Table of Magnetic Space Group Symbols

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Table of Magnetic Space Group Symbols

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P_I4/mnc [#128.410] (Type: 4 -- Type IV (klassengleiche))

[OG: I_P4/mm'm' #139.15.1193]

Wyckoff Positions of Group 128.410 (P_I4/mnc)

Multiplicity

Wyckoff
letter

Coordinates

32

o

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

n

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

16

m

(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+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+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)	(-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+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)

16

l

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

16

k

(x,x+1/2,1/4 \| m_x,m_x,0)	(-x+1/2,x,1/4 \| -m_x,m_x,0)	(x+1/2,-x,1/4 \| m_x,-m_x,0)
(-x,-x+1/2,1/4 \| -m_x,-m_x,0)	(-x,-x+1/2,3/4 \| m_x,m_x,0)	(x+1/2,-x,3/4 \| -m_x,m_x,0)
(-x+1/2,x,3/4 \| m_x,-m_x,0)	(x,x+1/2,3/4 \| -m_x,-m_x,0)	(x+1/2,x,3/4 \| -m_x,-m_x,0)
(-x,x+1/2,3/4 \| m_x,-m_x,0)	(x,-x+1/2,3/4 \| -m_x,m_x,0)	(-x+1/2,-x,3/4 \| m_x,m_x,0)
(-x+1/2,-x,1/4 \| -m_x,-m_x,0)	(x,-x+1/2,1/4 \| m_x,-m_x,0)	(-x,x+1/2,1/4 \| -m_x,m_x,0)
(x+1/2,x,1/4 \| m_x,m_x,0)

8

j

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

8

i

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

8

h

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

g

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

8

f

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

4

e

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

4

d

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

4

c

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

2

b

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

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

2

a

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

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

Site Symmetries of the Wyckoff Positions

WP	Representative	PG
2a	(0,0,0 \| 0,0,m_z)	4/m
2b	(0,0,1/2 \| 0,0,m_z)	4/m
4c	(0,1/2,0 \| 0,0,m_z)	2/m
4d	(0,1/2,1/4 \| 0,0,0)	-4'2m'
4e	(0,0,z \| 0,0,m_z)	4
8f	(1/4,1/4,1/4 \| 0,0,0)	2/m'
8g	(0,1/2,z \| 0,0,m_z)	2
8h	(x,x,0 \| 0,0,m_z)	m
8i	(x,0,0 \| 0,0,m_z)	m
8j	(x,1/2,0 \| 0,0,m_z)	m
16k	(x,x+1/2,1/4 \| m_x,m_x,0)	2
16l	(x,y,0 \| 0,0,m_z)	m
16m	(x,x,z \| m_x,m_x,m_z)	1
16n	(0,y,z \| 0,m_y,m_z)	1
32o	(x,y,z \| m_x,m_y,m_z)	1

List all the elements of the orbits

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