Open with JSmol

Structure of a modulated monoclinic phase of Na4TiP2O9

Authors:

Maximov, B.A.; Bolotina, N.B.; Simonov, V.I.; Petricek, V.; Schulz, H.

Journal:

Acta Cryst. B 50 261-268 (1994)

DOI:

https://doi.org/10.1107/S0108768193009917

B-IncStrDB ID: 642EGFEHT Entry date: 2010-11-08 Last revision: 2021-12-30

Download CIF
Open in JSmol

Na4Ti

Chemical data

Structural Formula Sum: Na3.912 O9 P2 Ti1 [ Help ]

Formula weight: 343.8 Da [ Help ]

Crystallographic data and experimental details

a: 8.631(1) Å [ Help ]

b: 7.541(1) Å [ Help ]

c: 7.049(1) Å [ Help ]

α: 90 ° [ Help ]

β: 116.10(2) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 412.01(12) Å3 [ Help ]

μ: 14.978 mm-1 [ Help ]

Z: 2 [ Help ]

Cell measurement temperature: 293 K [ Help ]

Crystal system: monoclinic [ Help ]

Superspace group name (WJJ): P:P 2/c:-1 s [ Help ]

Superspace group name: P2/c(α0γ)0s [ Help ]

Symmetry operations of the superspace group: [ Help ]

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

Space group name (H-M): P 1 2/c 1 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.2 0 0.2

Refinement details

Refinement remarks: Commensurate structure refined within the superspace formalism. Global phase fixed at t=1/2. [ Help ]

Modulation functions description: Displacive modulation:Fourier series. Up to 2nd-order harmonics. Occupational modulation:Fourier series. Up to 2nd-order harmonics. [ Help ]

Structure factors calc. details: Bessel functions [ Help ]

Nb. of observed reflections: 3056 [ Help ]

R(obs): 0.080 [ Help ]

wR(all): 0.091 [ Help ]

Structural Information

Average Structure: [ Help ]

Atom site label Atom symbol Symmetry multiplicity Occupancy x y z Uiso/equiv ADP type
Ti Ti 2 1 0.5 0.5 0 ? Uani
P P 4 1 0.2399(1) 0.2466(1) 0.6042(2) ? Uani
O1 O 2 1 0.5 0.6044(5) 0.75 ? Uani
O2 O 4 1 0.6525(4) 0.6940(4) 0.1637(7) ? Uani
O3 O 4 1 0.2935(4) 0.6428(4) -0.0440(7) ? Uani
O4 O 4 1 0.2793(4) 0.0542(4) 0.5899(8) ? Uani
O5 O 4 1 0.0533(4) 0.7144(4) 0.0418(7) ? Uani
Na1 Na 2 1 0.5 0 0 ? Uani
Na2 Na 2 1 0 0.5100(4) 0.75 ? Uani
Na3 Na 4 0.763(7) 0.2299(3) 0.2207(3) 0.1037(7) ? Uani
Na4 Na 2 0.386(8) 0 0.0194(6) 0.75 ? Uani

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 0.2 0 0.2
2 0.4 0 0.4

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

Modulation code Atom site label Displacement axis Wave vector code
Tix1 Ti x 1
Tix2 Ti x 2
Tiy1 Ti y 1
Tiy2 Ti y 2
Tiz1 Ti z 1
Tiz2 Ti z 2
Px1 P x 1
Px2 P x 2
Py1 P y 1
Py2 P y 2
Pz1 P z 1
Pz2 P z 2
O1x1 O1 x 1
O1x2 O1 x 2
O1y1 O1 y 1
O1y2 O1 y 2
O1z1 O1 z 1
O1z2 O1 z 2
O2x1 O2 x 1
O2x2 O2 x 2
O2y1 O2 y 1
O2y2 O2 y 2
O2z1 O2 z 1
O2z2 O2 z 2
O3x1 O3 x 1
O3x2 O3 x 2
O3y1 O3 y 1
O3y2 O3 y 2
O3z1 O3 z 1
O3z2 O3 z 2
O4x1 O4 x 1
O4x2 O4 x 2
O4y1 O4 y 1
O4y2 O4 y 2
O4z1 O4 z 1
O4z2 O4 z 2
O5x1 O5 x 1
O5x2 O5 x 2
O5y1 O5 y 1
O5y2 O5 y 2
O5z1 O5 z 1
O5z2 O5 z 2
Na1x1 Na1 x 1
Na1x2 Na1 x 2
Na1y1 Na1 y 1
Na1y2 Na1 y 2
Na1z1 Na1 z 1
Na1z2 Na1 z 2
Na2x1 Na2 x 1
Na2x2 Na2 x 2
Na2y1 Na2 y 1
Na2y2 Na2 y 2
Na2z1 Na2 z 1
Na2z2 Na2 z 2
Na3x1 Na3 x 1
Na3x2 Na3 x 2
Na3y1 Na3 y 1
Na3y2 Na3 y 2
Na3z1 Na3 z 1
Na3z2 Na3 z 2
Na4x1 Na4 x 1
Na4z1 Na4 z 1

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Tix1 0 0.0036(2)
Tix2 0 -0.0015(3)
Tiy1 0 0.0408(2)
Tiy2 0 0.0004(2)
Tiz1 0 0.0036(4)
Tiz2 0 -0.0040(5)
Px1 0.0177(2) -0.0081(2)
Px2 -0.0024(2) -0.0002(2)
Py1 -0.0012(2) 0.0408(2)
Py2 0.0020(2) -0.0021(2)
Pz1 0.0398(4) -0.0178(4)
Pz2 -0.0057(4) -0.0003(4)
O1x1 -0.0054(8) 0
O1x2 0 -0.0066(9)
O1y1 0 0.0423(8)
O1y2 -0.0003(8) 0
O1z1 -0.016(1) 0
O1z2 0 -0.012(2)
O2x1 -0.0104(6) -0.0017(6)
O2x2 -0.0010(7) -0.0033(7)
O2y1 -0.0036(6) 0.0369(6)
O2y2 0.0033(6) 0.0018(6)
O2z1 -0.029(1) -0.002(1)
O2z2 -0.002(1) -0.005(1)
O3x1 -0.0061(6) 0.0030(6)
O3x2 -0.0022(7) -0.0019(7)
O3y1 0.0052(6) 0.0423(6)
O3y2 -0.0015(6) 0.0040(6)
O3z1 -0.018(1) 0.008(1)
O3z2 -0.005(1) -0.005(1)
O4x1 0.0423(6) -0.0164(6)
O4x2 -0.0025(7) 0.0071(7)
O4y1 0.0004(6) 0.0403(6)
O4y2 0.0035(6) -0.0024(6)
O4z1 0.086(1) -0.041(1)
O4z2 -0.009(1) 0.017(1)
O5x1 -0.0093(6) 0.0108(6)
O5x2 -0.0019(7) -0.0013(7)
O5y1 -0.0070(6) 0.0538(6)
O5y2 -0.0003(7) 0.0076(7)
O5z1 -0.022(1) 0.024(1)
O5z2 -0.004(1) -0.002(1)
Na1x1 0 -0.0298(6)
Na1x2 0 0.0570(6)
Na1y1 0 -0.0107(6)
Na1y2 0 0.0444(6)
Na1z1 0 -0.084(1)
Na1z2 0 0.145(1)
Na2x1 0.0046(6) 0
Na2x2 0 0.0063(6)
Na2y1 0 0.0642(5)
Na2y2 -0.0046(6) 0
Na2z1 0.003(1) 0
Na2z2 0 0.013(1)
Na3x1 0.0171(4) 0.0055(6)
Na3x2 0 -0.0065(4)
Na3y1 0.0035(4) 0.0525(5)
Na3y2 0 0.0035(4)
Na3z1 0.0573(8) -0.011(1)
Na3z2 0 -0.0203(8)
Na4x1 -0.035(1) 0
Na4z1 -0.083(2) 0

Definition of the occupation Fourier series: [ Help ]

Modulation code Atom site label Wave vector code
Na3o1 Na3 1
Na3o2 Na3 2
Na4o1 Na4 1
Na4o2 Na4 2

Occupation Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Na3o1 -0.093(7) 0.373(7)
Na3o2 0.257(7) 0.046(8)
Na4o1 0 -0.55(1)
Na4o2 -0.17(1) 0

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Ti Ti 0.0069(5) 0.0142(6) 0.0179(6) -0.0002(4) 0.0055(5) -0.0118(4)
P P 0.0101(5) 0.0049(5) 0.0096(5) -0.0026(4) 0.0086(4) -0.0027(4)
O1 O 0.014(2) 0.006(2) 0.011(2) 0 0.011(2) 0
O2 O 0.022(2) 0.009(1) 0.013(1) -0.008(1) 0.015(1) -0.007(1)
O3 O 0.014(2) 0.016(2) 0.012(1) 0.010(1) 0.011(1) 0.006(1)
O4 O 0.025(2) 0.006(1) 0.021(2) 0.001(1) 0.019(2) -0.002(1)
O5 O 0.014(2) 0.021(2) 0.015(1) 0.002(1) 0.012(1) 0.000(1)
Na1 Na 0.030(2) 0.034(2) 0.033(2) 0.006(1) 0.028(2) 0.012(1)
Na2 Na 0.026(1) 0.018(1) 0.022(1) 0 0.020(1) 0
Na3 Na 0.014(1) 0.013(1) 0.021(1) 0.0015(8) 0.013(1) -0.0003(9)
Na4 Na 0.018(3) 0.010(2) 0.020(3) 0 0.015(3) 0