The crystal structure of alstonite, BaCa(CO3)2: an extraordinary example of ‘hidden’ complex twinning in large single crystals

Abstract Alstonite, BaCa(CO3)2, is a mineral described almost two centuries ago. It is widespread in Nature and forms magnificent cm-sized crystals. Notwithstanding, its crystal structure was still unknown. Here, we report the crystal-structure determination of the mineral and discuss it in relationship to other polymorphs of BaCa(CO3)2. Alstonite is trigonal, space group P31m, with unit-cell parameters a = 17.4360(6), c = 6.1295(2) Å, V = 1613.80(9) Å3 and Z = 12. The crystal structure was solved and refined to R1 = 0.0727 on the basis of 4515 reflections with Fo > 4σ(Fo) and 195 refined parameters. Alstonite is formed by the alternation, along c, of Ba-dominant and Ca-dominant layers, separated by CO3 groups parallel to {0001}. The main take-home message is to show that not all structure determinations of minerals/compounds can be solved routinely. Some crystals, even large ones displaying excellent diffraction quality, can be twinned in complex ways, thus making their study a crystallographic challenge.


Introduction
Alstonite, BaCa(CO 3 ) 2 , is polymorphous with barytocalcite, paralstonite and a recently published synthetic monoclinic phase (Spahr et al., 2019). It was first identified at the Brownley Hill mine near Alston, England, UK in 1834 (Spencer, 1910) and was initially described in the literature by Johnston (1835Johnston ( , 1837 and Thomson (1835Thomson ( , 1837. The latter author proposed the name 'bromlite' in allusion to an erroneous spelling, 'Bromley', of the mine (Palache et al., 1951). Breithaupt (1841) renamed the mineral 'alstonite' after nearby Alston Moor. Both mineral names had been cited in the literature up until Palache et al. (1951) accepted 'alstonite' as the more expressive, and hence, the more appropriate terminology. Alstonite has been identified in 13 different countries which encompass 25 different mineral localities (see http://www.mindat.org). It is typically found in lowtemperature hydrothermal veins associated with other bariumand calcium-rich phases.
A complete set of mineralogical properties of the mineral is summarised by Roberts (1976 and references therein). Crystallographically, the mineral has been described as orthorhombic (Gossner and Mussgnug, 1930), monoclinic (Dickens, 1971) and triclinic (Sartoril 1975, Roberts, 1976, 1978. Dickens (1971) studied alstonite from the New Brancepath Colliery, Durham, England (Smithsonian specimen USNM 95869) and found a C-centred, monoclinic cell with a = 30.163(9), b = 17.413(5), c = 6.110(1) Å and β = 90.10(1)°, with a unit-cell volume 12 times larger than the orthorhombic cell proposed by Gossner and Mussgnug (1930). Zero-and upper-level precession photographs revealed pseudo-hexagonal symmetry normal to (0001). Subsequent Patterson projections confirmed that the Ba and Ca atoms were in pseudo-hexagonal layers, according to the sequence ⋅⋅⋅ABAB⋅⋅⋅, with one layer containing predominantly Ba atoms and the next layer predominantly Ca atoms. Additional structural information by Dickens (1971) established the space group as C2. Unfortunately, the structure could only be refined partially as the location of the carbonate groups was uncertain.
A fully resolved crystal structure for alstonite has been unknown up to this point. It was always assumed that the symmetry was lower than hexagonal because of the optical character of the mineral. Numerous studies (Kreutz, 1909;Spencer, 1910;Bellanca, 1941;Rossman and Squires, 1974;Roberts, 1976) have shown that alstonite is biaxial negative with a 2V that ranges from 6 to 10°. The other three polymorphs of BaCa(CO 3 ) 2 have all had their crystal structures determined: barytocalcite (Dickens and Bowen, 1971), paralstonite (Effenberger, 1980) and the recently described synthetic monoclinic form (Spahr et al., 2019). Herein we document the crystal structure of alstonite.  (51.52845, −3.36820). Here we report only the results from the first locality (that is the co-type locality of alstonite) because the tested crystal is of excellent diffraction quality with respect to the others.

Experimental and structure solution
The intensity data were collected using a Bruker D8 Venture diffractometer equipped with a Photon 100 CMOS and using graphite-monochromatised MoKα radiation. The detector-tocrystal distance was 50 mm. Data were collected using ω and w scan modes, with a 0.5°frame-width and an exposure time of 20 s per frame. The data were corrected for Lorentz and polarisation factors and absorption using the software package APEX3 (Bruker AXS Inc., 2016).
In expectation of probable crystal twinning, a full diffraction sphere was collected. The diffraction pattern was apparently consistent with hexagonal symmetry [refined cell parameters are a = 17.4360(6) Å and c = 6.1295(2) Å]. The statistical tests on the distribution of |E| values (|E 2 -1| = 0.684) suggested the structure to be non-centrosymmetric. Although the collected data exhibited very good merging factors according to 3 (R int = 0.077), 3m1 (R int = 0.081), 31m (R int = 0.079), 6/m (R int = 0.080), and 6/mmm (R int = 0.081) Laue symmetries, the structure was solved initially through direct methods in the triclinic P1 space group because the mineral was always reported as optically biaxial (although with a very low 2V angle). After several cycles, an ordered solution with full site occupations was finally determined (R 1 = 0.18) by carefully removing atoms with low site occupations and/or non-realistic distances with neighbouring atoms and adding significant positions found in the difference Fourier syntheses. Given the very common twinning reported for this mineral, we then took into account the twin law which makes the twin lattice (L T ) trigonal (twinning by metric merohedry; Nespolo, 2004) using the program JANA2006 (Petříček et al., 2006) and the twinning matrices: |100/010/001|, | 100/0 10/00 1|, |100/ 110/00 1|, | 100/ 1 10/001|, | 110/010/001| and |1 10/0 10/00 1|. For details on the averaging of equivalent reflections for twins in JANA, see for instance the appendix in Gaudin et al. (2001). The R 1 index of the P1 model, refined with SHELXL-97 (Sheldrick, 1997) lowered to 0.093 for 25,532 F o > 4σ(F o ) and 0.095 for all 31,062 data. At this stage, an analysis of the structure with the ADDSYMM routine of the PLATON program (Spek, 2003) revealed the real symmetry to be P31m. The site occupancies of all the metal positions were allowed to vary using different combinations of the scattering curves for neutral Ba and Ca atoms (Ibers and Hamilton, 1974) but were found to be occupied by Ba or Ca atoms only. At the last stage, which involved refinement of the anisotropic atomic-displacement parameters for all atoms but C4 and C5 and no constraints, the residual value converged to R 1 = 0.073 for 4515 observed reflections [F o > 4σ(F o )] and 195 parameters and R 1 = 0.075 for all 5496 independent reflections. Table 1 reports further details of the refinement. Atom coordinates and isotropic or equivalent isotropic displacement parameters are given in Table 2 and Table 3 lists the bond distances. The crystallographic information files have been deposited with the Principal Editor of Mineralogical Magazine and are available as Supplementary material (see below). Although the structural model was optimised in the P31m space group, we decided to also have a look at the structure using the C-centred orthohexagonal cell (with a ≈ 3 ½ ⋅b; i.e., a ≈ 30 Å, b ≈ 17.4 Å and c ≈ 6.1 Å), as reported by previous authors (Gossner and Mussgnug, 1930;Dickens, 1971;Sartori, 1975). The reflection data set was transformed according to the transformation matrix |210/010/001|, again taking into account the twin law that makes the twin lattice hexagonal (i.e. twinning   Table S1 in the Supplementary materials). In the two other natural BaCa(CO 3 ) 2 polymorphs (Table 4), Ba is ten-fold coordinated in paralstonite, with an average <Ba-O> distance of 2.812 Å (Effenberger, 1980), and eleven-fold coordinated in barytocalcite, with an average <Ba-O> distance of 2.909 Å (Dickens and Bowen, 1971). Whereas in paralstonite an oversaturation of Ba atoms similar to that observed in alstonite can be calculated (2.44 vu, on the basis of the data of Effenberger, 1980), in barytocalcite such an overbonding is smaller, the BVS at the Ba site being 2.16 vu. Such an overbonding observed in alstonite could have different explanations: for instance, the bond character (covalent vs. ionic) may vary, and the relationship of Brese and O'Keeffe (1991), using a constant b value, does not account adequately for the different stiffness of the atoms. On the contrary, the observed overbonding can be only partially related to the replacement of Ba by smaller cations (e.g. Sr, as suggested by previous chemical analyses performed on samples from the type locality - Kreutz, 1909;Sartori, 1975 (Effenberger and Zemann, 1985), although recent structural investigations suggested a [6+6] coordination for norsethite and its Mn-analogue BaMn(CO 3 ) 2 (e.g. Effenberger et al., 2014;Pippinger et al., 2014;Wen et al., 2019). In witherite, BaCO 3 , Ba is nine-fold coordinated (e.g. Ye et al., 2012). Calcium is eight-fold coordinated, with <Ca-O> distances ranging between 2.500 and 2.544 Å; Ca-O distances vary between 2.184 (Ca1-O14) and 2.752 Å (Ca1-O2). This coordination is similar to that occurring in paralstonite, where <Ca-O> is 2.49 Å (Effenberger, 1980). On the contrary, barytocalcite has seven-fold coordinated Ca, with an average <Ca-O> distance of 2.388 Å (Dickens and Bowen, 1971).
The eight independent C sites show the typical flat triangular coordination, with <C-O> distances ranging between 1.235 (C4) and 1.340 Å (C1). Carbonate groups are parallel to {0001}, as in paralstonite (Effenberger, 1980). In barytocalcite, on the contrary, CO 3 groups are parallel to {201} (Dickens and Bowen, 1971). Figure 1 shows the crystal structure of alstonite as seen down c. Two kinds of sequences of CO 3 groups and Ca/Ba atoms running along a can be distinguished in such a projection. The first one (at y/b = 0) is ⋅⋅⋅CO 3 -Ca-Ca-CO 3 -Ba-Ba-CO 3 ⋅⋅⋅, whereas at y/b = ∼⅙, ⅓, ∼½, ⅔ and ∼⅚, Ba and Ca are neighbours. At y/b = ∼⅙ and ∼⅚, succeeding pairs of Ba and Ca atoms are inverted, whereas in the other layers ( y/b = ∼⅓, ∼½ and ∼⅔), the sequence Ba-Ca is maintained. In both cases, slices are mutually shifted. In addition, considering the O-O edge of the CO 3 triangle perpendicular to the b direction, two CO 3 configurations can be identified: the first one (hereafter called 'up') has the third oxygen in the +b direction, whereas the other (hereafter called 'down') has the third oxygen in the −b direction. Rows of CO 3 groups with 'up' and 'down' configurations at y/b = 0 alternate, along b, with rows of CO 3 groups in a 'down' configuration at y/b = ½. In this configuration, the C-O bonds always point towards the smaller Ca atoms. At y/b = ⅙, ⅓, ⅔ and ⅚, staggered CO 3 groups occur. These CO 3 groups show C-O bonds pointing towards different atoms, i.e. three Ca atoms, two Ca atoms and one Ba atom, one Ca atom and two Ba atoms, and three Ba atoms. It is worth noting that these sequences are the result of the projection of two different layers, with the staggered CO 3 groups having about the same z/c coordinates showing the same 'up' or 'down' configuration. Indeed, the crystal structure of alstonite can be described as a layered one, formed by the alternation of mixed (Ca/Ba) layers and CO 3 groups parallel to {0001}. The Ba/Ca layer at z/c ≈ 0.10 is Barich and it is composed by Ba1, Ba3 and Ca1 sites; the other layer, at z/c ≈ 0.60, is Carich and it is composed of Ba2, Ca2 and Ca3 sites. This is one of the main differences of alstonite with respect to its dimorph paralstonite. Indeed, the latter is characterised by the alternation, along c, of Ca and Ba layers, separated by CO 3 layers (Fig. 1). In addition, the projection along c shows the sequence ⋅⋅⋅Ca-Ba-CO 3 -Ca-Ba-CO 3 ⋅⋅⋅ along a; CO 3 groups have all the same 'up' configuration for y/b = 0, whereas they are staggered at y/b = ⅓ and ⅔. In paralstonite, staggered CO 3 groups at about the same z/c coordinates display different 'up' and 'down' configurations in a 1:1 ratio. The different sequences ⋅⋅⋅CO 3 -(Ba/Ca) ⋅⋅⋅ along a in alstonite and paralstonite are likely to be related to the doubling of the a axis in the former.

Calculated versus observed powder-diffraction pattern
To verify if the structural model obtained for alstonite matched its powder X-ray diffraction pattern, we also collected powderdiffraction data with a Bruker D8 Venture equipped with a Photon III CCD detector, with graphite-monochromatised CuKα radiation (λ = 1.54138 Å), and with 3 hours of exposure; the detector-to-sample distance was 6 cm. The program APEX3 (Bruker AXS Inc., 2016) was used to convert the measured diffraction rings to a conventional powder-diffraction pattern. The  excellent match between the calculated and observed X-ray powder-diffraction data is visually reported in Fig. 2 and testifies to the validity of the obtained structural model.

Summary and conclusion
The crystal structure of alstonite has been solved and refined in the space group P31m and its relationships with paralstonite and barytocalcite are discussed. It is worth noting that the solution of the crystal structure in a space group belonging to the trigonal symmetry, suggested by some morphological features, was initially discouraged by the biaxial optical behaviour of alstonite reported by previous authors. For this reason, these authors (e.g. Dickens, 1971;Sartori, 1975), continued to use a C-centred unit cell and persisted in using lower-symmetry models (monoclinic/triclinic) for their structure solutions. However, the present study strongly suggests that the symmetry is actually trigonal and the anomalous optical behaviour could be simulated by minor strain combined with the occurrence of widespread pervasive twinning. This phenomenon is quite common in uniaxial minerals having small 2V angles (e.g. calcite -Turner, 1975;quartz -Starkey, 2000). Notwithstanding its finding in the first half of the 19th Century and its occurrence in well-developed crystals, some up to a cm in size, the crystal structure of alstonite remained unsolved up to this contribution. Indeed, alstonite is a good example that shows even large crystals having excellent diffraction quality can hide crystallographic pitfalls, such as widespread and complex twinning, thus making the structure solution puzzle a headache.