A. Sample preparation

The mineral of interest was presented as a number of 1 mm diameter, white, vitreous hemispheres (Figure 1) formed within vugs of a 10 cm sized piece of bulk silicocarbonatite sill rock from the Francon Quarry in Montreal, Quebec, Canada. Hemispheres were removed from the bulk under an optical microscope and an attempt was made to clean their surface of impurities. Of the six hemispheres obtained, four were gently crushed in ethanol using a mortar and pestle for X-ray diffraction analysis. Once dried, the powder was loaded into a 0.5 mm quartz capillary and the capillary sealed with wax before mounting in a standard brass capillary pin. One of the remaining hemispheres was lightly crushed and mounted onto a scanning electron microscope (SEM) stub using adhesive carbon film. The sample was examined in a Hitachi S4800 field emission SEM. Images and elemental analysis were obtained at 5 and 20 kV accelerating voltages, respectively.

B. X-ray data collection

The X-ray data were collected using a Bruker-AXS D8 diffractometer using Cu K α radiation with a focusing primary mirror and a Vantec PSD detector. Although the diffractometer was a θ-θ instrument, data were collected in the range from 9° to 140° 2θ with a fixed incident angle (the Debye-Scherrer geometry) using a 10° detector window. A variable count/step scheme was employed to improve counting statistics at high angle and produce more accurate results in the final Rietveld refinement (Madsen and Hill, Reference Madsen and Hill1994). The data collection scheme is given in Table I.

The data ranges were combined into a single file in “xye” format to retain the counting statistics information. All of the data analysis was done using the Bruker-AXS TOPAS 4.2

TABLE I. Variable count-time data collection regime.

software (Bruker-AXS, 2008b). The least-squares indexing method (Coelho, Reference Coelho2003) was used to index the data from the first 25 peak positions determined through single-peak fitting. No background subtraction was necessary (including the capillary) to fit the background satisfactorily using a 15-term Chebyschev polynomial. This contrasts with the slight diffuseness in the powder diffraction data observed by Jambor et al. (Reference Jambor, Sabina, Roberts and Sturman1977) which they attributed to possible nonstoichiometry in carbonate and water content due to absorption from air.

C. Structure solution and refinement

The ability to extract intensities out to low d spacings and the presence of a heavy atom (Sr) were positive indications that charge flipping (Oszlányi and Süto, Reference Oszlányi and Süto2004) might yield some of the atomic positions. The initial structure solution was accordingly attempted with a combination of charge-flipping method and tangent formula (Coelho, Reference Coelho2007). Low-density elimination (Shiono and Woolfson, Reference Shiono and Woolfson1992) was used to sharpen the resulting electron density.

Charge flipping produced sensible positions for the strontium, aluminum, and some oxygen atoms. Use of fixed positions for strontium and aluminum atoms in subsequent simulated annealing runs with data up to 80° 2θ greatly eased the difficulty of extracting a successful solution.

Rigid bodies consisting of regular AlO₆ octahedra and CO₃ triangles were used in conjunction with a “box interaction” penalty function such that at least eight oxygen atoms should be within 2.65 Å of a strontium atom. This model with six oxygen atoms around each aluminum and three around each carbon therefore contained initially 18 oxygen atoms/f.u., compared with 10 or 11 in the chemical formula. Merging of oxygen atoms approaching one another within 0.9 Å was accordingly implemented. Separate isotropic displacement parameters (B _iso) were used for the cations and anions. The oxygen atom for a water molecule was located on a Fourier difference map. The final refinement step involved all variable atom positions as well as individual B _iso.

The final refinement used the full data ranged up to 140° 2θ. The peak profiles were fitted using convolution-based peak profiles in combination with double-Voigt sample size-strain model (Balzar and Ledbetter, Reference Balzar and Ledbetter1995). The simple axial divergence correction implemented in TOPAS (Bruker-AXS, 2008a) was used. Individual B _iso values were refined for the strontium, aluminum, carbon, and oxygen atoms, except for the equatorial AlO₆ oxygen atoms which were refined with an overall B _iso. The Sabine capillary absorption correction (Sabine et al., Reference Sabine, Hunter, Sabine and Ball1998) was applied to the intensities. The linear absorption coefficient used in the correction included the contribution from the extraneous fluorite content. The wide 2θ range indicated that the application of the Debye-Scherrer capillary displacement 2θ correction (McCusker et al., Reference McCusker, Von Dreele, Cox, Louer and Scardi1999) might be useful and was included in the input file as a user-defined macro.

D. Valence summation and location of hydrogen atoms

Bond valence sums were calculated using VaList (Wills, Reference Wills2008). The bond-valence parameter for the mixed Sr-Ca site (2.088) was determined by applying percentage contribution from the refined site occupancies for Sr and Ca. A value of 0.37 was assumed for B, which is common to the bond-valence entries for Ca and Sr used as end members. Bond valence parameters for OH were taken from the 2006 version of bond-valence parameters maintained by I.D. Brown (Reference Brown2006a). No hydrogen atoms were included in the X-ray refinement of the data. A unique model for H positions in space group P n m a was then derived from crystal-chemical considerations as detailed in Sec . IIIA.

E. Modeling, DFT energy minimization, and structure stability

A crystal structure model combining the X-ray atom coordinates and the above hydrogen atoms was prepared and optimized by ab initio total energy minimization using the Vienna Ab initio Simulation Package (VASP) (Kresse, Reference Kresse1993; Kresse and Hafner, Reference Kresse and Hafner1993) within the framework of density functional theory (DFT). Full occupancy by Sr of the (Sr,Ca) site was assumed. All modeling VASP input file preparation as well as output file interpretation was performed with Materials Toolkit (Le Page and Rodgers, Reference Le Page and Rodgers2005). The energy minimization scheme detailed by Mercier and Le Page (Reference Mercier and Le Page2008) was followed with a 4×4×4 k mesh. Distorted models for the structure-stability test were prepared with the NUDGE utility (Le Page and Rodgers, Reference Le Page and Rodgers2006) in Materials Toolkit and optimized with VASP.

A. The sample and its analysis

The sample under examination had been macroscopically identified as montroyalite, Sr₄Al₈[(OH),F]₂₆(CO₃)₃⋅10–11H₂O (Roberts et al., Reference Roberts, Sabina, Bonardi, Jambor, Ramik, Sturman and Carr1986), a mineral also found in the Francon Quarry that typically occurs as small white hemispheres (similar to strontiodresserite) and coincidentally has the same Sr:Al ratio as strontiodresserite. The hemispherical nature of the material in question is apparent in the optical micrograph shown in Figure 1. The identity of the mineral was called into question when the powder diffraction was examined as the data did not resemble that expected from montroyalite (Roberts et al., Reference Roberts, Sabina, Bonardi, Jambor, Ramik, Sturman and Carr1986). The possibility of a dehydration product of montroyalite was considered, but both the position and relative intensities of the reflections closely resembled those reported in the literature for strontiodresserite. Consequently, the structure solution process was started on the assumption that it was, in fact, strontiodresserite.

A small number of reflections from fluorite were visible and these were fitted as a secondary phase during the complete

Figure 2. A SEM micrograph of a crushed strontiodresserite hemisphere.

analysis process. Fluorite is not mentioned as a phase associated with strontiodresserite (Jambor et al., Reference Jambor, Sabina, Roberts and Sturman1977) but is associated with the fluorine-containing montroyalite (Roberts et al., Reference Roberts, Sabina, Bonardi, Jambor, Ramik, Sturman and Carr1986). None of the closely associated minerals mentioned by Jambor et al. (Reference Jambor, Sabina, Roberts and Sturman1977), such as quartz and dawsonite, were present in the diffraction pattern.

Examination of the material by SEM yielded heavily fractured lathlike needles as shown in Figure 2. Lathlike crystals are consistent both with the observations by Jambor et al. (Reference Jambor, Sabina, Roberts and Sturman1977) on strontiodresserite and those of Roberts et al. (Reference Roberts, Sabina, Bonardi, Jambor, Ramik, Sturman and Carr1986) on montroyalite including the “splintery fracture.” EDX measurements yielded a Sr:Al atomic ratio of approximately 1:2. No signal from fluorine was detected either at 20 kV or when the voltage was lowered to optimize the detection of lighter elements, which is additional evidence that the sample was strontiodresserite as opposed to montroyalite.

B. Unit-cell analysis

The crystallinity of strontiodresserite was found to be quite good with distinct reflections visible all the way up to the limit of 140° 2θ as can be seen in the inset of Figure 3. Single peak fitting to obtain the first 25 to 30 reflections was

Figure 3. (Color online) Rietveld difference plot for the refinement of the strontiodresserite structure. The inset shows a blowup of the region between 100° and 140° 2θ.

Figure 4. (Color online) Polyhedral representation of the experimental strontiodresserite crystal structure.

straightforward and 25 of those were used as input in the LSI indexing algorithm. Using a calculated lines to observed line ratio of 5, the first 70 solutions from the indexing in TOPAS gave the same orthorhombic lattice parameters with a=16.1, b=9.2, and c=5.6 Å, giving a very high confidence in the result. The first four solutions of the top 5 had the suggested space group P n a2₁ corresponding to the extinction symbol Pna-. Besides P n a2₁, the space group P n a m also belongs to the extinction symbol Pna-(Looijenga-Vos and Buerger, Reference Looijenga-Vos, Buerger and Hahn2006), yielding effectively the same choice as that presented by Roberts (Reference Roberts1978). The top solution had a GOF of 28.1 with a minimal zero point error. A Le Bail full pattern fit (Le Bail et al., Reference Le Bail, Duroy and Fourquet1988) to the data ranging from 9° to 80° 2θ, including the fluorite secondary phase, yielded good fits in both P n a2₁ and P n a m (R _wp=5.0%). P n a m and P b n m are alternate settings of the standard space group P n m a (No. 62).

C. Structure analysis

The first cycles of charge flipping yielded the strontium atom positions. Following cycles gave aluminum atom positions. The positions determined from the charge flipping accounted for the cell symmetry and identified the special position of the strontium atoms. Fixing the positions of the strontium and aluminum atoms in the simulated annealing assisted in finding the other atom positions relatively quickly. The oxygen atom of the water molecule was not subjected to any constraints, and took a little longer to locate reliably. The rigid-body octahedra used in the simulated annealing led to excess of oxygen atoms compared to the nominal stoichiometry. The partially merged oxygen atoms accordingly had to be consolidated in single sites for refinement upon removing the rigid-body constraints, leading to the expected stoichiometry.

A fourth-order spherical harmonics preferential orientation correction (Järvinen, Reference Järvinen1993) was necessary to finalize the refinement. The application of this correction did not alter the overall structure but greatly improved the geometry of the carbonate ions and significantly improved the fit. The refined B _iso of the Sr appeared to be sensitive to the preferential orientation correction, and the value increased after the application of the spherical harmonics. Orientation of a powder in a capillary is suggestive of needle or lath-shaped crystallites, which has been reported previously with strontiodresserite (Jambor et al., Reference Jambor, Sabina, Roberts and Sturman1977) and can be seen in Figure 2.

Although a Fourier difference map confirmed the location of the water oxygen atom, no additional water molecules were found and none of the hydrogen atoms could reliably be located by X-rays. As expected, the capillary displacement was minimal (x=+0.03 mm and y=+0.04 mm) but did improve the R _wp residual slightly.

The final refinement was carried out in the standard setting for space group number 62, which is P n m a. The cell and structure can be transformed to the P b n m cell by the application of a cab matrix transformation for comparison with the previously described structure of dundasite (Cocco et al., Reference Cocco, Fanfini, Nunzi and Zanazzi1972). The final refined lattice parameters in P n m a were a=16.0990(7), b=5.6133(3), and c=9.1804(4) Å, with Z=4. The fit to the experimental data was very good as shown in Figure 3, with a R _wp value of 5.2%. The density of strontiodresserite calculated with those cell parameters is 2.66 g/cm³, which compares quite well with the measured value of 2.71 g/cm³ (Jambor et al., Reference Jambor, Sabina, Roberts and Sturman1977) given that the refined Ca content on the Sr site is very slightly lower at 19.3% than the nominal value of 20%.

D. Structure description

The structure consists of corrugated chains extending along the b axis. Those chains are made of edge-sharing AlO₆ octahedra, as shown in Figure 4. Four coplanar oxygen atoms are shared in this way in an equatorial plane of each Al atom, while two axial oxygen atoms lie perpendicular to that plane. Next to each of the AlO₆ chains, the strontium atom shares edges with two AlO₆ octahedra. In the b direction the irregular-shaped SrO₉ polyhedra alternate with the carbonate ions which are corner sharing with two axial AlO₆ oxygen atoms and share an oxygen atom with the opposite SrO₉. The carbonate ions effectively tie together the two Al/Sr/O layers in the unit cell. The water molecules are located in channels running along the b direction and are not coordinated directly with any of the cations. The position of the oxygen atom does suggest the possibility of hydrogen bonding with oxygen atoms in the polyhedral network. Bond valence analysis confirmed that the hydroxyl oxygen atoms are O1, O2, O4, and O6, which are the equatorial oxygen atoms of the AlO₆ octahedra. Table II lists the atomic coordinates from Rietveld refinement of nonhydrogen atoms in space group P n m a. Table III shows the results of bond-valence summation using atom coordinates in Table II.

E. Location of hydrogen atoms

The fact that O9w could be refined to a B _iso of 2.0(2) with full oxygen occupancy is an indication that water molecules are strongly bound with just one scheme of hydrogen bonds, and that an ordered hydrogen-bond scheme most probably exists in strontiodresserite. Examination of experimental O-O approaches for O9w indicates that only three oxygen atoms, O3 (×2) and O6 at respective distances of 2.92 and 2.68 Å, can possibly be involved in hydrogen bonding with O9w. The next shortest distance of 3.19 Å is too long to be part of a significant hydrogen bond [see, e.g., Figure 1 in Ferraris and Ivaldi (Reference Ferraris and Ivaldi1988)]. From bond-valence summation, O6 is known to be an OH group, thus indicating an O6-H6…O9w hydrogen bond. The two short approaches between O9w and O3 are then the two O9w-H9…O3 hydrogen bonds of the water molecule. The remaining OH groups at O1, O2, and O4 are all bonded to two Al³⁺ ions. Simple electrostatic field considerations then suggest an initial location

TABLE IV. Ab initio optimized atomic coordinates for strontiodresserite.

of corresponding hydroxyl hydrogen atoms on the line joining the midpoint between the two Al³⁺ ions and the oxygen atom away from the aluminum ions. Qualitatively, this hydrogen-bond scheme is unique in space group P n m a. Initial O-H distances were assumed to be 1 Å.

F. DFT energy minimization of strontiodresserite and dundasite

DFT energy minimization by adjustment of atom coordinates of this model in the fixed experimental cell proceeded smoothly, without any large drift of the proposed hydrogen atoms or of the framework atoms, a strong indication of a sensible initial model. Table IV lists all atom coordinates, including hydrogen atoms after DFT optimization with VASP in space group P n m a. Selected bond distances are shown in two columns in Table V for easy comparison of X-ray and ab initio VASP results. Bond angles from ab initio VASP results pertaining to the hydrogen bonding are given in Table VI. The bonds involving hydrogens from the DFT model are shown graphically in Figure 5 for easy interpretation of Tables IV – VI. There are no large discrepancies from expected values including all optimized O-H distances of about 1 Å. As expected the agreement between experimental and DFT bond lengths tends to be better with the heavier elements as they are more easily localized with X-ray powder diffraction data. From Table VI, the H-O-H angle in the water molecule as well as H…O-H angles are all reasonably close to tetrahedral angles. The only deviation from an ideal model for a textbook seems to be that the O9w-H9w…O3 angle deviates from 180°. We consider this to be a minor imperfection because the H9w…O3 hydrogen bond is rather weak. H9w is accordingly pointing to an electrostatically negatively charged region on the wall of a wide channel rather than establishing a strong hydrogen bond with O3, which ought to be in straight line. We tested the energy of plausible disordered hydrogen-bond models at O9w, with lower symmetry. All those that did not revert to the above

TABLE V. Selected bond distances derived from the refinement of the experimental data and the DFT-optimized structure.

scheme failed to reduce the total energy and yielded atomic coordinates for O9w that differed from those found experimentally.

G. Space-group choice for strontiodresserite and dundasite

The success of the structure solution in a particular space group from diffraction intensities, as well as its DFT optimization in that space group, does not prove that the correct structure is not actually distorted with a lower symmetry. We accordingly tested the ab initio stability of the final tabulated crystal structure of strontiodresserite by creating models of it in P1, introducing random tiny individual distortions into all atom coordinates and all cell vectors. Total energy minimization will promptly return this randomly distorted crystal structure to its initial configuration and symmetry if it is stable. In contrast, an unstable model will converge to a new configuration with lower energy and lower symmetry. The test performed with the NUDGE utility (Le Page and Rodgers, Reference Le Page and Rodgers2006) on the strontiodresserite P1 model confirmed that the P n m a model of strontiodresserite is stable and lowering

TABLE VI. Selected bond angles from the DTF-optimized structure.

Figure 5. (Color online) The hydrogen bonding network in strontiodresserite.

the symmetry is not necessary. The same test, repeated with the literature structure of dundasite combined with hydrogen atoms from strontiodresserite, confirmed the structure and symmetry of dundasite as reported by Cocco et al. (Reference Cocco, Fanfini, Nunzi and Zanazzi1972).

H. Complementarity of powder methods, valence summation, and DFT optimization

This study illustrates the fact that the combination of laboratory X-ray Rietveld profile analysis with valence summation and ab initio methods can, in a number of cases, reliably elucidate crystal structures of a complexity that used to require X-ray single-crystal diffraction. As shown here, this possibility opens new perspectives with samples that can be obtained in powder form only. For oxides, bond-valence summation (Brown, Reference Brown2006b) provides a powerful check of the validity of the crystal structure, but ab initio optimization provides several additional and very stringent checks about the correctness of the structure model. The first such check is that stress calculated ab initio using experimental cell parameters was verified here to be small and uniform. With VASP, this stress is usually calculated as a small negative and essentially isotropic pressure, in part because ab initio calculations are performed at 0 K temperature and also due to tiny imperfections in the numerical representation of quantum-calculated core electron density. A second test is that calculated optimized atom coordinates for atoms should actually match the experimentally determined atom positions. This test is particularly powerful in cases like here, where some atoms were located experimentally while others are deduced from crystal-chemical considerations: a wrong assignment of hydrogen atoms would have repercussions on hydroxyl and water oxygen positions. Verification of the match of coordinates within least-squares uncertainties then validates both the framework architecture and the hydrogen-bond scheme deduced from it. The third test is that of the stability of the optimized structure model as explained previously. This test validated here the use of space group P n m a for the structure solution, demonstrating that a lower symmetry was not required.