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Modulated Structure of Wustite (Fe1-xO) (Three-Dimensional Modulation)

Authors:

Yamamoto, Akiji

Journal:

Acta Crystallographica Section B 38 1451-1456 (1982)

DOI:

https://doi.org/10.1107/S056774088200613X

B-IncStrDB ID: T3LPC7AKz8v Entry date: 2021-12-30 Last revision: 2026-01-19

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wustite

Chemical data

Mineral Name: Wustite [ Help ]

Structural Formula Sum: Fe0.902 O [ Help ]

Crystallographic data and experimental details

a: 4.30(4) Å [ Help ]

b: 4.30(4) Å [ Help ]

c: 4.30(4) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Modulation dimension: 3 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.398 0 0
2 0 0.398 0
3 0 0 0.398

Crystal system: cubic [ Help ]

Superspace group name (WJJ): P:Fm3m:Pm3m [ Help ]

Symmetry operations of the superspace group: [ Help ]

Operation code Operation in algebraic form
1 x1,x2,x3,x4,x5,x6
2 -x1,-x2,x3,-x4,-x5,x6
3 -x1,x2,-x3,-x4,x5,-x6
4 x1,-x2,-x3,x4,-x5,-x6
5 x3,x1,x2,x6,x4,x5
6 x3,-x1,-x2,x6,-x4,-x5
7 -x3,-x1,x2,-x6,-x4,x5
8 -x3,x1,-x2,-x6,x4,-x5
9 x2,x3,x1,x5,x6,x4
10 -x2,x3,-x1,-x5,x6,-x4
11 x2,-x3,-x1,x5,-x6,-x4
12 -x2,-x3,x1,-x5,-x6,x4
13 x2,x1,-x3,x5,x4,-x6
14 -x2,-x1,-x3,-x5,-x4,-x6
15 x2,-x1,x3,x5,-x4,x6
16 -x2,x1,x3,-x5,x4,x6
17 x1,x3,-x2,x4,x6,-x5
18 -x1,x3,x2,-x4,x6,x5
19 -x1,-x3,-x2,-x4,-x6,-x5
20 x1,-x3,x2,x4,-x6,x5
21 x3,x2,-x1,x6,x5,-x4
22 x3,-x2,x1,x6,-x5,x4
23 -x3,x2,x1,-x6,x5,x4
24 -x3,-x2,-x1,-x6,-x5,-x4
25 -x1,-x2,-x3,-x4,-x5,\-x6
26 x1,x2,-x3,x4,x5,-x6
27 x1,-x2,x3,x4,-x5,x6
28 -x1,x2,x3,-x4,x5,x6
29 -x3,-x1,-x2,-x6,-x4,-x5
30 -x3,x1,x2,-x6,x4,x5
31 x3,x1,-x2,x6,x4,-x5
32 x3,-x1,x2,x6,-x4,x5
33 -x2,-x3,-x1,-x5,-x6,-x4
34 x2,-x3,x1,x5,-x6,x4
35 -x2,x3,x1,-x5,x6,x4
36 x2,x3,-x1,x5,x6,-x4
37 -x2,-x1,x3,-x5,-x4,x6
38 x2,x1,x3,x5,x4,x6
39 -x2,x1,-x3,-x5,x4,-x6
40 x2,-x1,-x3,x5,-x4,-x6
41 -x1,-x3,x2,-x4,-x6,x5
42 x1,-x3,-x2,x4,-x6,-x5
43 x1,x3,x2,x4,x6,x5
44 -x1,x3,-x2,-x4,x6,-x5
45 -x3,-x2,x1,-x6,-x5,x4
46 -x3,x2,-x1,-x6,x5,-x4
47 x3,-x2,-x1,x6,-x5,-x4
48 x3,x2,x1,x6,x5,x4
49 1/2+x1,1/2+x2,x3,x4,x5,x6
50 1/2-x1,1/2-x2,x3,-x4,-x5,x6
51 1/2-x1,1/2+x2,-x3,-x4,x5,-x6
52 1/2+x1,1/2-x2,-x3,x4,-x5,-x6
53 1/2+x3,1/2+x1,x2,x6,x4,x5
54 1/2+x3,1/2-x1,-x2,x6,-x4,-x5
55 1/2-x3,1/2-x1,x2,-x6,-x4,x5
56 1/2-x3,1/2+x1,-x2,-x6,x4,-x5
57 1/2+x2,1/2+x3,x1,x5,x6,x4
58 1/2-x2,1/2+x3,-x1,-x5,x6,-x4
59 1/2+x2,1/2-x3,-x1,x5,-x6,-x4
60 1/2-x2,1/2-x3,x1,-x5,-x6,x4
61 1/2+x2,1/2+x1,-x3,x5,x4,-x6
62 1/2-x2,1/2-x1,-x3,-x5,-x4,-x6
63 1/2+x2,1/2-x1,x3,x5,-x4,x6
64 1/2-x2,1/2+x1,x3,-x5,x4,x6
65 1/2+x1,1/2+x3,-x2,x4,x6,-x5
66 1/2-x1,1/2+x3,x2,-x4,x6,x5
67 1/2-x1,1/2-x3,-x2,-x4,-x6,-x5
68 1/2+x1,1/2-x3,x2,x4,-x6,x5
69 1/2+x3,1/2+x2,-x1,x6,x5,-x4
70 1/2+x3,1/2-x2,x1,x6,-x5,x4
71 1/2-x3,1/2+x2,x1,-x6,x5,x4
72 1/2-x3,1/2-x2,-x1,-x6,-x5,-x4
73 1/2-x1,1/2-x2,-x3,-x4,-x5,-x6
74 1/2+x1,1/2+x2,-x3,x4,x5,-x6
75 1/2+x1,1/2-x2,x3,x4,-x5,x6
76 1/2-x1,1/2+x2,x3,-x4,x5,x6
77 1/2-x3,1/2-x1,-x2,-x6,-x4,-x5
78 1/2-x3,1/2+x1,x2,-x6,x4,x5
79 1/2+x3,1/2+x1,-x2,x6,x4,-x5
80 1/2+x3,1/2-x1,x2,x6,-x4,x5
81 1/2-x2,1/2-x3,-x1,-x5,-x6,-x4
82 1/2+x2,1/2-x3,x1,x5,-x6,x4
83 1/2-x2,1/2+x3,x1,-x5,x6,x4
84 1/2+x2,1/2+x3,-x1,x5,x6,-x4
85 1/2-x2,1/2-x1,x3,-x5,-x4,x6
86 1/2+x2,1/2+x1,x3,x5,x4,x6
87 1/2-x2,1/2+x1,-x3,-x5,x4,-x6
88 1/2+x2,1/2-x1,-x3,x5,-x4,-x6
89 1/2-x1,1/2-x3,x2,-x4,-x6,x5
90 1/2+x1,1/2-x3,-x2,x4,-x6,-x5
91 1/2+x1,1/2+x3,x2,x4,x6,x5
92 1/2-x1,1/2+x3,-x2,-x4,x6,-x5
93 1/2-x3,1/2-x2,x1,-x6,-x5,x4
94 1/2-x3,1/2+x2,-x1,-x6,x5,-x4
95 1/2+x3,1/2-x2,-x1,x6,-x5,-x4
96 1/2+x3,1/2+x2,x1,x6,x5,x4
97 1/2+x1,x2,1/2+x3,x4,x5,x6
98 1/2-x1,-x2,1/2+x3,-x4,-x5,x6
99 1/2-x1,x2,1/2-x3,-x4,x5,-x6
100 1/2+x1,-x2,1/2-x3,x4,-x5,-x6
101 1/2+x3,x1,1/2+x2,x6,x4,x5
102 1/2+x3,-x1,1/2-x2,x6,-x4,-x5
103 1/2-x3,-x1,1/2+x2,-x6,-x4,x5
104 1/2-x3,x1,1/2-x2,-x6,x4,-x5
105 1/2+x2,x3,1/2+x1,x5,x6,x4
106 1/2-x2,x3,1/2-x1,-x5,x6,-x4
107 1/2+x2,-x3,1/2-x1,x5,-x6,-x4
108 1/2-x2,-x3,1/2+x1,-x5,-x6,x4
109 1/2+x2,x1,1/2-x3,x5,x4,-x6
110 1/2-x2,-x1,1/2-x3,-x5,-x4,-x6
111 1/2+x2,-x1,1/2+x3,x5,-x4,x6
112 1/2-x2,x1,1/2+x3,-x5,x4,x6
113 1/2+x1,x3,1/2-x2,x4,x6,-x5
114 1/2-x1,x3,1/2+x2,-x4,x6,x5
115 1/2-x1,-x3,1/2-x2,-x4,-x6,-x5
116 1/2+x1,-x3,1/2+x2,x4,-x6,x5
117 1/2+x3,x2,1/2-x1,x6,x5,-x4
118 1/2+x3,-x2,1/2+x1,x6,-x5,x4
119 1/2-x3,x2,1/2+x1,-x6,x5,x4
120 1/2-x3,-x2,1/2-x1,-x6,-x5,-x4
121 1/2-x1,-x2,1/2-x3,-x4,-x5,-x6
122 1/2+x1,x2,1/2-x3,x4,x5,-x6
123 1/2+x1,-x2,1/2+x3,x4,-x5,x6
124 1/2-x1,x2,1/2+x3,-x4,x5,x6
125 1/2-x3,-x1,1/2-x2,-x6,-x4,-x5
126 1/2-x3,x1,1/2+x2,-x6,x4,x5
127 1/2+x3,x1,1/2-x2,x6,x4,-x5
128 1/2+x3,-x1,1/2+x2,x6,-x4,x5
129 1/2-x2,-x3,1/2-x1,-x5,-x6,-x4
130 1/2+x2,-x3,1/2+x1,x5,-x6,x4
131 1/2-x2,x3,1/2+x1,-x5,x6,x4
132 1/2+x2,x3,1/2-x1,x5,x6,-x4
133 1/2-x2,-x1,1/2+x3,-x5,-x4,x6
134 1/2+x2,x1,1/2+x3,x5,x4,x6
135 1/2-x2,x1,1/2-x3,-x5,x4,-x6
136 1/2+x2,-x1,1/2-x3,x5,-x4,-x6
137 1/2-x1,-x3,1/2+x2,-x4,-x6,x5
138 1/2+x1,-x3,1/2-x2,x4,-x6,-x5
139 1/2+x1,x3,1/2+x2,x4,x6,x5
140 1/2-x1,x3,1/2-x2,-x4,x6,-x5
141 1/2-x3,-x2,1/2+x1,-x6,-x5,x4
142 1/2-x3,x2,1/2-x1,-x6,x5,-x4
143 1/2+x3,-x2,1/2-x1,x6,-x5,-x4
144 1/2+x3,x2,1/2+x1,x6,x5,x4
145 x1,1/2+x2,1/2+x3,x4,x5,x6
146 -x1,1/2-x2,1/2+x3,-x4,-x5,x6
147 -x1,1/2+x2,1/2-x3,-x4,x5,-x6
148 x1,1/2-x2,1/2-x3,x4,-x5,-x6
149 x3,1/2+x1,1/2+x2,x6,x4,x5
150 x3,1/2-x1,1/2-x2,x6,-x4,-x5
151 -x3,1/2-x1,1/2+x2,-x6,-x4,x5
152 -x3,1/2+x1,1/2-x2,-x6,x4,-x5
153 x2,1/2+x3,1/2+x1,x5,x6,x4
154 -x2,1/2+x3,1/2-x1,-x5,x6,-x4
155 x2,1/2-x3,1/2-x1,x5,-x6,-x4
156 -x2,1/2-x3,1/2+x1,-x5,-x6,x4
157 x2,1/2+x1,1/2-x3,x5,x4,-x6
158 -x2,1/2-x1,1/2-x3,-x5,-x4,-x6
159 x2,1/2-x1,1/2+x3,x5,-x4,x6
160 -x2,1/2+x1,1/2+x3,-x5,x4,x6
161 x1,1/2+x3,1/2-x2,x4,x6,-x5
162 -x1,1/2+x3,1/2+x2,-x4,x6,x5
163 -x1,1/2-x3,1/2-x2,-x4,-x6,-x5
164 x1,1/2-x3,1/2+x2,x4,-x6,x5
165 x3,1/2+x2,1/2-x1,x6,x5,-x4
166 x3,1/2-x2,1/2+x1,x6,-x5,x4
167 -x3,1/2+x2,1/2+x1,-x6,x5,x4
168 -x3,1/2-x2,1/2-x1,-x6,-x5,-x4
169 -x1,1/2-x2,1/2-x3,-x4,-x5,-x6
170 x1,1/2+x2,1/2-x3,x4,x5,-x6
171 x1,1/2-x2,1/2+x3,x4,-x5,x6
172 -x1,1/2+x2,1/2+x3,-x4,x5,x6
173 -x3,1/2-x1,1/2-x2,-x6,-x4,-x5
174 -x3,1/2+x1,1/2+x2,-x6,x4,x5
175 x3,1/2+x1,1/2-x2,x6,x4,-x5
176 x3,1/2-x1,1/2+x2,x6,-x4,x5
177 -x2,1/2-x3,1/2-x1,-x5,-x6,-x4
178 x2,1/2-x3,1/2+x1,x5,-x6,x4
179 -x2,1/2+x3,1/2+x1,-x5,x6,x4
180 x2,1/2+x3,1/2-x1,x5,x6,-x4
181 -x2,1/2-x1,1/2+x3,-x5,-x4,x6
182 x2,1/2+x1,1/2+x3,x5,x4,x6
183 -x2,1/2+x1,1/2-x3,-x5,x4,-x6
184 x2,1/2-x1,1/2-x3,x5,-x4,-x6
185 -x1,1/2-x3,1/2+x2,-x4,-x6,x5
186 x1,1/2-x3,1/2-x2,x4,-x6,-x5
187 x1,1/2+x3,1/2+x2,x4,x6,x5
188 -x1,1/2+x3,1/2-x2,-x4,x6,-x5
189 -x3,1/2-x2,1/2+x1,-x6,-x5,x4
190 -x3,1/2+x2,1/2-x1,-x6,x5,-x4
191 x3,1/2-x2,1/2-x1,x6,-x5,-x4
192 x3,1/2+x2,1/2+x1,x6,x5,x4

Refinement details

Nb. of observed reflections: 152 [ Help ]

R(obs): 0.110 [ Help ]

Refinement remarks: WARNING: The published thermal displacement parameters, Biso, have been converted to Uiso [ Help ]

Structural Information

Average Structure: [ Help ]

Atom site label Atom symbol Occupancy Symmetry multiplicity x y z Uiso/equiv ADP type
Fe1 Fe 0.77 4 0 0 0 0.0063(9) Uiso
Fe2 Fe 0.06(1) 8 0.25 0.25 0.25 0.032(7) Uiso
O O 1.0 4 0.5 0 0 0.015(2) Uiso

Fourier Wave Vectors (explicit: q_x,q_y,q_z or coefficients: q_1,q_2,...): [ Help ]

Wave vector code q_x q_y q_z
1 0.398 0 0
2 0 0.398 0
3 0 0 0.398
4 0.398 0.398 0
5 0 0.398 0.398
6 0.398 0 0.398
7 0.398 -0.398 0
8 0.398 0 -0.398
9 0 0.398 -0.398

Definition of the displacive (translational) Fourier series: [ Help ]

Modulation code Atom site label Displacement axis Wave vector code
Fe1x1 Fe1 x 1
Fe1y2 Fe1 y 2
Fe1z3 Fe1 z 3
Fe1x4 Fe1 x 4
Fe1y4 Fe1 y 4
Fe1y5 Fe1 y 5
Fe1z5 Fe1 z 5
Fe1x6 Fe1 x 6
Fe1z6 Fe1 z 6
Fe1x7 Fe1 x 7
Fe1y7 Fe1 y 7
Fe1x8 Fe1 x 8
Fe1z8 Fe1 z 8
Fe1y9 Fe1 y 9
Fe1z9 Fe1 z 9
Fe2x1 Fe2 x 1
Fe2y2 Fe2 y 2
Fe2z3 Fe2 z 3
Fe2x4 Fe2 x 4
Fe2y4 Fe2 y 4
Fe2z4 Fe2 z 4
Fe2x5 Fe2 x 5
Fe2y5 Fe2 y 5
Fe2z5 Fe2 z 5
Fe2x6 Fe2 x 6
Fe2y6 Fe2 y 6
Fe2z6 Fe2 z 6
Fe2x7 Fe2 x 7
Fe2y7 Fe2 y 7
Fe2z7 Fe2 z 7
Fe2y8 Fe2 y 8
Fe2x8 Fe2 x 8
Fe2z8 Fe2 z 8
Fe2x9 Fe2 x 9
Fe2y9 Fe2 y 9
Fe2z9 Fe2 z 9
Ox1 O x 1
Oy2 O y 2
Oz3 O z 3
Ox4 O x 4
Oy4 O y 4
Oy5 O y 5
Oz5 O z 5
Ox6 O x 6
Oz6 O z 6
Ox7 O x 7
Oy7 O y 7
Ox8 O x 8
Oz8 O z 8
Oy9 O y 9
Oz9 O z 9

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Sine coefficient Cosine coefficient
Fe1x1 -0.0139(4) 0
Fe1y2 -0.0139(4) 0
Fe1z3 -0.0139(4) 0
Fe1x4 -0.0033(4) 0
Fe1y4 -0.0033(4) 0
Fe1y5 -0.0033(4) 0
Fe1z5 -0.0033(4) 0
Fe1x6 -0.0033(4) 0
Fe1z6 -0.0033(4) 0
Fe1x7 -0.0033(4) 0
Fe1y7 0.0033(4) 0
Fe1x8 -0.0033(4) 0
Fe1z8 0.0033(4) 0
Fe1y9 -0.0033(4) 0
Fe1z9 0.0033(4) 0
Fe2x1 0.0256(161) 0
Fe2y2 0.0256(161) 0
Fe2z3 0.0256(161) 0
Fe2x4 -0.0051(72) 0
Fe2y4 -0.0051(72) 0
Fe2z4 0 0.0234(52)
Fe2x5 0 0.0234(52)
Fe2y5 -0.0051(72) 0
Fe2z5 -0.0051(72) 0
Fe2x6 -0.0051(72) 0
Fe2y6 0 0.0234(52)
Fe2z6 -0.0051(72) 0
Fe2x7 -0.0051(72) 0
Fe2y7 0.0051(72) 0
Fe2z7 0 -0.0234(52)
Fe2y8 0 -0.0234(52)
Fe2x8 -0.0051(72) 0
Fe2z8 0.0051(72) 0
Fe2x9 0 -0.0234(52)
Fe2y9 -0.0051(72) 0
Fe2z9 0.0051(72) 0
Ox1 0.0078(19) 0
Oy2 0.0078(19) 0
Oz3 0.0078(19) 0
Ox4 -0.0119(14) 0
Oy4 -0.0119(14) 0
Oy5 -0.0119(14) 0
Oz5 -0.0119(14) 0
Ox6 -0.0119(14) 0
Oz6 -0.0119(14) 0
Ox7 -0.0119(14) 0
Oy7 0.0119(14) 0
Ox8 -0.0119(14) 0
Oz8 0.0119(14) 0
Oy9 -0.0119(14) 0
Oz9 0.0119(14) 0

Definition of the occupation Fourier series: [ Help ]

Modulation code Atom site label Wave vector code
Fe1o1 Fe1 1
Fe1o2 Fe1 2
Fe1o3 Fe1 3
Fe1o4 Fe1 4
Fe1o5 Fe1 5
Fe1o6 Fe1 6
Fe1o7 Fe1 7
Fe1o8 Fe1 8
Fe1o9 Fe1 9
Fe2o1 Fe2 1
Fe2o2 Fe2 2
Fe2o3 Fe2 3
Fe2o4 Fe2 4
Fe2o5 Fe2 5
Fe2o6 Fe2 6
Fe2o7 Fe2 7
Fe2o8 Fe2 8
Fe2o9 Fe2 9

Occupation Fourier coefficients: [ Help ]

Modulation code Cosine coefficient
Fe1o1 -0.16(1)
Fe1o2 -0.16(1)
Fe1o3 -0.16(1)
Fe1o4 -0.05(1)
Fe1o5 -0.05(1)
Fe1o6 -0.05(1)
Fe1o7 -0.05(1)
Fe1o8 -0.05(1)
Fe1o9 -0.05(1)
Fe2o1 0.06(1)
Fe2o2 0.06(1)
Fe2o3 0.06(1)
Fe2o4 0.03(1)
Fe2o5 0.03(1)
Fe2o6 0.03(1)
Fe2o7 0.03(1)
Fe2o8 0.03(1)
Fe2o9 0.03(1)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
Fe1U1 Fe1 Uiso 1
Fe1U2 Fe1 Uiso 2
Fe1U3 Fe1 Uiso 3
Fe1U4 Fe1 Uiso 4
Fe1U5 Fe1 Uiso 5
Fe1U6 Fe1 Uiso 6
Fe1U7 Fe1 Uiso 7
Fe1U8 Fe1 Uiso 8
Fe1U9 Fe1 Uiso 9
OU1 O Uiso 1
OU2 O Uiso 2
OU3 O Uiso 3
OU4 O Uiso 4
OU5 O Uiso 5
OU6 O Uiso 6
OU7 O Uiso 7
OU8 O Uiso 8
OU9 O Uiso 9

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient
Fe1U1 0.000(1)
Fe1U2 0.000(1)
Fe1U3 0.000(1)
Fe1U4 0.001(1)
Fe1U5 0.001(1)
Fe1U6 0.001(1)
Fe1U7 0.001(1)
Fe1U8 0.001(1)
Fe1U9 0.001(1)
OU1 0.002(2)
OU2 0.002(2)
OU3 0.002(2)
OU4 0.008(1)
OU5 0.008(1)
OU6 0.008(1)
OU7 0.008(1)
OU8 0.008(1)
OU9 0.008(1)