Geometry and symmetry of multilattices

International Journal of Plasticity

Volumn 14, Issue 1-3, 1998, Pages 139-157

  Pitteri, M ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

A. Multilattices; B. Lattice symmetry; C. Arithmetic equivalence; D. Crystallographic groups

Indexed keywords

CRYSTAL LATTICES; CRYSTAL SYMMETRY; CRYSTALLOGRAPHY; GEOMETRY; MATHEMATICAL MODELS;

ARITHMETIC EQUIVALENCE; CONTINUUM CONSTITUTIVE EQUATIONS; CRYSTALLOGRAPHIC GROUP; LATTICE SYMMETRY; MULTILATTICES;

ELASTICITY;

EID: 0032309308     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0749-6419(97)00045-4     Document Type: Article

References (25)

1. Bieberbach, L. (1912) Über die Bewegungsgruppen der Euklidische Räume. Math. Ann. 72, 400-412.
2. Burckhardt, J. J. (1947) Die Bewegungsgruppe der Kristallographie. Birkhäuser Verlag, Basel.
3. Engel, P. (1986) Geometric Crystallography. D. Reidel Publishing Co., Dordrecht.
4. Ericksen, J. L. (1979) On the symmetry of deformable crystals. Archive for Rational Mechanics and Analysis 72, 1-13.
5. Ericksen, J. L. (1987) Twinning of crystals. In Metastability and Incompletely Posed Problems. IMA Volumes in Mathematics and its Applications, vol. 3, eds S. S. Antman, J. L. Ericksen, D. Kinderlehrer and I. Müller. Springer-Verlag, New York, Berlin, Heidelberg.
6. Farkas, D. R. (1981) Crystallographic groups and their mathematics. Rocky Mountain Journal of Mathematics 11, 511-551.
7. James, R. D. (1987) The stability and metastability of quartz. In Metastability and Incompletely Posed Problems. IMA Volumes in Mathematics and its Applications, vol. 3, eds S. S. Antman, J. L. Ericksen, D. Kinderlehrer and I. Müller. Springer-Verlag, New York, Berlin, Heidelberg.
8. Janssen, T. (1973) Crystallographic Groups. North Holland, Amsterdam.
9. Jarič, M. V. and Senechal, M. (1984) Space groups and their isotropy subgroups. J. Math. Phys. 25, 3148-3154.
10. McLane, S. and Birkhoff, G. (1967) Algebra. MacMillan, London.
11. Miller, W. (1972) Symmetry Groups and Their Applications. Academic Press, New York and London.
12. Niggli, P. (1918) Geometrische Kristallographie des Diskontinuums. Bornträger, Leipzig.
13. Parry, G. P. (1981) On phase transitions involving internal strain. International Journal of Solids and Structures 17, 361-378.
14. Pitteri, M. (1985a) On crystallographic space groups and generalized lattice groups, unpublished.
15. Pitteri, M. (1985b) On v + 1-lattices. Journal of Elasticity 15, 3-25.
16. Pitteri, M. (1985c) On the kinematics of mechanical twinning in crystals. Archive for Rational Mechanics and Analysis 88, 25-57.
17. Pitteri, M. (1990) Some problems in non-linear elasticity of crystalline solids. Continuum Mech. Thermodyn. 2, 99-117.
18. Pitteri, M. and Zanzotto, G. (in press a) Continuum Models for Phase Transitions and Twinning in Crystals. Chapman & Hall, London.
19. Pitteri, M. and Zanzotto, G. (in press b) Symmetry-breaking and transformation twinning. Arch. Rat. Mech. Anal.
20. Schwarzenberger, R. L. (1972) Classification of crystal lattices. Proceedings of the Cambridge Philosophical Society 72, 325-349.
21. Schwarzenberger, R. L. (1980) N-dimensional Crystallography. Pitman, London.
22. Senechal, M. (1980) A simple characterization of the subgroups of space groups. Acta Crystallographica A36, 845-850.
23. Sohncke, L. (1874) Die regelmässigen ebenen Punktsysteme von ubegrentzer Ausdehnung. Journal reine Angewandte Mathematik 77, 47-101.
24. Sternberg, S. (1994) Group Theory and Physics. Cambridge University Press, Cambridge.
25. Zanzotto, G. (in press) Weak and symmetry-breaking phase transitions in simple lattices. Arch. Rat. Mech. Anal.