Refinement of the crystal structure of fresnoite, Ba₂TiSi₂O₈, from Löhley (Eifel district, Germany); Gladstone–Dale compatibility, electronic polarizability and vibrational spectroscopy of minerals and inorganic compounds with pentacoordinated Ti^IV and a titanyl bond

Most known compounds with five-coordinated Ti⁴⁺ are natural and synthetic titanosilicates. The crystal structure of natural fresnoite, Ba₂TiSi₂O₈ [tetragonal, space group P4bm, a = 8.510 (1) Å, c = 5.197 (1) Å, V = 376.4 (1) ų, Z = 2], has been refined to R = 0.011 on the basis of 807 unique single-crystal reflections with I > 2σ(I). Titanium has fivefold coordination with one short (`titanyl') bond of 1.692 (5) Å. Bonds in the TiO<sub>5</sub> polyhedron are discussed in comparison to analogous coordination polyhedra in other minerals and compounds. A review of all known compounds with Ti<sup>4+</sup>O<sub>5</sub> polyhedra shows that most of them are titanosilicates in which titanium forms a short Ti—O bond (∼1.61 to ∼1.77 Å). Poor Gladstone–Dale compatibility between chemical composition, optical characteristics and density of these compounds is explained by the anomalous contribution of <sup>[5]</sup>Ti<sup>4+</sup> to the optical properties as shown by calculations based on the relationship between electronic polarizabilities and refractive indices. An improved Gladstone–Dale coefficient of 0.29 is suggested for TiO<sub>2</sub> with <sup>[5]</sup>Ti<sup>4+</sup>. A negative correlation between `titanyl' bond lengths and wavenumbers of the bands of Ti—O stretching vibrations (in the range of 890–830 cm⁻¹) in infrared and Raman spectra is observed.

Computing details

Program(s) used to refine structure: SHELXL2018/3 (Sheldrick, 2018).

(I)

Crystal data

Ba2O8Si2Ti	Dx = 4.471 Mg m^−3
Mr = 506.76	Mo Kα radiation, λ = 0.71073 Å
Tetragonal, P4bm	Cell parameters from 11109 reflections
a = 8.5104 (12) Å	θ = 3.4–33.4°
c = 5.1975 (10) Å	µ = 11.71 mm^−1
V = 376.44 (13) Å^3	T = 293 K
Z = 2	Parallelepiped, yellow
F(000) = 452	0.25 × 0.14 × 0.13 mm

Data collection

Xcalibur, Eos diffractometer	θmax = 33.4°, θmin = 3.4°
25512 measured reflections	h = −13→13
807 independent reflections	k = −13→13
806 reflections with I > 2σ(I)	l = −8→8
Rint = 0.033

Refinement

Refinement on F^2	w = 1/[σ^2(Fo^2) + (0.0047P)^2 + 0.9597P] where P = (Fo^2 + 2Fc^2)/3
Least-squares matrix: full	(Δ/σ)max = 0.001
R[F^2 > 2σ(F^2)] = 0.012	Δρmax = 0.87 e Å^−3
wR(F^2) = 0.027	Δρmin = −0.65 e Å^−3
S = 1.20	Extinction correction: SHELXL-2018/3 (Sheldrick 2018), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
807 reflections	Extinction coefficient: 0.0165 (7)
40 parameters	Absolute structure: Refined as an inversion twin.
1 restraint	Absolute structure parameter: 0.01 (3)

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Refinement. Refined as a 2-component inversion twin.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Ba1	0.32715 (2)	0.82715 (2)	0.00051 (5)	0.00865 (7)
Ti2	0.000000	0.000000	0.53608 (18)	0.00667 (19)
Si1	0.12793 (9)	0.62793 (9)	0.5130 (4)	0.00767 (17)
O1	0.000000	0.000000	0.2106 (9)	0.0149 (9)
O2	0.000000	0.500000	0.6300 (10)	0.0250 (13)
O3	0.1260 (3)	0.6260 (3)	0.2067 (6)	0.0088 (5)
O4	0.2922 (3)	0.5761 (4)	0.6451 (5)	0.0236 (7)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ba1	0.00940 (8)	0.00940 (8)	0.00715 (9)	−0.00491 (6)	−0.00086 (9)	−0.00086 (9)
Ti2	0.0071 (2)	0.0071 (2)	0.0057 (5)	0.000	0.000	0.000
Si1	0.0087 (2)	0.0087 (2)	0.0055 (4)	0.0013 (3)	−0.0013 (4)	−0.0013 (4)
O1	0.0178 (14)	0.0178 (14)	0.0091 (18)	0.000	0.000	0.000
O2	0.035 (2)	0.035 (2)	0.0056 (18)	−0.022 (3)	0.000	0.000
O3	0.0098 (8)	0.0098 (8)	0.0067 (12)	−0.0013 (11)	−0.0002 (7)	−0.0002 (7)
O4	0.0142 (11)	0.0462 (19)	0.0105 (10)	0.0150 (12)	−0.0035 (9)	−0.0075 (11)

Geometric parameters (Å, º)

Ba1—O3	2.647 (3)	Ba1—Si1	3.5838 (17)
Ba1—O3^i	2.789 (2)	Ti2—O1	1.692 (5)
Ba1—O3^ii	2.789 (2)	Ti2—O4^viii	1.967 (3)
Ba1—O4^iii	2.840 (3)	Ti2—O4^ix	1.967 (3)
Ba1—O4^iv	2.840 (3)	Ti2—O4^x	1.967 (3)
Ba1—O2^v	2.835 (3)	Ti2—O4^xi	1.967 (3)
Ba1—O4^vi	2.989 (4)	Si1—O3	1.592 (4)
Ba1—O4^vii	2.989 (4)	Si1—O4^xii	1.619 (3)
Ba1—Si1^iv	3.4885 (16)	Si1—O4	1.619 (3)
Ba1—Si1^vii	3.6220 (15)	Si1—O2	1.655 (2)
Ba1—Si1^v	3.6220 (15)
O3—Ba1—O3^i	121.77 (10)	O4^ix—Ti2—Ba1^xiv	112.91 (10)
O3—Ba1—O3^ii	121.77 (10)	O4^x—Ti2—Ba1^xiv	109.48 (9)
O3^i—Ba1—O3^ii	65.89 (12)	O4^xi—Ti2—Ba1^xiv	42.28 (9)
O3—Ba1—O4^iii	73.10 (9)	Ba1^xiii—Ti2—Ba1^xiv	68.276 (14)
O3^i—Ba1—O4^iii	162.00 (10)	O1—Ti2—Ba1^xv	127.473 (13)
O3^ii—Ba1—O4^iii	116.94 (8)	O4^viii—Ti2—Ba1^xv	112.91 (10)
O3—Ba1—O4^iv	73.10 (9)	O4^ix—Ti2—Ba1^xv	109.48 (9)
O3^i—Ba1—O4^iv	116.94 (8)	O4^x—Ti2—Ba1^xv	42.28 (9)
O3^ii—Ba1—O4^iv	162.00 (9)	O4^xi—Ti2—Ba1^xv	46.84 (11)
O4^iii—Ba1—O4^iv	54.51 (11)	Ba1^xiii—Ti2—Ba1^xv	105.05 (3)
O3—Ba1—O2^v	161.09 (10)	Ba1^xiv—Ti2—Ba1^xv	68.276 (14)
O3^i—Ba1—O2^v	73.36 (8)	O1—Ti2—Ba1^xvi	127.473 (13)
O3^ii—Ba1—O2^v	73.36 (8)	O4^viii—Ti2—Ba1^xvi	109.48 (9)
O4^iii—Ba1—O2^v	90.16 (10)	O4^ix—Ti2—Ba1^xvi	42.28 (9)
O4^iv—Ba1—O2^v	90.16 (10)	O4^x—Ti2—Ba1^xvi	46.84 (11)
O3—Ba1—O4^vi	119.26 (6)	O4^xi—Ti2—Ba1^xvi	112.91 (10)
O3^i—Ba1—O4^vi	116.50 (7)	Ba1^xiii—Ti2—Ba1^xvi	68.276 (14)
O3^ii—Ba1—O4^vi	68.87 (9)	Ba1^xiv—Ti2—Ba1^xvi	105.05 (3)
O4^iii—Ba1—O4^vi	54.30 (10)	Ba1^xv—Ti2—Ba1^xvi	68.276 (14)
O4^iv—Ba1—O4^vi	95.49 (8)	O3—Si1—O4^xii	115.48 (13)
O2^v—Ba1—O4^vi	52.32 (6)	O3—Si1—O4	115.48 (13)
O3—Ba1—O4^vii	119.26 (6)	O4^xii—Si1—O4	106.9 (2)
O3^i—Ba1—O4^vii	68.87 (9)	O3—Si1—O2	110.7 (2)
O3^ii—Ba1—O4^vii	116.50 (7)	O4^xii—Si1—O2	103.48 (17)
O4^iii—Ba1—O4^vii	95.49 (8)	O4—Si1—O2	103.48 (17)
O4^iv—Ba1—O4^vii	54.30 (10)	O3—Si1—Ba1^xvii	137.41 (13)
O2^v—Ba1—O4^vii	52.32 (6)	O4^xii—Si1—Ba1^xvii	53.45 (12)
O4^vi—Ba1—O4^vii	95.74 (11)	O4—Si1—Ba1^xvii	53.45 (12)
O3—Ba1—Si1^iv	70.46 (7)	O2—Si1—Ba1^xvii	111.87 (18)
O3^i—Ba1—Si1^iv	142.36 (7)	O3—Si1—Ba1^xviii	133.90 (8)
O3^ii—Ba1—Si1^iv	142.36 (7)	O4^xii—Si1—Ba1^xviii	54.53 (13)
O4^iii—Ba1—Si1^iv	27.26 (6)	O4—Si1—Ba1^xviii	110.02 (13)
O4^iv—Ba1—Si1^iv	27.26 (6)	O2—Si1—Ba1^xviii	49.28 (11)
O2^v—Ba1—Si1^iv	90.63 (8)	Ba1^xvii—Si1—Ba1^xviii	77.53 (4)
O4^vi—Ba1—Si1^iv	74.36 (6)	O3—Si1—Ba1^xiii	133.90 (8)
O4^vii—Ba1—Si1^iv	74.36 (6)	O4^xii—Si1—Ba1^xiii	110.02 (13)
O3—Ba1—Si1^vii	143.94 (5)	O4—Si1—Ba1^xiii	54.53 (13)
O3^i—Ba1—Si1^vii	67.00 (7)	O2—Si1—Ba1^xiii	49.28 (11)
O3^ii—Ba1—Si1^vii	94.10 (5)	Ba1^xvii—Si1—Ba1^xiii	77.53 (4)
O4^iii—Ba1—Si1^vii	95.03 (8)	Ba1^xviii—Si1—Ba1^xiii	70.11 (3)
O4^iv—Ba1—Si1^vii	72.44 (7)	O3—Si1—Ba1	42.82 (13)
O2^v—Ba1—Si1^vii	26.27 (3)	O4^xii—Si1—Ba1	92.03 (13)
O4^vi—Ba1—Si1^vii	74.52 (6)	O4—Si1—Ba1	92.03 (13)
O4^vii—Ba1—Si1^vii	26.17 (5)	O2—Si1—Ba1	153.54 (18)
Si1^iv—Ba1—Si1^vii	83.49 (4)	Ba1^xvii—Si1—Ba1	94.59 (3)
O3—Ba1—Si1^v	143.94 (5)	Ba1^xviii—Si1—Ba1	143.548 (14)
O3^i—Ba1—Si1^v	94.10 (5)	Ba1^xiii—Si1—Ba1	143.548 (14)
O3^ii—Ba1—Si1^v	67.00 (7)	O3—Si1—Ba1^xix	43.69 (7)
O4^iii—Ba1—Si1^v	72.44 (7)	O4^xii—Si1—Ba1^xix	91.58 (11)
O4^iv—Ba1—Si1^v	95.03 (8)	O4—Si1—Ba1^xix	158.05 (12)
O2^v—Ba1—Si1^v	26.27 (3)	O2—Si1—Ba1^xix	82.98 (14)
O4^vi—Ba1—Si1^v	26.17 (5)	Ba1^xvii—Si1—Ba1^xix	143.696 (15)
O4^vii—Ba1—Si1^v	74.52 (6)	Ba1^xviii—Si1—Ba1^xix	90.22 (2)
Si1^iv—Ba1—Si1^v	83.49 (4)	Ba1^xiii—Si1—Ba1^xix	130.33 (3)
Si1^vii—Ba1—Si1^v	50.31 (4)	Ba1—Si1—Ba1^xix	75.19 (4)
O3—Ba1—Si1	24.13 (7)	O3—Si1—Ba1^xx	43.69 (7)
O3^i—Ba1—Si1	102.32 (6)	O4^xii—Si1—Ba1^xx	158.05 (12)
O3^ii—Ba1—Si1	102.32 (6)	O4—Si1—Ba1^xx	91.58 (11)
O4^iii—Ba1—Si1	94.48 (7)	O2—Si1—Ba1^xx	82.98 (14)
O4^iv—Ba1—Si1	94.48 (7)	Ba1^xvii—Si1—Ba1^xx	143.696 (15)
O2^v—Ba1—Si1	174.78 (8)	Ba1^xviii—Si1—Ba1^xx	130.33 (3)
O4^vi—Ba1—Si1	129.34 (5)	Ba1^xiii—Si1—Ba1^xx	90.22 (2)
O4^vii—Ba1—Si1	129.34 (5)	Ba1—Si1—Ba1^xx	75.19 (4)
Si1^iv—Ba1—Si1	94.59 (3)	Ba1^xix—Si1—Ba1^xx	68.13 (3)
Si1^vii—Ba1—Si1	154.718 (15)	Si1^xxi—O2—Si1	136.9 (3)
Si1^v—Ba1—Si1	154.718 (15)	Si1^xxi—O2—Ba1^xiii	104.45 (9)
O1—Ti2—O4^viii	106.75 (9)	Si1—O2—Ba1^xiii	104.45 (9)
O1—Ti2—O4^ix	106.75 (9)	Si1^xxi—O2—Ba1^xviii	104.45 (9)
O4^viii—Ti2—O4^ix	85.24 (5)	Si1—O2—Ba1^xviii	104.45 (9)
O1—Ti2—O4^x	106.75 (9)	Ba1^xiii—O2—Ba1^xviii	94.41 (15)
O4^viii—Ti2—O4^x	146.51 (18)	Si1—O3—Ba1	113.05 (17)
O4^ix—Ti2—O4^x	85.24 (5)	Si1—O3—Ba1^xix	113.09 (11)
O1—Ti2—O4^xi	106.75 (9)	Ba1—O3—Ba1^xix	109.98 (8)
O4^viii—Ti2—O4^xi	85.24 (5)	Si1—O3—Ba1^xx	113.09 (11)
O4^ix—Ti2—O4^xi	146.51 (18)	Ba1—O3—Ba1^xx	109.98 (8)
O4^x—Ti2—O4^xi	85.24 (5)	Ba1^xix—O3—Ba1^xx	96.49 (10)
O1—Ti2—Ba1^xiii	127.473 (13)	Si1—O4—Ti2^xxii	138.08 (18)
O4^viii—Ti2—Ba1^xiii	42.28 (9)	Si1—O4—Ba1^xvii	99.29 (14)
O4^ix—Ti2—Ba1^xiii	46.84 (11)	Ti2^xxii—O4—Ba1^xvii	109.95 (13)
O4^x—Ti2—Ba1^xiii	112.91 (10)	Si1—O4—Ba1^xiii	99.30 (15)
O4^xi—Ti2—Ba1^xiii	109.48 (9)	Ti2^xxii—O4—Ba1^xiii	104.49 (13)
O1—Ti2—Ba1^xiv	127.473 (13)	Ba1^xvii—O4—Ba1^xiii	99.60 (9)
O4^viii—Ti2—Ba1^xiv	46.84 (11)

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