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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 {\overline 3}m symmetry, the other Tl and one of the O atoms occupy sites with 3m symmetry, the Se atom is at a site with {\overline 6}m2 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.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270105003100/ty1005sup1.cif
Contains datablocks global, I

rtv

Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108270105003100/ty1005Isup2.rtv
Contains datablock I

Comment top

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.

Experimental top

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

Refinement top

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 top

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 top
[Figure 1] Fig. 1. The fitted diffraction profile for Tl2SeO4, showing calculated (line), observed (solid circle) and difference (lower) profiles.
[Figure 2] 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 top
Crystal data top
Tl2SeO4Dx = 6.52 (2) Mg m3
Mr = 551.78Cu Kα radiation, λ = 1.54184 Å
Hexagonal, P63/mmcT = 683 K
Hall symbol: -P 6 c 2 cParticle morphology: plate-like
a = 6.2916 (2) Åwhite
c = 8.1964 (2) Åflat sheet, 15 × 20 mm
V = 280.98 (1) Å3Specimen preparation: Prepared at 313 K and 100kPa kPa
Z = 2
Data collection top
Rigaku RINT-2000
diffractometer
Data collection mode: reflection
Radiation source: rotating-anode X-ray tubeScan method: step
Specimen mounting: packed powder pellet2θmin = 5.000°, 2θmax = 119.00°, 2θstep = 0.01°
Refinement top
Refinement on Inet11491 data points
Least-squares matrix: full with fixed elements per cycleProfile function: pseudo-Voigt
Rp = 0.06069 parameters
Rwp = 0.094(Δ/σ)max = 0.01
Rexp = 0.076Background function: square polynomial for each range
χ2 = 1.742Preferred orientation correction: March-Dollase function, axis (001) (Dollase, 1986)
Crystal data top
Tl2SeO4V = 280.98 (1) Å3
Mr = 551.78Z = 2
Hexagonal, P63/mmcCu Kα radiation, λ = 1.54184 Å
a = 6.2916 (2) ÅT = 683 K
c = 8.1964 (2) Åflat sheet, 15 × 20 mm
Data collection top
Rigaku RINT-2000
diffractometer
Scan method: step
Specimen mounting: packed powder pellet2θmin = 5.000°, 2θmax = 119.00°, 2θstep = 0.01°
Data collection mode: reflection
Refinement top
Rp = 0.060χ2 = 1.742
Rwp = 0.09411491 data points
Rexp = 0.07669 parameters
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Tl10.00.00.00.093 (3)*
Tl20.33330.66670.7979 (2)0.084 (4)*0.5
Se10.33330.66670.25000.112 (4)*
O10.33330.66670.4240 (5)0.132 (5)*0.5
O20.2101 (18)0.7899 (18)0.2000 (1)0.132 (7)*0.5
Geometric parameters (Å, º) top
Se1—O11.426 (4)O2—O2i2.326 (2)
Se1—O21.404 (4)Tl2—O13.065 (9)
O1—O22.275 (3)
O1—Se1—O2106.97 (5)O2—Se1—O2i111.85 (5)
Symmetry code: (i) x+y, y, z.

Experimental details

Crystal data
Chemical formulaTl2SeO4
Mr551.78
Crystal system, space groupHexagonal, P63/mmc
Temperature (K)683
a, c (Å)6.2916 (2), 8.1964 (2)
V3)280.98 (1)
Z2
Radiation typeCu Kα, λ = 1.54184 Å
Specimen shape, size (mm)Flat sheet, 15 × 20
Data collection
DiffractometerRigaku RINT-2000
diffractometer
Specimen mountingPacked powder pellet
Data collection modeReflection
Scan methodStep
2θ values (°)2θmin = 5.000 2θmax = 119.00 2θstep = 0.01
Refinement
R factors and goodness of fitRp = 0.060, Rwp = 0.094, Rexp = 0.076, χ2 = 1.742
No. of data points11491
No. of parameters69
No. of restraints?

Computer programs: RINT Server Software (Rigaku, 1994), RINT Server Software, RIETAN2000 (Izumi & Ikeda, 2000), RIETAN2000, ORTEP-3 (Farrugia, 2001).

Selected geometric parameters (Å, º) top
Se1—O11.426 (4)O1—O22.275 (3)
Se1—O21.404 (4)Tl2—O13.065 (9)
O1—Se1—O2106.97 (5)O2—Se1—O2i111.85 (5)
Symmetry code: (i) x+y, y, z.
 

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