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Symmetry Groups for the Crystal Systems
- Practical Electron Microscopy and Database -
- An Online Book -
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https://www.globalsino.com/EM/
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This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers.
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Table 3545a. Symmetry groups for the crystal systems.
System |
Essential symmetry |
Lattice symmetry |
Diffraction (Laue) symmetry |
Point Groups (Hermann–Mauguin notation) |
Triclinic |
None |
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1, -1 |
Monoclinic |
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2/m |
2/m |
2, m, 2/m |
Orthorhombic |
222 or 2mm
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mmm
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mmm |
222, mm2, mmm |
Tetragonal |
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4/mmm
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4/m
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4, -4, 4/m |
4/mmm |
422, -42m, 4mm, 4/mmm |
Trigonal |
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3 |
3, -3 |
-3m1 |
321, 3m1, -3m1 |
-31m |
312, 31m, -31m |
Hexagonal |
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6/mmm
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6/m |
6, -6, 6/m |
6/mmm |
622, -62m, 6mm, 6/mmm |
Cubic |
23 |
m3m
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m-3 |
23, m-3 |
m-3m |
432, -43m, m-3m |
Table 3545b. Minimum number of symmetry elements.
System |
Minimum number of symmetry elements |
Triclinic |
None |
Monoclinic |
One 2-fold rotation or roto-inversion,
axis parallel to y-axis |
Orthorhombic |
Three 2-fold rotation or roto-inversion,
axes parallel to x,y,z-axes |
Tetragonal |
One 4-fold rotation or roto-inversion,
axis parallel to z-axis |
Rhombohedral (Trigonal) |
One 3-fold rotation or roto-inversion, axis parallel to z-axis |
Hexagonal |
One 6-fold rotation or rotoinversion,
axis parallel to z-axis |
Cubic |
Four 3-fold rotation or roto-inversion,
axes parallel to body diagonals |
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Non-pyroelectric |
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Non-ferroelectric |
Figure 3545. Schematic illustration of the different classes of crystal systems and their properties.
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The book author (Yougui Liao) welcomes your comments, suggestions, and corrections, please click here for submission. If you let book author know once you have cited this book, the brief information of your publication will appear on the “Times Cited” page.
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