Triclinic Crystals
- Practical Electron Microscopy and Database -
- An Online Book -

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Table 3554a and Figure 3554 show the triclinic crystal system and the schematic illustration of the triclinic lattice, respectively.

Table 3554a. Triclinic crystal systems.

Crystal
family
Crystal
system
Required 
symmetries
of point group
Point 
group
Space 
group
Lattice
system
Triclinic
None 2 2 1 Triclinic

Schematic illustrations of the triclinic lattices

Figure 3554. Schematic illustrations of the Bravais lattice of triclinic crystals.

Table 3554b. Relationship between Laue classes and point groups.

System Essential symmetry  Lattice symmetry  Laue class (Diffraction symmetry) Point Groups (Hermann–Mauguin notation)
Triclinic None Triclinic Triclinic 1, -1
Monoclinic Monoclinic 2/m 2/m 2, m, 2/m
Orthorhombic 222 or 2mm
mmm
mmm 222, mm2, mmm
Tetragonal Tetragonal 4/mmm
4/m
4, -4, 4/m
4/mmm 422, -42m, 4mm, 4/mmm
Trigonal Trigonal Trigonal 3 3, -3
-3m1 321, 3m1, -3m1
-31m 312, 31m, -31m
Hexagonal 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 triclinic structures, the lattice spacing (d-spacing) can be given by, (You can download the excel file for your own calculations)

         lattice spacing (d-spacing)  of triclinic structures --------------------------------- [3554a]
         lattice spacing (d-spacing)  of triclinic structures --------------------------------- [3554b]
where,
        a, b and c -- The lattice constants.
        h, k, and l -- The Miller indices.

Table 3554c. Centrosymmetric, non-centrosymmetric, and chiral space groups for triclinic crystals.

Crystal system Laue group Point group Space group
Triclinic -1 1 P1
-1 P1
Red: chiral; green: non-centrosymmetric; and yellow: centrosymmetric.

Table 3554d. Other characteristics of triclinic 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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