International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. B. ch. 1.5, p. 169   | 1 | 2 |

Figure 1.5.5.1 

M. I. Aroyoa* and H. Wondratschekb

a Faculty of Physics, University of Sofia, bulv. J. Boucher 5, 1164 Sofia, Bulgaria , and bInstitut für Kristallographie, Universität, D-76128 Karlsruhe, Germany
Correspondence e-mail:  aroyo@phys.uni-sofia.bg

[Figure 1.5.5.1]
Figure 1.5.5.1

Symmorphic space group [Fm\bar{3}m] (isomorphic to the reciprocal-space group [{\cal G}^*] of [m\bar{3}mI]). (a) The asymmetric unit (thick dashed edges) imbedded in the Brillouin zone, which is a cubic rhombdodecahedron. (b) The asymmetric unit ΓHNP, IT A, p. 678. The representation domain [\Gamma NH_{3}P] of CDML is obtained by reflecting ΓHNP through the plane of ΓNP. Coordinates of the points: [\Gamma = 0, 0, 0]; [N = {1 \over 4}, {1 \over 4}, 0 \sim N_{1}={1 \over 4}, {1 \over 4}, {1 \over 2}]; [H = {1 \over 2}, 0, 0 \sim H_{1} = 0, 0, {1 \over 2} \sim H_{2} = {1 \over 2}, {1 \over 2}, {1 \over 2} \sim H_{3} = 0, {1 \over 2}, 0]; [P = {1 \over 4}, {1 \over 4}, {1 \over 4}]; the sign ∼ means symmetrically equivalent. Lines: [\Lambda = \Gamma P = x, x, x]; [F = HP = {1 \over 2} - x, x, x \sim F_{1}=PH_{2}=x, x, x \sim F_{2} = PH_{1} =x, x, {1 \over 2} - x]; [\Delta = \Gamma H = x, 0, 0]; [\Sigma = \Gamma N = x, x, 0]; [D = NP = {1 \over 4}, {1 \over 4}, z]; [G = NH =] [x, {1 \over 2} - x, 0]. Planes: [\hbox{A} = \Gamma HN = x, y, 0]; [B = HNP = x,{1 \over 2} - x, z ] [\sim PN_{1} H_{1} = x, x, z]; [C = \Gamma NP = x, x, z]; [J = \Gamma HP = x, y, y \sim \Gamma PH_{1} =] [ x, x, z]. Large black circles: corners of the asymmetric unit (special points); small open circles: other special points; dashed lines: edges of the asymmetric unit (special lines). For the parameter ranges see Table 1.5.5.1[link].