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

International Tables for Crystallography (2010). Vol. B, ch. 1.5, p. 184   | 1 | 2 |

Table 1.5.5.2 

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:  wmpararm@lg.ehu.es

Table 1.5.5.2| top | pdf |
List of k-vector types for arithmetic crystal class [m\overline{3}I]

See Fig. 1.5.5.2[link]. Parameter relations: [x=\textstyle{1 \over 2}\beta + \textstyle{1 \over 2}\gamma], [y=\textstyle{1 \over 2}\alpha+\textstyle{1 \over 2}\gamma], [z=\textstyle{1 \over 2}\alpha+\textstyle{1 \over 2}\beta].

k-vector label, CDMLWyckoff position of IT A, cf. Section 1.5.4.3[link]Parameters
[\Gamma\quad 0,0,0]   [4 \quad a \quad m\overline3.] [0,0,0]
[H \quad \textstyle{1 \over 2},-\textstyle{1 \over 2},\textstyle{1 \over 2}]   [4 \quad b \quad m\overline3.] [0,\textstyle{1 \over 2},0]
[P \quad \textstyle{1 \over 4},\textstyle{1 \over 4},\textstyle{1 \over 4}]   [8 \quad c \quad 23.] [\textstyle{1 \over 4},\textstyle{1 \over 4},\textstyle{1 \over 4}]
[N \quad 0,0,\textstyle{1 \over 2}]   [24 \quad d \quad 2/m..] [\textstyle{1 \over 4},\textstyle{1 \over 4},0]
[\Delta\quad \alpha,-\alpha,\alpha]   [24 \quad e \quad mm2..] [0,y,0]: [0\,\lt \, y\,\lt \, \textstyle{1 \over 2}]
[\Lambda \quad \alpha,\alpha,\alpha] ex [32 \quad f \quad .3.] [x,x,x]: [0\,\lt \, x\,\lt \, \textstyle{1 \over 4}]
[F \quad \textstyle{1 \over 2}-\alpha, -\textstyle{1 \over 2}+3\alpha, \textstyle{1 \over 2}-\alpha] ex [32 \quad f \quad .3.] [x,\textstyle{1 \over 2}-x,x]: [0\,\lt \, x\,\lt \, \textstyle{1 \over 4}]
[F\sim F_1 =[P\,R]]     [x,x,x]: [\textstyle{1 \over 4}\,\lt \, x\,\lt \, \textstyle{1 \over 2}]
[\Lambda \cup F_1\sim[\Gamma\, R]\backslash[P]]   [32 \quad f\quad .3.] [x,x,x]: [0\,\lt \, x\,\lt \, \textstyle{1 \over 2}, x\neq\textstyle{1 \over 4}]
[D\quad \alpha,\alpha,\textstyle{1 \over 2}-\alpha]   [48 \quad g \quad 2..] [\textstyle{1 \over 4},\textstyle{1 \over 4},z]: [0\,\lt \, z\,\lt \, \textstyle{1 \over 4}]
[\Sigma\quad 0,0,\alpha] ex [48 \quad h \quad m..] [x,x,0]: [0\,\lt \, x\,\lt \, \textstyle{1 \over 4}]
[G \quad\textstyle{1 \over 2}-\alpha,-\textstyle{1 \over 2}+\alpha,\textstyle{1 \over 2}] ex [48 \quad h \quad m..] [x,\textstyle{1 \over 2}-x,0]: [0\,\lt \, x\,\lt \, \textstyle{1 \over 4}]
[A = [\Gamma\, N\, H] \quad \alpha,-\alpha,\beta] ex [48\quad h \quad m..] [x,y,0]: [0\,\lt \, x\,\lt \, y\,\lt \, \textstyle{1 \over 2}-x]
[AA = [\Gamma\,H_2\,N] \quad {-\alpha},\alpha,\beta] ex [48 \quad h \quad m..] [x,y,0]: [0\,\lt \, y\,\lt \, x\,\lt \, \textstyle{1 \over 2}-y]
[\Sigma\cup G\cup A\cup AA]   [48 \quad h \quad m..] [x,y,0]: [0\,\lt \, y\,\lt \, \textstyle{1 \over 2}-x\,\lt \, \textstyle{1 \over 2}\ \cup] [\cup \ x,\textstyle{1 \over 2}-x,0]: [0\,\lt \, x\,\lt \, \textstyle{1 \over 4} ]
[GP \quad \alpha,\beta,\gamma]   [96 \quad i \quad 1] [x,y,z]: [0\,\lt \, z\leq x\,\lt \, y\,\lt \, \textstyle{1 \over 2}-x \ \cup] [\cup \ x,y,z]: [0\,\lt \, z\,\lt \, y\,\lt \, x\leq\textstyle{1 \over 2}-y\ \cup] [\cup \ x,x,z]: [0\,\lt \, z\,\lt \, x\,\lt \, \textstyle{1 \over 4}]