INTRODUCTION
The crystal structure of anhydrite was investigated by Wasastjerna (Reference Wasastjerna1925) and by Dickinson and Binks (Reference Dickinson and Binks1926). Later works by Höhne (Reference Höhne1961, 1962) and Cheng and Zussman (Reference Cheng and Zussman1963) confirmed the structure proposed by Wasastjerna (Reference Wasastjerna1925). Single-crystal X-ray diffraction studies were reported by Morikawa et al. (Reference Morikawa, Minato, Tomita and Iwai1975), Hawthorne and Ferguson (Reference Hawthorne and Ferguson1975), and Kirfel and Will (Reference Kirfel and Will1980). Swanson et al. (Reference Swanson, Fuyat and Ugrinic1955) reported unit-cell parameters of a = 6.991, b = 6.996, and c = 6.238 Å for anhydrite; the a and b parameters are slightly different from each other. Höhne (Reference Höhne1962) and Cheng and Zussman (Reference Cheng and Zussman1963) assigned the space group Amma and adopted the unit-cell values of Swanson et al. (Reference Swanson, Fuyat and Ugrinic1955). Morikawa et al. (Reference Morikawa, Minato, Tomita and Iwai1975) pointed out that their labelling of a and b should be interchanged for space group Amma, so that a > b, whereas for space group Bmmb, b > a. Hartman (Reference Hartman1989) also observed contradictions in unit-cell dimensions for anhydrite; the powder data of the JCPDS card 6-226 and the unit-cell data of Hawthorne and Ferguson (Reference Hawthorne and Ferguson1975) gave contradictory results. The relevant data are given in Table I. Based on data available in the literature, Hartman (Reference Hartman1989) calculated an average structure for anhydrite. On the basis of the contradictory unit-cell parameters, further work on anhydrite is necessary.
Hartman (Reference Hartman1989) chose space group Bmmb because the slice (200) has a zircon-like arrangement of Ca and SO4 that also occurs in the (200) slice of monoclinic monazite, with a slight deformation. In addition, the Ca and S atoms are nearly linearly arranged in [100] and [001] directions, giving the (020) slice a NaCl-like appearance, which also holds with larger deformation for the (020) slice of monazite. Hawthorne and Ferguson (Reference Hawthorne and Ferguson1975) and Kirfel and Will (Reference Kirfel and Will1980) used the Amma setting and showed the relation between anhydrite and gypsum, CaSO4·2H2O, which also accounted for the orientated nature of the high-temperature dehydration of gypsum to anhydrite (Atoji, Reference Atoji1959). Structural data in space group Amma can be transformed to Bmmb.
Jacobsen et al. (Reference Jacobsen, Smyth, Swope and Downs1998) refined the structures for the isostructural minerals celestite (SrSO4), anglesite (PbSO4), and barite (BaSO4). They concluded that the average <M-O> distance increases linearly with unit-cell volume, but SO4 behaves as rigid group with an average <S-O> distance of 1.476 Å, which is constant 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 M 2+ cation across the isostructural series, but their SO4 geometry was statistically identical, as pointed out by Jacobsen et al. (Reference Jacobsen, Smyth, Swope and Downs1998). The CO3 and SiO4 groups are often considered as rigid groups, but Antao et al. (Reference Antao, Hassan, Wang, Lee and Toby2008) and Antao and Hassan (Reference Antao and Hassan2009) have shown that their geometries do vary in a systematic way. Therefore, systematic variation in the geometry of the SO4 group is expected as the M 2+ cation changes.
This study examines trends in the unit-cell parameters and the geometry of the SO4 group in anhydrite. The Rietveld structure refinements were carried out in space group Amma and data from the literature in space group Bmmb were transformed to Amma for comparison (Table I).
EXPERIMENTAL
Sample characterization
The four anhydrite samples used in this study are from: (1) Hants County, Nova Scotia (UC8215); (2) Naica, Mexico; samples (3) and (4) are from the Baldonnel sedimentary formation in west-central Alberta. These two samples are from two different drill cores and the crystals occur at depths of 1190 (Baldonnel-1) and 1135 (Baldonnel-2) meters below sea level.
TABLE I. Unit-cell parameters (Å) and average bond distances (Å) for anhydrite in space group Amma.
a data were transformed from Bmmb to Amma. Values for a and b given in italic have a < b, which are incorrect for space group Amma.
b Sample from Nova Scotia.
The samples were analyzed using a JEOL JXA-8200 electron microprobe and the standard JEOL operating program on a Solaris platform. The wavelength-dispersive operating conditions were 15-kV accelerating voltage, 10-nA beam current, a beam diameter of 5 μm, and using various standards. The chemical compositions of the samples are given (Table II). The samples are homogeneous based on optical observations and microprobe analyses of at least eight spots. Based on the chemical analyses, the four samples are chemically similar, and the pure CaSO4 formula was used in the structure refinements.
HRPXRD
The anhydrite samples at 23 °C were studied by high-resolution synchrotron powder X-ray diffraction (HRPXRD) experiments performed at Beam-line 11-BM, Advanced Photon Source (APS), and Argonne National Laboratory (ANL). The samples were crushed to fine powders using an agate mortar and pestle. The samples were loaded into Kapton capillaries 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 traces were collected with twelve silicon (111) crystal analyzers that increase detector
TABLE II. Electron microprobe analysis (EMPA) of four anhydrite samples.
a Atoms per formula unit.
TABLE III. Unit-cell parameters and Rietveld refinement statistics for anhydrite in space group Amma.
a R F2 = R-structure factor based on observed and calculated structure amplitudes = [∑(F o2–F c2)/∑(F o2)]1/2. N obs = number of observed reflections. The number of data points for each trace is 39499 and the 2θ data range was 3.5 to 43°.
efficiency, reduce the angular range to be scanned, and allow for rapid acquisition of data. A silicon and alumina NIST standard (ratio of ⅓ Si : ⅔ Al2O3) was used to calibrate the instrument and to determine and refine the monochromatic wavelength [e.g., k¼ 0.41220(2) Å] used in the experiment (Table III). Additional details of the
TABLE IV. Atom positions and isotropic displacement parameters ( ×100 Å2) for anhydrite in space group Amma.
Figure 1. The HRPXRD trace for anhydrite from Nova Scotia 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 intensities and difference curve beyond 20° 2θ are scaled by a factor of ×30.
experimental set-up are given elsewhere (Antao et al., Reference Antao, Hassan, Wang, Lee and Toby2008b; Lee et al., Reference Cole and Lancucki2008; Wang et al., Reference Wang, Toby, Lee, Ribaud, Antao, Kurtz, Ramanathan, Von Dreele and Beno2008).
Rietveld structure refinements
The HRPXRD data were analyzed 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 neutral atoms were used. Initial atom coordinates and unit-cell parameters were taken from Kirfel and Will (Reference Kirfel and Will1980) for space group Amma. The background was modeled using a Chebyschev polynomial (12 terms). Each reflection-peak profile was fitted using a type-3 profile in the GSAS program. Full-matrix least-squares refinements were carried out by varying the parameters in the following sequence: scale factor, unit-cell parameters, atom coordinates, and
TABLE V. Selected bond distancesFootnote a (Å) and angles (º) for anhydrite in space group Amma.
a For the four samples, the grand mean for <Ca-O> and <S-O> are 2.4660(2) and 1.4848(3) Å, respectively.
isotropic displacement parameters. Toward the end of the refinement, all the parameters were allowed to vary simultaneously, and the refinement proceeded to convergence. A HRPXRD pattern for the anhydrite sample from Nova Scotia is shown in Figure 1.
The unit-cell parameters and the Rietveld refinement statistics are listed in Table II. Atom positions and isotropic displacement parameters are given in Table IV. Bond distances and angles are given in Table V.
RESULTS AND DISCUSSION
In the anhydrite structure, parallel to the c direction, alternating CaO8 dodecahedra and SO4 tetrahedra share
Figure 2. (Color online) Projection of the structure of anhydrite down: (a) close to the b axis showing edge-sharing between CaO8 dodecahedra and SO4 tetrahedra, and (b) close to the a axis showing the Ca dodecahedra and S tetrahedra sharing corners.
edges and form a chain (Figure 2). In the a direction, the chains are connected by edge-shared CaO8 dodecahedra [Figure 2(a)], and in the b direction by corner-shared CaO8 dodecahedra and SO4 tetrahedra [Figure 2(b)]. The anhydrite structure is related to the structures of gypsum, zircon, monazite, and halite (Atoji, Reference Atoji1959; Robinson et al., Reference Robinson, Gibbs and Ribbe1971; Wyckoff, Reference Wyckoff1965; Hartman, Reference Hartman1989).
The unit-cell parameters for anhydrite are in the sequence indicated by Morikawa et al. (Reference Morikawa, Minato, Tomita and Iwai1975) and Hartman (Reference Hartman1989): a > b for space group Amma (Tables I and III). HRPXRD data have a large 2θ range and a large number of data points, which enables unit-cell parameters to be determined reliably. The precision and internal consistency of the structural data can be seen from the errors reported (Table I).
Values of the a, b, and c unit-cell parameters increase linearly with increasing unit-cell volume, V [Figures 3(a) and 3(b)]. Such linear relations were not previously observed. These linear trend lines are derived from the four samples that have quite similar chemical composition and nearly identical structural parameters. The large and small unit-cell data from Kirfer and Will (1980) and Morikawa et al. (Reference Morikawa, Minato, Tomita and Iwai1975), respectively, fall close to the extension of the linear least-squares lines that represent the data from this study [Figures 3(a) and 3(b)]. The trend lines representing the variations of the a and b parameters are parallel to each other and indicate that a and b parameters differ by about 0.008 Å in anhydrite [Figure 3(a)]. The unit-cell data from Hawthorne and Ferguson (Reference Hawthorne and Ferguson1975) do not fall on the observed trend lines because their data are incorrect, as pointed out by Hartman (Reference Hartman1989). The anhydrite sample studied by Kirfel and Will (Reference Kirfel and Will1980) is quite interesting, as it has the largest unit-cell parameters [Figures 3(a) and 3(b)]. Unfortunately, a modern chemical analysis is not available for this sample, so the reason for their large unit-cell parameters is not known. The reason for the linear relations may be related to the trace element contents in anhydrite, such as Mg and Sr replacing Ca atoms to some extent.
For eight-coordinated Ca, the grand mean <Ca-O> distance is 2.4660(2) Å for the four anhydrite samples [Figure 3(b); Table V], which is comparable with 2.470 Å obtained by Hawthorne and Ferguson (Reference Hawthorne and Ferguson1975) and Kirfel and Will (Reference Kirfel and Will1980), and 2.468 Å reported by Morikawa et al. (Reference Morikawa, Minato, Tomita and Iwai1975) and Hartman (Reference Hartman1989) [Table I]. Based on ionic radii (Ca2 +[8] = 1.12 Å and O2-[3] = 1.36 Å; Shannon, Reference Shannon1976), Ca-O = 2.48 Å. In gypsum, CaSO4·2H2O, the average <Ca-O>[8] is 2.458 Å (Cole and Lancucki, Reference Cole and Lancucki1974), which is similar to the grand mean <Ca-O> = 2.4660(2) Å in anhydrite. The average <Ca-O> distances are closer to the data of Morikawa et al. (Reference Morikawa, Minato, Tomita and Iwai1975), but do not match those of Hawthorne and Ferguson (Reference Hawthorne and Ferguson1975) or Kirfel and Will (Reference Kirfel and Will1980; Figure 3(c)).
The anhydrite sample from Nova Scotia has tetrahedral SO4 group with two independent S-O distances of 1.484(1) to O1 and 1.478(1) Å to O2 (Table V). These distances are different from each other, and their average <S-O> distance is 1.4810(5) Å, which is slightly different from values previously reported in the literature that are typically about 1.475 Å (Table I). The three independent O-S-O angles
Figure 3. Structural variations in anhydrite (space group Amma). The a and b unit-cell parameters in (a) and c parameter in (b) increase linearly with increasing V. Data from the literature are included for comparison, but are not fitted to the trend lines. Errors in (a) and (b) are smaller than the symbols. The average <Ca-O> distances and their grand mean (horizontal line) are shown in (c), whereas the average <S-O> distances and their grand mean (horizontal line) are shown in (d).
[108.99(8) × 1, 110.38(3) × 4, 106.34(9)° × 1] and the S-O distances indicate that the geometry of the SO4 group is quite distorted in CaSO4. In gypsum, CaSO4.2H2O, the S-O distances are 1.457 and 1.461 Å, and the average <S-O> distance of 1.459 Å is shorter than the present values for anhydrite (Cole and Lancucki, Reference Cole and Lancucki1974). For the isostructural minerals celestite (SrSO4), anglesite (PbSO4), and barite (BaSO4), the SO4 behaves as a rigid group with an average <S-O> distance of 1.476 Å, which is constant across the series (Jacobsen et al., Reference Jacobsen, Smyth, Swope and Downs1998). The four anhydrite samples in this study have a grand mean <S-O> distance of 1.4848(3) Å, which is larger than those in the isostructural series because the eight-coordinated Ca has a smaller size than the other twelve-coordinated M 2+ (= Sr, Pb, and Ba) cations. The Ca atom satisfies the charge on the O atoms more effectively, thereby allowing the S-O distance to be larger in anhydrite. The <S-O> distance in anhydrite can be compared with an average <S-O> distance of 1.49 Å in other inorganic structures (International Tables of X-Ray Crystallography, 1962).
The geometry of the SO4 group should vary in a regular manner as the M 2+ (= Ca, Sr, Pb and Ba) cation changes, as proposed by Miyake et al. (Reference Miyake, Minato, Morikawa and Iwai1978). That is, the <S-O> distance is longest in CaSO4 and shortest in BaSO4; it should change in the following sequence: CaSO4 > SrSO4 > PbSO4 > BaSO4 because as the M 2 + cation radius increases, the effective charge decreases (Antao, Reference Antao2012).
ACKNOWLEDGMENTS
R. Marr is thanked for his help with the microprobe analyses. The HRPXRD data were collected at the X-ray Operations and Research beamline 11-BM, Advanced Photon Source (APS), Argonne National Laboratory (ANL). Use of the APS was supported by the U.S. Dept. of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. This work was support by a Discovery Grant from NSERC and an Alberta Ingenuity Faculty Award.
