

Journal Article · Sun Sep 01 04:00:00 EDT 1985 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.526824· OSTI ID:5345896

Bloomer, I; Charap, J M

Dislocation continuity is derived from the Bilby--Kondo theory of dislocations using exterior calculus. Dislocation density is represented by the torsion vector-valued two-form. Burgers vectors are associated with the vector part of the torsion while dislocation lines are associated with the two-form part. The exterior derivative of the torsion is shown to vanish when the crystal curvature vanishes. This implies two simultaneous continuity conditions: Burgers vector conservation and continuity of dislocation lines. On the other hand, dislocation continuity is violated when the curvature does not vanish. Since this can occur on grain boundaries it is inferred that grain boundaries are regions where crystal curvature is concentrated.

• Research Organization: Department of Physics, San Jose State University, San Jose, California 95192
• DOE Contract Number: AC07-76ET10723
• OSTI ID: 5345896
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 26:9; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

656000* -- Condensed Matter Physics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BURGERS VECTOR
CONSERVATION LAWS
CONTINUITY EQUATIONS
CRYSTAL DEFECTS
CRYSTAL LATTICES
CRYSTAL STRUCTURE
CRYSTALS
DIFFERENTIAL EQUATIONS
DISLOCATIONS
EQUATIONS
GEOMETRY
GRAIN BOUNDARIES
LINE DEFECTS
MATHEMATICS
MICROSTRUCTURE
PARTIAL DIFFERENTIAL EQUATIONS
TORSION