Table of Magnetic Space Group Symbols

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Table of Magnetic Space Group Symbols

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P_c-31c [#163.84] (Type: 4 -- Type IV (klassengleiche))

[OG: P_2c-31m' #162.7.1309]

Wyckoff Positions of Group 163.84 (P_c-31c)

Multiplicity

Wyckoff
letter

Coordinates

24

l

(x,y,z \| m_x,m_y,m_z)	(-y,x-y,z \| -m_y,m_x-m_y,m_z)	(-x+y,-x,z \| -m_x+m_y,-m_x,m_z)
(x,x-y,-z+1/2 \| m_x,m_x-m_y,-m_z)	(-x+y,y,-z+1/2 \| -m_x+m_y,m_y,-m_z)	(-y,-x,-z+1/2 \| -m_y,-m_x,-m_z)
(-x,-y,-z \| m_x,m_y,m_z)	(y,-x+y,-z \| -m_y,m_x-m_y,m_z)	(x-y,x,-z \| -m_x+m_y,-m_x,m_z)
(-x,-x+y,z+1/2 \| m_x,m_x-m_y,-m_z)	(x-y,-y,z+1/2 \| -m_x+m_y,m_y,-m_z)	(y,x,z+1/2 \| -m_y,-m_x,-m_z)
(x,y,z+1/2 \| -m_x,-m_y,-m_z)	(-y,x-y,z+1/2 \| m_y,-m_x+m_y,-m_z)	(-x+y,-x,z+1/2 \| m_x-m_y,m_x,-m_z)
(x,x-y,-z \| -m_x,-m_x+m_y,m_z)	(-x+y,y,-z \| m_x-m_y,-m_y,m_z)	(-y,-x,-z \| m_y,m_x,m_z)
(-x,-y,-z+1/2 \| -m_x,-m_y,-m_z)	(y,-x+y,-z+1/2 \| m_y,-m_x+m_y,-m_z)	(x-y,x,-z+1/2 \| m_x-m_y,m_x,-m_z)
(-x,-x+y,z \| -m_x,-m_x+m_y,m_z)	(x-y,-y,z \| m_x-m_y,-m_y,m_z)	(y,x,z \| m_y,m_x,m_z)

12

k

(x,0,z \| m_x,0,m_z)	(0,x,z \| 0,m_x,m_z)	(-x,-x,z \| -m_x,-m_x,m_z)
(x,x,-z+1/2 \| m_x,m_x,-m_z)	(-x,0,-z+1/2 \| -m_x,0,-m_z)	(0,-x,-z+1/2 \| 0,-m_x,-m_z)
(-x,0,-z \| m_x,0,m_z)	(0,-x,-z \| 0,m_x,m_z)	(x,x,-z \| -m_x,-m_x,m_z)
(-x,-x,z+1/2 \| m_x,m_x,-m_z)	(x,0,z+1/2 \| -m_x,0,-m_z)	(0,x,z+1/2 \| 0,-m_x,-m_z)

12

j

(x,-x,1/4 \| m_x,-m_x,0)	(x,2x,1/4 \| m_x,2m_x,0)	(-2x,-x,1/4 \| -2m_x,-m_x,0)
(-x,x,3/4 \| m_x,-m_x,0)	(-x,-2x,3/4 \| m_x,2m_x,0)	(2x,x,3/4 \| -2m_x,-m_x,0)
(x,-x,3/4 \| -m_x,m_x,0)	(x,2x,3/4 \| -m_x,-2m_x,0)	(-2x,-x,3/4 \| 2m_x,m_x,0)
(-x,x,1/4 \| -m_x,m_x,0)	(-x,-2x,1/4 \| -m_x,-2m_x,0)	(2x,x,1/4 \| 2m_x,m_x,0)

12

i

(x,-x,0 \| m_x,m_x,m_z)	(x,2x,0 \| -m_x,0,m_z)	(-2x,-x,0 \| 0,-m_x,m_z)
(x,2x,1/2 \| m_x,0,-m_z)	(-2x,-x,1/2 \| 0,m_x,-m_z)	(x,-x,1/2 \| -m_x,-m_x,-m_z)
(-x,x,0 \| m_x,m_x,m_z)	(-x,-2x,0 \| -m_x,0,m_z)	(2x,x,0 \| 0,-m_x,m_z)
(-x,-2x,1/2 \| m_x,0,-m_z)	(2x,x,1/2 \| 0,m_x,-m_z)	(-x,x,1/2 \| -m_x,-m_x,-m_z)

8

h

(1/3,2/3,z \| 0,0,m_z)	(1/3,2/3,-z+1/2 \| 0,0,-m_z)	(2/3,1/3,-z \| 0,0,m_z)
(2/3,1/3,z+1/2 \| 0,0,-m_z)	(1/3,2/3,z+1/2 \| 0,0,-m_z)	(1/3,2/3,-z \| 0,0,m_z)
(2/3,1/3,-z+1/2 \| 0,0,-m_z)	(2/3,1/3,z \| 0,0,m_z)

6

g

(1/2,0,1/4 \| 0,0,0)	(0,1/2,1/4 \| 0,0,0)	(1/2,1/2,1/4 \| 0,0,0)
(1/2,0,3/4 \| 0,0,0)	(0,1/2,3/4 \| 0,0,0)	(1/2,1/2,3/4 \| 0,0,0)

6

f

(1/2,0,0 \| m_x,0,m_z)	(0,1/2,0 \| 0,m_x,m_z)	(1/2,1/2,0 \| -m_x,-m_x,m_z)
(1/2,1/2,1/2 \| m_x,m_x,-m_z)	(1/2,0,1/2 \| -m_x,0,-m_z)	(0,1/2,1/2 \| 0,-m_x,-m_z)

4

e

(0,0,z \| 0,0,m_z)	(0,0,-z+1/2 \| 0,0,-m_z)	(0,0,-z \| 0,0,m_z)
(0,0,z+1/2 \| 0,0,-m_z)

4

d

(1/3,2/3,1/4 \| 0,0,0)	(2/3,1/3,3/4 \| 0,0,0)	(1/3,2/3,3/4 \| 0,0,0)
(2/3,1/3,1/4 \| 0,0,0)

4

c

(1/3,2/3,0 \| 0,0,m_z)	(1/3,2/3,1/2 \| 0,0,-m_z)	(2/3,1/3,0 \| 0,0,m_z)
(2/3,1/3,1/2 \| 0,0,-m_z)

2

b

(0,0,1/4 | 0,0,0)

(0,0,3/4 | 0,0,0)

2

a

(0,0,0 | 0,0,m_z)

(0,0,1/2 | 0,0,-m_z)

Site Symmetries of the Wyckoff Positions

WP	Representative	PG
2a	(0,0,0 \| 0,0,m_z)	-3
2b	(0,0,1/4 \| 0,0,0)	-3'm'
4c	(1/3,2/3,0 \| 0,0,m_z)	1
4d	(1/3,2/3,1/4 \| 0,0,0)	2
4e	(0,0,z \| 0,0,m_z)	3
6f	(1/2,0,0 \| m_x,0,m_z)	-1
6g	(1/2,0,1/4 \| 0,0,0)	2/m'
8h	(1/3,2/3,z \| 0,0,m_z)	1
12i	(x,-x,0 \| m_x,m_x,m_z)	1
12j	(x,-x,1/4 \| m_x,-m_x,0)	2
12k	(x,0,z \| m_x,0,m_z)	1
24l	(x,y,z \| m_x,m_y,m_z)	1

List all the elements of the orbits

Go to the operators of (P_c-31c)
Go to the extinction rules of (P_c-31c)

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