A new modification of thallium chromate related to the β-K₂SO₄ family

The title structure is a new modification of Tl₂CrO₄. There are four independent Tl⁺ cations and two [CrO₄]²⁻ anions in the structure. It is closely related to the already known modification, which belongs to the β-K₂SO₄ family with two independent cations and one anion. In both modifications, the cations and anions are situated on crystallographic mirror planes. The volume of the asymmetric unit of the title structure is ∼0.4% smaller than that of the known modification belonging to the β-K₂SO₄ family. The other difference between the two modifications is seen in the environment of the cations. In the title structure, none of the Tl⁺ cations is underbonded, in contrast with the modification isostructural with β-K₂SO₄. In the β-K₂SO₄ family with simple cations, underbonding of one of the constituent cations is typical. The dependence of the unit-cell parameters on temperature does not indicate a phase transition in the inter­val 90–300 K.

S1. Comment

The aim of the present work was the growth of single crystals of Tl₂CrO₄ of the known modification belonging to the β-K₂SO₄ family. Spectroscopic experiments were planned for these samples. Moreover, the previous structure determination of Tl₂CrO₄ (Carter & Margulis, 1972) does not meet current standards: R_obs = 0.07, and some structural features deviate slightly from the trends in the β-K₂SO₄ family (see below and Table 1). Therefore, we also aimed to carry out a new single-crystal X-ray structure determination of the compound. As a result of our experiment a new modification of Tl₂CrO₄ has been prepared, the structure of which is presented here and discussed.

Tl₂SeO₄ (Fábry & Breczewski, 1993; Friese et al., 2004), Tl₂CrO₄ (Carter & Margulis, 1972), K₂SeO₄ (see, for example, González-Silgo et al., 1996) and K₂CrO₄ (Toriumi & Saito, 1978) are isostructural compounds belonging to the β-K₂SO₄ family, a structural family characterised by its variety of low-temperature phase transitions. Thus, K₂SeO₄ and Tl₂SeO₄ are known to undergo low-temperature phase transitions, while K₂CrO₄ and Tl₂CrO₄ do not (Fábry & Pérez-Mato, 1994).

Tl₂SeO₄, a compound chemically and structurally closely related to the title structure, is exceptional among the members of the β-K₂SO₄ family because it undergoes a unique sequence of phase transitions during cooling. A second-order phase transition takes place at 97 K (Matsuo & Ikehata, 2004), followed by a first-order low-temperature phase transition at about 72 K (Grunwald et al., 1984a,b). The latter phase transition is accompanied by a change in symmetry from Pnma to P2₁2₁2₁ without multiplication of the number of formula units in the unit cell (see, for example, Friese et al., 2004). A reverse phase transition during heating takes place at 76 K (Matsuo et al., 2000; Matsuo & Ikehata, 2004). In other members of this structural family a sequence of phase transitions often takes place from the incommensurately modulated to commensurately modulated phases on lowering the temperature.

The difference between Tl₂SeO₄ and the other members of the β-K₂SO₄ family may be related to the extreme underbonding (Table 1) of one of the two independent cations that are present in this structural type. This underbonding is quite common in the members of the β-K₂SO₄ family. In the case of Tl₂SeO₄, however, and to a lesser extent in Tl₂CrO₄ (Carter & Margulis, 1972), underbonding is quite prominent (Fábry & Pérez-Mato, 1994). It is interesting that this underbonded cation is often bonded by quite a short cation–anion bond, often the shortest one in the structure (Fábry & Pérez-Mato, 1994). This holds for, among others, the structures of Tl₂SeO₄ (Fábry & Breczewski, 1993; Friese et al., 2004), Tl₂CrO₄ (Carter & Margulis, 1972) and K₂SeO₄ (González-Silgo et al., 1996).

Although the respective cations in Tl₂CrO₄ and K₂CrO₄ are underbonded, low-temperature phase transitions are not known, in contrast with Tl₂SeO₄ and K₂SeO₄ (González-Silgo et al., 1996). However, spectroscopic measurements indicated a pretransitional phenomenon in K₂CrO₄, i.e. an incomplete mode softening (Etxebarría et al., 1992). It cannot be excluded that a similar pretransitional phenomenon may occur in Tl₂CrO₄.

The unit-cell volume of the title polymorph is almost exactly doubled compared with the known polymorph described by Carter & Margulis (1972). The volumes of the asymmetric units in the title structure and the β-K₂SO₄ polymorph are 124.88 and 125.37 ų, respectively. There are four independent Tl⁺ cations and two [CrO₄]^2- anions in the title structure, in contrast with the β-K₂SO₄ polymorph with two independent cations and one anion. Nevertheless, both modifications of Tl₂CrO₄ show similar structural features. The constituent cations and anions are situated on the crystallographic mirror planes in the two polymorphs. The transformation of the lattice parameters of the β-K₂SO₄ modification (o index), [a_m,b_m,c_m] = [/0 - 1 -1/1 0 0/0 0 2/] [a_o,b_o,c_o], leads to a unit cell similar to that of the title structure (m index). ([a_m,b_m,c_m] and [a_o,b_o,c_o] are the column matrices, while /0 - 1 -1/, /1 0 0/ and /0 0 2/ are the first, second and third rows, respectively, of the 3 × 3 matrix.) The transformed unit-cell parameters are 13.328 (5), 5.910 (4) and 15.820 (8) Å, 90, 126.40 (3) and 90°, and V = 1003 (1) ų.

Fig. 1 shows the packing of the constituents in the unit cell of the title structure when viewed along the unit-cell b axis. Fig. 2 shows a view of the β-K₂SO₄ polymorph (Carter & Margulis, 1972), also perpendicular to the mirror plane m, using the original unit-cell setting Pmcn. It can be seen from Fig. 1 that the cation pairs Tl1/Tl2 and Tl3/Tl4 are situated along planes parallel to (001); the former pairs are situated at approximately z = 1/2 and the latter ones at approximately z = 0. The arrangements within the sections in the title structure and the β-K₂SO₄ polymorph show similarities that are depicted by boxes in the figures.

Cations Tl1, Tl2, Tl3 and Tl4 are surrounded by eight, nine, nine and eight O atoms, respectively (Figs. 3 and 4), within a distance of 4.0 Å. In fact, the longest Tl—O distance among the coordinated O atoms in the title structure is 3.407 (15) Å for Tl1—O1(x + 1/2, y + 1/2, z). The coordination numbers (CN) in the title structure are on average lower than in the β-K₂SO₄ polymorph, where the CN up to 3.5 Å is 9 for both cations, and 11 and 9, respectively, up to 4.0 Å. Comparing the two polymorphs, the cations are more equally coordinated in the title structure. In both polymorphs, neighbouring cationic polyhedra around the Tl⁺ cation pairs share a plane in most cases (Tables 2 and 3), although in the title structure the the polyhedra are also shared by the edges.

A comparison of the bond-valence sums (BVS) in the title structure with those of related structures is given in Table 1. The cation BVS are much closer to each other than in the β-K₂SO₄ polymorph of Tl₂CrO₄ (Carter & Margulis, 1972), where one of the cations is underbonded while the other is bound significantly more firmly. This is a tendency observed elsewhere in the β-K₂SO₄ structural family (Fábry & Pérez-Mato, 1994).

In the title structure, the relative contributions of the bond valence pertinent to the shortest Tl⁺—O^2- contact within the coordination environments of each cation, Tl1, Tl2, Tl3 and Tl4, are 0.166 (8), 0.189 (5), 0.268 (8) and 0.196 (5), respectively. In the case of Tl3, the highest bond valence [0.308 (9)] corresponds to the shortest cation–anion bond in the structure, which is 2.608 (11) Å. On the other hand, in the β-K₂SO₄ polymorph (Carter & Margulis, 1972), the shortest Tl⁺—O^2- contacts were determined as 2.70 (9) Å (eleven-oxygen coordinated Tl) and 2.71 (8) (nine-oxygen coordinated Tl), with relative contributions of the respective bond valences of 0.277 (67) and 0.179 (39). However, by analogy with Tl₂SeO₄ (Friese et al., 2004; Fábry & Breczewski, 1993), it can be expected that the former distance should be somewhat shorter and the latter longer.

In general, a higher CN means that the pertinent cation tends to be situated in a larger anionic cavity (Brown, 1992), as seen in the β-K₂SO₄ family, i.e. also in the β-K₂SO₄ polymorph of Tl₂CrO₄. Despite this, the title structure, with lower CN, is less densely packed. This could be attributed to a different packing of the anions in each polymorph. However, in the title structure even the closest anions are somewhat closer to each other than in the β-K₂SO₄ polymorph: the closest distances between Cr atoms are 4.236 (6) and 4.887 (19) Å, respectively.

It is difficult to predict which of either modification of Tl₂CrO₄ is thermodynamically more stable. The somewhat smaller unit-cell volume of the title structure indicates that it should be rather more stable than its β-K₂SO₄ polymorph. Also, the distribution of the cation BVS in the title structure, where not all the cations are underbonded, rather supports the view that it may be more stable than the modification isostructural with β-K₂SO₄. Also, the fact that, in the title structure, the anionic polyhedra are interconnected by the edges, and not by the faces, would enhance the probability that it would relax without abrupt changes (Tables 2 and 3) when cooled down. The low-temperature phase transition in the closely related Tl₂SeO₄ (Table 1) causes a decrease in the CN of the cations from 11 to 10 and from 9 to 8 (up to 4.0 Å from the central cation), i.e. the situation is similar in this respect to the title structure. It is also of interest that, in the title structure, there are significantly and unusually underbonded O atoms, O1a and O2b (Table 1). The dependence of the lattice parameters on temperature in the interval 90–300 K did not indicate a phase transition. (The scan was performed in 10 K intervals.) The differential scanning calorimetric experiments did not reveal a low-temperature phase transition either. However, the sample could contain the β-K₂SO₄ polymorph as well, since the temperatures pertinent to the high-temperature phase transition during heating and cooling corresponded well with the experiments carried out by Natarajan & Secco (1974).

The chemical strains GII (global instability indices) of some related compounds (Brown, 2005; Table 1) do not permit any definite conclusion about the structural stability of the title structure compared with the β-K₂SO₄ polymorph. This is partly due to the fact that, in most cases, there are both overbonded and underbonded cations in the β-K₂SO₄ structures (such as Tl₂SeO₄), while it has been shown that precisely the underbonding of one of the constituent cations is related to the structural stability (Fábry & Pérez-Mato, 1994). The low-temperature phase transitions cause an increase in the BVS of both cations, though mostly the underbonded ones. Thus, the GII are not sensitive for this structural group. For example, the GII of the low-temperature phase of K₂SeO₄ (Yamada et al., 1984) is 0.212 (24), which is larger than that of the room-temperature phase of K₂SeO₄ [0.161 (10)] (Table 1). The other reason for the lower sensitivity of GII in this case is due to the lower reliability of structure determinations of compounds with heavy cations such as Tl⁺, which causes severe absorption at commonly used radiation wavelengths.

S2. Experimental

Tl₂CrO₄ cannot be prepared by simply mixing aqueous solutions of suitable salts, since it is scarcely soluble: K_p = 8.67 × 10^-13 (CRC Handbook of Chemistry and Physics, 2009). The title structure was prepared by a similar procedure to that described by Carter & Margulis (1972), although they used silica gel, which is different to the present preparation. The title crystals were prepared by the reaction of TlNO₃, previously dispersed in a gel formed by hydrolysis of tetramethoxysilane, with K₂CrO₄, as follows. TlNO₃ (0.5 g) was dissolved in H₂O (20 ml) at room temperature. After 1 h, H₂O (27.5 ml) was added together with tetramethoxysilane (2.5 ml). The mixture was stirred for 70 min and then distributed into seven test tubes. The mixtures were left for 2 d until a firm gel formed. A solution of K₂CrO₄ (0.185 g) in H₂O (25 ml) was then prepared, i.e. in the approximate overall molar ratio of 2:1 for TlNO₃ and K₂CrO₄. A small quantity (about 3 ml) of this solution was introduced into each test tube in which the title crystals were to be grown. During the growth of the crystals, Liesegang rings developed: on the front of the precipitation zone the gel was yellow, while behind it a had an orange tint. Crystals of two shapes and colours could be distinguished, namely one type that formed tiny cubes with a more intense orange colour and the other forming needle or plate-like crystals that were yellowish. However, the diffraction patterns of either sample were the same. After four months, crystals were selected manually from the gel. Calorimetric measurements the indicated possible presence of the β-K₂SO₄ polymorph.

The differential scanning calorimetric experiments were performed using a Perkin–Elmer DSC 7 instrument for the measurements from 93 to 323 K and a Perkin–Elmer Pyris Diamond instrument for the measurements from 298 to 823 K (scanning rate 10 K min^-1, sample mass 17 mg, Al pans 40 µl). PYRIS software (Perkin–Elmer, 2001) was used for control and evaluation. A reversible phase transition was found at 783 K on heating and 777 K on cooling (enthalpy change 4.0 J g^-1). This is in good agreement with the phase transitions observed for the β-K₂SO₄ polymorph of Tl₂CrO₄ by differential thermal analysis at 795 K on heating and 774 K on cooling (Natarajan & Secco, 1974).

S3. Refinement

Two refined models were used, one with all atoms independent (79 parameters refined and with slightly lower refinement indicators: R_obs = 0.0324, wR_obs = 0.0777, R_all = 0.0804, wR_all = 0.0841, S_obs = 1.22 and S_all = 0.93; otherwise, the refinement conditions were the same), and the other where the atomic parameters were constrained in such a way that the independent chromates in the two positions were assumed to be identical, i.e. the atomic parameters of the reference chromate situated on the mirror plane were refined. Further refined parameters of the chromate were the rotation and the displacement parameters of the molecules in each site, in order to localize their true positions. Some rotations, however, were excluded, in order to respect the localization of the chromates on the crystallographic mirror planes, i.e. only the rotation whose axis is parallel to the y axis was released. (The rotation of the A chromate about the axis parallel to y was excluded for computational reasons.) Also, the possible translations were limited beacuse of the presence of the mirror plane. (For further details, see the refinement instruction file in the archived CIF.) The latter model, with the assumed identical independent chromates, was given preference, because the displacement parameters of some O atoms seemed to be more probable and the lowering of the refinement indicators was negligible with respect to the decrease of 24 in the number of refined parameters. The maximum residual electron-density peak (2.43 eÅ^-3) is situated 0.2872 (11) Å from Tl3(x, y, z), while the minimum electron density (-2.71 eÅ^-3) is situated 1.2728 (12) Å from Tl2(x - 1/2, y - 1/2, z).

Computing details

Data collection: CrysAlis PRO (Oxford Diffraction, 2009); cell refinement: CrysAlis PRO (Oxford Diffraction, 2009); data reduction: CrysAlis PRO (Oxford Diffraction, 2009); program(s) used to solve structure: SIR97 (Altomare et al., 1999); program(s) used to refine structure: JANA2006 (Petříček et al., 2006); molecular graphics: PLATON (Spek, 2009); software used to prepare material for publication: JANA2006 (Petříček et al., 2006).

Figures

	Fig. 1. A view of the unit cell of the title structure of Tl2CrO4, along the monoclinic axis. The dashed-line boxes indicate similar environments for the cations, cf. Fig. 2.
	Fig. 2. A view of the β-K2SO4 polymorph of Tl2CrO4, along the a axis [setting Pmcn, as given by Carter & Margulis (1972)], cf. Fig. 1.
	Fig. 3. A view of the environment around atoms Tl1 and Tl2. The distance between Tl1 and Tl2 is 3.9772 (15) Å. Displacement ellipsoids are drawn at the 50% probability level. [Symmetry codes: (i) x, 1 + y, z; (ii) 1/2 + x, 1/2 + y, z; (iii) 3/2 - x, 1/2 + y, 1 - z; (iv) -1/2 + x, 1/2 + y, z; (v) x, 1 - y, z; (vi) 1/2 + x, -1/2 + y, z; (vii) 1/2 + x, 3/2 - y, z.]
	Fig. 4. A view of the environment around atoms Tl3 and Tl4. The distance between Tl1 and Tl2 is 4.0127 (14) Å. Displacement ellipsoids are drawn at the 50% probability level. [Symmetry codes: as for Fig. 3. In addition: (viii) -1/2 + x, -1/2 + y, -z; (ix) 1/2 - x, 1/2 - y, z; (x) -1/2 + x, -1/2 + y, z; (xi) 1/2 - x, -1/2 + y, -z; (xii) x, -y, z; (xiii) x, -1 + y, z; (xiv) 1/2 + x, 1/2 -y, z.]

Dithallium chromate

Crystal data

Tl2CrO4	F(000) = 1744
Mr = 524.8	Dx = 6.975 Mg m^−3
Monoclinic, C2/m	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -C 2y	Cell parameters from 2300 reflections
a = 12.7458 (8) Å	θ = 3.0–26.5°
b = 5.8070 (3) Å	µ = 66.39 mm^−1
c = 14.721 (1) Å	T = 292 K
β = 113.519 (7)°	Needle, yellow
V = 999.06 (12) Å^3	0.25 × 0.03 × 0.03 mm
Z = 8

Data collection

Oxford Gemini diffractometer	1363 independent reflections
Radiation source: Enhance (Mo) X-ray Source	710 reflections with I > 3σ(I)
Graphite monochromator	Rint = 0.063
Detector resolution: 10.3784 pixels mm^-1	θmax = 29.1°, θmin = 3.0°
Rotation method data acquisition using ω scans	h = −16→15
Absorption correction: analytical [CrysAlis PRO (Oxford Diffraction, 2009), analytical numerical absorption correction using a multifaceted crystal model (Clark & Reid, 1995); it seemed that one part of the sample did not diffract well and the following dimensions were therefore used: 0.065 × 0.034 × 0.027 mm]	k = −7→7
Tmin = 0.055, Tmax = 0.210	l = −18→19
5287 measured reflections

Refinement

Refinement on F^2	0 restraints
R[F^2 > 2σ(F^2)] = 0.033	24 constraints
wR(F^2) = 0.086	Weighting scheme based on measured s.u.'s w = 1/[σ^2(I) + 0.0016I^2]
S = 0.94	(Δ/σ)max = 0.006
1363 reflections	Δρmax = 2.43 e Å^−3
55 parameters	Δρmin = −2.71 e Å^−3

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

	x	y	z	Uiso*/Ueq
Tl1	0.88189 (7)	0.5	0.37055 (7)	0.0347 (3)
Tl2	0.57729 (7)	0.5	0.38579 (7)	0.0338 (3)
Tl3	0.18384 (7)	0	0.11434 (7)	0.0351 (3)
Tl4	0.50548 (7)	0	0.13009 (7)	0.0333 (4)
Cr1a	0.7235 (2)	0	0.3606 (2)	0.0232 (9)
O1a	0.6716 (10)	0	0.4484 (9)	0.033 (4)
O2a	0.8650 (8)	0	0.4137 (10)	0.042 (5)
O3a	0.6777 (6)	0.2356 (10)	0.2909 (6)	0.026 (3)
Cr1b	0.3596 (2)	0.5	0.1410 (2)	0.0232 (9)
O1b	0.4407 (11)	0.5	0.0757 (8)	0.033 (4)
O2b	0.2231 (9)	0.5	0.0639 (9)	0.042 (4)
O3b	0.3886 (7)	0.7356 (10)	0.2118 (5)	0.026 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Tl1	0.0332 (5)	0.0332 (5)	0.0358 (6)	0	0.0120 (4)	0
Tl2	0.0341 (5)	0.0360 (5)	0.0341 (6)	0	0.0165 (4)	0
Tl3	0.0288 (4)	0.0365 (5)	0.0357 (6)	0	0.0084 (4)	0
Tl4	0.0371 (5)	0.0304 (5)	0.0360 (6)	0	0.0185 (4)	0
Cr1a	0.0240 (11)	0.0193 (11)	0.0268 (15)	0	0.0108 (10)	0
O1a	0.030 (5)	0.042 (6)	0.036 (7)	0	0.024 (5)	0
O2a	0.019 (5)	0.033 (6)	0.062 (9)	0	0.004 (5)	0
O3a	0.033 (3)	0.031 (4)	0.018 (4)	0.006 (3)	0.016 (3)	0.005 (3)
Cr1b	0.0235 (13)	0.0193 (11)	0.0267 (13)	0	0.0100 (10)	0
O1b	0.024 (6)	0.042 (6)	0.040 (6)	0	0.022 (5)	0
O2b	0.024 (6)	0.033 (6)	0.050 (7)	0	−0.006 (5)	0
O3b	0.031 (4)	0.031 (4)	0.023 (3)	−0.005 (3)	0.019 (3)	−0.006 (3)

Geometric parameters (Å, º)

Tl1—O1a^i	3.402 (12)	Tl3—O2b^xi	3.087 (5)
Tl1—O1a^ii	3.003 (15)	Tl3—O2b	3.087 (5)
Tl1—O2a	2.998 (4)	Tl3—O2b^x	3.283 (15)
Tl1—O2a^iii	2.998 (4)	Tl3—O3b^xi	2.870 (7)
Tl1—O3a	2.841 (7)	Tl3—O3b^iv	2.870 (7)
Tl1—O3a^iv	2.841 (7)	Tl4—O3a	2.854 (6)
Tl1—O3b^v	2.826 (8)	Tl4—O3a^xii	2.854 (6)
Tl1—O3b^vi	2.826 (8)	Tl4—O1b^xi	3.037 (3)
Tl2—O1a	3.137 (4)	Tl4—O1b	3.037 (3)
Tl2—O1a^iii	3.137 (4)	Tl4—O2b^v	3.286 (14)
Tl2—O1a^ii	3.157 (10)	Tl4—O2b^x	3.163 (10)
Tl2—O2a^vii	2.894 (13)	Tl4—O3b^xi	2.730 (9)
Tl2—O2a^ii	2.742 (15)	Tl4—O3b^iv	2.730 (9)
Tl2—O3a	2.715 (9)	Cr1a—O1a	1.670 (16)
Tl2—O3a^iv	2.715 (9)	Cr1a—O2a	1.655 (9)
Tl2—O3b	3.049 (7)	Cr1a—O3a	1.670 (7)
Tl2—O3b^iv	3.049 (7)	Cr1a—O3a^xii	1.670 (7)
Tl3—O3a^viii	3.047 (9)	Cr1b—O1b	1.670 (16)
Tl3—O3a^ix	3.047 (9)	Cr1b—O2b	1.655 (10)
Tl3—O1b^viii	2.918 (14)	Cr1b—O3b	1.670 (7)
Tl3—O1b^x	2.608 (11)	Cr1b—O3b^iv	1.670 (7)
O1a—Cr1a—O2a	109.2 (7)	O1b—Cr1b—O2b	109.2 (7)
O1a—Cr1a—O3a	109.0 (4)	O1b—Cr1b—O3b	109.0 (4)
O1a—Cr1a—O3a^xii	109.0 (4)	O1b—Cr1b—O3b^iv	109.0 (4)
O2a—Cr1a—O3a	109.8 (4)	O2b—Cr1b—O3b	109.8 (4)
O2a—Cr1a—O3a^xii	109.8 (4)	O2b—Cr1b—O3b^iv	109.8 (4)
O3a—Cr1a—O3a^xii	110.1 (4)	O3b—Cr1b—O3b^iv	110.1 (4)

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