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

International Tables for Crystallography (2010). Vol. B, ch. 1.5, p. 186   | 1 | 2 |

Table 1.5.5.4 

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

See Fig. 1.5.5.4[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] [0,0,\textstyle{1 \over 2}]
[M\sim M_2]     [\textstyle{1 \over 2},\textstyle{1 \over 2},0]
[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]   [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] ex [8 \quad h \quad m.2m] [x,x,0]: [0\,\lt \, x\leq s_2]
[F \quad \textstyle{1 \over 2}-\alpha,\textstyle{1 \over 2}+\alpha,-\textstyle{1 \over 2}+\alpha] ex [8\quad h \quad m.2m] [x,x,\textstyle{1 \over 2}]: [0\,\lt \, x\,\lt \, s=\textstyle{1 \over 2}-s_2]
[F\sim\Sigma_1=[S_2\,M_2]]     [x,x,0]: [s_2\,\lt \, x\,\lt \, \textstyle{1 \over 2}]
[\Sigma\cup \Sigma_1=[\Gamma M_2]]   [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}] ex [8 \quad j \quad m2m.] [x,\textstyle{1 \over 2},0]: [0\,\lt \, x\leq r]
[U \quad \textstyle{1 \over 2},\textstyle{1 \over 2},-\textstyle{1 \over 2}+\alpha] ex [8 \quad j \quad m2m.] [0,y, \textstyle{1 \over 2}]: [0\,\lt \, y\,\lt \, g=\textstyle{1 \over 2}-r]
[U\sim Y_1=[R\,M_2]]     [x,\textstyle{1 \over 2},0]: [r\,\lt \, x\,\lt \, \textstyle{1 \over 2}]
[Y\cup Y_1=[X\,M_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] ex [16 \quad l \quad m..] [x,y,0]: [[\Gamma\,S_2\,R\,X]]
[D \quad\textstyle{1 \over 2}-\alpha,\textstyle{1 \over 2}+\alpha,-\textstyle{1 \over 2}+\beta] ex [16 \quad l \quad m..] [x,y,\textstyle{1 \over 2}]: [[M\,S\,G]]
[D\sim C_1]     [x,y,0]: [[M_2\,R\,S_2]]
[C\cup C_1=[\Gamma\,M_2\,X]]   [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\,S_2\,S\,M]]
[B=B_1\cup B_2] = [[\Gamma\,S_2\,N\,T]\cup[T\,N\,S\,M]]      
[B_2\sim B_3]     [x,x,z]: [[T_2\,N\,S_2\,M_2]]
[B_1\cup B_3=[\Gamma\,M_2\,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\,G\,M]]
[E \quad\alpha - \beta, \alpha+\beta, \textstyle{1 \over 2}-\alpha] ex [16 \quad n \quad .m.] [x,\textstyle{1 \over 2},z]: [[X\,P\,R]]
[E\sim A_1]     [0,y,z]: [[X_2\,G\,P]]
[A\cup A_1=[\Gamma\,X\,X_2\,M]]   [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]