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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: 10602Ed3v26 Entry date: 2015-04-26 Last revision: 2022-01-02

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Chemical data

Structural Formula Sum: Bi0.428 Fe1.034 O2.736 Pb0.541 [ Help ]

Formula weight: 303.1 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: 3.9146(13) Å [ Help ]

b: 3.91271(10) Å [ Help ]

c: 4.13775(16) Å [ Help ]

α: 90 ° [ Help ]

β: 91.554(3) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 63.353(4) Å3 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.040963 0 0.074474

Z: 1 [ Help ]

Cell measurement temperature: 900 K [ Help ]

μ: 0.005 mm-1 [ Help ]

Refinement details

R(obs): 0.0521 [ Help ]

wR(obs): 0.0581 [ Help ]

R(all): 0.0528 [ Help ]

wR(all): 0.0582 [ Help ]

S(all): 2.06 [ Help ]

Nb. of parameters: 66 [ Help ]

Number of constraints: 7 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0527 [ Help ]

Δ/σ(mean): 0.0252 [ 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 0.0096(4) 2 0.51676(10) d ? ? ?
Pb1 Pb 0 0 0 Uiso 0.0438(11) 2 0.27062(6) d ? ? ?
Bi1 Bi 0 0 0 Uiso 0.0438(11) 2 0.2142 d ? ? ?
O1 O 0 0.5 0 Uani 0.0245(18) 2 0.51676(10) d ? ? ?
O2 O 0.5 0 0 Uiso 0.0447(16) 2 0.4088(2) d ? ? ?
O3 O 0 0 0.5 Uiso 0.0498(13) 2 0.44228(10) d ? ? ?

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
O1 O 0.04(4) 0.0046(15) 0.028(3) 0 -0.019(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 0.51676(10)
Pb1 0.5 0.48324(10)
Bi1 0.5 0.4868
O1 0 0.51676(10)
O2 0 0.4088(2)
O3 0 0.44228(10)

Displacive (translational) Legendre coefficients: [ Help ]

Atom site label Displacement axis Polynomial order Polynomial coeff.
Fe1 x 1 0.0419(18)
Fe1 y 1 0
Fe1 z 1 0.0223(12)
Fe1 x 2 0
Fe1 y 2 0
Fe1 z 2 0
Fe1 x 3 -0.054(3)
Fe1 y 3 0
Fe1 z 3 0.097(3)
Fe1 x 4 0
Fe1 y 4 0
Fe1 z 4 0
Pb1 x 1 0.023(3)
Pb1 y 1 0
Pb1 z 1 -0.081(2)
Pb1 x 2 0
Pb1 y 2 0
Pb1 z 2 0
Pb1 x 3 -0.102(6)
Pb1 y 3 0
Pb1 z 3 0.126(5)
Pb1 x 4 0
Pb1 y 4 0
Pb1 z 4 0
Bi1 x 1 0.023(3)
Bi1 y 1 0
Bi1 z 1 -0.081(2)
Bi1 x 2 0
Bi1 y 2 0
Bi1 z 2 0
Bi1 x 3 -0.102(6)
Bi1 y 3 0
Bi1 z 3 0.126(5)
Bi1 x 4 0
Bi1 y 4 0
Bi1 z 4 0
O1 x 1 0.044(4)
O1 y 1 0
O1 z 1 0.227(3)
O1 x 2 0
O1 y 2 0
O1 z 2 0
O1 x 3 -0.117(10)
O1 y 3 0
O1 z 3 0.083(5)
O1 x 4 0
O1 y 4 0
O1 z 4 0
O2 x 1 0.056(5)
O2 y 1 0
O2 z 1 0.133(3)
O2 x 2 0
O2 y 2 0
O2 z 2 0
O2 x 3 -0.039(16)
O2 y 3 0
O2 z 3 0.041(11)
O2 x 4 0
O2 y 4 0
O2 z 4 0
O3 x 1 0.053(3)
O3 y 1 0
O3 z 1 0.114(2)
O3 x 2 0
O3 y 2 0
O3 z 2 0
O3 x 3 -0.037(11)
O3 y 3 0
O3 z 3 0.065(8)
O3 x 4 0
O3 y 4 0
O3 z 4 0