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Cation Ordering and Flexibility of the BO42- Tetrahedra in Incommensurately Modulated CaEu2(BO4)4 (B = Mo, W) Scheelites

Authors:

Abakumov, Artem M.; Morozov, Vladimir A.; Tsirlin, Alexander A.; Verbeeck, Johan; Hadermann, Joke

Journal:

Inorganic Chemistry 53 9407-9415 (2014)

DOI:

https://dx.doi.org/10.1021/ic5015412

B-IncStrDB ID: PiM3j2Q7o8h Entry date: 2021-12-21 Last revision: 2022-02-12

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Chemical data

Structural Formula Sum: Ca1 Eu2 Mo4 O16 [ Help ]

Formula weight: 983.7 Da [ Help ]

Crystallographic data and experimental details

Crystal system: tetragonal [ Help ]

Space group name (H-M): I 41/a [ Help ]

Superspace group name: I41/a(αβ0)00(-βα0)00 [ Help ]

Symmetry operations of the superspace group: [ Help ]

Operation code Operation in algebraic form
1 x1,x2,x3,x4,x5
2 -x1+1/2,-x2+1/2,x3+1/2,-x4,-x5
3 -x2,x1+1/2,x3+1/4,-x5,x4
4 x2+1/2,-x1,x3+3/4,x5,-x4
5 -x1,-x2+1/2,-x3+1/4,-x4,-x5
6 x1+1/2,x2,-x3+3/4,x4,x5
7 x2,-x1,-x3,x5,-x4
8 -x2+1/2,x1+1/2,-x3+1/2,-x5,x4
9 x1+1/2,x2+1/2,x3+1/2,x4,x5
10 -x1,-x2,x3,-x4,-x5
11 -x2+1/2,x1,x3+3/4,-x5,x4
12 x2,-x1+1/2,x3+1/4,x5,-x4
13 -x1+1/2,-x2,-x3+3/4,-x4,-x5
14 x1,x2+1/2,-x3+1/4,x4,x5
15 x2+1/2,-x1+1/2,-x3+1/2,x5,-x4
16 -x2,x1,-x3,-x5,x4

a: 5.238670(10) Å [ Help ]

b: 5.238670(10) Å [ Help ]

c: 11.54843(2) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 316.9312(10) Å3 [ Help ]

Modulation dimension: 2 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.553311 0.820681 0.000000
2 -0.820681 0.553311 0.000000

Z: 1 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 7.434 mm-1 [ Help ]

Refinement details

R(obs): 0.0609 [ Help ]

wR(obs): 0.0472 [ Help ]

R(all): 0.0609 [ Help ]

wR(all): 0.0472 [ Help ]

S(all): 1.55 [ Help ]

Nb. of parameters: 57 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 4 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0964 [ Help ]

Δ/σ(mean): 0.0841 [ 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
Eu Eu 0 0 0.5 Uiso 0.00425(19) 4 0.5 d . . .
Ca Ca 0 0 0.5 Uiso 0.00425(19) 4 0.25 d . . .
Mo Mo 0 0 0 Uiso 0.0107(2) 4 1 d . . .
O O 0.2463(4) 0.1491(4) 0.0839(2) Uiso 0.0121(7) 16 1 d . . .

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

Wave vector code q_1 q_2
1 1 0
2 0 1

Table: [ Help ]

_jana_atom_site_occ_Fourier_absolute_site_label _jana_atom_site_occ_Fourier_absolute
Eu 0.5
Ca 0.25

Definition of the occupation Fourier series: [ Help ]

Modulation code Atom site label Wave vector code
Euo1 Eu 1
Euo2 Eu 2
Cao1 Ca 1
Cao2 Ca 2

Occupation Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Euo1 0.25 0
Euo2 0.25 0
Cao1 -0.125 0
Cao2 -0.125 0

Definition of the displacive (translational) Fourier series: [ Help ]

Modulation code Atom site label Displacement axis Wave vector code
Eux1 Eu x 1
Euy1 Eu y 1
Euz1 Eu z 1
Eux2 Eu x 2
Euy2 Eu y 2
Euz2 Eu z 2
Cax1 Ca x 1
Cay1 Ca y 1
Caz1 Ca z 1
Cax2 Ca x 2
Cay2 Ca y 2
Caz2 Ca z 2
Mox1 Mo x 1
Moy1 Mo y 1
Moz1 Mo z 1
Mox2 Mo x 2
Moy2 Mo y 2
Moz2 Mo z 2
Ox1 O x 1
Oy1 O y 1
Oz1 O z 1
Ox2 O x 2
Oy2 O y 2
Oz2 O z 2

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Eux1 0 0.0044(2)
Euy1 0 0.0034(2)
Euz1 0 0
Eux2 0 -0.0034(2)
Euy2 0 0.0044(2)
Euz2 0 0
Cax1 0 0.0044(2)
Cay1 0 0.0034(2)
Caz1 0 0
Cax2 0 -0.0034(2)
Cay2 0 0.0044(2)
Caz2 0 0
Mox1 0 -0.0043(2)
Moy1 0 -0.0069(2)
Moz1 0.00164(14) 0
Mox2 0 0.0069(2)
Moy2 0 -0.0043(2)
Moz2 -0.00164(14) 0
Ox1 0 -0.0088(13)
Oy1 0 0
Oz1 0.0074(5) 0.0040(5)
Ox2 0.0182(11) 0.0087(11)
Oy2 0.0067(11) -0.0085(11)
Oz2 -0.0087(5) 0.0055(5)