I. INTRODUCTION
The crystal structure of tin (II) sulphate was determined by Rentzeperis (Reference Rentzeperis1962) based on the suggestion of James and Wood (Reference James and Wood1925) that SnSO4 has a barite structure. However, Donaldson and Moser (Reference Donaldson and Moser1960) indicated that such a relation is unlikely because of the large difference in the ionic radii of Ba2+ and Sn2+ [r Ba = 1.61 Å (Shannon, Reference Shannon1976); r Sn = 0.85 Å (Donaldson and Puxley, Reference Donaldson and Puxley1972)]. Using single-crystal data, the structure of SnSO4 was refined by Donaldson and Puxley (Reference Donaldson and Puxley1972). The main structural features of SnSO4 are illustrated (Figure 1). A lone pair of electrons of the sp3 hybridized Sn2+ orbitals may explain the high degree of distortion in SnSO4 and its relation to the barite structure. In SnSO4, the Sn2+ atom is in a pyramidal coordination that forms three bonds with the O atoms and the fourth orbital in the sp3 hybridization is occupied by a lone pair of electrons [Figure 1(a)]. The lone pair of electrons is viewed as pseudo-ligands, which prevents close approach of other anions in this direction and significantly changes the space requirements (Gillespie, Reference Gillespie1967; Gillespie and Robinson, Reference Gillespie and Robinson1996). Crystal structures that have cations with a lone pair of electrons are quite open and they undergo pressure-induced phase transitions (Crichton et al., Reference Crichton, Parise, Antao and Grzechnik2005; Hinrichsen et al., Reference Hinrichsen, Dinnebier, Liu and Jansen2008).
(a) Projection of the SnSO4 structure showing the pyramidal [3]-coordination of a Sn atom to three O atoms of three different SO4 groups. (b) Sharing of SO4 and SnO12 polyhedral edges in the SnSO4 structure that are the same as in the BaSO4 structure.
The crystal structure of celestite, anglesite, and barite was recently refined by Antao (Reference Antao2012), and interesting structural trends were observed across the series. Miyake et al. (Reference Miyake, Minato, Morikawa and Iwai1978) indicated a possible systemic variation in the SO4 tetrahedron with field strength of the M2+ cation across the series. Jacobsen et al. (Reference Jacobsen, Smyth, Swope and Downs1998) concluded that the average 〈M–O〉 distance increases linearly with unit-cell volume, but SO4 behaves as a rigid group with an average 〈S–O〉 distance of about 1.476 Å, which is constant across the series. Hawthorne and Ferguson (Reference Hawthorne and Ferguson1975) and Hill (Reference Hill1977) reported that the SO4 groups in all three structures display identical geometries. These studies indicate that the M2+ cations have no effect on the shape or size of the SO4 tetrahedron. The M2+ cations have different sizes and effective charge, so systematic variation in the geometry of the SO4 group across the series is expected, and this was recently confirmed by Antao (Reference Antao2012). Although the structure of the isostructural MSO4 materials is well known, previous studies have not shown the change in the geometry of the SO4 group observed by Antao (Reference Antao2012) using high-resolution powder X-ray diffraction (HRPXRD), which is the same technique used in this study to examine the structure of SnSO4.
The purpose of this study is to refine the crystal structure of SnSO4 and to examine its relation to the structural trends that were recently observed by Antao (Reference Antao2012) for the isostructural sulphates SrSO4, PbSO4, and BaSO4. Of particular interest is the variation in the geometry of the SO4 group for these sulphates and the radius of the [12]-coordinated Sn2+ cation.
II. EXPERIMENTAL
A. Synchrotron HRPXRD
The SnSO4 sample was studied by HRPXRD that was performed at beamline 11-BM, Advanced Photon Source (APS), Argonne National Laboratory (ANL). The synthetic tin (II) sulphate, SnSO4, was obtained as 99% reagent grade powder from ACROS organics, and the HRPXRD trace showed no impurity phase. The sample was crushed to a fine powder using an agate mortar and pestle. The powder sample was loaded into a Kapton capillary (0.8 mm internal diameter) and rotated during the experiment at a rate of 90 rotations per second. The data were collected to a maximum 2θ of about 43° with a step size of 0.001° and a step time of 0.1 s per step. The HRPXRD trace was collected with 12 silicon (111) crystal analysers that increase detector efficiency, reduce the angular range to be scanned, and allow rapid acquisition of data. A silicon (NIST 640c) and alumina (NIST 676a) standard (ratio of ⅓ Si :⅔ Al2O3) was used to calibrate the instrument and to refine the monochromatic wavelength [0.41399(2) Å] used in the experiment. Additional details of the experimental set-up are given elsewhere (Antao et al., Reference Antao, Hassan, Wang, Lee and Toby2008; Lee et al., Reference Lee, Shu, Ramanathan, Preissner, Wang, Beno, Von Dreele, Ribaud, Kurtz, Antao, Jiao and Toby2008; Wang et al., Reference Wang, Toby, Lee, Ribaud, Antao, Kurtz, Ramanathan, Von Dreele and Beno2008).
B. Rietveld structure refinement
The HRPXRD data were analysed by the Rietveld method (Rietveld, Reference Rietveld1969), as implemented in the GSAS program (Larson and Von Dreele, Reference Larson and Von Dreele2000), and using the EXPGUI interface (Toby, Reference Toby2001). Scattering curves for ionized atoms were used in the refinement. The starting atom coordinates, unit-cell parameters, and space group Pbnm were taken from Donaldson and Puxley (Reference Donaldson and Puxley1972). Pure SnSO4 formula was used in the structure refinement. The background was modeled using a Chebyschev polynomial (12 terms). The reflection-peak profiles were fitted using type 3 profile in the GSAS program. Full-matrix least-squares refinements were carried out by varying the parameters in the following sequence: a scale factor, unit-cell parameters, atom coordinates, and isotropic displacement parameters. Towards the end of the refinement, all the parameters were allowed to vary simultaneously, and the refinement proceeded to convergence. The fitted HRPXRD trace is shown in Figure 2.
The HRPXRD trace for SnSO4 together with the calculated (continuous line) and observed (crosses) profiles. The difference curve (I obs − I calc) is shown at the bottom and has the same scale as that for intensity. The short vertical lines indicate allowed reflection positions. The intensity beyond 20 °2θ is scaled by a factor of ×30. The FWHM of the strongest (121) peak at 7.75 °2θ is 0.009°.
The unit-cell parameters and the Rietveld refinement statistics are listed in Table I. Atom coordinates and isotropic displacement parameters are given in Table II. Bond distances and angles are given in Table III.
Unit-cell parameters and Rietveld refinement statistics for SnSO4.
aR (F 2) = R-structure factor based on observed and calculated structure amplitudes = [∑(F o2–F c2)/∑(F o2)]1/2. Space group is Pbnm; the number of formula units per cell, Z = 4.
Atom positions and isotropic displacement parameters (×100 Å2) for SnSO4.
Selected distances (Å) and angles (°) in SnSO4.
III. RESULTS AND DISCUSSION
The Sn atom is in a pyramidal coordination and is bonded to three O atoms from different SO4 groups [Figure 1(b)]. If the Sn2+ cation is coordinated to 12 O atoms, then the SnSO4 structure is similar to the BaSO4 structure [Figure 1(b)].
Donaldson and Puxley (Reference Donaldson and Puxley1972) refined the structure of SnSO4 in space group Pnma, and they concluded that the radius of the Sn atom is too small (they used 0.85 Å) to form a stable BaSO4-type structure. Although they mentioned that SnSO4 and BaSO4 are not isostructural, they indicated that SnSO4 could be considered as a highly distorted form of the barite structure with the Sn atom surrounded by 12 O atoms, as in barite.
In this study, the structure of SnSO4 was refined in space group Pbnm, the same as that for barite, and the results are similar to those obtained by Donaldson and Puxley (Reference Donaldson and Puxley1972). [Note that space group Pnma and Pbnm are the same (#62) in different settings. So, structural data from one space group can easily be transformed to the other]. Three of the O atoms are close to an Sn atom [1 × 2.254(2) and 2 × 2.280(1) Å; 〈Sn–O〉 = 2.271(1) Å] and the other O atoms are further away [≥2.980(2) Å]. The Sn atom is in a pyramidal three coordination and the pyramidal bond angles are 2 × 77.56(5) and 1 × 79.61(7)° [Figure 1(a) and Table III]. The Sn atom environment was explained in terms of covalent bonding involving sp3 hybridization of the Sn (II) orbitals (Donaldson and Puxley, Reference Donaldson and Puxley1972). In the sp3 hybridization, the Sn atom forms three covalent bonds to O atoms and the fourth orbital is occupied by a lone pair of electrons, which prevents close approach of other O atoms in this direction, and gives rise to an open structure. Moreover, the O–Sn–O bond angles of 77.56 and 79.61° obtained in this study agree with the bond-pair and lone-pair repulsion arguments predicting that the O–Sn–O angles are less than 109.5°. The SO4 group in SnSO4 has a distorted tetrahedral geometry with S–O bond lengths of 1 × 1.442(2), 1 × 1.479(2), and 2 × 1.483(1) Å, and the average 〈S–O〉 distance is 1.472(1) Å, compared to 1.487(5) Å obtained by Donaldson and Puxley (Reference Donaldson and Puxley1972).
A. Structural trends among SrSO4, PbSO4, SnSO4, and BaSO4
The relevant structural parameters for the isostructural materials are given in Table IV together with the bond–valence sums around the M and S cations and the three independent O atoms. The valence sums for the S cation is close to the expected value of six for all four sulphate compounds. However, the expected valence sum value of two is only observed for the Sr cation and deviates the most for the Sn cation. The valence sums around the O atoms (especially O1) deviate the most from the expected value of −2.0 for SnSO4, whereas the values for the other compounds are not unreasonable (Table IV).
Comparison of structural parameters for the isostructural sulphates.
Data for SrSO4, PbSO4, and BaSO4 are taken from Antao (Reference Antao2012).
*These values and the radii for O2−[4] = 1.38 Å are from Shannon (Reference Shannon1976), so r Sn = 2.939–1.38 = 1.56 Å. Bond valence sums (v.u. = valence units) around the M, S, and O atoms were calculated using the program VaList (Wills and Brown, Reference Wills and Brown1999).
The radii of 12-coordinated M2+ cations, r M (Shannon, Reference Shannon1976), and the a, b, c unit-cell parameters are plotted against the volume, V (Figure 3). The trend lines shown in Figures 3–5 are based only on data from Antao (Reference Antao2012) to which the SnO4 data are compared, but the SnSO4 data are not included in the computation of the trend lines. The unit-cell parameters a, b, and V for SnSO4 are intermediate between those for PbSO4 and BaSO4, but the c parameter is similar to that for SrSO4 (Figure 3). The r M increases linearly with increasing unit-cell V [Figure 3(d)]. The increase in unit-cell parameters arises from the increase in size of the M2+ cation. A radius of 1.56 Å was deduced for a [12]-coordinated Sn2+ cation (see Table IV).
The a, b, c unit-cell parameters and radii of the [12]-coordinated M2+ cations, r M, vs. volume, V, for the isostructural sulphates. The unit-cell parameters for SnSO4 are intermediate between PbSO4 and BaSO4. The radii, r M, increase linearly with V. Error bars are smaller than the symbols in Figure 3 and 4. In Figure 3–5, the data for SnSO4 are plotted but they are not included in the computation of the least-squares fitted trend lines.
Linear increase in average 〈M–O〉 distance with volume, V, for the [12]-coordinated M-site in the isostructural sulphates. Data for SnSO4 are close to the trend line for the other sulphates.
Structural variations of: (a) average 〈S–O〉 vs. V, and (b) average 〈S–O〉 vs. radius of [12]-coordinated M cation, r M. Data for SnSO4 are close to the linear trends for the other sulphates.
The average 〈M–O〉 [12] distance is plotted against V (Figure 4). Linear trends are observed for the data from Antao (Reference Antao2012), but the average 〈Sn–O〉 distance is offset from the predicted value based on the trend lines (Figure 4), and is larger because of the lone pair of electrons that causes the SnO12 polyhedra to be quite open.
The interesting aspect of this study is the geometrical features of the SO4 group that are plotted against V and r M (Figure 5). The average 〈S–O〉 distance decreases linearly with V [Figure 5(a)], whereas the average 〈O–S–O〉 angle is constant with V (Table IV). The average 〈S–O〉 distance decreases linearly with increasing r M [(Figure 5(c)]. The structural parameters for these isostructural minerals are correlated with the effective size of the M2+ cation. In SrSO4, the small Sr2+ cation forms a short average 〈Sr–O〉 distance so the charge on the O atoms is less and the average 〈S–O〉 distance is longer, whereas in BaSO4, the large Ba2+ cation forms a longer average 〈Ba–O〉 distance so the charge on the O atoms is more and the average 〈S–O〉 distance is shorter (Figures 4 and 5). The change in the average 〈S–O〉 distances parallels the change in valence sums around the S cation (Table IV). The SO4 group does not have a rigid-body character, as was previously suggested by Jacobsen et al. (Reference Jacobsen, Smyth, Swope and Downs1998).
The average 〈S–O〉 and 〈M–O〉 distances are consistent with expected variations. However, the bond-strength sums around the M cations and O atoms are not consistent (Table IV); but those around the S cations are consistent.
This study shows that in the isostructural sulphate minerals, several well-defined structural trends are observed. Of particular interest is the geometry of the SO4 group that changes in a regular manner, as expected. Moreover, the average 〈S–O〉 distance in anhydrite [CaSO4; 〈S–O〉 = 1.4848(3) Å] is expected to be longer than that in celestite [SrSO4; 〈S–O〉 = 1.480(1) Å], which was recently confirmed (Antao, Reference Antao2011, Reference Antao2012). Similar results were observed for the orthorhombic carbonates (Antao and Hassan, Reference Antao and Hassan2009), where the geometry of the CO3 group changes in a regular manner. In addition, for the SiO4 group in framework silicates, the geometry also changes in a regular manner (Antao et al., Reference Antao, Hassan, Wang, Lee and Toby2008). Such expected structural trends were not previously observed.
ACKNOWLEDGEMENT
The HRPXRD data were collected at the X-ray Operations and Research beamline 11-BM, APS, and ANL. Use of the APS was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. This work was supported with a Discovery grant from NSERC and an Alberta Ingenuity Award.
