Modulation functions of incommensurately modulated Cr2P2O7 studied by the Maximum Entropy Method (MEM)

Authors:

Li, Liang; Schoenleber, Andreas; van Smaalen, Sander

Journal:

Acta Crystallographica, Section B 66 130-140 (2010)

DOI:

https://doi.org/10.1107/S0108768110003393

B-IncStrDB ID: pJGRmRH8TMk Entry date: 2022-01-21 Last revision: 2024-01-02

I

Chemical data


Structural Formula Sum: Cr2 O7 P2 [ Help ]

Formula weight: 277.9 Da [ Help ]

Crystallographic data and experimental details


Crystal system: monoclinic [ Help ]

Superspace group name: C2/m(α0γ)-1s [ Help ]

Symmetry operations of the superspace group: [ Help ]

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

a: 7.0192(5) Å [ Help ]

b: 8.4063(6) Å [ Help ]

c: 4.6264(3) Å [ Help ]

α: 90 ° [ Help ]

β: 108.6111(64) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 258.7078 Å3 [ Help ]

Z: 2 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 -0.361(1) 0.00000 0.471(1)

μ: 4.799 mm-1 [ Help ]

Absorption correction type: gaussian [ Help ]

Absorption correction remarks: CrysAlis RED, Oxford Diffraction Ltd., Version 1.171.27p5 beta Analytical numeric absorption correction using a multifaceted crystal model. [ Help ]

Minimum transmission factor: 0.43451 [ Help ]

Maximum transmission factor: 0.67729 [ Help ]

Refinement details


Total nb. of reflections: 2409 [ Help ]

Nb. of observed reflections: 1433 [ Help ]

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

Refinement based on: F [ Help ]

R(all): 0.0484 [ Help ]

R(obs): 0.0217 [ Help ]

wR(obs): 0.0396 [ Help ]

wR(all): 0.0568 [ Help ]

S(all): 1.58 [ Help ]

Nb. of reflections: 2409 [ Help ]

Nb. of parameters: 170 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 46 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ2(F)+0.0004F2) [ Help ]

Δ/σ(max): 0.0003 [ Help ]

Δ/σ(mean): 0.0000 [ Help ]

Δρ(max): 0.48 e_Å-3 [ Help ]

Δρ(min): -0.47 e_Å-3 [ Help ]

Extinction method: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) [ Help ]

Extinction coefficient: 62E1(10) [ 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
P P 0.80672(9) -0.01175(12) 0.58376(17) 0.00636(19) Uani d . 0.4157(14) . .
P P(a) 0.80672(9) -0.01175(12) 0.58376(17) 0.0165(17) Uani d . 0.0421(7) . .
P P(b) 0.80672(9) -0.01175(12) 0.58376(17) 0.0114(16) Uani d . 0.0421(7) . .
O O1 0.63754(19) 0 0.2775(3) 0.0089(4) Uani d . 1 . .
O O2 1 -0.0644(3) 0.5 0.0179(6) Uani d . 0.4157(14) . .
O O2(a) 1.0014(13) -0.0545(9) 0.532(2) 0.027(3) Uani d . 0.0421(7) . .
O O3 0.80628(16) -0.14636(13) 0.7591(3) 0.0130(3) Uani d . 1 . .
O O3(a) 0.8438(15) -0.1466(13) 0.729(2) 0.030(4) Uani d . 0.0421(7) . .
O O3(b) 0.7622(11) -0.1517(11) 0.772(2) 0.001(2) Uani d . 0.0421(7) . .
Cr Cr 0.5 -0.18798(6) 0 0.00790(15) Uani d . 1 . .
Cr Cr(a) 0.4749(11) -0.1898(3) 0.019(2) 0.0113(14) Uani d . 0.0423(8) . .

ADP components: [ Help ]

Atom site label U11 U22 U33 U12 U13 U23 Atom site symbol
P 0.0053(3) 0.0074(3) 0.0052(3) -0.00064(18) 0 -0.0012(3) P
P(a) 0.003(2) 0.027(3) 0.017(3) 0.009(2) 0.000(2) 0.010(3) P
P(b) 0.013(2) 0.010(2) 0.006(3) -0.005(2) -0.004(2) 0.021(3) P
O1 0.0096(7) 0.0069(6) 0.0083(7) 0 0.0000(5) 0 O
O2 0.0090(9) 0.0233(11) 0.0236(10) 0 0.0081(7) 0 O
O2(a) 0.011(3) 0.054(6) 0.021(4) -0.004(5) 0.015(3) -0.013(5) O
O3 0.0152(6) 0.0099(5) 0.0110(5) 0.0027(4) 0.0002(4) 0.0026(4) O
O3(a) 0.036(7) 0.021(5) 0.016(5) 0.009(5) -0.016(5) -0.005(4) O
O3(b) -0.002(4) 0.001(3) 0.002(3) 0.004(3) -0.003(3) 0.000(2) O
Cr 0.0083(2) 0.0051(2) 0.0073(2) 0 -0.00179(14) 0 Cr
Cr(a) 0.016(3) 0.0040(7) 0.010(2) -0.0014(8) -0.0012(16) 0.0006(9) Cr

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

Wave vector code q_x q_z
1 -0.36100 0.47100
2 -0.72200 0.94200
3 -1.08300 1.41300
4 -1.44400 1.88400

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

Modulation code Atom site label Displacement axis Wave vector code
Px1 P x 1
Py1 P y 1
Pz1 P z 1
Px2 P x 2
Py2 P y 2
Pz2 P z 2
Px3 P x 3
Py3 P y 3
Pz3 P z 3
Px4 P x 4
Py4 P y 4
Pz4 P z 4
P(a)x1 P(a) x 1
P(a)y1 P(a) y 1
P(a)z1 P(a) z 1
P(a)x2 P(a) x 2
P(a)y2 P(a) y 2
P(a)z2 P(a) z 2
P(a)x3 P(a) x 3
P(a)y3 P(a) y 3
P(a)z3 P(a) z 3
P(a)x4 P(a) x 4
P(a)y4 P(a) y 4
P(a)z4 P(a) z 4
P(b)x1 P(b) x 1
P(b)y1 P(b) y 1
P(b)z1 P(b) z 1
P(b)x2 P(b) x 2
P(b)y2 P(b) y 2
P(b)z2 P(b) z 2
P(b)x3 P(b) x 3
P(b)y3 P(b) y 3
P(b)z3 P(b) z 3
P(b)x4 P(b) x 4
P(b)y4 P(b) y 4
P(b)z4 P(b) z 4
O1x1 O1 x 1
O1y1 O1 y 1
O1z1 O1 z 1
O1x2 O1 x 2
O1y2 O1 y 2
O1z2 O1 z 2
O2x1 O2 x 1
O2y1 O2 y 1
O2z1 O2 z 1
O3x1 O3 x 1
O3y1 O3 y 1
O3z1 O3 z 1
O3x2 O3 x 2
O3y2 O3 y 2
O3z2 O3 z 2
O3x3 O3 x 3
O3y3 O3 y 3
O3z3 O3 z 3
Crx1 Cr x 1
Cry1 Cr y 1
Crz1 Cr z 1
Crx2 Cr x 2
Cry2 Cr y 2
Crz2 Cr z 2
Crx3 Cr x 3
Cry3 Cr y 3
Crz3 Cr z 3
Crx4 Cr x 4
Cry4 Cr y 4
Crz4 Cr z 4

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Px1 -0.0026 -0.0029
Py1 -0.0034 0.0032
Pz1 0.0059 0.0045
Px2 -0.0008 -0.0022
Py2 -0.0006 -0.0011
Pz2 0.0011 0.003
Px3 0.0003 -0.0005
Py3 0.0007 0
Pz3 0.0003 0.0002
Px4 0 0.0003
Py4 0 -0.0001
Pz4 0 -0.0002
P(a)x1 -0.0026 -0.0029
P(a)y1 -0.0034 0.0032
P(a)z1 0.0059 0.0045
P(a)x2 -0.0008 -0.0022
P(a)y2 -0.0006 -0.0011
P(a)z2 0.0011 0.003
P(a)x3 0.0003 -0.0005
P(a)y3 0.0007 0
P(a)z3 0.0003 0.0002
P(a)x4 0 0.0003
P(a)y4 0 -0.0001
P(a)z4 0 -0.0002
P(b)x1 -0.0026 -0.0029
P(b)y1 -0.0034 0.0032
P(b)z1 0.0059 0.0045
P(b)x2 -0.0008 -0.0022
P(b)y2 -0.0006 -0.0011
P(b)z2 0.0011 0.003
P(b)x3 0.0003 -0.0005
P(b)y3 0.0007 0
P(b)z3 0.0003 0.0002
P(b)x4 0 0.0003
P(b)y4 0 -0.0001
P(b)z4 0 -0.0002
O1x1 0 0
O1y1 -0.00147(15) 0.00650(15)
O1z1 0 0
O1x2 0.00174(16) -0.00535(16)
O1y2 0 0
O1z2 -0.0016(2) 0.0005(2)
O2x1 0.0059(3) 0
O2y1 0 0.0106(3)
O2z1 0.0433(4) 0
O3x1 -0.01698(16) 0.00907(19)
O3y1 -0.00274(13) -0.00222(16)
O3z1 0.0155(2) -0.0146(3)
O3x2 -0.00260(17) -0.00705(16)
O3y2 0.00084(14) -0.00064(13)
O3z2 0.0041(2) 0.0047(2)
O3x3 0.00051(18) -0.00045(16)
O3y3 -0.00005(15) -0.00079(12)
O3z3 -0.0031(3) -0.0009(2)
Crx1 0.01166(6) 0
Cry1 0 0.00209(12)
Crz1 -0.01334(7) 0
Crx2 0 -0.00342(5)
Cry2 -0.00027(12) 0
Crz2 0 0.00195(6)
Crx3 0.00072(7) 0
Cry3 0 -0.00066(11)
Crz3 -0.00122(8) 0
Crx4 0 0.00056(9)
Cry4 -0.00080(12) 0
Crz4 0 0.00022(10)

Definition of the occupation Fourier series: [ Help ]

Modulation code Atom site label Wave vector code
P(a)o1 P(a) 1
P(a)o2 P(a) 2
P(b)o1 P(b) 1
P(b)o2 P(b) 2

Occupation Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
P(a)o1 3.1457 -3.976
P(a)o2 -0.6242 0.1476
P(b)o1 3.1461 -3.9765
P(b)o2 0.6245 -0.1476

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
PU111 P U11 1
PU221 P U22 1
PU331 P U33 1
PU121 P U12 1
PU131 P U13 1
PU231 P U23 1
O3U111 O3 U11 1
O3U221 O3 U22 1
O3U331 O3 U33 1
O3U121 O3 U12 1
O3U131 O3 U13 1
O3U231 O3 U23 1
CrU111 Cr U11 1
CrU221 Cr U22 1
CrU331 Cr U33 1
CrU121 Cr U12 1
CrU131 Cr U13 1
CrU231 Cr U23 1
CrU112 Cr U11 2
CrU222 Cr U22 2
CrU332 Cr U33 2
CrU122 Cr U12 2
CrU132 Cr U13 2
CrU232 Cr U23 2

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
PU111 0 0
PU221 0 0
PU331 0.0007(3) -0.0016(3)
PU121 0.0005(2) 0
PU131 0.00041(17) 0
PU231 0.0010(3) -0.0016(3)
O3U111 -0.0046(6) 0.0048(6)
O3U221 0.0001(5) 0.0001(5)
O3U331 -0.0004(5) 0.0026(5)
O3U121 0.0001(4) -0.0004(4)
O3U131 0.0034(4) -0.0022(4)
O3U231 -0.0001(4) 0.0000(4)
CrU111 0 -0.0004(2)
CrU221 0 -0.00007(19)
CrU331 0 0.00131(19)
CrU121 0.00024(12) 0
CrU131 0 0.00070(15)
CrU231 -0.00011(11) 0
CrU112 0.0019(2) 0
CrU222 -0.00020(19) 0
CrU332 0.00087(19) 0
CrU122 0 -0.00025(12)
CrU132 -0.00055(16) 0
CrU232 0 -0.00015(12)

Displacive sawtooth coefficients: [ Help ]

Atom site label Ax Ay Az Center (x0) Width
O3 -0.0327 -0.0044 0.0057 0.69197(13) 0.9157(14)
Cr -0.0238 0 0.0133 0.25 0.9154(15)

Occupation crenel coefficients: [ Help ]

Atom site label Center (x0) Width
P 0.85681(8) 0.4157(14)
P(a) 1.10681(15) 0.0843(14)
P(b) 0.60681(15) 0.0843(14)
O2 0.75 0.4157(14)
O2(a) 1.0147(10) 0.0843(14)
O3(a) 1.1644(13) 0.0843(14)
O3(b) 1.2140(10) 0.0843(14)
Cr(a) 0.7679(11) 0.0846(15)

B

Chemical data


Structural Formula Sum: Cr2 O7 P2 [ Help ]

Formula weight: 277.9 Da [ Help ]

Crystallographic data and experimental details


Crystal system: monoclinic [ Help ]

Superspace group name: C2/m(α0γ)0s [ Help ]

Symmetry operations of the superspace group: [ Help ]

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

a: 7.0192(5) Å [ Help ]

b: 8.4063(6) Å [ Help ]

c: 4.6264(3) Å [ Help ]

α: 90 ° [ Help ]

β: 108.6111(64) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 258.7078 Å3 [ Help ]

Z: 2 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 -0.361(1) 0.00000 0.471(1)

μ: 4.799 mm-1 [ Help ]

Absorption correction type: gaussian [ Help ]

Absorption correction remarks: CrysAlis RED, Oxford Diffraction Ltd., Version 1.171.27p5 beta Analytical numeric absorption correction using a multifaceted crystal model. [ Help ]

Minimum transmission factor: 0.43451 [ Help ]

Maximum transmission factor: 0.67729 [ Help ]

Refinement details


Δρ(max): 0.53 e_Å-3 [ Help ]

Δρ(min): -0.48 e_Å-3 [ Help ]

Extinction method: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) [ Help ]

Extinction coefficient: 594.45 [ 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
P P 0.802777 -0.019373 0.583385 0.0059 Uani d . 0.416 . .
P P(a) 0.78983 -0.015268 0.57442 0.0073 Uani d . 0.042 . .
P P(b) 0.819682 0.005666 0.588919 0.0033 Uani d . 0.042 . .
O O1 0.637449 0 0.277283 0.0087 Uani d . 1 . .
O O2 1 -0.064282 0.5 0.0176 Uani d . 0.416 . .
O O2(a) 1.000445 -0.054036 0.530873 0.0264 Uani d . 0.042 . .
O O3 0.806158 -0.146553 0.758822 0.0129 Uani d . 1 . .
O O3(a) 0.842688 -0.147832 0.731592 0.0294 Uani d . 0.042 . .
O O3(b) 0.761605 -0.149954 0.771546 0.0012 Uani d . 0.042 . .
Cr Cr 0.5 -0.187867 0 0.0077 Uani d . 1 . .
Cr Cr(a) 0.474309 -0.189819 0.018535 0.0113 Uani d . 0.0418 . .

ADP components: [ Help ]

Atom site label U11 U22 U33 U12 U13 U23 Atom site symbol
P 0.005593 0.005891 0.004706 -0.00034 -0.000391 0.000052 P
P(a) -0.000148 0.007406 0.01524 -0.006225 0.003177 -0.013938 P
P(b) -0.007628 0.002302 0.008033 -0.004147 -0.009847 -0.002724 P
O1 0.009786 0.006013 0.008194 0 -0.000218 0 O
O2 0.008582 0.023118 0.023054 0 0.007945 0 O
O2(a) 0.009804 0.054417 0.021878 -0.000069 0.014969 -0.010542 O
O3 0.01492 0.009897 0.011161 0.002627 0.000389 0.002558 O
O3(a) 0.03646 0.011932 0.019891 0.01184 -0.019054 -0.00522 O
O3(b) -0.002903 0.003676 0.000273 0.004606 -0.004163 -0.002141 O
Cr 0.008253 0.00475 0.0072 0 -0.001756 0 Cr
Cr(a) 0.01418 0.003552 0.012183 -0.001728 -0.001452 0.000734 Cr

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

Wave vector code q_x q_z
1 -0.36100 0.47100
2 -0.72200 0.94200
3 -1.08300 1.41300
4 -1.44400 1.88400

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

Modulation code Atom site label Displacement axis Wave vector code
Px1 P x 1
Py1 P y 1
Pz1 P z 1
Px2 P x 2
Py2 P y 2
Pz2 P z 2
O1x1 O1 x 1
O1y1 O1 y 1
O1z1 O1 z 1
O1x2 O1 x 2
O1y2 O1 y 2
O1z2 O1 z 2
O2x1 O2 x 1
O2y1 O2 y 1
O2z1 O2 z 1
O3x1 O3 x 1
O3y1 O3 y 1
O3z1 O3 z 1
O3x2 O3 x 2
O3y2 O3 y 2
O3z2 O3 z 2
O3x3 O3 x 3
O3y3 O3 y 3
O3z3 O3 z 3
Crx1 Cr x 1
Cry1 Cr y 1
Crz1 Cr z 1
Crx2 Cr x 2
Cry2 Cr y 2
Crz2 Cr z 2
Crx3 Cr x 3
Cry3 Cr y 3
Crz3 Cr z 3
Crx4 Cr x 4
Cry4 Cr y 4
Crz4 Cr z 4

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Px1 0.0013 -0.01
Py1 0.0044 -0.0083
Pz1 0.0061 0.0051
Px2 0.0023 0.0019
Py2 0.0062 0.0051
Pz2 0.0015 0.0031
O1x1 0 0
O1y1 -0.0014 0.0064
O1z1 0 0
O1x2 0.0017 -0.0054
O1y2 0 0
O1z2 -0.0017 0.0004
O2x1 0.0062 0
O2y1 0 0.0109
O2z1 0.0439 0
O3x1 -0.017 0.009
O3y1 -0.0027 -0.0024
O3z1 0.0155 -0.015
O3x2 -0.0026 -0.0071
O3y2 0.0008 -0.0008
O3z2 0.0045 0.0044
O3x3 0.0011 -0.0005
O3y3 0.0002 -0.001
O3z3 -0.0022 -0.0006
Crx1 0.0117 0
Cry1 0 0.0019
Crz1 -0.0134 0
Crx2 0 -0.0034
Cry2 -0.0005 0
Crz2 0 0.0019
Crx3 0.0008 0
Cry3 0 -0.0003
Crz3 -0.0013 0
Crx4 0 0.0005
Cry4 -0.0004 0
Crz4 0 0.0004

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
PU111 P U11 1
PU221 P U22 1
PU331 P U33 1
PU121 P U12 1
PU131 P U13 1
PU231 P U23 1
O3U111 O3 U11 1
O3U221 O3 U22 1
O3U331 O3 U33 1
O3U121 O3 U12 1
O3U131 O3 U13 1
O3U231 O3 U23 1
CrU111 Cr U11 1
CrU221 Cr U22 1
CrU331 Cr U33 1
CrU121 Cr U12 1
CrU131 Cr U13 1
CrU231 Cr U23 1
CrU112 Cr U11 2
CrU222 Cr U22 2
CrU332 Cr U33 2
CrU122 Cr U12 2
CrU132 Cr U13 2
CrU232 Cr U23 2

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
PU111 -0.000443 -0.000013
PU221 0.001083 0.000276
PU331 0.001311 -0.002131
PU121 0.000133 0.000429
PU131 0.000992 -0.000545
PU231 -0.000368 -0.000607
O3U111 -0.004768 0.004802
O3U221 0.000012 0.000196
O3U331 -0.00037 0.002744
O3U121 -0.00012 -0.000073
O3U131 0.003258 -0.002039
O3U231 0.000005 0.000215
CrU111 0 -0.000499
CrU221 0 -0.000102
CrU331 0 0.001606
CrU121 0.000208 0
CrU131 0 0.000706
CrU231 -0.000123 0
CrU112 0.00173 0
CrU222 -0.000162 0
CrU332 0.001193 0
CrU122 0 -0.000285
CrU132 -0.000582 0
CrU232 0 -0.000086

Displacive sawtooth coefficients: [ Help ]

Atom site label Ax Ay Az Center (x0) Width
O3 -0.0327 -0.0044 0.0057 0.6919 0.916
Cr -0.0238 0 0.0133 0.25 0.9163

Occupation crenel coefficients: [ Help ]

Atom site label Center (x0) Width
P 0.8606 0.416
P(a) 1.1109 0.084
P(b) 1.107 0.084
O2 0.75 0.416
O2(a) 1.0144 0.084
O3(a) 1.1659 0.084
O3(b) 1.214 0.084
Cr(a) 0.768 0.0837

M

Chemical data


Structural Formula Sum: Cr2 O7 P2 [ Help ]

Formula weight: 277.9 Da [ Help ]

Crystallographic data and experimental details


Crystal system: monoclinic [ Help ]

Superspace group name: C2/m(α0γ)-1s [ Help ]

Symmetry operations of the superspace group: [ Help ]

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

a: 7.0192(5) Å [ Help ]

b: 8.4063(6) Å [ Help ]

c: 4.6264(3) Å [ Help ]

α: 90 ° [ Help ]

β: 108.6111(64) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 258.7078 Å3 [ Help ]

Z: 2 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 -0.361(1) 0.00000 0.471(1)

μ: 4.799 mm-1 [ Help ]

Absorption correction type: gaussian [ Help ]

Absorption correction remarks: CrysAlis RED, Oxford Diffraction Ltd., Version 1.171.27p5 beta Analytical numeric absorption correction using a multifaceted crystal model. [ Help ]

Minimum transmission factor: 0.43451 [ Help ]

Maximum transmission factor: 0.67729 [ Help ]

Refinement details


Total nb. of reflections: 2409 [ Help ]

Nb. of observed reflections: 1433 [ Help ]

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

Refinement based on: F [ Help ]

R(all): 0.0484 [ Help ]

R(obs): 0.0217 [ Help ]

wR(obs): 0.0396 [ Help ]

wR(all): 0.0568 [ Help ]

S(all): 1.58 [ Help ]

Nb. of reflections: 2409 [ Help ]

Nb. of parameters: 170 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 46 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ2(F)+0.0004F2) [ Help ]

Δ/σ(max): 0.0003 [ Help ]

Δ/σ(mean): 0.0000 [ Help ]

Δρ(max): 0.48 e_Å-3 [ Help ]

Δρ(min): -0.47 e_Å-3 [ Help ]

Extinction method: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) [ Help ]

Extinction coefficient: 62E1(10) [ 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
P P 0.80672(9) -0.01175(12) 0.58376(17) 0.00636(19) Uani d . 0.4157(14) . .
P P(a) 0.80672(9) -0.01175(12) 0.58376(17) 0.0165(17) Uani d . 0.0421(7) . .
P P(b) 0.80672(9) -0.01175(12) 0.58376(17) 0.0114(16) Uani d . 0.0421(7) . .
O O1 0.63754(19) 0 0.2775(3) 0.0089(4) Uani d . 1 . .
O O2 1 -0.0644(3) 0.5 0.0179(6) Uani d . 0.4157(14) . .
O O2(a) 1.0014(13) -0.0545(9) 0.532(2) 0.027(3) Uani d . 0.0421(7) . .
O O3 0.80628(16) -0.14636(13) 0.7591(3) 0.0130(3) Uani d . 1 . .
O O3(a) 0.8438(15) -0.1466(13) 0.729(2) 0.030(4) Uani d . 0.0421(7) . .
O O3(b) 0.7622(11) -0.1517(11) 0.772(2) 0.001(2) Uani d . 0.0421(7) . .
Cr Cr 0.5 -0.18798(6) 0 0.00790(15) Uani d . 1 . .
Cr Cr(a) 0.4749(11) -0.1898(3) 0.019(2) 0.0113(14) Uani d . 0.0423(8) . .

ADP components: [ Help ]

Atom site label U11 U22 U33 U12 U13 U23 Atom site symbol
P 0.0053(3) 0.0074(3) 0.0052(3) -0.00064(18) 0 -0.0012(3) P
P(a) 0.003(2) 0.027(3) 0.017(3) 0.009(2) 0.000(2) 0.010(3) P
P(b) 0.013(2) 0.010(2) 0.006(3) -0.005(2) -0.004(2) 0.021(3) P
O1 0.0096(7) 0.0069(6) 0.0083(7) 0 0.0000(5) 0 O
O2 0.0090(9) 0.0233(11) 0.0236(10) 0 0.0081(7) 0 O
O2(a) 0.011(3) 0.054(6) 0.021(4) -0.004(5) 0.015(3) -0.013(5) O
O3 0.0152(6) 0.0099(5) 0.0110(5) 0.0027(4) 0.0002(4) 0.0026(4) O
O3(a) 0.036(7) 0.021(5) 0.016(5) 0.009(5) -0.016(5) -0.005(4) O
O3(b) -0.002(4) 0.001(3) 0.002(3) 0.004(3) -0.003(3) 0.000(2) O
Cr 0.0083(2) 0.0051(2) 0.0073(2) 0 -0.00179(14) 0 Cr
Cr(a) 0.016(3) 0.0040(7) 0.010(2) -0.0014(8) -0.0012(16) 0.0006(9) Cr

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

Wave vector code q_x q_z
1 -0.36100 0.47100
2 -0.72200 0.94200
3 -1.08300 1.41300
4 -1.44400 1.88400

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

Modulation code Atom site label Displacement axis Wave vector code
Px1 P x 1
Py1 P y 1
Pz1 P z 1
Px2 P x 2
Py2 P y 2
Pz2 P z 2
Px3 P x 3
Py3 P y 3
Pz3 P z 3
Px4 P x 4
Py4 P y 4
Pz4 P z 4
P(a)x1 P(a) x 1
P(a)y1 P(a) y 1
P(a)z1 P(a) z 1
P(a)x2 P(a) x 2
P(a)y2 P(a) y 2
P(a)z2 P(a) z 2
P(a)x3 P(a) x 3
P(a)y3 P(a) y 3
P(a)z3 P(a) z 3
P(a)x4 P(a) x 4
P(a)y4 P(a) y 4
P(a)z4 P(a) z 4
P(b)x1 P(b) x 1
P(b)y1 P(b) y 1
P(b)z1 P(b) z 1
P(b)x2 P(b) x 2
P(b)y2 P(b) y 2
P(b)z2 P(b) z 2
P(b)x3 P(b) x 3
P(b)y3 P(b) y 3
P(b)z3 P(b) z 3
P(b)x4 P(b) x 4
P(b)y4 P(b) y 4
P(b)z4 P(b) z 4
O1x1 O1 x 1
O1y1 O1 y 1
O1z1 O1 z 1
O1x2 O1 x 2
O1y2 O1 y 2
O1z2 O1 z 2
O2x1 O2 x 1
O2y1 O2 y 1
O2z1 O2 z 1
O3x1 O3 x 1
O3y1 O3 y 1
O3z1 O3 z 1
O3x2 O3 x 2
O3y2 O3 y 2
O3z2 O3 z 2
O3x3 O3 x 3
O3y3 O3 y 3
O3z3 O3 z 3
Crx1 Cr x 1
Cry1 Cr y 1
Crz1 Cr z 1
Crx2 Cr x 2
Cry2 Cr y 2
Crz2 Cr z 2
Crx3 Cr x 3
Cry3 Cr y 3
Crz3 Cr z 3
Crx4 Cr x 4
Cry4 Cr y 4
Crz4 Cr z 4

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Px1 -0.0026 -0.0029
Py1 -0.0034 0.0032
Pz1 0.0059 0.0045
Px2 -0.0008 -0.0022
Py2 -0.0006 -0.0011
Pz2 0.0011 0.003
Px3 0.0003 -0.0005
Py3 0.0007 0
Pz3 0.0003 0.0002
Px4 0 0.0003
Py4 0 -0.0001
Pz4 0 -0.0002
P(a)x1 -0.0026 -0.0029
P(a)y1 -0.0034 0.0032
P(a)z1 0.0059 0.0045
P(a)x2 -0.0008 -0.0022
P(a)y2 -0.0006 -0.0011
P(a)z2 0.0011 0.003
P(a)x3 0.0003 -0.0005
P(a)y3 0.0007 0
P(a)z3 0.0003 0.0002
P(a)x4 0 0.0003
P(a)y4 0 -0.0001
P(a)z4 0 -0.0002
P(b)x1 -0.0026 -0.0029
P(b)y1 -0.0034 0.0032
P(b)z1 0.0059 0.0045
P(b)x2 -0.0008 -0.0022
P(b)y2 -0.0006 -0.0011
P(b)z2 0.0011 0.003
P(b)x3 0.0003 -0.0005
P(b)y3 0.0007 0
P(b)z3 0.0003 0.0002
P(b)x4 0 0.0003
P(b)y4 0 -0.0001
P(b)z4 0 -0.0002
O1x1 0 0
O1y1 -0.00147(15) 0.00650(15)
O1z1 0 0
O1x2 0.00174(16) -0.00535(16)
O1y2 0 0
O1z2 -0.0016(2) 0.0005(2)
O2x1 0.0059(3) 0
O2y1 0 0.0106(3)
O2z1 0.0433(4) 0
O3x1 -0.01698(16) 0.00907(19)
O3y1 -0.00274(13) -0.00222(16)
O3z1 0.0155(2) -0.0146(3)
O3x2 -0.00260(17) -0.00705(16)
O3y2 0.00084(14) -0.00064(13)
O3z2 0.0041(2) 0.0047(2)
O3x3 0.00051(18) -0.00045(16)
O3y3 -0.00005(15) -0.00079(12)
O3z3 -0.0031(3) -0.0009(2)
Crx1 0.01166(6) 0
Cry1 0 0.00209(12)
Crz1 -0.01334(7) 0
Crx2 0 -0.00342(5)
Cry2 -0.00027(12) 0
Crz2 0 0.00195(6)
Crx3 0.00072(7) 0
Cry3 0 -0.00066(11)
Crz3 -0.00122(8) 0
Crx4 0 0.00056(9)
Cry4 -0.00080(12) 0
Crz4 0 0.00022(10)

Definition of the occupation Fourier series: [ Help ]

Modulation code Atom site label Wave vector code
P(a)o1 P(a) 1
P(a)o2 P(a) 2
P(b)o1 P(b) 1
P(b)o2 P(b) 2

Occupation Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
P(a)o1 3.1457 -3.976
P(a)o2 -0.6242 0.1476
P(b)o1 3.1461 -3.9765
P(b)o2 0.6245 -0.1476

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
PU111 P U11 1
PU221 P U22 1
PU331 P U33 1
PU121 P U12 1
PU131 P U13 1
PU231 P U23 1
O3U111 O3 U11 1
O3U221 O3 U22 1
O3U331 O3 U33 1
O3U121 O3 U12 1
O3U131 O3 U13 1
O3U231 O3 U23 1
CrU111 Cr U11 1
CrU221 Cr U22 1
CrU331 Cr U33 1
CrU121 Cr U12 1
CrU131 Cr U13 1
CrU231 Cr U23 1
CrU112 Cr U11 2
CrU222 Cr U22 2
CrU332 Cr U33 2
CrU122 Cr U12 2
CrU132 Cr U13 2
CrU232 Cr U23 2

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
PU111 0 0
PU221 0 0
PU331 0.0007(3) -0.0016(3)
PU121 0.0005(2) 0
PU131 0.00041(17) 0
PU231 0.0010(3) -0.0016(3)
O3U111 -0.0046(6) 0.0048(6)
O3U221 0.0001(5) 0.0001(5)
O3U331 -0.0004(5) 0.0026(5)
O3U121 0.0001(4) -0.0004(4)
O3U131 0.0034(4) -0.0022(4)
O3U231 -0.0001(4) 0.0000(4)
CrU111 0 -0.0004(2)
CrU221 0 -0.00007(19)
CrU331 0 0.00131(19)
CrU121 0.00024(12) 0
CrU131 0 0.00070(15)
CrU231 -0.00011(11) 0
CrU112 0.0019(2) 0
CrU222 -0.00020(19) 0
CrU332 0.00087(19) 0
CrU122 0 -0.00025(12)
CrU132 -0.00055(16) 0
CrU232 0 -0.00015(12)

Displacive sawtooth coefficients: [ Help ]

Atom site label Ax Ay Az Center (x0) Width
O3 -0.0327 -0.0044 0.0057 0.69197(13) 0.9157(14)
Cr -0.0238 0 0.0133 0.25 0.9154(15)

Occupation crenel coefficients: [ Help ]

Atom site label Center (x0) Width
P 0.85681(8) 0.4157(14)
P(a) 1.10681(15) 0.0843(14)
P(b) 0.60681(15) 0.0843(14)
O2 0.75 0.4157(14)
O2(a) 1.0147(10) 0.0843(14)
O3(a) 1.1644(13) 0.0843(14)
O3(b) 1.2140(10) 0.0843(14)
Cr(a) 0.7679(11) 0.0846(15)