(3 + 1)-Dimensional structure refinement of the fresnoite framework-structure type compound Ba₂TiGe₂O₈

The incommensurately modulated structure of the fresnoite framework-structure type compound Ba₂TiGe₂O₈ has been solved using a (3 + 1)-dimensional superspace approach. The structure is orthorhombic and adopts the superspace group Cmm2(0,β,1/2)s00 with β ≃ 0.635 at room temperature. The refinement was based on neutron powder diffraction data obtained from a powdered single crystal grown by Czochralski pulling. The modulation parameters that were obtained support the idea that frozen-in rigid-unit modes cause the modulation. The modulation is mainly manifested by positional displacements of O atoms. Barium ions are either eightfold, ninefold or tenfold coordinated in the one-dimensional modulated structure. A significant improvement of the bond-valence sum for both barium positions is achieved by the introduction of the positional modulation. This finding strongly suggests that underbonded barium positions are critically involved in provoking the incommensurate modulation in Ba₂TiGe₂O₈.

Computing details

Program(s) used to refine structure: (Jana2000; Petricek and Dusek, 2000); software used to prepare material for publication: (Jana2000; Petricek and Dusek, 2000).

Figures

(I)

Crystal data

Ba2Ge2O8Ti	V = 1622.39 Å^3
Mr = 595.7	Z = 8
Orthorhombic, Xmm2(0β0)s00†	F(000) = 556
q = 0.63497b*	Dx = 4.876 Mg m^−3
a = 12.3014 Å	Neutron radiation, λ = 1 Å
b = 12.2837 Å	colourless
c = 10.7367 Å	?, ? × ? × ? mm

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

Data collection

2θmin = 23.207°, 2θmax = 97.808°, 2θstep = −1°

Refinement

Rp = 0.060	Profile function: Pseudo-Voigt
Rwp = 0.059	127 parameters
Rexp = 0.025	Weighting scheme based on measured s.u.'s
R(F) = 0.102	(Δ/σ)max = 1.118
χ^2 = NOT FOUND	Background function: 8 Chebyshev polynoms
4404 data points	Preferred orientation correction: none
Excluded region(s): from 26.85 to 27.200

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

	x	y	z	Uiso*/Ueq
Ba1	0	0.3267 (6)	0	0.057 (3)
Ba2	0.1699 (5)	0	−0.0022 (13)	0.036 (2)
Ge1	0	0.1309 (4)	0.2425 (9)	0.0472 (16)
Ge2	0.3695 (4)	0	0.2450 (10)	0.057 (2)
Ti1	0.25	0.25	0.2271 (10)	0.034 (3)
O1	0.1076 (3)	0.1951 (4)	0.1784 (11)	0.059 (2)
O2	0	0	0.1793 (13)	0.035 (3)
O3	0.3063 (4)	0.1116 (3)	0.1718 (10)	0.0450 (16)
O4	0.5	0	0.1767 (14)	0.047 (3)
O5	0	0.1259 (4)	0.3987 (12)	0.042 (2)
O6	0.3752 (4)	0	0.4045 (11)	0.046 (3)
O7	0.25	0.25	0.3877 (9)	0.057 (2)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ba1	0.065 (4)	0.043 (3)	0.064 (5)	0	0	−0.036 (4)
Ba2	0.029 (3)	0.060 (4)	0.019 (4)	0	−0.014 (3)	0
Ge1	0.046 (3)	0.048 (2)	0.048 (3)	0	0	−0.005 (2)
Ge2	0.078 (4)	0.027 (2)	0.065 (4)	0	−0.019 (3)	0
Ti1	0.017 (4)	0.052 (6)	0.032 (4)	0.012 (5)	0	0
O1	0.039 (2)	0.037 (3)	0.103 (5)	0.003 (2)	0.007 (3)	0.017 (4)
O2	0.024 (6)	0.067 (6)	0.014 (4)	0	0	0
O3	0.054 (3)	0.042 (3)	0.039 (3)	0.015 (2)	−0.001 (3)	−0.016 (3)
O4	0.007 (4)	0.070 (6)	0.065 (6)	0	0	0
O5	0.046 (4)	0.032 (3)	0.048 (5)	0	0	0.010 (3)
O6	0.025 (3)	0.064 (4)	0.050 (5)	0	0.002 (3)	0
O7	0.053 (3)	0.063 (5)	0.055 (3)	−0.011 (5)	0	0

Bond lengths (Å)

	Average	Minimum	Maximum
Ge1—O1	1.746 (14)	1.665 (14)	1.833 (14)
Ge1—O1^i	1.741 (14)	1.665 (14)	1.833 (14)
Ge1—O2	1.780 (8)	1.746 (8)	1.810 (8)
Ge1—O5	1.680 (16)	1.679 (16)	1.681 (16)
Ge2—O3	1.771 (12)	1.742 (12)	1.798 (12)
Ge2—O3^ii	1.771 (12)	1.742 (12)	1.798 (12)
Ge2—O4	1.768 (12)	1.747 (17)	1.783 (16)
Ge2—O6	1.715 (19)	1.714 (16)	1.72 (2)
Ti1—O1	1.988 (13)	1.941 (16)	2.064 (12)
Ti1—O1^iii	1.990 (13)	1.941 (14)	2.066 (12)
Ti1—O3	1.950 (13)	1.880 (17)	1.987 (11)
Ti1—O3^iii	1.953 (13)	1.880 (17)	1.987 (11)
Ti1—O7	1.725 (18)	1.71 (2)	1.74 (2)

Symmetry codes: (i) −x₁, x₂, x₃, x₁/2; (ii) x₁, −x₂, x₃, −x₄; (iii) −x₁+1/2, −x₂+1/2, x₃, −x₁/2.