Pbcm D2h11 mmm Orthorhombic info
No. 57 P2/b21/c21/m Patterson symmetry Pmmm

symmetry group diagram

Origin at -1 on b 1 21

Asymmetric unit 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1; 0 ≤ z ≤ 1/4

Symmetry operations

(1)  1   (2)  2(0, 0, 1/2)   0, 0, z(3)  2(0, 1/2, 0)   0, y1/4(4)  2   x1/4, 0
(5)  -1   0, 0, 0(6)  m   xy1/4(7)  c   x1/4z(8)  b   0, yz

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 General:
8 e 1
(1) xyz(2) -x-yz + 1/2(3) -xy + 1/2-z + 1/2(4) x-y + 1/2-z
(5) -x-y-z(6) xy-z + 1/2(7) x-y + 1/2z + 1/2(8) -xy + 1/2z
0kl : k = 2n
h0l : l = 2n
0k0 : k = 2n
00l : l = 2n
    Special: as above, plus
4 d  . . m 
xy1/4 -x-y3/4 -xy + 1/21/4x-y + 1/23/4
no extra conditions
4 c  2 . . 
x1/4, 0 -x3/41/2 -x3/4, 0x1/41/2
hkl : l = 2n
4 b  -1 
1/2, 0, 0 1/2, 0, 1/2 1/21/21/2 1/21/2, 0
hkl : kl = 2n
4 a  -1 
0, 0, 0 0, 0, 1/2 0, 1/21/2 0, 1/2, 0
hkl : kl = 2n

Symmetry of special projections

Along [001]   p2gm
a' = a   b' = b   
Origin at 0, 0, z
Along [100]   p2gm
a' = 1/2b   b' = c   
Origin at x, 0, 0
Along [010]   p2mm
a' = 1/2c   b' = a   
Origin at 0, y, 0

Maximal non-isomorphic subgroups

I [2] Pbc21 (Pca21, 29)1; 2; 7; 8
  [2] P2cm (Pma2, 28)1; 4; 6; 7
  [2] Pb21m (Pmc21, 26)1; 3; 6; 8
  [2] P22121 (P21212, 18)1; 2; 3; 4
  [2] P121/c1 (P21/c, 14)1; 3; 5; 7
  [2] P2/b11 (P2/c, 13)1; 4; 5; 8
  [2] P1121/m (P21/m, 11)1; 2; 5; 6
IIa none
IIb[2] Pbnm (a' = 2a) (Pnma, 62); [2] Pbca (a' = 2a) (61); [2] Pbna (a' = 2a) (Pbcn, 60)

Maximal isomorphic subgroups of lowest index

IIc[2] Pbcm (a' = 2a) (57); [3] Pbcm (b' = 3b) (57); [3] Pbcm (c' = 3c) (57)

Minimal non-isomorphic supergroups

Inone
II[2] Cmcm (63); [2] Bbem (Cmce, 64); [2] Aemm (Cmme, 67); [2] Ibam (72); [2] Pmcm (b' = 1/2b) (Pmma, 51); [2] Pbmm (c' = 1/2c) (Pmma, 51)








































to end of page
to top of page