The modulated low-temperature structure of malayaite, CaSnOSiO4
Authors:Malcherek, Thomas; Paulenz, Bianca; Fischer, Michael; Paulmann, Carsten
Journal:Acta Crystallographica Section B 76 316-321 (2020)
DOI:https://doi.org/10.1107/S2052520620003807
B-IncStrDB ID: 16372EQKyWN Entry date: 2020-04-03 Last revision: 2021-12-12
I
Chemical data
Structural Formula Sum: Ca1 O5 Si1 Sn1 [ Help ]
Formula weight: 266.9 Da [ Help ]
Crystallographic data and experimental details
Crystal system: monoclinic [ Help ]
Superspace group name: C2/c(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+1/2 |
| 3 | -x1,-x2,-x3,-x4 |
| 4 | x1,-x2,x3+1/2,-x4+1/2 |
| 5 | x1+1/2,x2+1/2,x3,x4 |
| 6 | -x1+1/2,x2+1/2,-x3+1/2,x4+1/2 |
| 7 | -x1+1/2,-x2+1/2,-x3,-x4 |
| 8 | x1+1/2,-x2+1/2,x3+1/2,-x4+1/2 |
a: 6.6663(3) Å [ Help ]
b: 8.8954(4) Å [ Help ]
c: 7.1475(3) Å [ Help ]
α: 90 ° [ Help ]
β: 113.405(5) ° [ Help ]
γ: 90 ° [ Help ]
Volume: 388.97(3) Å3 [ Help ]
Modulation dimension: 1 [ Help ]
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.000000 | 0.260600 | 0.000000 |
Z: 4 [ Help ]
Cell determination reflection Nb.: 7943 [ Help ]
θ(min) for cell determination: 2.69 ° [ Help ]
θ(max) for cell determination: 51.02 ° [ Help ]
Cell measurement temperature: 20 K [ Help ]
μ: 5.527 mm-1 [ Help ]
Absorption correction type: multi-scan [ Help ]
Absorption correction remarks: CrysAlisPro 1.171.38.46 (Rigaku Oxford Diffraction, 2015) Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm. [ Help ]
Minimum transmission factor: 0.742 [ Help ]
Maximum transmission factor: 1 [ Help ]
Refinement details
Total nb. of reflections: 7250 [ Help ]
Nb. of observed reflections: 5161 [ Help ]
Intense reflections threshold: I>3σ(I) [ Help ]
Refinement based on: Fsqd [ Help ]
R(obs): 0.0436 [ Help ]
wR(obs): 0.1862 [ Help ]
R(all): 0.0490 [ Help ]
wR(all): 0.2040 [ Help ]
S(all): 1.30 [ Help ]
S(obs): 1.40 [ Help ]
Nb. of reflections: 7250 [ Help ]
Nb. of parameters: 68 [ Help ]
Weighting scheme: sigma [ Help ]
Weighting scheme remarks: w=1/(σ2(I)+0.01I2) [ Help ]
Δ/σ(max): 0.0007 [ Help ]
Δ/σ(mean): 0.0001 [ Help ]
Δρ(max): 1.48 e_Å-3 [ Help ]
Δρ(min): -2.04 e_Å-3 [ Help ]
Extinction method: B-C type 1 Lorentzian isotropic (Becker & Coppens, 1974) [ Help ]
Extinction coefficient: 9000(1200) [ 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Sn | Sn | 0 | 0 | 0 | Uani | 0.00218(5) | 4 | 1 | d | ? | ? | ? |
| Si | Si | 0 | 0.68161(8) | 0.25 | Uani | 0.00251(8) | 4 | 1 | d | ? | ? | ? |
| Ca | Ca | 0 | 0.33686(4) | 0.25 | Uani | 0.00636(6) | 4 | 1 | d | ? | ? | ? |
| O1 | O | 0 | 0.08680(8) | 0.25 | Uani | 0.00419(13) | 4 | 1 | d | ? | ? | ? |
| O2 | O | 0.32451(8) | 0.06735(6) | 0.08692(6) | Uani | 0.00470(10) | 8 | 1 | d | ? | ? | ? |
| O3 | O | 0.39036(8) | 0.28755(6) | 0.37253(6) | Uani | 0.00441(10) | 8 | 1 | d | ? | ? | ? |
ADP components: (Show/hide table) [ Help ]
| Atom site label | Atom site symbol | U11 | U22 | U33 | U12 | U13 | U23 |
|---|---|---|---|---|---|---|---|
| Sn | Sn | 0.00195(7) | 0.00243(7) | 0.00197(6) | -0.000036(7) | 0.00059(4) | -0.000037(7) |
| Si | Si | 0.00203(12) | 0.00273(16) | 0.00246(9) | 0 | 0.00057(7) | 0 |
| Ca | Ca | 0.00311(9) | 0.00301(9) | 0.01036(8) | 0 | -0.00008(6) | 0 |
| O1 | O | 0.0063(2) | 0.0032(2) | 0.00339(13) | 0 | 0.00219(12) | 0 |
| O2 | O | 0.00358(15) | 0.00427(16) | 0.00513(11) | -0.00070(10) | 0.00053(9) | -0.00116(9) |
| O3 | O | 0.00412(15) | 0.00376(18) | 0.00522(12) | -0.00012(9) | 0.00172(9) | -0.00076(9) |
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 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| Snx1 | Sn | x | 1 |
| Sny1 | Sn | y | 1 |
| Snz1 | Sn | z | 1 |
| Six1 | Si | x | 1 |
| Siy1 | Si | y | 1 |
| Siz1 | Si | z | 1 |
| Cax1 | Ca | x | 1 |
| Cay1 | Ca | y | 1 |
| Caz1 | Ca | z | 1 |
| O1x1 | O1 | x | 1 |
| O1y1 | O1 | y | 1 |
| O1z1 | O1 | z | 1 |
| O2x1 | O2 | x | 1 |
| O2y1 | O2 | y | 1 |
| O2z1 | O2 | z | 1 |
| O3x1 | O3 | x | 1 |
| O3y1 | O3 | y | 1 |
| O3z1 | O3 | z | 1 |
Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Snx1 | 0 | -0.001232(7) |
| Sny1 | 0 | 0.000334(3) |
| Snz1 | 0 | 0.001413(7) |
| Six1 | 0.00050(3) | -0.00142(3) |
| Siy1 | 0 | 0 |
| Siz1 | 0.00014(2) | 0.00129(2) |
| Cax1 | 0.001127(18) | -0.001361(19) |
| Cay1 | 0 | 0 |
| Caz1 | -0.00415(2) | 0.00326(2) |
| O1x1 | 0.00092(6) | -0.00137(6) |
| O1y1 | 0 | 0 |
| O1z1 | -0.00011(5) | 0.00137(5) |
| O2x1 | -0.00006(4) | -0.00127(4) |
| O2y1 | 0.00099(3) | -0.00005(3) |
| O2z1 | -0.00161(4) | 0.00124(4) |
| O3x1 | 0.00102(4) | -0.00152(4) |
| O3y1 | -0.00026(3) | -0.00016(3) |
| O3z1 | 0.00038(4) | 0.00141(4) |
II
Chemical data
Structural Formula Sum: Ca1 O5 Si1 Sn1 [ Help ]
Formula weight: 266.9 Da [ Help ]
Crystallographic data and experimental details
Crystal system: monoclinic [ Help ]
Space group name (H-M): C 1 2/c 1 [ Help ]
Space group name (Hall): -C 2yc [ Help ]
Space group nb.: 15 [ Help ]
Symmetry operations of the space group: (Show/hide table) [ Help ]
| Operation code | Operation in algebraic form |
|---|---|
| 1 | x,y,z |
| 2 | -x,y,-z+1/2 |
| 3 | -x,-y,-z |
| 4 | x,-y,z+1/2 |
| 5 | x+1/2,y+1/2,z |
| 6 | -x+1/2,y+1/2,-z+1/2 |
| 7 | -x+1/2,-y+1/2,-z |
| 8 | x+1/2,-y+1/2,z+1/2 |
a: 6.6667(2) Å [ Help ]
b: 8.8934(3) Å [ Help ]
c: 7.1520(3) Å [ Help ]
α: 90 ° [ Help ]
β: 113.323(3) ° [ Help ]
γ: 90 ° [ Help ]
Volume: 389.39(3) Å3 [ Help ]
Z: 4 [ Help ]
Cell determination reflection Nb.: 11467 [ Help ]
θ(min) for cell determination: 3.67 ° [ Help ]
θ(max) for cell determination: 51 ° [ Help ]
Cell measurement temperature: 298 K [ Help ]
μ: 5.521 mm-1 [ Help ]
Absorption correction type: multi-scan [ Help ]
Absorption correction remarks: CrysAlisPro 1.171.38.46 (Rigaku Oxford Diffraction, 2015) Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm. [ Help ]
Minimum transmission factor: 0.754 [ Help ]
Maximum transmission factor: 1 [ Help ]
Refinement details
Total nb. of reflections: 2748 [ Help ]
Nb. of observed reflections: 2651 [ Help ]
Intense reflections threshold: I>3σ(I) [ Help ]
Refinement based on: Fsqd [ Help ]
R(obs): 0.0258 [ Help ]
wR(obs): 0.1104 [ Help ]
R(all): 0.0263 [ Help ]
wR(all): 0.1127 [ Help ]
S(all): 1.06 [ Help ]
S(obs): 1.05 [ Help ]
Nb. of reflections: 2748 [ Help ]
Nb. of parameters: 41 [ Help ]
Weighting scheme: sigma [ Help ]
Weighting scheme remarks: w=1/(σ2(I)+0.01I2) [ Help ]
Δ/σ(max): 0.0007 [ Help ]
Δ/σ(mean): 0.0001 [ Help ]
Δρ(max): 0.70 e_Å-3 [ Help ]
Δρ(min): -0.67 e_Å-3 [ Help ]
Extinction method: B-C type 1 Lorentzian isotropic (Becker & Coppens, 1974) [ Help ]
Extinction coefficient: 5800(900) [ 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Sn | Sn | 0 | 0 | 0 | Uani | 0.00385(4) | 4 | 1 | d | ? | ? | ? |
| Si | Si | 0 | 0.68145(5) | 0.25 | Uani | 0.00444(6) | 4 | 1 | d | ? | ? | ? |
| Ca | Ca | 0 | 0.33729(4) | 0.25 | Uani | 0.01704(7) | 4 | 1 | d | ? | ? | ? |
| O1 | O | 0 | 0.08665(6) | 0.25 | Uani | 0.00729(10) | 4 | 1 | d | ? | ? | ? |
| O2 | O | 0.32452(6) | 0.06780(5) | 0.08695(6) | Uani | 0.00756(7) | 8 | 1 | d | ? | ? | ? |
| O3 | O | 0.39029(6) | 0.28799(4) | 0.37214(5) | Uani | 0.00670(8) | 8 | 1 | d | ? | ? | ? |
ADP components: (Show/hide table) [ Help ]
| Atom site label | Atom site symbol | U11 | U22 | U33 | U12 | U13 | U23 |
|---|---|---|---|---|---|---|---|
| Sn | Sn | 0.00400(5) | 0.00386(5) | 0.00362(5) | -0.000007(5) | 0.00145(4) | -0.000202(5) |
| Si | Si | 0.00380(8) | 0.00502(13) | 0.00446(8) | 0 | 0.00157(6) | 0 |
| Ca | Ca | 0.00667(7) | 0.00372(8) | 0.03245(15) | 0 | -0.00108(7) | 0 |
| O1 | O | 0.01245(16) | 0.00528(15) | 0.00510(12) | 0 | 0.00450(11) | 0 |
| O2 | O | 0.00522(10) | 0.00704(11) | 0.00912(11) | -0.00141(7) | 0.00147(7) | -0.00274(8) |
| O3 | O | 0.00687(10) | 0.00537(13) | 0.00879(11) | -0.00077(7) | 0.00408(8) | -0.00228(7) |