Abstract
The role of groups and their representations in the physics of periodic order is well-known. The symmetry of the atomic density under a discrete translation group T yields the concepts of the lattice and of the discrete cell structure. The inclusion of point symmetry leads to a description in terms of space groups. The representations of space groups appear in the Fourier and diffraction analysis, in the electronic band structure, and in the lattice dynamics.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
H. Bohr, Fastperiodische Funktionen, Berlin (1932)
H. Bohr, Acta Math. 45: 29 (1925)
H. Bohr, Acta Math. 46: 101 (1925)
H. Bohr, Acta Math. 47: 237 (1926)
A. Schoenflies, Krystallsysteme und Krystallstruktur, Teubner, Leipzig (1891)
E.S. Fedorov, The symmetry of regular systems of figures, Not. of the Imp. St. Petersburg Min. Soc. 28: 1 (1891)
P. Kramer and R. Neri, Acta Cryst. A40: 580 (1984)
R.W. Haase, P. Kramer, L. Kramer and H. Lalvani, Acta Cryst. A43: 574 (1987)
H. Brown, R. Bülow, J. Neubüser, H. Wondratschek and H. Zassenhaus, Crystallographic Groups of Four-dimensional Space, Wiley, New York (1978)
R.L.E. Schwarzenberger, N-dimensional Crystallography, Pitman, San Francisco (1980)
G. Voronoi, Crelles J. f. d. reine und ang. Math. 134: 198 (1908)
G. Voronoi, Crelles J. f. d. reine und ang. Math. 136: 67 (1909)
J.R. Munkres, Elements of Algebraic Topology, Addison-Wesley, Menlo Park (1984)
P. Kramer, submitted for publication
P. Kramer, Mod. Phys. Lett. B 1: 7 (1987)
P. Kramer, Int. J. Mod. Phys. B 1: 145 (1987)
P. Kramer, Mod. Phys. Lett. B 2: 605 (1988)
M. Lothaire, Combinatorics on Words, Addison-Wesley, Reading (1983)
D. Shechtman, I. Blech, D. Gratias, and J.W. Cahn, Phys. Rev. Lett. 53: 2477 (1984)
A.L. Mackay, Int. J. of Rapid Solidification 2: S1 (1987)
R. Penrose, Bull. Inst. Math. Appl. 10: 266 (1974)
N.G. de Bruijn, Proc. Konig. Ned. Akad. Weten. A 84: 39 (1981)
A.L. Mackay, Physica 114 A: 609 (1982)
P.J. Steinhardt and St. Ostlund, The Physics of Quasicrystals, World Scientific, Singapore (1987)
Ch. Janot and J.M. Dubois, Editors, Quasicrystalline Materials, World Scientific, Singapore (1988)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Plenum Press, New York
About this chapter
Cite this chapter
Kramer, P. (1989). Group Theory for Non-Periodic Long-Range Order in Solids. In: Gruber, B., Iachello, F. (eds) Symmetries in Science III. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0787-7_13
Download citation
DOI: https://doi.org/10.1007/978-1-4613-0787-7_13
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-8082-8
Online ISBN: 978-1-4613-0787-7
eBook Packages: Springer Book Archive