Garnet-type Mn₃Cr₂(GeO₄)₃

Single crystals of garnet-type trimanganese(II) dichrom­i­um(III) tris­[orthogermanate(IV)], Mn^II₃Cr^III₂(GeO₄)₃, were obtained by utilizing a chemical transport reaction. Corres­ponding to the mineral garnet with the general formula A^II₃B^III₂(SiO₄)₃, each of the four elements occupies only one crystallographically distinct position. Mn²⁺ occupies the respective A position (Wyckoff site 24c, site symmetry 2.22), being surrounded by eight O atoms that form a distorted cube [d(Mn—O) = 2.291 (2) and 2.422 (2) Å, 4× each], while Cr³⁺ on the B position (Wyckoff site 16a, site symmetry .-3.) is situated in a slightly distorted octa­hedron of six O²⁻ anions [d(Cr—O) = 1.972 (2) Å, 6×]. In addition, the O atoms on general site 96h form isolated [GeO₄]⁴⁻ tetra­hedra with Ge⁴⁺ on site 24d [site symmetry -4..; d(Ge—O) = 1.744 (2) Å, 4×].

Related literature

For general background to garnets, see: Geller (1967); Geusic et al. (1964); Menzer (1925, 1926, 1928); Nishikawa (1917); Novak & Gibbs (1971). For synthetic details, see: Binnewies et al. (2011); Pajączkowska & Majcher (1985, 1986); Pajączk­owska et al. (1986). For isotypic structures, see: Andrut & Wildner (2002); Belov et al. (1972); Fursenko (1981); Geller et al. (1960); Golosovskii et al. (1976); Lind & Geller (1969); Prandl (1973); Tauber et al. (1958a,b, 1961); Wildner & Andrut (2001).

Experimental

Crystal data

• Mn₃Cr₂(GeO₄)₃

• M_r = 678.59

• Cubic,

• a = 12.0001 (3) Å

• V = 1728.04 (7) ų

• Z = 8

• Mo Kα radiation

• μ = 17.01 mm⁻¹

• T = 293 K

• 0.18 × 0.15 × 0.09 mm

Data collection

• Nonius KappaCCD diffractometer

• Absorption correction: numerical (HABITUS; Herrendorf & Bärnighausen, 1997) T_min = 0.063, T_max = 0.201

• 7635 measured reflections

• 277 independent reflections

• 265 reflections with I > 2σ(I)

• R_int = 0.084

Refinement

• R[F² > 2σ(F²)] = 0.025

• wR(F²) = 0.068

• S = 1.26

• 277 reflections

• 18 parameters

• Δρ_max = 0.63 e Å⁻³

• Δρ_min = −0.72 e Å⁻³

Data collection: COLLECT (Nonius, 1998); cell refinement: SCALEPACK (Otwinowski & Minor, 1997); data reduction: DENZO (Otwinowski & Minor, 1997) and SCALEPACK; program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg & Putz, 2012); software used to prepare material for publication: publCIF (Westrip, 2010).

Supporting information

S1. Comment

Garnet can be found among the very early attempts to solve crystal structures with the help of X-ray diffraction (Nishikawa, 1917), soon being followed by the understanding of the regular structure (Menzer, 1925, 1926) and the variability of garnet in a systematic way (Menzer, 1928; Geller, 1967; Novak & Gibbs, 1971). The variability of the garnet-type structure led for example to the well known Nd:YAG lasers (Y₃Al₅O₁₂:Nd³⁺; Geusic et al., 1964). A much more apparent variation is of course the replacement of Si by Ge (Tauber et al., 1961; Geller, 1967), resulting in germanate garnets that are accessible via chemical transport reactions. The latter are an elegant way to grow crystals (Binnewies et al., 2011) when other methods deliver only fine powders or require very high temperatures if the growth from melts is necessary.

The formation of garnet-type Mn₃Cr₂(GeO₄)₃ by chemical transport reactions was already successfully demonstrated for transporting agents like Cl₂, CCl₄, SCl₄ and TeCl₄ (Pajączkowska & Majcher, 1985, Pajączkowska et al. 1986; Mn₃Fe₂(GeO₄)₃: Pajączkowska & Majcher, 1986). While only 0.5 mm edge length as a maximum crystal size was stated when TeCl₄ was used as a transporting agent, we achieved sizes of up to 4 mm within twelve days with the same agent. Quite interestingly Pajączkowska & Majcher (1985) determined only the unit-cell dimensions by using powder X-ray diffraction (a = 12.030 (1) Å), but not the structural details. The same germanate Mn₃Cr₂(GeO₄)₃ was already presented before, but each time again only by mentioning the unit-cell dimensions, being obtained by powder diffraction (Tauber et al., 1958a (a = 12.027 Å); Tauber et al., 1958b (a = 12.027 Å); Geller et al., 1960 (a = 12.027 (3) Å); Belov et al., 1972 (a = 12.028 (4) Å)). In addition some experiments on the magnetic properties have been conducted (Tauber et al., 1958b; Belov et al., 1972; Golosovskii et al. 1976), but again without the determination of structural details of Mn₃Cr₂(GeO₄)₃. Golosovskii et al. (1976) conducted neutron diffraction experiments and discussed the magnetic structure. They achieved results similar to the ones obtained for the spessartite-type germanate garnet Mn₃Al₂(GeO₄)₃ by Prandl (1973), thus finding confirmation for Mn²⁺ on site 24i where it is eightfold coordinated by oxygen.

The obtained dark green garnet-type Mn₃Cr₂(GeO₄)₃ (see Fig. 1) crystallizes isotypically with regular garnets. While Mn²⁺, Cr³⁺ and Ge⁴⁺ are located on the special sites 24c, 16a and 24d, oxygen is found on general site 96h. Manganese(II) is eightfold coordinated by oxygen in a distorted cube (Fig. 2) with Mn–O distances of 2.291 (2) and 2.422 (2) Å (4× each). These values are in good agreement with those reported for Mn₃Fe₂(GeO₄)₃ (2.303 (7) and 2.421 (7) Å; Lind & Geller, 1969). For additional comparison the analogous garnet Mn₃Cr₂(SiO₄)₃ would be of interest, but once more only the unit-cell parameters, determined by powder diffraction, are mentioned (a = 11.766 (2) Å; synthesis at 80 kbar/1273 K; Fursenko, 1981). The green color of Mn₃Cr₂(GeO₄)₃ may be taken as an indicator for the +III oxidation state of chromium. Oxygen surrounds chromium(III) in a slightly distorted octahedron (Fig. 3) with d(Cr—O) = 1.972 (2) Å (6×), whereas 1.9942 (6) Å is reported for chromium on the same position in synthetic uvarovite (Ca₃Cr₂(SiO₄)₃; Andrut & Wildner, 2002; for natural uvarovite, see: Wildner & Andrut, 2001). Due to the slight distortion, the (O—Cr—O) angles within the [CrO₆] octahedra deviate from 90°, viz 86.33 (8)° and 93.67 (8)°. Completing the description of the cation environments, Ge⁴⁺ is situated in slightly elongated tetrahedra of four O^2– anions where d(Ge—O) = 1.744 (2) Å, and the angles (O—Ge—O) are found to be 99.02 (14)° (2×) and 114.93 (7)° (4×). This is again similar to the values detected for Mn₃Fe₂(GeO₄)₃ (d(Ge—O) = 1.766 (7) Å, (O—Ge—O) = 98.8 (5)° (2×) and 115.1 (3)° (4×); Lind & Geller, 1969). Keeping in mind only a single site is occupied by oxygen, the structure of garnets might be described as two interpenetrating networks in Mn₃Cr₂(GeO₄)₃, the first made up of edge sharing [CrO₆] octahedra and [GeO₄]^4– tetrahedra (Fig. 2 & 3), while the second consists of groups of three edge sharing [MnO₈] polyhedra (see Fig. 2), with each distorted [MnO₈] cube being part of two of these units of three polyhedra. Therefore, each [MnO₈] polyhedron shares four edges with four [MnO₈] polyhedra, four edges with four [CrO₆] octahedra, and two edges and four vertices with six [GeO₄]^4– tetrahedra.

Related literature

For general background to garnets, see: Geller (1967); Geusic et al. (1964); Menzer (1925, 1926, 1928); Nishikawa (1917); Novak & Gibbs (1971). For synthetic details, see: Binnewies et al. (2011); Pajączkowska & Majcher (1985, 1986); Pajączkowska et al. (1986). For isotypic structures, see: Andrut & Wildner (2002); Belov et al. (1972); Fursenko (1981); Geller et al. (1960); Golosovskii et al. (1976); Lind & Geller (1969); Prandl (1973); Tauber et al. (1958a,b, 1961); Wildner & Andrut (2001).

S2. Experimental

MnO, Cr₂O₃ and GeO₂ (molar ratios of 3:1:3; MnO (Riedel-de Haën, rein): 212.8 mg, Cr₂O₃ (Riedel-de Haën, rein): 152.0 mg, GeO₂ (ChemPur, 99.999%): 313.8 mg) and the transporting agent TeCl₄ (Alfa-Aesar, 99.9%; 8.5 mg ml^-1) were brought into a fused silica ampule (length: 120 mm, inner diameter: 16 mm) and sealed under vacuum. The following transport reaction was conducted within twelve days in a two-zone tube furnace with a temperature gradient of 70 K (T₂ = 1293 K, T₁ = 1223 K, with the transport direction T₂ → T₁). Subsequent to the cooling to a temperature of 673 K within five hours, ambient temperature was reached by quenching in water. The obtained crystals had a size of up to 4 mm and shapes that are typically observed in garnets, i.e. derived from rhombic dodecahedra with often truncated edges. Larger crystals appear virtually black and opaque while smaller ones are transparent and dark green in color (see Fig. 1).

Computing details

Data collection: COLLECT (Nonius, 1998); cell refinement: SCALEPACK (Otwinowski & Minor, 1997); data reduction: DENZO and SCALEPACK (Otwinowski & Minor, 1997); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg & Putz, 2012); software used to prepare material for publication: publCIF (Westrip, 2010).

Figures

	Fig. 1. Dark green crystals of garnet-type Mn^II3Cr^III2(GeO4)3 in the shape of rhombic dodecahedra, often with truncated edges. The photograph shows the crystals as they were grown after twelve days.
	Fig. 2. Overview of the structure of Mn^II3Cr^III2(GeO4)3. For a better understanding only a group of three edge-connected distorted cubes [MnO8], representing the polyhedra about Mn^2+, are drawn besides [CrO6] octahedra and [GeO4]^4– tetrahedra (displacement ellipsoids are drawn at the 95% probability level).
	Fig. 3. The network of vertex sharing [CrO6] octahedra and [GeO4]^4– tetrahedra in the neso germanate Mn3Cr2(GeO4)3 (displacement ellipsoids are drawn at the 95% probability level).

Trimanganese(II) dichromium(III) tris[orthogermanate(IV)]

Crystal data

Mn3Cr2(GeO4)3	Dx = 5.217 Mg m^−3
Mr = 678.59	Mo Kα radiation, λ = 0.71073 Å
Cubic, Ia3d	Cell parameters from 6052 reflections
Hall symbol: -I 4bd 2c 3	θ = 0.4–40.3°
a = 12.0001 (3) Å	µ = 17.01 mm^−1
V = 1728.04 (7) Å^3	T = 293 K
Z = 8	Truncated rhombic dodecahedron, dark green
F(000) = 2520	0.18 × 0.15 × 0.09 mm

Data collection

Nonius KappaCCD diffractometer	277 independent reflections
Radiation source: fine-focus sealed tube	265 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.084
ω scans	θmax = 33.1°, θmin = 4.2°
Absorption correction: numerical (HABITUS; Herrendorf & Bärnighausen, 1997)	h = −18→16
Tmin = 0.063, Tmax = 0.201	k = −18→15
7635 measured reflections	l = −17→15

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.025	w = 1/[σ^2(Fo^2) + (0.0115P)^2 + 25.1758P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.068	(Δ/σ)max < 0.001
S = 1.26	Δρmax = 0.63 e Å^−3
277 reflections	Δρmin = −0.72 e Å^−3
18 parameters	Extinction correction: SHELXL97 (Sheldrick, 2008), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.0031 (2)

Special details

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Mn	0.1250	0.0000	0.2500	0.0080 (3)
Cr	0.0000	0.0000	0.0000	0.0023 (3)
Ge	0.3750	0.0000	0.2500	0.0045 (2)
O	0.03061 (17)	0.05245 (18)	0.65268 (17)	0.0065 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Mn	0.0039 (4)	0.0100 (3)	0.0100 (3)	0.000	0.000	0.0019 (3)
Cr	0.0023 (3)	0.0023 (3)	0.0023 (3)	0.00006 (17)	0.00006 (17)	0.00006 (17)
Ge	0.0036 (3)	0.0050 (3)	0.0050 (3)	0.000	0.000	0.000
O	0.0068 (9)	0.0082 (9)	0.0044 (8)	0.0016 (7)	−0.0018 (7)	−0.0006 (7)

Geometric parameters (Å, º)

Mn—O^i	2.291 (2)	Cr—O^xi	1.972 (2)
Mn—O^ii	2.291 (2)	Cr—O^xii	1.972 (2)
Mn—O^iii	2.291 (2)	Cr—O^ii	1.972 (2)
Mn—O^iv	2.291 (2)	Ge—O^xiii	1.744 (2)
Mn—O^v	2.422 (2)	Ge—O^iii	1.744 (2)
Mn—O^vi	2.422 (2)	Ge—O^i	1.744 (2)
Mn—O^vii	2.422 (2)	Ge—O^xiv	1.744 (2)
Mn—O^viii	2.422 (2)	O—Ge^xv	1.744 (2)
Cr—O^viii	1.972 (2)	O—Cr^x	1.972 (2)
Cr—O^ix	1.972 (2)	O—Mn^iv	2.291 (2)
Cr—O^x	1.972 (2)	O—Mn^xvi	2.422 (2)
O^i—Mn—O^ii	112.61 (10)	O^v—Mn—Ge^xvii	97.88 (5)
O^i—Mn—O^iii	70.78 (10)	O^vi—Mn—Ge^xvii	82.12 (5)
O^ii—Mn—O^iii	160.86 (10)	O^vii—Mn—Ge^xvii	82.12 (5)
O^i—Mn—O^iv	160.86 (10)	O^viii—Mn—Ge^xvii	97.88 (5)
O^ii—Mn—O^iv	70.78 (10)	O^viii—Cr—O^ix	180.00 (17)
O^iii—Mn—O^iv	112.61 (10)	O^viii—Cr—O^x	93.67 (8)
O^i—Mn—O^v	94.58 (6)	O^ix—Cr—O^x	86.33 (8)
O^ii—Mn—O^v	124.69 (4)	O^viii—Cr—O^xi	93.67 (8)
O^iii—Mn—O^v	72.34 (8)	O^ix—Cr—O^xi	86.33 (8)
O^iv—Mn—O^v	69.78 (10)	O^x—Cr—O^xi	86.33 (8)
O^i—Mn—O^vi	124.69 (4)	O^viii—Cr—O^xii	86.33 (8)
O^ii—Mn—O^vi	94.58 (6)	O^ix—Cr—O^xii	93.67 (8)
O^iii—Mn—O^vi	69.78 (10)	O^x—Cr—O^xii	93.67 (8)
O^iv—Mn—O^vi	72.34 (8)	O^xi—Cr—O^xii	180.00 (17)
O^v—Mn—O^vi	108.41 (10)	O^viii—Cr—O^ii	86.33 (8)
O^i—Mn—O^vii	69.78 (10)	O^ix—Cr—O^ii	93.67 (8)
O^ii—Mn—O^vii	72.34 (8)	O^x—Cr—O^ii	180.00 (17)
O^iii—Mn—O^vii	124.69 (4)	O^xi—Cr—O^ii	93.67 (8)
O^iv—Mn—O^vii	94.58 (6)	O^xii—Cr—O^ii	86.33 (8)
O^v—Mn—O^vii	73.85 (10)	O^xiii—Ge—O^iii	114.93 (7)
O^vi—Mn—O^vii	164.23 (10)	O^xiii—Ge—O^i	114.93 (7)
O^i—Mn—O^viii	72.34 (8)	O^iii—Ge—O^i	99.02 (14)
O^ii—Mn—O^viii	69.78 (10)	O^xiii—Ge—O^xiv	99.02 (14)
O^iii—Mn—O^viii	94.58 (6)	O^iii—Ge—O^xiv	114.93 (7)
O^iv—Mn—O^viii	124.69 (4)	O^i—Ge—O^xiv	114.93 (7)
O^v—Mn—O^viii	164.23 (10)	O^xiii—Ge—Mn	130.49 (7)
O^vi—Mn—O^viii	73.85 (10)	O^iii—Ge—Mn	49.51 (7)
O^vii—Mn—O^viii	108.41 (10)	O^i—Ge—Mn	49.51 (7)
O^i—Mn—Ge	35.39 (5)	O^xiv—Ge—Mn	130.49 (7)
O^ii—Mn—Ge	144.61 (5)	O^xiii—Ge—Mn^xviii	49.51 (7)
O^iii—Mn—Ge	35.39 (5)	O^iii—Ge—Mn^xviii	130.49 (7)
O^iv—Mn—Ge	144.61 (5)	O^i—Ge—Mn^xviii	130.49 (7)
O^v—Mn—Ge	82.12 (5)	O^xiv—Ge—Mn^xviii	49.51 (7)
O^vi—Mn—Ge	97.88 (5)	Ge^xv—O—Cr^x	128.90 (11)
O^vii—Mn—Ge	97.88 (5)	Ge^xv—O—Mn^iv	95.10 (9)
O^viii—Mn—Ge	82.12 (5)	Cr^x—O—Mn^iv	103.54 (9)
O^i—Mn—Ge^xvii	144.61 (5)	Ge^xv—O—Mn^xvi	122.92 (10)
O^ii—Mn—Ge^xvii	35.39 (5)	Cr^x—O—Mn^xvi	99.02 (8)
O^iii—Mn—Ge^xvii	144.61 (5)	Mn^iv—O—Mn^xvi	102.43 (8)
O^iv—Mn—Ge^xvii	35.39 (5)

Symmetry codes: (i) x+1/4, −z+3/4, −y+1/4; (ii) −x, y, z−1/2; (iii) x+1/4, z−3/4, y+1/4; (iv) −x, −y, −z+1; (v) z−1/2, x, −y+1/2; (vi) −z+3/4, y−1/4, −x+1/4; (vii) −z+3/4, −y+1/4, x+1/4; (viii) z−1/2, −x, y; (ix) −z+1/2, x, −y; (x) x, −y, −z+1/2; (xi) −y, −z+1/2, x; (xii) y, z−1/2, −x; (xiii) −x+1/2, y, −z+1; (xiv) −x+1/2, −y, z−1/2; (xv) −x+1/2, −y, z+1/2; (xvi) −y, z, x+1/2; (xvii) x−1/2, y, −z+1/2; (xviii) x+1/2, y, −z+1/2.