Table 1.5.5.2

Aroyo, M. I.; Wondratschek, H.

doi:10.1107/97809553602060000553

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

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International Tables for Crystallography (2006). Vol. B. ch. 1.5, p. 170 | 1 | 2 |

Table 1.5.5.2

M. I. Aroyo^a ^* and H. Wondratschek^b

^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

Table 1.5.5.2 | top | pdf |
The k-vector types for the space groups $[Im\bar{3}]$ and $[Ia\bar{3}]$

Comparison of the k-vector labels and parameters of CDML with the Wyckoff positions of IT A for $[Fm\bar{3}]$ $[(T_{h}^{3})]$ , isomorphic to the reciprocal-space group $[{\cal G}^*]$ of $[m\bar{3}I]$ . The parameter ranges in $[Fm\bar{3}]$ are obtained by extending those of $[Fm\bar{3} m]$ such that each star of k is represented exactly once. The k-vector types of $[(Fm\bar{3}m)^*]$ , see Table 1.5.5.1, are also listed. The sign ∼ means symmetrically equivalent. Lines in parentheses are not special lines but belong to special planes. As in Table 1.5.5.1, the coordinates x, y, z of IT A are related to the k-vector coefficients of CDML by $[x = 1/2(k_{2} + k_{3})]$ , $[y = 1/2(k_{1} + k_{3})]$ , $[z = 1/2(k_{1} + k_{2})]$ .

k -vector label, CDML		Wyckoff position, IT A	Parameters (see Fig. 1.5.5.2 b), IT A
$[(Fm\bar{3}m)^*]$	$[(Fm\bar{3})^*]$	$[Fm\bar{3}]$
Γ	Γ	$[4\,\,a\,\,m\bar{3}]$ .	0, 0, 0
H	H	$[4\,\,b\,\,m\bar{3}]$ .	$[{1 \over 2}, 0, 0]$
P	P	8 c 23.	$[{1 \over 4}, {1 \over 4}, {1 \over 4}]$
N	N	$[24\,\,d\,\,2/m..]$	$[{1 \over 4}, {1 \over 4}, 0]$
Δ	Δ	24 e mm2..	$[x,0,0\hbox{:}\,\,0 \lt x \lt {1 \over 2}]$
Λ	Λ	32 f .3.	$[x,x,x\hbox{:}\,\,0 \lt x \lt {1 \over 4}]$
F	F	32 f .3.	$[{1 \over 2} - x,x,x\hbox{:}\,\,0 \lt x \lt {1 \over 4}]$
$[\sim F_{1}]$	$[\sim F_{1}]$	32 f .3.	$[x,x,x\hbox{:}\,\,{1 \over 4} \lt x \lt {1 \over 2}]$
$[\Lambda \cup F_1 \sim \Gamma H_{2}\backslash{}P]$	$[\Lambda \cup F_1 \sim \Gamma H_{2}\backslash{}P]$	32 f .3.	$[x,x,x\hbox{:}\,\,0 \lt x \lt {1 \over 2}]$ with $[x \neq {1 \over 4}]$
D	D	48 g 2..	$[{1 \over 4}, {1 \over 4}, z\hbox{:}\,\,0 \lt z \lt {1 \over 4}]$
Σ	Σ	48 h m..	$[x, y, 0\!: \ 0 \lt x = y \lt {1 \over 4}]$
G	G	48 h m..	$[x, y, 0\!: \ 0 \lt y = {1 \over 2} - x \lt {1 \over 4}]$
A	A	48 h m..	$[x, y, 0\!: \ 0 \lt y \lt x \lt {1 \over 2} - y]$
	AA −α, α, β	48 h m..	$[x, y, 0\!: \ 0 \lt {1 \over 2} - x \lt y \lt x]$
	$[A \cup AA \cup \Sigma \cup G]$	48 h m..	$[\displaylines{x, y, 0\!: \ 0 \lt y \lt x \lt {\textstyle{1 \over 2}} \;\cup\hfill\cr\quad \cup\; 0 \lt y = x \lt {\textstyle{1 \over 4}}\hfill}]$
C	$[\subset GP]$	96 i 1	$[x, y, z\!: 0 \lt z \lt x = y \lt {1 \over 4}]$
B	$[\subset GP]$	96 i 1	$[x, y, z\!: 0 \lt z \lt y = {1 \over 2} - x \lt {1 \over 4}]$
J	$[\subset GP]$	96 i 1	$[x, y, z\!: 0 \lt z = y \lt x \lt {1 \over 2} - y]$
GP	$[\subset GP]$	96 i 1	$[x, y, z\!: 0 \lt z \lt y \lt x \lt {1 \over 2} - y]$
	$[\subset GP]$	96 i 1	$[x, y, z\!: 0 \lt z \lt {1 \over 2} - x \lt y \lt x]$
	GP	96 i 1	$[\displaylines{x, y, z\!:0 \lt z \leq y \leq x \leq {\textstyle{1 \over 2}} - y \;\cup\hfill\cr \quad\cup\; x, y, z\!: 0 \lt z \lt {\textstyle{1 \over 2}} - x \lt y \lt x\hfill}]$