International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 5.2, p. 492

Table 5.2.1.1 

W. Parrish,a A. J. C. Wilsonb and J. I. Langfordc

aIBM Almaden Research Center, San Jose, CA, USA,bSt John's College, Cambridge CB2 1TP, England, and cSchool of Physics & Astronomy, University of Birmingham, Birmingham B15 2TT, England

Table 5.2.1.1| top | pdf |
Functions of the cell angles in equation (5.2.1.3)[link] for the possible unit cells

FunctionCell
Cubic
tetragonal
orthorhombic
HexagonalMonoclinic (c unique)RhombohedralTriclinic
A 1 1 1 [\sin^2\alpha] [\sin^2\alpha]
B 1 1 1 [\sin^2\alpha] [\sin^2\beta]
C 1 [3\over4] [\sin^2\gamma] [\sin^2\alpha] [\sin^2\gamma]
D 0 0 0 [\cos^2\alpha-\cos\alpha] [\cos\beta\cos\gamma-\cos\alpha]
E 0 0 0 [\cos^2\alpha-\cos\alpha] [\cos\gamma\cos\alpha - \cos\beta]
F 0 [1\over2] [-\cos\gamma] [\cos^2\alpha-\cos\alpha] [\cos\alpha\cos\beta - \cos\gamma]
G 1 [3\over4] [\sin^2 \gamma] [1+2\cos^3\alpha-3\cos^2\alpha] [1+2\cos\alpha\cos\beta\cos\gamma] [-\cos^2\alpha-\cos^2\beta-\cos^2\gamma]