Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270100002560/br1278sup1.cif | |
Structure factor file (CIF format) https://doi.org/10.1107/S0108270100002560/br1278Isup2.hkl |
Crystals were grown by slowly diffusing acetone into a saturated aqueous solution of the title compound at 278 (1) K. This yielded well developed clear colourless isometric crystals of approximately 110 µm in diameter. The predominating form was the rhombohedron {101}. Sometimes very small pinacoids {001} were observed.
The dispersion of birefringence, Δn(λ) = n_{e}(λ) - n_{o}(λ), was determined at room temperature under a polarizing microscope with an Ehringhaus compensator. A crystal of approximately 140 µm in diameter and 76 (2) µm thickness was placed on a rhombohedral face so that the viewing direction and the optical axis formed an angle of 43.20 (2)°. For seven wavelengths, Δn'(λ) = n_{e}'(λ) - n_{o}(λ) was measured and the values of Δn(λ) were calculated under the assumption of an ordinary refractive index n_{o} of 1.475. This value was given by Zambonini (1930) for n_{o}(598 nm).
Data collection: CD (Stoe & Cie, 1987); cell refinement: DL (Stoe & Cie, 1987); data reduction: REDU4 (Stoe & Cie, 1987); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: ORTEPIII (Burnett & Johnson, 1996).
K_{2}[TiF_{6}] | D_{x} = 3.001 Mg m^{−}^{3} |
M_{r} = 240.10 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, P3m1 | Cell parameters from 26 reflections |
a = 5.7354 (11) Å | θ = 8.4–12.1° |
c = 4.6635 (18) Å | µ = 3.21 mm^{−}^{1} |
V = 132.85 (6) Å^{3} | T = 298 K |
Z = 1 | Rhombohedron, colourless |
F(000) = 114 | 0.12 × 0.12 × 0.12 mm |
Siemens AED-II four-circle diffractometer | R_{int} = 0.054 |
Radiation source: fine-focus sealed tube | θ_{max} = 49.8°, θ_{min} = 4.1° |
Graphite monochromator | h = −12→12 |
θ/2θ scans | k = −12→12 |
4637 measured reflections | l = −8→10 |
553 independent reflections | 3 standard reflections every 120 min |
465 reflections with I > 2σ(I) | intensity decay: none |
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})] = 0.028 | Calculated w = 1/[σ^{2}(F_{o}^{2}) + (0.0183P)^{2} + 0.0142P] where P = (F_{o}^{2} + 2F_{c}^{2})/3 |
wR(F^{2}) = 0.050 | (Δ/σ)_{max} < 0.001 |
S = 1.15 | Δρ_{max} = 0.57 e Å^{−}^{3} |
553 reflections | Δρ_{min} = −0.70 e Å^{−}^{3} |
13 parameters | Extinction correction: SHELXL (Sheldrick, 1997), Fc^{*}=kFc[1+0.001xFc^{2}λ^{3}/sin(2θ)]^{-1/4} |
0 restraints | Extinction coefficient: 0.54 (3) |
K_{2}[TiF_{6}] | Z = 1 |
M_{r} = 240.10 | Mo Kα radiation |
Trigonal, P3m1 | µ = 3.21 mm^{−}^{1} |
a = 5.7354 (11) Å | T = 298 K |
c = 4.6635 (18) Å | 0.12 × 0.12 × 0.12 mm |
V = 132.85 (6) Å^{3} |
Siemens AED-II four-circle diffractometer | R_{int} = 0.054 |
4637 measured reflections | 3 standard reflections every 120 min |
553 independent reflections | intensity decay: none |
465 reflections with I > 2σ(I) |
R[F^{2} > 2σ(F^{2})] = 0.028 | 13 parameters |
wR(F^{2}) = 0.050 | 0 restraints |
S = 1.15 | Δρ_{max} = 0.57 e Å^{−}^{3} |
553 reflections | Δρ_{min} = −0.70 e Å^{−}^{3} |
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 F^{2} against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F^{2}, conventional R-factors R are based on F, with F set to zero for negative F^{2}. The threshold expression of F^{2} > σ(F^{2}) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F^{2} are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger. |
x | y | z | U_{iso}*/U_{eq} | ||
K | 1/3 | 2/3 | 0.69254 (7) | 0.02169 (8) | |
Ti | 0 | 0 | 0 | 0.01220 (7) | |
F | 0.15549 (6) | 0.31099 (11) | 0.22237 (13) | 0.02376 (12) |
U^{11} | U^{22} | U^{33} | U^{12} | U^{13} | U^{23} | |
K | 0.01963 (9) | 0.01963 (9) | 0.02581 (15) | 0.00981 (5) | 0 | 0 |
Ti | 0.01101 (8) | 0.01101 (8) | 0.01457 (11) | 0.00550 (4) | 0 | 0 |
F | 0.0256 (2) | 0.0171 (2) | 0.0257 (2) | 0.00856 (11) | −0.00366 (8) | −0.00732 (17) |
K—F | 2.8158 (9) | Ti—K^{iv} | 3.6084 (6) |
K—F^{i} | 2.8158 (9) | Ti—K^{xvii} | 3.6084 (6) |
K—F^{ii} | 2.8158 (9) | Ti—K^{vii} | 3.6085 (6) |
K—F^{iii} | 2.8971 (6) | Ti—K^{xviii} | 3.6085 (6) |
K—F^{iv} | 2.8971 (6) | Ti—K^{xix} | 3.6085 (6) |
K—F^{v} | 2.8972 (6) | Ti—K^{xx} | 3.6085 (6) |
K—F^{vi} | 2.8972 (6) | F—K^{iv} | 2.8971 (5) |
K—F^{vii} | 2.8972 (6) | F—K^{vii} | 2.8972 (6) |
K—F^{viii} | 2.8972 (6) | F—K^{xx} | 3.0375 (11) |
K—F^{ix} | 3.0375 (11) | F—F^{xv} | 2.5860 (12) |
K—F^{x} | 3.0375 (11) | F—F^{xii} | 2.5860 (12) |
K—F^{xi} | 3.0375 (11) | F—F^{xvi} | 2.6754 (11) |
Ti—F^{xii} | 1.8605 (6) | F—F^{xiii} | 2.6754 (11) |
Ti—F^{xiii} | 1.8605 (6) | F—F^{viii} | 3.0152 (14) |
Ti—F^{xiv} | 1.8605 (6) | F—F^{vi} | 3.0152 (14) |
Ti—F^{xv} | 1.8605 (6) | F—F^{ii} | 3.0600 (10) |
Ti—F^{xvi} | 1.8605 (6) | F—F^{i} | 3.0600 (11) |
Ti—F | 1.8605 (6) | F—F^{xiv} | 3.7209 (13) |
F—K—F^{i} | 65.82 (3) | F^{xii}—Ti—F | 88.05 (3) |
F—K—F^{ii} | 65.82 (3) | F^{xiii}—Ti—F | 91.95 (3) |
F^{i}—K—F^{ii} | 65.82 (3) | F^{xiv}—Ti—F | 180.0 |
F—K—F^{iii} | 129.233 (11) | F^{xv}—Ti—F | 88.05 (3) |
F^{i}—K—F^{iii} | 63.69 (3) | F^{xvi}—Ti—F | 91.95 (3) |
F^{ii}—K—F^{iii} | 97.509 (12) | F^{xii}—Ti—K^{iv} | 57.29 (3) |
F—K—F^{iv} | 97.510 (12) | F^{xiii}—Ti—K^{iv} | 122.71 (3) |
F^{i}—K—F^{iv} | 63.69 (3) | F^{xiv}—Ti—K^{iv} | 127.045 (6) |
F^{ii}—K—F^{iv} | 129.232 (11) | F^{xv}—Ti—K^{iv} | 127.045 (6) |
F^{iii}—K—F^{iv} | 55.00 (2) | F^{xvi}—Ti—K^{iv} | 52.955 (6) |
F—K—F^{v} | 129.231 (11) | F—Ti—K^{iv} | 52.956 (6) |
F^{i}—K—F^{v} | 97.510 (12) | F^{xii}—Ti—K^{xvii} | 122.71 (3) |
F^{ii}—K—F^{v} | 63.69 (3) | F^{xiii}—Ti—K^{xvii} | 57.29 (3) |
F^{iii}—K—F^{v} | 63.75 (2) | F^{xiv}—Ti—K^{xvii} | 52.955 (6) |
F^{iv}—K—F^{v} | 118.157 (6) | F^{xv}—Ti—K^{xvii} | 52.955 (6) |
F—K—F^{vi} | 63.69 (3) | F^{xvi}—Ti—K^{xvii} | 127.045 (6) |
F^{i}—K—F^{vi} | 97.510 (12) | F—Ti—K^{xvii} | 127.044 (6) |
F^{ii}—K—F^{vi} | 129.231 (11) | K^{iv}—Ti—K^{xvii} | 180.0 |
F^{iii}—K—F^{vi} | 118.157 (6) | F^{xii}—Ti—K^{vii} | 127.044 (6) |
F^{iv}—K—F^{vi} | 63.75 (2) | F^{xiii}—Ti—K^{vii} | 52.956 (6) |
F^{v}—K—F^{vi} | 163.65 (3) | F^{xiv}—Ti—K^{vii} | 127.043 (6) |
F—K—F^{vii} | 97.508 (12) | F^{xv}—Ti—K^{vii} | 57.29 (3) |
F^{i}—K—F^{vii} | 129.232 (11) | F^{xvi}—Ti—K^{vii} | 122.71 (3) |
F^{ii}—K—F^{vii} | 63.69 (3) | F—Ti—K^{vii} | 52.957 (6) |
F^{iii}—K—F^{vii} | 118.155 (6) | K^{iv}—Ti—K^{vii} | 105.259 (11) |
F^{iv}—K—F^{vii} | 163.65 (3) | K^{xvii}—Ti—K^{vii} | 74.741 (11) |
F^{v}—K—F^{vii} | 55.00 (2) | F^{xii}—Ti—K^{xviii} | 52.956 (6) |
F^{vi}—K—F^{vii} | 118.154 (6) | F^{xiii}—Ti—K^{xviii} | 127.044 (6) |
F—K—F^{viii} | 63.69 (3) | F^{xiv}—Ti—K^{xviii} | 52.957 (6) |
F^{i}—K—F^{viii} | 129.232 (11) | F^{xv}—Ti—K^{xviii} | 122.71 (3) |
F^{ii}—K—F^{viii} | 97.509 (12) | F^{xvi}—Ti—K^{xviii} | 57.29 (3) |
F^{iii}—K—F^{viii} | 163.65 (3) | F—Ti—K^{xviii} | 127.043 (5) |
F^{iv}—K—F^{viii} | 118.155 (6) | K^{iv}—Ti—K^{xviii} | 74.741 (11) |
F^{v}—K—F^{viii} | 118.154 (7) | K^{xvii}—Ti—K^{xviii} | 105.259 (11) |
F^{vi}—K—F^{viii} | 55.00 (2) | K^{vii}—Ti—K^{xviii} | 180.0 |
F^{vii}—K—F^{viii} | 63.75 (2) | F^{xii}—Ti—K^{xix} | 127.044 (6) |
F—K—F^{ix} | 144.676 (13) | F^{xiii}—Ti—K^{xix} | 52.956 (5) |
F^{i}—K—F^{ix} | 105.58 (3) | F^{xiv}—Ti—K^{xix} | 57.29 (3) |
F^{ii}—K—F^{ix} | 144.675 (12) | F^{xv}—Ti—K^{xix} | 127.043 (6) |
F^{iii}—K—F^{ix} | 51.601 (19) | F^{xvi}—Ti—K^{xix} | 52.958 (6) |
F^{iv}—K—F^{ix} | 51.60 (2) | F—Ti—K^{xix} | 122.71 (3) |
F^{v}—K—F^{ix} | 84.887 (14) | K^{iv}—Ti—K^{xix} | 105.259 (11) |
F^{vi}—K—F^{ix} | 84.887 (14) | K^{xvii}—Ti—K^{xix} | 74.741 (11) |
F^{vii}—K—F^{ix} | 112.088 (17) | K^{vii}—Ti—K^{xix} | 105.257 (12) |
F^{viii}—K—F^{ix} | 112.088 (17) | K^{xviii}—Ti—K^{xix} | 74.743 (12) |
F—K—F^{x} | 144.675 (13) | F^{xii}—Ti—K^{xx} | 52.956 (5) |
F^{i}—K—F^{x} | 144.676 (12) | F^{xiii}—Ti—K^{xx} | 127.044 (6) |
F^{ii}—K—F^{x} | 105.58 (3) | F^{xiv}—Ti—K^{xx} | 122.71 (3) |
F^{iii}—K—F^{x} | 84.886 (14) | F^{xv}—Ti—K^{xx} | 52.958 (6) |
F^{iv}—K—F^{x} | 112.088 (17) | F^{xvi}—Ti—K^{xx} | 127.043 (6) |
F^{v}—K—F^{x} | 51.601 (19) | F—Ti—K^{xx} | 57.29 (3) |
F^{vi}—K—F^{x} | 112.087 (17) | K^{iv}—Ti—K^{xx} | 74.741 (11) |
F^{vii}—K—F^{x} | 51.601 (19) | K^{xvii}—Ti—K^{xx} | 105.259 (11) |
F^{viii}—K—F^{x} | 84.886 (14) | K^{vii}—Ti—K^{xx} | 74.743 (12) |
F^{ix}—K—F^{x} | 60.49 (3) | K^{xviii}—Ti—K^{xx} | 105.257 (12) |
F—K—F^{xi} | 105.58 (3) | K^{xix}—Ti—K^{xx} | 180.0 |
F^{i}—K—F^{xi} | 144.676 (13) | Ti—F—K | 162.74 (3) |
F^{ii}—K—F^{xi} | 144.675 (13) | Ti—F—K^{iv} | 96.208 (11) |
F^{iii}—K—F^{xi} | 112.088 (16) | K—F—K^{iv} | 82.491 (12) |
F^{iv}—K—F^{xi} | 84.886 (14) | Ti—F—K^{vii} | 96.208 (11) |
F^{v}—K—F^{xi} | 112.087 (17) | K—F—K^{vii} | 82.492 (12) |
F^{vi}—K—F^{xi} | 51.60 (2) | K^{iv}—F—K^{vii} | 163.65 (3) |
F^{vii}—K—F^{xi} | 84.886 (14) | Ti—F—K^{xx} | 91.69 (3) |
F^{viii}—K—F^{xi} | 51.601 (19) | K—F—K^{xx} | 105.58 (3) |
F^{ix}—K—F^{xi} | 60.49 (3) | K^{iv}—F—K^{xx} | 95.113 (14) |
F^{x}—K—F^{xi} | 60.49 (3) | K^{vii}—F—K^{xx} | 95.114 (14) |
F^{xii}—Ti—F^{xiii} | 180.0 | F^{xv}—F—F^{xii} | 62.30 (4) |
F^{xii}—Ti—F^{xiv} | 91.95 (3) | F^{xv}—F—F^{xvi} | 90.00 (1) |
F^{xiii}—Ti—F^{xiv} | 88.05 (3) | F^{xv}—F—F^{xiii} | 58.85 (2) |
F^{xii}—Ti—F^{xv} | 91.95 (3) | F^{xv}—F—F^{xiv} | 45.97 (2) |
F^{xiii}—Ti—F^{xv} | 88.05 (3) | F^{xii}—F—F^{xvi} | 58.85 (2) |
F^{xiv}—Ti—F^{xv} | 91.95 (3) | F^{xii}—F—F^{xiii} | 90.000 (5) |
F^{xii}—Ti—F^{xvi} | 88.05 (3) | F^{xii}—F—F^{xiv} | 45.973 (15) |
F^{xiii}—Ti—F^{xvi} | 91.95 (3) | F^{xvi}—F—F^{xiii} | 60.000 (14) |
F^{xiv}—Ti—F^{xvi} | 88.05 (3) | F^{xvi}—F—F^{xiv} | 44.027 (16) |
F^{xv}—Ti—F^{xvi} | 180.0 | F^{xiii}—F—F^{xiv} | 44.027 (17) |
Symmetry codes: (i) −x+y, −x+1, z; (ii) −y+1, x−y+1, z; (iii) y, −x+y+1, −z+1; (iv) −x, −y+1, −z+1; (v) x−y+1, x+1, −z+1; (vi) x−y, x, −z+1; (vii) −x+1, −y+1, −z+1; (viii) y, −x+y, −z+1; (ix) −x+y, −x+1, z+1; (x) −y+1, x−y+1, z+1; (xi) x, y, z+1; (xii) x−y, x, −z; (xiii) −x+y, −x, z; (xiv) −x, −y, −z; (xv) y, −x+y, −z; (xvi) −y, x−y, z; (xvii) x, y−1, z−1; (xviii) x−1, y−1, z−1; (xix) −x, −y, −z+1; (xx) x, y, z−1. |
Experimental details
Crystal data | |
Chemical formula | K_{2}[TiF_{6}] |
M_{r} | 240.10 |
Crystal system, space group | Trigonal, P3m1 |
Temperature (K) | 298 |
a, c (Å) | 5.7354 (11), 4.6635 (18) |
V (Å^{3}) | 132.85 (6) |
Z | 1 |
Radiation type | Mo Kα |
µ (mm^{−}^{1}) | 3.21 |
Crystal size (mm) | 0.12 × 0.12 × 0.12 |
Data collection | |
Diffractometer | Siemens AED-II four-circle diffractometer |
Absorption correction | – |
No. of measured, independent and observed [I > 2σ(I)] reflections | 4637, 553, 465 |
R_{int} | 0.054 |
(sin θ/λ)_{max} (Å^{−}^{1}) | 1.074 |
Refinement | |
R[F^{2} > 2σ(F^{2})], wR(F^{2}), S | 0.028, 0.050, 1.15 |
No. of reflections | 553 |
No. of parameters | 13 |
Δρ_{max}, Δρ_{min} (e Å^{−}^{3}) | 0.57, −0.70 |
Computer programs: CD (Stoe & Cie, 1987), DL (Stoe & Cie, 1987), REDU4 (Stoe & Cie, 1987), SHELXL97 (Sheldrick, 1997), ORTEPIII (Burnett & Johnson, 1996).
K—F | 2.8158 (9) | Ti—F | 1.8605 (6) |
K—F^{i} | 2.8972 (6) | F—F^{iii} | 2.5860 (12) |
K—F^{ii} | 3.0375 (11) | F—F^{iv} | 2.6754 (11) |
F^{v}—Ti—F | 88.05 (3) | F^{iii}—F—F^{v} | 62.30 (4) |
F^{iv}—Ti—F | 91.95 (3) | F^{iii}—F—F^{iv} | 58.85 (2) |
Symmetry codes: (i) x−y, x, −z+1; (ii) x, y, z+1; (iii) y, −x+y, −z; (iv) −x+y, −x, z; (v) x−y, x, −z. |
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The crystal structure of K_{2}[TiF_{6}] (P3m1, Z = 1, K_{2}[GeF_{6}] structure type) was first described by Siegel (1952). However, it was not fully resolved since no displacement parameters were given. It seemed desirable to redo the refinement to achieve higher accuracy. The displacement parameters have been determined in the present study. The corresponding ellipsoids of both the K^{+} and the Ti^{4+} ions were found to be elongated ellipsoids of revolution. The lattice parameters, measured by single-crystal X-ray reflections on a four-circle diffractometer, are a = 5.7354 (11) and c = 4.6635 (18) Å. These are in fair agreement with earlier results by Siegel (1952), Cox & Sharpe (1953) and Swanson et al. (1957).
The distances and angles within the coordination polyhedra of the two cations, calculated with SHELXL97 (Sheldrick, 1997) and ORFFE4 (Busing et al., 1976), are compiled in Table 1. The [TiF_{6}] trigonal antiprism, having symmetry 3 m, is a slightly distorted octahedron, which is compressed along the c axis by a factor of 0.9494 (8). This leads to small deviations of some F—F—F angles from 60° (Table 1). This is contrary to Siegel's results, who found an elongated antiprism with a stretch factor of 1.042 (26). The Ti—F bond length is 1.8605 (6) Å. The distances between neighbouring F^{-} ions within the [TiF_{6}] antiprism are 2.6754 (11) Å (F^{-} ions within the same basal plane of the antiprism) and 2.5860 (12) Å (F^{-} ions of two different basal planes).
The coordination polyhedron around the K^{+} ion is a slightly distorted anticuboctahedron, the 12-cornered coordination polyhedron of the hexagonal closest packing with site symmetry 62m. The reduced site symmetry in the case of K_{2}[TiF_{6}], 3 m, causes the K^{+} ion to be displaced by 0.1391 (7) Å from the midpoint of the two (triangular) basal planes of this polyhedron. The equatorial plane with six F^{-} anions is displaced by 0.2577 (8) Å in the opposite direction. The average K—F distance is 2.91 (8) Å.
The optical character of K_{2}[TiF_{6}] was found to be negative, in agreement with Zambonini (1930). Since the birefringence Δn = n_{e} - n_{o} appeared to be very low for white light, there was a chance of finding a certain wavelength λ_{0} where it might vanish completely. Therefore, the dispersion of birefringence, Δn(λ) = n_{e}(λ) - n_{o}(λ), was measured at room temperature. A straight line was fitted to seven data points using GNUPLOT (Williams et al., 1998). An extrapolation of this line indicates that the birefringence should disappear at 720 nm. At this wavelength, λ_{0}, the optical behaviour of K_{2}[TiF_{6}] should be isotropic and the sign of birefringence should change.