Wyckoff Positions of Magnetic Space Groups

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Wyckoff Positions of Magnetic Space Groups

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Wyckoff Positions of the Group P-3m'1 (#164.89)
**164.89 P-3m'1 (UNI symbol)**

For this space group, BNS and OG settings coincide.
Its label in the OG setting is given as: P-3m'1 (#164.5.1319)

Multiplicity

Wyckoff
letter

Coordinates

12

j

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

6

i

(x,-x,z \| m_x,-m_x,m_z)	(x,2x,z \| m_x,2m_x,m_z)
(-2x,-x,z \| -2m_x,-m_x,m_z)	(2x,x,-z \| -2m_x,-m_x,m_z)
(-x,x,-z \| m_x,-m_x,m_z)	(-x,-2x,-z \| m_x,2m_x,m_z)

6

h

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

6

g

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

3

f

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

3

e

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

2

d

(1/3,2/3,z | 0,0,m_z)

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

2

c

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

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

1

b

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

1

a

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

Site Symmetries of the Wyckoff Positions

WP	Representative	Site symmetry
1a	(0,0,0 \| 0,0,m_z)	-3m'.
1b	(0,0,1/2 \| 0,0,m_z)	-3m'.
2c	(0,0,z \| 0,0,m_z)	3m'.
2d	(1/3,2/3,z \| 0,0,m_z)	3m'.
3e	(1/2,0,0 \| m_x,2m_x,m_z)	.2'/m'.
3f	(1/2,0,1/2 \| m_x,2m_x,m_z)	.2'/m'.
6g	(x,0,0 \| m_x,2m_x,m_z)	.2'.
6h	(x,0,1/2 \| m_x,2m_x,m_z)	.2'.
6i	(x,-x,z \| m_x,-m_x,m_z)	.m'.
12j	(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 P-3m'1 (#164.89)
Go to the Systematic absences for the Group P-3m'1 (#164.89)

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