Orthorhombic Lattices

Chapter/Index: Introduction | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | Appendix

Orthorhombic Lattices

Table 3552a and Figure 3552 show the orthorhombic crystal systems and the schematic illustrations of the orthorhombic lattices, respectively. Furthermore, Table 3552c shows the cell edges and angles of orthorhombic crystals.

Table 3552a. Orthorhombic crystal systems.

Crystal family	Crystal system	Required symmetries of point group	Point group	Space group	Bravais lattices	Lattice system
Orthorhombic		3 two-fold axes of rotation or 1 two-fold axis of rotation and two mirror planes	3	59	4	Orthorhombic

Schematic illustrations of the orthorhombic lattices

Figure 3552. Schematic illustrations of the Bravais lattices of orthorhombic crystals.

Table 3552b. 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
Tetragonal		4/mmm	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
Hexagonal		6/mmm	6/mmm	622, -62m, 6mm, 6/mmm
Cubic	23	m3m	m-3	23, m-3
Cubic	23	m3m	m-3m	432, -43m, m-3m

For orthorhombic 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 orthorhombic structures --------------------------------- [3552]
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 orthorhombic lattices.

Crystal system	Laue group	Point group	Space group
Orthorhombic	mmm	222	P222, P222₁, P2₁2₁2, P2₁2₁2₁, C222, C222₁, I222, I2₁2₁2₁, F222
		mm2	Pmm2, Pmc2₁, Pcc2, Pma2, Pca2₁, Pnc2, Pmn2₁, Pba2, Pna2₁, Pnn2, Cmm2, Cmc2₁, Ccc2, Amm2, Abm2, Ama2, Aba2, Imm2, Iba2, Ima2, Fmm2, Fdd2
		mmm	Pmmm, Pnnn, Pccm, Pban, Pmma, Pnna, Pmna, Pcca, Pbam, Pccn, Pbcm, Pnnm, Pmmn, Pbcn, Pbca, Pnma, Cmcm, Cmca, Cmmm, Cccm, Cmma, Ccca, Immm, Ibam, Ibca, Imma, Fmmm, Fddd
Red: chiral; green: non-centrosymmetric; and yellow: centrosymmetric.

Table 3552c. Other characteristics of orthorhombic 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

Practical Electron Microscopy and Database

An Online Book, Second Edition by Dr. Yougui Liao (2006)

Orthorhombic Lattices