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

International Tables for Crystallography (2010). Vol. B, ch. 1.5, p. 183   | 1 | 2 |

Table 1.5.5.1 

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

See Fig. 1.5.5.1[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\overline3m] 0, 0, 0
[H \quad \textstyle{1 \over 2},-\textstyle{1 \over 2},\textstyle{1 \over 2}]   [4 \quad b \quad m\overline3m] [0,\textstyle{1 \over 2},0]
[P \quad \textstyle{1 \over 4}, \textstyle{1 \over 4}, \textstyle{1 \over 4}]   [8 \quad c \quad\overline43m ] [\textstyle{1 \over 4}, \textstyle{1 \over 4}, \textstyle{1 \over 4} ]
[N\quad 0,0,\textstyle{1 \over 2}]   [24 \quad d \quad m.mm] [\textstyle{1 \over 4},\textstyle{1 \over 4},0 ]
[\Delta \quad \alpha,-\alpha,\alpha]   [24 \quad e \quad 4m.m] [0,y,0]: [0 \,\lt \, y \,\lt \, \textstyle{1 \over 2}]
[\Lambda \quad \alpha,\alpha,\alpha] ex [32 \quad f \quad .3m] [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 .3m] [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}]
[F\sim F_3=[P\,H_2]]     [x,x,\textstyle{1 \over 2}-x]: [0 \,\lt \, x\,\lt \, \textstyle{1 \over 4}]
[\Lambda\cup F_1=[\Gamma R]\backslash [P] ]   [32 \quad f \quad .3m] [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.mm] [\textstyle{1 \over 4},\textstyle{1 \over 4},z]: [0\,\lt \, z\,\lt \, \textstyle{1 \over 4}]
[\Sigma \quad 0,0,\alpha]   [48 \quad h \quad m.m2] [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}]   [48 \quad i \quad m.m2] [x,\textstyle{1 \over 2}-x,0]: [0\,\lt \, x\,\lt \, \textstyle{1 \over 4}]
[A \quad \alpha, -\alpha, \beta]   [96 \quad j \quad m..] [x,y,0]: [0\,\lt \, x\,\lt \, y\,\lt \, \textstyle{1 \over 2}-x]
[B\quad \alpha+\beta,-\alpha+\beta,\textstyle{1 \over 2}-\beta] ex [96 \quad k \quad ..m] [x,\textstyle{1 \over 2}-x,z]: [0\,\lt \, z\,\lt \, x\,\lt \, \textstyle{1 \over 4}]
[B\sim B_1=[P\,N_2\,H_2]]     [x,x,z]: [0\,\lt \, x\,\lt \, \textstyle{1 \over 2}-x\,\lt \, z\,\lt \, \textstyle{1 \over 2}]
[C \quad \alpha,\alpha,\beta] ex [96 \quad k \quad ..m] [x,x,z]: [0\,\lt \, z\,\lt \, x\,\lt \, \textstyle{1 \over 4}]
[J \quad \alpha, \beta, \alpha] ex [96\quad k \quad ..m] [x,y,x]: [0\,\lt \, x\,\lt \, y\,\lt \, \textstyle{1 \over 2}-x]
[J\sim J_1=[\Gamma\,P\,H_2]]     [x,x,z]: [0\,\lt \, x\,\lt \, z\,\lt \, \textstyle{1 \over 2}-x]
[C\cup B_1\cup J_1=[\Gamma\,N\,N_2\,H_2]\backslash[\Lambda,\,F_3]]   [96 \quad k \quad ..m] [x,x,z]: [0\,\lt \, x\,\lt \, \textstyle{1 \over 4}, 0\,\lt \, z\,\lt \, \textstyle{1 \over 2}] with [z\neq x, z\neq\textstyle{1 \over 2}-x]
[GP \quad \alpha,\beta,\gamma]   [192 \quad l \quad 1] [x,y,z]: [0\,\lt \, z\,\lt \, x\,\lt \, y\,\lt \, \textstyle{1 \over 2}-x]