Monoclinic Crystal Systems
- Practical Electron Microscopy and Database -
- An Online Book -

http://www.globalsino.com/EM/

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 3553a and Figure 3553 show the monoclinic crystal systems and the schematic illustration of the monoclinic lattices, respectively.

Table 3553a. Monoclinic crystal systems.

Crystal
family
Crystal
system
Required
symmetries
of point group
Point
group
Space
group
Bravais
lattices
Lattice
system
Monoclinic
1 two-fold axis of rotation or 1 mirror plane 3
13
2
Monoclinic

Figure 3553. Schematic illustrations of the Bravais lattices of monoclinic crystals.

Table 3553b. Relationship between Laue classes and point groups.

System Essential symmetry  Lattice symmetry  Laue class (Diffraction symmetry) Point Groups (Hermann–Mauguin notation)
Triclinic None 1, -1
Monoclinic 2/m 2/m 2, m, 2/m
Orthorhombic 222 or 2mm
mmm
mmm 222, mm2, mmm
Tetragonal 4/mmm
4/m
4, -4, 4/m
4/mmm 422, -42m, 4mm, 4/mmm
Trigonal 3 3, -3
-3m1 321, 3m1, -3m1
-31m 312, 31m, -31m
Hexagonal 6/mmm
6/m 6, -6, 6/m
6/mmm 622, -62m, 6mm, 6/mmm
Cubic 23 m3m
m-3 23, m-3
m-3m 432, -43m, m-3m

For monoclinic structures, the lattice spacing (d-spacing) can be given by, (You can download the excel file for your own calculations)

--------------------------------- [3553]
where,
a, b and c -- The lattice constants.
h, k, and l -- The Miller indices.

In crystals, anisotropy of many properties clearly arises because the arrangement of their atoms varies in different directions. In general, cubic crystals is less anisotropic than monoclinic ones because of their greater symmetry, for instance, with respect to electrical conductivity. Therefore, cubic crystals do not exhibit electrical polarization when the temperature is changed, so that their pyroelectric effect is isotropic.

Table 3553c. Centrosymmetric, non-centrosymmetric, and chiral space groups for monoclinic crystal systems.

 Crystal system Laue group Point group Space group Monoclinic 2/m 2 P2, P21, C2 m Pm, Pc, Cm, Cc 2/m P2/m, P21/m, C2/m, P2/c, P21/c, C2/c Red: chiral; green: non-centrosymmetric; and yellow: centrosymmetric.

Table 3553d. Other characteristics of monoclinic structures.

Contents
Page
Angles in unit cells page3555
Volume of unit cells page3033
Bravais lattices page4546
Relationship between three-dimensional crystal families, crystal systems, space group, point group, lattice systems and symmetries page4549

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