Table 1.5.5.3

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. 172 | 1 | 2 |

Table 1.5.5.3

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 1.5.5.3 | top | pdf |
The k-vector types for the space groups [I4/mmm] , [I4/mcm] , $[I4_{1}/amd]$ and $[I4_{1}/acd]$

Comparison of the k-vector labels and parameters of CDML with the Wyckoff positions of IT A for [I4/mmm] $[(D_{4h}^{17})]$ , isomorphic to the reciprocal-space group $[{\cal G}^*]$ of [4/mmmI] . For the asymmetric unit, see Fig. 1.5.5.3. Two ratios of the lattice constants are distinguished for the representation domains of CDML: $[a \gt c]$ and $[a \lt c]$ , see Figs. 1.5.5.3(a, b) and (c, d). The sign ∼ means symmetrically equivalent. The parameter ranges for the planes and the general position GP refer to the asymmetric unit. The coordinates x, y, z of IT A are related to the k-vector coefficients of CDML by $[x = 1/2(-k_{1} + k_{2})]$ , $[y = 1/2(k_{1} + k_{2} + 2k_{3})]$ , $[z = 1/2(k_{1}+ k_{2})]$ .

k -vector labels, CDML		Wyckoff position, IT A	Parameters (see Fig. 1.5.5.3), IT A
$[a \gt c]$	$[a \lt c]$	Wyckoff position, IT A	$[a \gt c]$	$[a \lt c]$ ^†
Γ 0, 0, 0	Γ 0, 0, 0	$[2\,\,a\,\,4/mmm]$	0, 0, 0
$[M\,\,- {1 \over 2}, {1 \over 2}, {1 \over 2}]$	$[M\,\,{1 \over 2}, {1 \over 2}, - {1 \over 2}]$	$[2\,\,b\,\,4/mmm]$	$[{1 \over 2}, {1 \over 2},0]$	$[0,0,{1 \over 2}]$
$[X\,\,0,0,{1 \over 2}]$	$[X\,\,0,0,{1 \over 2}]$	4 c mmm.	$[0,{1 \over 2},0]$
$[P\,\,{1 \over 4}, {1 \over 4}, {1 \over 4}]$	$[P\,\,{1 \over 4}, {1 \over 4}, {1 \over 4}]$	$[4\,\,d\,\,\bar{4}m2]$	$[0,{1 \over 2}, {1 \over 4}]$
$[N\,\,0,{1 \over 2},0]$	$[N\,\,0,{1 \over 2},0]$	$[8\,\,f\,\,..2/m]$	$[{1 \over 4}, {1 \over 4}, {1 \over 4}]$
Λ α, α, −α	Λ α, α, −α	4 e 4mm	$[0,0,z\hbox{:}\,\,0 \lt z \leq z_{0}]$ ^‡	$[0 \lt z \lt {1 \over 2}]$
$[V\,\,- {1 \over 2} + \alpha, {1 \over 2} + \alpha, {1 \over 2} - \alpha]$	—	4 e 4mm	$[{1 \over 2}, {1 \over 2}, z\!: 0 \lt z \lt z_{1} = {1 \over 2} - z_{0}]$	—
$[W\,\,\alpha, \alpha, {1 \over 2} - \alpha]$	$[W\,\,\alpha, \alpha, {1 \over 2} - \alpha]$	8 g 2mm.	$[0, {1 \over 2},z\hbox{:}\,\,0 \lt z \lt {1 \over 4}]$
Σ −α, α, α	Σ −α, α, α	8 h m.2m	$[x, x, 0\!: 0 \lt x \lt {1 \over 2}]$	$[0 \lt x \leq s_{1}]$
—	$[F\,\,{1 \over 2} - \alpha, {1 \over 2} + \alpha, - {1 \over 2} + \alpha]$	8 h m.2m	—	$[x,x,{1 \over 2}\hbox{:}\,\, 0 \lt x \lt s = {1 \over 2} - s_{1}]$
Δ 0, 0, α	Δ 0, 0, α	8 i m2m.	$[0,y,0\hbox{:}\,\,0 \lt y \lt {1 \over 2}]$
$[Y\,\,- \alpha, \alpha, {1 \over 2}]$	$[Y\,\,- \alpha, \alpha, {1 \over 2}]$	8 j m2m.	$[x, {1 \over 2}, 0\!\!: 0 \lt x \lt {1 \over 2}]$	$[0 \lt x \leq r]$
—	$[U\,\,{1 \over 2}, {1 \over 2}, - {1 \over 2} + \alpha]$	8 j m2m.	—	$[0,y,{1 \over 2}\hbox{:}\,\, 0 \lt y \lt g = {1 \over 2} - r]$
$[Q\,\,{1 \over 4} - \alpha, {1 \over 4} + \alpha, {1 \over 4} - \alpha]$	$[Q\,\,{1 \over 4} - \alpha, {1 \over 4} + \alpha, {1 \over 4} - \alpha]$	16 k ..2	$[x, {1 \over 2} - x, {1 \over 4}\!\!: 0 \lt x \lt {1 \over 4}]$
C −α, α, β	C −α, α, β	16 l m..	$[x,y,0\hbox{:}\,\,0 \lt x \lt y \lt {1 \over 2}]$ ^§	—
—	$[D\,\,{1 \over 2} - \alpha, {1 \over 2} + \alpha, - {1 \over 2} + \beta]$	16 l m..	—	$[x,y,{1 \over 2}]$
B α, β, −α	B α, β, −α	16 m ..m	$[x,x,z\hbox{:}\,\,0 \lt x \lt {1 \over 2},0 \lt z \lt {1 \over 4} \cup 0 \lt x \lt {1 \over 4},z = {1 \over 4}]$
A α, α, β	A α, α, β	16 n .m.	$[0,y,z\hbox{:}\,\,0 \lt y \lt {1 \over 2},0 \lt z \lt {1 \over 2}]$ ^¶
$[E\,\,\alpha - \beta, \alpha + \beta, {1 \over 2} - \alpha]$	$[E\,\,\alpha - \beta, \alpha + \beta, {1 \over 2} - \alpha]$	16 n .m.	$[x, {1 \over 2},z]$ : transferred to
GP α, β, γ	GP α, β, γ	32 o 1	$[x,y,z\hbox{:}\,\,0 \lt x \lt y \lt {1 \over 2},0 \lt z \lt {1 \over 4} \cup 0 \lt x \lt y \lt {1 \over 2} - x,z = {1 \over 4}]$