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

International Tables for Crystallography (2010). Vol. B, ch. 1.5, p. 185   | 1 | 2 |

Table 1.5.5.3 

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 1.5.5.3| top | pdf |
List of k-vector types for arithmetic crystal class [4/mmmI]: [c/a \,\lt\, 1]

See Fig. 1.5.5.3[link]. Wyckoff positions e and f exchanged. Parameter relations: [x=-\textstyle{1 \over 2}\alpha+\textstyle{1 \over 2}\beta], [y=\textstyle{1 \over 2}\alpha+\textstyle{1 \over 2}\beta+\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]   [2 \quad a \quad 4/mmm] [0,0,0]
[M \quad {-\textstyle{1 \over 2}},\textstyle{1 \over 2},\textstyle{1 \over 2}]   [2 \quad b \quad 4/mmm] [\textstyle{1 \over 2},\textstyle{1 \over 2},0]
[M\sim M_2]     [0,0,\textstyle{1 \over 2}]
[X \quad 0,0,\textstyle{1 \over 2}]   [4 \quad c \quad mmm.] [0,\textstyle{1 \over 2},0]
[P \quad \textstyle{1 \over 4}, \textstyle{1 \over 4}, \textstyle{1 \over 4}]   [4 \quad d \quad \overline 4m2] [0,\textstyle{1 \over 2},\textstyle{1 \over 4}]
[N \quad 0, \textstyle{1 \over 2}, 0]   [8 \quad f\quad ..2/m] [\textstyle{1 \over 4},\textstyle{1 \over 4},\textstyle{1 \over 4}]
[\Lambda\quad \alpha, \alpha, -\alpha] ex [4 \quad e \quad 4mm] [0,0,z]: [0\,\lt \, z\leq z_0]
[V \quad {-\textstyle{1 \over 2}} + \alpha,\textstyle{1 \over 2} + \alpha,\textstyle{1 \over 2} -\alpha] ex [4 \quad e \quad 4mm] [\textstyle{1 \over 2},\textstyle{1 \over 2},z]: [0\,\lt \, z\,\lt \, z_2=\textstyle{1 \over 2}-z_0]
[V \sim \Lambda_1=[Z_0\,M_2]]     [0,0,z]: [\,z_0\,\lt \, z\,\lt \, \textstyle{1 \over 2}]
[\Lambda \cup \Lambda_1 = [\Gamma\,M_2]]   [4 \quad e \quad 4mm] [0,0,z]: [0\,\lt \, z\,\lt \, \textstyle{1 \over 2}]
[W \quad \alpha, \alpha, \textstyle{1 \over 2}-\alpha]   [8\quad g \quad 2mm.] [0,\textstyle{1 \over 2},z]: [\, 0\,\lt \, z\,\lt \, \textstyle{1 \over 4}]
[\Sigma \quad{-\alpha}, \alpha, \alpha]   [8 \quad h \quad m.2m] [x,x,0]: [0\,\lt \, x\,\lt \, \textstyle{1 \over 2}]
[\Delta \quad 0,0,\alpha]   [8 \quad i \quad m2m.] [0,y,0]: [0\,\lt \, y\,\lt \, \textstyle{1 \over 2}]
[Y \quad {-\alpha}, \alpha, \textstyle{1 \over 2}]   [8 \quad j \quad m2m.] [x,\textstyle{1 \over 2},0]: [0\,\lt \, x\,\lt \, \textstyle{1 \over 2}]
[Q \quad\textstyle{1 \over 4}-\alpha,\textstyle{1 \over 4}+\alpha,\textstyle{1 \over 4}-\alpha]   [16 \quad k \quad ..2] [x,\textstyle{1 \over 2}-x,\textstyle{1 \over 4}]: [0\,\lt \, x\,\lt \, \textstyle{1 \over 4}]
[C \quad {-\alpha},\alpha,\beta]   [16 \quad l \quad m..] [x,y,0]: [0\,\lt \, x\,\lt \, y\,\lt \, \textstyle{1 \over 2}]
[B \quad \alpha,\beta,-\alpha]   [16 \quad m \quad ..m] [x,x,z]: [[\Gamma\,M\,Z_2\,Z_0]]
[B=B_1\cup B_2] = [[\Gamma\,M\,Z_2\,N\,T]\cup [T\,N\,Z_0]]      
[B_2 \sim B_3]     [x,x,z]: [[N\,Z_2\,T_2]]
[B_1\cup B_3=[\Gamma\,M\,T_2\,T]]   [16 \quad m \quad ..m] [x,x,z]: [0\,\lt \, x\,\lt \, \textstyle{1 \over 2},\,0\,\lt \, z\,\lt \, \textstyle{1 \over 4}\ \cup] [\cup \ x,x,\textstyle{1 \over 4}]: [0\,\lt \, x\,\lt \, \textstyle{1 \over 4}]
[A \quad \alpha,\alpha,\beta] ex [16 \quad n \quad .m.] [0,y,z]: [[\Gamma\,X\,P\,Z_0]]
[E\quad \alpha - \beta, \alpha+\beta, \textstyle{1 \over 2}-\alpha] ex [16 \quad n \quad .m.] [x,\textstyle{1 \over 2},z]: [[M\,X\,P\,Z_2]]
[E \sim A_1]     [0,y,z]: [[P\,X_2\,M_2\,Z_0]]
[A \cup A_1=[\Gamma\,X\,X_2\,M_2]]   [16 \quad n \quad .m.] [0,y,z]: [0\,\lt \, y,z\,\lt \, \textstyle{1 \over 2}]
[GP \quad \alpha,\beta,\gamma]   [32 \quad o \quad 1] [x,y,z]: [0\,\lt \, x\,\lt \, y\,\lt \, \textstyle{1 \over 2}]; [0\,\lt \, z\,\lt \, \textstyle{1 \over 4}\ \cup] [\cup \ x,y,\textstyle{1 \over 4}]: [0\,\lt \, x\,\lt \, y\,\lt \, \textstyle{1 \over 2}-x]