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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: 2024-01-02

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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
Fe(1) Fe 0.77 4 0 0 0 0.0063(9) Uiso
Fe(2) 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 Fe(1) x 1
Fe1y2 Fe(1) y 2
Fe1z3 Fe(1) z 3
Fe1x4 Fe(1) x 4
Fe1y4 Fe(1) y 4
Fe1y5 Fe(1) y 5
Fe1z5 Fe(1) z 5
Fe1x6 Fe(1) x 6
Fe1z6 Fe(1) z 6
Fe1x7 Fe(1) x 7
Fe1y7 Fe(1) y 7
Fe1x8 Fe(1) x 8
Fe1z8 Fe(1) z 8
Fe1y9 Fe(1) y 9
Fe1z9 Fe(1) z 9
Fe2x1 Fe(2) x 1
Fe2y2 Fe(2) y 2
Fe2z3 Fe(2) z 3
Fe2x4 Fe(2) x 4
Fe2y4 Fe(2) y 4
Fe2z4 Fe(2) z 4
Fe2x5 Fe(2) x 5
Fe2y5 Fe(2) y 5
Fe2z5 Fe(2) z 5
Fe2x6 Fe(2) x 6
Fe2y6 Fe(2) y 6
Fe2z6 Fe(2) z 6
Fe2x7 Fe(2) x 7
Fe2y7 Fe(2) y 7
Fe2z7 Fe(2) z 7
Fe2y8 Fe(2) y 8
Fe2x8 Fe(2) x 8
Fe2z8 Fe(2) z 8
Fe2x9 Fe(2) x 9
Fe2y9 Fe(2) y 9
Fe2z9 Fe(2) 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 Fe(1) 1
Fe1o2 Fe(1) 2
Fe1o3 Fe(1) 3
Fe1o4 Fe(1) 4
Fe1o5 Fe(1) 5
Fe1o6 Fe(1) 6
Fe1o7 Fe(1) 7
Fe1o8 Fe(1) 8
Fe1o9 Fe(1) 9
Fe2o1 Fe(2) 1
Fe2o2 Fe(2) 2
Fe2o3 Fe(2) 3
Fe2o4 Fe(2) 4
Fe2o5 Fe(2) 5
Fe2o6 Fe(2) 6
Fe2o7 Fe(2) 7
Fe2o8 Fe(2) 8
Fe2o9 Fe(2) 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 Fe(1) Uiso 1
Fe1U2 Fe(1) Uiso 2
Fe1U3 Fe(1) Uiso 3
Fe1U4 Fe(1) Uiso 4
Fe1U5 Fe(1) Uiso 5
Fe1U6 Fe(1) Uiso 6
Fe1U7 Fe(1) Uiso 7
Fe1U8 Fe(1) Uiso 8
Fe1U9 Fe(1) 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)