Abstract
I use the theory of Lie groups/algebras to discuss the symmetries of crystals with uniform distributions of defects.
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References
Davini, C.: A proposal for a continuum theory of defective crystals. Arch. Ration. Mech. Anal. 96, 295–317 (1986)
Pontryagin, L.S.: Topological Groups, 2nd edn. Gordon and Breach, New York (1955)
Olver, P.J.: Equivalence, Invariants, and Symmetry. Cambridge University Press, Cambridge (1996)
Varadarajan, V.S.: Lie Groups, Lie Algebras, and Their Representations. Prentice-Hall, Englewood Cliffs (1974)
Warner, F.W.: Foundations of Differentiable Manifolds and Lie Groups. Springer, New York (1983)
Belinfante, J.G.F.: Lie algebras and inhomogeneous simple materials. SIAM J. Appl. Math. 25, 260–268 (1973)
Bilby, B.A.: Geometry and continuum mechanics, Reprint
Parry, G.P.: Group properties of defective crystal structures. Math. Mech. Solids 8, 515–538 (2003)
Cermelli, P., Parry, G.P.: The structure of uniform discrete defective crystals. Contin. Mech. Thermodyn. 18(1–2), 47–61 (2006)
Elzanowksi, M., Parry, G.P.: Material symmetry in a theory of continuously defective crystals. J. Elast. 74(3), 215–237 (2004)
Caratheodory, C.: Calculus of Variations and Partial Differential Equations of the First Order, Part I. Holden-Day, San Francisco (1965)
Magnus, W., Karrass, A., Solitar, D.: Combinatorial Group Theory. Dover, New York (1976)
Pitteri, M., Zanzotto, G.: Continuum Models for Phase Transitions and Twinning in Crystals. Chapman and Hall/CRC, Boca Raton (2003)
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Parry, G.P. Rotational Symmetries of Crystals with Defects. J Elasticity 94, 147–166 (2009). https://doi.org/10.1007/s10659-008-9188-7
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DOI: https://doi.org/10.1007/s10659-008-9188-7