The twofold superstructure of titanium(III) oxybromide at T = 17.5 K

The low-temperature (T = 17.5 K) structure of titanium(III) oxybromide, TiOBr, is reported as a twofold superstructure of the crystal structure at room temperature. Weak superlattice reflections were measured with synchrotron radiation X-rays and were analyzed by structure refinements employing superspace techniques. Both the low-temperature and the room-temperature structures of TiOBr are isostructural with the corresponding structures of TiOCl. The results indicate that at low temperatures TiOBr is in a spin-Peierls state, similar to that of TiOCl, but with the modulations and relevant inter­actions smaller than in the latter compound.

S1. Comment

TiOBr (von Schnering et al., 1972) and TiOCl (Schäfer et al., 1958) are isostructural compounds that crystallize in the FeOCl structure type (Fig. 1). On cooling, they undergo two phase transitions, as evidenced by anomalies in the temperature dependencies of the magnetic susceptibilites (Seidel et al., 2003; Kato et al., 2005; Lemmens et al., 2005). Previously, we have shown that in the lowest-temperature phase (T < 67 K) the crystal structure of TiOCl is a twofold superstructure of the structure at room temperature (Shaz et al., 2005). The superstructure involves the formation of Ti—Ti dimers on the chains of Ti atoms parallel to [010], thus suggesting a spin-Peierls state by direct exchange on the quasi-one-dimensional chains of Ti atoms (Shaz et al., 2005). Recently Sasaki et al. (2005) reported superlattice reflections for TiOBr at low temperatures, but they did not report a satisfactory structure model because of the limited number of measured reflections (two reflections).

We report here the low-temperature twofold superstructure of TiOBr at T = 17.5 K. It is found that the pattern of displacements in TiOBr is similar to that in TiOCl, but with amplitudes that are only about half of the displacement amplitudes in TiOCl (Fig. 2 and Table 1). These results indicate that TiOBr is in a spin-Peierls state at low temperatures, similar to that of TiOCl but with the relevant interactions smaller than in TiOCl, in accordance with the transition temperatures being lower in TiOBr (T_c1 = 27 K and T_c2 = 47 K) than in TiOCl (T_c1 = 67 K and T_c2 = 90 K; Seidel et al., 2003; Shaz et al., 2005).

S2. Experimental

Single crystals for TiOBr were grown by gas transport following published procedures (Schäfer et al., 1958). The starting materials for synthesis were Ti (Alpha, 99.99% purity), TiO₂ (Alpha, 99.99%) and TiBr₄ (Aldrich, 99.99%). They were mixed with a 40% surplus of Ti and TiBr₄. The sealed evacuated (p = 1.5 10⁻² hPa) quartz glass tube was heated in a temperature gradient of 923:823 K for 72 h. The tube was cooled to room-temperature at a rate of 15.6 K h⁻¹. The yellow–brown crystals have a needle-to-plate-like habit and develop a grey–white patina in air. Therefore they were further handled under inert gasses.

S3. Refinement

Diffraction at room-temperature confirmed the FeOCl structure type with an orthorhombic lattice and space group Pmmn. Diffraction at 17.5 K indicated the presence of superlattice reflections at positions q = (0, 1/2, 0) from the main reflections. Accordingly, all Bragg reflections at low temperature were indexed with respect to the orthorhombic unit cell of the room-temperature structure and the modulation wavevector q, employing four integers (hklm). The main reflections are described by m = 0, while m = 1 indicates the superlattice reflections.

Owing to the presence of the cryostat, only a limited range of setting angles of the crystal could be reached. This allowed the measurement of most Bragg reflections in one octant that represents the unique reflections with respect to mmm symmetry. Furthermore, 16 observed main reflections and 24 observed satellite reflections could be measured within a second octant that would be required for a complete unique data set within monoclinic symmetry.

The structure was refined within the superspace formalism as a commensurately modulated structure with superspace group Pmmn(0β0), with β = 1/2 and t₀ = 1/8. Section t₀ = 1/8 of superspace indicates monoclinic symmetry for the supercell. Therefore, one parameter was introduced for pseudo-merohedral twinning of the monoclinic structure on the pseudo-orthorhombic lattice. The refined volume fraction of the second twin domain was obtained as 0.492 (7). This implies a 1:1 ratio of volumes of the two twin domains and an apparent mmm symmetry of the diffraction pattern. Therefore, the measured single octant represents a complete data set for the twinned crystal, as was confirmed by the good fit to the reflections measured for the second octant.

The superspace refinement allowed the structural parameters to be separated into parameters of the basic structure, as defined by the strong main reflections, and modulation parameters that give rise to the weak superstructure reflections (satellites). One modulation wave was refined, leading to two modulation parameters for each atom. Partial R values at convergence R(main reflections) = 1.59% and R(satellites) = 4.86% show that a good fit to the superstructure reflections was obtained.

Subsequently the structure was transformed to a twofold superstructure, leading to two independent atoms in the supercell instead of one in the basic structure unit cell. To allow for direct comparison of the superstructure and the room-temperature structure, a non-standard setting `monoclinic a unique' with inversion center at (1/4 3/8 0) was used. An ordinary structure refinement was performed in the supercell but with additional restrictions as they were derived from the superspace approach; displacement parameters of the two independent atoms of the same species were made equal, the displacement parameter U₂₃ of all atoms was set equal to 0, and y(A2) = [1/2 + y_ave − y(A1)], were y_ave is the y coordinate of atom A in the room-temperature structure with values y_ave = 0.5 when A is Ti, and y_ave = 0 when A is O or Br. Omitting these restrictions leads to severe correlations between the parameters as a result of the pseudo-orthorhombic nature of the structure.

Computing details

Data collection: DIF4 (Eichhorn, 1996); cell refinement: DIF4; data reduction: REDUCE (Eichhorn, 1991) and JANA2000 (Petricek et al., 2000); program(s) used to solve structure: program (reference)?; program(s) used to refine structure: JANA2000; molecular graphics: DIAMOND (Brandenburg, 1999); software used to prepare material for publication: JANA2000.

Figures

	Fig. 1. A perspective view of one layer of the crystal structure of TiOBr (color online: blue for Ti, red for O and green for Br). Atomic labels and symmetry codes correspond to those given in Table 1 [(x) x − 1, y − 1, z].
	Fig. 2. One ribbon parallel to [010] at x = 0, containing the chain of Ti atoms. Deviations from the average structure are given by arrows (20 times their true values). Unit-cell axes are indicated (color online: blue for Ti, red for O and green for Br). Atomic labels and symmetry codes correspond to those given in Table 1.

titanium(III) oxybromide

Crystal data

TiOBr	F(000) = 260
Mr = 143.8	pseudo-orthorhombic, non-standard setting "monoclinic a unique", origin shift by (1/4 1/8 0), therefore inversion center at (1/4 3/8 0). The standard uncertainty of the monoclinic angle α was estimated on the basis of the width of the reflections. Splitting of reflections was not observed. Mass absorbtion coefficients and anomalous dispersion parameters were calculated by the refinement program JANA2000 (Petricek et al., 2000), using a table of the coefficients for a range of wavelengths and interpolating between these values in order to obtain the values for any desired wavelength. The source of the tables is: CrossSec_McMaster.dat: Photon-Atom Cross Section and attenuation coefficients (McMaster); and f1f2_asf_Kissel.dat: Elastic Photon-Atom Scattering, anomalous scattering factors. The files belong to the DABAX library created at ESRF. More information on DABAX can be found at: https://www.esrf.fr/computing/scientific/dabax/
Monoclinic, P21/m11	Dx = 4.277 Mg m^−3
Hall symbol: P -2x 2xabv	Synchrotron radiation, λ = 0.5 Å
a = 3.7852 (12) Å	Cell parameters from 24 reflections
b = 6.9366 (9) Å	θ = 10.0–23.0°
c = 8.501 (3) Å	µ = 8.35 mm^−1
β = 90°	T = 18 K
V = 223.21 (10) Å^3	Platelet, translucent light brown
Z = 4	0.27 × 0.13 × 0.002 mm

Data collection

Huber four-circle diffractometer	336 reflections with I > 3σ(I)
Radiation source: synchrotron	Rint = 0.054
Double-crystal flat Si(111) monochromator	θmax = 20.5°, θmin = 1.7°
Profile data with ω scans	h = −5→5
Absorption correction: gaussian (Jana2000; Petricek et al., 2000)	k = −9→3
Tmin = 0.475, Tmax = 0.978	l = −10→0
989 measured reflections	3 standard reflections every 90 min
416 independent reflections	intensity decay: none

Refinement

Refinement on F	0 constraints
R[F^2 > 2σ(F^2)] = 0.018	Weighting scheme based on measured s.u.'s w = 1/[σ^2(F) + 0.0004F^2]
wR(F^2) = 0.029	(Δ/σ)max = 0.0001
S = 1.03	Δρmax = 0.53 e Å^−3
416 reflections	Δρmin = −0.57 e Å^−3
21 parameters	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
0 restraints	Extinction coefficient: 0.09 (2)

Special details

Experimental. Asingle crystal of TiOBr was glued onto a carbon fiber that was attached to a closed-cycle helium cryostat mounted on a four-circle Huber diffractometer. X-ray diffraction with synchrotron radiation was measured at beamline D3 of Hasylab in Hamburg.

Refinement. The crystal is twinned by pseudo-merohedry and it contains two

twin domains. The twinning matrix for the second domain is: | 1.000 0.000 0.000 | | 0.000 1.000 0.000 | | 0.000 0.000 − 1.000 |

The refined volume fractions are v1=0.508 (7) and v2=0.492 (7) for the first and second domains, respectively. The restriction v1+v2=1 was applied.

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

	x	y	z	Uiso*/Ueq
Ti1	0	0.25414 (8)	0.11268 (8)	0.00280 (18)
Ti2	0	0.74586 (8)	0.10897 (7)	0.00280 (18)
Br1	0	−0.00149 (4)	0.32743 (4)	0.00364 (13)
Br2	0	0.50149 (4)	0.33158 (4)	0.00364 (13)
O1	0	0.0025 (2)	−0.0486 (3)	0.0040 (6)
O2	0	0.4975 (2)	−0.0534 (3)	0.0040 (6)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ti1	0.0020 (3)	0.0020 (3)	0.0045 (3)	0	0	0
Ti2	0.0020 (3)	0.0020 (3)	0.0045 (3)	0	0	0
Br1	0.0050 (2)	0.0017 (2)	0.0042 (2)	0	0	0
Br2	0.0050 (2)	0.0017 (2)	0.0042 (2)	0	0	0
O1	0.0033 (11)	0.0021 (10)	0.0066 (9)	0	0	0
O2	0.0033 (11)	0.0021 (10)	0.0066 (9)	0	0	0

Geometric parameters (Å, º)

Ti1—Ti2	3.4110 (8)	Ti2—O2	2.208 (2)
Ti1—Ti2^i	3.5259 (8)	Ti1—Br1	2.5451 (7)
Ti1—Ti1^ii	3.7852 (13)	Ti1—Br2	2.5312 (7)
Ti2—Ti2^ii	3.7852 (13)	Ti2—Br1^v	2.5535 (7)
Ti1—Ti1^iii	3.1723 (7)	Ti2—Br2	2.5406 (7)
Ti1—Ti2^iii	3.1843 (7)	Ti1—Ti1^iv	3.1723 (7)
Ti2—Ti2^iii	3.1976 (7)	Ti1—Ti2^iv	3.1843 (7)
Ti1—O1	2.219 (2)	Ti2—Ti2^vi	3.1976 (7)
Ti1—O2	2.201 (2)	O1—O1^vii	2.7192 (19)
Ti1—O2^iii	1.9586 (6)	O1—O1^viii	2.7192 (19)
Ti1—O2^iv	1.9586 (6)	O1—O2^iii	2.7093 (19)
Ti2—O1^v	2.228 (2)	O1—O2^iv	2.7093 (19)
Ti2—O1^iii	1.9611 (6)	O2—O2^iii	2.7006 (19)
Ti2—O1^iv	1.9611 (6)	O2—O2^iv	2.7006 (19)
Ti1—Br2—Ti2	84.53 (2)	O1^iii—Ti2—O2	80.83 (6)
Ti1—Br1—Ti2^i	87.51 (2)	O1^iv—Ti2—O1^v	80.68 (6)
Ti1—O2—Ti2	101.39 (9)	O1^iv—Ti2—O1^iii	149.63 (10)
Ti1—O1—Ti2^i	104.91 (10)	O1^iv—Ti2—O2	80.83 (6)
Ti1—O1—Ti2^iv	99.05 (6)	Ti1—O1—O1^vii	108.92 (8)
Ti2^i—O1—Ti2^iv	99.32 (6)	Ti1—O1—O1^viii	108.92 (8)
Ti2^iii—O1—Ti2^iv	149.63 (13)	Ti1—O1—O2^iii	45.49 (4)
Ti1—O2—Ti1^iv	99.25 (6)	Ti1—O1—O2^iv	45.49 (4)
Ti1^iii—O2—Ti1^iv	150.17 (13)	Ti2^i—O1—O1^vii	45.37 (4)
Ti1^iv—O2—Ti2	99.52 (6)	Ti2^i—O1—O1^viii	45.37 (4)
Ti1—O1—Ti2^iii	99.05 (6)	Ti2^i—O1—O2^iii	108.62 (8)
Ti2^i—O1—Ti2^iii	99.32 (6)	Ti2^i—O1—O2^iv	108.62 (8)
Ti2^iii—O1—Ti2^i	99.32 (6)	Ti2^iii—O1—O1^vii	53.95 (4)
Ti2^iv—O1—Ti2^i	99.32 (6)	Ti2^iii—O1—O1^viii	139.02 (8)
Ti2^iv—O1—Ti2^iii	149.63 (13)	Ti2^iii—O1—O2^iii	53.56 (4)
Ti1^iv—O2—Ti1	99.25 (6)	Ti2^iii—O1—O2^iv	138.96 (8)
Ti1—O2—Ti1^iii	99.25 (6)	Ti2^iv—O1—O1^vii	139.02 (8)
Ti1^iii—O2—Ti1	99.25 (6)	Ti2^iv—O1—O1^viii	53.95 (4)
Ti1^iv—O2—Ti1^iii	150.17 (13)	Ti2^iv—O1—O2^iii	138.96 (8)
Ti1^iii—O2—Ti2	99.52 (6)	Ti2^iv—O1—O2^iv	53.56 (4)
Br1—Ti1—Br2	86.84 (2)	O1^vii—O1—O1^viii	88.22 (7)
Br1—Ti1—O1	83.98 (6)	O1^vii—O1—O2^iii	80.39 (5)
Br1—Ti1—O2	174.08 (6)	O1^vii—O1—O2^iv	143.66 (11)
Br1—Ti1—O2^iii	100.40 (6)	O1^viii—O1—O1^vii	88.22 (7)
Br1—Ti1—O2^iv	100.40 (6)	O1^viii—O1—O2^iii	143.66 (11)
Br2—Ti1—O1	170.82 (6)	O1^viii—O1—O2^iv	80.39 (5)
Br2—Ti1—O2	87.24 (6)	O2^iii—O1—O2^iv	88.62 (7)
Br2—Ti1—O2^iii	101.13 (6)	O2^iv—O1—O2^iii	88.62 (7)
Br2—Ti1—O2^iv	101.13 (6)	Ti1—O2—O1^iii	106.60 (8)
O1—Ti1—O2	101.94 (8)	Ti1—O2—O1^iv	106.60 (8)
O1—Ti1—O2^iii	80.60 (6)	Ti1—O2—O2^iii	45.71 (4)
O1—Ti1—O2^iv	80.60 (6)	Ti1—O2—O2^iv	45.71 (4)
O2—Ti1—O2^iii	80.75 (6)	Ti1^iii—O2—O1^iii	53.91 (4)
O2—Ti1—O2^iv	80.75 (6)	Ti1^iii—O2—O1^iv	139.55 (8)
O2^iii—Ti1—O2	80.75 (6)	Ti1^iii—O2—O2^iii	53.54 (4)
O2^iii—Ti1—O2^iv	150.17 (10)	Ti1^iii—O2—O2^iv	139.48 (8)
O2^iv—Ti1—O2	80.75 (6)	Ti1^iv—O2—O1^iii	139.55 (8)
O2^iv—Ti1—O2^iii	150.17 (10)	Ti1^iv—O2—O1^iv	53.91 (4)
Br1^v—Ti2—Br2	85.19 (2)	Ti1^iv—O2—O2^iii	139.48 (8)
Br1^v—Ti2—O1^v	83.61 (6)	Ti1^iv—O2—O2^iv	53.54 (4)
Br1^v—Ti2—O1^iii	100.75 (6)	Ti2—O2—O1^iii	45.61 (4)
Br1^v—Ti2—O1^iv	100.75 (6)	Ti2—O2—O1^iv	45.61 (4)
Br1^v—Ti2—O2	172.04 (6)	Ti2—O2—O2^iii	106.31 (8)
Br2—Ti2—O1^v	168.80 (6)	Ti2—O2—O2^iv	106.31 (8)
Br2—Ti2—O1^iii	101.47 (6)	O1^iii—O2—O1^iv	88.62 (7)
Br2—Ti2—O1^iv	101.47 (6)	O1^iii—O2—O2^iii	78.79 (5)
Br2—Ti2—O2	86.85 (6)	O1^iii—O2—O2^iv	141.69 (11)
O1^v—Ti2—O1^iii	80.68 (6)	O1^iv—O2—O1^iii	88.62 (7)
O1^v—Ti2—O1^iv	80.68 (6)	O1^iv—O2—O2^iii	141.69 (11)
O1^v—Ti2—O2	104.35 (8)	O1^iv—O2—O2^iv	78.79 (5)
O1^iii—Ti2—O1^v	80.68 (6)	O2^iii—O2—O2^iv	88.98 (7)
O1^iii—Ti2—O1^iv	149.63 (10)	O2^iv—O2—O2^iii	88.98 (7)

Symmetry codes: (i) x, y−1, z; (ii) x−1, y, z; (iii) x−1/2, −y+3/4, −z; (iv) x+1/2, −y+3/4, −z; (v) x, y+1, z; (vi) x+1/2, −y+7/4, −z; (vii) x−1/2, −y−1/4, −z; (viii) x+1/2, −y−1/4, −z.