Thallium selenate (Tl₂SeO₄) in a paraelastic phase by X-ray powder diffraction

The structure of thallium selenate, Tl₂SeO₄, in a paraelastic phase (above 661 K) has been analysed by Rietveld analysis of the X-ray powder diffraction pattern. Atomic parameters based on the isomorphic K₂SO₄ crystal in the paraelastic phase were used as the starting model. The structure was determined in the hexagonal space group P6₃/mmc, with a = 6.2916 (2) Å and c = 8.1964 (2) Å. From the Rietveld refinement it was found that two orientations are possible for the SeO₄ tetrahedra, in which one of their apices points randomly up and down with respect to [001]. One Tl atom lies at the origin with symmetry, the other Tl and one of the O atoms occupy sites with 3m symmetry, the Se atom is at a site with symmetry and the remaining O atom is at a site with m symmetry. Furthermore, it was also found that the Tl atoms display anomalously large positional disorder along [001] in the paraelastic phase.

S1. Comment

The M₂XO₄ type compounds (where M = K, Rb, Cs, NH₄ or Tl, and X = Se or S) exhibit interesting characteristics, such as ferroelectricity, ferroelasticity and structural incommensurate modulation (Matthias & Remeika, 1956; Aiki et al., 1969; Aizu, 1974; Iizumi et al., 1977; Matsuo et al., 1996, 2000). It is known that the Tl₂SeO₄ crystal, which is one of a family of M₂XO₄ type compounds, shows ferroelasticity at room temperature and undergoes a ferroelastic phase transition at 661 K (Matsuo et al., 1996). At room temperature, the Tl₂SeO₄ crystal structure is orthorhombic, Pnma, which is the same as the space group in β-K₂SeO₄ type crystals (Fábry & Breczewski, 1993; Matsuo et al., 1996). Recently, it has been reported that Tl₂SeO₄ is hexagonal in the paraelastic phase, P6₃/mmc (Matsuo et al., 1996), which is the same space group as that in the paraelastic phase of the isomorphic K₂SO₄ crystal structure. However, there are no reports of the crystal structure of this phase of Tl₂SeO₄. Moreover, it is also known that, in the paraelastic phase of the isomorphic compound K₂SO₄, the SO₄ tetrahedra randomly show two orientations, in which the apices of the tetrahedra point up and down along [001] (van den Berg & Tuinstra, 1978; Miyake et al., 1980; Arnold et al., 1981). This anomalously large degree of disorder may be a characteristic feature in the paraelastic phase of M₂XO₄ type compounds. However, there are no comprehensive viewpoints for this feature in M₂XO₄ type crystals. In order to summarize the characteristic features of the ferroelastic phase transition in M₂XO₄ type compounds, it is important to clarify the crystal structure of Tl₂SeO₄ in the paraelastic phase. Therefore, in this study we have measured the X-ray diffraction pattern of Tl₂SeO₄ and have determined the crystal structure in the paraelastic phase using Rietveld analysis, with the atomic parameters of the isomorphic compound K₂SO₄ in its paraelastic phase as the starting model.

The atomic parameters and isotropic displacement parameters for Tl₂SeO₄ are given as supplementary data, and selected geometric parameters are given in Table 1. The fitted diffraction profile for Tl₂SeO₄ is shown in Fig. 1, and the crystal structure of the paraelastic phase of the Tl₂SeO₄ crystal is shown in Fig. 2.

The structure of Tl₂SeO₄ consists of isolated SeO₄ tetrahedra with Tl atoms distributed between them. It is also evident that the SeO₄ tetrahedra have two orientations, with the apices pointing in opposite directions along [001], as shown in Fig. 2. Moreover, it can be clearly seen that one of the Tl atoms (Tl2) occupies two stable positions along [001]. The distance between these positions is 0.786 Å. Thus, the crystal structure of the paraelastic phase is characterized by the existence of the large disordered rotation of the SeO₄ tetrahedra and the anomalously large positional disorder of the Tl2 atoms along [001]. This structure is similar to that of the K₂SO₄ crystal in the high-temperature paraelastic phase (Arnold et al., 1981). On the other hand, in the ferroelastic phase of Tl₂SeO₄, it is noted that the disorder of the Tl2 atoms and the orientational disorder of the SeO₄ tetrahedra are not observed (Fábry & Breczewski, 1993).

The phase transition at 661 K is accompanied by a structural change from P6₃/mmc, with lattice parameters a = 6.2916 (2) and c = 8.1964 (2) Å, to Pnma, with lattice parameters a = 7.927 (2), b = 6.086 (2) and c = 10.934 (3) Å (Fábry & Breczewski, 1993). From these results, it is deduced that the ferroelastic phase transition of Tl₂SeO₄ is closely related to the appearance of the order–disorder motion of Tl2 atoms and SeO₄ tetrahedra with the increase in temperature.

S2. Experimental

Crystals of Tl₂SeO₄ were grown by slow evaporation of a saturated aqueous solution of Tl₂SeO₄ at 313 K, after several recrystallizations for purification.

S3. Refinement

It is known that K₂SO₄ undergoes a ferroelastic phase transition from the low-temperature ferroelastic phase to the high-temperature paraelastic phase at 860 K (Shiozaki et al., 1977). The structure is hexagonal, P6₃/mmc, in the paraelastic phase and monoclinic, Pnma, in the ferroelastic phase. The Tl₂SeO₄ crystal also undergoes a ferroelastic phase transition at 661 K (Matsuo et al., 1996), with the symmetry change at this transition being the same as that of the isomorphic compound K₂SO₄. Therefore, the starting model for the determination of the structure of the Tl₂SeO₄ paraelastic phase was based on the isomorphic P6₃/mmc K₂SO₄ crystal structure. In the analysis of the crystal structure, we have used both single- and split-atom models for the Tl2 atoms. The result was strongly in favour of truly split-atom positions (goodness of fit factor s = 1.32; in the single model, s = 2.08). Therefore, the single-atom model for the Tl2 atom (z = 3/4) was rejected and the split-atom model was used in the refinement. Refinements were also carried out using a range of occupancies for atoms O1 and O2 in the disordered tetrahedra. However, the goodness of fit factor was lowest for 50% occupancy. The profile shape was represented by a pseudo-Voigt function. In addition to the profile, lattice and structure parameters, the zero-point shift, ten background parameters and the scale factor were determined with corrections for preferred orientation along [001] (the crystal shape is plate-like). Rietveld analysis was carried out with the RIETAN2000 program (Izumi & Ikeda, 2000). Isotropic thermal vibrations were assumed. The interatomic distances and bond angles were calculated using ORFFE (Busing et al., 1964) and ORTEP-3 (Farrugia, 2001).

Computing details

Data collection: RINT Server Software (Rigaku, 1994); cell refinement: RINT Server Software; data reduction: RINT Server Software; program(s) used to solve structure: RIETAN2000 (Izumi & Ikeda, 2000); program(s) used to refine structure: RIETAN2000; molecular graphics: ORTEP-3 (Farrugia, 2001); software used to prepare material for publication: RIETAN2000.

Figures

	Fig. 1. The fitted diffraction profile for Tl2SeO4, showing calculated (line), observed (solid circle) and difference (lower) profiles.
	Fig. 2. A view of the unit cell of the crystal structure of Tl2SeO4. The Tl2 atom statistically occupies two equivalent positions, with probability 1/2. There are two orientations of the SeO4 tetrahedra, with the apices pointing either up or down along [001].

Thallium selenate

Crystal data

Tl2SeO4	Dx = 6.52 (2) Mg m^−3
Mr = 551.78	Cu Kα radiation, λ = 1.54184 Å
Hexagonal, P63/mmc	T = 683 K
Hall symbol: -P 6 c 2 c	Particle morphology: plate-like
a = 6.2916 (2) Å	white
c = 8.1964 (2) Å	flat sheet, 15 × 20 mm
V = 280.98 (1) Å^3	Specimen preparation: Prepared at 313 K and 100kPa kPa
Z = 2

Data collection

Rigaku RINT-2000 diffractometer	Data collection mode: reflection
Radiation source: rotating-anode X-ray tube	Scan method: step
Specimen mounting: packed powder pellet	2θmin = 5.000°, 2θmax = 119.00°, 2θstep = 0.01°

Refinement

Refinement on Inet	11491 data points
Least-squares matrix: full with fixed elements per cycle	Profile function: pseudo-Voigt
Rp = 0.060	69 parameters
Rwp = 0.094	(Δ/σ)max = 0.01
Rexp = 0.076	Background function: square polynomial for each range
χ^2 = 1.742	Preferred orientation correction: March-Dollase function, axis (001) (Dollase, 1986)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Tl1	0.0	0.0	0.0	0.093 (3)*
Tl2	0.3333	0.6667	0.7979 (2)	0.084 (4)*	0.5
Se1	0.3333	0.6667	0.2500	0.112 (4)*
O1	0.3333	0.6667	0.4240 (5)	0.132 (5)*	0.5
O2	0.2101 (18)	0.7899 (18)	0.2000 (1)	0.132 (7)*	0.5

Geometric parameters (Å, º)

Se1—O1	1.426 (4)	O2—O2^i	2.326 (2)
Se1—O2	1.404 (4)	Tl2—O1	3.065 (9)
O1—O2	2.275 (3)
O1—Se1—O2	106.97 (5)	O2—Se1—O2^i	111.85 (5)

Symmetry code: (i) −x+y, y, z.