Wyckoff Positions of Magnetic Space Groups

Bilbao Crystallographic Server

Wyckoff Positions of Magnetic Space Groups

Help

Wyckoff Positions of the Group P4₂/m'n'm' (#136.503)
**136.503 P4₂/m'n'm' (UNI symbol)**

For this space group, BNS and OG settings coincide.
Its label in the OG setting is given as: P4₂/m'n'm' (#136.9.1160)

Multiplicity

Wyckoff
letter

Coordinates

16

k

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

j

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

8

i

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

8

h

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

4

g

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

4

f

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

4

e

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

4

d

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

4

c

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

2

b

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

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

2

a

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

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

Site Symmetries of the Wyckoff Positions

WP	Representative	Site symmetry
2a	(0,0,0 \| 0,0,0)	m'.m'm'
2b	(0,0,1/2 \| 0,0,0)	m'.m'm'
4c	(0,1/2,0 \| 0,0,0)	2/m'..
4d	(0,1/2,1/4 \| 0,0,0)	-4'..
4e	(0,0,z \| 0,0,m_z)	2.m'm'
4f	(x,x,0 \| m_x,m_x,0)	m'.2m'
4g	(x,-x,0 \| m_x,-m_x,0)	m'.m'2
8h	(0,1/2,z \| 0,0,m_z)	2..
8i	(x,y,0 \| m_x,m_y,0)	m'..
8j	(x,x,z \| m_x,m_x,m_z)	..m'
16k	(x,y,z \| m_x,m_y,m_z)	1

List the original elements of the orbits
List all the elements of the orbits

Go to the list of the Symmetry Operators of the Group P4₂/m'n'm' (#136.503)
Go to the Systematic absences for the Group P4₂/m'n'm' (#136.503)

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

Licencia de Creative Commons

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