Theory of color symmetry for periodic and quasiperiodic crystals

Reviews of Modern Physics

Volumn 69, Issue 4, 1997, Pages 1181-1218

  Lifshitz, Ron ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031514042     PISSN: 00346861     EISSN: None     Source Type: Journal    
DOI: 10.1103/revmodphys.69.1181     Document Type: Article

References (43)

1. Ashcroft, N. W., and N. D. Mermin, 1976, Solid State Physics (Saunders College, Philadelphia).
2. Baake, M., 1997, "Combinatorial aspects of colour symmetries," J. Phys. A: Math. Gen. 30, 2687-2698.
3. Boyle, L. L., 1969, "Non-crystallographic Shubnikov groups," Acta Crystallogr., Sect. A 25, 455-459.
4. de Wolff, P. M., T. Janssen, and A. Janner, 1981, "The superspace groups for incommensurate crystal structures with a one-dimensional modulation," Acta Crystallogr., Sect. A 37, 625-636.
5. Dräger, J., and N. D. Mermin, 1996, "Superspace groups without the embedding: The link between superspace and Fourier-space crystallography," Phys. Rev. Lett. 76, 1489-1492.
6. Elser, V. 1995, private communication.
7. Harker, D., 1976, "A table of colored crystallographic and icosahedral point groups, including their chirality and diamorphism," Acta Crystallogr., Sect. A 32, 133-139.
8. Harker, D., 1978a, "Colored lattices," Proc. Natl. Acad. Sci. USA 75, 5264-5267.
9. Harker, D., 1978b, "Effect of rotational symmetry on colored lattices," Proc. Natl. Acad. Sci. USA 75, 5751-5754.
10. International Union of Crystallography 1992, "Report of the Executive Committee for 1991," Acta Crystallogr., Sect. A 48, 922-946.
11. International Union of Crystallography, 1995, International Tables for Crystallography, Volume A, 4th revised edition, edited by T. Hahn (Kluwer Academic, Dordrecht).
12. Janssen, T., A. Janner, A. Looijenga-Vos, and P. M. de Wolff, 1992, "Incommensurate and commensurate modulated structures," in International Tables for Crystallography, Volume C, edited by A. J. C. Wilson (Kluwer Academic, Dordrecht), pp. 797-844.
13. Lang, S., 1971, Algebra (Addison-Wesley, Reading, MA).
14. Li, X. Z., J. M. Dubois, and K. H. Kuo, 1994, "Two-colour Penrose tiling," Philos. Mag. Lett. 69, 93-98.
15. Lifshitz, R., 1995, Ph.D. thesis (Cornell University).
16. Lifshitz, R., 1996a, "The symmetry of quasiperiodic crystals," Physica A 232, 633-647.
17. Lifshitz, R., 1996b, "Extinctions in scattering from magnetically ordered quasiperiodic crystals," in Extended Abstracts of the Workshop on Application of Symmetry Analysis to Diffraction Investigation, edited by W. Sikora (University of Mining and Metallurgy, Kraków), pp. 70-75.
18. Lifshitz, R., and N. D. Mermin, 1995, "Color Symmetry of Aperiodic Structures," in Aperiodic '94, edited by G. Chapuis and W. Paciorek (World Scientific, Singapore), pp. 77-81.
19. Lück, R., 1987, "Frequency of vertex configurations and imperfections in a semiperiodic three-dimensional Penrose tiling," Mater. Sci. Forum 22-24, 231-246.
20. Lück, R., 1995, "Screw dislocations in decagonal quasicrystals," in Aperiodic '94, edited by G. Chapuis and W. Paciorek (World Scientific, Singapore), pp. 35-39.
21. Macgillavry, C. H., 1965, Symmetry Aspects of M. C. Escher's Periodic Drawings (A. Oosthoek's Uitgeversmaatschappij NV, Utrecht).
22. Mermin, N. D., 1992, "The space groups of icosahedral quasicrystals and cubic, orthorhombic, monoclinic, and triclinic crystals," Rev. Mod. Phys. 64, 3-49.
23. Mermin, N. D., and R. Lifshitz, 1992, "Bravais Classes for the Simplest Incommensurate Crystal Phases," Acta Crystallogr., Sect. A 48, 515-532.
24. Mermin, N. D., D. A. Rabson, D. S. Rokhsar, and D. C. Wright, 1990, "Stacking quasicrystallographic lattices," Phys. Rev. B 41, 10498-10502.
25. Mermin, N. D., D. S. Rokhsar, and D. C. Wright, 1987, "Beware of 46-fold symmetry: The classification of two-dimensional quasicrystallographic lattices," Phys. Rev. Lett. 58, 2099-2101.
26. Moody, R. V., and J. Patera, 1994, "Colourings of quasicrystals," Can. J. Phys. 72, 442-452.
27. Niizeki, K., 1990a, "Icosahedral black-and-white Bravais quasilattices and order-disorder transformations of icosahedral quasicrystals," J. Phys. A: Math. Gen. 23, L1069-L1072.
28. Niizeki, K., 1990b, "Three-dimensional black-and-white Bravais quasilattices with (2+1)-reducible point groups," J. Phys. A: Math. Gen. 23, 5011-5016.
29. Opechowski, W., 1986, Crystallographic and Metacrystallographic Groups (North-Holland, Amsterdam).
30. jgm," Acta Crystallogr., Sect. A 44, 678-688.
31. Rabson, D. A., N. D. Mermin, D. S. Rokhsar, and D. C. Wright, 1991, [RMRW], "The space groups of axial crystals and quasicrystals," Rev. Mod. Phys. 63, 699-733.
32. Rokhsar, D. S., N. D. Mermin, and D. C. Wright, 1987, "Rudimentary crystallography: The icosahedral and decagonal reciprocal lattices," Phys. Rev. B 35, 5487-5495.
33. Rokhsar, D. S., D. C. Wright, and N. D. Mermin, 1988a, "The two-dimensional quasicrystallographic space groups with rotational symmetries less than 23-fold," Acta Crystallogr., Sect. A 44, 197-211.
34. Rokhsar, D. S., D. C. Wright, and N. D. Mermin, 1988b, "Scale equivalence of quasicrystallographic space groups," Phys. Rev. B 37, 8145-8149.
35. Scheffer, M., and R. Lück, 1996, "New decagonal LI classes with five colour symmetry," in Extended Abstracts of the Workshop on Aperiodic Structures, edited by J. Wolny (University of Mining and Metallurgy, Kraków), pp. 21-23.
36. Schwarzenberger, R. L. E., 1984, "Colour symmetry," Bull. London Math. Soc. 16, 209-240.
37. Senechal, M., 1975, "Point groups and color symmetry," Z. Kristallogr. 142, 1-23.
38. Senechal, M., 1979, "Color groups," Discrete Appl. Math. 1, 51-73.
39. Senechal, M., 1990, Crystalline Symmetries: An Informal Mathematical Introduction (Adam Hilger, Bristol).
40. Sheng, Q., 1994, Ph.D. thesis (Cornell University).
41. Sheng, Q., and V. Elser, 1994, "Quasicrystalline minimal surfaces," Phys. Rev. B 49, 9977-9980.
42. Shubnikov, A. V., N. V. Belov, and others, 1964, Colored Symmetry (Pergamon, New York).
43. Yamamoto, A., T. Janssen, A. Janner, and P. M. de Wolff, 1985, "A note on the superspace groups for one-dimensionally modulated structures," Acta Crystallogr., Sect. A 41, 528-530.