Modulation of quartz-like GeO₂ structure by Si substitution: an X-ray diffraction study of Ge_1−xSi_xO₂ (0 ≤ x < 0.2) flux-grown single crystals

The spontaneous nucleation by the high-temperature flux method of GeO₂ and SiO₂-substituted GeO₂ (Ge_1−xSi_xO₂) compounds was improved to give single crystals free of hydroxy groups. The crystal structure and quality of these α-quartz-like piezoelectric materials were studied by single-crystal X-ray diffraction at room temperature. The refinements gave excellent final reliability factors, which are an indication of single crystals with a low level of defects. A good correlation was found between the silicon content in Ge_1−xSi_xO₂ crystals determined through extrapolation from the inter-tetrahedral bridging angle and that found from energy-dispersive X-ray spectroscopy. The effect of germanium replacement by silicon on the distortion of the α-quartz-type GeO₂ structure was followed by the evolution of the intra-tetrahedral angle and other structural parameters. The TO₄ (T = Si, Ge) distortion was found to be larger in α-GeO₂ than in α-SiO₂ and, as expected, the irregularity of the TO₄ tetrahedra decreased linearly as the substitution of Si for Ge increased.

Computing details

For all compounds, program(s) used to refine structure: SHELXL97 (Sheldrick, 2008).

(GeO2)

Crystal data

GeO2	V = 121.85 (1) Å^3
Mr = 104.59	Z = 3
?, P3121	F(000) = 144
a = 4.9890 (3) Å	Dx = 4.276 Mg m^−3
b = 4.9890 (3) Å	Mo Kα radiation, λ = 0.71073 Å
c = 5.6527 (3) Å	θ = 3.6–37.0°
α = 90°	µ = 18.33 mm^−1
β = 90°	T = 298 K
γ = 120°	0.12 × 0.08 × 0.08 mm

Data collection

Radiation source: fine-focus sealed tube	410 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.019
Absorption correction: gaussian CrysAlisPro_Software_system,_Version_1.171.32.	θmax = 37.0°, θmin = 4.7°
Tmin = 0.251, Tmax = 0.360	h = −8→8
2023 measured reflections	k = −8→7
416 independent reflections	l = −9→9

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0085P)^2 + 0.0233P] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.009	(Δ/σ)max < 0.001
wR(F^2) = 0.021	Δρmax = 0.32 e Å^−3
S = 1.15	Δρmin = −0.34 e Å^−3
416 reflections	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
16 parameters	Extinction coefficient: 0.226 (6)
0 restraints	Absolute structure: Flack H D (1983), 151 Friedel pairs
Primary atom site location: structure-invariant direct methods	Absolute structure parameter: 0.09 (2)

Special details

Geometry. All s.u.'s (except the s.u. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell s.u.'s are taken into account individually in the estimation of s.u.'s in distances, angles and torsion angles; correlations between s.u.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell s.u.'s is used for estimating s.u.'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 > 2σ(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
Ge1	0.45124 (3)	0.0000	0.3333	0.00686 (5)
O	0.3974 (2)	0.3022 (2)	0.24285 (14)	0.01203 (16)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ge1	0.00766 (7)	0.00644 (8)	0.00609 (6)	0.00322 (4)	0.00019 (3)	0.00039 (6)
O	0.0172 (4)	0.0121 (4)	0.0105 (3)	0.0101 (4)	0.0045 (3)	0.0047 (3)

Geometric parameters (Å, º)

Ge1—O	1.7357 (10)	Ge1—O^iii	1.7432 (8)
Ge1—O^i	1.7357 (10)	O—Ge1^iv	1.7432 (8)
Ge1—O^ii	1.7432 (8)
O—Ge1—O^i	107.80 (6)	O^i—Ge1—O^iii	106.31 (2)
O—Ge1—O^ii	106.31 (2)	O^ii—Ge1—O^iii	110.58 (6)
O^i—Ge1—O^ii	112.97 (5)	Ge1—O—Ge1^iv	130.11 (6)
O—Ge1—O^iii	112.97 (5)

Symmetry codes: (i) x−y, −y, −z+2/3; (ii) −x+1, −x+y, −z+1/3; (iii) −y+1, x−y, z+1/3; (iv) −x+y+1, −x+1, z−1/3.

(Ge0.974Si0.026O2)

Crystal data

Ge0.97O2Si0.03	V = 121.15 (1) Å^3
Mr = 103.43	Z = 3
?, P3221	F(000) = 143
a = 4.9830 (1) Å	Dx = 4.253 Mg m^−3
b = 4.9830 (1) Å	Mo Kα radiation, λ = 0.71073 Å
c = 5.6339 (2) Å	θ = 3.6–32.3°
α = 90°	µ = 17.98 mm^−1
β = 90°	T = 298 K
γ = 120°	0.28 × 0.16 × 0.13 mm

Data collection

Radiation source: fine-focus sealed tube	283 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.032
Absorption correction: gaussian CrysAlisPro_Software_system,_Version_1.171.32.	θmax = 32.4°, θmin = 4.7°
Tmin = 0.080, Tmax = 0.254	h = −7→7
2144 measured reflections	k = −7→7
285 independent reflections	l = −8→8

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0168P)^2 + 0.2243P] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.015	(Δ/σ)max < 0.001
wR(F^2) = 0.038	Δρmax = 0.54 e Å^−3
S = 1.18	Δρmin = −0.43 e Å^−3
285 reflections	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
16 parameters	Extinction coefficient: 0.407 (18)
0 restraints	Absolute structure: Flack H D (1983), 99 friedel pairs
Primary atom site location: structure-invariant direct methods	Absolute structure parameter: 0.07 (4)

Special details

Geometry. All s.u.'s (except the s.u. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell s.u.'s are taken into account individually in the estimation of s.u.'s in distances, angles and torsion angles; correlations between s.u.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell s.u.'s is used for estimating s.u.'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 > 2σ(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	Occ. (<1)
Ge1	−0.54829 (8)	0.0000	0.6667	0.00759 (16)	0.97
Si1	−0.54829 (8)	0.0000	0.6667	0.00759 (16)	0.03
O	−0.3975 (5)	−0.0967 (5)	0.9087 (3)	0.0126 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ge1	0.00833 (18)	0.0073 (2)	0.00680 (19)	0.00365 (10)	−0.00019 (6)	−0.00038 (12)
Si1	0.00833 (18)	0.0073 (2)	0.00680 (19)	0.00365 (10)	−0.00019 (6)	−0.00038 (12)
O	0.0175 (9)	0.0092 (8)	0.0124 (7)	0.0076 (7)	−0.0050 (7)	−0.0004 (7)

Geometric parameters (Å, º)

Ge1—O^i	1.729 (2)	Ge1—O^iii	1.7371 (18)
Ge1—O^ii	1.729 (2)	O—Si1^iv	1.729 (2)
Ge1—O	1.7372 (18)	O—Ge1^iv	1.729 (2)
O^i—Ge1—O^ii	107.72 (13)	O^ii—Ge1—O^iii	112.96 (11)
O^i—Ge1—O	112.96 (11)	O—Ge1—O^iii	110.33 (13)
O^ii—Ge1—O	106.48 (5)	Si1^iv—O—Ge1	130.49 (12)
O^i—Ge1—O^iii	106.48 (5)	Ge1^iv—O—Ge1	130.49 (12)

Symmetry codes: (i) −y−1, x−y, z−1/3; (ii) −x−1, −x+y, −z+5/3; (iii) x−y, −y, −z+4/3; (iv) −x+y−1, −x−1, z+1/3.

(Ge0.957Si0.043)

Crystal data

Ge0.96O2Si0.04	V = 120.88 (1) Å^3
Mr = 102.71	Z = 3
?, P3121	F(000) = 142
a = 4.9805 (2) Å	Dx = 4.233 Mg m^−3
b = 4.9805 (2) Å	Mo Kα radiation, λ = 0.71073 Å
c = 5.6270 (3) Å	θ = 3.6–32.5°
α = 90°	µ = 17.74 mm^−1
β = 90°	T = 298 K
γ = 120°	0.19 × 0.13 × 0.08 mm

Data collection

Radiation source: fine-focus sealed tube	284 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.024
Absorption correction: gaussian CrysAlisPro_Software_system,_Version_1.171.32.	θmax = 32.6°, θmin = 4.7°
Tmin = 0.121, Tmax = 0.318	h = −7→7
2157 measured reflections	k = −7→7
288 independent reflections	l = −8→8

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0085P)^2 + 0.0833P] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.010	(Δ/σ)max < 0.001
wR(F^2) = 0.024	Δρmax = 0.34 e Å^−3
S = 1.20	Δρmin = −0.43 e Å^−3
288 reflections	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
16 parameters	Extinction coefficient: 0.302 (9)
0 restraints	Absolute structure: Flack H D (1983), 95 Friedel pairs
Primary atom site location: structure-invariant direct methods	Absolute structure parameter: −0.04 (3)

Special details

Geometry. All s.u.'s (except the s.u. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell s.u.'s are taken into account individually in the estimation of s.u.'s in distances, angles and torsion angles; correlations between s.u.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell s.u.'s is used for estimating s.u.'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 > 2σ(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	Occ. (<1)
Ge1	0.45197 (5)	0.0000	0.3333	0.00749 (10)	0.96
Si1	0.45197 (5)	0.0000	0.3333	0.00749 (10)	0.04
O	0.6020 (3)	−0.0975 (4)	0.0917 (2)	0.0129 (2)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ge1	0.00832 (12)	0.00730 (14)	0.00652 (12)	0.00365 (7)	0.00021 (5)	0.00042 (10)
Si1	0.00832 (12)	0.00730 (14)	0.00652 (12)	0.00365 (7)	0.00021 (5)	0.00042 (10)
O	0.0172 (7)	0.0109 (6)	0.0115 (5)	0.0078 (5)	0.0039 (5)	−0.0007 (5)

Geometric parameters (Å, º)

Ge1—O^i	1.7268 (15)	Ge1—O^iii	1.7333 (12)
Ge1—O^ii	1.7268 (15)	O—Si1^iv	1.7268 (15)
Ge1—O	1.7333 (12)	O—Ge1^iv	1.7268 (15)
O^i—Ge1—O^ii	107.83 (9)	O^ii—Ge1—O^iii	106.50 (3)
O^i—Ge1—O	106.50 (3)	O—Ge1—O^iii	110.36 (9)
O^ii—Ge1—O	112.87 (8)	Si1^iv—O—Ge1	130.72 (9)
O^i—Ge1—O^iii	112.87 (8)	Ge1^iv—O—Ge1	130.72 (9)

Symmetry codes: (i) −x+1, −x+y+1, −z+1/3; (ii) −y, x−y−1, z+1/3; (iii) x−y, −y, −z+2/3; (iv) −x+y+1, −x, z−1/3.

(Ge0.8961Si0.1039O2)

Crystal data

Ge0.90O2Si0.10	V = 120.16 (1) Å^3
Mr = 99.94	Z = 3
?, P3221	F(000) = 138
a = 4.97517 (17) Å	Dx = 4.143 Mg m^−3
b = 4.97517 (17) Å	Mo Kα radiation, λ = 0.71073 Å
c = 5.60565 (19) Å	θ = 3.6–32.4°
α = 90°	µ = 16.74 mm^−1
β = 90°	T = 298 K
γ = 120°	0.38 × 0.18 × 0.09 mm

Data collection

Radiation source: fine-focus sealed tube	274 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.036
Absorption correction: gaussian CrysAlisPro_Software_system,_Version_1.171.32.	θmax = 32.5°, θmin = 4.7°
Tmin = 0.091, Tmax = 0.365	h = −7→7
2860 measured reflections	k = −7→7
282 independent reflections	l = −8→8

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0095P)^2 + 0.1155P] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.013	(Δ/σ)max < 0.001
wR(F^2) = 0.030	Δρmax = 0.30 e Å^−3
S = 1.19	Δρmin = −0.29 e Å^−3
282 reflections	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
16 parameters	Extinction coefficient: 0.275 (11)
0 restraints	Absolute structure: Flack H D (1983), 91 Friedel pairs
Primary atom site location: structure-invariant direct methods	Absolute structure parameter: −0.07 (4)

Special details

Geometry. All s.u.'s (except the s.u. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell s.u.'s are taken into account individually in the estimation of s.u.'s in distances, angles and torsion angles; correlations between s.u.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell s.u.'s is used for estimating s.u.'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 > 2σ(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	Occ. (<1)
Ge1	−0.45280 (7)	0.0000	0.6667	0.00885 (13)	0.90
Si1	−0.45280 (7)	0.0000	0.6667	0.00885 (13)	0.10
O	−0.3997 (4)	−0.2992 (4)	0.7599 (3)	0.0145 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ge1	0.00968 (16)	0.00879 (19)	0.00778 (16)	0.00439 (10)	0.00028 (7)	0.00056 (13)
Si1	0.00968 (16)	0.00879 (19)	0.00778 (16)	0.00439 (10)	0.00028 (7)	0.00056 (13)
O	0.0183 (9)	0.0147 (8)	0.0128 (6)	0.0102 (8)	0.0037 (6)	0.0051 (6)

Geometric parameters (Å, º)

Ge1—O	1.718 (2)	Ge1—O^iii	1.7226 (15)
Ge1—O^i	1.718 (2)	O—Si1^iv	1.7226 (15)
Ge1—O^ii	1.7226 (15)	O—Ge1^iv	1.7226 (15)
O—Ge1—O^i	108.12 (12)	O^i—Ge1—O^iii	106.63 (4)
O—Ge1—O^ii	106.63 (4)	O^ii—Ge1—O^iii	110.34 (12)
O^i—Ge1—O^ii	112.60 (10)	Ge1—O—Si1^iv	131.54 (11)
O—Ge1—O^iii	112.60 (10)	Ge1—O—Ge1^iv	131.54 (11)

Symmetry codes: (i) x−y, −y, −z+4/3; (ii) −x−1, −x+y, −z+5/3; (iii) −y−1, x−y, z−1/3; (iv) −x+y−1, −x−1, z+1/3.

(Ge0.8257Si0.1743O2)

Crystal data

Ge0.83O2Si0.17	V = 119.56 (1) Å^3
Mr = 96.83	Z = 3
?, P3121	F(000) = 135
a = 4.9707 (3) Å	Dx = 4.035 Mg m^−3
b = 4.9707 (3) Å	Mo Kα radiation, λ = 0.71073 Å
c = 5.5873 (3) Å	θ = 3.6–32.3°
α = 90°	µ = 15.59 mm^−1
β = 90°	T = 298 K
γ = 120°	0.18 × 0.16 × 0.10 mm

Data collection

Radiation source: fine-focus sealed tube	277 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.026
Absorption correction: gaussian CrysAlisPro_Software_system,_Version_1.171.32.	θmax = 32.4°, θmin = 4.7°
Tmin = 0.461, Tmax = 1.000	h = −7→7
2176 measured reflections	k = −7→7
279 independent reflections	l = −7→8

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0064P)^2 + 0.0732P] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.010	(Δ/σ)max < 0.001
wR(F^2) = 0.024	Δρmax = 0.33 e Å^−3
S = 1.22	Δρmin = −0.29 e Å^−3
279 reflections	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
16 parameters	Extinction coefficient: 0.031 (3)
0 restraints	Absolute structure: Flack H D (1983), 94 Friedel pairs
Primary atom site location: structure-invariant direct methods	Absolute structure parameter: −0.01 (3)

Special details

Geometry. All s.u.'s (except the s.u. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell s.u.'s are taken into account individually in the estimation of s.u.'s in distances, angles and torsion angles; correlations between s.u.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell s.u.'s is used for estimating s.u.'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 > 2σ(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	Occ. (<1)
Ge1	0.54634 (6)	0.0000	0.3333	0.00800 (8)	0.83
Si1	0.54634 (6)	0.0000	0.3333	0.00800 (8)	0.17
O	0.5998 (3)	0.7041 (3)	0.2382 (2)	0.0145 (2)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ge1	0.00867 (11)	0.00796 (14)	0.00714 (11)	0.00398 (7)	−0.00029 (5)	−0.00057 (10)
Si1	0.00867 (11)	0.00796 (14)	0.00714 (11)	0.00398 (7)	−0.00029 (5)	−0.00057 (10)
O	0.0180 (6)	0.0147 (6)	0.0133 (5)	0.0101 (6)	−0.0030 (5)	−0.0047 (4)

Geometric parameters (Å, º)

Ge1—O^i	1.7053 (15)	O—Si1^v	1.7053 (15)
Ge1—O^ii	1.7053 (15)	O—Ge1^v	1.7053 (15)
Ge1—O^iii	1.7158 (12)	O—Si1^vi	1.7158 (12)
Ge1—O^iv	1.7158 (12)	O—Ge1^vi	1.7158 (12)
O^i—Ge1—O^ii	108.08 (9)	O^iii—Ge1—O^iv	109.87 (9)
O^i—Ge1—O^iii	112.57 (7)	Si1^v—O—Si1^vi	132.49 (9)
O^ii—Ge1—O^iii	106.91 (3)	Ge1^v—O—Si1^vi	132.49 (9)
O^i—Ge1—O^iv	106.91 (3)	Si1^v—O—Ge1^vi	132.49 (9)
O^ii—Ge1—O^iv	112.57 (7)	Ge1^v—O—Ge1^vi	132.49 (9)

Symmetry codes: (i) x−y+1, −y+1, −z+2/3; (ii) x, y−1, z; (iii) −x+1, −x+y, −z+1/3; (iv) −y+1, x−y, z+1/3; (v) x, y+1, z; (vi) −x+y+1, −x+1, z−1/3.

(SiO2)

Crystal data

O2Si	V = 113.21 (1) Å^3
Mr = 60.09	Z = 3
?, P3221	F(000) = 90
a = 4.91636 (19) Å	Dx = 2.644 Mg m^−3
b = 4.91636 (18) Å	Mo Kα radiation, λ = 0.71073 Å
c = 5.4084 (2) Å	θ = 3.8–34.7°
α = 90°	µ = 0.99 mm^−1
β = 90°	T = 298 K
γ = 120°	0.34 × 0.20 × 0.15 mm

Data collection

Radiation source: fine-focus sealed tube	318 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.029
Absorption correction: gaussian CrysAlisPro_Software_system,_Version_1.171.32.	θmax = 34.8°, θmin = 4.8°
Tmin = 0.782, Tmax = 0.899	h = −7→7
7027 measured reflections	k = −7→7
319 independent reflections	l = −8→8

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0238P)^2 + 0.0151P] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.013	(Δ/σ)max < 0.001
wR(F^2) = 0.040	Δρmax = 0.21 e Å^−3
S = 1.25	Δρmin = −0.26 e Å^−3
319 reflections	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
16 parameters	Extinction coefficient: 12.8 (4)
0 restraints	Absolute structure: Flack H D (1983), 113 Friedel pairs
Primary atom site location: structure-invariant direct methods	Absolute structure parameter: −0.02 (17)

Special details

Geometry. All s.u.'s (except the s.u. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell s.u.'s are taken into account individually in the estimation of s.u.'s in distances, angles and torsion angles; correlations between s.u.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell s.u.'s is used for estimating s.u.'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 > 2σ(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
Si	0.46973 (7)	0.0000	0.6667	0.00691 (16)
O	0.41354 (17)	0.26758 (17)	−0.21442 (12)	0.01245 (18)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Si	0.00752 (18)	0.00582 (19)	0.0068 (2)	0.00291 (10)	−0.00008 (4)	−0.00015 (9)
O	0.0162 (3)	0.0118 (3)	0.0125 (3)	0.0094 (3)	−0.0029 (2)	−0.0044 (2)

Geometric parameters (Å, º)

Si—O^i	1.6075 (8)	Si—O^iv	1.6128 (7)
Si—O^ii	1.6075 (8)	O—Si^v	1.6075 (8)
Si—O^iii	1.6128 (7)	O—Si^vi	1.6128 (7)
O^i—Si—O^ii	108.95 (6)	O^ii—Si—O^iv	110.53 (4)
O^i—Si—O^iii	110.53 (4)	O^iii—Si—O^iv	109.34 (5)
O^ii—Si—O^iii	108.751 (14)	Si^v—O—Si^vi	143.62 (5)
O^i—Si—O^iv	108.751 (14)

Symmetry codes: (i) x−y, −y, −z+1/3; (ii) x, y, z+1; (iii) −x+1, −x+y, −z+2/3; (iv) −y+1, x−y, z+2/3; (v) x, y, z−1; (vi) −x+y+1, −x+1, z−2/3.