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Crystals of dipotassium hexa­fluoro­titanate(IV), K2[TiF6], were grown from aqueous solution. The crystal structure was refined with anisotropic displacement parameters. Ti4+ is octahedrally coordinated by F- (point group {\overline 3}m), and K+ is 12-coordinate (point group 3m). The dispersion of birefringence is presented.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270100002560/br1278sup1.cif
Contains datablocks tita, I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108270100002560/br1278Isup2.hkl
Contains datablock I

Comment top

The crystal structure of K2[TiF6] (P3m1, Z = 1, K2[GeF6] 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 Ti4+ 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 [TiF6] 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 [TiF6] 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 K2[TiF6], 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 K2[TiF6] was found to be negative, in agreement with Zambonini (1930). Since the birefringence Δn = ne - no appeared to be very low for white light, there was a chance of finding a certain wavelength λ0 where it might vanish completely. Therefore, the dispersion of birefringence, Δn(λ) = ne(λ) - no(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, λ0, the optical behaviour of K2[TiF6] should be isotropic and the sign of birefringence should change.

Experimental top

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.

Refinement top

The dispersion of birefringence, Δn(λ) = ne(λ) - no(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) = ne'(λ) - no(λ) was measured and the values of Δn(λ) were calculated under the assumption of an ordinary refractive index no of 1.475. This value was given by Zambonini (1930) for no(598 nm).

Computing details top

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).

Figures top
[Figure 1] Fig. 1. A stereoscopic view of the crystal structure of K2[TiF6] along the c axis. In the upper right-hand corner the edges of a [TiF6] antiprism are drawn and on the left-hand side the edges of a KF12 coordination polyhedron.
[Figure 2] Fig. 2. The birefringence of K2[TiF6] as a function of wavelength.
dipotassium hexafluorotitanate(IV) top
Crystal data top
K2[TiF6]Dx = 3.001 Mg m3
Mr = 240.10Mo Kα radiation, λ = 0.71073 Å
Trigonal, P3m1Cell parameters from 26 reflections
a = 5.7354 (11) Åθ = 8.4–12.1°
c = 4.6635 (18) ŵ = 3.21 mm1
V = 132.85 (6) Å3T = 298 K
Z = 1Rhombohedron, colourless
F(000) = 1140.12 × 0.12 × 0.12 mm
Data collection top
Siemens AED-II four-circle
diffractometer
Rint = 0.054
Radiation source: fine-focus sealed tubeθmax = 49.8°, θmin = 4.1°
Graphite monochromatorh = 1212
θ/2θ scansk = 1212
4637 measured reflectionsl = 810
553 independent reflections3 standard reflections every 120 min
465 reflections with I > 2σ(I) intensity decay: none
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.028Calculated w = 1/[σ2(Fo2) + (0.0183P)2 + 0.0142P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.050(Δ/σ)max < 0.001
S = 1.15Δρmax = 0.57 e Å3
553 reflectionsΔρmin = 0.70 e Å3
13 parametersExtinction correction: SHELXL (Sheldrick, 1997), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
0 restraintsExtinction coefficient: 0.54 (3)
Crystal data top
K2[TiF6]Z = 1
Mr = 240.10Mo Kα radiation
Trigonal, P3m1µ = 3.21 mm1
a = 5.7354 (11) ÅT = 298 K
c = 4.6635 (18) Å0.12 × 0.12 × 0.12 mm
V = 132.85 (6) Å3
Data collection top
Siemens AED-II four-circle
diffractometer
Rint = 0.054
4637 measured reflections3 standard reflections every 120 min
553 independent reflections intensity decay: none
465 reflections with I > 2σ(I)
Refinement top
R[F2 > 2σ(F2)] = 0.02813 parameters
wR(F2) = 0.0500 restraints
S = 1.15Δρmax = 0.57 e Å3
553 reflectionsΔρmin = 0.70 e Å3
Special details top

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
xyzUiso*/Ueq
K1/32/30.69254 (7)0.02169 (8)
Ti0000.01220 (7)
F0.15549 (6)0.31099 (11)0.22237 (13)0.02376 (12)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
K0.01963 (9)0.01963 (9)0.02581 (15)0.00981 (5)00
Ti0.01101 (8)0.01101 (8)0.01457 (11)0.00550 (4)00
F0.0256 (2)0.0171 (2)0.0257 (2)0.00856 (11)0.00366 (8)0.00732 (17)
Geometric parameters (Å, º) top
K—F2.8158 (9)Ti—Kiv3.6084 (6)
K—Fi2.8158 (9)Ti—Kxvii3.6084 (6)
K—Fii2.8158 (9)Ti—Kvii3.6085 (6)
K—Fiii2.8971 (6)Ti—Kxviii3.6085 (6)
K—Fiv2.8971 (6)Ti—Kxix3.6085 (6)
K—Fv2.8972 (6)Ti—Kxx3.6085 (6)
K—Fvi2.8972 (6)F—Kiv2.8971 (5)
K—Fvii2.8972 (6)F—Kvii2.8972 (6)
K—Fviii2.8972 (6)F—Kxx3.0375 (11)
K—Fix3.0375 (11)F—Fxv2.5860 (12)
K—Fx3.0375 (11)F—Fxii2.5860 (12)
K—Fxi3.0375 (11)F—Fxvi2.6754 (11)
Ti—Fxii1.8605 (6)F—Fxiii2.6754 (11)
Ti—Fxiii1.8605 (6)F—Fviii3.0152 (14)
Ti—Fxiv1.8605 (6)F—Fvi3.0152 (14)
Ti—Fxv1.8605 (6)F—Fii3.0600 (10)
Ti—Fxvi1.8605 (6)F—Fi3.0600 (11)
Ti—F1.8605 (6)F—Fxiv3.7209 (13)
F—K—Fi65.82 (3)Fxii—Ti—F88.05 (3)
F—K—Fii65.82 (3)Fxiii—Ti—F91.95 (3)
Fi—K—Fii65.82 (3)Fxiv—Ti—F180.0
F—K—Fiii129.233 (11)Fxv—Ti—F88.05 (3)
Fi—K—Fiii63.69 (3)Fxvi—Ti—F91.95 (3)
Fii—K—Fiii97.509 (12)Fxii—Ti—Kiv57.29 (3)
F—K—Fiv97.510 (12)Fxiii—Ti—Kiv122.71 (3)
Fi—K—Fiv63.69 (3)Fxiv—Ti—Kiv127.045 (6)
Fii—K—Fiv129.232 (11)Fxv—Ti—Kiv127.045 (6)
Fiii—K—Fiv55.00 (2)Fxvi—Ti—Kiv52.955 (6)
F—K—Fv129.231 (11)F—Ti—Kiv52.956 (6)
Fi—K—Fv97.510 (12)Fxii—Ti—Kxvii122.71 (3)
Fii—K—Fv63.69 (3)Fxiii—Ti—Kxvii57.29 (3)
Fiii—K—Fv63.75 (2)Fxiv—Ti—Kxvii52.955 (6)
Fiv—K—Fv118.157 (6)Fxv—Ti—Kxvii52.955 (6)
F—K—Fvi63.69 (3)Fxvi—Ti—Kxvii127.045 (6)
Fi—K—Fvi97.510 (12)F—Ti—Kxvii127.044 (6)
Fii—K—Fvi129.231 (11)Kiv—Ti—Kxvii180.0
Fiii—K—Fvi118.157 (6)Fxii—Ti—Kvii127.044 (6)
Fiv—K—Fvi63.75 (2)Fxiii—Ti—Kvii52.956 (6)
Fv—K—Fvi163.65 (3)Fxiv—Ti—Kvii127.043 (6)
F—K—Fvii97.508 (12)Fxv—Ti—Kvii57.29 (3)
Fi—K—Fvii129.232 (11)Fxvi—Ti—Kvii122.71 (3)
Fii—K—Fvii63.69 (3)F—Ti—Kvii52.957 (6)
Fiii—K—Fvii118.155 (6)Kiv—Ti—Kvii105.259 (11)
Fiv—K—Fvii163.65 (3)Kxvii—Ti—Kvii74.741 (11)
Fv—K—Fvii55.00 (2)Fxii—Ti—Kxviii52.956 (6)
Fvi—K—Fvii118.154 (6)Fxiii—Ti—Kxviii127.044 (6)
F—K—Fviii63.69 (3)Fxiv—Ti—Kxviii52.957 (6)
Fi—K—Fviii129.232 (11)Fxv—Ti—Kxviii122.71 (3)
Fii—K—Fviii97.509 (12)Fxvi—Ti—Kxviii57.29 (3)
Fiii—K—Fviii163.65 (3)F—Ti—Kxviii127.043 (5)
Fiv—K—Fviii118.155 (6)Kiv—Ti—Kxviii74.741 (11)
Fv—K—Fviii118.154 (7)Kxvii—Ti—Kxviii105.259 (11)
Fvi—K—Fviii55.00 (2)Kvii—Ti—Kxviii180.0
Fvii—K—Fviii63.75 (2)Fxii—Ti—Kxix127.044 (6)
F—K—Fix144.676 (13)Fxiii—Ti—Kxix52.956 (5)
Fi—K—Fix105.58 (3)Fxiv—Ti—Kxix57.29 (3)
Fii—K—Fix144.675 (12)Fxv—Ti—Kxix127.043 (6)
Fiii—K—Fix51.601 (19)Fxvi—Ti—Kxix52.958 (6)
Fiv—K—Fix51.60 (2)F—Ti—Kxix122.71 (3)
Fv—K—Fix84.887 (14)Kiv—Ti—Kxix105.259 (11)
Fvi—K—Fix84.887 (14)Kxvii—Ti—Kxix74.741 (11)
Fvii—K—Fix112.088 (17)Kvii—Ti—Kxix105.257 (12)
Fviii—K—Fix112.088 (17)Kxviii—Ti—Kxix74.743 (12)
F—K—Fx144.675 (13)Fxii—Ti—Kxx52.956 (5)
Fi—K—Fx144.676 (12)Fxiii—Ti—Kxx127.044 (6)
Fii—K—Fx105.58 (3)Fxiv—Ti—Kxx122.71 (3)
Fiii—K—Fx84.886 (14)Fxv—Ti—Kxx52.958 (6)
Fiv—K—Fx112.088 (17)Fxvi—Ti—Kxx127.043 (6)
Fv—K—Fx51.601 (19)F—Ti—Kxx57.29 (3)
Fvi—K—Fx112.087 (17)Kiv—Ti—Kxx74.741 (11)
Fvii—K—Fx51.601 (19)Kxvii—Ti—Kxx105.259 (11)
Fviii—K—Fx84.886 (14)Kvii—Ti—Kxx74.743 (12)
Fix—K—Fx60.49 (3)Kxviii—Ti—Kxx105.257 (12)
F—K—Fxi105.58 (3)Kxix—Ti—Kxx180.0
Fi—K—Fxi144.676 (13)Ti—F—K162.74 (3)
Fii—K—Fxi144.675 (13)Ti—F—Kiv96.208 (11)
Fiii—K—Fxi112.088 (16)K—F—Kiv82.491 (12)
Fiv—K—Fxi84.886 (14)Ti—F—Kvii96.208 (11)
Fv—K—Fxi112.087 (17)K—F—Kvii82.492 (12)
Fvi—K—Fxi51.60 (2)Kiv—F—Kvii163.65 (3)
Fvii—K—Fxi84.886 (14)Ti—F—Kxx91.69 (3)
Fviii—K—Fxi51.601 (19)K—F—Kxx105.58 (3)
Fix—K—Fxi60.49 (3)Kiv—F—Kxx95.113 (14)
Fx—K—Fxi60.49 (3)Kvii—F—Kxx95.114 (14)
Fxii—Ti—Fxiii180.0Fxv—F—Fxii62.30 (4)
Fxii—Ti—Fxiv91.95 (3)Fxv—F—Fxvi90.00 (1)
Fxiii—Ti—Fxiv88.05 (3)Fxv—F—Fxiii58.85 (2)
Fxii—Ti—Fxv91.95 (3)Fxv—F—Fxiv45.97 (2)
Fxiii—Ti—Fxv88.05 (3)Fxii—F—Fxvi58.85 (2)
Fxiv—Ti—Fxv91.95 (3)Fxii—F—Fxiii90.000 (5)
Fxii—Ti—Fxvi88.05 (3)Fxii—F—Fxiv45.973 (15)
Fxiii—Ti—Fxvi91.95 (3)Fxvi—F—Fxiii60.000 (14)
Fxiv—Ti—Fxvi88.05 (3)Fxvi—F—Fxiv44.027 (16)
Fxv—Ti—Fxvi180.0Fxiii—F—Fxiv44.027 (17)
Symmetry codes: (i) x+y, x+1, z; (ii) y+1, xy+1, z; (iii) y, x+y+1, z+1; (iv) x, y+1, z+1; (v) xy+1, x+1, z+1; (vi) xy, 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, xy+1, z+1; (xi) x, y, z+1; (xii) xy, x, z; (xiii) x+y, x, z; (xiv) x, y, z; (xv) y, x+y, z; (xvi) y, xy, z; (xvii) x, y1, z1; (xviii) x1, y1, z1; (xix) x, y, z+1; (xx) x, y, z1.

Experimental details

Crystal data
Chemical formulaK2[TiF6]
Mr240.10
Crystal system, space groupTrigonal, P3m1
Temperature (K)298
a, c (Å)5.7354 (11), 4.6635 (18)
V3)132.85 (6)
Z1
Radiation typeMo Kα
µ (mm1)3.21
Crystal size (mm)0.12 × 0.12 × 0.12
Data collection
DiffractometerSiemens AED-II four-circle
diffractometer
Absorption correction
No. of measured, independent and
observed [I > 2σ(I)] reflections
4637, 553, 465
Rint0.054
(sin θ/λ)max1)1.074
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.028, 0.050, 1.15
No. of reflections553
No. of parameters13
Δρmax, Δρmin (e Å3)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).

Selected geometric parameters (Å, º) top
K—F2.8158 (9)Ti—F1.8605 (6)
K—Fi2.8972 (6)F—Fiii2.5860 (12)
K—Fii3.0375 (11)F—Fiv2.6754 (11)
Fv—Ti—F88.05 (3)Fiii—F—Fv62.30 (4)
Fiv—Ti—F91.95 (3)Fiii—F—Fiv58.85 (2)
Symmetry codes: (i) xy, x, z+1; (ii) x, y, z+1; (iii) y, x+y, z; (iv) x+y, x, z; (v) xy, x, z.
 

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