pbam mmm Orthorhombic/Rectangular
No. 44 p21/b21/a2/m Patterson symmetry pmmm

symmetry group diagram

Origin at centre (2/m)

Asymmetric unit 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; 0 ≤ z

Symmetry operations

(1)  1
      (1 | 0, 0, 0)
(2)  2   0, 0, z
      (2z | 0, 0, 0)
(3)  2 (0, 1/2, 0)   1/4y, 0
      (2y | 1/21/2, 0)
(4)  2 (1/2, 0, 0)   x1/4, 0
      (2x | 1/21/2, 0)
(5)  -1   0, 0, 0
      (-1 | 0, 0, 0)
(6)  m   xy, 0
      (mz | 0, 0, 0)
(7)  a   x1/4z
      (my | 1/21/2, 0)
(8)  b   1/4yz
      (mx | 1/21/2, 0)

Generators selected (1); t(1, 0, 0); t(0, 1, 0); (2); (3); (5)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

  General:
8 f 1
(1) xyz (2) -x-yz (3) -x + 1/2y + 1/2-z (4) x + 1/2-y + 1/2-z
(5) -x-y-z (6) xy-z (7) x + 1/2-y + 1/2z (8) -x + 1/2y + 1/2z
0k: k = 2n
h0: h = 2n
    Special: as above, plus
4 e  . . m 
xy, 0 -x-y, 0 -x + 1/2y + 1/2, 0 x + 1/2-y + 1/2, 0
no extra conditions
4 d  . . 2 
0, 1/2z 1/2, 0, -z 0, 1/2-z 1/2, 0, z
hk: h + k = 2n
4 c  . . 2 
0, 0, z 1/21/2-z 0, 0, -z 1/21/2z
hk: h + k = 2n
2 b  . . 2/m 
0, 1/2, 0 1/2, 0, 0
hk: h + k = 2n
2 a  . . 2/m 
0, 0, 0 1/21/2, 0
hk: h + k = 2n

Symmetry of special projections

Along [001]   p2gg
a' = a   b' = b   
Origin at 0, 0, z
Along [100]   [script p]2mm
a' = 1/2b   
Origin at x, 0, 0
Along [010]   [script p]2mm
a' = 1/2a   
Origin at 0, y, 0

Maximal non-isotypic subgroups


I [2] pb21m (29) 1; 3; 6; 8
  [2] p21am (pb21m, 29) 1; 4; 6; 7
  [2] pba2 (25) 1; 2; 7; 8
  [2] p21212 (21) 1; 2; 3; 4
  [2] p121/a1 (p21/b11, 17) 1; 3; 5; 7
  [2] p21/b11 (17) 1; 4; 5; 8
  [2] p112/m (6) 1; 2; 5; 6
IIa none
IIb none

Maximal isotypic subgroups of lowest index


IIc [3] pbam (a' = 3a or b' = 3b) (44)

Minimal non-isotypic supergroups


I [2] p4/mbm (63)
II [2] cmmm (47); [2] pmam (b' = 1/2b) (40)








































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