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

International Tables for Crystallography (2010). Vol. B, ch. 1.5, p. 189   | 1 | 2 |

Table 1.5.5.7 

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 1.5.5.7| top | pdf |
List of k-vector types for arithmetic crystal class [mm2F]: [a^{-2}\,\gt \, b^{-2}+c^{-2}]

See Fig. 1.5.5.7[link]. Parameter relations: [x=-\textstyle{1 \over 2} \alpha+\textstyle{1 \over 2}\beta+\textstyle{1 \over 2}\gamma], [y=\textstyle{1 \over 2} \alpha-\textstyle{1 \over 2}\beta+\textstyle{1 \over 2}\gamma], [z=\textstyle{1 \over 2} \alpha+\textstyle{1 \over 2}\beta-\textstyle{1 \over 2}\gamma].

k-vector label, CDMLWyckoff position of IT A, cf. Section 1.5.4.3[link]Parameters
[\Gamma \quad 0,0,0] ex [2 \quad a \quad mm2] [0,0,0]
[Z \quad \textstyle{1 \over 2},\textstyle{1 \over 2} ,0] ex [2 \quad a \quad mm2] [0,0,\textstyle{1 \over 2}]
[\Lambda \quad \alpha, \alpha, 0] ex [2 \quad a\quad mm2] [0,0,z]: [0\,\lt \, z\,\lt \, \textstyle{1 \over 2}]
[LE \quad {-\alpha}, -\alpha, 0] ex [2 \quad a \quad mm2] [0,0,z]: [-\textstyle{1 \over 2}\,\lt \, z\,\lt \, 0]
[\Gamma\cup Z\cup\Lambda\cup LE]   [2 \quad a\quad mm2] [0,0,z]: [-\textstyle{1 \over 2}\,\lt \, z\leq\textstyle{1 \over 2}]
[T\quad 1,\textstyle{1 \over 2},\textstyle{1 \over 2}] ex [2 \quad b \quad mm2] [0,\textstyle{1 \over 2},\textstyle{1 \over 2}]
[Y \quad \textstyle{1 \over 2}, 0, \textstyle{1 \over 2}] ex [2 \quad b \quad mm2] [0,\textstyle{1 \over 2},0]
[H \quad \textstyle{1 \over 2}+\alpha, \alpha, \textstyle{1 \over 2}] ex [2 \quad b \quad mm2] [0,\textstyle{1 \over 2},z]: [0\,\lt \, z\,\lt \, \textstyle{1 \over 2}]
[HA \quad \textstyle{1 \over 2}-\alpha, -\alpha, \textstyle{1 \over 2}] ex [2 \quad b \quad mm2] [0,\textstyle{1 \over 2},z]: [-\textstyle{1 \over 2}\,\lt \, z\,\lt \, 0]
[T \cup Y \cup H \cup HA]   [2 \quad b \quad mm2] [0,\textstyle{1 \over 2},z]: [-\textstyle{1 \over 2}\,\lt \, z\leq \textstyle{1 \over 2}]
[\Sigma \quad 0,\alpha,\alpha] ex [4 \quad c \quad .m.] [x,0,0]: [0\,\lt \, x\leq\sigma_0]
[U \quad 1,\textstyle{1 \over 2}+\alpha,\textstyle{1 \over 2}+\alpha] ex [4 \quad c \quad .m.] [x,\textstyle{1 \over 2},\textstyle{1 \over 2}]: [0\,\lt \, x\,\lt \, u_0]
[U \sim \Sigma_1=[\Sigma_0\,T_2]]     [x,0,0]: [\textstyle{1 \over 2}-u_0=\sigma_0\,\lt \, x\,\lt \, \textstyle{1 \over 2}]
[A \quad \textstyle{1 \over 2}, \textstyle{1 \over 2}+\alpha, \alpha] ex [4\quad c \quad .m.] [x,0,\textstyle{1 \over 2}]: [0\,\lt \, x\,\lt \, a_0]
[C \quad\textstyle{1 \over 2}, \alpha, \textstyle{1 \over 2}+\alpha] ex [4 \quad c \quad .m.] [x,\textstyle{1 \over 2},0]: [0\,\lt \, x\leq c_0]
[C \sim A_1=[A_0\,Y_2]]     [x,0,\textstyle{1 \over 2}]: [a_0=\textstyle{1 \over 2} -c_0\leq x\,\lt \, \textstyle{1 \over 2}]
[J \quad \alpha, \alpha+\beta, \beta] ex [4 \quad c \quad .m.] [x,0,z]: [[\Gamma\,Z\,A_0\,\Sigma_0]]
[JA \quad {-\alpha}, -\alpha+\beta, \beta] ex [4 \quad c \quad .m.] [x,0,z]: [[\Gamma\,\Sigma_0\,A_2\,Z_4]]
[K \quad \textstyle{1 \over 2}+\alpha,\alpha+\beta,\textstyle{1 \over 2}+\beta] ex [4\quad c\quad .m.] [x,\textstyle{1 \over 2},z]: [[Y\,T\,U_0\,C_0]]
[K\sim J_3]     [x,0,z]: [[T_2\,\Sigma_0\,A_2\,Y_4]]
[KA \quad \textstyle{1 \over 2}-\alpha,-\alpha+\beta,\textstyle{1 \over 2}+\beta] ex [4 \quad c \quad .m.] [x,\textstyle{1 \over 2},z]: [[Y\,C_0\,U_2\,T_4]]
[KA\sim J_1]     [x,0,z]: [[T_2\,\Sigma_0\,A_0\,Y_2]]
[A \cup A_1 \cup J \cup J_1 \cup \Sigma\cup\Sigma_1 \cup JA \cup J_3]   [4 \quad c \quad .m.] [x,0,z]: [0\,\lt \, x\,\lt \, \textstyle{1 \over 2}, -\textstyle{1 \over 2} \,\lt \, z\leq \textstyle{1 \over 2}]
[\Delta\quad \alpha, 0, \alpha] ex [4 \quad d \quad m..] [0,y,0]: [0\,\lt \, y\,\lt \, \textstyle{1 \over 2}]
[B \quad \textstyle{1 \over 2}+\alpha, \textstyle{1 \over 2}, \alpha] ex [4 \quad d \quad m..] [0,y,\textstyle{1 \over 2}]: [0\,\lt \, y\,\lt \, \textstyle{1 \over 2}]
[E \quad \alpha+\beta, \alpha, \beta] ex [4 \quad d \quad m..] [0,y,z]: [0\,\lt \, y,z\,\lt \, \textstyle{1 \over 2}]
[EA \quad {-\alpha+\beta}, -\alpha, \beta] ex [4\quad d \quad m..] [0,y,z]: [0\,\lt \, y\,\lt \, \textstyle{1 \over 2}, -\textstyle{1 \over 2}\,\lt \, z\,\lt \, 0]
[\Delta\cup B\cup E\cup EA]   [4 \quad d \quad m..] [0,y,z:] [0\,\lt \, y\,\lt \, \textstyle{1 \over 2},-\textstyle{1 \over 2}\,\lt \, z\leq \textstyle{1 \over 2}]
[GP \quad \alpha,\beta,\gamma]   [8 \quad e \quad 1] [x,y,z]: [0\,\lt \, x,y\,\lt \, \textstyle{1 \over 2}, 0\leq z\,\lt \, \textstyle{1 \over 2}]