Incommensurate structure of InAl1-xTixO3+x/2 [x=0.701(1)]: comparison between a modulated and a composite model
Authors:Bereciartua, Pablo J.; Zuniga, F. Javier; Breczewski, Tomasz
Journal:Acta Crystallographica, Section B 64 405-416 (2008)
DOI:https://doi.org/10.1107/S0108768108012317
B-IncStrDB ID: XDtXvQzKOoy Entry date: 2022-01-24 Last revision: 2022-01-24
mod
Chemical data
Formula moiety: Al0.256 In1.044 O3.35 Ti0.700 [ Help ]
Structural Formula Sum: Al0.256 In1.044 O3.35 Ti0.700 [ Help ]
Formula weight: 213.89 Da [ Help ]
Crystallographic data and experimental details
Crystal system: monoclinic [ Help ]
Superspace group name: C2/m(0β0)s0 [ Help ]
Symmetry operations of the superspace group: (Show/hide table) [ Help ]
| Operation code | Operation in algebraic form |
|---|---|
| 1 | x1,x2,x3,x4 |
| 2 | -x1,x2,-x3,1/2+x4 |
| 3 | -x1,-x2,-x3,-x4 |
| 4 | x1,-x2,x3,1/2-x4 |
| 5 | 1/2+x1,1/2+x2,x3,x4 |
| 6 | 1/2-x1,1/2+x2,-x3,1/2+x4 |
| 7 | 1/2-x1,1/2-x2,-x3,-x4 |
| 8 | 1/2+x1,1/2-x2,x3,1/2-x4 |
a: 5.857(4) Å [ Help ]
b: 3.361(3) Å [ Help ]
c: 6.355(5) Å [ Help ]
α: 90 ° [ Help ]
β: 107.96(5) ° [ Help ]
γ: 90 ° [ Help ]
Volume: 119.00(17) Å3 [ Help ]
Z: 2 [ Help ]
Cell measurement temperature: 293 K [ Help ]
Modulation dimension: 1 [ Help ]
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.00000 | 0.3503(5) | 0.00000 |
μ: 12.349 mm-1 [ Help ]
Absorption correction type: numerical [ Help ]
Absorption correction remarks: gaussian [ Help ]
Minimum transmission factor: 0.31 [ Help ]
Maximum transmission factor: 0.83 [ Help ]
Refinement details
Total nb. of reflections: 1733 [ Help ]
Nb. of observed reflections: 994 [ Help ]
Intense reflections threshold: I>3σ(I) [ Help ]
Refinement based on: F [ Help ]
R(all): 0.0539 [ Help ]
R(obs): 0.0315 [ Help ]
wR(obs): 0.0462 [ Help ]
wR(all): 0.0587 [ Help ]
S(all): 1.49 [ Help ]
Nb. of reflections: 1733 [ Help ]
Nb. of parameters: 57 [ Help ]
Number of restraints: 6 [ Help ]
Number of constraints: 1 [ Help ]
Weighting scheme: sigma [ Help ]
Weighting scheme remarks: w=1/(σ2(F)+0.0004F2) [ Help ]
Δ/σ(max): 0.0008 [ Help ]
Δ/σ(mean): 0.0002 [ Help ]
Δρ(max): 2.47 e_Å-3 [ Help ]
Δρ(min): -2.37 e_Å-3 [ Help ]
Extinction method: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) [ Help ]
Extinction coefficient: 0.00103(6) [ Help ]
Structural Information
Average Structure: (Show/hide table) [ 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| In | In1 | 0 | 0 | 0 | 0.00571(11) | Uani | d | . | 1 | . | . |
| Al | Al | 0.5 | 0 | 0.5 | 0.0100(3) | Uani | d | . | 0.256(8) | . | . |
| Ti | Ti | 0.5 | 0 | 0.5 | 0.0100(3) | Uani | d | . | 0.700(6) | . | . |
| In | In2 | 0.5 | 0 | 0.5 | 0.0100(3) | Uani | d | . | 0.044(10) | . | . |
| O | O1 | 0.3888(4) | 0 | 0.1709(4) | 0.0053(6) | Uani | d | . | 1 | . | . |
| O | O2 | 0.1597(4) | 0 | 0.4983(4) | 0.0181(7) | Uani | d | . | 0.6751 | . | . |
ADP components: (Show/hide table) [ Help ]
| Atom site label | U11 | U22 | U33 | U12 | U13 | U23 | Atom site symbol |
|---|---|---|---|---|---|---|---|
| In1 | 0.00514(15) | 0.00373(16) | 0.0086(2) | 0 | 0.00267(11) | 0 | In |
| Al | 0.0110(4) | 0.0137(4) | 0.0045(4) | 0 | 0.0012(3) | 0 | Al |
| Ti | 0.0110(4) | 0.0137(4) | 0.0045(4) | 0 | 0.0012(3) | 0 | Ti |
| In2 | 0.0110(4) | 0.0137(4) | 0.0045(4) | 0 | 0.0012(3) | 0 | In |
| O1 | 0.0061(8) | 0.0055(10) | 0.0039(9) | 0 | 0.0011(7) | 0 | O |
| O2 | 0.0232(13) | 0.0181(10) | 0.0092(11) | 0 | -0.0007(9) | 0 | O |
Fourier Wave Vectors (explicit: q_x,q_y,q_z or coefficients: q_1,q_2,...): (Show/hide table) [ Help ]
| Wave vector code | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.00000 | 0.3503 | 0.00000 |
| 2 | 0.00000 | 0.7006 | 0.00000 |
| 3 | 0.00000 | 1.0509 | 0.00000 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| In1x1 | In1 | x | 1 |
| In1y1 | In1 | y | 1 |
| In1z1 | In1 | z | 1 |
| In1x2 | In1 | x | 2 |
| In1y2 | In1 | y | 2 |
| In1z2 | In1 | z | 2 |
| In1x3 | In1 | x | 3 |
| In1y3 | In1 | y | 3 |
| In1z3 | In1 | z | 3 |
| Alx1 | Al | x | 1 |
| Aly1 | Al | y | 1 |
| Alz1 | Al | z | 1 |
| Alx2 | Al | x | 2 |
| Aly2 | Al | y | 2 |
| Alz2 | Al | z | 2 |
| Alx3 | Al | x | 3 |
| Aly3 | Al | y | 3 |
| Alz3 | Al | z | 3 |
| Tix1 | Ti | x | 1 |
| Tiy1 | Ti | y | 1 |
| Tiz1 | Ti | z | 1 |
| Tix2 | Ti | x | 2 |
| Tiy2 | Ti | y | 2 |
| Tiz2 | Ti | z | 2 |
| Tix3 | Ti | x | 3 |
| Tiy3 | Ti | y | 3 |
| Tiz3 | Ti | z | 3 |
| In2x1 | In2 | x | 1 |
| In2y1 | In2 | y | 1 |
| In2z1 | In2 | z | 1 |
| In2x2 | In2 | x | 2 |
| In2y2 | In2 | y | 2 |
| In2z2 | In2 | z | 2 |
| In2x3 | In2 | x | 3 |
| In2y3 | In2 | y | 3 |
| In2z3 | In2 | z | 3 |
| O2x1 | O1 | x | 1 |
| O2y1 | O1 | y | 1 |
| O2z1 | O1 | z | 1 |
| O2x2 | O2 | x | 1 |
| O2y2 | O2 | y | 1 |
| O2z2 | O2 | z | 1 |
| O2x3 | O2 | x | 2 |
| O2y3 | O2 | y | 2 |
| O2z3 | O2 | z | 2 |
Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| In1x1 | 0 | 0.02003(6) |
| In1y1 | 0 | 0 |
| In1z1 | 0 | 0.00511(5) |
| In1x2 | 0 | 0 |
| In1y2 | 0 | -0.00228(7) |
| In1z2 | 0 | 0 |
| In1x3 | 0 | -0.00016(5) |
| In1y3 | 0 | 0 |
| In1z3 | 0 | -0.00004(5) |
| Alx1 | 0 | 0.0545(2) |
| Aly1 | 0 | 0 |
| Alz1 | 0 | 0.00745(13) |
| Alx2 | 0 | 0 |
| Aly2 | 0 | -0.0261(2) |
| Alz2 | 0 | 0 |
| Alx3 | 0 | -0.00242(18) |
| Aly3 | 0 | 0 |
| Alz3 | 0 | 0.00158(16) |
| Tix1 | 0 | 0.0545(2) |
| Tiy1 | 0 | 0 |
| Tiz1 | 0 | 0.00745(13) |
| Tix2 | 0 | 0 |
| Tiy2 | 0 | -0.0261(2) |
| Tiz2 | 0 | 0 |
| Tix3 | 0 | -0.00242(18) |
| Tiy3 | 0 | 0 |
| Tiz3 | 0 | 0.00158(16) |
| In2x1 | 0 | 0.0545(2) |
| In2y1 | 0 | 0 |
| In2z1 | 0 | 0.00745(13) |
| In2x2 | 0 | 0 |
| In2y2 | 0 | -0.0261(2) |
| In2z2 | 0 | 0 |
| In2x3 | 0 | -0.00242(18) |
| In2y3 | 0 | 0 |
| In2z3 | 0 | 0.00158(16) |
| O2x1 | 0 | 0.0285(4) |
| O2y1 | -0.0003(5) | 0 |
| O2z1 | 0 | 0.0011(3) |
| O2x2 | 0 | 0.0352(5) |
| O2y2 | -0.0003(7) | 0 |
| O2z2 | 0 | 0.0008(4) |
| O2x3 | -0.0001(5) | 0 |
| O2y3 | 0 | 0.0006(6) |
| O2z3 | -0.0036(4) | 0 |
Definition of the occupation Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Wave vector code |
|---|---|---|
| Alo1 | Al | 1 |
| Alo2 | Al | 2 |
| Tio1 | Ti | 1 |
| Tio2 | Ti | 2 |
| In2o1 | In2 | 1 |
| In2o2 | In2 | 2 |
Occupation Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Alo1 | 0 | 0 |
| Alo2 | 0.256(8) | 0 |
| Tio1 | 0 | 0 |
| Tio2 | -0.242(9) | 0 |
| In2o1 | 0 | 0 |
| In2o2 | -0.014(3) | 0 |
Definition of the ADP Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Tensor element | Wave vector code |
|---|---|---|---|
| In1U111 | In1 | U11 | 1 |
| In1U221 | In1 | U22 | 1 |
| In1U331 | In1 | U33 | 1 |
| In1U121 | In1 | U12 | 1 |
| In1U131 | In1 | U13 | 1 |
| In1U231 | In1 | U23 | 1 |
| In1U112 | In1 | U11 | 2 |
| In1U222 | In1 | U22 | 2 |
| In1U332 | In1 | U33 | 2 |
| In1U122 | In1 | U12 | 2 |
| In1U132 | In1 | U13 | 2 |
| In1U232 | In1 | U23 | 2 |
| AlU111 | Al | U11 | 1 |
| AlU221 | Al | U22 | 1 |
| AlU331 | Al | U33 | 1 |
| AlU121 | Al | U12 | 1 |
| AlU131 | Al | U13 | 1 |
| AlU231 | Al | U23 | 1 |
| AlU112 | Al | U11 | 2 |
| AlU222 | Al | U22 | 2 |
| AlU332 | Al | U33 | 2 |
| AlU122 | Al | U12 | 2 |
| AlU132 | Al | U13 | 2 |
| AlU232 | Al | U23 | 2 |
| TiU111 | Ti | U11 | 1 |
| TiU221 | Ti | U22 | 1 |
| TiU331 | Ti | U33 | 1 |
| TiU121 | Ti | U12 | 1 |
| TiU131 | Ti | U13 | 1 |
| TiU231 | Ti | U23 | 1 |
| TiU112 | Ti | U11 | 2 |
| TiU222 | Ti | U22 | 2 |
| TiU332 | Ti | U33 | 2 |
| TiU122 | Ti | U12 | 2 |
| TiU132 | Ti | U13 | 2 |
| TiU232 | Ti | U23 | 2 |
| In2U111 | In2 | U11 | 1 |
| In2U221 | In2 | U22 | 1 |
| In2U331 | In2 | U33 | 1 |
| In2U121 | In2 | U12 | 1 |
| In2U131 | In2 | U13 | 1 |
| In2U231 | In2 | U23 | 1 |
| In2U112 | In2 | U11 | 2 |
| In2U222 | In2 | U22 | 2 |
| In2U332 | In2 | U33 | 2 |
| In2U122 | In2 | U12 | 2 |
| In2U132 | In2 | U13 | 2 |
| In2U232 | In2 | U23 | 2 |
ADP Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| In1U111 | 0 | 0 |
| In1U221 | 0 | 0 |
| In1U331 | 0 | 0 |
| In1U121 | 0.00003(7) | 0 |
| In1U131 | 0 | 0 |
| In1U231 | -0.00163(8) | 0 |
| In1U112 | 0.00082(11) | 0 |
| In1U222 | -0.00006(10) | 0 |
| In1U332 | 0.00084(14) | 0 |
| In1U122 | 0 | 0 |
| In1U132 | 0.00040(10) | 0 |
| In1U232 | 0 | 0 |
| AlU111 | 0 | 0 |
| AlU221 | 0 | 0 |
| AlU331 | 0 | 0 |
| AlU121 | -0.0028(3) | 0 |
| AlU131 | 0 | 0 |
| AlU231 | -0.0006(3) | 0 |
| AlU112 | 0.0033(5) | 0 |
| AlU222 | -0.0090(4) | 0 |
| AlU332 | 0.0004(4) | 0 |
| AlU122 | 0 | 0 |
| AlU132 | 0.0017(3) | 0 |
| AlU232 | 0 | 0 |
| TiU111 | 0 | 0 |
| TiU221 | 0 | 0 |
| TiU331 | 0 | 0 |
| TiU121 | -0.0028(3) | 0 |
| TiU131 | 0 | 0 |
| TiU231 | -0.0006(3) | 0 |
| TiU112 | 0.0033(5) | 0 |
| TiU222 | -0.0090(4) | 0 |
| TiU332 | 0.0004(4) | 0 |
| TiU122 | 0 | 0 |
| TiU132 | 0.0017(3) | 0 |
| TiU232 | 0 | 0 |
| In2U111 | 0 | 0 |
| In2U221 | 0 | 0 |
| In2U331 | 0 | 0 |
| In2U121 | -0.0028(3) | 0 |
| In2U131 | 0 | 0 |
| In2U231 | -0.0006(3) | 0 |
| In2U112 | 0.0033(5) | 0 |
| In2U222 | -0.0090(4) | 0 |
| In2U332 | 0.0004(4) | 0 |
| In2U122 | 0 | 0 |
| In2U132 | 0.0017(3) | 0 |
| In2U232 | 0 | 0 |
Displacive sawtooth coefficients: (Show/hide table) [ Help ]
| Atom site label | Ax | Ay | Az | Center (x0) | Width |
|---|---|---|---|---|---|
| O2 | 0 | -0.1545 | 0 | 0.75 | 0.6751 |
comp
Chemical data
Formula moiety: Al0.253 In1.046 O3.35 Ti0.701 [ Help ]
Structural Formula Sum: Al0.253 In1.046 O3.35 Ti0.701 [ Help ]
Formula weight: 214.08 Da [ Help ]
Crystallographic data and experimental details
Crystal system: monoclinic [ Help ]
Superspace group name: C2/m(0β0)s0 [ Help ]
Symmetry operations of the superspace group: (Show/hide table) [ Help ]
| Operation code | Operation in algebraic form |
|---|---|
| 1 | x1,x2,x3,x4 |
| 2 | -x1,x2,-x3,1/2+x4 |
| 3 | -x1,-x2,-x3,-x4 |
| 4 | x1,-x2,x3,1/2-x4 |
| 5 | 1/2+x1,1/2+x2,x3,x4 |
| 6 | 1/2-x1,1/2+x2,-x3,1/2+x4 |
| 7 | 1/2-x1,1/2-x2,-x3,-x4 |
| 8 | 1/2+x1,1/2-x2,x3,1/2-x4 |
a: 5.857(4) Å [ Help ]
b: 3.361(3) Å [ Help ]
c: 6.355(5) Å [ Help ]
α: 90 ° [ Help ]
β: 107.96(5) ° [ Help ]
γ: 90 ° [ Help ]
Volume: 119.00(17) Å3 [ Help ]
Z: 2 [ Help ]
Cell measurement temperature: 293 K [ Help ]
Modulation dimension: 1 [ Help ]
Number of subsystems: 2 [ Help ]
Subsystem code: 1 [ Help ]
Subsystem description: 1-st subsystem [ Help ]
W matrix:
| 1.0 | 0.0 | 0.0 | 0.0 |
| 0.0 | 1.0 | 0.0 | 0.0 |
| 0.0 | 0.0 | 1.0 | 0.0 |
| 0.0 | 0.0 | 0.0 | 1.0 |
Subsystem code: 2 [ Help ]
Subsystem description: 2-nd subsystem [ Help ]
W matrix:
| 1.0 | 0.0 | 0.0 | 0.0 |
| 0.0 | 1.0 | 0.0 | 1.0 |
| 0.0 | 0.0 | 1.0 | 0.0 |
| 0.0 | 1.0 | 0.0 | 0.0 |
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.00000 | 0.3503(5) | 0.00000 |
μ: 12.368 mm-1 [ Help ]
Absorption correction type: numerical [ Help ]
Absorption correction remarks: gaussian [ Help ]
Minimum transmission factor: 0.31 [ Help ]
Maximum transmission factor: 0.83 [ Help ]
Refinement details
Total nb. of reflections: 1733 [ Help ]
Nb. of observed reflections: 994 [ Help ]
Intense reflections threshold: I>3σ(I) [ Help ]
Refinement based on: F [ Help ]
R(all): 0.0564 [ Help ]
R(obs): 0.0322 [ Help ]
wR(obs): 0.0470 [ Help ]
wR(all): 0.0603 [ Help ]
S(all): 1.53 [ Help ]
Nb. of reflections: 1733 [ Help ]
Nb. of parameters: 57 [ Help ]
Number of restraints: 6 [ Help ]
Number of constraints: 1 [ Help ]
Weighting scheme: sigma [ Help ]
Weighting scheme remarks: w=1/(σ2(F)+0.0004F2) [ Help ]
Δ/σ(max): 0.0004 [ Help ]
Δ/σ(mean): 0.0001 [ Help ]
Δρ(max): 2.47 e_Å-3 [ Help ]
Δρ(min): -2.36 e_Å-3 [ Help ]
Extinction method: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) [ Help ]
Extinction coefficient: 0.00100(6) [ Help ]
Structural Information
Average Structure: (Show/hide table) [ Help ]
| Atom symbol | Atom site label | Subsystem | x | y | z | Uiso/equiv | ADP type | Coords from (d)iffraction or (c)alculated | Coords restraints or constraints | Occupancy | Disordered cluster | Disordered group |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| In | In1 | 1 | 0 | 0 | 0 | 0.00571(11) | Uani | d | . | 1 | . | . |
| Al | Al | 1 | 0.5 | 0 | 0.5 | 0.0100(3) | Uani | d | . | 0.255(8) | . | . |
| Ti | Ti | 1 | 0.5 | 0 | 0.5 | 0.0100(3) | Uani | d | . | 0.701(6) | . | . |
| In | In2 | 1 | 0.5 | 0 | 0.5 | 0.0100(3) | Uani | d | . | 0.044(10) | . | . |
| O | O1 | 1 | 0.3888(4) | 0 | 0.1709(4) | 0.0052(6) | Uani | d | . | 1 | . | . |
| O | O2 | 2 | 0.6597(4) | 0.25 | 0.4983(4) | 0.0181(8) | Uani | d | . | 0.5 | . | . |
ADP components: (Show/hide table) [ Help ]
| Atom site label | U11 | U22 | U33 | U12 | U13 | U23 | Atom site symbol |
|---|---|---|---|---|---|---|---|
| In1 | 0.00514(15) | 0.00373(16) | 0.0086(2) | 0 | 0.00267(11) | 0 | In |
| Al | 0.0110(4) | 0.0137(4) | 0.0045(4) | 0 | 0.0012(3) | 0 | Al |
| Ti | 0.0110(4) | 0.0137(4) | 0.0045(4) | 0 | 0.0012(3) | 0 | Ti |
| In2 | 0.0110(4) | 0.0137(4) | 0.0045(4) | 0 | 0.0012(3) | 0 | In |
| O1 | 0.0061(8) | 0.0055(10) | 0.0039(9) | 0 | 0.0011(7) | 0 | O |
| O2 | 0.0232(13) | 0.0180(10) | 0.0092(11) | 0 | -0.0007(9) | 0 | O |
Fourier Wave Vectors (explicit: q_x,q_y,q_z or coefficients: q_1,q_2,...): (Show/hide table) [ Help ]
| Wave vector code | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.00000 | 0.3503 | 0.00000 |
| 2 | 0.00000 | 0.7006 | 0.00000 |
| 3 | 0.00000 | 1.0509 | 0.00000 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| In1x1 | In1 | x | 1 |
| In1y1 | In1 | y | 1 |
| In1z1 | In1 | z | 1 |
| In1x2 | In1 | x | 2 |
| In1y2 | In1 | y | 2 |
| In1z2 | In1 | z | 2 |
| In1x3 | In1 | x | 3 |
| In1y3 | In1 | y | 3 |
| In1z3 | In1 | z | 3 |
| Alx1 | Al | x | 1 |
| Aly1 | Al | y | 1 |
| Alz1 | Al | z | 1 |
| Alx2 | Al | x | 2 |
| Aly2 | Al | y | 2 |
| Alz2 | Al | z | 2 |
| Alx3 | Al | x | 3 |
| Aly3 | Al | y | 3 |
| Alz3 | Al | z | 3 |
| Tix1 | Ti | x | 1 |
| Tiy1 | Ti | y | 1 |
| Tiz1 | Ti | z | 1 |
| Tix2 | Ti | x | 2 |
| Tiy2 | Ti | y | 2 |
| Tiz2 | Ti | z | 2 |
| Tix3 | Ti | x | 3 |
| Tiy3 | Ti | y | 3 |
| Tiz3 | Ti | z | 3 |
| In2x1 | In2 | x | 1 |
| In2y1 | In2 | y | 1 |
| In2z1 | In2 | z | 1 |
| In2x2 | In2 | x | 2 |
| In2y2 | In2 | y | 2 |
| In2z2 | In2 | z | 2 |
| In2x3 | In2 | x | 3 |
| In2y3 | In2 | y | 3 |
| In2z3 | In2 | z | 3 |
| O1x1 | O1 | x | 1 |
| O1y1 | O1 | y | 1 |
| O1z1 | O1 | z | 1 |
| O2x1 | O2 | x | 1 |
| O2y1 | O2 | y | 1 |
| O2z1 | O2 | z | 1 |
| O2x2 | O2 | x | 2 |
| O2y2 | O2 | y | 2 |
| O2z2 | O2 | z | 2 |
Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| In1x1 | 0 | 0.02003(6) |
| In1y1 | 0 | 0 |
| In1z1 | 0 | 0.00511(5) |
| In1x2 | 0 | 0 |
| In1y2 | 0 | -0.00228(7) |
| In1z2 | 0 | 0 |
| In1x3 | 0 | -0.00017(5) |
| In1y3 | 0 | 0 |
| In1z3 | 0 | -0.00004(5) |
| Alx1 | 0 | 0.0545(2) |
| Aly1 | 0 | 0 |
| Alz1 | 0 | 0.00745(13) |
| Alx2 | 0 | 0 |
| Aly2 | 0 | -0.0261(2) |
| Alz2 | 0 | 0 |
| Alx3 | 0 | -0.00243(18) |
| Aly3 | 0 | 0 |
| Alz3 | 0 | 0.00158(16) |
| Tix1 | 0 | 0.0545(2) |
| Tiy1 | 0 | 0 |
| Tiz1 | 0 | 0.00745(13) |
| Tix2 | 0 | 0 |
| Tiy2 | 0 | -0.0261(2) |
| Tiz2 | 0 | 0 |
| Tix3 | 0 | -0.00243(18) |
| Tiy3 | 0 | 0 |
| Tiz3 | 0 | 0.00158(16) |
| In2x1 | 0 | 0.0545(2) |
| In2y1 | 0 | 0 |
| In2z1 | 0 | 0.00745(13) |
| In2x2 | 0 | 0 |
| In2y2 | 0 | -0.0261(2) |
| In2z2 | 0 | 0 |
| In2x3 | 0 | -0.00243(18) |
| In2y3 | 0 | 0 |
| In2z3 | 0 | 0.00158(16) |
| O1x1 | 0 | 0.0285(4) |
| O1y1 | -0.0003(5) | 0 |
| O1z1 | 0 | 0.0011(3) |
| O2x1 | 0.0353(5) | 0 |
| O2y1 | 0 | 0.0010(9) |
| O2z1 | 0.0010(4) | 0 |
| O2x2 | 0.0014(5) | 0 |
| O2y2 | 0 | 0.0007(8) |
| O2z2 | -0.0035(4) | 0 |
Definition of the occupation Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Wave vector code |
|---|---|---|
| Alo1 | Al | 1 |
| Alo2 | Al | 2 |
| Tio1 | Ti | 1 |
| Tio2 | Ti | 2 |
| In2o1 | In2 | 1 |
| In2o2 | In2 | 2 |
Occupation Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Alo1 | 0 | 0 |
| Alo2 | 0.255(8) | 0 |
| Tio1 | 0 | 0 |
| Tio2 | -0.241(9) | 0 |
| In2o1 | 0 | 0 |
| In2o2 | -0.014(3) | 0 |
Definition of the ADP Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Tensor element | Wave vector code |
|---|---|---|---|
| In1U111 | In1 | U11 | 1 |
| In1U221 | In1 | U22 | 1 |
| In1U331 | In1 | U33 | 1 |
| In1U121 | In1 | U12 | 1 |
| In1U131 | In1 | U13 | 1 |
| In1U231 | In1 | U23 | 1 |
| In1U112 | In1 | U11 | 2 |
| In1U222 | In1 | U22 | 2 |
| In1U332 | In1 | U33 | 2 |
| In1U122 | In1 | U12 | 2 |
| In1U132 | In1 | U13 | 2 |
| In1U232 | In1 | U23 | 2 |
| AlU111 | Al | U11 | 1 |
| AlU221 | Al | U22 | 1 |
| AlU331 | Al | U33 | 1 |
| AlU121 | Al | U12 | 1 |
| AlU131 | Al | U13 | 1 |
| AlU231 | Al | U23 | 1 |
| AlU112 | Al | U11 | 2 |
| AlU222 | Al | U22 | 2 |
| AlU332 | Al | U33 | 2 |
| AlU122 | Al | U12 | 2 |
| AlU132 | Al | U13 | 2 |
| AlU232 | Al | U23 | 2 |
| TiU111 | Ti | U11 | 1 |
| TiU221 | Ti | U22 | 1 |
| TiU331 | Ti | U33 | 1 |
| TiU121 | Ti | U12 | 1 |
| TiU131 | Ti | U13 | 1 |
| TiU231 | Ti | U23 | 1 |
| TiU112 | Ti | U11 | 2 |
| TiU222 | Ti | U22 | 2 |
| TiU332 | Ti | U33 | 2 |
| TiU122 | Ti | U12 | 2 |
| TiU132 | Ti | U13 | 2 |
| TiU232 | Ti | U23 | 2 |
| In2U111 | In2 | U11 | 1 |
| In2U221 | In2 | U22 | 1 |
| In2U331 | In2 | U33 | 1 |
| In2U121 | In2 | U12 | 1 |
| In2U131 | In2 | U13 | 1 |
| In2U231 | In2 | U23 | 1 |
| In2U112 | In2 | U11 | 2 |
| In2U222 | In2 | U22 | 2 |
| In2U332 | In2 | U33 | 2 |
| In2U122 | In2 | U12 | 2 |
| In2U132 | In2 | U13 | 2 |
| In2U232 | In2 | U23 | 2 |
ADP Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| In1U111 | 0 | 0 |
| In1U221 | 0 | 0 |
| In1U331 | 0 | 0 |
| In1U121 | 0.00003(7) | 0 |
| In1U131 | 0 | 0 |
| In1U231 | -0.00164(8) | 0 |
| In1U112 | 0.00082(11) | 0 |
| In1U222 | -0.00006(10) | 0 |
| In1U332 | 0.00083(14) | 0 |
| In1U122 | 0 | 0 |
| In1U132 | 0.00039(10) | 0 |
| In1U232 | 0 | 0 |
| AlU111 | 0 | 0 |
| AlU221 | 0 | 0 |
| AlU331 | 0 | 0 |
| AlU121 | -0.0028(3) | 0 |
| AlU131 | 0 | 0 |
| AlU231 | -0.0006(3) | 0 |
| AlU112 | 0.0033(5) | 0 |
| AlU222 | -0.0090(4) | 0 |
| AlU332 | 0.0004(4) | 0 |
| AlU122 | 0 | 0 |
| AlU132 | 0.0017(3) | 0 |
| AlU232 | 0 | 0 |
| TiU111 | 0 | 0 |
| TiU221 | 0 | 0 |
| TiU331 | 0 | 0 |
| TiU121 | -0.0028(3) | 0 |
| TiU131 | 0 | 0 |
| TiU231 | -0.0006(3) | 0 |
| TiU112 | 0.0033(5) | 0 |
| TiU222 | -0.0090(4) | 0 |
| TiU332 | 0.0004(4) | 0 |
| TiU122 | 0 | 0 |
| TiU132 | 0.0017(3) | 0 |
| TiU232 | 0 | 0 |
| In2U111 | 0 | 0 |
| In2U221 | 0 | 0 |
| In2U331 | 0 | 0 |
| In2U121 | -0.0028(3) | 0 |
| In2U131 | 0 | 0 |
| In2U231 | -0.0006(3) | 0 |
| In2U112 | 0.0033(5) | 0 |
| In2U222 | -0.0090(4) | 0 |
| In2U332 | 0.0004(4) | 0 |
| In2U122 | 0 | 0 |
| In2U132 | 0.0017(3) | 0 |
| In2U232 | 0 | 0 |
Displacive sawtooth coefficients: (Show/hide table) [ Help ]
| Atom site label | Ax | Ay | Az | Center (x0) | Width |
|---|---|---|---|---|---|
| O2 | 0 | -0.1265 | 0 | 0.5 | 0.5 |