Rerefinement of K₂[TiF₆]

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 m), and K⁺ is 12-coordinate (point group 3m). The dispersion of birefringence is presented.

S1. Comment

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 = n_e - n_o 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) = 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, λ₀, the optical behaviour of K₂[TiF₆] should be isotropic and the sign of birefringence should change.

S2. Experimental

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.

S3. Refinement

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).

Computing details

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

	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.
	Fig. 2. The birefringence of K2[TiF6] as a function of wavelength.

dipotassium hexafluorotitanate(IV)

Crystal data

K2[TiF6]	Dx = 3.001 Mg m^−3
Mr = 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

Data collection

Siemens AED-II four-circle diffractometer	Rint = 0.054
Radiation source: fine-focus sealed tube	θmax = 49.8°, θmin = 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

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(Fo^2) + (0.0183P)^2 + 0.0142P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.050	(Δ/σ)max < 0.001
S = 1.15	Δρmax = 0.57 e Å^−3
553 reflections	Δρmin = −0.70 e Å^−3
13 parameters	Extinction correction: SHELXL (Sheldrick, 1997), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.54 (3)

Special details

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 (Ų)

	x	y	z	Uiso*/Ueq
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)

Atomic displacement parameters (Ų)

	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)

Geometric parameters (Å, º)

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.