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Superspace description of the homologous series Ga4Tim-4O2m-2 with the crystallographic shear structure based on rutile

Authors:

Michiue, Yuichi; Yamamoto, Akiji; Tanaka, Masahiko

Journal:

Acta Crystallographica, Section B 62 737-744 (2006)

DOI:

https://doi.org/10.1107/S010876810602369X

B-IncStrDB ID: li6FJrtkohb Entry date: 2021-12-26 Last revision: 2021-12-26

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Chemical data

Structural Formula Sum: Ga0.444 O3.556 Ti1.444 [ Help ]

Formula weight: 157 Da [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Superspace group name: P2/m(α1/2γ)00 [ Help ]

Symmetry operations of the superspace group: [ Help ]

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

a: 4.09045(2) Å [ Help ]

b: 2.97554(1) Å [ Help ]

c: 4.73593(2) Å [ Help ]

α: 90 ° [ Help ]

β: 90.2935(2) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 57.64159 Å3 [ Help ]

Z: 1 [ Help ]

Cell measurement temperature: 295 K [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.11111 0.00000 -0.05556

μ: 13.73 mm-1 [ Help ]

Absorption correction remarks: (Jana2000; Petricek and Dusek, 2000) [ Help ]

Refinement details

R(all): 0.0408 [ Help ]

R(obs): 0.0398 [ Help ]

wR(obs): 0.0387 [ Help ]

wR(all): 0.0387 [ Help ]

Nb. of parameters: 78 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 9.4983 [ Help ]

Δ/σ(mean): 0.4337 [ Help ]

Extinction method: none [ Help ]

Refinement remarks: WARNING: The published values for some parameters are not consistent with those in the deposited CIF. Discrepant parameters have been substituted for the final parameters in Table 4 of the article. [ 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
Ti M1 0 0 0 0.0093(4) Uiso d . 0.965(5) . .
Ga M1' 0.1363(5) 0 0.1050(4) 0.0118(6) Uiso d . 1 . .
Ti M2 0.5 0.5 0.5 0.0095(4) Uiso d . 0.919(6) . .
Ga M2' 0.6738(6) 0.5 0.5838(5) 0.0045(7) Uiso d . 0.63(2) . .
O O1 0.301(7) 0 0.311(5) 0.0041(6) Uiso d . 1 . .
O O1' 0.055(2) 0 0.267(2) 0.002(2) Uiso d . 1 . .
O O1" 0.456(3) 0 0.390(2) 0.013(3) Uiso d . 1 . .
O O2 0.219(7) 0.5 -0.178(5) 0.0080(7) Uiso d . 1 . .
O O2' 0.003(3) 0.5 -0.291(2) 0.009(3) Uiso d . 1 . .
O O2" 0.415(3) 0.5 -0.076(2) 0.019(3) Uiso d . 1 . .

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 0.11111 -0.05556
2 0.22222 -0.11111

Occupation crenel coefficients: [ Help ]

Atom site label Center (x0) Width
M1' 0.23153(6) 0.05556
M2' 0.20910(7) 0.05556
O1' -0.2309(3) 0.05556
O1" 0.1957(3) 0.05556
O2' -0.2057(3) 0.05556
O2" 0.2170(3) 0.05556

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

Modulation code Atom site label Displacement axis Wave vector code
M1x1 M1 x 1
M1z1 M1 z 1
M1x2 M1 x 2
M1z2 M1 z 2
M2x1 M2 x 1
M2z1 M2 z 1
M2x2 M2 x 2
M2z2 M2 z 2
O1x1 O1 x 1
O1z1 O1 z 1
O2x1 O2 x 1
O2z1 O2 z 1

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
M1x1 0 -0.050(3)
M1z1 0 -0.018(3)
M1x2 0 0.025(2)
M1z2 0 0.006(2)
M2x1 0 -0.025(6)
M2z1 0 0.028(5)
M2x2 0 0.004(4)
M2z2 0 -0.018(3)
O1x1 -0.020(7) -0.0102(18)
O1z1 -0.010(6) -0.0104(15)
O2x1 -0.017(7) -0.0087(18)
O2z1 -0.010(6) -0.0131(14)

Displacive sawtooth coefficients: [ Help ]

Atom site label Ax Ay Az Center (x0) Width
M1 0.2121 0 0.1061 0 0.3889
M2 0.1818 0 0.0909 0 0.3333
O1 0.1818 0 0.0909 -0.0116(8) 0.3333
O2 0.1818 0 0.0909 0.0064(8) 0.3333