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

International Tables for Crystallography (2010). Vol. B, ch. 1.5, p. 188   | 1 | 2 |

Table 1.5.5.6 

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

See Fig. 1.5.5.6[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} ,1] ex [2 \quad a \quad mm2] [\textstyle{1 \over 2},\textstyle{1 \over 2},0]
[Z \sim Z_2]     [0,0,\textstyle{1 \over 2}]
[\Lambda \quad \alpha, \alpha, 0] ex [2 \quad a \quad mm2] [0,0,z]: [0\,\lt \, z\leq\lambda_0]
[LE \quad {-\alpha}, -\alpha, 0] ex [2 \quad a \quad mm2] [0,0,z]: [\lambda_2=-\lambda_0 \,\lt \, z\,\lt \, 0]
[Q \quad \textstyle{1 \over 2}+\alpha,\textstyle{1 \over 2}+ \alpha, 1] ex [2 \quad a \quad mm2] [\textstyle{1 \over 2},\textstyle{1 \over 2},z]: [0\,\lt \, z\leq q_0]
[Q \sim \Lambda_3=[\Lambda_2\,Z_4]]     [0,0,z]: [-\textstyle{1 \over 2} \,\lt \, z \leq -\textstyle{1 \over 2} + q_0 = -\lambda_0]
[QA \quad \textstyle{1 \over 2}-\alpha,\textstyle{1 \over 2}- \alpha, 1] ex [2 \quad a \quad mm2] [\textstyle{1 \over 2},\textstyle{1 \over 2},z]: [q_2= -q_0\,\lt \, z\,\lt \, 0]
[QA\sim \Lambda_1=[\Lambda_0\,Z_2]]     [0,0,z]: [\textstyle{1 \over 2}-q_0=\lambda_0\,\lt \, z\,\lt \, \textstyle{1 \over 2}]
[Z_2 \cup \Lambda_1 \cup \Lambda \cup \Gamma \cup LE \cup \Lambda_3]   [2 \quad a \quad mm2] [0,0,z]: [-\textstyle{1 \over 2} \,\lt \, z \leq \textstyle{1 \over 2}]
[T\quad 0,\textstyle{1 \over 2},\textstyle{1 \over 2}] ex [2 \quad b \quad mm2] [\textstyle{1 \over 2},0,0]
[T\sim T_2]     [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]
[G \quad \alpha, \textstyle{1 \over 2}+\alpha, \textstyle{1 \over 2}] ex [2 \quad b \quad mm2] [\textstyle{1 \over 2},0,z]: [0\,\lt \, z\leq g_0]
[G \sim H_3=[H_2\,T_4]]     [0,\textstyle{1 \over 2},z]: [-\textstyle{1 \over 2} \,\lt \, z \leq -\textstyle{1 \over 2}+g_0]
[GA \quad {-\alpha}, \textstyle{1 \over 2}-\alpha, \textstyle{1 \over 2}] ex [2 \quad b \quad mm2] [\textstyle{1 \over 2},0,z]: [g_2=-g_0\,\lt \, z\,\lt \, 0]
[GA \sim H_1=[H_0\,T_2]]     [0,\textstyle{1 \over 2},z]: [\textstyle{1 \over 2}-g_0=h_0\,\lt \, z\,\lt \, \textstyle{1 \over 2}]
[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\leq h_0]
[HA \quad \textstyle{1 \over 2}-\alpha, -\alpha, \textstyle{1 \over 2}] ex [2 \quad b \quad mm2] [0,\textstyle{1 \over 2},z]: [h_2=-h_0\,\lt \, z\,\lt \, 0]
[T_2 \cup H_1 \cup H\cup Y \cup HA \cup H_3]   [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\,\lt \, \textstyle{1 \over 2}]
[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\,\lt \, \textstyle{1 \over 2}]
[C \sim A=[Z_2\,Y_2]]     [x,0,\textstyle{1 \over 2}]: [0\,\lt \, z\,\lt \, \textstyle{1 \over 2}]
[J \quad \alpha, \alpha+\beta, \beta] ex [4 \quad c \quad .m.] [x,0,z]: [[\Gamma\, \Lambda_0\,G_0\,T]]
[JA \quad {-\alpha}, -\alpha+\beta, \beta] ex [4 \quad c \quad .m.] [x,0,z]: [[\Gamma\,T\,G_2\,\Lambda_2]]
[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\,H_0\,Q_0\,Z]]
[K \sim J_3]     [x, 0 ,z]: [[Y_4\,G_2\,\Lambda_2\,Z_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]: [[Z\,Q_2\,H_2\,Y]]
[KA \sim J_1]     [x,0,z]: [[Z_2\,Y_2\,G_0\,\Lambda_0]]
[A \cup J_1 \cup J \cup \Sigma \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}]
[D\quad \alpha, \textstyle{1 \over 2}, \textstyle{1 \over 2}+\alpha] ex [4 \quad d \quad m..] [\textstyle{1 \over 2},y,0]: [0\,\lt \, y\,\lt \, \textstyle{1 \over 2}]
[D \sim B]     [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]: [[\Gamma\,Y\,H_0\,\Lambda_0]]
[EA \quad {-\alpha}+\beta, -\alpha, \beta] ex [4 \quad d \quad m..] [0,y,z]: [[\Gamma\,\Lambda_2\,H_2\,Y]]
[F \quad \alpha+\beta, \textstyle{1 \over 2}+\alpha, \textstyle{1 \over 2}+\beta] ex [4 \quad d \quad m..] [\textstyle{1 \over 2},y,z]: [[T\,Z\,Q_0\,G_0]]
[F \sim E_3]     [0,y,z]: [[Z_4\,\Lambda_2\,H_2\,T_4]]
[FA \quad {-\alpha}+\beta, \textstyle{1 \over 2}-\alpha, \textstyle{1 \over 2}+\beta] ex [4 \quad d \quad m..] [\textstyle{1 \over 2},y,z]: [[T\,G_2\,Q_2\,Z]]
[FA \sim E_1]     [0,y,z]: [[Z_2\,\Lambda_0\,H_0\,T_2]]
[B \cup E_1 \cup E \cup \Delta \cup EA \cup E_3]   [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\,\lt \, z \leq \textstyle{1 \over 2}]