Abstract
A new approach for describing dislocations and other topological defects in crystals, based on the density wave theory of Ramakrishnan and Yussouff is presented. Quantitative calculations are discussed in brief for the order parameter profiles, the atomic configuration and the free energy of a screw dislocation with Burgers vector\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {b} = (a/2, a/2,a/2 )\) in a bcc solid. Our results for the free energy of the dislocation in a crystal of sizeR, when expressed as (λb 2/4π) ln (αR/|b|) whereλ is the shear elastic constant, yield, for example, the valueα ⋍ 1·85 for sodium at its freezing temperature (371°K). The density distribution in the presence of the dislocation shows that the dislocation core has a columnar character. To our knowledge, this study represents the first calculation of dislocation structure, including the core, within the framework of an order parameter theory incorporating thermal effects.
Similar content being viewed by others
References
Christian J W 1983Metall. Trans. A14 123
Duesbery M S 1986Contemp. Phys. 27 145
Fetter A L and Hohenberg P C 1969Superconductivity (ed.) R D Parks (New York: M. Dekker), Vol. 2
Haymet A D J 1987Ann. Rev. Phys. Chem. (submitted).
Haymet A D J and Oxtoby D W 1982J. Chem. Phys. 74 2559
Landau L and Lifshitz L D 1970Theory of elasticity 2nd ed. (Oxford: Pergamon).
Oxtoby D W and Haymet A D J 1982J. Chem. Phys. 76 6262
Puls M P 1981 inProc. Int. Conf. on Dislocation Modelling of Physical Systems (Oxford: Pergamon) p. 249
Raj Lakshmi M, Krishnamurthy H R and Ramakrishnan T V 1987Phys. Rev. B (submitted).
Ramakrishnan T V 1984Pramana — J. Phys. 22 365
Ramakrisnan T V and Yussouff M 1979Phys. Rev. B19 2775
Vitek V, Perrin R C and Bowen D K 1970Philos. Mag. 21 1049
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lakshmi, M.R., Krishna-Murthy, H.R. & Ramakrishnan, T.V. Topological defects in crystals: A density-wave theory. Bull. Mater. Sci. 10, 45–51 (1988). https://doi.org/10.1007/BF02747429
Issue Date:
DOI: https://doi.org/10.1007/BF02747429