Tables for
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2010). Vol. B, ch. 1.5, p. 175   | 1 | 2 |

Section 1.5.1. List of abbreviations and symbols

M. I. Aroyoa* and H. Wondratschekb

aDepartamento de Fisíca de la Materia Condensada, Facultad de Cienca y Technología, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain , and bInstitut für Kristallographie, Universität, D-76128 Karlsruhe, Germany
Correspondence e-mail:

1.5.1. List of abbreviations and symbols

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BC Bradley & Cracknell (1972[link])
CDML Cracknell, Davies, Miller & Love (1979[link])
IT A International Tables for Crystallography, Volume A (2005[link])
irreps Irreducible representations
L; [{\bf L}^*] Vector lattice of a space group [\cal G]; reciprocal lattice of [\cal G]
t Vector of the lattice L of [\cal G]
k Vector of the reciprocal space
K Vector of the reciprocal lattice [{\bf L}^*] [see Note (1)]
[{\bf a}, {\bf b}, {\bf c}\semi {\bf a}^*,{\bf b}^*,{\bf c}^*] Basis vectors of the crystal lattice; basis vectors of the reciprocal lattice
[({\bf a})^{T}] Row of basis vectors [see Note (2)]
[({\bf a}^*)] Column of basis vectors of the reciprocal lattice [{\bf L}^*]
X Point of point space
[x,y,z\semi\ k_x,k_y,k_z] Point coordinates; vector coefficients
x; r Column of point coordinates; column of vector coefficients
[({\bi k})^{T}] Row of coefficients of a reciprocal-space vector [see Note (2)]
[a,b,c] Lengths of the basis vectors of the lattice
[\alpha,\beta,\gamma] Parameters of k-vector coefficients in CDML
[a^*,b^*,c^*] Lengths of the basis vectors of the reciprocal lattice
M, R, D, S Matrices
W Matrix part of a mapping
w Column part of a mapping
(A, a), (W, w) Matrix–column pairs
[\cal G]; [{\cal G}_0]; [({\cal G})^*] Group or space group; symmorphic space group; reciprocal-space group
[\cal T] Translation subgroup of [\cal G]
[\cal P] or [\overline{\cal{G}}]; [\cal Q] Point group; holohedral point group
[\cal S] Site-symmetry group
[\overline{\cal{G}}^{\bf k}]; [{\cal L}^{\bf k}] Little co-group of k; little group of k
[\sf g], [\sf h], [\sf e] Group elements of [\cal G]
[\sf 2], [\sf 3], [\sf m] Symmetry operations
[\Gamma({\cal G})] (Matrix) representation of the group [\cal G]

Notes: (1) In crystallography, vectors are designated by lower-case bold-face letters. With K we make an exception in order to follow the tradition of physics. A crystallographic alternative could be [{\bf t}^{*}]. (2) In crystallography, point coordinates or vector coefficients are written as columns. Therefore, columns are taken as `normal'. In order to distinguish rows from columns (the coefficients [k_i] of vectors in reciprocal space, i.e. the Miller indices, and the basis of the crystal lattice are written as rows), rows are regarded as transposed columns and are thus marked by [(\ldots)^{T}].


International Tables for Crystallography (2005). Vol. A, Space-Group Symmetry, edited by Th. Hahn, 5th ed. Heidelberg: Springer.
Bradley, C. J. & Cracknell, A. P. (1972). The Mathematical Theory of Symmetry in Solids: Representation Theory for Point Groups and Space Groups. Oxford: Clarendon Press.
Cracknell, A. P., Davies, B. L., Miller, S. C. & Love, W. F. (1979). Kronecker Product Tables, Vol. 1, General Introduction and Tables of Irreducible Representations of Space Groups. New York: IFI/Plenum.

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