Structural investigations on bredigite from the Hatrurim Complex

Bredigite, Сa7Mg(SiO4)4, is an indicator mineral of metasomatic rocks of the sanidinite facies formed at high temperatures (>800 °C) and low pressures (<1–2 kbar). Bredigite samples from ternesite-gazeevite-larnite pyrometamorphic rocks of the Hatrurim Complex (Negev Desert, Israel) have been studied by electron probe micro analysis and single-crystal diffraction using synchrotron radiation. They are characterized by a relatively uniform composition. The empirical formula calculated on the basis of 16 O atoms per formula unit is: (Ca7.006Na0.015Ba0.014)Σ7.035Mg0.938(Si4.000P0.014)Σ4.014O16. Basic crystallographic data of a sample studied by X-ray diffraction are as follows: orthorhombic symmetry, space group Pnnm, a = 18.38102(17) Å, b = 6.74936(7) Å, c = 10.90328(11) Å, V = 1352.66(2) Å3, Z = 4. Structure solution and subsequent least-squares refinements resulted in a residual of R(|F|) = 0.023 for 2584 independent observed reflections with I > 2σ(I) and 149 parameters. To the best of our knowledge this is the first detailed structural investigation on natural bredigite. In contrast to previous studies on samples retrieved from metallurgical slags there was no need to describe the structure in the acentric space group Pnn2. Furthermore, the problem of Ba incorporation into the bredigite structure is discussed. Data on the composition of Ba-bearing bredigites from pyrometamorphic rocks of the Hatrurim Complex from Jordan with simplified formula Ba0.7Ca13.3Mg2(SiO4)8 (based on 32 oxygen atoms) are provided for the first time, pointing out perspectives of finding new Ba-bearing minerals isostructural with bredigite in nature.


Introduction
Bredigite (idealized chemical composition Ca 7 Mg(SiO 4 ) 4 ) is a rare mineral that has been described from petrological settings related to pyrometamorphism (Grapes 2011). It has been observed, for example, in contact-metamorphized rocks or in altered carbonate-silicate xenoliths within volcanites based on siliceous limestone-dolomite protoliths.
Characteristic localities for this type of occurrence are Scawt Hill, Northern Ireland (Tilley and Vincent 1948;Sabine et al. 1985) or the Christmas Mountains, Texas (Joesten 1976).
In pyrometamorphic rocks of the Hatrurim Complex consisting of products of combustion metamorphism, we and other researchers (Gross 1977;Sharygin et al. 2008;Sokol et al. 2010;Vapnik and Vardi 2013) repeatedly noted small bredigite grains, mainly, in larnite rocks. The Hatrurim Complex is distributed over a wide area along the Dead Sea rift zone in the territories of Israel, Palestine and Jordan (Bentor 1960;Gross 1977;Vapnik et al. 2007;Novikov et al. 2013). Its formation was driven by combustion processes of a sedimentary protolith, however, the detailed genesis of the Hatrurim Complex is still under discussion (Sokol et al. 2010;Kolodny et al. 2013;Vapnik and Novikov 2013). The main hypothesis is pyrometamorphic rock-formation due to combustion of organic matter contained in primary sedimentary rocks (Kolodny and Gross 1974;Matthews and Gross 1980;Geller et al. 2012). Recently, a Bmud-volcanic^hypothesis has b e e n p r o p o s e d , s u g g e s t i n g h i g h -t e m p e r a t u r e pyrometamorphic alteration of primary rocks driven by methane fire exhaling from tectonic active zones of the Dead Sea rift (Sokol et al. 2010;Novikov et al. 2013 There are a few classes of pyrometamorphic rocks in the Hatrurim Complex, including gehlenite hornfelses, larnite pseudoconglomerates and spurrite marbles, and also melted rocks (paralavas) of several types (Gross 1977;Vapnik et al. 2007). Rocks containing more exotic minerals such as ternesite, silicocarnotite, nabimusiate, gazeevite, jasmundite, fluorkyuygenite are less abundant. Their formation is related to processes of high-temperature alteration of early clinker-like mineral associations under the influence of combustion by-products (gases, fluids) in the course of pyrometamorphism (Galuskina et al. 2014;Galuskin et al. 2016). Relatively large bredigite grains suitable for structural investigations are the objects of this work and were found in unusual ternesite-gazeevite-larnite rocks in the Negev Desert, Israel.
Practically in all known localities, bredigite forms small, twinned and often intensely altered grains (Armbruster et al. 2011;Galuskina et al. 2015). Probably, this is the reason for the lack of structural investigations on natural single-crystals so far.
Apart from being a mineralogical curiosity, bredigite is also of interest for the field of material science and has been intensively studied as a host for rare earth elements for synthesis of new photoluminescent compounds (Lee et al. 2012;Jia et al. 2012;Zhang and Jiang 2014;Sun et al. 2015). In addition, research on bredigite included areas as diverse as bioactive ceramics (Wu et al. 2005;Huang and Chang 2008;Rahmati et al. 2018), steelmaking slags (Wang et al. 2015;Kriskova et al. 2018) or chemical stabilizing of radioactive waste (Jantzen et al. 1984). Lin and Foster (1975) placed the upper stability limit of bredigite at 1372°C where it starts to decompose into Ca 2 SiO 4 and Ca 3 Mg(SiO 4 ) 2 . According to Essene (1980) the question of the lower stability is not resolved. The value of 979°C reported by Schlaudt and Roy (1966) may actually represent rather a synthesis than an equilibrium boundary.
Notably, when comparing morphological and optical properties of natural and synthetic samples, Tilley and Vincent (1948) postulated that bredigite is isostructural with α'-Ca 2 SiO 4 . More detailed crystallographic investigations on the same samples were subsequently performed by Douglas (1952). Focusing on the orthorhombic unit-cell parameters (a = 10.93 Å, b = 6.75 Å, c = 18.41 Å) she recognized a close resemblance to the values previously reported for α'-Ca 2 SiO 4 . However, two lattice parameters found for bredigite were approximately twice those of the pure calcium silicate. Saalfeld (1974) confirmed the orthorhombic cell. Based on electron microprobe analysis he determined that the chemical formula of this phase is Ca 7 Mg(SiO 4 ) 4 . The trials and tribulations of the bredigite -α'-Ca 2 SiO 4 interrelationship have been summarized by Moseley and Glasser (1981). A complete structure determination of bredigite was eventually presented by Moore and Araki (1976). They came to the conclusions that (i) bredigite is a stoichiometric compound with idealized composition Ca 7 Mg(SiO 4 ) 4 (or Ca 1.75 Mg 0.25 SiO 4 ) and (ii) α'-Ca 2 SiO 4 and bredigite are not isostructural. Based on Moore's landmark paper on relations between different orthosilicates and sulfates (Moore 1973) a detailed topological analysis of bredigite was given as well.
Interestingly, Moore used the same synthetic sample of Tilley and Vincent from 1948 which had been obtained from a metallurgical slag of the so-called spiegeleisen production. The German word spiegeleisen (literally Bmirror iron^) is a technical term that found its way into the English language and describes a ferromanganese alloy containing small quantities of carbon and silicon. Therefore, it is not surprising that chemical analysis of the abovementioned sample revealed the presence of manganese in the crystal structure, substituting for magnesium.
The present contribution reports the first results of detailed chemical and crystallographic investigations of natural bredigite samples retrieved from the Hatrurim Complex.
Samples for the single-crystal diffraction studies were screened with a petrographic microscope. Finally, a crystal showing sharp extinction when observed under crossed polarizers was selected and mounted on a loop using epoxy resin. The diffraction experiment was performed on the X06DA beamline at the Swiss Light Source, Paul Scherrer Institute, Villigen, Switzerland. Diffraction data were collected at 25°C using the DA+ acquisition software and a Pilatus 2 M-F detector in shutterless operation at a wavelength of 0.70848 Å (= 17.5 keV). The detector was placed 80 mm from the sample, without a vertical offset, resulting in a maximum resolution of 0.7 Å. 1800 frames were recorded using fine-sliced (0.1°) ω-scans with 0.2 s per frame. Table 1 contains a summary of the conditions pertaining to data collection. The CrysAlis PRO software package (Rigaku Oxford Diffraction 2015) was employed to process the data. After indexing, the diffraction patterns were integrated. Further data reduction included Lorentz and polarization corrections as well as an absorption correction based on spherical harmonics. Diffraction symmetry of the crystal conformed to the orthorhombic Laue group 2/m2/m2/m. Systematic absences were compatible with the space groups P2 1 /n2 1 / n2/m (Pnnm) or Pnn2, respectively.
Refinement calculations were performed using the program SHELX-97 (Sheldrick 2008) implemented in the WinGX software package (Farrugia 1999). X-ray scattering factors for neutral atoms were taken from the International Tables for Crystallography, Vol. C (Wilson 1992). After transformation to standard setting, structure refinement was initiated from the atomic coordinates reported by Moore and Araki (1976) in the acentric space group Pnn2. This model rapidly converged to a residual of R(|F|) = 0.023 (266 parameters). Validation of the structure was accomplished using the program PSEUDO (Capillas et al. 2011). It turned out that the atomic coordinates fulfilled the symmetry requirements of Pnnm and, therefore, the final calculations were conducted in the centrosymmetric space group. The updated model converged to R(|F|) = 0.023 (149 parameters), i.e. the residuals of the refinements in Pnnm and Pnn2 are identical, though the number of parameters in Pnnm is roughly halved. We shall present a more detailed analysis of the relationships between the Pnn2 and Pnnm structures further on in the Discussion section.
Within three standard uncertainties, site population refinements indicated full occupancy for most of the different Ca-and Mg-positions in the asymmetric unit of the centrosymmetric structure. Ca1, however, exhibited a slightly but significantly increased scattering density. Since chemical analysis proved the presence of a small amount of barium, we attributed this observation to a Ca -Ba substitution on this site. The corresponding Ca/Ba content was determined from a site occupancy refinement where the total amount of both alkaline earth ions on this position was constraint to 100 %. The optimized atomic coordinates, equivalent isotropic and anisotropic displacement factors as well as selected interatomic distances and angles are given in Tables 2, 3

3.23
Structural investigations on bredigite from the Hatrurim Complex centimeters. It can be assumed, that the fine-grained rocks containing the clinker-like larnite-ye'elimite-fluorellestadite association formed at the pyrometamorphism peak as a result of transformations in a relatively dry isochemical system. The rocks provided a substrate for later mineral assemblages of poikilitic crystals of ternesite, merwinite, gazeevite and bredigite (see Fig. 1). For the formation of poikilitic crystals (metacrysts), the presence of a fluid and a capillary system where dissolution and crystallization processes can take place is a pre-requisite (Beus 1962). Bredigite metacryst growth was accompanied with removing of ye'elimite inclusions, a mechanism that resulted in relatively pure material suitable for our investigations (Fig. 1d). Closely spaced combustion foci can be sources of high-temperature fluids. The activity of these foci is reflected by the presence of melted rocks nearby. In Fig. 1d, a bredigite intergrowth is shown, from which the fragment used for single-crystal X-ray diffraction investigation was retrieved. Bredigite is characterized by a relatively uniform composition, (Ca 7.006 Na 0.015 Ba 0.014 ) Σ7.035 Mg 0.938 (Si 4.000 P 0.014 ) Σ4.014 O 16 , close to the composition of the ideal end-member (Table 5). As a result of the structure refinement, a slightly higher Ba content of ca. 0.03 Ba atoms p.f.u. was obtained (Table 1). Most likely, intergrowth and twin boundaries of the bredigite grains are somewhat richer in Ba, but these areas are not routinely analyzed by electron microprobe. In the BSE image fine twinning of bredigite is clearly visible (Fig. 1d).

Crystal-structure analysis
Bredigite belongs to the group of orthosilicates. Three crystallographically different [SiO 4 ]-tetrahedra can be distinguished in the asymmetric unit. The spread of the Si-O bond distances and O-Si-O angles in these polyhedra is not very pronounced, resulting in low values for the quadratic elongations and bond angle variances (see Table 4). Both parameters can be conveniently used for numerical quantification of the distortions (Robinson et al. 1971). Linkage between the tetrahedra is provided by alkaline earth cations showing variable coordination numbers between 6 and 10. Two octahedrally coordinated sites in the asymmetric unit are occupied with Mg. The coordination polyhedron about Ca2 can be described as an octahedron (trigonal antiprism) as well, though its degree of distortion is larger than that of the [MgO 6 ]-units (see Table 4). Barium replacement for calcium is restricted to the site with the largest average cationanion bond distances also showing the largest number of next oxygen neighbors. Its coordination figure could be approximated as a strongly distorted octahedron with four additional Ca/Ba-O bonds. A projection of the whole crystal structure parallel to [010] is presented in Fig. 2.
As already pointed out by Moore and Araki (1976), pinwheel-like clusters consisting of a central [MgO 6 ]-octahedron and six attached [SiO 4 ]-tetrahedra are characteristic building blocks of bredigite. As can be seen in Fig. 3, the sequence of directedness, i.e. the sequence of up (u) and down (d) pointing tetrahedra within a cluster is ududud. Using the Fig. 1 Fine-grained larniteye'elimite hornfels from the Hatrurim Complex (Negev Desert, Israel): awith poikilitic gazeevite, ternesite and bredigite crystals. bgazeevite-free fragments with merwinite metacrysts; cfragments with gazeevite and bredigite poikilitic crystals; dintergrowth of bredigite crystals, which are purged of ye'elimite inclusions (black) during crystal growth. Brg = bredigite, Els = fluorellestadite, Gzv = gazeevite, Lrn = larnite, Mfr = magnesioferrite, Mw = merwinite, Trn = ternesite, Ye = ye'elimite nomenclature of mixed tetrahedral-octahedral networks, the clusters can be considered as so-called polyhedral microensembles or PME's. According to the classification given by Ilyushin and Blatov (2002) based on the calculation of the coordination sequences up to k = 3, the PME's in bredigite can be denoted as {6,6,18}.  Neighboring pinwheels form chains running parallel to [001], where a single central [MgO 6 ]-octahedron shares two tetrahedra on each side with the adjacent octahedra (see Fig. 2). The chains are located in about 7 Å wide layers parallel to (100) (see Fig. 4) Proximate chains in a layer are connected by Ca/Ba1, Ca2 and Ca4 whose coordination polyhedra exclusively involve oxygen atoms from the same layer. The layers in turn are linked by the remaining calcium positions (Ca3, Ca5 and Ca6). A detailed analysis of the topological features of bredigite and its structural interrelationship to other orthosilicates and sulfates has been already presented by Moore and Araki (1976) and will not be repeated here.
A characteristic of the bredigite structure is a pronounced underbonding of the positions Ca/Ba1 and Ca5, indicating that these cations are actually too small for their coordination environment. Bond valence sum (BVS) calculations using the parameter sets for Ca-O and Ba-O bonds published by Brown and Altermatt (1985) and Ca/Ba-O bonds up to 3.0 Å resulted in values of 1.53 (Ca/Ba1) and 1.62 (Ca5) valence units (v.u.). Using the bond distances from the refinement of Moore and Araki (1976), we obtained similar strong deviations from the ideal values of 2 v.u., though the crystal structure was described in a lower symmetry. At this point we would like to mention that in the previous study the Ca/Ba1 site (called X11) was suggested to be 12-coordinated, involving two additional distances of about 3.51 Å. The corresponding bond valences, however, are 0.02 v.u., i.e. from a stability point of view an inclusion of these two bonds can be hardly justified, though it helps for deciphering topological relationships with similar compounds (Moore 1973).

Discussion
In order to study the question concerning the correct space group of bredigite in more detail, the Pnn2 model obtained from the initial refinement of our data was tested using the program PSEUDO (Capillas et al. 2011), accessible via the Bilbao Crystallographic Server. This program checks if a structure S of space group H is pseudosymmetric for a supergroup G > H. As a first step of the analysis, a left coset decomposition of G with respect to H is performed: G = e × H + g 2 × H + …. + g n × H. The operations {e,g 2 ,….,g n } are the coset representatives. Subsequently, the input structure S is transformed into the image g i × S. Both structures are compared and in case that the shifts between corresponding atoms  in S and g i × S are below a certain threshold, pseudosymmetry is indicated. In the present case, H = Pnn2 and G = Pnnm. H is a translationengleiche subgroup of index two and, therefore, only one coset representative g has to be considered. From the set of four potential representatives, −x + ½, y + ½,-z + ½ (corresponding to a 2 1 -screw axis parallel to [010] in ¼, y, ¼), has been selected. The resulting maximum displacement between the two structures S and g × S is 0.133 Å, i.e. the maximum deviation from centrosymmetry is half this value (0.066 Å). This clearly demonstrates that the crystal structures of the bredigite samples that we studied can be allocated to space group Pnnm. As expected, the analysis revealed that the number of atoms in the asymmetric unit of the structure when described in Pnnm has been reduced, due to the higher symmetry. Notably, however, for some positions the multiplicities did not change. A detailed list of the mappings between the corresponding atoms in Pnnm and Pnn2 is presented in Appendix 1 (Table 6). In the latter case the labeling scheme given in Moore and Araki (1976) was used.
The main difference between the structure determination of Moore and Araki (1976) performed on a slag sample and our analysis of a natural specimen results from the choice of space group symmetry. Their decision that the space group was Pnn2 resulted from the observation that in the centrosymmetric model Bspecial positions on the mirror plane were misbehaving; there electron densities proceeded split across the mirror plane or merged into broad ellipsoidal contours^. Therefore, one should expect that in Pnnm (i) the thermal displacement ellipsoids of the atoms located on m [001] should exhibit a distinct prolate shape with their longest principal axes parallel to [001] and (ii) this effect should be less distinct (or even disappear) when a Pnn2 model is selected. A calculation of the ratio U 3 /((U 2 + U 1 )/2) involving the values along the principal axes determined from our refined data of the anisotropic displacement parameters in Pnnm showed, that only in three cases these quotients were larger than 3: Ca/ Ba1 (3.6), Ca2 (4.2) and O9 (3.2). For all other atoms located on the mirror planes in z = 0 and z = ½ the ratios were between 0.7 and 2.3. In case of the Ca/Ba1 site, for example, the distinct anisotropy may directly reflect the pronounced differences in size between the two substituting cation species. For the corresponding atoms of the first group the refinements in Pnn2 resulted in similar deviations from isotropic behavior (X11: 3.5, X12: 4.0; O22-2: 3.5). In summary, we do not think that a symmetry reduction is justifiedat least what concerns the natural sample that we studied.
In principle, significantly anisotropic thermal motions can be an indication for the presence of split positions. Therefore, we finally tested a model in Pnnm where the distinctly underbonded Ca/Ba1 atoms are distributed among two split positions above and below the mirror plane. The refinement converged at a slightly higher residual when compared with the anisotropic approach (R(|F|) = 0.0326). In addition, the resulting shift of about 0.185 Å away from m [001] leads to only a very small increase of the bond valence sum (1.55 v.u.) for this site. Consequently, it was not deemed necessary to introduce split atoms into the Pnnm model.
The crystal chemistry of bredigite has been already studied to some extent using synthetic samples obtained from solid state reactions Glasser 1981, 1982). Notably, the preparation of phase-pure polycrystalline material is a rather sluggish process and requires many weeks with intermediate re-homogenization. Divalent cations such as Zn 2+ , Co 2+ or Ni 2+ could not be replaced for Mg between 1300 and 1350°C. It is well known that larger amounts of Mn can be found in bredigites from metallurgical slags. Quite surprisingly, however, the incorporation of Mn 2+ by the abovementioned synthesis route was not possible either. Substitutions of larger alkaline earth cations (Sr,Ba) for Ca were more successful (Moseley and Glasser 1982) and cell parameters of potential bredigite-structured phases with general composition XYCa 12 Mg 2 (SiO 4 ) 8 have been published, albeit there are indications that the so-called BBa-Ba-bredigite^(X,Y: Ba) has a slightly different structure (Moseley and Glasser 1982). A thorough re-investigation of this solid solution series would be definitely worthwhile.
All findings of bredigite in nature are related to hightemperature metasomatic rocks (Tilley and Vincent 1948;Sabine et al. 1985;Sokol et al. 2010;Grapes 2011;Armbruster et al. 2011;Galuskina et al. 2015). As mentioned above, bredigite is stable up to about 1372°С. Taking the relations between the minerals in the studied rocks into consideration (Fig. 1), it can be assumed that bredigite formed according to the known chemical reaction: 2Ca 2 SiO 4 (larnite) + Ca 4 Mg(SiO 4 ) 2 (merwinite) = Ca 7 Mg(SiO 4 ) 4 (bredigite) (Grapes 2011). The formation of bredigite and gazeevite occurred simultaneously, i.e. both Ba and S were supplied to the mineral-forming system. Sulfur compounds can play a role as a catalyst and slightly reduce the crystallization temperature of bredigite, but this hypothesis needs confirmation.
Consequently, bredigite originally investigated as a Babearing phase from slags (Tilley and Vincent 1948) is still on the IMA List of Minerals (http://nrmima.nrm.se) with crystal chemical formula (Ca,Ba)Ca 13 Mg 2 (SiO 4 ) 8 . Bredigite should have an end-member formula Ca 14 Mg 2 (SiO 4 ) 8 or Ca 7 Mg(SiO 4 ) 4 , as all known natural bredigites contain negligible amounts of Ba as an impurity, as already emphasized by Sabine et al. in 1985. As shown in our recent structural study on bredigite, barium incorporation seems to be restricted to the cation site Ca/Ba1 in (0,0,0). As mentioned above, Ba-bearing synthetic bredigites with composition Ba 2 Ca 12 Mg 2 (SiO 4 ) 8 have been prepared by Moseley and Glasser (1982), indicating that in this case both positions Ca1 and Ca2 (or X11 and X12, according to the nomenclature of Moore and Araki (1976)) should be probably involved in the Ba-Ca exchange. Due to the formal criteria of the CNMNC IMA BВа-Са-bredigite^with formula (Ba,Ca)CaCa 12 Mg 2 (SiO 4 ) 8 could be approved as a new mineral species as Ba>Ca at the Ca1-site. These criteria are met by Ba-bearing bredigite from Jordan. Unfortunately, the sample could not be investigated in more detail because of the small size of the crystals and its mineralogical rarity. In general, pyrometamorphic rocks of the Hatrurim Complex and also of other larnite-bearing pyrometamorphic rocks, the protoliths of which were carbonate-silicate sedimentary rocks enriched in barium, are potential sources of the new Ba-analogue of bredigite.