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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: 10542EJs2b2 Entry date: 2015-04-26 Last revision: 2022-02-12

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Chemical data

Structural Formula Sum: Bi0.097 Fe1.049 O2.585 Pb0.856 [ Help ]

Formula weight: 297.6 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: 3.93492(13) Å [ Help ]

b: 3.93193(10) Å [ Help ]

c: 4.00171(14) Å [ Help ]

α: 90 ° [ Help ]

β: 92.603(3) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 61.850(3) Å3 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.066678 0.000000 0.115975

Z: 1 [ Help ]

Cell measurement temperature: 900 K [ Help ]

μ: 0.005 mm-1 [ Help ]

Refinement details

R(obs): 0.0386 [ Help ]

wR(obs): 0.0499 [ Help ]

R(all): 0.0396 [ Help ]

wR(all): 0.0500 [ Help ]

S(all): 2.51 [ Help ]

Nb. of parameters: 65 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 7 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0574 [ Help ]

Δ/σ(mean): 0.0353 [ 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 0.0174(4) 2 0.52465(11) d . . .
Pb1 Pb 0 0 0 Uiso 0.0536(9) 2 0.42782(10) d . . .
Bi1 Bi 0 0 0 Uiso 0.0536(9) 2 0.0487 d . . .
O1 O 0 0.5 0 Uani 0.0393(16) 2 0.52465(11) d . . .
O2 O 0.5 0 0 Uiso 0.0463(17) 2 0.35938(19) d . . .
O3 O 0 0 0.5 Uiso 0.0489(12) 2 0.40867(11) d . . .

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
O1 O 0.065(3) 0.0036(12) 0.050(4) 0 0.006(2) 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 0.52465(11)
Pb1 0.5 0.47535(11)
Bi1 0.5 0.4868
O1 0 0.52465(11)
O2 0 0.35938(19)
O3 0 0.40867(11)

Displacive (translational) Legendre coefficients: [ Help ]

Atom site label Displacement axis Polynomial order Polynomial coeff.
Fe1 x 1 0.0300(12)
Fe1 y 1 0
Fe1 z 1 0.0584(10)
Fe1 x 2 0
Fe1 y 2 0
Fe1 z 2 0
Fe1 x 3 -0.025(3)
Fe1 y 3 0
Fe1 z 3 0.090(3)
Fe1 x 4 0
Fe1 y 4 0
Fe1 z 4 0
Pb1 x 1 0.007(2)
Pb1 y 1 0
Pb1 z 1 -0.0299(18)
Pb1 x 2 0
Pb1 y 2 0
Pb1 z 2 0
Pb1 x 3 -0.078(5)
Pb1 y 3 0
Pb1 z 3 0.095(5)
Pb1 x 4 0
Pb1 y 4 0
Pb1 z 4 0
Bi1 x 1 0.007(2)
Bi1 y 1 0
Bi1 z 1 -0.0299(18)
Bi1 x 2 0
Bi1 y 2 0
Bi1 z 2 0
Bi1 x 3 -0.078(5)
Bi1 y 3 0
Bi1 z 3 0.095(5)
Bi1 x 4 0
Bi1 y 4 0
Bi1 z 4 0
O1 x 1 0.033(5)
O1 y 1 0
O1 z 1 0.266(3)
O1 x 2 0
O1 y 2 0
O1 z 2 0
O1 x 3 -0.070(10)
O1 y 3 0
O1 z 3 0.049(6)
O1 x 4 0
O1 y 4 0
O1 z 4 0
O2 x 1 0.055(7)
O2 y 1 0
O2 z 1 0.138(4)
O2 x 2 0
O2 y 2 0
O2 z 2 0
O2 x 3 -0.04(2)
O2 y 3 0
O2 z 3 0.040(14)
O2 x 4 0
O2 y 4 0
O2 z 4 0
O3 x 1 0.024(3)
O3 y 1 0
O3 z 1 0.132(3)
O3 x 2 0
O3 y 2 0
O3 z 2 0
O3 x 3 0
O3 y 3 0
O3 z 3 0.048(9)
O3 x 4 0
O3 y 4 0
O3 z 4 0