Three-dimensional electron diffraction on clinkers: the belite α'H incommensurate modulated structure
Authors:Plana-Ruiz, Sergi ; Gotz, Emilia; Neumann, Thomas; Schwesig, Peter; Kolb, Ute
Journal:Acta Crystallographica Section B 80 105-116 (2024)
DOI:https://doi.org/10.1107/S205252062400146X
B-IncStrDB ID: 7bhGderGvHs Entry date: 2024-03-06 Last revision: 2024-07-10
0k_average_dyn
Chemical data
Structural Formula Sum: Ca8 O16 Si4 [ Help ]
Formula weight: 689 Da [ Help ]
Absolute configuration: . [ Help ]
Crystallographic data and experimental details
Crystal system: orthorhombic [ Help ]
Space group name (H-M): P n m a [ Help ]
Space group name (Hall): -P -2xabc;-2yb;-2zac [ Help ]
Space group nb.: 62 [ Help ]
Symmetry operations of the space group: (Show/hide table) [ Help ]
| Operation code | Operation in algebraic form |
|---|---|
| 1 | x,y,z |
| 2 | -x+1/2,-y,z+1/2 |
| 3 | -x,y+1/2,-z |
| 4 | x+1/2,-y+1/2,-z+1/2 |
| 5 | -x,-y,-z |
| 6 | x+1/2,y,-z+1/2 |
| 7 | x,-y+1/2,z |
| 8 | -x+1/2,y+1/2,z+1/2 |
a: 6.776 Å [ Help ]
b: 5.496 Å [ Help ]
c: 9.252 Å [ Help ]
α: 90 ° [ Help ]
β: 90 ° [ Help ]
γ: 90 ° [ Help ]
Volume: 344.5527 Å3 [ Help ]
Z: 1 [ Help ]
μ: 0 mm-1 [ Help ]
Refinement details
Total nb. of reflections: 2439 [ Help ]
Nb. of observed reflections: 1709 [ Help ]
Intense reflections threshold: I>3σ(I) [ Help ]
Refinement based on: F [ Help ]
R(obs): 0.0557 [ Help ]
wR(obs): 0.0562 [ Help ]
R(all): 0.0787 [ Help ]
wR(all): 0.0585 [ Help ]
S(all): 2.03 [ Help ]
S(obs): 1.77 [ Help ]
Nb. of reflections: 2439 [ Help ]
Nb. of parameters: 137 [ Help ]
Number of restraints: 0 [ Help ]
Number of constraints: 0 [ Help ]
Weighting scheme: sigma [ Help ]
Weighting scheme remarks: w=1/(σ2(F)+0.0001F2) [ Help ]
Δ/σ(max): 0.0325 [ Help ]
Δ/σ(mean): 0.0029 [ Help ]
Extinction method: none [ Help ]
Structural Information
Average Structure: (Show/hide table) [ 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Ca1 | Ca | 0.66658(12) | 0.75 | 0.5706(2) | Uani | 0.0251(6) | 4 | 1 | d | . | . | . |
| Ca2 | Ca | 0.49080(11) | 0.25 | 0.79563(19) | Uani | 0.0161(5) | 4 | 1 | d | . | . | . |
| Si1 | Si | 0.78069(16) | 0.25 | 0.4128(3) | Uani | 0.0158(7) | 4 | 1 | d | . | . | . |
| O1 | O | 0.7521(6) | 0.5203(6) | 0.8014(7) | Uani | 0.0258(18) | 8 | 0.621(4) | d | . | . | . |
| O2 | O | 0.6574(3) | 0.3219(4) | 0.5622(7) | Uani | 0.030(2) | 8 | 0.5 | d | . | . | . |
| O3 | O | 1.0073(3) | 0.3122(5) | 0.4500(7) | Uani | 0.024(2) | 8 | 0.5 | d | . | . | . |
| O1_2 | O | 0.8219(9) | 0.5103(11) | 0.8563(14) | Uani | 0.0258(18) | 8 | 0.379(2) | d | . | . | . |
ADP components: (Show/hide table) [ Help ]
| Atom site label | Atom site symbol | U11 | U22 | U33 | U12 | U13 | U23 |
|---|---|---|---|---|---|---|---|
| Ca1 | Ca | 0.0123(4) | 0.0387(6) | 0.0244(17) | 0 | -0.0005(6) | 0 |
| Ca2 | Ca | 0.0090(4) | 0.0275(5) | 0.0118(14) | 0 | -0.0004(5) | 0 |
| Si1 | Si | 0.0114(5) | 0.0201(7) | 0.016(2) | 0 | 0.0002(7) | 0 |
| O1 | O | 0.026(2) | 0.0194(9) | 0.032(5) | -0.0089(13) | 0.0070(18) | -0.0099(17) |
| O2 | O | 0.0141(11) | 0.037(2) | 0.039(6) | -0.0012(8) | 0.0088(17) | 0.0096(17) |
| O3 | O | 0.0159(11) | 0.042(3) | 0.014(5) | -0.0063(8) | 0.0023(15) | -0.0050(14) |
| O1_2 | O | 0.026(2) | 0.0194(9) | 0.032(5) | -0.0089(13) | 0.0070(18) | -0.0099(17) |
0k_modulated_dyn
Chemical data
Structural Formula Sum: Ca8 O16 Si4 [ Help ]
Formula weight: 689 Da [ Help ]
Absolute configuration: . [ Help ]
Crystallographic data and experimental details
Crystal system: orthorhombic [ Help ]
Superspace group name: Pnma(α00)0ss [ Help ]
Symmetry operations of the superspace group: (Show/hide table) [ Help ]
| Operation code | Operation in algebraic form |
|---|---|
| 1 | x1,x2,x3,x4 |
| 2 | -x1+1/2,-x2,x3+1/2,-x4+1/2 |
| 3 | -x1,x2+1/2,-x3,-x4+1/2 |
| 4 | x1+1/2,-x2+1/2,-x3+1/2,x4 |
| 5 | -x1,-x2,-x3,-x4 |
| 6 | x1+1/2,x2,-x3+1/2,x4+1/2 |
| 7 | x1,-x2+1/2,x3,x4+1/2 |
| 8 | -x1+1/2,x2+1/2,x3+1/2,-x4 |
a: 6.776 Å [ Help ]
b: 5.496 Å [ Help ]
c: 9.252 Å [ Help ]
α: 90 ° [ Help ]
β: 90 ° [ Help ]
γ: 90 ° [ Help ]
Volume: 344.5527 Å3 [ Help ]
Modulation dimension: 1 [ Help ]
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.372500 | 0.000000 | 0.000000 |
Z: 1 [ Help ]
Cell measurement temperature: 293 K [ Help ]
μ: 0 mm-1 [ Help ]
Refinement details
Total nb. of reflections: 7296 [ Help ]
Nb. of observed reflections: 3733 [ Help ]
Intense reflections threshold: I>3σ(I) [ Help ]
Refinement based on: F [ Help ]
R(obs): 0.1228 [ Help ]
wR(obs): 0.1122 [ Help ]
R(all): 0.1824 [ Help ]
wR(all): 0.1197 [ Help ]
S(all): 2.38 [ Help ]
S(obs): 3.10 [ Help ]
Nb. of reflections: 7296 [ Help ]
Nb. of parameters: 126 [ Help ]
Number of restraints: 0 [ Help ]
Number of constraints: 0 [ Help ]
Weighting scheme: sigma [ Help ]
Weighting scheme remarks: w=1/(σ2(F)+0.0001F2) [ Help ]
Δ/σ(max): 0.0401 [ Help ]
Δ/σ(mean): 0.0059 [ Help ]
Δρ(max): 21.89 e_Å-3 [ Help ]
Δρ(min): -5.27 e_Å-3 [ Help ]
Extinction method: none [ Help ]
Structural Information
Average Structure: (Show/hide table) [ 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Ca1 | Ca | 1.16654(15) | 0.75 | 0.5714(2) | Uiso | 0.0130(3) | 4 | 1 | d | . | . | . |
| Ca2 | Ca | 1.00881(13) | 0.75 | 0.2045(2) | Uiso | 0.0069(3) | 4 | 1 | d | . | . | . |
| Si1 | Si | 0.7195(2) | 0.75 | 0.5881(4) | Uiso | 0.0100(4) | 4 | 1 | d | . | . | . |
| O1 | O | 0.7772(3) | 0.9827(3) | 0.6781(5) | Uiso | 0.0150(5) | 8 | 1 | d | . | . | . |
| O2 | O | 0.8422(4) | 0.6772(5) | 0.4352(7) | Uiso | 0.0215(7) | 8 | 0.5 | d | . | . | . |
| O3 | O | 0.4913(4) | 0.8101(4) | 0.5485(6) | Uiso | 0.0194(7) | 8 | 0.5 | d | . | . | . |
Fourier Wave Vectors (explicit: q_x,q_y,q_z or coefficients: q_1,q_2,...): (Show/hide table) [ Help ]
| Wave vector code | q_1 |
|---|---|
| 1 | 1 |
Occupation crenel coefficients: (Show/hide table) [ Help ]
| Atom site label | Center (x0) | Width |
|---|---|---|
| O2 | 0.0025(18) | 0.5 |
| O3 | 0.715(2) | 0.5 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| Ca1x1 | Ca1 | x | 1 |
| Ca1y1 | Ca1 | y | 1 |
| Ca1z1 | Ca1 | z | 1 |
| Ca2x1 | Ca2 | x | 1 |
| Ca2y1 | Ca2 | y | 1 |
| Ca2z1 | Ca2 | z | 1 |
| Si1x1 | Si1 | x | 1 |
| Si1y1 | Si1 | y | 1 |
| Si1z1 | Si1 | z | 1 |
| O1x1 | O1 | x | 1 |
| O1y1 | O1 | y | 1 |
| O1z1 | O1 | z | 1 |
Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Ca1x1 | 0 | 0 |
| Ca1y1 | 0.0281(3) | -0.0237(3) |
| Ca1z1 | 0 | 0 |
| Ca2x1 | 0 | 0 |
| Ca2y1 | -0.0154(3) | -0.0325(3) |
| Ca2z1 | 0 | 0 |
| Si1x1 | 0 | 0 |
| Si1y1 | -0.0170(4) | -0.0178(4) |
| Si1z1 | 0 | 0 |
| O1x1 | 0.0382(5) | -0.0264(5) |
| O1y1 | 0.0049(5) | -0.0207(5) |
| O1z1 | -0.0365(7) | 0.0096(8) |
2p5K_average_dyn
Chemical data
Structural Formula Sum: Ca8 O16 Si4 [ Help ]
Formula weight: 689 Da [ Help ]
Absolute configuration: . [ Help ]
Crystallographic data and experimental details
Crystal system: orthorhombic [ Help ]
Space group name (H-M): P n m a [ Help ]
Space group name (Hall): -P -2xabc;-2yb;-2zac [ Help ]
Space group nb.: 62 [ Help ]
Symmetry operations of the space group: (Show/hide table) [ Help ]
| Operation code | Operation in algebraic form |
|---|---|
| 1 | x,y,z |
| 2 | -x+1/2,-y,z+1/2 |
| 3 | -x,y+1/2,-z |
| 4 | x+1/2,-y+1/2,-z+1/2 |
| 5 | -x,-y,-z |
| 6 | x+1/2,y,-z+1/2 |
| 7 | x,-y+1/2,z |
| 8 | -x+1/2,y+1/2,z+1/2 |
a: 6.765 Å [ Help ]
b: 5.514 Å [ Help ]
c: 9.25 Å [ Help ]
α: 90 ° [ Help ]
β: 90 ° [ Help ]
γ: 90 ° [ Help ]
Volume: 345.0454 Å3 [ Help ]
Z: 1 [ Help ]
μ: 0 mm-1 [ Help ]
Refinement details
Total nb. of reflections: 1995 [ Help ]
Nb. of observed reflections: 1488 [ Help ]
Intense reflections threshold: I>3σ(I) [ Help ]
Refinement based on: F [ Help ]
R(obs): 0.0550 [ Help ]
wR(obs): 0.0607 [ Help ]
R(all): 0.0708 [ Help ]
wR(all): 0.0623 [ Help ]
S(all): 2.37 [ Help ]
S(obs): 2.09 [ Help ]
Nb. of reflections: 1995 [ Help ]
Nb. of parameters: 143 [ Help ]
Number of restraints: 0 [ Help ]
Number of constraints: 0 [ Help ]
Weighting scheme: sigma [ Help ]
Weighting scheme remarks: w=1/(σ2(F)+0.0001F2) [ Help ]
Δ/σ(max): 0.0417 [ Help ]
Δ/σ(mean): 0.0057 [ Help ]
Extinction method: none [ Help ]
Structural Information
Average Structure: (Show/hide table) [ 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Ca1 | Ca | 0.16773(15) | 0.75 | 0.42906(13) | Uani | 0.0256(5) | 4 | 1 | d | . | . | . |
| Ca2 | Ca | 0.50905(13) | 0.75 | 0.70488(13) | Uani | 0.0172(4) | 4 | 1 | d | . | . | . |
| Si1 | Si | 0.28113(18) | 0.25 | 0.58717(17) | Uani | 0.0170(6) | 4 | 1 | d | . | . | . |
| O1 | O | 0.7470(7) | 0.4794(8) | 0.8050(5) | Uani | 0.0313(14) | 8 | 0.647(5) | d | . | . | . |
| O2 | O | 0.4946(5) | 0.770(4) | 0.4509(4) | Uani | 0.095(3) | 8 | 0.5 | d | . | . | . |
| O3 | O | 0.1579(4) | 0.3184(9) | 0.4389(4) | Uani | 0.032(2) | 8 | 0.5 | d | . | . | . |
| O1_2 | O | 0.6761(12) | 0.4871(16) | 0.8553(12) | Uani | 0.0313(14) | 8 | 0.353(2) | d | . | . | . |
ADP components: (Show/hide table) [ Help ]
| Atom site label | Atom site symbol | U11 | U22 | U33 | U12 | U13 | U23 |
|---|---|---|---|---|---|---|---|
| Ca1 | Ca | 0.0156(5) | 0.0412(11) | 0.0200(8) | 0 | 0.0016(5) | 0 |
| Ca2 | Ca | 0.0114(5) | 0.0286(8) | 0.0117(6) | 0 | -0.0009(4) | 0 |
| Si1 | Si | 0.0146(7) | 0.0258(13) | 0.0106(10) | 0 | -0.0008(6) | 0 |
| O1 | O | 0.030(2) | 0.0249(19) | 0.039(3) | -0.0082(18) | -0.0135(17) | 0.0129(19) |
| O2 | O | 0.0247(17) | 0.239(10) | 0.020(2) | 0.067(6) | 0.0038(14) | 0.007(7) |
| O3 | O | 0.0181(13) | 0.060(6) | 0.018(2) | 0.0032(17) | -0.0090(12) | -0.0079(17) |
| O1_2 | O | 0.030(2) | 0.0249(19) | 0.039(3) | -0.0082(18) | -0.0135(17) | 0.0129(19) |
2p5K_modulated_dyn
Chemical data
Structural Formula Sum: Ca8 O16 Si4 [ Help ]
Formula weight: 689 Da [ Help ]
Absolute configuration: . [ Help ]
Crystallographic data and experimental details
Crystal system: orthorhombic [ Help ]
Superspace group name: Pnma(α00)0ss [ Help ]
Symmetry operations of the superspace group: (Show/hide table) [ Help ]
| Operation code | Operation in algebraic form |
|---|---|
| 1 | x1,x2,x3,x4 |
| 2 | -x1+1/2,-x2,x3+1/2,-x4+1/2 |
| 3 | -x1,x2+1/2,-x3,-x4+1/2 |
| 4 | x1+1/2,-x2+1/2,-x3+1/2,x4 |
| 5 | -x1,-x2,-x3,-x4 |
| 6 | x1+1/2,x2,-x3+1/2,x4+1/2 |
| 7 | x1,-x2+1/2,x3,x4+1/2 |
| 8 | -x1+1/2,x2+1/2,x3+1/2,-x4 |
a: 6.765 Å [ Help ]
b: 5.514 Å [ Help ]
c: 9.25 Å [ Help ]
α: 90 ° [ Help ]
β: 90 ° [ Help ]
γ: 90 ° [ Help ]
Volume: 345.0454 Å3 [ Help ]
Modulation dimension: 1 [ Help ]
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.379500 | 0.000000 | 0.000000 |
Z: 1 [ Help ]
Cell measurement temperature: 293 K [ Help ]
μ: 0 mm-1 [ Help ]
Refinement details
Total nb. of reflections: 6997 [ Help ]
Nb. of observed reflections: 3076 [ Help ]
Intense reflections threshold: I>3σ(I) [ Help ]
Refinement based on: F [ Help ]
R(obs): 0.0964 [ Help ]
wR(obs): 0.0985 [ Help ]
R(all): 0.1694 [ Help ]
wR(all): 0.1049 [ Help ]
S(all): 2.22 [ Help ]
S(obs): 3.14 [ Help ]
Nb. of reflections: 6997 [ Help ]
Nb. of parameters: 129 [ Help ]
Number of restraints: 0 [ Help ]
Number of constraints: 0 [ Help ]
Weighting scheme: sigma [ Help ]
Weighting scheme remarks: w=1/(σ2(F)+0.0001F2) [ Help ]
Δ/σ(max): 0.0248 [ Help ]
Δ/σ(mean): 0.0043 [ Help ]
Extinction method: none [ Help ]
Structural Information
Average Structure: (Show/hide table) [ 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Ca1 | Ca | 0.49106(12) | 0.75 | 0.20467(11) | Uiso | 0.0091(2) | 4 | 1 | d | . | . | . |
| Ca2 | Ca | 0.83234(13) | 0.75 | -0.07067(11) | Uiso | 0.0169(3) | 4 | 1 | d | . | . | . |
| Si1 | Si | 0.21886(16) | 0.25 | 0.41267(15) | Uiso | 0.0101(3) | 4 | 1 | d | . | . | . |
| O1 | O | 0.2760(3) | 0.4818(4) | 0.3217(2) | Uiso | 0.0278(5) | 8 | 1 | d | . | . | . |
| O2 | O | 0.6575(3) | 0.8153(5) | 0.4402(3) | Uiso | 0.0261(6) | 8 | 0.5 | d | . | . | . |
| O3 | O | 0.5086(3) | 0.8056(5) | -0.0482(3) | Uiso | 0.0270(7) | 8 | 0.5 | d | . | . | . |
Fourier Wave Vectors (explicit: q_x,q_y,q_z or coefficients: q_1,q_2,...): (Show/hide table) [ Help ]
| Wave vector code | q_1 |
|---|---|
| 1 | 1 |
Occupation crenel coefficients: (Show/hide table) [ Help ]
| Atom site label | Center (x0) | Width |
|---|---|---|
| O2 | 0.496(2) | 0.5 |
| O3 | 0.777(2) | 0.5 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| Ca1x1 | Ca1 | x | 1 |
| Ca1y1 | Ca1 | y | 1 |
| Ca1z1 | Ca1 | z | 1 |
| Ca2x1 | Ca2 | x | 1 |
| Ca2y1 | Ca2 | y | 1 |
| Ca2z1 | Ca2 | z | 1 |
| Si1x1 | Si1 | x | 1 |
| Si1y1 | Si1 | y | 1 |
| Si1z1 | Si1 | z | 1 |
| O1x1 | O1 | x | 1 |
| O1y1 | O1 | y | 1 |
| O1z1 | O1 | z | 1 |
Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Ca1x1 | 0 | 0 |
| Ca1y1 | -0.0105(4) | 0.0274(3) |
| Ca1z1 | 0 | 0 |
| Ca2x1 | 0 | 0 |
| Ca2y1 | -0.0231(3) | -0.0174(4) |
| Ca2z1 | 0 | 0 |
| Si1x1 | 0 | 0 |
| Si1y1 | 0.0209(5) | 0.0141(5) |
| Si1z1 | 0 | 0 |
| O1x1 | -0.0333(4) | 0.0257(4) |
| O1y1 | -0.0025(6) | 0.0194(6) |
| O1z1 | -0.0292(3) | 0.0106(4) |