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The possible occurrence of static/dynamic disorder at the Mg site in pyrope (Mg3Al2Si3O12), with or without anharmonic contribution to the thermal vibrations even at low temperatures, has been largely debated but conclusions were contrasting. Here a report is given on the experimental charge density distribution, ρEXP, of synthetic pyrope at T = 30 K, built through a Stewart multipolar expansion up to l = 5 and based on a very precise and accurate set of in-home measured single-crystal X-ray diffraction amplitudes with a maximum resolution of 0.44 Å. Local and integral topological properties of ρEXP are in substantial agreement with those of ρTHEO, the corresponding DFT-grade quantum charge density of an ideal pyrope crystal, and those derived from synchrotron investigations of chemical bonding in olivines. Relevant thermal atomic displacements, probably anharmonic in nature, clearly affect the whole structure down to 30 K. No significant (> 2.5σ) residual Fourier peaks are detectable from the ρEXP distribution around Mg, after least-squares refinement of a multipole model with anharmonic thermal motion at the Mg site. Experimental findings were confirmed by a full analysis of normal vibration modes of the DFT-optimized structure of the perfect pyrope crystal. Mg undergoes wide displacements from its equilibrium position even at very low temperatures, as it is allocated in a ∼ 4.5 Å large dodecahedral cavity and involved in several soft phonon modes. Implications on the interplay among static/dynamic disorder of Mg and lattice vibrational degrees of freedom are discussed.

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Symmetry-independent reflections and structural data for VALRAY2000, used to build a multipole model for the charge density of the title compound

CCDC reference: 1545443

Computing details top

Program(s) used to solve structure: SHELXS97 (Sheldrick, 1990); program(s) used to refine structure: VALRAY2000 (Stewart, Spackman & Flensburg, 2000)'.

(I) top
Crystal data top
2(AL)3(MG)3(SIO4)Mo Kα radiation, λ = 0.71073 Å
Mr = 403.16Cell parameters from 406 reflections
Cubic, Ia3dθ = 11.0–53.5°
a = 11.4405 (3) ŵ = 1.22 mm1
V = 1497.39 (12) Å3T = 30 K
Z = 8Sphere, colourless
F(000) = 16000.45 × 0.45 × 0.45 × 0.45 (radius) mm
Dx = 3.576 Mg m3
Data collection top
Syntex P1-
Rint = 0.013
Graphite monochromatorθmax = 54.5°, θmin = 1.0°
2θ/ω scansh = 026
Absorption correction: for a sphere
TBAR, home written program
k = 018
Tmin = 0.668, Tmax = 0.687l = 014
7486 measured reflections3 standard reflections every 97 reflections
788 independent reflections intensity decay: none
785 reflections with > 0
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.008
wR(F2) = 0.008(Δ/σ)max = 0.001
S = 0.76Δρmax = 0.12 e Å3
785 reflectionsΔρmin = 0.16 e Å3
93 parametersExtinction correction: type 1
0 restraintsExtinction coefficient: 0.248
Special details top

Experimental. To determine the cell dimensions 406 reflections were centered in both negative and positive 2theta regions. A least-square fit to the resulting values of (sin(theta))**2 gave the reported cell parameters.

Refinement. Refinement of F2 against ALL reflections. To adjust for the deviations from kinematic theory, the formalism of Becker and Coppens was used, assuming type I crystals and a Lorentzian "mosaic" distribution.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
O10.03282 (3)0.05077 (3)0.65326 (3)0.00319
Atomic displacement parameters (Å2) top
Al10.00217 (4)0.00217 (4)0.00217 (4)0.00001 (2)0.00001 (2)0.00001 (2)
Mg10.00485 (7)0.00485 (7)0.00298 (8)0.00096 (5)0.00000.0000
Si10.00180 (2)0.00180 (2)0.00153 (2)0.00000.00000.0000
O10.00321 (4)0.00375 (4)0.00261 (4)0.00040 (2)0.00057 (2)0.00009 (2)
Geometric parameters (Å, º) top
Al1—O1i1.8848 (3)Mg1—O1v2.3326 (4)
Al1—O1ii1.8848 (3)Mg1—O1xvi2.3326 (4)
Al1—O1iii1.8848 (3)Mg1—O1xvii2.3326 (4)
Al1—O1iv1.8848 (3)Mg1—Si12.8601 (1)
Al1—O1v1.8848 (3)Mg1—Si1v2.8601 (1)
Al1—O1vi1.8848 (3)Mg1—Al1xviii3.1977 (1)
Al1—Mg1vii3.1977 (1)Mg1—Al1xix3.1977 (1)
Al1—Mg1viii3.1977 (1)Si1—O1xx1.6354 (4)
Al1—Mg1ix3.1977 (1)Si1—O1xiii1.6354 (4)
Al1—Mg1x3.1977 (1)Si1—O1xxi1.6354 (4)
Al1—Mg1xi3.1977 (1)Si1—O1xii1.6354 (4)
Al1—Mg13.1977 (1)Si1—Mg1xvi2.8601 (1)
Mg1—O1xii2.1960 (4)O1—Si1xxii1.6354 (4)
Mg1—O1xiii2.1960 (4)O1—Al1vi1.8848 (3)
Mg1—O1iii2.1960 (4)O1—Mg1xxii2.1960 (4)
Mg1—O1xiv2.1960 (4)O1—Mg1xvi2.3326 (4)
Mg1—O1xv2.3326 (4)
O1i—Al1—O1ii180.0 (2)O1xiii—Mg1—O1v93.640 (10)
O1i—Al1—O1iii87.70 (2)O1iii—Mg1—O1v70.370 (10)
O1ii—Al1—O1iii92.30 (2)O1xiv—Mg1—O1v124.330 (10)
O1i—Al1—O1iv92.30 (2)O1xv—Mg1—O1v164.080 (10)
O1ii—Al1—O1iv87.70 (2)O1xii—Mg1—O1xvi124.330 (10)
O1iii—Al1—O1iv180.0 (2)O1xiii—Mg1—O1xvi70.370 (10)
O1i—Al1—O1v87.70 (2)O1iii—Mg1—O1xvi93.640 (10)
O1ii—Al1—O1v92.30 (2)O1xiv—Mg1—O1xvi73.070 (10)
O1iii—Al1—O1v87.70 (2)O1xv—Mg1—O1xvi109.490 (10)
O1iv—Al1—O1v92.30 (2)O1v—Mg1—O1xvi72.830 (10)
O1i—Al1—O1vi92.30 (2)O1xii—Mg1—O1xvii70.370 (10)
O1ii—Al1—O1vi87.70 (2)O1xiii—Mg1—O1xvii124.330 (10)
O1iii—Al1—O1vi92.30 (2)O1iii—Mg1—O1xvii73.070 (10)
O1iv—Al1—O1vi87.70 (2)O1xiv—Mg1—O1xvii93.640 (10)
O1v—Al1—O1vi180.0 (2)O1xv—Mg1—O1xvii72.830 (10)
O1i—Al1—Mg1vii87.690 (10)O1v—Mg1—O1xvii109.490 (10)
O1ii—Al1—Mg1vii92.310 (10)O1xvi—Mg1—O1xvii164.080 (10)
O1iii—Al1—Mg1vii137.990 (10)O1xii—Mg1—Si134.700 (10)
O1iv—Al1—Mg1vii42.010 (10)O1xiii—Mg1—Si134.700 (10)
O1v—Al1—Mg1vii133.770 (10)O1iii—Mg1—Si1145.300 (10)
O1vi—Al1—Mg1vii46.230 (10)O1xiv—Mg1—Si1145.300 (10)
O1i—Al1—Mg1viii133.770 (10)O1xv—Mg1—Si182.040 (9)
O1ii—Al1—Mg1viii46.230 (10)O1v—Mg1—Si182.040 (9)
O1iii—Al1—Mg1viii87.690 (10)O1xvi—Mg1—Si197.960 (8)
O1iv—Al1—Mg1viii92.310 (10)O1xvii—Mg1—Si197.960 (8)
O1v—Al1—Mg1viii137.990 (10)O1xii—Mg1—Si1v145.300 (10)
O1vi—Al1—Mg1viii42.010 (10)O1xiii—Mg1—Si1v145.300 (10)
Mg1vii—Al1—Mg1viii66.4220 (10)O1iii—Mg1—Si1v34.700 (10)
O1i—Al1—Mg1ix46.230 (10)O1xiv—Mg1—Si1v34.700 (10)
O1ii—Al1—Mg1ix133.770 (10)O1xv—Mg1—Si1v97.960 (9)
O1iii—Al1—Mg1ix92.310 (10)O1v—Mg1—Si1v97.960 (9)
O1iv—Al1—Mg1ix87.690 (10)O1xvi—Mg1—Si1v82.040 (9)
O1v—Al1—Mg1ix42.010 (10)O1xvii—Mg1—Si1v82.040 (9)
O1vi—Al1—Mg1ix137.990 (10)Si1—Mg1—Si1v180.0
Mg1vii—Al1—Mg1ix113.5780 (10)O1xii—Mg1—Al1xviii35.060 (10)
Mg1viii—Al1—Mg1ix180.000O1xiii—Mg1—Al1xviii94.780 (10)
O1i—Al1—Mg1x137.990 (10)O1iii—Mg1—Al1xviii97.530 (10)
O1ii—Al1—Mg1x42.010 (10)O1xiv—Mg1—Al1xviii127.180 (10)
O1iii—Al1—Mg1x133.770 (10)O1xv—Mg1—Al1xviii78.112 (9)
O1iv—Al1—Mg1x46.230 (10)O1v—Mg1—Al1xviii94.702 (9)
O1v—Al1—Mg1x87.690 (10)O1xvi—Mg1—Al1xviii159.386 (9)
O1vi—Al1—Mg1x92.310 (10)O1xvii—Mg1—Al1xviii35.707 (9)
Mg1vii—Al1—Mg1x66.4220 (10)Si1—Mg1—Al1xviii63.4350 (10)
Mg1viii—Al1—Mg1x66.4220 (10)Si1v—Mg1—Al1xviii116.5650 (10)
Mg1ix—Al1—Mg1x113.5780 (10)O1xii—Mg1—Al1xix94.780 (10)
O1i—Al1—Mg1xi42.010 (10)O1xiii—Mg1—Al1xix35.060 (10)
O1ii—Al1—Mg1xi137.990 (10)O1iii—Mg1—Al1xix127.180 (10)
O1iii—Al1—Mg1xi46.230 (10)O1xiv—Mg1—Al1xix97.530 (10)
O1iv—Al1—Mg1xi133.770 (10)O1xv—Mg1—Al1xix94.702 (9)
O1v—Al1—Mg1xi92.310 (10)O1v—Mg1—Al1xix78.112 (9)
O1vi—Al1—Mg1xi87.690 (10)O1xvi—Mg1—Al1xix35.707 (9)
Mg1vii—Al1—Mg1xi113.5780 (10)O1xvii—Mg1—Al1xix159.386 (9)
Mg1viii—Al1—Mg1xi113.5780 (10)Si1—Mg1—Al1xix63.4350 (10)
Mg1ix—Al1—Mg1xi66.4220 (10)Si1v—Mg1—Al1xix116.5650 (10)
Mg1x—Al1—Mg1xi180.000Al1xviii—Mg1—Al1xix126.870 (2)
O1i—Al1—Mg192.310 (10)O1xx—Si1—O1xiii114.57 (2)
O1ii—Al1—Mg187.690 (10)O1xx—Si1—O1xxi99.69 (2)
O1iii—Al1—Mg142.010 (10)O1xiii—Si1—O1xxi114.57 (2)
O1iv—Al1—Mg1137.990 (10)O1xx—Si1—O1xii114.57 (2)
O1v—Al1—Mg146.230 (10)O1xiii—Si1—O1xii99.69 (2)
O1vi—Al1—Mg1133.770 (10)O1xxi—Si1—O1xii114.57 (2)
Mg1vii—Al1—Mg1180.000O1xx—Si1—Mg1130.150 (10)
Mg1viii—Al1—Mg1113.5780 (10)O1xiii—Si1—Mg149.850 (10)
Mg1ix—Al1—Mg166.4220 (10)O1xxi—Si1—Mg1130.150 (10)
Mg1x—Al1—Mg1113.5780 (10)O1xii—Si1—Mg149.850 (10)
Mg1xi—Al1—Mg166.4220 (10)O1xx—Si1—Mg1xvi49.850 (10)
O1xii—Mg1—O1xiii69.390 (10)O1xiii—Si1—Mg1xvi130.150 (10)
O1xii—Mg1—O1iii114.1670 (10)O1xxi—Si1—Mg1xvi49.850 (10)
O1xiii—Mg1—O1iii160.490 (10)O1xii—Si1—Mg1xvi130.150 (10)
O1xii—Mg1—O1xiv160.490 (10)Mg1—Si1—Mg1xvi180.000
O1xiii—Mg1—O1xiv114.170 (10)Si1xxii—O1—Al1vi130.43 (2)
O1iii—Mg1—O1xiv69.390 (10)Si1xxii—O1—Mg1xxii95.45 (2)
O1xii—Mg1—O1xv93.640 (10)Al1vi—O1—Mg1xxii102.93 (2)
O1xiii—Mg1—O1xv73.070 (10)Si1xxii—O1—Mg1xvi122.99 (2)
O1iii—Mg1—O1xv124.330 (10)Al1vi—O1—Mg1xvi98.07 (2)
O1xiv—Mg1—O1xv70.370 (10)Mg1xxii—O1—Mg1xvi101.31 (2)
O1xii—Mg1—O1v73.070 (10)
Symmetry codes: (i) z1/2, x, y; (ii) z+1/2, x, y; (iii) y, z1/2, x; (iv) y, z+1/2, x; (v) x, y, z1/2; (vi) x, y, z+1/2; (vii) x, y, z; (viii) z1/4, y+1/4, x1/4; (ix) z+1/4, y1/4, x+1/4; (x) x1/4, z1/4, y+1/4; (xi) x+1/4, z+1/4, y1/4; (xii) z+3/4, y+1/4, x+1/4; (xiii) z3/4, y+1/4, x+1/4; (xiv) y, z+1, x; (xv) x, y+1/2, z1/2; (xvi) y1/4, x+1/4, z+3/4; (xvii) y+1/4, x+1/4, z+3/4; (xviii) y+1/4, x+1/4, z+1/4; (xix) x1/4, z+1/4, y+1/4; (xx) y, z+1, x+1/2; (xxi) y, z1/2, x+1/2; (xxii) z1/4, y+1/4, x+3/4.

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