research papers
A rigid-ion lattice-dynamical treatment accounts reasonably well for most of the atomic displacement parameters (ADPs) reported in the literature for a synthetic sample of spessartine Mn3Al2Si3O12; the model accounts less well for the ADPs of the Mn atom. These results are similar to those obtained for the corresponding garnets pyrope Mg3Al2Si3O12 and almandine Fe3Al2Si3O12. The results are confirmed by a very good agreement of the lattice-dynamical estimates with the experimental values of the heat capacity that are currently available, as well as those of the Raman and infrared vibrational spectra. The anomalous behaviour of the Mn atom is reflected in the entropy values. As is the case for pyrope and almandine, here the agreement with the experimental results can be markedly improved if the existence of a low-temperature order-disorder transition concerning the Mn atom is considered. The lattice-dynamical estimates for all the atoms presented here do not agree with the corresponding ADPs obtained in a crystal structure refinement of a supposedly `pure' natural sample from Elba. In turn, these experimental ADPs do not agree with those observed for the synthetic sample, thereby showing a physical difference; such a possibility is in agreement with recent observations by other authors, who found an unexpected fluorine content in several natural specimens of spessartine. Therefore, theoretical estimates of ADPs are reliable enough to point out unexpected situations if disagreement with the observed values occurs.
Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768102017925/av0058sup1.cif | |
Structure factor file (CIF format) https://doi.org/10.1107/S0108768102017925/av0058sup2.hkl |
Computing details top
Data collection: CAD4 (Enraf Nonius); cell refinement: CAD4 (Enraf Nonius); data reduction: SDP for Windows; program(s) used to refine structure: Full-matrix least-squares (SDP for Windows); molecular graphics: SDP for Windows; software used to prepare material for publication: SDP for Windows.
(I) top
Crystal data top
Al2Mn3O12Si3 | Dx = 4.180 Mg m−3 |
Mr = 495.03 | Mo Kα radiation, λ = 0.71073 Å |
Cubic, Ia3d | Cell parameters from 25 reflections |
Hall symbol: -I 4bd 2ab 3 | θ = 12.2–22.1° |
a = 11.630 (1) Å | µ = 5.31 mm−1 |
V = 1573.0 (2) Å3 | T = 293 K |
Z = 8 | [ENTER SHAPE], orange |
F(000) = 1912 | 0.13 × 0.10 × 0.10 mm |
Data collection top
CAD4 (Enraf Nonius) diffractometer | 289 reflections with Fo > 2.0 * 3.00 * σ(Fo) |
Graphite monochromator | θmax = 40.0°, θmin = 3.0° |
ω/2θ scans | h = 0→20 |
Absorption correction: empirical (using intensity measurements) ? | k = 0→20 |
Tmin = 0.703, Tmax = 1.000 | l = 0→20 |
2701 measured reflections | 1 standard reflections every 120 min |
417 independent reflections |
Refinement top
Refinement on F | 20 constraints |
Least-squares matrix: full | |
R[F2 > 2σ(F2)] = 0.013 | (Δ/σ)max = 0.034 |
wR(F2) = 0.016 | Δρmax = 0.48 e Å−3 |
S = 0.65 | Δρmin = 0.00 e Å−3 |
259 reflections | Extinction correction: secondary Zachariasen |
40 parameters | Extinction coefficient: 0.0000 |
0 restraints |
Crystal data top
Al2Mn3O12Si3 | Z = 8 |
Mr = 495.03 | Mo Kα radiation |
Cubic, Ia3d | µ = 5.31 mm−1 |
a = 11.630 (1) Å | T = 293 K |
V = 1573.0 (2) Å3 | 0.13 × 0.10 × 0.10 mm |
Data collection top
CAD4 (Enraf Nonius) diffractometer | 417 independent reflections |
Absorption correction: empirical (using intensity measurements) ? | 289 reflections with Fo > 2.0 * 3.00 * σ(Fo) |
Tmin = 0.703, Tmax = 1.000 | 1 standard reflections every 120 min |
2701 measured reflections |
Refinement top
R[F2 > 2σ(F2)] = 0.013 | 40 parameters |
wR(F2) = 0.016 | 0 restraints |
S = 0.65 | Δρmax = 0.48 e Å−3 |
259 reflections | Δρmin = 0.00 e Å−3 |
Special details top
Refinement. Weight = (4*Fo2)/[σ2(Fo2)] (refinement on F) σ(Fo2) = [σ2(I) + (P*Fo2)2](1/2) P = 0.0100 |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
x | y | z | Uiso*/Ueq | Occ. (<1) | |
Al | 0.0000 (1) | 0.0000 (1) | 0.0000 (1) | 0.00414 (4) | -.17 |
Mn | 0.1250 (1) | 0.0000 (1) | 0.2500 (1) | 0.00832 (3) | -.26 |
Si | 0.3750 (1) | 0.0000 (1) | 0.2500 (1) | 0.00389 (6) | 0.25 |
O | 0.03473 (5) | 0.04789 (5) | 0.65210 (5) | 0.0052 (1) |
Atomic displacement parameters (Å2) top
U11 | U22 | U33 | U12 | U13 | U23 | |
AL | 0.00443 (8) | 0.0044 (1) | 0.0044 (1) | −0.0003 (1) | −0.0003 (1) | −0.0003 (1) |
Mn | 0.00476 (8) | 0.00923 (5) | 0.0092 (1) | 0.0000 (1) | 0.0000 (1) | 0.00174 (8) |
SI | 0.0035 (1) | 0.00407 (9) | 0.0041 (1) | 0.0000 (1) | 0.0000 (1) | 0.0000 (1) |
O | 0.0054 (2) | 0.0062 (2) | 0.0043 (2) | 0.0005 (2) | −0.0005 (2) | −0.0004 (2) |
Experimental details
Crystal data | |
Chemical formula | Al2Mn3O12Si3 |
Mr | 495.03 |
Crystal system, space group | Cubic, Ia3d |
Temperature (K) | 293 |
a (Å) | 11.630 (1) |
V (Å3) | 1573.0 (2) |
Z | 8 |
Radiation type | Mo Kα |
µ (mm−1) | 5.31 |
Crystal size (mm) | 0.13 × 0.10 × 0.10 |
Data collection | |
Diffractometer | CAD4 (Enraf Nonius) diffractometer |
Absorption correction | Empirical (using intensity measurements) |
Tmin, Tmax | 0.703, 1.000 |
No. of measured, independent and observed [Fo > 2.0 * 3.00 * σ(Fo)] reflections | 2701, 417, 289 |
Rint | ? |
(sin θ/λ)max (Å−1) | 0.904 |
Refinement | |
R[F2 > 2σ(F2)], wR(F2), S | 0.013, 0.016, 0.65 |
No. of reflections | 259 |
No. of parameters | 40 |
Δρmax, Δρmin (e Å−3) | 0.48, 0.00 |
Computer programs: CAD4 (Enraf Nonius), Full-matrix least-squares (SDP for Windows).