Optical anomaly in artificial cubic hieratite, K₂[SiF₆]

Crystals of K₂[SiF₆] were grown in agar gel, silica gel and jelly. Crystals grown in agar gel or jelly exhibit birefringence and consist of six double refracting growth sectors, each having the shape of a tetragonal pyramid. Nevertheless, the structure of the crystals from agar gel could be refined as cubic (space group ) with a weighted R factor of 0.043. The amount of birefringence was estimated by the Senarmont compensation method and the rotating polarizer method.

Computing details

Data collection: Apex2 (Bruker, 2010); cell refinement: SAINT V7.68A (Bruker, 2010); data reduction: SAINT V7.68A (Bruker, 2010), SADABS2008/1 (Sheldrick, 2008); program(s) used to solve structure: SHELXS97 (Sheldrick, 1990); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997).

(I)

Crystal data

F6K2Si	Mo Kα radiation, λ = 0.71073 Å
Mr = 220.29	Cell parameters from 2659 reflections
Cubic, Fm3m	θ = 5.0–40.0°
a = 8.1345 (8) Å	µ = 2.02 mm^−1
V = 538.26 (9) Å^3	T = 298 K
Z = 4	Cube, colourless
F(000) = 424	0.26 × 0.26 × 0.26 mm
Dx = 2.718 Mg m^−3

Data collection

Bruker Kappa ApexII area detector diffractometer	116 independent reflections
Radiation source: fine-focus sealed tube	113 reflections with I > 2σ(I)
Triumph monochromator	Rint = 0.014
ω scans	θmax = 40.3°, θmin = 5.0°
Absorption correction: multi-scan SADABS-2008/1 (Sheldrick, 2008)	h = −14→12
Tmin = 0.706, Tmax = 0.748	k = −13→14
3622 measured reflections	l = −14→12

Refinement

Refinement on F^2	0 restraints
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F^2 > 2σ(F^2)] = 0.016	Secondary atom site location: difference Fourier map
wR(F^2) = 0.043	w = 1/[σ^2(Fo^2) + (0.0189P)^2 + 0.3956P] where P = (Fo^2 + 2Fc^2)/3
S = 1.12	(Δ/σ)max < 0.001
116 reflections	Δρmax = 0.28 e Å^−3
6 parameters	Δρmin = −0.30 e Å^−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
F	0.20675 (11)	0.0000	0.0000	0.0292 (2)
Si	0.0000	0.0000	0.0000	0.01660 (16)
K	0.2500	0.2500	0.2500	0.02396 (14)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
F	0.0163 (3)	0.0356 (3)	0.0356 (3)	0.000	0.000	0.000
Si	0.01660 (16)	0.01660 (16)	0.01660 (16)	0.000	0.000	0.000
K	0.02396 (14)	0.02396 (14)	0.02396 (14)	0.000	0.000	0.000

Geometric parameters (Å, º)

F—Si	1.6818 (9)	Si—K^x	3.5223 (3)
F—K	2.8974 (3)	Si—K^i	3.5223 (3)
F—K^i	2.8974 (3)	K—F^v	2.8974 (3)
F—K^ii	2.8974 (3)	K—F^viii	2.8974 (3)
F—K^iii	2.8974 (3)	K—F^xi	2.8974 (3)
Si—F^iv	1.6818 (9)	K—F^xii	2.8974 (3)
Si—F^v	1.6818 (9)	K—F^xiii	2.8974 (3)
Si—F^vi	1.6818 (9)	K—F^xiv	2.8974 (3)
Si—F^vii	1.6818 (9)	K—F^ii	2.8974 (3)
Si—F^viii	1.6818 (9)	K—F^xv	2.8974 (3)
Si—K^vii	3.5223 (3)	K—F^xvi	2.8974 (3)
Si—K	3.5223 (3)	K—F^xvii	2.8974 (3)
Si—K^ii	3.5223 (3)	K—F^iii	2.8974 (3)
Si—K^ix	3.5223 (3)
Si—F—K	96.974 (18)	K^vii—Si—K^i	70.5
Si—F—K^i	96.974 (18)	K—Si—K^i	109.5
K—F—K^i	166.05 (4)	K^ii—Si—K^i	70.5
Si—F—K^ii	96.974 (18)	K^ix—Si—K^i	109.5
K—F—K^ii	89.155 (4)	K^x—Si—K^i	109.5
K^i—F—K^ii	89.155 (4)	F—K—F^v	48.47 (3)
Si—F—K^iii	96.974 (18)	F—K—F^viii	48.47 (3)
K—F—K^iii	89.155 (4)	F^v—K—F^viii	48.46 (3)
K^i—F—K^iii	89.155 (4)	F—K—F^xi	119.513 (2)
K^ii—F—K^iii	166.05 (4)	F^v—K—F^xi	166.05 (4)
F^iv—Si—F^v	180.0	F^viii—K—F^xi	119.513 (2)
F^iv—Si—F^vi	90.0	F—K—F^xii	119.513 (2)
F^v—Si—F^vi	90.0	F^v—K—F^xii	119.513 (2)
F^iv—Si—F^vii	90.0	F^viii—K—F^xii	166.05 (4)
F^v—Si—F^vii	90.0	F^xi—K—F^xii	71.21 (3)
F^vi—Si—F^vii	90.0	F—K—F^xiii	166.05 (4)
F^iv—Si—F^viii	90.0	F^v—K—F^xiii	119.513 (2)
F^v—Si—F^viii	90.0	F^viii—K—F^xiii	119.513 (2)
F^vi—Si—F^viii	180.0	F^xi—K—F^xiii	71.21 (3)
F^vii—Si—F^viii	90.0	F^xii—K—F^xiii	71.21 (3)
F^iv—Si—F	90.0	F—K—F^xiv	71.21 (3)
F^v—Si—F	90.0	F^v—K—F^xiv	90.845 (4)
F^vi—Si—F	90.0	F^viii—K—F^xiv	119.513 (2)
F^vii—Si—F	180.0	F^xi—K—F^xiv	90.845 (4)
F^viii—Si—F	90.0	F^xii—K—F^xiv	48.46 (3)
F^iv—Si—K^vii	54.740 (10)	F^xiii—K—F^xiv	119.513 (2)
F^v—Si—K^vii	125.3	F—K—F^ii	90.845 (4)
F^vi—Si—K^vii	54.740 (10)	F^v—K—F^ii	119.513 (2)
F^vii—Si—K^vii	54.740 (10)	F^viii—K—F^ii	71.21 (3)
F^viii—Si—K^vii	125.3	F^xi—K—F^ii	48.46 (3)
F—Si—K^vii	125.3	F^xii—K—F^ii	119.513 (2)
F^iv—Si—K	125.3	F^xiii—K—F^ii	90.845 (4)
F^v—Si—K	54.740 (10)	F^xiv—K—F^ii	119.513 (2)
F^vi—Si—K	125.3	F—K—F^xv	119.514 (2)
F^vii—Si—K	125.3	F^v—K—F^xv	71.21 (3)
F^viii—Si—K	54.740 (10)	F^viii—K—F^xv	90.845 (4)
F—Si—K	54.740 (10)	F^xi—K—F^xv	119.513 (2)
K^vii—Si—K	180.0	F^xii—K—F^xv	90.845 (4)
F^iv—Si—K^ii	54.740 (10)	F^xiii—K—F^xv	48.46 (3)
F^v—Si—K^ii	125.3	F^xiv—K—F^xv	119.513 (2)
F^vi—Si—K^ii	125.3	F^ii—K—F^xv	119.513 (2)
F^vii—Si—K^ii	125.3	F—K—F^xvi	71.21 (3)
F^viii—Si—K^ii	54.740 (10)	F^v—K—F^xvi	119.513 (2)
F—Si—K^ii	54.740 (10)	F^viii—K—F^xvi	90.845 (4)
K^vii—Si—K^ii	109.5	F^xi—K—F^xvi	48.46 (3)
K—Si—K^ii	70.5	F^xii—K—F^xvi	90.845 (4)
F^iv—Si—K^ix	54.740 (10)	F^xiii—K—F^xvi	119.513 (2)
F^v—Si—K^ix	125.3	F^xiv—K—F^xvi	71.21 (3)
F^vi—Si—K^ix	125.3	F^ii—K—F^xvi	48.46 (3)
F^vii—Si—K^ix	54.740 (10)	F^xv—K—F^xvi	166.05 (4)
F^viii—Si—K^ix	54.740 (10)	F—K—F^xvii	119.514 (2)
F—Si—K^ix	125.3	F^v—K—F^xvii	90.845 (4)
K^vii—Si—K^ix	70.5	F^viii—K—F^xvii	71.21 (3)
K—Si—K^ix	109.5	F^xi—K—F^xvii	90.845 (4)
K^ii—Si—K^ix	70.5	F^xii—K—F^xvii	119.513 (2)
F^iv—Si—K^x	125.3	F^xiii—K—F^xvii	48.46 (3)
F^v—Si—K^x	54.740 (10)	F^xiv—K—F^xvii	166.05 (4)
F^vi—Si—K^x	54.740 (10)	F^ii—K—F^xvii	71.21 (3)
F^vii—Si—K^x	54.740 (10)	F^xv—K—F^xvii	48.46 (3)
F^viii—Si—K^x	125.3	F^xvi—K—F^xvii	119.513 (2)
F—Si—K^x	125.3	F—K—F^iii	90.845 (4)
K^vii—Si—K^x	70.5	F^v—K—F^iii	71.21 (3)
K—Si—K^x	109.5	F^viii—K—F^iii	119.513 (2)
K^ii—Si—K^x	180.0	F^xi—K—F^iii	119.513 (2)
K^ix—Si—K^x	109.5	F^xii—K—F^iii	48.46 (3)
F^iv—Si—K^i	54.740 (10)	F^xiii—K—F^iii	90.845 (4)
F^v—Si—K^i	125.3	F^xiv—K—F^iii	48.46 (3)
F^vi—Si—K^i	54.740 (10)	F^ii—K—F^iii	166.05 (4)
F^vii—Si—K^i	125.3	F^xv—K—F^iii	71.21 (3)
F^viii—Si—K^i	125.3	F^xvi—K—F^iii	119.513 (2)
F—Si—K^i	54.740 (10)	F^xvii—K—F^iii	119.513 (2)

Symmetry codes: (i) x, y−1/2, z−1/2; (ii) −x+1/2, −y+1/2, −z; (iii) −x+1/2, −y, −z+1/2; (iv) −y, −z, −x; (v) y, z, x; (vi) −z, −x, −y; (vii) −x, −y, −z; (viii) z, x, y; (ix) x−1/2, y, z−1/2; (x) x−1/2, y−1/2, z; (xi) y+1/2, z+1/2, x; (xii) z+1/2, x, y+1/2; (xiii) x, y+1/2, z+1/2; (xiv) −y+1/2, −z, −x+1/2; (xv) −z, −x+1/2, −y+1/2; (xvi) −z+1/2, −x+1/2, −y; (xvii) −y, −z+1/2, −x+1/2.