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The incommensurately modulated crystal structure of β-Pb2BiVO6: interpretation of the phase transition α \→ β \→ δ and conduction properties of related materials

Authors:

Roussel, Pascal; Labidi, Olfa; Huve, Marielle; Drache, Michel; Wignacourta, Jean-Pierre; Petricek, Vaclav

Journal:

Acta Crystallographica, Section B 65 416-425 (2009)

DOI:

https://doi.org/10.1107/S0108768109020898

B-IncStrDB ID: Fba14ZwK4ip Entry date: 2022-01-22 Last revision: 2024-01-02

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Chemical data

Structural Formula Sum: Bi1 O6 Pb2 V1 [ Help ]

Formula weight: 770.3 Da [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Space group name (H-M): P 1 21/m 1 [ Help ]

Space group name (Hall): -P 2yb [ Help ]

Superspace group name (ITC): P 21/m (0 β 0) s 0 [ Help ]

Symmetry operations of the superspace group: [ Help ]

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

a: 15.0501(5) Å [ Help ]

b: 5.9011(3) Å [ Help ]

c: 7.5322(5) Å [ Help ]

α: 90 ° [ Help ]

β: 101.57(2) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 655.37(6) Å3 [ Help ]

Z: 4 [ Help ]

Cell measurement temperature: 298 K [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.00000 0.2338(3) 0.00000

μ: 81.173 mm-1 [ Help ]

Absorption correction type: analytical [ Help ]

Absorption correction remarks: Sadabs (Sheldrick 2004) [ Help ]

Minimum transmission factor: 0.3005 [ Help ]

Maximum transmission factor: 1 [ Help ]

Refinement details

Total nb. of reflections: 24247 [ Help ]

Nb. of observed reflections: 4097 [ Help ]

Intense reflections threshold: I>3σ(I) [ Help ]

Refinement based on: F [ Help ]

R(all): 0.0362 [ Help ]

R(obs): 0.0362 [ Help ]

wR(obs): 0.0321 [ Help ]

wR(all): 0.0321 [ Help ]

S(all): 1.07 [ Help ]

Nb. of reflections: 4097 [ Help ]

Nb. of parameters: 189 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 1 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ2(F)+0.0001F2) [ Help ]

Δ/σ(max): 0.0000 [ Help ]

Δ/σ(mean): 0.0000 [ Help ]

Δρ(max): 3.44 e_Å-3 [ Help ]

Δρ(min): -6.04 e_Å-3 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: [ Help ]

Atom symbol Atom site label x y z Uiso/equiv ADP type Coords from (d)iffraction or (c)alculated Coords restraints or constraints Occupancy Disordered cluster Disordered group
Bi Bi1 0.80070(4) 0.25 0.42521(7) 0.02056(19) Uani d . 1 . .
Bi Bi2 0.71083(4) 0.75 0.64948(8) 0.01813(19) Uani d . 1 . .
Pb Pb1 0.95280(4) 0.75 0.70209(9) 0.0196(2) Uani d . 1 . .
Pb Pb2 0.55636(4) 0.25 0.37273(8) 0.01834(19) Uani d . 1 . .
Pb Pb3 0.84761(5) 0.25 0.91902(8) 0.0207(2) Uani d . 1 . .
Pb Pb4 0.64789(4) 0.75 0.15756(8) 0.0254(2) Uani d . 1 . .
O O1 0.6787(4) 0.5092(13) 0.4078(8) 0.025(3) Uani d . 1 . .
O O2 0.8346(4) 0.9943(14) 0.6793(9) 0.026(3) Uani d . 1 . .
V V1a 0.59555(16) 0.2348(10) 0.8701(3) 0.0171(9) Uani d . 0.5 . .
O O11a 0.5883(7) 0.233(4) 1.0878(16) 0.031(4) Uiso d . 0.5 . .
O O12a 0.6925(9) 0.340(3) 0.8386(19) 0.048(5) Uiso d . 0.5 . .
O O13a 0.5895(11) -0.017(3) 0.778(2) 0.041(5) Uiso d . 0.5 . .
O O14a 0.5093(9) 0.381(3) 0.7476(18) 0.035(4) Uiso d . 0.5 . .
V V2a 0.1185(4) 0.25 0.8139(8) 0.0197(13) Uani d . 0.5 . .
O O21a 0.0348(13) 0.25 0.928(3) 0.051(4) Uiso d . 0.5 . .
O O22a 0.0827(13) 0.25 0.595(2) 0.059(5) Uiso d . 0.5 . .
O O23a 0.1894(7) 0.4721(14) 0.8728(19) 0.041(3) Uiso d . 0.5 . .
V V2b 0.1004(4) 0.25 0.7768(8) 0.0197(13) Uani d . 0.5 . .
O O21b 0.0455(13) 0.25 0.947(3) 0.051(4) Uiso d . 0.5 . .
O O22b 0.2104(11) 0.25 0.844(3) 0.059(5) Uiso d . 0.5 . .
O O23b 0.0695(9) 0.0279(14) 0.6357(15) 0.041(3) Uiso d . 0.5 . .

ADP components: [ Help ]

Atom site label U11 U22 U33 U12 U13 U23 Atom site symbol
Bi1 0.0194(3) 0.0219(3) 0.0200(3) 0 0.0029(2) 0 Bi
Bi2 0.0166(3) 0.0161(3) 0.0215(3) 0 0.0032(2) 0 Bi
Pb1 0.0152(3) 0.0216(4) 0.0214(3) 0 0.0021(2) 0 Pb
Pb2 0.0168(3) 0.0201(3) 0.0179(3) 0 0.0030(2) 0 Pb
Pb3 0.0245(4) 0.0198(3) 0.0169(3) 0 0.0019(3) 0 Pb
Pb4 0.0235(3) 0.0310(4) 0.0209(3) 0 0.0023(2) 0 Pb
O1 0.028(4) 0.017(4) 0.028(5) -0.004(4) -0.001(3) -0.003(4) O
O2 0.026(4) 0.027(4) 0.024(5) -0.004(3) 0.001(3) -0.002(4) O
V1a 0.0165(13) 0.0183(18) 0.0167(16) -0.0011(16) 0.0043(11) 0.0015(18) V
V2a 0.027(2) 0.0155(15) 0.017(2) 0 0.0071(17) 0 V
V2b 0.017(2) 0.0155(15) 0.027(2) 0 0.0073(17) 0 V

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

Wave vector code q_x q_y q_z
1 0.00000 0.2338 0.00000

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

Modulation code Atom site label Displacement axis Wave vector code
Bi1x1 Bi1 x 1
Bi1y1 Bi1 y 1
Bi1z1 Bi1 z 1
Bi2x1 Bi2 x 1
Bi2y1 Bi2 y 1
Bi2z1 Bi2 z 1
Pb1x1 Pb1 x 1
Pb1y1 Pb1 y 1
Pb1z1 Pb1 z 1
Pb2x1 Pb2 x 1
Pb2y1 Pb2 y 1
Pb2z1 Pb2 z 1
Pb3x1 Pb3 x 1
Pb3y1 Pb3 y 1
Pb3z1 Pb3 z 1
Pb4x1 Pb4 x 1
Pb4y1 Pb4 y 1
Pb4z1 Pb4 z 1
O1x1 O1 x 1
O1y1 O1 y 1
O1z1 O1 z 1
O2x1 O2 x 1
O2y1 O2 y 1
O2z1 O2 z 1
V1ax1 V1a x 1
V1ay1 V1a y 1
V1az1 V1a z 1
O11ax1 O11a x 1
O11ay1 O11a y 1
O11az1 O11a z 1
O12ax1 O12a x 1
O12ay1 O12a y 1
O12az1 O12a z 1
O13ax1 O13a x 1
O13ay1 O13a y 1
O13az1 O13a z 1
O14ax1 O14a x 1
O14ay1 O14a y 1
O14az1 O14a z 1
V2ax1 V2a x 1
V2ay1 V2a y 1
V2az1 V2a z 1
O21ax1 O21a x 1
O21ay1 O21a y 1
O21az1 O21a z 1
O22ax1 O22a x 1
O22ay1 O22a y 1
O22az1 O22a z 1
O23ax1 O23a x 1
O23ay1 O23a y 1
O23az1 O23a z 1
V2bx1 V2b x 1
V2by1 V2b y 1
V2bz1 V2b z 1
O21bx1 O21b x 1
O21by1 O21b y 1
O21bz1 O21b z 1
O22bx1 O22b x 1
O22by1 O22b y 1
O22bz1 O22b z 1
O23bx1 O23b x 1
O23by1 O23b y 1
O23bz1 O23b z 1

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Bi1x1 0 0.00481(8)
Bi1y1 0.0126(2) 0
Bi1z1 0 0.00519(16)
Bi2x1 0 0.00413(8)
Bi2y1 0.01946(18) 0
Bi2z1 0 0.00345(16)
Pb1x1 0 0.00458(8)
Pb1y1 -0.04752(18) 0
Pb1z1 0 0.01444(16)
Pb2x1 0 0.00244(7)
Pb2y1 0.03212(17) 0
Pb2z1 0 -0.01358(14)
Pb3x1 0 0.01381(7)
Pb3y1 -0.03633(17) 0
Pb3z1 0 0.00421(15)
Pb4x1 0 0.00532(8)
Pb4y1 0.03296(18) 0
Pb4z1 0 -0.00411(16)
O1x1 0.0060(8) 0.0053(8)
O1y1 0.0503(17) -0.014(2)
O1z1 -0.0051(17) 0.0000(16)
O2x1 0.0061(8) 0.0094(7)
O2y1 -0.0363(17) -0.001(2)
O2z1 -0.0222(17) 0.0076(14)
V1ax1 -0.0002(6) 0.0036(2)
V1ay1 0.0005(18) 0.0128(17)
V1az1 -0.0011(10) -0.0179(4)
O11ax1 0.0026(12) 0.0016(7)
O11ay1 0.058(3) -0.009(3)
O11az1 0.0007(13) -0.0191(6)
O12ax1 0.0016(8) 0.0115(5)
O12ay1 -0.034(3) -0.022(3)
O12az1 -0.022(2) -0.0043(15)
O13ax1 -0.0081(13) -0.0133(9)
O13ay1 -0.021(2) 0.025(2)
O13az1 0.036(2) -0.042(2)
O14ax1 0.0025(10) 0.0146(7)
O14ay1 -0.008(3) 0.060(3)
O14az1 -0.019(2) -0.0062(17)
V2ax1 0 0.0036(10)
V2ay1 0.0189(14) 0
V2az1 0 0.005(2)
O21ax1 0 0.0110(14)
O21ay1 -0.008(3) 0
O21az1 0 0.024(4)
O22ax1 0 -0.007(2)
O22ay1 0.086(3) 0
O22az1 0 0.008(3)
O23ax1 0.0069(9) 0.0051(12)
O23ay1 -0.004(2) 0
O23az1 0.0431(19) -0.008(3)
V2bx1 0 -0.0099(8)
V2by1 -0.0024(15) 0
V2bz1 0 -0.0146(19)
O21bx1 0 0.0029(16)
O21by1 0.029(3) 0
O21bz1 0 0.005(3)
O22bx1 0 -0.0084(10)
O22by1 -0.029(4) 0
O22bz1 0 -0.042(4)
O23bx1 -0.0093(11) -0.0185(14)
O23by1 -0.006(3) 0
O23bz1 0.009(2) -0.010(2)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
Bi1U111 Bi1 U11 1
Bi1U221 Bi1 U22 1
Bi1U331 Bi1 U33 1
Bi1U121 Bi1 U12 1
Bi1U131 Bi1 U13 1
Bi1U231 Bi1 U23 1
Bi2U111 Bi2 U11 1
Bi2U221 Bi2 U22 1
Bi2U331 Bi2 U33 1
Bi2U121 Bi2 U12 1
Bi2U131 Bi2 U13 1
Bi2U231 Bi2 U23 1
Pb1U111 Pb1 U11 1
Pb1U221 Pb1 U22 1
Pb1U331 Pb1 U33 1
Pb1U121 Pb1 U12 1
Pb1U131 Pb1 U13 1
Pb1U231 Pb1 U23 1
Pb2U111 Pb2 U11 1
Pb2U221 Pb2 U22 1
Pb2U331 Pb2 U33 1
Pb2U121 Pb2 U12 1
Pb2U131 Pb2 U13 1
Pb2U231 Pb2 U23 1
Pb3U111 Pb3 U11 1
Pb3U221 Pb3 U22 1
Pb3U331 Pb3 U33 1
Pb3U121 Pb3 U12 1
Pb3U131 Pb3 U13 1
Pb3U231 Pb3 U23 1
Pb4U111 Pb4 U11 1
Pb4U221 Pb4 U22 1
Pb4U331 Pb4 U33 1
Pb4U121 Pb4 U12 1
Pb4U131 Pb4 U13 1
Pb4U231 Pb4 U23 1

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Bi1U111 0 0.0010(7)
Bi1U221 0 -0.0012(6)
Bi1U331 0 -0.0030(6)
Bi1U121 0.0005(4) 0
Bi1U131 0 -0.0018(5)
Bi1U231 0.0014(4) 0
Bi2U111 0 -0.0032(7)
Bi2U221 0 0.0027(5)
Bi2U331 0 -0.0019(6)
Bi2U121 -0.0018(4) 0
Bi2U131 0 -0.0004(5)
Bi2U231 -0.0032(5) 0
Pb1U111 0 0.0020(6)
Pb1U221 0 -0.0126(7)
Pb1U331 0 -0.0043(6)
Pb1U121 0.0057(4) 0
Pb1U131 0 0.0018(5)
Pb1U231 0.0033(4) 0
Pb2U111 0 0.0002(7)
Pb2U221 0 0.0025(6)
Pb2U331 0 -0.0009(7)
Pb2U121 0.0001(4) 0
Pb2U131 0 0.0005(5)
Pb2U231 0.0022(4) 0
Pb3U111 0 -0.0081(6)
Pb3U221 0 -0.0100(6)
Pb3U331 0 0.0002(6)
Pb3U121 -0.0013(5) 0
Pb3U131 0 -0.0009(5)
Pb3U231 0.0004(4) 0
Pb4U111 0 -0.0011(7)
Pb4U221 0 -0.0181(7)
Pb4U331 0 -0.0009(7)
Pb4U121 0.0048(5) 0
Pb4U131 0 0.0027(5)
Pb4U231 0.0042(5) 0

Occupation crenel coefficients: [ Help ]

Atom site label Center (x0) Width
V1a 0.4965 0.5
O11a 0.4965 0.5
O12a 0.4965 0.5
O13a 0.4965 0.5
O14a 0.4965 0.5
V2a 0.75 0.5
O21a 0.75 0.5
O22a 0.75 0.5
O23a 0.75 0.5
V2b 0.25 0.5
O21b 0.25 0.5
O22b 0.25 0.5
O23b 0.25 0.5