Abstract
A set of rules has been developed that allows for an exact description of various types of dislocation configurations in solids. These rules are in the form of conservation laws that exist between six uniquely defined Burgers vectors. Whereas four such laws are required for a lattice dislocation, the number may increase to as many as seven for a grain boundary dislocation. These findings are shown to be directly applicable to recent high-resolution electron microscopy observations of grain boundaries.
Similar content being viewed by others
References
J. M. Burgers, Proc. Kon. Nederl. Akad. Wetensch.,42, 293, 1939.
J. W. Christian and A. G. Crocker, “Dislocations and Lattice Transformations”, p. 165, in Dislocations in Solids, Vol. 3, ed. F. R. N. Nabarro, North-Holland Publ. Co. New York, 1980.
M. J. Marcinkowski, Phys. Stat. Sol. (a)96, 425, 1986.
A. P. Sutton, Int. Metals Rev.,29, 377, 1984.
T. Penisson, T. Nowicki and M. Biscondi, Phil. Mag.,A58, 947, 1988.
J. P. Hirth and J. Lothe, Theory of Dislocations, McGraw-Hill, New York, 1968.
Y. C. Fung, Foundations of Solid Mechanics, Prentice-Hall, Englewood Cliffs, New Jersey, 1965.
M. J. Marcinkowski, Phys. Stat. Sol. (a),98, 25, 1986.
M. J. Marcinkowski, Unified Theory of Mechanical Behavior of Matter, John Wiley and Sons, New York, 1979.
E. Kröner, Arch. Rational Mech. Anal.,4, 273, 1959.
J. A. Schouten, Ricci-Calculus, Springer, Berlin, 1954.
K. Kondo, Memoirs of the Unifying Study of the Basic Problems in Engineering Sciences by Means of Geometry, Vol. I, Gakujutsu Bunken Fukyu-Kai, Tokyo, 1955.
S. Golab, Tensor Calculus, Elsevier Scientific, Amsterdam, 1974.
R. deWit, J. Res. Nat. Bur. Stand.,77A (Phys. and Chem.), 607, 1973.
R. deWit, Int. J. Engng. Sci.,19, 1475, 1981.
B. A. Bilby, Defects in Crystalline Solids, p. 124, The Physical Society, London, 1955.
F. C. Frank, Report of the Symposium on the Plastic Deformation of Crystalline Solids, p. 150, Carnegie Institute of Technology, Pittsburgh, 1950.
M. J. Marcinkowski, Phys. Stat. Sol. (b),152, 9, 1989.
M. J. Marcinkowski, Phys. Stat. Sol. (a),73, 409, 1982.
M. J. Marcinkowski, J. Mater. Sci.,18, 827, 1983.
M. J. Marcinkowski, K. Sadananda and W. F. Tseng, Phys. Stat. Sol. (a)17, 423, 1973.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Marcinkowski, M.J. Burgers vector conservation laws. Acta Physica Hungarica 69, 37–52 (1991). https://doi.org/10.1007/BF03054132
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF03054132