Table of Magnetic Space Group Symbols

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Table of Magnetic Space Group Symbols

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P4'/m'm'm [#123.344] (Type: 3 -- Type III (translationgleiche))

[OG: P4'/m'm'm #123.6.1004]

Wyckoff Positions of Group 123.344 (P4'/m'm'm)

Multiplicity

Wyckoff
letter

Coordinates

16

u

(x,y,z \| m_x,m_y,m_z)	(-y,x,z \| m_y,-m_x,-m_z)	(y,-x,z \| -m_y,m_x,-m_z)
(x,-y,-z \| m_x,-m_y,-m_z)	(-x,y,-z \| -m_x,m_y,-m_z)	(-x,-y,z \| -m_x,-m_y,m_z)
(y,x,-z \| -m_y,-m_x,m_z)	(-y,-x,-z \| m_y,m_x,m_z)	(-x,-y,-z \| -m_x,-m_y,-m_z)
(y,-x,-z \| -m_y,m_x,m_z)	(-y,x,-z \| m_y,-m_x,m_z)	(-x,y,z \| -m_x,m_y,m_z)
(x,-y,z \| m_x,-m_y,m_z)	(x,y,-z \| m_x,m_y,-m_z)	(-y,-x,z \| m_y,m_x,-m_z)
(y,x,z \| -m_y,-m_x,-m_z)

8

t

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

8

s

(x,0,z \| m_x,0,m_z)	(0,x,z \| 0,-m_x,-m_z)	(0,-x,z \| 0,m_x,-m_z)
(x,0,-z \| m_x,0,-m_z)	(-x,0,-z \| -m_x,0,-m_z)	(-x,0,z \| -m_x,0,m_z)
(0,x,-z \| 0,-m_x,m_z)	(0,-x,-z \| 0,m_x,m_z)

8

r

(x,x,z \| m_x,-m_x,0)	(-x,x,z \| -m_x,-m_x,0)	(x,-x,z \| m_x,m_x,0)
(x,-x,-z \| m_x,m_x,0)	(-x,x,-z \| -m_x,-m_x,0)	(-x,-x,z \| -m_x,m_x,0)
(x,x,-z \| m_x,-m_x,0)	(-x,-x,-z \| -m_x,m_x,0)

8

q

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

8

p

(x,y,0 \| m_x,m_y,0)	(-y,x,0 \| m_y,-m_x,0)	(y,-x,0 \| -m_y,m_x,0)
(x,-y,0 \| m_x,-m_y,0)	(-x,y,0 \| -m_x,m_y,0)	(-x,-y,0 \| -m_x,-m_y,0)
(y,x,0 \| -m_y,-m_x,0)	(-y,-x,0 \| m_y,m_x,0)

4

o

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

4

n

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

4

m

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

4

l

(x,0,0 \| m_x,0,0)	(0,x,0 \| 0,-m_x,0)	(0,-x,0 \| 0,m_x,0)
(-x,0,0 \| -m_x,0,0)

4

k

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

4

j

(x,x,0 \| m_x,-m_x,0)	(-x,x,0 \| -m_x,-m_x,0)	(x,-x,0 \| m_x,m_x,0)
(-x,-x,0 \| -m_x,m_x,0)

4

i

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

2

h

(1/2,1/2,z | 0,0,0)

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

2

g

(0,0,z | 0,0,0)

(0,0,-z | 0,0,0)

2

f

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

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

2

e

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

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

1

d

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

1

c

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

1

b

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

1

a

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

Site Symmetries of the Wyckoff Positions

WP	Representative	PG
1a	(0,0,0 \| 0,0,0)	4'/m'm'm
1b	(0,0,1/2 \| 0,0,0)	4'/m'm'm
1c	(1/2,1/2,0 \| 0,0,0)	4'/m'm'm
1d	(1/2,1/2,1/2 \| 0,0,0)	4'/m'm'm
2e	(0,1/2,1/2 \| 0,0,0)	m'm'm'
2f	(0,1/2,0 \| 0,0,0)	m'm'm'
2g	(0,0,z \| 0,0,0)	4'mm'
2h	(1/2,1/2,z \| 0,0,0)	4'mm'
4i	(0,1/2,z \| 0,0,m_z)	2
4j	(x,x,0 \| m_x,-m_x,0)	m
4k	(x,x,1/2 \| m_x,-m_x,0)	m
4l	(x,0,0 \| m_x,0,0)	2
4m	(x,0,1/2 \| m_x,0,0)	2
4n	(x,1/2,0 \| m_x,0,0)	2
4o	(x,1/2,1/2 \| m_x,0,0)	2
8p	(x,y,0 \| m_x,m_y,0)	1
8q	(x,y,1/2 \| m_x,m_y,0)	1
8r	(x,x,z \| m_x,-m_x,0)	m
8s	(x,0,z \| m_x,0,m_z)	1
8t	(x,1/2,z \| m_x,0,m_z)	1
16u	(x,y,z \| m_x,m_y,m_z)	1

List all the elements of the orbits

Go to the operators of (P4'/m'm'm)
Go to the extinction rules of (P4'/m'm'm)

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