I41cd C4v12 4mm Tetragonal info
No. 110 I41cd Patterson symmetry I4/mmm

symmetry group diagram

Origin on 2 c 1

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

Symmetry operations

For (0, 0, 0)+ set

(1)  1   (2)  2(0, 0, 1/2)   1/41/4z(3)  4+(0, 0, 1/4)   -1/41/4z(4)  4-(0, 0, 3/4)   1/4, -1/4z
(5)  c   x, 0, z(6)  b   1/4yz(7)  d(-1/41/43/4)   x + 1/4-xz(8)  d(1/41/41/4)   x + 1/4xz

For (1/21/21/2)+ set

(1)  t(1/21/21/2)   (2)  2   0, 0, z(3)  4+(0, 0, 3/4)   1/41/4z(4)  4-(0, 0, 1/4)   1/41/4z
(5)  a   x1/4z(6)  c   0, yz(7)  d(1/4, -1/41/4)   x + 1/4-xz(8)  d(1/41/43/4)   x - 1/4xz

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/21/21/2); (2); (3); (5)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 (0, 0, 0)+  (1/21/21/2)+  General:
16 b 1
(1) xyz(2) -x + 1/2-y + 1/2z + 1/2(3) -yx + 1/2z + 1/4(4) y + 1/2-xz + 3/4
(5) x-yz + 1/2(6) -x + 1/2y + 1/2z(7) -y-x + 1/2z + 3/4(8) y + 1/2xz + 1/4
hkl: h + k + l = 2n
hk0: h + k = 2n
0kl: kl = 2n
hhl: 2h + l = 4n
00l: l = 4n
h00: h = 2n
h-h0: h = 2n
    Special: as above, plus
8 a  2 . . 
0, 0, z 0, 1/2z + 1/4 0, 0, z + 1/2 0, 1/2z + 3/4
hkl: 2h  +  l  =  4n

Symmetry of special projections

Along [001]   p4gm
a' = 1/2(a - b)   b' = 1/2(a + b)   
Origin at 1/41/4z
Along [100]   p1m1
a' = 1/2b   b' = 1/2c   
Origin at x, 0, 0
Along [110]   c1m1
a' = 1/2(-a + b)   b' = 1/2c   
Origin at xx, 0








































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