The spontaneous nucleation by the high-temperature flux method of GeO2 and SiO2-substituted GeO2 (Ge1−xSixO2) 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 Ge1−xSixO2 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.
Supporting information
For all compounds, program(s) used to refine structure: SHELXL97 (Sheldrick, 2008).
Crystal data top
GeO2 | V = 121.85 (1) Å3 |
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 top
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 top
Refinement on F2 | Secondary atom site location: difference Fourier map |
Least-squares matrix: full | w = 1/[σ2(Fo2) + (0.0085P)2 + 0.0233P] where P = (Fo2 + 2Fc2)/3 |
R[F2 > 2σ(F2)] = 0.009 | (Δ/σ)max < 0.001 |
wR(F2) = 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+0.001xFc2λ3/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) |
Crystal data top
GeO2 | γ = 120° |
Mr = 104.59 | V = 121.85 (1) Å3 |
?, P3121 | Z = 3 |
a = 4.9890 (3) Å | Mo Kα radiation |
b = 4.9890 (3) Å | µ = 18.33 mm−1 |
c = 5.6527 (3) Å | T = 298 K |
α = 90° | 0.12 × 0.08 × 0.08 mm |
β = 90° | |
Data collection top
Absorption correction: gaussian CrysAlisPro_Software_system,_Version_1.171.32. | 416 independent reflections |
Tmin = 0.251, Tmax = 0.360 | 410 reflections with I > 2σ(I) |
2023 measured reflections | Rint = 0.019 |
Refinement top
R[F2 > 2σ(F2)] = 0.009 | 0 restraints |
wR(F2) = 0.021 | Δρmax = 0.32 e Å−3 |
S = 1.15 | Δρmin = −0.34 e Å−3 |
416 reflections | Absolute structure: Flack H D (1983), 151 Friedel pairs |
16 parameters | Absolute structure parameter: 0.09 (2) |
Special details top
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 (Å2) top | 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 (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
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) top
Ge1—O | 1.7357 (10) | Ge1—Oiii | 1.7432 (8) |
Ge1—Oi | 1.7357 (10) | O—Ge1iv | 1.7432 (8) |
Ge1—Oii | 1.7432 (8) | | |
| | | |
O—Ge1—Oi | 107.80 (6) | Oi—Ge1—Oiii | 106.31 (2) |
O—Ge1—Oii | 106.31 (2) | Oii—Ge1—Oiii | 110.58 (6) |
Oi—Ge1—Oii | 112.97 (5) | Ge1—O—Ge1iv | 130.11 (6) |
O—Ge1—Oiii | 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. |
Crystal data top
Ge0.97O2Si0.03 | V = 121.15 (1) Å3 |
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 top
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 top
Refinement on F2 | Secondary atom site location: difference Fourier map |
Least-squares matrix: full | w = 1/[σ2(Fo2) + (0.0168P)2 + 0.2243P] where P = (Fo2 + 2Fc2)/3 |
R[F2 > 2σ(F2)] = 0.015 | (Δ/σ)max < 0.001 |
wR(F2) = 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+0.001xFc2λ3/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) |
Crystal data top
Ge0.97O2Si0.03 | γ = 120° |
Mr = 103.43 | V = 121.15 (1) Å3 |
?, P3221 | Z = 3 |
a = 4.9830 (1) Å | Mo Kα radiation |
b = 4.9830 (1) Å | µ = 17.98 mm−1 |
c = 5.6339 (2) Å | T = 298 K |
α = 90° | 0.28 × 0.16 × 0.13 mm |
β = 90° | |
Data collection top
Absorption correction: gaussian CrysAlisPro_Software_system,_Version_1.171.32. | 285 independent reflections |
Tmin = 0.080, Tmax = 0.254 | 283 reflections with I > 2σ(I) |
2144 measured reflections | Rint = 0.032 |
Refinement top
R[F2 > 2σ(F2)] = 0.015 | 0 restraints |
wR(F2) = 0.038 | Δρmax = 0.54 e Å−3 |
S = 1.18 | Δρmin = −0.43 e Å−3 |
285 reflections | Absolute structure: Flack H D (1983), 99 friedel pairs |
16 parameters | Absolute structure parameter: 0.07 (4) |
Special details top
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 (Å2) top | 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 (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
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) top
Ge1—Oi | 1.729 (2) | Ge1—Oiii | 1.7371 (18) |
Ge1—Oii | 1.729 (2) | O—Si1iv | 1.729 (2) |
Ge1—O | 1.7372 (18) | O—Ge1iv | 1.729 (2) |
| | | |
Oi—Ge1—Oii | 107.72 (13) | Oii—Ge1—Oiii | 112.96 (11) |
Oi—Ge1—O | 112.96 (11) | O—Ge1—Oiii | 110.33 (13) |
Oii—Ge1—O | 106.48 (5) | Si1iv—O—Ge1 | 130.49 (12) |
Oi—Ge1—Oiii | 106.48 (5) | Ge1iv—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. |
Crystal data top
Ge0.96O2Si0.04 | V = 120.88 (1) Å3 |
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 top
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 top
Refinement on F2 | Secondary atom site location: difference Fourier map |
Least-squares matrix: full | w = 1/[σ2(Fo2) + (0.0085P)2 + 0.0833P] where P = (Fo2 + 2Fc2)/3 |
R[F2 > 2σ(F2)] = 0.010 | (Δ/σ)max < 0.001 |
wR(F2) = 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+0.001xFc2λ3/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) |
Crystal data top
Ge0.96O2Si0.04 | γ = 120° |
Mr = 102.71 | V = 120.88 (1) Å3 |
?, P3121 | Z = 3 |
a = 4.9805 (2) Å | Mo Kα radiation |
b = 4.9805 (2) Å | µ = 17.74 mm−1 |
c = 5.6270 (3) Å | T = 298 K |
α = 90° | 0.19 × 0.13 × 0.08 mm |
β = 90° | |
Data collection top
Absorption correction: gaussian CrysAlisPro_Software_system,_Version_1.171.32. | 288 independent reflections |
Tmin = 0.121, Tmax = 0.318 | 284 reflections with I > 2σ(I) |
2157 measured reflections | Rint = 0.024 |
Refinement top
R[F2 > 2σ(F2)] = 0.010 | 0 restraints |
wR(F2) = 0.024 | Δρmax = 0.34 e Å−3 |
S = 1.20 | Δρmin = −0.43 e Å−3 |
288 reflections | Absolute structure: Flack H D (1983), 95 Friedel pairs |
16 parameters | Absolute structure parameter: −0.04 (3) |
Special details top
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 (Å2) top | 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 (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
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) top
Ge1—Oi | 1.7268 (15) | Ge1—Oiii | 1.7333 (12) |
Ge1—Oii | 1.7268 (15) | O—Si1iv | 1.7268 (15) |
Ge1—O | 1.7333 (12) | O—Ge1iv | 1.7268 (15) |
| | | |
Oi—Ge1—Oii | 107.83 (9) | Oii—Ge1—Oiii | 106.50 (3) |
Oi—Ge1—O | 106.50 (3) | O—Ge1—Oiii | 110.36 (9) |
Oii—Ge1—O | 112.87 (8) | Si1iv—O—Ge1 | 130.72 (9) |
Oi—Ge1—Oiii | 112.87 (8) | Ge1iv—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. |
Crystal data top
Ge0.90O2Si0.10 | V = 120.16 (1) Å3 |
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 top
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 top
Refinement on F2 | Secondary atom site location: difference Fourier map |
Least-squares matrix: full | w = 1/[σ2(Fo2) + (0.0095P)2 + 0.1155P] where P = (Fo2 + 2Fc2)/3 |
R[F2 > 2σ(F2)] = 0.013 | (Δ/σ)max < 0.001 |
wR(F2) = 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+0.001xFc2λ3/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) |
Crystal data top
Ge0.90O2Si0.10 | γ = 120° |
Mr = 99.94 | V = 120.16 (1) Å3 |
?, P3221 | Z = 3 |
a = 4.97517 (17) Å | Mo Kα radiation |
b = 4.97517 (17) Å | µ = 16.74 mm−1 |
c = 5.60565 (19) Å | T = 298 K |
α = 90° | 0.38 × 0.18 × 0.09 mm |
β = 90° | |
Data collection top
Absorption correction: gaussian CrysAlisPro_Software_system,_Version_1.171.32. | 282 independent reflections |
Tmin = 0.091, Tmax = 0.365 | 274 reflections with I > 2σ(I) |
2860 measured reflections | Rint = 0.036 |
Refinement top
R[F2 > 2σ(F2)] = 0.013 | 0 restraints |
wR(F2) = 0.030 | Δρmax = 0.30 e Å−3 |
S = 1.19 | Δρmin = −0.29 e Å−3 |
282 reflections | Absolute structure: Flack H D (1983), 91 Friedel pairs |
16 parameters | Absolute structure parameter: −0.07 (4) |
Special details top
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 (Å2) top | 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 (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
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) top
Ge1—O | 1.718 (2) | Ge1—Oiii | 1.7226 (15) |
Ge1—Oi | 1.718 (2) | O—Si1iv | 1.7226 (15) |
Ge1—Oii | 1.7226 (15) | O—Ge1iv | 1.7226 (15) |
| | | |
O—Ge1—Oi | 108.12 (12) | Oi—Ge1—Oiii | 106.63 (4) |
O—Ge1—Oii | 106.63 (4) | Oii—Ge1—Oiii | 110.34 (12) |
Oi—Ge1—Oii | 112.60 (10) | Ge1—O—Si1iv | 131.54 (11) |
O—Ge1—Oiii | 112.60 (10) | Ge1—O—Ge1iv | 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. |
Crystal data top
Ge0.83O2Si0.17 | V = 119.56 (1) Å3 |
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 top
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 top
Refinement on F2 | Secondary atom site location: difference Fourier map |
Least-squares matrix: full | w = 1/[σ2(Fo2) + (0.0064P)2 + 0.0732P] where P = (Fo2 + 2Fc2)/3 |
R[F2 > 2σ(F2)] = 0.010 | (Δ/σ)max < 0.001 |
wR(F2) = 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+0.001xFc2λ3/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) |
Crystal data top
Ge0.83O2Si0.17 | γ = 120° |
Mr = 96.83 | V = 119.56 (1) Å3 |
?, P3121 | Z = 3 |
a = 4.9707 (3) Å | Mo Kα radiation |
b = 4.9707 (3) Å | µ = 15.59 mm−1 |
c = 5.5873 (3) Å | T = 298 K |
α = 90° | 0.18 × 0.16 × 0.10 mm |
β = 90° | |
Data collection top
Absorption correction: gaussian CrysAlisPro_Software_system,_Version_1.171.32. | 279 independent reflections |
Tmin = 0.461, Tmax = 1.000 | 277 reflections with I > 2σ(I) |
2176 measured reflections | Rint = 0.026 |
Refinement top
R[F2 > 2σ(F2)] = 0.010 | 0 restraints |
wR(F2) = 0.024 | Δρmax = 0.33 e Å−3 |
S = 1.22 | Δρmin = −0.29 e Å−3 |
279 reflections | Absolute structure: Flack H D (1983), 94 Friedel pairs |
16 parameters | Absolute structure parameter: −0.01 (3) |
Special details top
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 (Å2) top | 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 (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
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) top
Ge1—Oi | 1.7053 (15) | O—Si1v | 1.7053 (15) |
Ge1—Oii | 1.7053 (15) | O—Ge1v | 1.7053 (15) |
Ge1—Oiii | 1.7158 (12) | O—Si1vi | 1.7158 (12) |
Ge1—Oiv | 1.7158 (12) | O—Ge1vi | 1.7158 (12) |
| | | |
Oi—Ge1—Oii | 108.08 (9) | Oiii—Ge1—Oiv | 109.87 (9) |
Oi—Ge1—Oiii | 112.57 (7) | Si1v—O—Si1vi | 132.49 (9) |
Oii—Ge1—Oiii | 106.91 (3) | Ge1v—O—Si1vi | 132.49 (9) |
Oi—Ge1—Oiv | 106.91 (3) | Si1v—O—Ge1vi | 132.49 (9) |
Oii—Ge1—Oiv | 112.57 (7) | Ge1v—O—Ge1vi | 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. |
Crystal data top
O2Si | V = 113.21 (1) Å3 |
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 top
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 top
Refinement on F2 | Secondary atom site location: difference Fourier map |
Least-squares matrix: full | w = 1/[σ2(Fo2) + (0.0238P)2 + 0.0151P] where P = (Fo2 + 2Fc2)/3 |
R[F2 > 2σ(F2)] = 0.013 | (Δ/σ)max < 0.001 |
wR(F2) = 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+0.001xFc2λ3/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) |
Crystal data top
O2Si | γ = 120° |
Mr = 60.09 | V = 113.21 (1) Å3 |
?, P3221 | Z = 3 |
a = 4.91636 (19) Å | Mo Kα radiation |
b = 4.91636 (18) Å | µ = 0.99 mm−1 |
c = 5.4084 (2) Å | T = 298 K |
α = 90° | 0.34 × 0.20 × 0.15 mm |
β = 90° | |
Data collection top
Absorption correction: gaussian CrysAlisPro_Software_system,_Version_1.171.32. | 319 independent reflections |
Tmin = 0.782, Tmax = 0.899 | 318 reflections with I > 2σ(I) |
7027 measured reflections | Rint = 0.029 |
Refinement top
R[F2 > 2σ(F2)] = 0.013 | 0 restraints |
wR(F2) = 0.040 | Δρmax = 0.21 e Å−3 |
S = 1.25 | Δρmin = −0.26 e Å−3 |
319 reflections | Absolute structure: Flack H D (1983), 113 Friedel pairs |
16 parameters | Absolute structure parameter: −0.02 (17) |
Special details top
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 (Å2) top | 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 (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
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) top
Si—Oi | 1.6075 (8) | Si—Oiv | 1.6128 (7) |
Si—Oii | 1.6075 (8) | O—Siv | 1.6075 (8) |
Si—Oiii | 1.6128 (7) | O—Sivi | 1.6128 (7) |
| | | |
Oi—Si—Oii | 108.95 (6) | Oii—Si—Oiv | 110.53 (4) |
Oi—Si—Oiii | 110.53 (4) | Oiii—Si—Oiv | 109.34 (5) |
Oii—Si—Oiii | 108.751 (14) | Siv—O—Sivi | 143.62 (5) |
Oi—Si—Oiv | 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. |
Experimental details
| (GeO2) | (Ge0.974Si0.026O2) | (Ge0.957Si0.043) | (Ge0.8961Si0.1039O2) |
Crystal data |
Chemical formula | GeO2 | Ge0.97O2Si0.03 | Ge0.96O2Si0.04 | Ge0.90O2Si0.10 |
Mr | 104.59 | 103.43 | 102.71 | 99.94 |
Crystal system, space group | ?, P3121 | ?, P3221 | ?, P3121 | ?, P3221 |
Temperature (K) | 298 | 298 | 298 | 298 |
a, b, c (Å) | 4.9890 (3), 4.9890 (3), 5.6527 (3) | 4.9830 (1), 4.9830 (1), 5.6339 (2) | 4.9805 (2), 4.9805 (2), 5.6270 (3) | 4.97517 (17), 4.97517 (17), 5.60565 (19) |
α, β, γ (°) | 90, 90, 120 | 90, 90, 120 | 90, 90, 120 | 90, 90, 120 |
V (Å3) | 121.85 (1) | 121.15 (1) | 120.88 (1) | 120.16 (1) |
Z | 3 | 3 | 3 | 3 |
Radiation type | Mo Kα | Mo Kα | Mo Kα | Mo Kα |
µ (mm−1) | 18.33 | 17.98 | 17.74 | 16.74 |
Crystal size (mm) | 0.12 × 0.08 × 0.08 | 0.28 × 0.16 × 0.13 | 0.19 × 0.13 × 0.08 | 0.38 × 0.18 × 0.09 |
|
Data collection |
Diffractometer | ? | ? | ? | ? |
Absorption correction | Gaussian CrysAlisPro_Software_system,_Version_1.171.32. | Gaussian CrysAlisPro_Software_system,_Version_1.171.32. | Gaussian CrysAlisPro_Software_system,_Version_1.171.32. | Gaussian CrysAlisPro_Software_system,_Version_1.171.32. |
Tmin, Tmax | 0.251, 0.360 | 0.080, 0.254 | 0.121, 0.318 | 0.091, 0.365 |
No. of measured, independent and observed [I > 2σ(I)] reflections | 2023, 416, 410 | 2144, 285, 283 | 2157, 288, 284 | 2860, 282, 274 |
Rint | 0.019 | 0.032 | 0.024 | 0.036 |
(sin θ/λ)max (Å−1) | 0.848 | 0.753 | 0.757 | 0.755 |
|
Refinement |
R[F2 > 2σ(F2)], wR(F2), S | 0.009, 0.021, 1.15 | 0.015, 0.038, 1.18 | 0.010, 0.024, 1.20 | 0.013, 0.030, 1.19 |
No. of reflections | 416 | 285 | 288 | 282 |
No. of parameters | 16 | 16 | 16 | 16 |
Δρmax, Δρmin (e Å−3) | 0.32, −0.34 | 0.54, −0.43 | 0.34, −0.43 | 0.30, −0.29 |
Absolute structure | Flack H D (1983), 151 Friedel pairs | Flack H D (1983), 99 friedel pairs | Flack H D (1983), 95 Friedel pairs | Flack H D (1983), 91 Friedel pairs |
Absolute structure parameter | 0.09 (2) | 0.07 (4) | −0.04 (3) | −0.07 (4) |
| (Ge0.8257Si0.1743O2) | (SiO2) |
Crystal data |
Chemical formula | Ge0.83O2Si0.17 | O2Si |
Mr | 96.83 | 60.09 |
Crystal system, space group | ?, P3121 | ?, P3221 |
Temperature (K) | 298 | 298 |
a, b, c (Å) | 4.9707 (3), 4.9707 (3), 5.5873 (3) | 4.91636 (19), 4.91636 (18), 5.4084 (2) |
α, β, γ (°) | 90, 90, 120 | 90, 90, 120 |
V (Å3) | 119.56 (1) | 113.21 (1) |
Z | 3 | 3 |
Radiation type | Mo Kα | Mo Kα |
µ (mm−1) | 15.59 | 0.99 |
Crystal size (mm) | 0.18 × 0.16 × 0.10 | 0.34 × 0.20 × 0.15 |
|
Data collection |
Diffractometer | ? | ? |
Absorption correction | Gaussian CrysAlisPro_Software_system,_Version_1.171.32. | Gaussian CrysAlisPro_Software_system,_Version_1.171.32. |
Tmin, Tmax | 0.461, 1.000 | 0.782, 0.899 |
No. of measured, independent and observed [I > 2σ(I)] reflections | 2176, 279, 277 | 7027, 319, 318 |
Rint | 0.026 | 0.029 |
(sin θ/λ)max (Å−1) | 0.753 | 0.802 |
|
Refinement |
R[F2 > 2σ(F2)], wR(F2), S | 0.010, 0.024, 1.22 | 0.013, 0.040, 1.25 |
No. of reflections | 279 | 319 |
No. of parameters | 16 | 16 |
Δρmax, Δρmin (e Å−3) | 0.33, −0.29 | 0.21, −0.26 |
Absolute structure | Flack H D (1983), 94 Friedel pairs | Flack H D (1983), 113 Friedel pairs |
Absolute structure parameter | −0.01 (3) | −0.02 (17) |