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

International Tables for Crystallography (2010). Vol. B, ch. 2.2, pp. 218-219

Table 2.2.3.2 

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 2.2.3.2| top | pdf |
Allowed origin translations, seminvariant moduli and phases for noncentrosymmetric primitive space groups

 H–K group
[(h, k, l)P(0, 0, 0)][(h, k, l)P(2, 0, 2)][(h, k, l)P(0, 2, 0)][(h, k, l)P(2, 2, 2)][(h, k, l)P(2, 2, 0)][(h + k, l)P(2, 0)][(h + k, l)P(2, 2)][(h - k, l)P(3, 0)][(2h + 4k + 3l)P(6)][(l)P(0)][(l)P(2)][(h + k + l)P(0)][(h + k + l)P(2)]
Space group P1 P2 Pm P222 Pmm2 P4 [P\bar{4}] P3 P312 P31m P321 R3 R32
  [P2_{1}] Pc [P222_{1}] [Pmc2_{1}] [P4_{1}] P422 [P3_{1}] [P3_{1}12] P31c [P3_{1}21] R3m P23
      [P2_{1}2_{1}2] Pcc2 [P4_{2}] [P42_{1}2] [P3_{2}] [P3_{2}12] P6 [P3_{2}21] R3c [P2_{1}3]
      [P2_{1}2_{1}2_{1}] Pma2 [P4_{3}] [P4_{1}22] P3m1 P6 [P6_{1}] P622   P432
        [Pca2_{1}] P4mm [P4_{1}2_{1}2] P3c1 [P\bar{6}m2] [P6_{5}] [P6_{1}22]   [P4_{2}32]
        Pnc2 P4bm [P4_{2}22]   [P\bar{6}c2] [P6_{4}] [P6_{5}22]   [P4_{3}32]
        [Pmn2_{1}] [P4_{2}cm] [P4_{2}2_{1}2]     [P6_{3}] [P6_{2}22]   [P4_{1}32]
        Pba2 [P4_{2}nm] [P4_{3}22]     [P6_{2}] [P6_{4}22]   [P\bar{4}3m]
        [Pna2_{1}] P4cc [P4_{3}2_{1}2]     P6mm [P6_{3}22]   [P\bar{4}3n]
        Pnn2 P4nc [P\bar{4}2m]     P6cc [P\bar{6}2m]    
          [P4_{2}mc] [P\bar{4}2c]     [P6_{3}cm] [P\bar{6}2c]    
          [P4_{2}bc] [P\bar{4}2_{1}m]     [P6_{3}mc]      
            [P\bar{4}2_{1}c]            
            [P\bar{4}m2]            
            [P\bar{4}c2]            
            [P\bar{4}b2]            
            [P\bar{4}n2]            
Allowed origin translations (x, y, z) (0, y, 0) (x, 0, z) (0, 0, 0) (0, 0, z) (0, 0, z) (0, 0, 0) (0, 0, z) (0, 0, 0) (0, 0, z) (0, 0, 0) (x, x, x) (0, 0, 0)
  [(0, y, {1\over 2})] [(x, {1\over 2}, z)] [({1\over 2}, 0, 0)] [(0, {1\over 2}, z)] [({1\over 2}, {1\over 2}, z)] [(0, 0, {1\over 2})] [({1\over 3}, {2\over 3}, z)] [(0, 0, {1\over 2})]   [(0, 0, {1\over 2})]   [({1\over 2}, {1\over 2}, {1\over 2})]
  [({1\over 2}, y, 0)]   [(0, {1\over 2}, 0)] [({1\over 2}, 0, z)]   [({1\over 2}, {1\over 2}, 0)] [({2\over 3}, {1\over 3}, z)] [({1\over 3}, {2\over 3}, 0)]        
  [({1\over 2}, y, {1\over 2})]   [(0, 0, {1\over 2})] [({1\over 2}, {1\over 2}, z)]   [({1\over 2}, {1\over 2}, {1\over 2})]   [({1\over 3}, {2\over 3}, {1\over 2})]        
      [(0, {1\over 2}, {1\over 2})]         [({2\over 3}, {1\over 3}, 0)]        
      [({1\over 2}, 0, {1\over 2})]         [({2\over 3}, {1\over 3}, {1\over 2})]        
      [({1\over 2}, {1\over 2}, 0)]                  
      [({1\over 2}, {1\over 2}, {1\over 2})]                  
Vector [{\bf h}_{s}] seminvariantly associated with [{\bf h} = (h, k, l)] (h, k, l) (h, k, l) (h, k, l) (h, k, l) (h, k, l) [(h + k, l)] [(h + k, l)] [(h - k, l)] [(2h + 4k + 3l)] (l) (l) [(h + k + l)] [(h + k + l)]
Seminvariant modulus [\boldomega_{s}] (0, 0, 0) (2, 0, 2) (0, 2, 0) (2, 2, 2) (2, 2, 0) (2, 0) (2, 2) (3, 0) (6) (0) (2) (0) (2)
Seminvariant phases [\varphi_{000}] [\varphi_{\rm e0e}] [\varphi_{\rm 0e0}] [\varphi_{\rm eee}] [\varphi_{\rm ee0}] [\varphi_{\rm ee0}] [\varphi_{\rm eee}] [\varphi_{hk0}] if [h - k = 0] [\varphi_{hkl}] if [2h + 4k + 3l = 0] [\varphi_{hk0}] [\varphi_{hk{\rm e}}] [\varphi_{h, \, k, \, \bar{h} + \bar{k}}] [\varphi_{\rm eee}]; [\varphi_{\rm ooe}]
          [\varphi_{\rm oo0}] [\varphi_{\rm ooe}] (mod 3) (mod 6)       [\varphi_{\rm oeo}]; [\varphi_{\rm ooe}]
Allowed variations for the semindependent phases [\|\infty\|] [\|\infty\|], [\|2\|] if [k = 0] [\|\infty\|], [\|2\|] if [h = l = 0] [\|2\|] [\|\infty\|], [\|2\|] if [l = 0] [\|\infty\|], [\|2\|] if [l = 0] [\|2\|] [\|\infty\|], [\|3\|] if [l = 0] [\|2\|] if [h \equiv k] (mod 3)
[\|3\|] if [l \equiv 0] (mod 2)
[\|\infty\|] [\|2\|] [\|\infty\|] [\|2\|]
Number of semindependent phases to be specified 3 3 3 3 3 2 2 2 1 1 1 1 1