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The optical rotation (OR) of CsLiB
6O
10 (CLBO, space group
) along the
a axis has been determined by the HAUP method [Kobayashi & Uesu (1983).
J Appl. Cryst. 16, 204–211] at a wavelength of 632.8 nm and by the TILTER method [Kaminsky & Glazer (1996).
Ferroelectrics,
183, 133–141] at 532 nm and 650 nm. The respective rotatory powers were found to be 17 (1), 24 (2) and 19 (2)° mm
−1. The absolute chirality has been established by comparing Bijvoet differences, {
hkl} and {
}, on the same crystal on which OR was measured. Atomic positions and electron density Fourier peak heights were exploited as input for semi-empirical calculations of refractive indices and OR, using
WinOPTACT [Glazer (2002).
J. Appl. Cryst. 35, 652] with only one free parameter fitted to match the average refractive index.
Supporting information
Data collection: KappaCCD; cell refinement: HKL SCALEPACK (Otwinowski & Minor 1997); data reduction: HKL SCALEPACK (Otwinowski & Minor 1997); program(s) used to solve structure: SIR97; program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: maXus, ZORTEP; software used to prepare material for publication: SHELXL97 (Sheldrick, 1997).
Crystal data top
B12O20·2(Cs)·2(Li) | F(000) = 672 |
Mr = 729.42 | Dx = 2.478 Mg m−3 |
Tetragonal, I42d | Mo Kα radiation, λ = 0.71070 Å |
Hall symbol: I -4 2bw | Cell parameters from 135 reflections |
a = 10.4670 (9) Å | µ = 3.83 mm−1 |
c = 8.9220 (6) Å | T = 295 K |
V = 977.48 (14) Å3 | Cut block, colorless |
Z = 2 | 0.58 × 0.55 × 0.54 mm |
Data collection top
Nonius KappaCCD diffractometer | 477 independent reflections |
Radiation source: fine-focus sealed tube | 466 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.031 |
φ and ω scans | θmax = 26.3°, θmin = 3.0° |
Absorption correction: multi-scan HKL2000 | h = −13→13 |
Tmin = 0.130, Tmax = 0.132 | k = −13→13 |
477 measured reflections | l = −11→11 |
Refinement top
Refinement on F2 | Primary atom site location: structure-invariant direct methods |
Least-squares matrix: full | Secondary atom site location: difference Fourier map |
R[F2 > 2σ(F2)] = 0.055 | w = 1/[σ2(Fo2) + (0.0963P)2 + 6.8411P] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.144 | (Δ/σ)max < 0.001 |
S = 1.24 | Δρmax = 0.70 e Å−3 |
477 reflections | Δρmin = −1.52 e Å−3 |
43 parameters | Absolute structure: Flack (1983), 172 Friedel pairs |
0 restraints | Absolute structure parameter: 0.28 (24) |
Special details top
Experimental. Data was collected with ω and φ scans in 2° increments with 15 second
exposures per degree. Crystal-to-detector distance was 30 mm. 16894 full and
partial reflection were integrated. |
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 (Å2) top | x | y | z | Uiso*/Ueq | |
Li1 | 0.0000 | 0.0000 | 0.5000 | 0.010 (4) | |
B1 | 0.2326 (7) | 0.1484 (7) | 0.5601 (9) | 0.0095 (15) | |
B2 | 0.2500 | −0.0244 (8) | 0.3750 | 0.005 (2) | |
O1 | 0.1022 (5) | 0.1444 (5) | 0.5703 (7) | 0.0127 (11) | |
O2 | 0.2994 (7) | 0.2500 | 0.6250 | 0.026 (2) | |
O3 | 0.3020 (5) | 0.0575 (5) | 0.4948 (7) | 0.0125 (10) | |
Cs1 | 0.0000 | 0.0000 | 0.0000 | 0.0277 (5) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Li1 | 0.006 (6) | 0.006 (6) | 0.019 (12) | 0.000 | 0.000 | 0.000 |
B1 | 0.010 (4) | 0.009 (3) | 0.010 (4) | 0.001 (3) | −0.004 (3) | −0.002 (3) |
B2 | 0.009 (4) | 0.006 (5) | 0.002 (5) | 0.000 | 0.000 (3) | 0.000 |
O1 | 0.008 (2) | 0.012 (3) | 0.018 (3) | 0.0016 (18) | 0.002 (2) | −0.009 (2) |
O2 | 0.012 (3) | 0.023 (3) | 0.029 (4) | 0.000 | 0.000 | −0.016 (3) |
O3 | 0.013 (2) | 0.011 (2) | 0.013 (2) | 0.0023 (17) | −0.001 (2) | −0.006 (2) |
Cs1 | 0.0291 (5) | 0.0291 (5) | 0.0250 (7) | 0.000 | 0.000 | 0.000 |
Geometric parameters (Å, º) top
Li1—O1i | 1.954 (5) | O2—Cs1x | 3.536 (5) |
Li1—O1ii | 1.954 (5) | O2—Cs1v | 3.536 (5) |
Li1—O1 | 1.954 (5) | O3—Cs1v | 3.137 (5) |
Li1—O1iii | 1.954 (5) | Cs1—O3xi | 3.137 (5) |
Li1—Cs1iv | 4.4610 (3) | Cs1—O3vii | 3.137 (5) |
Li1—Cs1 | 4.4610 (3) | Cs1—O3xii | 3.137 (5) |
B1—O3 | 1.331 (9) | Cs1—O3xiii | 3.137 (5) |
B1—O1 | 1.369 (9) | Cs1—O2xiv | 3.536 (5) |
B1—O2 | 1.398 (8) | Cs1—O2xi | 3.536 (5) |
B1—Cs1v | 3.622 (7) | Cs1—O2xiii | 3.536 (5) |
B2—O1ii | 1.457 (7) | Cs1—O2xv | 3.536 (5) |
B2—O1vi | 1.457 (7) | Cs1—B1xi | 3.622 (7) |
B2—O3vii | 1.474 (7) | Cs1—B1vii | 3.622 (7) |
B2—O3 | 1.474 (7) | Cs1—B1xii | 3.622 (7) |
O1—B2viii | 1.457 (6) | Cs1—B1xiii | 3.622 (7) |
O2—B1ix | 1.398 (8) | | |
| | | |
O1i—Li1—O1ii | 142.6 (4) | O2xiv—Cs1—O2xi | 95.711 (15) |
O1i—Li1—O1 | 95.91 (12) | O3xi—Cs1—O2xiii | 107.78 (12) |
O1ii—Li1—O1 | 95.90 (12) | O3vii—Cs1—O2xiii | 81.60 (11) |
O1i—Li1—O1iii | 95.90 (12) | O3xii—Cs1—O2xiii | 127.16 (13) |
O1ii—Li1—O1iii | 95.90 (12) | O3xiii—Cs1—O2xiii | 40.25 (10) |
O1—Li1—O1iii | 142.6 (4) | O2xiv—Cs1—O2xiii | 95.710 (15) |
O1i—Li1—Cs1iv | 108.71 (19) | O2xi—Cs1—O2xiii | 143.23 (5) |
O1ii—Li1—Cs1iv | 108.71 (19) | O3xi—Cs1—O2xv | 127.16 (13) |
O1—Li1—Cs1iv | 71.29 (19) | O3vii—Cs1—O2xv | 107.78 (12) |
O1iii—Li1—Cs1iv | 71.29 (19) | O3xii—Cs1—O2xv | 40.25 (10) |
O1i—Li1—Cs1 | 71.29 (19) | O3xiii—Cs1—O2xv | 81.60 (11) |
O1ii—Li1—Cs1 | 71.29 (19) | O2xiv—Cs1—O2xv | 143.23 (5) |
O1—Li1—Cs1 | 108.71 (19) | O2xi—Cs1—O2xv | 95.710 (15) |
O1iii—Li1—Cs1 | 108.71 (19) | O2xiii—Cs1—O2xv | 95.709 (15) |
Cs1iv—Li1—Cs1 | 180.0 | O3xi—Cs1—B1xi | 21.20 (15) |
O3—B1—O1 | 123.4 (6) | O3vii—Cs1—B1xi | 118.35 (15) |
O3—B1—O2 | 116.9 (6) | O3xii—Cs1—B1xi | 101.79 (16) |
O1—B1—O2 | 119.6 (7) | O3xiii—Cs1—B1xi | 104.66 (17) |
O3—B1—Cs1v | 58.5 (4) | O2xiv—Cs1—B1xi | 80.24 (13) |
O1—B1—Cs1v | 136.6 (5) | O2xi—Cs1—B1xi | 22.49 (12) |
O2—B1—Cs1v | 75.3 (3) | O2xiii—Cs1—B1xi | 128.96 (13) |
O1ii—B2—O1vi | 112.1 (7) | O2xv—Cs1—B1xi | 117.69 (14) |
O1ii—B2—O3vii | 106.7 (3) | O3xi—Cs1—B1vii | 101.79 (16) |
O1vi—B2—O3vii | 111.2 (4) | O3vii—Cs1—B1vii | 21.20 (15) |
O1ii—B2—O3 | 111.2 (4) | O3xii—Cs1—B1vii | 104.66 (17) |
O1vi—B2—O3 | 106.7 (3) | O3xiii—Cs1—B1vii | 118.35 (15) |
O3vii—B2—O3 | 108.9 (7) | O2xiv—Cs1—B1vii | 22.49 (12) |
B1—O1—B2viii | 123.8 (6) | O2xi—Cs1—B1vii | 117.69 (14) |
B1—O1—Li1 | 123.3 (4) | O2xiii—Cs1—B1vii | 80.24 (13) |
B2viii—O1—Li1 | 112.9 (4) | O2xv—Cs1—B1vii | 128.96 (13) |
B1ix—O2—B1 | 120.0 (8) | B1xi—Cs1—B1vii | 102.65 (10) |
B1ix—O2—Cs1x | 82.2 (3) | O3xi—Cs1—B1xii | 118.35 (15) |
B1—O2—Cs1x | 136.8 (3) | O3vii—Cs1—B1xii | 104.66 (17) |
B1ix—O2—Cs1v | 136.8 (3) | O3xii—Cs1—B1xii | 21.20 (15) |
B1—O2—Cs1v | 82.2 (3) | O3xiii—Cs1—B1xii | 101.79 (16) |
Cs1x—O2—Cs1v | 107.1 (2) | O2xiv—Cs1—B1xii | 128.96 (13) |
B1—O3—B2 | 122.1 (5) | O2xi—Cs1—B1xii | 80.24 (13) |
B1—O3—Cs1v | 100.3 (4) | O2xiii—Cs1—B1xii | 117.69 (14) |
B2—O3—Cs1v | 131.2 (4) | O2xv—Cs1—B1xii | 22.49 (12) |
O3xi—Cs1—O3vii | 121.79 (13) | B1xi—Cs1—B1xii | 102.65 (10) |
O3xi—Cs1—O3xii | 121.79 (13) | B1vii—Cs1—B1xii | 124.2 (2) |
O3vii—Cs1—O3xii | 86.9 (2) | O3xi—Cs1—B1xiii | 104.66 (17) |
O3xi—Cs1—O3xiii | 86.9 (2) | O3vii—Cs1—B1xiii | 101.79 (16) |
O3vii—Cs1—O3xiii | 121.79 (13) | O3xii—Cs1—B1xiii | 118.35 (15) |
O3xii—Cs1—O3xiii | 121.79 (13) | O3xiii—Cs1—B1xiii | 21.20 (15) |
O3xi—Cs1—O2xiv | 81.60 (11) | O2xiv—Cs1—B1xiii | 117.69 (14) |
O3vii—Cs1—O2xiv | 40.25 (10) | O2xi—Cs1—B1xiii | 128.96 (13) |
O3xii—Cs1—O2xiv | 107.78 (12) | O2xiii—Cs1—B1xiii | 22.49 (12) |
O3xiii—Cs1—O2xiv | 127.16 (13) | O2xv—Cs1—B1xiii | 80.24 (13) |
O3xi—Cs1—O2xi | 40.25 (10) | B1xi—Cs1—B1xiii | 124.2 (2) |
O3vii—Cs1—O2xi | 127.16 (13) | B1vii—Cs1—B1xiii | 102.65 (10) |
O3xii—Cs1—O2xi | 81.60 (11) | B1xii—Cs1—B1xiii | 102.65 (11) |
O3xiii—Cs1—O2xi | 107.78 (12) | | |
Symmetry codes: (i) −y, x, −z+1; (ii) y, −x, −z+1; (iii) −x, −y, z; (iv) x, y, z+1; (v) x+1/2, −y, −z+3/4; (vi) −y+1/2, −x, z−1/4; (vii) −x+1/2, y, −z+3/4; (viii) −y, −x+1/2, z+1/4; (ix) x, −y+1/2, −z+5/4; (x) x+1/2, y+1/2, z+1/2; (xi) −y, −x+1/2, z−3/4; (xii) x−1/2, −y, −z+3/4; (xiii) y, x−1/2, z−3/4; (xiv) −x+1/2, −y+1/2, z−1/2; (xv) x−1/2, y−1/2, z−1/2. |
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