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

International Tables for Crystallography (2010). Vol. B, ch. 2.2, pp. 220-221

Table 2.2.3.4 

C. Giacovazzoa*

aDipartimento Geomineralogico, Campus Universitario, 70125 Bari, Italy, and Institute of Crystallography, Via G. Amendola, 122/O, 70125 Bari, Italy
Correspondence e-mail: carmelo.giacovazzo@ic.cnr.it

Table 2.2.3.4| top | pdf |
Allowed origin translations, seminvariant moduli and phases for noncentrosymmetric non-primitive space groups

 H–K group
[(k, l)C(0, 2)][(h, l)C(0, 0)][(h, l)C(2, 0)][(h, l)C(2, 2)][(h, l)A(2, 0)][(h, l)I(2, 0)][(h, l)I(2, 2)][(h + k + l)F(2)][(h + k + l)F(4)][(l)I(0)][(l)I(2)][(2k - l)I(4)][(l)F(0)][ I]
Space group C2 Cm Cmm2 C222 Amm2 Imm2 I222 F432 F222 I4 I422 [I\bar{4}] Fmm2 I23
  Cc [Cmc2_{1}] [C222_{1}] Abm2 Iba2 [I2_{1}2_{1}2_{1}] [F4_{1}32] F23 [I4_{1}] [I4_{1}22] [I\bar{4}m2] Fdd2 [I2_{1}3]
    Ccc2   Ama2 Ima2     [F\bar{4}3m] I4mm [I\bar{4}2m] [I\bar{4}c2]   I432
        Aba2       [F\bar{4}3c] I4cm [I\bar{4}2d]     [I4_{1}32]
                  [I4_{1}md]       [I\bar{4}3m]
                  [I4_{1}cd]       [I\bar{4}3d]
Allowed origin translations (0, y, 0) (x, 0, z) (0, 0, z) (0, 0, 0) (0, 0, z) (0, 0, z) (0, 0, 0) (0, 0, 0) (0, 0, 0) (0, 0, z) (0, 0, 0) (0, 0, 0) (0, 0, z) (0, 0, 0)
[(0, y, {1\over 2})]   [({1\over 2}, 0, z)] [(0, 0, {1\over 2})] [({1\over 2}, 0, z)] [({1\over 2}, 0, z)] [(0, 0, {1\over 2})] [({1\over 2}, {1\over 2}, {1\over 2})] [({1\over 4}, {1\over 4}, {1\over 4})]   [(0, 0, {1\over 2})] [(0, 0, {1\over 2})]    
      [({1\over 2}, 0, 0)]     [(0, {1\over 2}, 0)]   [({1\over 2}, {1\over 2}, {1\over 2})]     [({1\over 2}, 0, {3\over 4})]    
      [({1\over 2}, 0, {1\over 2})]     [({1\over 2}, 0, 0)]   [({3\over 4}, {3\over 4}, {3\over 4})]     [({1\over 2}, 0, {1\over 4})]    
Vector [{\bf h}_{s}] seminvariantly associated with [{\bf h} = (h, k, l)] (k, l) (h, l) (h, l) (h, l) (h, l) (h, l) (h, l) [(h + k + l)] [(h + k + l)] (l) (l) [(2k - l)] (l) [(h, k, l)]
Seminvariant modulus [\boldomega _{s}] (0, 2) (0, 0) (2, 0) (2, 2) (2, 0) (2, 0) (2, 2) (2) (4) (0) (2) (4) (0) (1, 1, 1)
Seminvariant phases [\varphi_{\rm e0e}] [\varphi_{\rm 0e0}] [\varphi_{\rm ee0}] [\varphi_{\rm eee}] [\varphi_{\rm ee0}] [\varphi_{\rm ee0}] [\varphi_{\rm eee}] [\varphi_{\rm eee}] [\varphi_{hkl}] with [h + k + l \equiv 0] (mod 4) [\varphi_{hk0}] [\varphi_{hk{\rm e}}] [\varphi_{hkl}] with [(2k - l) \equiv 0] (mod 4) [\varphi_{hk0}] All
Allowed variations for the semindependent phases [\|\infty\|], [\|2\|] if [k = 0] [\|\infty\|] [\|\infty\|], [\|2\|] if [l = 0] [\|2\|] [\|\infty\|], [\|2\|] if [l = 0] [\|\infty\|], [\|2\|] if [l = 0] [\|2\|] [\|2\|] [\|2\|] if [h + k + l \equiv 0] (mod 2)
[\|4\|] if [h+k+l] [\equiv 1] (mod 2)
[\|\infty\|] [\|2\|] [\|2\|] if [h + k + l \equiv 0] (mod 2)
[\|4\|] if [2k-l\equiv] 1 (mod 2)
[\|\infty\|] All
Number of semindependent phases to be specified 2 2 2 2 2 2 2 1 1 1 1 1 1 0