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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: 10622E902Zs Entry date: 2015-04-26 Last revision: 2022-01-02

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Chemical data

Structural Formula Sum: Bi0.545 Fe1.027 O2.783 Pb0.428 [ Help ]

Formula weight: 304.5 Da [ 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: 3.90908(15) Å [ Help ]

b: 3.90585(12) Å [ Help ]

c: 4.16564(17) Å [ Help ]

α: 90 ° [ Help ]

β: 91.318(3) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 63.585(4) Å3 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.034196 0 0.060882

Z: 1 [ Help ]

Cell measurement temperature: 900 K [ Help ]

μ: 0.004 mm-1 [ Help ]

Refinement details

R(obs): 0.0555 [ Help ]

wR(obs): 0.0712 [ Help ]

R(all): 0.0578 [ Help ]

wR(all): 0.0713 [ Help ]

S(all): 2.44 [ Help ]

Nb. of parameters: 66 [ Help ]

Number of constraints: 7 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0693 [ Help ]

Δ/σ(mean): 0.0378 [ 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 0.0202(6) 2 0.51334(11) d ? ? ?
Pb1 Pb 0 0 0 Uiso 0.0557(11) 2 0.21413(5) d ? ? ?
Bi1 Bi 0 0 0 Uiso 0.0557(11) 2 0.2726 d ? ? ?
O1 O 0 0.5 0 Uani 0.0326(18) 2 0.51334(11) d ? ? ?
O2 O 0.5 0 0 Uiso 0.0635(18) 2 0.4258(3) d ? ? ?
O3 O 0 0 0.5 Uiso 0.065(13) 2 0.45246(11) d ? ? ?

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
O1 O 0.056(4) 0.0119(16) 0.028(4) 0 -0.029(3) 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 0.51334(11)
Pb1 0.5 0.48666(11)
Bi1 0.5 0.4868
O1 0 0.51334(11)
O2 0 0.4258(3)
O3 0 0.45246(11)

Displacive (translational) Legendre coefficients: [ Help ]

Atom site label Displacement axis Polynomial order Polynomial coeff.
Fe1 x 1 0.0571(17)
Fe1 y 1 0
Fe1 z 1 0.0158(13)
Fe1 x 2 0
Fe1 y 2 0
Fe1 z 2 0
Fe1 x 3 -0.066(4)
Fe1 y 3 0
Fe1 z 3 0.114(3)
Fe1 x 4 0
Fe1 y 4 0
Fe1 z 4 0
Pb1 x 1 0.047(3)
Pb1 y 1 0
Pb1 z 1 -0.085(2)
Pb1 x 2 0
Pb1 y 2 0
Pb1 z 2 0
Pb1 x 3 -0.093(6)
Pb1 y 3 0
Pb1 z 3 0.156(5)
Pb1 x 4 0
Pb1 y 4 0
Pb1 z 4 0
Bi1 x 1 0.047(3)
Bi1 y 1 0
Bi1 z 1 -0.085(2)
Bi1 x 2 0
Bi1 y 2 0
Bi1 z 2 0
Bi1 x 3 -0.093(6)
Bi1 y 3 0
Bi1 z 3 0.156(5)
Bi1 x 4 0
Bi1 y 4 0
Bi1 z 4 0
O1 x 1 0.056(3)
O1 y 1 0
O1 z 1 0.208(2)
O1 x 2 0
O1 y 2 0
O1 z 2 0
O1 x 3 -0.115(9)
O1 y 3 0
O1 z 3 0.061(5)
O1 x 4 0
O1 y 4 0
O1 z 4 0
O2 x 1 0.062(5)
O2 y 1 0
O2 z 1 0.105(4)
O2 x 2 0
O2 y 2 0
O2 z 2 0
O2 x 3 -0.05(12)
O2 y 3 0
O2 z 3 0.098(10)
O2 x 4 0
O2 y 4 0
O2 z 4 0
O3 x 1 0.056(3)
O3 y 1 0
O3 z 1 0.099(2)
O3 x 2 0
O3 y 2 0
O3 z 2 0
O3 x 3 -0.046(10)
O3 y 3 0
O3 z 3 0.077(8)
O3 x 4 0
O3 y 4 0
O3 z 4 0