Synergy between transmission electron microscopy and powder diffraction: application to modulated structures

Authors:

Batuk, Dmitry; Batuk, Maria; Abakumov, Artem M.; Hadermann, Joke

Journal:

Acta Crystallographica Section B 71 127-143 (2015)

DOI:

https://doi.org/10.1107/S2052520615005466

B-IncStrDB ID: 10562EplZqM Entry date: 2015-04-26 Last revision: 2022-02-12

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Chemical data


Structural Formula Sum: Bi0.195 Fe1.046 O2.633 Pb0.763 [ Help ]

Formula weight: 299.4 Da [ Help ]

Absolute configuration: . [ Help ]

Crystallographic data and experimental details


Crystal system: monoclinic [ Help ]

Superspace group name: X2/m(α0γ)00 [ Help ]

Symmetry operations of the superspace group: [ Help ]

Operation code Operation in algebraic form
1 x1,x2,x3,x4
2 -x1,x2,-x3,-x4
3 -x1,-x2,-x3,-x4
4 x1,-x2,x3,x4
5 x1+1/2,x2+1/2,x3+1/2,x4+1/2
6 -x1+1/2,x2+1/2,-x3+1/2,-x4+1/2
7 -x1+1/2,-x2+1/2,-x3+1/2,-x4+1/2
8 x1+1/2,-x2+1/2,x3+1/2,x4+1/2

a: 3.92822(13) Å [ Help ]

b: 3.92661(10) Å [ Help ]

c: 4.05202(14) Å [ Help ]

α: 90 ° [ Help ]

β: 92.209(3) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 62.454(3) Å3 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.057008 0.000000 0.103473

Z: 1 [ Help ]

Cell measurement temperature: 900 K [ Help ]

μ: 0.005 mm-1 [ Help ]

Refinement details


R(obs): 0.0400 [ Help ]

wR(obs): 0.0554 [ Help ]

R(all): 0.0406 [ Help ]

wR(all): 0.0555 [ Help ]

S(all): 2.38 [ Help ]

Nb. of parameters: 63 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 7 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0511 [ Help ]

Δ/σ(mean): 0.0345 [ Help ]

Structural Information


Average Structure: [ Help ]

Atom site label Atom symbol x y z ADP type Uiso/equiv Symmetry multiplicity Occupancy Coords from (d)iffraction or (c)alculated Coords restraints or constraints Disordered cluster Disordered group
Fe1 Fe 0 0 0 Uiso 0.0177(4) 2 0.52323(10) d . . .
Pb1 Pb 0 0 0 Uiso 0.0519(10) 2 0.38141(8) d . . .
Bi1 Bi 0 0 0 Uiso 0.0519(10) 2 0.0974 d . . .
O1 O 0 0.5 0 Uani 0.0458(18) 2 0.52323(10) d . . .
O2 O 0.5 0 0 Uiso 0.0402(15) 2 0.37329(20) d . . .
O3 O 0 0 0.5 Uiso 0.0491(12) 2 0.41976(10) d . . .

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
O1 O 0.061(4) 0.0084(13) 0.067(4) 0 0 0

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

Wave vector code q_1
1 1
2 2

Occupation crenel coefficients: [ Help ]

Atom site label Center (x0) Width
Fe1 0 0.52323(10)
Pb1 0.5 0.47677(10)
Bi1 0.5 0.4868
O1 0 0.52323(10)
O2 0 0.37329(20)
O3 0 0.41976(10)

Displacive (translational) Legendre coefficients: [ Help ]

Atom site label Displacement axis Polynomial order Polynomial coeff.
Fe1 x 1 0.0299(14)
Fe1 y 1 0
Fe1 z 1 0.0501(10)
Fe1 x 2 0
Fe1 y 2 0
Fe1 z 2 0
Fe1 x 3 -0.024(3)
Fe1 y 3 0
Fe1 z 3 0.105(3)
Fe1 x 4 0
Fe1 y 4 0
Fe1 z 4 0
Pb1 x 1 0.004(2)
Pb1 y 1 0
Pb1 z 1 -0.0445(18)
Pb1 x 2 0
Pb1 y 2 0
Pb1 z 2 0
Pb1 x 3 -0.085(5)
Pb1 y 3 0
Pb1 z 3 0.096(5)
Pb1 x 4 0
Pb1 y 4 0
Pb1 z 4 0
Bi1 x 1 0.004(2)
Bi1 y 1 0
Bi1 z 1 -0.0445(18)
Bi1 x 2 0
Bi1 y 2 0
Bi1 z 2 0
Bi1 x 3 -0.085(5)
Bi1 y 3 0
Bi1 z 3 0.096(5)
Bi1 x 4 0
Bi1 y 4 0
Bi1 z 4 0
O1 x 1 0.028(4)
O1 y 1 0
O1 z 1 0.249(3)
O1 x 2 0
O1 y 2 0
O1 z 2 0
O1 x 3 -0.100(11)
O1 y 3 0
O1 z 3 0.069(5)
O1 x 4 0
O1 y 4 0
O1 z 4 0
O2 x 1 0.039(6)
O2 y 1 0
O2 z 1 0.157(3)
O2 x 2 0
O2 y 2 0
O2 z 2 0
O2 x 3 -0.031(15)
O2 y 3 0
O2 z 3 0
O2 x 4 0
O2 y 4 0
O2 z 4 0
O3 x 1 0.034(3)
O3 y 1 0
O3 z 1 0.134(3)
O3 x 2 0
O3 y 2 0
O3 z 2 0
O3 x 3 0
O3 y 3 0
O3 z 3 0.071(8)
O3 x 4 0
O3 y 4 0
O3 z 4 0