Crystalline Symmetries: an informal mathematical introduction is a guided tour through the maze of mathematical models and classifications that are used today to describe the symmetries of crystals. The mathematical basis of crystallography and the interpretation of The International Tables for X-ray Crystallography are explained in a heuristic and accessible way. In addition to discussing standard crystals, a special feature of this book is the chapter on generalised crystals and the Penrose tile model for the kinds of generalised crystals known as quasicrystals. This fruitful interaction between pure mathematics (symmetry, tilings) and physics should prove invaluable to final year undergraduate/graduate physicists and materials scientists; the reader gets a flavour of the powerful coherence of a group theoretical approach to crystallography. Mathematicians interested in applications of group theory to physical science will also find this book useful.
|Publisher:||Taylor & Francis|
|Product dimensions:||5.51(w) x 8.66(h) x (d)|
Table of ContentsMathematical crystals: What is mathematical crystallography? Un peu d'histoire. Models of crystal structure. Symmetry and point groups: Symmetries and isometries. Symmetry groups. Point groups in 3-space. Lattices: Lattices and symmetry. Unit cells. The Voronoi cell. The reciprocal lattice. The space groups: Chronology. The orbits of a space group. Cosets and normal subgroups. Constructing the space groups. Symmorphic and nonsymmorphic space groups. Subgroups of space groups. Color symmetry: Why colors: Coloring finite figures. Coloring infinite patterns. Color groups, color symmetry, and colorings. Classification and the international tables: The classification problem. Why symmetry? Crystallographic classifications. Translating a page of the international tables. N-dimensional crystallography?: The view from N-dimensional space. Projections. The Penrose tiles. De Bruijn's interpretation. Generalized crystallography. Further reading and appendices.