Crystal structure and composition of hiärneite, Ca2Zr4Mn3+SbTiO16, and constitution of the calzirtite group

Abstract The crystal structure of hiärneite has been refined from single-crystal X-ray diffraction data (λ = 0.71073 Å) on type material from Långban, Värmland, Sweden. The refinement converged to R1 = 0.046 based on 1073 reflections with F2 > 4σ(F2). The tetragonal unit cell, space group I41/acd, has the parameters a = 15.2344(6) Å and c = 10.0891(6) Å with Z = 8. The mineral is isostructural with calzirtite, ideally Ca2Zr5Ti2O16, with a structural topology derived from fluorite. In hiärneite, Mn3+ is ordered at a 4- to 8-fold coordinated site (with a distorted polyhedral coordination figure), without the atom splitting encountered at the corresponding Zr-dominated site of calzirtite. The end-member formula for hiärneite is established as Ca2Zr4Mn3+SbTiO16. The calzirtite group, with calzirtite, hiärneite and tazheranite (cubic ZrO2-x), has been approved by the IMA–CNMNC.

Hiärneite, having a tetragonal unit cell with a = 15.264(1), c = 10.089(2) Å, space-group symmetry I4 1 /acd, was inferred to be isostructural with calzirtite, ideally Ca 2 Zr 5 Ti 2 O 16 (Holtstam, 1997). The crystal structure was, however, not studied in detail at the time of discovery. We have now collected single-crystal diffraction data and refined the crystal structure of type hiärneite (sample from the mineral collection of the Swedish Museum of Natural History, GEO-NRM #19920776).
X-ray diffraction data and refinement X-ray diffraction data of hiärneite were obtained with an Oxford Diffraction Xcalibur 3 diffractometer (MoKα radiation, λ = 0.71073 Å) fitted with a Sapphire 2 CCD detector (see Table 1 for details). Intensity integration and standard Lorentz-polarisation corrections were done with the CrysAlis RED (Oxford Diffraction, 2006) software package. Crystal shape and dimension optimisation were performed with X-shape (Stoe and Cie, 1996), based on the Habitus program (Herrendorf, 1993). The set of reflections was corrected for absorption via a Gaussian analytical method and averaged according to the 4/mmm point group. Following an absorption correction, the merging R for the data set decreased from 0.081 to 0.054. The analysis of the reflection conditions unequivocally led to the choice of the space group I4 1 /acd. Given the close similarity in terms of unit-cell dimensions and crystal symmetry, the crystal structure was refined starting from the atomic coordinates of calzirtite, ideally Ca 2 Zr 5 Ti 2 O 16 (Rossel 1982;Sinclair et al., 1986;Rastsvetaeva et al., 1995;Jafar et al., 2016).
The site occupancy factor (s.o.f.) at the cation sites was allowed to vary (Mn vs. structural vacancy, Sb vs. structural vacancy, Ca vs. structural vacancy and Zr vs. structural vacancy for M1, M2, M3 and M4, respectively) using scattering curves for neutral atoms taken from the International Tables for Crystallography (Ibers and Hamilton, 1974). The mean electron numbers obtained for each site were modelled considering the observed bond distances and the electron microprobe analysis (see below). These proportions were then fixed in subsequent refinement cycles (see Table 2 constrained refinement). The full-matrix least-squares program Shelxl-97 (Sheldrick, 2008) was used for the refinement of the structure. Convergence was easily achieved up to R 1 = 0.046. Atomic coordinates and bond distances are given in Tables 2 and 3, respectively. The crystallographic information file has been deposited with the Principal Editor of Mineralogical Magazine and is available as Supplementary material.

Crystal structure
The crystal structure (Fig. 2) is a derivative of the fluorite-type structure, with a tetragonal symmetry. Here we use the same site nomenclature previously used for calzirtite. The cations are arranged on planes parallel to (010) and constitute double heteropolyhedral layers (at y = ⅙, ⅓) containing the M2, M3, and M4 sites (with 8-, 6-and 7-fold coordination, respectively), intercalated between Ml + M4 layers (at y = 0, ½). A special feature of the calzirtite structure is the splitting of the Zr-dominated M1 site (Zr-Zr contact 0.54 Å) within a distorted cube of O atoms. In hiärneite, metal atoms occupying the 4-to 8-coordinated site M1 are fixed at (0, ¼, ⅛) without any spreading of electron density. For the remaining parts, calzirtite has an identical structural topology as hiärneite. Bond distances are the same within 0.02 Å as obtained for previous studies of the calzirtite structure, except for average M1-O distances that are slightly longer in hiärneite (2.31 Å vs. 2.26 Å).

Chemical composition
Calzirtite is normally chemically relatively pure, with minor Nb and Ta substituting for Ti, Hf for Zr and Fe for Ca (Bellatreccia et al., 1999); it may also host rare earth elements and actinides at low concentrations (Pascal et al., 2009). As the concentration of common Pb is usually negligible, calzirtite has proven to be useful for 207 Pb-206 Pb age determination (Wu et al., 2010). Hiärneite is more complex in composition (Table 4, data from Holtstam, 1997).
The distribution of the cations present at the structural sites of hiärneite is based primarily on ionic radii and electronic charge. Calcium, Na and a fraction of Mn 2+ are assigned to M3. The M2 site is a mixed Sb, Ti site with minor Fe 3+ . The M4 site, as for calzirtite, is dominated totally by Zr (+ Hf). The M1 site hosts mainly Mn and a small fraction of Zr. These cation assignments are supported by refined site-scattering values (Table 5) and bond-valence sums (  (Holtstam, 1997). Ordering of Mn 3+ to a normally Zr-dominated site is a very rare phenomenon, but the similar ionic radii (0.65 and 0.72 Å, respectively) and electronic charges make it      *Analytical conditions: wavelength-dispersive spectroscopy, 20 kV accelerating voltage and 12 nA beam current. HfO 2 concentration is estimated from energy-dispersive X-ray spectrometry. Data from Holtstam (1997), reproduced with permission. **Calculated from stoichiometry (9 cations, 16 oxygen atoms).
dominant-constituent rule. The application of the site-total-charge (STC) approach (Bosi et al., 2019), however, gives a STC value of +2.81 for M1 and +9.33 for M2, close to +3 and +9, respectively. The dominant atomic arrangement is then Mn 3+ at M1 and (SbTi) 9+ at M2, giving the end-member formula presented here.

Classification
As calzirtite and hiärneite are nearly isostructural, and consist of similar chemical components, they constitute a mineral group (Mills et al., 2009b). The calzirtite group was introduced informally by Strunz and Nickel (2001), and includes calzirtite, an orthorhombic modification, calzirtite-1O (described by Callegari et al., 1997), hiärneite and the structurally closely related cubic mineral tazheranite (Zr,Ti,Ca)(O,□) 2 (where □ = vacancy). Tazheranite is considered as a natural form of ZrO 2 , 'cubic zirconia', stabilised by impurity elements and oxygen vacancies (Rastsvetaeva et al., 1998;Konzett et al., 2013). Its structure is characterised by Zr and Ca, Ti etc. distributed randomly over the regular 8-coordinated sites in a fluorite-type Fm 3m unit cell, whereas the anion sites are only partially occupied for charge compensation (also shown for synthetic analogues; Howard et al., 1988). In calzirtite and hiärneite, the ordering of the cations over specific sites leads to a lower symmetry and a tripled a parameter and doubled c parameter (Table 7). More pure variants of cubic ZrO 2 have also been reported to form from shock-metamorphism of zircon (e.g. Kenny and Pasek, 2021). All of the group members belong to the Nickel-Strunz subdivision 4.DL (Strunz and Nickel, 2001 Table 6. Weighted bond-valence sums (in valence units) for hiärneite according to the parameters of Brese and O'Keffe (1991) for all the elements (site occupancies in Table 2) apart from Sb 5+ , which was calculated according to Mills et al. (2009a).  Sinclair et al. (1986); 2 this work; 3 Rastsvetaeva et al. (1998).