Table of Magnetic Space Group Symbols

Bilbao Crystallographic Server

Table of Magnetic Space Group Symbols

Help

P_Cmmm [#47.255] (Type: 4 -- Type IV (klassengleiche))

[OG: C_Pmmm #65.9.553]

Wyckoff Positions of Group 47.255 (P_Cmmm)

Multiplicity

Wyckoff
letter

Coordinates

16

r

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

8

q

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

8

p

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

8

o

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

8

n

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

8

m

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

4

l

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

4

k

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

4

j

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

4

i

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

4

h

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

4

g

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

4

f

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

4

e

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

2

d

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

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

2

c

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

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

2

b

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

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

2

a

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

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

Site Symmetries of the Wyckoff Positions

WP	Representative	PG
2a	(0,0,0 \| 0,0,0)	mmm
2b	(1/2,0,0 \| 0,0,0)	mmm
2c	(1/2,0,1/2 \| 0,0,0)	mmm
2d	(0,0,1/2 \| 0,0,0)	mmm
4e	(1/4,1/4,0 \| 0,0,0)	2'/m
4f	(1/4,1/4,1/2 \| 0,0,0)	2'/m
4g	(x,0,0 \| 0,0,0)	mm2
4h	(x,0,1/2 \| 0,0,0)	mm2
4i	(0,y,0 \| 0,0,0)	mm2
4j	(0,y,1/2 \| 0,0,0)	mm2
4k	(0,0,z \| 0,0,0)	mm2
4l	(0,1/2,z \| 0,0,0)	mm2
8m	(1/4,1/4,z \| m_x,m_y,0)	1
8n	(0,y,z \| m_x,0,0)	m
8o	(x,0,z \| 0,m_y,0)	m
8p	(x,y,0 \| 0,0,m_z)	m
8q	(x,y,1/2 \| 0,0,m_z)	m
16r	(x,y,z \| m_x,m_y,m_z)	1

List all the elements of the orbits

Go to the operators of (P_Cmmm)
Go to the extinction rules of (P_Cmmm)

Back to the list of magnetic space groups derived from Pmmm
Back to the list of Magnetic Space Groups

Bilbao Crystallographic Server
http://www.cryst.ehu.es

For comments, please mail to
administrador.bcs@ehu.es