Table of Magnetic Space Group Symbols

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Table of Magnetic Space Group Symbols

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P_C4/mbm [#127.397] (Type: 4 -- Type IV (klassengleiche))

[OG: P_P4'/mmm' #123.17.1015]

Wyckoff Positions of Group 127.397 (P_C4/mbm)

Multiplicity

Wyckoff
letter

Coordinates

32

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

16

t

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

16

s

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

16

r

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

16

q

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

16

p

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

8

o

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

8

n

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

8

m

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

8

l

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

8

k

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

8

j

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

8

i

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

4

h

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

4

g

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

4

f

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

4

e

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

2

d

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

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

2

c

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

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

2

b

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

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

2

a

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

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

Site Symmetries of the Wyckoff Positions

WP	Representative	PG
2a	(0,1/2,0 \| 0,0,0)	4'/mmm'
2b	(0,1/2,1/2 \| 0,0,0)	4'/mmm'
2c	(0,0,0 \| 0,0,m_z)	4/m
2d	(0,0,1/2 \| 0,0,m_z)	4/m
4e	(3/4,3/4,1/2 \| 0,0,0)	mmm'
4f	(3/4,3/4,0 \| 0,0,0)	mmm'
4g	(0,1/2,z \| 0,0,0)	4'mm'
4h	(0,0,z \| 0,0,m_z)	4
8i	(3/4,3/4,z \| m_x,m_x,0)	m
8j	(0,y,0 \| 0,0,m_z)	m
8k	(0,y,1/2 \| 0,0,m_z)	m
8l	(x,x+1/2,0 \| 0,0,0)	mm2
8m	(x,x+1/2,1/2 \| 0,0,0)	mm2
8n	(x,x,0 \| 0,0,m_z)	m
8o	(x,x,1/2 \| 0,0,m_z)	m
16p	(x,y,0 \| 0,0,m_z)	m
16q	(x,y,1/2 \| 0,0,m_z)	m
16r	(0,y,z \| 0,m_y,m_z)	1
16s	(x,x+1/2,z \| m_x,-m_x,0)	m
16t	(x,x,z \| m_x,m_x,m_z)	1
32u	(x,y,z \| m_x,m_y,m_z)	1

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