Senechal M. — Crystalline Symmetries, An informal mathematical introduction :: Электронная библиотека попечительского совета мехмата МГУ

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Senechal M. — Crystalline Symmetries, An informal mathematical introduction

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Название: Crystalline Symmetries, An informal mathematical introduction

Автор: Senechal M.

Аннотация:

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.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1990

Количество страниц: 137

Добавлена в каталог: 18.10.2010

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Предметный указатель

(r, R) system      15
(r, R) system, regular      16
Agricola, G.      89 121
Aristotle      3 12 88 121
Barlow, W.      60
Bieberbach, L.      17 59 121
Bragg's condition      54
Bragg, W.H.      54
Bravais class      93
Bravais lattice      42
Bravais, A.      42 56 58 59 93 101 121
Brillouin zone      43
Burckhardt, J.J.      61 121
Cell, centered      43
Cell, unit      42
Cell, Voronoi      43
Center of symmetry      25
Centrosymmetric      25
Color group      85
Color symmetry      74
Convex      9
Coset      62
Coset, left      63
Coset, right      63
Crystal class      38
Crystal class, arithmetic      92
Crystal class, geometric      92
Crystal system      41 93
Crystallographic restriction      17
Curie, P.      8 122
de Bruijn, N.G.      111 112 113 114 115 121
de Wolff, P.      107 108
Delone, B.N.      15 18 46 122
Density function      55
Density of planar lattice      42
Diffraction      54
Dimension of a lattice      39
Dirac delta function      55
Dirichlet domain      43
Discrete      9
Donnay, J.D.H.      101
Eigenvalues      26
Engel, P.      12
Equivalent (units)      21
Escher, M.C.      75 76 77 83 87 122
Euler, L.      33 122
Ewald sphere      55
Fedorov, E.S.      12 45 59 89 122
Fourier transform      54 55
Frankenheim, M.      7 122
Frobenius congruence      69
Frobenius, G.      59 105 122
Frost, R.      88
Gadolin, A.      90 122
Generalized crystallography      115
Glide reflection      25
Graph      9
grid      113
Group, color      85
Group, commutative      27
Group, crystallographic      59 105
Group, cyclic      28
Group, generator      27 28
Group, orbit      28
Group, order of      28
Group, orthogonal      32
Group, point      32
Group, quotient      65
Group, space      59
Group, subgroup      29
Group, symmetry      27
Harker, D.      101
Hauey, R.-J.      4 6 7 12 17 39 56 59 90 122
Hermann, C.      72 75 122
Hilbert, D.      11 105 123
Hooke, R.      4 11 123
Index of a pentagrid vertex      115
Index of a subgroup      31
inversion      25
Isometry      22
Isomorphic      30
Isotropy group      30
Jordan, C.      59 60 123
Kepler, J.      4 9 10 11 12 13 15 103 108 123

Klein, F.      33 90 123
Lagrange's theorem      31 63
Lattice      16 39
Lattice, Bravais      42
Lattice, dual      50
Lattice, reciprocal      53
Laue class      96
Laue, M.      v 123
Law of Reticular Density      56
Linnaeus, C.      4 123
Little group      30
Mackay, A.      108 117 123
Matching rules for tiles      109
Miers, H.      60
Minkowski, H.      105
Modulated crystal      107
N-dimensional space group      105
Needham, J.      2
Network      13
Node of a graph      10
O(3)      32
Orbit      28
Orbit, generic      31
Parallelohedron      45
Pasteur, L.      60 123
Patterson symmetry      99
Penrose tiles      108
Penrose, R.      103 118 124
Pentagrid      113
Perfect coloring      77
Periodic pattern      16
Plato      3 6 88 124
Point group      32
Pole of rotation axis      33
Polyhedra, space-filling      11
Projection      105
Quasicrystal      x 2 118
Reflection      23
Reflection conditions      101
Regular system of points      16
Relatively dense set of points      10
Rogers, C.A.      11
Rotary inversion      25
Rotary reflection      24
Rotation      24
Schoenflies symbol      98
Schoenflies, A.      16 59 98 124
Screw rotation      25
Semi-direct product      70
Shubnikov, A.V.      75 77
Site-symmetry group      30
Sohncke, L.      59 124
Space group      59
Space group, nonsymmorphic      71
Space group, symmorphic      70
Sphere-packing      10
Sphere-packing, densest      11
Split extension      70
Stabilizer      29
Steno, N.      4 124
Strata      91
Subgroup      29
Subgroup, class-equivalent      72
Subgroup, conjugate      30
Subgroup, index      31
Subgroup, maximal      73
Subgroup, normal      64
Subgroup, proper      29
Subgroup, translation-equivalent      72
Symmetry group      27
Symmetry, color      74
Symmetry, element      23
Symmetry, five-fold      17 108
Symmetry, operation      22
Translation      25
Unit cell      42
Voronoi cell      43
Voronoi, G.      105 124
Wigner — Seitz cell      43
Willson, S.      58
Wulff equilibrium form      56
Wulff, G.      56 57 124
Wyckoff position      95
Zassenhaus, H.      61 124

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