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International Journal of Theoretical Physics
Article . 1990 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
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The differential geometry of elementary point and line defects in Bravais crystals

Authors: E. Kr�ner;

The differential geometry of elementary point and line defects in Bravais crystals

Abstract

Since line defects (dislocations) and point defects (vacancies, self-interstitials, point stacking faults) in Bravais crystals can mutually convert, only theories which comprise these two sorts of defects can be closed in the sense of general field theory. Since the pioneering work of Kondo and of Bilby, Bullough, and Smith it is clear that differential geometry is the appropriate mathematical tool to formulate a field theory of defects in ordered structures. This is done here on the example of the Bravais crystal, where the above-mentioned defects are the only elementary point and line defects. It is shown that point defects can be described by a step-counting procedure which makes it possible to include also point stacking faults as elementary point defects. The results comprise two equations with the appropriate interpretation of the mathematical symbols. The point defects are step-counting defects and are essentially described by a metric tensorg, which supplements the torsion∑ responsible for the dislocations. The proposed theory is meant to form a framework for defect phenomena, in a similar way that Maxwell's theory is a framework for the electromagnetic world.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
64
Top 10%
Top 10%
Top 10%
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