Superspace-symmetry determination and multi­dimensional refinement of the incommensurately modulated structure of natural fresnoite

Bindi, L.; Dusek, M.; Petricek, V.; Bonazzi, P.

doi:10.1107/S0108768106030059

Superspace-symmetry determination and multidimensional refinement of the incommensurately modulated structure of natural fresnoite

L. Bindi, M. Dusek, V. Petricek and P. Bonazzi

The structure of natural fresnoite, Ba₂TiSi₂O₈, from the sanbornite deposits of eastern Fresno County, California, has been solved and refined as an incommensurate structure in five-dimensional superspace. The structure is tetragonal, superspace group $P4bm\left({\alpha, \alpha, 1/2} \right)\left({ - \alpha, \alpha, 1/2} \right)0gg$ , cell parameters a = 8.5353 (6), c = 10.4128 (7) Å, modulation vectors ${\bf q}_1 = 0.3020\,\left(3 \right)\,\left({{\bf a}^* + {\bf b}^* } \right)$ , ${\bf q}_2 = 0.3020\,\left(3 \right)\,\left({ - {\bf a}^* + {\bf b}^* } \right)$ . Data collection was performed on an Xcalibur CCD diffractometer at 110 K. The structure was refined from 3452 reflections to final R = 0.0123. The model includes modulation of both atomic positions and displacement parameters. As a consequence of the Ba and O positional modulation, eight-, nine- and tenfold Ba coordinations occur throughout the structure. The change of coordination around the Ba atom is clearly represented by the deformation of the pentagonal rings, as seen from a projection along [001]. The deformed pentagonal rings correspond to Ba atoms with eight- and ninefold coordinations and form octagonal clusters closely resembling those observed in the incommensurate structure of melilite-type compounds.

Keywords: fresnoite; (3+2)-dimensional refinement; chemical analysis; modulated structure.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768106030059/ck5019sup1.cif Contains datablocks global, I
	Structure factor file (CIF format) https://doi.org/10.1107/S0108768106030059/ck5019sup2.hkl Supplementary material

Computing details top

Data collection: CrysAlis PRO CCD (Oxford diffraction, 2005); cell refinement: CrysAlis PRO RED (Oxford diffraction, 2005); data reduction: CrysAlis PRO RED (Oxford diffraction, 2005); program(s) used to solve structure: SIR2002 (Burla et al., 2003); program(s) used to refine structure: (Jana2000; Petricek, Dusek and Palatinus, 2000); software used to prepare material for publication: (Jana2000; Petricek, Dusek and Palatinus, 2000).

Figures top

(I) top

Crystal data top

Ba₂O₈Si₂Ti	D_x = 4.435 Mg m⁻³
M_r = 506.7	Mo Kα radiation, λ = 0.71069 Å
Tetragonal, X4bm†	Cell parameters from 20966 reflections
q₁ = 0.30200a* + 0.30200b; q₂ = -0.30200a + 0.30200b*	θ = 3.2–36.2°
a = 8.5353 Å	µ = 11.67 mm⁻¹
c = 10.4128 Å	T = 110 K
V = 758.59 Å³	Irregular, yellow
Z = 4	0.09 × 0.06 × 0.03 mm
F(000) = 904

† Symmetry operations: (1) x₁, x₂, x₃, x₄, x₅; (2) −x₂, x₁, x₃, −x₅, x₄; (3) 1/2−x₁, 1/2+x₂, x₃, 1/2+x₅, 1/2+x₄; (4) −x₁, −x₂, x₃, −x₄, −x₅; (5) 1/2−x₂, 1/2−x₁, x₃, 1/2−x₄, 1/2+x₅; (6) x₂, −x₁, x₃, x₅, −x₄; (7) 1/2+x₁, 1/2−x₂, x₃, 1/2−x₅, 1/2−x₄; (8) 1/2+x₂, 1/2+x₁, x₃, 1/2+x₄, 1/2−x₅; (9) x₁, x₂, 1/2+x₃, 1/2+x₄, 1/2+x₅; (10) −x₂, x₁, 1/2+x₃, 1/2−x₅, 1/2+x₄; (11) 1/2−x₁, 1/2+x₂, 1/2+x₃, x₅, x₄; (12) −x₁, −x₂, 1/2+x₃, 1/2−x₄, 1/2−x₅; (13) 1/2−x₂, 1/2−x₁, 1/2+x₃, −x₄, x₅; (14) x₂, −x₁, 1/2+x₃, 1/2+x₅, 1/2−x₄; (15) 1/2+x₁, 1/2−x₂, 1/2+x₃, −x₅, −x₄; (16) 1/2+x₂, 1/2+x₁, 1/2+x₃, x₄, −x₅.

Data collection top

O110rd Diffraction CCD diffractometer	3452 independent reflections
Radiation source: X-ray tube	2554 reflections with I > 3σ(I)
Graphite monochromator	R_int = 0.030
Detector resolution: 8.3438 pixels mm^-1	θ_max = 36.2°, θ_min = 2.6°
Rotation method data acquisition using ω scans	h = −12→12
Absorption correction: gaussian (Jana2000; Petricek, Dusek & Palatinus, 2000)	k = −13→13
T_min = 0.314, T_max = 0.520	l = −14→14
43094 measured reflections

Refinement top

Refinement on F	Weighting scheme based on measured s.u.'s w = 1/(σ²(F) + 0.0001F²)
R[F² > 2σ(F²)] = 0.012	(Δ/σ)_max = 0.028
wR(F²) = 0.018	Δρ_max = 0.27 e Å⁻³
S = 0.94	Δρ_min = −0.32 e Å⁻³
3452 reflections	Absolute structure: The absolute configuration was determined by the refinement of the twin fraction (Flack, 1983) of two domains related by the inversion center in the refinement program Jana2000 (Petricek and Dusek, 2000).
259 parameters	Absolute structure parameter: 0.932 (9)

Crystal data top

Ba₂O₈Si₂Ti	V = 758.59 Å³
M_r = 506.7	Z = 4
Tetragonal, X4bm†	Mo Kα radiation
q₁ = 0.30200a* + 0.30200b; q₂ = -0.30200a + 0.30200b*	µ = 11.67 mm⁻¹
a = 8.5353 Å	T = 110 K
c = 10.4128 Å	0.09 × 0.06 × 0.03 mm

Data collection top

O110rd Diffraction CCD diffractometer	3452 independent reflections
Absorption correction: gaussian (Jana2000; Petricek, Dusek & Palatinus, 2000)	2554 reflections with I > 3σ(I)
T_min = 0.314, T_max = 0.520	R_int = 0.030
43094 measured reflections

Refinement top

R[F² > 2σ(F²)] = 0.012	Δρ_max = 0.27 e Å⁻³
wR(F²) = 0.018	Δρ_min = −0.32 e Å⁻³
S = 0.94	Absolute structure: The absolute configuration was determined by the refinement of the twin fraction (Flack, 1983) of two domains related by the inversion center in the refinement program Jana2000 (Petricek and Dusek, 2000).
3452 reflections	Absolute structure parameter: 0.932 (9)
259 parameters

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Ba1	0.327017 (7)	−0.827017 (7)	0	0.00593 (3)
Ti1	0	0	0.26787 (5)	0.00429 (13)
Si1	0.12809 (4)	−0.62809 (4)	0.25638 (7)	0.00478 (9)
O1	0	−0.5	0.3150 (2)	0.0108 (4)
O2	0.12591 (12)	−0.62591 (12)	0.10297 (15)	0.0063 (3)
O3	0.29256 (12)	−0.57809 (10)	0.32144 (11)	0.0109 (2)
O4	0	0	0.1049 (2)	0.0100 (4)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Ba1	0.00617 (5)	0.00617 (5)	0.00544 (7)	0.00286 (3)	−0.00014 (4)	0.00014 (4)
Ti1	0.00301 (13)	0.00301 (13)	0.0068 (3)	0	0	0
Si1	0.00484 (12)	0.00484 (12)	0.0047 (2)	−0.00072 (18)	0.00021 (17)	−0.00021 (17)
O1	0.0112 (5)	0.0112 (5)	0.0099 (9)	0.0053 (6)	0	0
O2	0.0064 (4)	0.0064 (4)	0.0061 (7)	−0.0001 (5)	0.0008 (4)	−0.0008 (4)
O3	0.0073 (4)	0.0139 (4)	0.0115 (5)	−0.0040 (3)	−0.0012 (4)	0.0034 (3)
O4	0.0085 (6)	0.0085 (6)	0.0129 (10)	0	0	0

Bond lengths (Å) top

	Average	Minimum	Maximum
Ba1—Si1ⁱ	3.4960 (17)	3.4616 (17)	3.5285 (17)
Ba1—O1ⁱⁱ	2.850 (3)	2.733 (3)	2.961 (3)
Ba1—O2	2.655 (3)	2.642 (3)	2.672 (3)
Ba1—O2ⁱⁱⁱ	2.797 (3)	2.756 (3)	2.843 (3)
Ba1—O2^iv	2.799 (3)	2.756 (3)	2.843 (3)
Ba1—O3ⁱ	2.844 (4)	2.729 (4)	3.017 (4)
Ba1—O3ⁱⁱ	3.011 (4)	2.747 (4)	3.503 (4)
Ba1—O3^v	3.007 (4)	2.747 (4)	3.503 (4)
Ba1—O3^vi	2.846 (4)	2.729 (4)	3.016 (4)
Ba1—O4^vii	3.344 (3)	3.100 (3)	3.553 (3)
Ba1—O4^iv	3.345 (3)	3.100 (3)	3.553 (3)
Ti1—Si1^viii	3.3610 (14)	3.3502 (14)	3.3697 (14)
Ti1—Si1^ix	3.3610 (14)	3.3502 (14)	3.3697 (14)
Ti1—Si1^x	3.3610 (14)	3.3502 (14)	3.3697 (14)
Ti1—Si1^xi	3.3610 (14)	3.3502 (14)	3.3697 (14)
Ti1—O3^x	1.979 (4)	1.962 (4)	1.995 (4)
Ti1—O3^xii	1.979 (4)	1.962 (4)	1.995 (4)
Ti1—O3^xiii	1.979 (4)	1.962 (4)	1.995 (4)
Ti1—O3^xiv	1.979 (4)	1.962 (4)	1.995 (4)
Ti1—O4	1.696 (4)	1.688 (6)	1.703 (6)
Ti1—O4^xv	3.508 (4)	3.405 (6)	3.617 (6)
Si1—Si1^xi	3.0936 (18)	3.0924 (18)	3.0949 (18)
Si1—O1	1.669 (3)	1.655 (2)	1.685 (4)
Si1—O2	1.598 (4)	1.597 (3)	1.601 (3)
Si1—O2^xi	3.460 (4)	3.438 (4)	3.481 (4)
Si1—O3	1.623 (4)	1.611 (4)	1.638 (4)
Si1—O3^xvi	1.623 (4)	1.611 (4)	1.638 (4)
O1—O2	2.686 (4)	2.665 (4)	2.708 (4)
O1—O2^xv	3.366 (4)	3.292 (4)	3.448 (4)
O1—O2^xi	2.687 (4)	2.665 (4)	2.708 (4)
O1—O2^xvii	3.369 (4)	3.292 (4)	3.448 (4)
O1—O3	2.599 (5)	2.564 (4)	2.651 (5)
O1—O3^xi	2.599 (4)	2.564 (4)	2.651 (5)
O1—O3^xvi	2.598 (5)	2.564 (4)	2.651 (5)
O1—O3^xiv	2.597 (4)	2.564 (4)	2.651 (5)
O2—O2^xi	3.042 (5)	3.027 (5)	3.059 (5)
O2—O3	2.718 (5)	2.699 (5)	2.737 (5)
O2—O3ⁱ	3.290 (5)	3.184 (5)	3.446 (5)
O2—O3^xvi	2.718 (5)	2.699 (5)	2.737 (5)
O2—O3^vi	3.286 (5)	3.184 (5)	3.446 (5)
O2—O4^vii	3.372 (4)	3.296 (5)	3.442 (4)
O2—O4^iv	3.370 (4)	3.296 (5)	3.442 (4)
O3—O3ⁱⁱⁱ	2.686 (5)	2.644 (5)	2.711 (5)
O3—O3^xvi	2.603 (5)	2.573 (5)	2.624 (5)
O3—O3^xviii	2.684 (5)	2.643 (5)	2.711 (5)
O3—O4^iv	2.947 (5)	2.915 (5)	2.971 (5)
O3—O4^xix	3.516 (5)	3.364 (5)	3.697 (5)

Symmetry codes: (i) x₁, x₂, x₃−1/2, x₁/2, x₁/2; (ii) −x₂, x₁−1, x₃−1/2, −x₁/2, x₁/2; (iii) −x₂, x₁−1, x₃, −x₅, x₄; (iv) −x₁+1/2, x₂−1/2, x₃, x₁/2, x₁/2; (v) −x₁+1/2, x₂−1/2, x₃−1/2, x₅, x₄; (vi) −x₂−1/2, −x₁−1/2, x₃−1/2, −x₄, x₅; (vii) x₁, x₂−1, x₃, x₄, x₅; (viii) x₁, x₂+1, x₃, x₄, x₅; (ix) −x₂−1, x₁, x₃, −x₅, x₄; (x) −x₁+1/2, x₂+1/2, x₃, x₁/2, x₁/2; (xi) −x₁, −x₂−1, x₃, −x₄, −x₅; (xii) −x₂−1/2, −x₁+1/2, x₃, −x₁/2, x₁/2; (xiii) x₁−1/2, −x₂−1/2, x₃, −x₁/2, −x₁/2; (xiv) x₂+1/2, x₁−1/2, x₃, x₁/2, −x₁/2; (xv) x₁, x₂, x₃+1/2, x₁/2, x₁/2; (xvi) −x₂−1/2, −x₁−1/2, x₃, −x₁/2, x₁/2; (xvii) −x₁, −x₂−1, x₃+1/2, −x₁/2, −x₁/2; (xviii) x₂+1, −x₁, x₃, x₅, −x₄; (xix) −x₁+1/2, x₂−1/2, x₃+1/2, x₅, x₄.

Experimental details

Crystal data
Chemical formula	Ba₂O₈Si₂Ti
M_r	506.7
Crystal system, space group	Tetragonal, X4bm†
Temperature (K)	110
Wave vectors	q₁ = 0.30200a* + 0.30200b; q₂ = -0.30200a + 0.30200b*
a, c (Å)	8.5353, 10.4128
V (Å³)	758.59
Z	4
Radiation type	Mo Kα
µ (mm⁻¹)	11.67
Crystal size (mm)	0.09 × 0.06 × 0.03

Data collection
Diffractometer	O110rd Diffraction CCD diffractometer
Absorption correction	Gaussian (Jana2000; Petricek, Dusek & Palatinus, 2000)
T_min, T_max	0.314, 0.520
No. of measured, independent and observed [I > 3σ(I)] reflections	43094, 3452, 2554
R_int	0.030
(sin θ/λ)_max (Å⁻¹)	0.830

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.012, 0.018, 0.94
No. of reflections	3452
No. of parameters	259
No. of restraints	?
Δρ_max, Δρ_min (e Å⁻³)	0.27, −0.32
Absolute structure	The absolute configuration was determined by the refinement of the twin fraction (Flack, 1983) of two domains related by the inversion center in the refinement program Jana2000 (Petricek and Dusek, 2000).
Absolute structure parameter	0.932 (9)

Computer programs: CrysAlis PRO CCD (Oxford diffraction, 2005), CrysAlis PRO RED (Oxford diffraction, 2005), SIR2002 (Burla et al., 2003), (Jana2000; Petricek, Dusek and Palatinus, 2000).

Selected bond lengths (Å) top

	Average	Minimum	Maximum
Ba1—Si1ⁱ	3.4960 (17)	3.4616 (17)	3.5285 (17)
Ba1—O1ⁱⁱ	2.850 (3)	2.733 (3)	2.961 (3)
Ba1—O2	2.655 (3)	2.642 (3)	2.672 (3)
Ba1—O2ⁱⁱⁱ	2.797 (3)	2.756 (3)	2.843 (3)
Ba1—O2^iv	2.799 (3)	2.756 (3)	2.843 (3)
Ba1—O3ⁱ	2.844 (4)	2.729 (4)	3.017 (4)
Ba1—O3ⁱⁱ	3.011 (4)	2.747 (4)	3.503 (4)
Ba1—O3^v	3.007 (4)	2.747 (4)	3.503 (4)
Ba1—O3^vi	2.846 (4)	2.729 (4)	3.016 (4)
Ba1—O4^vii	3.344 (3)	3.100 (3)	3.553 (3)
Ba1—O4^iv	3.345 (3)	3.100 (3)	3.553 (3)
Ti1—Si1^viii	3.3610 (14)	3.3502 (14)	3.3697 (14)
Ti1—Si1^ix	3.3610 (14)	3.3502 (14)	3.3697 (14)
Ti1—Si1^x	3.3610 (14)	3.3502 (14)	3.3697 (14)
Ti1—Si1^xi	3.3610 (14)	3.3502 (14)	3.3697 (14)
Ti1—O3^x	1.979 (4)	1.962 (4)	1.995 (4)
Ti1—O3^xii	1.979 (4)	1.962 (4)	1.995 (4)
Ti1—O3^xiii	1.979 (4)	1.962 (4)	1.995 (4)
Ti1—O3^xiv	1.979 (4)	1.962 (4)	1.995 (4)
Ti1—O4	1.696 (4)	1.688 (6)	1.703 (6)
Ti1—O4^xv	3.508 (4)	3.405 (6)	3.617 (6)
Si1—Si1^xi	3.0936 (18)	3.0924 (18)	3.0949 (18)
Si1—O1	1.669 (3)	1.655 (2)	1.685 (4)
Si1—O2	1.598 (4)	1.597 (3)	1.601 (3)
Si1—O2^xi	3.460 (4)	3.438 (4)	3.481 (4)
Si1—O3	1.623 (4)	1.611 (4)	1.638 (4)
Si1—O3^xvi	1.623 (4)	1.611 (4)	1.638 (4)
O1—O2	2.686 (4)	2.665 (4)	2.708 (4)
O1—O2^xv	3.366 (4)	3.292 (4)	3.448 (4)
O1—O2^xi	2.687 (4)	2.665 (4)	2.708 (4)
O1—O2^xvii	3.369 (4)	3.292 (4)	3.448 (4)
O1—O3	2.599 (5)	2.564 (4)	2.651 (5)
O1—O3^xi	2.599 (4)	2.564 (4)	2.651 (5)
O1—O3^xvi	2.598 (5)	2.564 (4)	2.651 (5)
O1—O3^xiv	2.597 (4)	2.564 (4)	2.651 (5)
O2—O2^xi	3.042 (5)	3.027 (5)	3.059 (5)
O2—O3	2.718 (5)	2.699 (5)	2.737 (5)
O2—O3ⁱ	3.290 (5)	3.184 (5)	3.446 (5)
O2—O3^xvi	2.718 (5)	2.699 (5)	2.737 (5)
O2—O3^vi	3.286 (5)	3.184 (5)	3.446 (5)
O2—O4^vii	3.372 (4)	3.296 (5)	3.442 (4)
O2—O4^iv	3.370 (4)	3.296 (5)	3.442 (4)
O3—O3ⁱⁱⁱ	2.686 (5)	2.644 (5)	2.711 (5)
O3—O3^xvi	2.603 (5)	2.573 (5)	2.624 (5)
O3—O3^xviii	2.684 (5)	2.643 (5)	2.711 (5)
O3—O4^iv	2.947 (5)	2.915 (5)	2.971 (5)
O3—O4^xix	3.516 (5)	3.364 (5)	3.697 (5)

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Superspace-symmetry determination and multi­dimensional refinement of the incommensurately modulated structure of natural fresnoite

Supporting information

Superspace-symmetry determination and multidimensional refinement of the incommensurately modulated structure of natural fresnoite