P4/n C4h3 4/m Tetragonal info
No. 85 P4/n Patterson symmetry P4/m
ORIGIN CHOICE 2

symmetry group diagram

Origin at -1 on n, at 1/4, -1/4, 0 from -4

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

Symmetry operations

(1)  1   (2)  2   1/41/4z(3)  4+   1/41/4z(4)  4-   1/41/4z
(5)  -1   0, 0, 0(6)  n(1/21/2, 0)   xy, 0(7)  -4+   1/4, -1/4z; 1/4, -1/4, 0(8)  -4-   -1/41/4z; -1/41/4, 0

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 g 1
(1) xyz(2) -x + 1/2-y + 1/2z(3) -y + 1/2xz(4) y-x + 1/2z
(5) -x-y-z(6) x + 1/2y + 1/2-z(7) y + 1/2-x-z(8) -yx + 1/2-z
hk0 : h + k = 2n
h00 : h = 2n
    Special: as above, plus
4 f  2 . . 
1/43/4z 3/41/4z 3/41/4-z 1/43/4-z
hkl : h + k = 2n
4 e  -1 
0, 0, 1/2 1/21/21/2 1/2, 0, 1/2 0, 1/21/2
hkl : hk = 2n
4 d  -1 
0, 0, 0 1/21/2, 0 1/2, 0, 0 0, 1/2, 0
hkl : hk = 2n
2 c  4 . . 
1/41/4z 3/43/4-z
no extra conditions
2 b  -4 . . 
1/43/41/2 3/41/41/2
hkl : h + k = 2n
2 a  -4 . . 
1/43/4, 0 3/41/4, 0
hkl : h + k = 2n

Symmetry of special projections

Along [001]   p4
a' = 1/2(a - b)   b' = 1/2(a + b)   
Origin at 1/41/4z
Along [100]   p2mg
a' = b   b' = c   
Origin at x, 0, 0
Along [110]   p2mm
a' = 1/2(-a + b)   b' = c   
Origin at xx, 0

Maximal non-isomorphic subgroups

I [2] P-4 (81)1; 2; 7; 8
  [2] P4 (75)1; 2; 3; 4
  [2] P2/n (P2/c, 13)1; 2; 5; 6
IIa none
IIb[2] P42/n (c' = 2c) (86)

Maximal isomorphic subgroups of lowest index

IIc[2] P4/n (c' = 2c) (85); [5] P4/n (a' = a + 2bb' = -2a + b or a' = a - 2bb' = 2a + b) (85)

Minimal non-isomorphic supergroups

I[2] P4/nbm (125); [2] P4/nnc (126); [2] P4/nmm (129); [2] P4/ncc (130)
II[2] C4/m (P4/m, 83); [2] I4/m (87)








































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