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Dipole-moment modulation in a new incommensurate ferrocene phase

Authors:

Katrusiak, Andrzej; Michalina, Rusek; Dusek, Michal; Petricek, Vaclav; Szafranski, Marek

B-IncStrDB ID: Fxhs6DE1VaT Entry date: 2022-11-07 Last revision: 2023-01-27

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I

Chemical data

Full Name: Dicyclopentadienyl iron [ Help ]

Common Name: ferrocene [ Help ]

Structural Formula Sum: C10 H10 Fe1 [ Help ]

Formula weight: 186 Da [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Space group name (H-M): P 1 21/n 1 [ 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,x5+1/2,x4+1/2
3 -x1,-x2,-x3,-x4,-x5
4 x1+1/2,-x2+1/2,x3+1/2,-x5+1/2,-x4+1/2

a: 5.7982(2) Å [ Help ]

b: 7.5645(3) Å [ Help ]

c: 8.9915(4) Å [ Help ]

α: 90 ° [ Help ]

β: 92.911(3) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 393.86(3) Å3 [ Help ]

Modulation dimension: 2 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.500000 0.388000 0.166000
2 -0.500000 0.388000 -0.166000

Z: 2 [ Help ]

Cell determination reflection Nb.: 4595 [ Help ]

θ(min) for cell determination: 4.09 ° [ Help ]

θ(max) for cell determination: 28.22 ° [ Help ]

Cell measurement temperature: 166.00(10) K [ Help ]

μ: 1.834 mm-1 [ Help ]

Absorption correction type: multi-scan [ Help ]

Absorption correction remarks: CrysAlisPro 1.171.40.53 (Rigaku Oxford Diffraction, 2019) Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm. [ Help ]

Minimum transmission factor: 0.83 [ Help ]

Maximum transmission factor: 1 [ Help ]

Refinement details

Total nb. of reflections: 4755 [ Help ]

Nb. of observed reflections: 2360 [ Help ]

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

Refinement based on: Fsqd [ Help ]

R(obs): 0.0348 [ Help ]

wR(obs): 0.0783 [ Help ]

R(all): 0.0696 [ Help ]

wR(all): 0.0911 [ Help ]

S(all): 1.1439 [ Help ]

S(obs): 1.4150 [ Help ]

Nb. of reflections: 4755 [ Help ]

Nb. of parameters: 149 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 0 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ2(I)+0.0004I2) [ Help ]

Refinement of hydrogen atoms: refxyz [ Help ]

Δ/σ(max): 0.0007 [ Help ]

Δ/σ(mean): 0.0002 [ Help ]

Δρ(max): 0.52 e_Å-3 [ Help ]

Δρ(min): -0.67 e_Å-3 [ Help ]

Extinction method: none [ 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 0.5 0 0.5 Uani 0.02352(8) 2 1 d . . .
C1a C 0.4984(6) 0.2646(4) 0.4597(4) Uani 0.0294(8) 4 0.5 d . . .
C2a C 0.2738(7) 0.2031(6) 0.4671(5) Uani 0.034(3) 4 0.5 d . . .
C4a C 0.4373(11) 0.0610(7) 0.2787(6) Uani 0.029(6) 4 0.5 d . . .
C3a C 0.2352(10) 0.0769(7) 0.3555(6) Uani 0.033(5) 4 0.5 d . . .
C5a C 0.5993(8) 0.1770(6) 0.3436(5) Uani 0.027(3) 4 0.5 d . . .
H1c1a H 0.570(3) 0.3498(19) 0.5211(17) Uani 0.0480(19) 4 0.5 d . . .
H1c2a H 0.170(3) 0.236(2) 0.5417(15) Uani 0.058(4) 4 0.5 d . . .
H1c4a H 0.461(3) -0.0151(19) 0.2008(18) Uani 0.047(11) 4 0.5 d . . .
H1c3a H 0.094(3) 0.008(2) 0.337(2) Uani 0.057(9) 4 0.5 d . . .
H1c5a H 0.743(2) 0.193(2) 0.3172(18) Uani 0.044(4) 4 0.5 d . . .
C1b C 0.4358(5) 0.2626(4) 0.4886(3) Uani 0.0262(8) 4 0.5 d . . .
C2b C 0.2342(8) 0.1682(9) 0.4567(7) Uani 0.026(2) 4 0.5 d . . .
C4b C 0.4922(18) 0.0901(13) 0.2891(10) Uani 0.040(5) 4 0.5 d . . .
C3b C 0.2682(15) 0.0611(12) 0.3335(11) Uani 0.035(4) 4 0.5 d . . .
C5b C 0.5950(11) 0.2144(9) 0.3854(6) Uani 0.035(2) 4 0.5 d . . .
H1c1b H 0.462(3) 0.3443(19) 0.5655(17) Uani 0.0385(16) 4 0.5 d . . .
H1c2b H 0.101(3) 0.170(2) 0.5153(17) Uani 0.039(4) 4 0.5 d . . .
H1c4b H 0.562(4) 0.035(2) 0.212(2) Uani 0.063(9) 4 0.5 d . . .
H1c3b H 0.157(3) -0.023(3) 0.289(2) Uani 0.055(8) 4 0.5 d . . .
H1c5b H 0.738(3) 0.256(3) 0.3831(18) Uani 0.053(4) 4 0.5 d . . .

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Fe1 Fe 0.02633(14) 0.01874(13) 0.02531(13) 0.00138(7) -0.00049(9) 0.00417(7)
C1a C 0.0450(16) 0.0205(13) 0.0225(14) -0.0009(11) 0.0003(13) 0.0056(8)
C2a C 0.035(2) 0.030(5) 0.039(5) 0.014(3) 0.008(2) 0.009(4)
C4a C 0.037(12) 0.024(11) 0.026(10) 0.000(7) -0.002(6) 0.003(9)
C3a C 0.024(7) 0.037(9) 0.038(11) 0.000(7) -0.008(6) 0.012(7)
C5a C 0.027(5) 0.028(6) 0.026(4) -0.001(4) 0.000(3) 0.006(4)
H1c1a H 0.083(3) 0.033(3) 0.028(3) -0.019(3) 0.003(2) -0.001(2)
H1c2a H 0.057(3) 0.055(10) 0.064(8) 0.021(5) 0.030(4) 0.005(7)
H1c4a H 0.07(2) 0.036(19) 0.035(16) -0.008(11) 0.007(9) -0.009(16)
H1c3a H 0.033(12) 0.074(15) 0.062(19) -0.018(12) -0.013(10) 0.014(13)
H1c5a H 0.032(5) 0.057(10) 0.043(6) -0.009(6) 0.008(5) 0.004(6)
C1b C 0.0326(11) 0.0166(12) 0.0287(16) -0.0065(8) -0.0057(10) 0.0044(9)
C2b C 0.022(2) 0.022(5) 0.035(4) 0.001(2) -0.008(2) 0.004(3)
C4b C 0.065(10) 0.034(9) 0.022(8) 0.014(6) 0.006(5) 0.010(7)
C3b C 0.050(7) 0.026(8) 0.027(9) -0.002(6) -0.020(5) 0.002(6)
C5b C 0.032(4) 0.036(5) 0.037(3) -0.002(4) 0.004(3) 0.020(3)
H1c1b H 0.064(3) 0.015(3) 0.035(3) -0.013(2) -0.010(2) 0.003(2)
H1c2b H 0.022(3) 0.037(9) 0.057(7) 0.009(4) 0.000(4) 0.013(6)
H1c4b H 0.115(18) 0.051(15) 0.026(13) 0.033(10) 0.023(9) 0.016(12)
H1c3b H 0.083(11) 0.036(14) 0.041(16) -0.014(10) -0.044(9) 0.005(11)
H1c5b H 0.035(5) 0.060(8) 0.064(5) -0.008(5) 0.008(4) 0.043(5)

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

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

Modulation code Atom site label Displacement axis Wave vector code
Fe1x1 Fe1 x 1
Fe1y1 Fe1 y 1
Fe1z1 Fe1 z 1
Fe1x2 Fe1 x 2
Fe1y2 Fe1 y 2
Fe1z2 Fe1 z 2
C1ax1 C1a x 1
C1ay1 C1a y 1
C1az1 C1a z 1
C1ax2 C1a x 2
C1ay2 C1a y 2
C1az2 C1a z 2
C2ax1 C2a x 1
C2ay1 C2a y 1
C2az1 C2a z 1
C2ax2 C2a x 2
C2ay2 C2a y 2
C2az2 C2a z 2
C4ax1 C4a x 1
C4ay1 C4a y 1
C4az1 C4a z 1
C4ax2 C4a x 2
C4ay2 C4a y 2
C4az2 C4a z 2
C3ax1 C3a x 1
C3ay1 C3a y 1
C3az1 C3a z 1
C3ax2 C3a x 2
C3ay2 C3a y 2
C3az2 C3a z 2
C5ax1 C5a x 1
C5ay1 C5a y 1
C5az1 C5a z 1
C5ax2 C5a x 2
C5ay2 C5a y 2
C5az2 C5a z 2
H1c1ax1 H1c1a x 1
H1c1ay1 H1c1a y 1
H1c1az1 H1c1a z 1
H1c1ax2 H1c1a x 2
H1c1ay2 H1c1a y 2
H1c1az2 H1c1a z 2
H1c2ax1 H1c2a x 1
H1c2ay1 H1c2a y 1
H1c2az1 H1c2a z 1
H1c2ax2 H1c2a x 2
H1c2ay2 H1c2a y 2
H1c2az2 H1c2a z 2
H1c4ax1 H1c4a x 1
H1c4ay1 H1c4a y 1
H1c4az1 H1c4a z 1
H1c4ax2 H1c4a x 2
H1c4ay2 H1c4a y 2
H1c4az2 H1c4a z 2
H1c3ax1 H1c3a x 1
H1c3ay1 H1c3a y 1
H1c3az1 H1c3a z 1
H1c3ax2 H1c3a x 2
H1c3ay2 H1c3a y 2
H1c3az2 H1c3a z 2
H1c5ax1 H1c5a x 1
H1c5ay1 H1c5a y 1
H1c5az1 H1c5a z 1
H1c5ax2 H1c5a x 2
H1c5ay2 H1c5a y 2
H1c5az2 H1c5a z 2
C1bx1 C1b x 1
C1by1 C1b y 1
C1bz1 C1b z 1
C1bx2 C1b x 2
C1by2 C1b y 2
C1bz2 C1b z 2
C2bx1 C2b x 1
C2by1 C2b y 1
C2bz1 C2b z 1
C2bx2 C2b x 2
C2by2 C2b y 2
C2bz2 C2b z 2
C4bx1 C4b x 1
C4by1 C4b y 1
C4bz1 C4b z 1
C4bx2 C4b x 2
C4by2 C4b y 2
C4bz2 C4b z 2
C3bx1 C3b x 1
C3by1 C3b y 1
C3bz1 C3b z 1
C3bx2 C3b x 2
C3by2 C3b y 2
C3bz2 C3b z 2
C5bx1 C5b x 1
C5by1 C5b y 1
C5bz1 C5b z 1
C5bx2 C5b x 2
C5by2 C5b y 2
C5bz2 C5b z 2
H1c1bx1 H1c1b x 1
H1c1by1 H1c1b y 1
H1c1bz1 H1c1b z 1
H1c1bx2 H1c1b x 2
H1c1by2 H1c1b y 2
H1c1bz2 H1c1b z 2
H1c2bx1 H1c2b x 1
H1c2by1 H1c2b y 1
H1c2bz1 H1c2b z 1
H1c2bx2 H1c2b x 2
H1c2by2 H1c2b y 2
H1c2bz2 H1c2b z 2
H1c4bx1 H1c4b x 1
H1c4by1 H1c4b y 1
H1c4bz1 H1c4b z 1
H1c4bx2 H1c4b x 2
H1c4by2 H1c4b y 2
H1c4bz2 H1c4b z 2
H1c3bx1 H1c3b x 1
H1c3by1 H1c3b y 1
H1c3bz1 H1c3b z 1
H1c3bx2 H1c3b x 2
H1c3by2 H1c3b y 2
H1c3bz2 H1c3b z 2
H1c5bx1 H1c5b x 1
H1c5by1 H1c5b y 1
H1c5bz1 H1c5b z 1
H1c5bx2 H1c5b x 2
H1c5by2 H1c5b y 2
H1c5bz2 H1c5b z 2

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Fe1x1 0 -0.00018(4)
Fe1y1 0 0.00295(3)
Fe1z1 0 0.00842(3)
Fe1x2 0 -0.00245(4)
Fe1y2 0 0.00432(3)
Fe1z2 0 -0.00214(3)
C1ax1 0.0378(5) -0.0502(6)
C1ay1 -0.0031(3) 0.0053(3)
C1az1 -0.0131(3) 0.0177(3)
C1ax2 0.0125(6) -0.0230(6)
C1ay2 -0.0044(4) 0.0045(4)
C1az2 -0.0027(3) 0.0048(3)
C2ax1 0.0312(5) -0.0424(6)
C2ay1 0.0172(5) -0.0199(5)
C2az1 0.0046(4) -0.0064(4)
C2ax2 0.0114(6) -0.0195(7)
C2ay2 0.0014(6) -0.0067(6)
C2az2 0.0071(5) -0.0059(4)
C4ax1 -0.0215(9) 0.0267(10)
C4ay1 -0.0087(6) 0.0137(6)
C4az1 -0.0021(5) 0.0026(5)
C4ax2 -0.0145(10) 0.0107(11)
C4ay2 -0.0046(6) 0.0089(6)
C4az2 0.0003(5) -0.0024(5)
C3ax1 -0.0055(8) 0.0052(8)
C3ay1 0.0138(6) -0.0148(6)
C3az1 0.0115(5) -0.0159(5)
C3ax2 -0.0053(9) 0.0014(9)
C3ay2 0.0013(7) -0.0040(7)
C3az2 0.0091(6) -0.0104(6)
C5ax1 0.0053(7) -0.0077(7)
C5ay1 -0.0191(5) 0.0260(5)
C5az1 -0.0172(3) 0.0233(3)
C5ax2 -0.0034(8) -0.0044(8)
C5ay2 -0.0081(5) 0.0141(5)
C5az2 -0.0069(4) 0.0070(4)
H1c1ax1 0.0601(7) -0.0789(8)
H1c1ay1 -0.0057(5) 0.0080(5)
H1c1az1 -0.0210(4) 0.0285(4)
H1c1ax2 0.0222(7) -0.0356(8)
H1c1ay2 -0.0056(5) 0.0055(5)
H1c1az2 -0.0061(4) 0.0098(4)
H1c2ax1 0.0488(7) -0.0657(8)
H1c2ay1 0.0309(7) -0.0375(7)
H1c2az1 0.0108(5) -0.0148(5)
H1c2ax2 0.0208(7) -0.0297(7)
H1c2ay2 0.0048(8) -0.0147(8)
H1c2az2 0.0116(6) -0.0094(6)
H1c4ax1 -0.0457(12) 0.0581(13)
H1c4ay1 -0.0156(8) 0.0228(9)
H1c4az1 -0.0012(6) 0.0013(7)
H1c4ax2 -0.0257(14) 0.0245(14)
H1c4ay2 -0.0060(8) 0.0132(8)
H1c4az2 -0.0005(6) -0.0032(6)
H1c3ax1 -0.0179(10) 0.0208(11)
H1c3ay1 0.0251(8) -0.0287(9)
H1c3az1 0.0237(8) -0.0325(8)
H1c3ax2 -0.0096(11) 0.0082(11)
H1c3ay2 0.0047(9) -0.0101(9)
H1c3az2 0.0154(8) -0.0178(8)
H1c5ax1 0.0025(8) -0.0036(9)
H1c5ay1 -0.0334(7) 0.0439(7)
H1c5az1 -0.0278(4) 0.0376(5)
H1c5ax2 -0.0059(8) -0.0026(9)
H1c5ay2 -0.0120(7) 0.0221(7)
H1c5az2 -0.0132(5) 0.0133(5)
C1bx1 0.0138(4) -0.0239(4)
C1by1 -0.0005(3) 0.0004(3)
C1bz1 -0.0089(3) 0.0188(3)
C1bx2 0.0035(4) -0.0030(4)
C1by2 -0.0016(4) 0.0034(4)
C1bz2 0.0041(3) 0.0051(3)
C2bx1 0.0054(4) -0.0050(5)
C2by1 0.0063(5) -0.0137(5)
C2bz1 0.0009(4) -0.0059(4)
C2bx2 0.0013(5) -0.0011(5)
C2by2 0.0006(5) 0.0022(5)
C2bz2 0.0054(4) 0.0020(4)
C4bx1 -0.0164(8) 0.0493(9)
C4by1 -0.0090(6) 0.0185(6)
C4bz1 -0.0082(4) 0.0188(5)
C4bx2 -0.0032(9) 0.0026(9)
C4by2 -0.0022(6) 0.0099(6)
C4bz2 0.0035(5) 0.0019(5)
C3bx1 -0.0133(7) 0.0403(8)
C3by1 0.0011(6) -0.0026(6)
C3bz1 0.0014(5) -0.0060(5)
C3bx2 -0.0029(8) 0.0023(8)
C3by2 0.0003(6) 0.0062(6)
C3bz2 0.0050(6) 0.0000(6)
C5bx1 0.0004(5) 0.0095(6)
C5by1 -0.0099(5) 0.0203(5)
C5bz1 -0.0145(3) 0.0340(3)
C5bx2 0.0007(6) -0.0007(6)
C5by2 -0.0034(5) 0.0081(5)
C5bz2 0.0029(4) 0.0050(4)
H1c1bx1 0.0263(5) -0.0538(7)
H1c1by1 0.0009(4) -0.0027(5)
H1c1bz1 -0.0113(3) 0.0244(4)
H1c1bx2 0.0063(5) -0.0054(5)
H1c1by2 -0.0019(4) 0.0014(4)
H1c1bz2 0.0040(4) 0.0068(4)
H1c2bx1 0.0115(5) -0.0209(7)
H1c2by1 0.0132(6) -0.0284(7)
H1c2bz1 0.0063(5) -0.0200(5)
H1c2bx2 0.0024(5) -0.0020(5)
H1c2by2 0.0021(7) -0.0009(7)
H1c2bz2 0.0064(5) 0.0012(5)
H1c4bx1 -0.0275(11) 0.0765(13)
H1c4by1 -0.0141(7) 0.0293(8)
H1c4bz1 -0.0101(6) 0.0242(7)
H1c4bx2 -0.0056(12) 0.0046(12)
H1c4by2 -0.0030(8) 0.0129(8)
H1c4bz2 0.0029(6) 0.0012(6)
H1c3bx1 -0.0226(9) 0.0618(11)
H1c3by1 0.0039(8) -0.0085(8)
H1c3bz1 0.0073(7) -0.0208(8)
H1c3bx2 -0.0052(10) 0.0043(10)
H1c3by2 0.0015(8) 0.0064(8)
H1c3bz2 0.0057(8) -0.0023(8)
H1c5bx1 0.0024(6) 0.0057(8)
H1c5by1 -0.0155(6) 0.0320(7)
H1c5bz1 -0.0210(4) 0.0506(5)
H1c5bx2 0.0014(7) -0.0013(7)
H1c5by2 -0.0050(7) 0.0097(7)
H1c5bz2 0.0020(5) 0.0067(5)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
Fe1U111 Fe1 U11 1
Fe1U221 Fe1 U22 1
Fe1U331 Fe1 U33 1
Fe1U121 Fe1 U12 1
Fe1U131 Fe1 U13 1
Fe1U231 Fe1 U23 1
Fe1U112 Fe1 U11 2
Fe1U222 Fe1 U22 2
Fe1U332 Fe1 U33 2
Fe1U122 Fe1 U12 2
Fe1U132 Fe1 U13 2
Fe1U232 Fe1 U23 2

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Fe1U111 0.00000(15) 0
Fe1U221 -0.00030(14) 0
Fe1U331 -0.00090(13) 0
Fe1U121 0.00072(12) 0
Fe1U131 0.00109(11) 0
Fe1U231 -0.00007(11) 0
Fe1U112 -0.00016(15) 0
Fe1U222 0.00030(15) 0
Fe1U332 0.00175(13) 0
Fe1U122 0.00012(12) 0
Fe1U132 0.00060(11) 0
Fe1U232 0.00064(11) 0