Pressure-enforced Cr substitution in Cr1+xAl1−xO(SiO4), synthetic analogues of kyanite

Cr3+ can substitute for Al3+ in the crystal structure of kyanite, Al2O(SiO4). Cr3+-rich solid solutions along the binary Al2O(SiO4)–Cr2O(SiO4) joint were synthesized under distinct high-pressure conditions. Sample crystals of Cr1+xAl1−xO(SiO4) with x = 0.025(12) and 0.188(8) have been synthesized at pressures of 7 GPa and temperatures up to 1200 °C. Unit-cell dimensions and single-crystal X-ray diffraction of the new Cr3+-rich kyanite-type phases show a linear increase of lattice parameters a, b and c with increasing Cr3+ content. Cr3+ replaces Al3+ on the octahedrally coordinated M-sites with Cr3+ preferentially occupying large [MO6]-octahedra. Cr3+ substitution for Al3+ is highest on the M3 site in a sequence of Cr3+(M3) > Cr3+(M2) > Cr3+(M1) > Cr3+(M4) following the polyhedral volumes V(M3O6) > V(M2O6) > V(M1O6) > V(M4O6). The compressibility of Cr1.19Al0.81O(SiO4) has been determined via precise lattice parameters up to 6.00(4) GPa. The pressure–volume data fitted to the third-order Birch–Murnaghan equation of state yielded an isothermal bulk modulus (KT0) of 196(16) GPa and a pressure derivative K′T0 of 2(4) at V0 = 310.3(1) Å3. The value of KT0 is in accordance to the Anderson–Anderson relation but it is slightly smaller than the respective value for natural Cr3+-free kyanite.


Introduction
The Al 2 O(SiO 4 ) polymorphs are amongst the most important rock-forming minerals of the Earth's crust where they typically appear as minor constituents of metapelites and Al-rich metabasites. They serve as important indicators for regional and contact metamorphic P-T conditions from greenschist to granulite-facies P-T conditions. In appropriate bulk compositions, the high-P polymorph kyanite may be stable at upper mantle P-T conditions as evidenced by kyanite inclusions in diamond (e.g., Prinz et al. 1975;Smith et al. 2009) and the frequent presence of kyanite in mantle eclogites (e.g., Carswell et al. 1981;Smyth et al. 1989). High P-T experiments Konzett et al. 2008) indicate that the upper P-stability limit of kyanite defined by the reaction kyanite = corundum + stishovite is located at P ≥ 12-15 GPa in the T range 800-1500 °C, thus extending the stability of kyanite to transition zone depths of ∼ 360-450 km.
The only crystal chemical substituent in natural kyanite that has been found so far in significant concentrations is Cr 3+ with all known occurrences of kyanites with > 1 wt% Cr 2 O 3 was reported from high-P environments (e.g., Cooper 1980;Delor and Leyreloup 1986;Gil Ibarguchi et al. 1991). The highest naturally occuring Cr 2 O 3 contents known so far are in the range 15.6-17.0 wt% and were reported from chromite-bearing meta-gabbroic eclogites of the Eastern Alps and the Karpathians (Negulescu and Sabau 2012;Janák et al. 2015;Hauzenberger et al. 2016). P-T conditions estimated for the formation of these eclogitic kyanites are in the range 2.1-2.8 GPa and 700-900 °C. Cr 3+ -rich kyanites that are also known to be from upper mantle settings. Sobolev et al. (1968) and Pivin et al. (2011) reported the presence of kyanites with up to 12.7 and 11.8 wt% Cr 2 O 3 from Electronic supplementary material The online version of this article (https ://doi.org/10.1007/s0026 9-019-01024 -2) contains supplementary material, which is available to authorized users.
1 3 kimberlite-hosted grosspydite and clinopyroxenite xenoliths. Fe 3+ , too, is a common substituent in natural kyanite, however, with concentrations not exceeding approximately 1 wt% Fe 2 O 3 and usually on the order of a few hundred to a few thousand µg/g. Other elements such as Ti, V, Mg, Ca or Na show concentrations ≤ 150-200 µg/g (e.g., Pivin et al. 2011;Müller et al. 2005Müller et al. , 2016Pyka et al. 2014).
High P-T experiments in the system SiO 2 -Al 2 O 3 -Cr 2 O 3 have shown that at 3 GPa and 1300 °C, up to 38 wt% Cr 2 O 3 can be substituted into the synthetic analogue of kyanite which is equivalent to 25 mol% Cr 2 O(SiO 4 ) exchange component (Langer and Seifert 1971). Based on these experiments, the present study was conducted to further explore the limits of Cr 3+ substitution in kyanite-structure type Cr 1 + x Al 1−x O(SiO 4 ), assuming that P > 3 GPa will stabilize Cr 1 + x Al 1−x O(SiO 4 ) with > 25 mol% Cr 2 O(SiO 4 ) component. Moreover, the experimental study was performed to shed light on the site occupancies, the distribution of Cr 3+ within the kyanite crystal's structure, and the impact of Cr 3+ substitution on the elastic properties of kyanite. In this study, we investigated the crystal chemistry of two selected synthetic Cr 3+ -rich single-crystal samples, corresponding to compositions with 51.3 and 59.3 mol% Cr 2 O(SiO 4 ), using singlecrystal X-ray diffraction.

Synthesis and chemical composition
The starting materials (Table 1) were made from synthetic high-purity (≥ 99.99%) SiO 2 , Al 2 O 3 and Cr 2 O 3 powders that were mixed in appropriate stoichiometric proportions, homogenized in ethanol and dried at 150 °C for at least 48 h. The oxide mixtures were then filled into Pt tubes with 2.0/1.8 mm outer/inner diameter and a length of ≤ 3.5 mm and welded shut. The high-P-T synthesis experiments (Table 2) were conducted with a 500 t Walker-type multianvil device at the University of Innsbruck using 18/11 assemblies with pre-fabricated MgO-based ceramic octahedra and a graphite furnace combined with pyrophyllite gaskets. After the experiment, the sample capsules were removed from the assemblies, embedded longitudinally in epoxy resin and ground to expose the run products within the sample capsule ( Fig. 1) as suitable for both electron microprobe analysis (EMPA) and extraction of crystal fragments for single-crystal X-ray diffraction studies. The composition of phases (Table 3) was determined with a JEOL 8100 electron microprobe using 15 kV acceleration voltage and 20 nA beam current. The duration of measurement was 20 s on peaks and 10 s on backgrounds of the Si-Kα, Al-Kα and Cr-Kα lines. Pure synthetic SiO 2 and Al 2 O 3 , and natural chromite were used as standard materials. Raw counts were corrected with the PRZ correction procedure. MA53 resulted in crystals with a size of a few tens of micrometres and a bulk composition of Cr 1.05 Al 0.95 SiO 5 , very close to CrAlSiO 5 . In run MA69, crystals grew in a fine-grained matrix to form up to several 100 μm in size. The average composition of these crystals determined by electron microprobe was Cr 1.33 Al 0.66 SiO 5 .

Single-crystal diffraction
Several single crystal fragments of intense emerald-green colour ( Fig. 1) were selected under polarised light for clarity and optically sharp extinction under crossed polarizers, and finally checked for sharp XRD Bragg peak profiles thus giving small uncertainties for the refined lattice parameters. Subsequently a crystal from run MA69 with the size of 80 × 140 × 140 µm 3 was mounted for single X-ray diffraction intensity data collection of a full sphere on an Oxford Diffraction Gemini four-circle diffractometer, equipped with a Ruby CCD detector and using graphitemonochromatized Mo-Kα radiation (50 kV, 40 mA) at the University of Innsbruck. Data collection was performed at room temperature. Data reduction included intensity integration, background and Lorentz-polarisation correction performed with the CrysAlisPRO Version 1.171.36.20 software package (Rigaku 2015). The morphologies of the crystal fragments were approximated by faces and an analytical absorption correction based on these indexed faces was applied. Because of the small size of crystals from MA53 X-ray intensity data of a crystal from MA53, measuring approximately 10 × 10 × 20 µm 3 , were collected using a Stoe StadiVari diffractometer equipped with a Dectris Pilatus 300 K pixel detector (with a 450 µm silicon layer) and using a 100 W air-cooled Incoatec IµS microfocus source (50 kV, 1 mA) with a Mo target and high-brilliance 2D-focussing Quazar multilayer mirrors at the University of Vienna. Recorded images were integrated using X-Area 1.76 (STOE & Cie GmbH, Germany 2015) and integrated intensities were corrected for absorption. The crystal structures were solved by charge flipping using the program SUPER-FLIP (Palatinus and Chapuis 2007) and refined with the program JANA2006 (Petříček et al. 2014). Experimental details of data collection and crystal structure refinement are summarised in Table 4, atomic coordinates, interatomic distances and polyhedral volumes (Balić-Žunić and Vicković 1996) of the refined crystal structures are given in Tables 5  and 6. The crystal structure refinement of the data measured from a crystal of MA53 was performed with scattering factors for neutral atoms with anisotropic displacement parameters for all atoms. Due to an unfavourable ratio of measured reflections to refined parameter the refinement of the dataset measured from a crystal of run MA69 was performed with anisotropic displacement parameters for the cation positions and isotropic displacement parameters for the oxygen atoms. For the list of anisotropic displacement parameters refer to the deposited cif-file. In the initial stages of the crystal structure refinement Al and Cr atoms were placed on all M sites with an Al:Cr ratio of 1:1 for the crystal of MA53 and 1:2 for the crystal of run MA69. The substitution of Cr 3+ for Al 3+ was subsequently refined and found to be in excellent agreement for crystals of MA53 (Tables 3,  4): according to microprobe analysis the chemical composition is Cr 1.05 Al 0.95 O(SiO 4 ) and the chemical formula from single-crystal structure refinement is Cr 1.03 Al 0.98 O(SiO 4 ). However, for crystals of run MA69 a refined composition of Cr 1.19 Al 0.81 O(SiO 4 ) was reproducibly obtained from the single-crystal data. This formula exhibits 6 mol% Cr 2 O(SiO 4 ) less than the composition Cr 1.33 Al 0.67 O(SiO 4 ) expected from synthesis and from the electron-microprobe analysis. Considering the given texture of inclusion-containing macrocrystals in a fine-grained matrix (cf. Fig. 1b), it cannot be ruled out that sub-microscopic Cr 2 O 3 inclusions are responsible for apparently higher Cr 3+ -contents in the EMPA analysis. Microprobe data might thus reflect compositions adding up Cr 1+x Al 1−x O(SiO 4 ) and Cr 2 O 3 -inclusions whereas the site-occupations derived from measured XRD intensities exclusively correspond to the kyanite lattice. Moreover, the crystal composition derived from site-occupation factors is confirmed by the fact that lattice-related data points follow     (4) b (Å) 7.9861 (4) 8.0019 (7) c (Å) 5.6704 (6) 5.6887 (9) α (°) 90.319 (5) 90.468 (9) β (°) 101.056 (5) 101.067 (8) γ (°) 106.009 (3) 106.012 (7) V (Å 3 ) 307.70 (4) (Fig. 2a, b). Plotting the lattice parameters (Fig. 2a)

Equation-of-state measurement
Equation-of-state measurements of a single crystal of Cr 1.19 Al 0.81 O(SiO 4 ) were performed through static compression at room temperature in an ETH-type diamond anvil cell (Miletich et al. 1999), using anvils with culets of 0.6 mm diameter and a gasket prepared from 0.25 mm thick stainless steel was pre-indented to a thickness of approximately 100 µm. The sample chamber of 250 µm diameter was drilled with an electronic spark eroder. A ruby chip and a quartz single crystal were loaded together with the specimen crystal and a 16:3:1 mixture of methanol-ethanol-water was used as hydrostatic pressure-transmitting medium. Ruby was used as internal pressure standard (Jacobsen et al. 2008) for a quick estimation of the pressure upon pressure change. After each change in pressure, the sample was left to settle for 36-48 h and subsequently high-precision measurements of the unit-cell parameters of Cr 1.19 Al 0.8 O(SiO 4 ) and of quartz were performed at pressures up to 6.00(4) GPa on a four-circle Siemens P4 diffractometer, equipped with an Eulerian cradle and a point detector with slits parallel and perpendicular to the diffraction plane. Non-monochromatized Mo Kα radiation from a standard sealed-tube source, operated at 40 kV and 35 mA power setting, was used for the measurement of the Bragg intensities of the peak positions obtained for Mo Kα1/2 radiation. The setting angles of diffracted Bragg peaks were recorded with a point detector (crystal-to-detector distance 170 mm), the slits of which were set to 2 and 9 mm, respectively, for scan directions within and perpendicular to the diffraction plane. Each reflection was centred in eight positions according to King and Finger (1979), so as to eliminate systematic aberrations for diffractometer settings and sample positioning. During the fitting of reflection profiles, the α1-α2 peak splitting was treated by setting constraints on both the position and intensity (α2/α1 = 0.53) of the α2peak components as implemented in the SINGLE software (Angel and Finger 2011). The pressure of the respective data point was determined from the lattice parameters of quartz (Scheidl et al. 2016). Equation-of-state parameters were fitted using the program EoSFit7-GUI (Gonzalez-Platas et al. 2016), while the strain analyses were performed using Win_Strain Vers. 4.11 (Angel 2011). The crystal of Cr 1.03 Al 0.98 O(SiO 4 ) used for the singlecrystal intensity data collection was covered with insoluble epoxy glue and could therefore not be used for EoS measurements. Unfortunately, it was not possible to extract another single crystal of sufficient size and quality to collect volume-pressure data from MA53. 1 3

Results and discussion
The crystallographically unconventional cell setting with lattice parameter c < a < b has been retained since the first crystal structure description of Taylor and Jackson (1928) and eases the comparison to the crystal structures of the two Al 2 O(SiO 4 ) 5 polymorphs, sillimanite and andalusite. The crystal structure of kyanite (Nárayo-Szabe et al. 1929;Burnham 1963;Winter and Ghose 1979) is a distorted cubic closed packing of oxygen atoms in an arrangement of the densely packed layers parallel to (110), in which Si atoms occupy 10% of the tetrahedral sites and Al atoms 40% of the octahedra in the adjacent mixed tetrahedral-octahedral layer on alternating sides of the chain in a step-like fashion (Fig. 3a). Viewed along the c-axis, a broad layer-like package of octahedra parallel to (100) are connected by [SiO 4 ] tetrahedra (Fig. 3b). Gatta et al. (2006Gatta et al. ( , 2009 have described this octahedral arrangement as building block units with a zig-zag evolution along the b-axis.  Langer and Seifert (1971) have raised the question if one of the octahedra may be preferentially occupied by Cr 3+ . Their powder diffraction data on Cr 1+x Al 1−x O(SiO 4 ) with up to 25% of the Al 3+ replaced by Cr 3+ did not allow a reliable refinement of the distribution of Al 3+ /Cr 3+ on the M-sites. According to their findings on the intensity ratio of the (300) and (200) reflections, they concluded that the M1and M2-site might be highly enriched with Cr 3+ over Al 3+ . However, in contrast to this expected result, the highest Cr 3+ content in the refined crystal structures of Cr 1+x Al 1−x O(SiO 4 ) is found for M3 followed by M2 and M1, whereas the lowest Cr 3+ concentration can be found on the M4 site ( Table 6). The finding can be satisfyingly explained by considering the polyhedral volumes (Tables 5, 6; Fig. 4), which follow the same sequence V(M3O 6 ) > V(M2O 6 ) > V(M1O 6 ) > V(M 4O 6 ). This leads to the suggestion, that the larger octahedra can substitute more of the relatively larger Cr 3+ atoms than the smaller octahedra. Interestingly, a comparison with the high-pressure data measured on natural Cr 3+ -free kyanite (Yang et al. 1997a) shows an almost linear increase of the octahedral volumes as a function of V/V 0 , which confirms the above assumption (Fig. 4).
Unit-cell parameters were collected at room temperature to pressures of up to 6.00(4) GPa, ( Table 7). The EoS parameters V 0 , K T0 , K′ T0 , a, b, c and their axial compressibilities M′ T0 were computed by fitting the P-V, P-a, P-b, and P-c data by a third-order Birch-Murnaghan EoS formulation. On a quick glance, the compressibility of the lattice parameters a, b, and c (Fig. 5a) look isotropic. However, detailed examination reveals a slight anisotropy: the axial compressibilities given in Table 8 show that Cr 1+x Al 1−x O(SiO 4 ) is least compressible along the c-axis. To facilitate comparison with existing data of Cr 3+ -free kyanite (Yang et al. 1997a, b;Liu et al. 2009), we performed the analyses of lattice strain on compression between 1 bar and 4.6 and 5.9 GPa, respectively. The eigenvalues of the strain ellipsoid (e 1 = 185(8) × 10 − 5 , e 2 = 168(8) × 10 − 5 , e 3 = 148(10) × 10 − 5 ) are very similar to those in Cr 3+ -free kyanite (e 1 = 188(3) × 10 − 5 , e 2 = 169(7) × 10 − 5 , e 3 = 140(3) × 10 − 5 ) thus confirming approximately isotropic elasticity as expected for a close packing of the oxygens, with the direction of lowest compressibility approaching the c-axis. This is a general feature of the Al 2 O(SiO 4 ) polymorphs with edge-sharing octahedral chains along the c-axis (Ralph et al. 1984;Yang et al. 1997b;Comodi et al. 1997;Friedrich et al. 2004;Burt et al. 2006). However, in the close-packed crystal structure of kyanite, the octahedra share several edges in a very complex manner. This results in a more uniformly distributed compression, as discussed by Yang et al. (1997a). Figure 5b-d show the effect of pressure on the unit-cell parameters a, b, and c in Cr 1.19 Al 0.81 O(SiO 4 ) in comparison to the respective data measured in natural Cr 3+ -free kyanite. It is obvious that due to being isotypic Cr 3+ -free kyanite and Cr 1+x Al 1−x O(SiO 4 ) show the same pressure response. The pressure response of the unit-cell angles α, β, and γ is shown in Fig. 5e-g: α increases, whereas β and γ decrease, if only slightly, with increasing pressure. This trend has also been observed for natural Cr 3+ -free kyanite with high-precision single-crystal data from Yang et al. (1997a) being exceptionally similar, whereas observations from Friedrich et al. (2004) and Liu et al. (2009) show a more distributed scatter.
A third-order Birch-Murnagham equation of state (EoS) was fit into fourteen pressure-volume data to yield an isothermal bulk modulus K 0T of 196 ± 16 GPa, a pressure derivative K′ 0T of 2 ± 4 GPa and a refined V 0 of 310.3(1). For a truncation to second order, i.e., when K′ 0T is fixed to 4.0, K 0T refines to a value of 188 ± 4 GPa. Values for K 0 of natural kyanite have been reported in the range of 156(10)-202(15) (see Table 2 in Liu et al. 2009 and Table 2 in Friedrich et al. 2004). Considering only the latest and most accurate EoS data measured on single crystals (Yang et al. 1997a;Friedrich et al. 2004) and powdered samples (Liu et al. 2009) computed for a Birch-Murnaghman of second order, the reported K 0T values of 193(1), 190(3) and 201(2) GPa, respectively, are slightly larger than K 0T of 188(4) of Cr 1.19 Al 0.81 O(SiO 4 ). This is in accordance with observations made by Anderson and Anderson (1970) for isostructural materials, i.e., that the product of volume and bulk modulus follows a constant value. Comparing the V 0 K 0T -products for the above-mentioned natural kyanite samples, i.e., 56,611 ± 210, 55,803 ± 650 and 58,692 ± 712 Å 3 GPa, respectively, with the one of Cr 1.19 Al 0.81 O(SiO 4 ) of 58,327 ± 877 Å 3 GPa, it is determined that the Anderson-Anderson statement is fulfilled within the obtained standard deviations.

Summary
It has been demonstrated that substitution of Cr 3+ in the kyanite crystal structure type is possible up to at least 59.3 mol% Cr 2 O(SiO 4 ) component. Cr 3+ substitutes for Al 3+ and gives rise to a linear increase of the unit-cell parameters a, b, c and V. In contrast to previous assumptions (Langer and Seifert 1971), Cr 3+ preferentially occupies the larger [M3O 6 ] and [M2O 6 ] octahedra, whereas Cr 3+ replacement on the smaller octahedra around the M1-and M4-site occurs to a smaller degree. The pressure response of Cr 1.19 Al 0.81 O(SiO 4 ) in regards to the behaviour of the lattice parameters is comparable to the one of Cr 3+ -free kyanite with a, b, c, β, and γ decreasing with increasing pressure, whereas α increases. As expected from the Anderson-Anderson relationship (Anderson and Anderson 1970), Cr 1.19 Al 0.81 O(SiO 4 ) has a lower compressibility in comparison to Cr 3+ -free kyanite. Fig. 5 a Relative unit-cell parameters of Cr 1.19 Al 0.81 O(SiO 4 ) as a function of pressure and comparison of the pressure dependence of the unit-cell parameters b-h a, b, c, α, β, γ and V with compressional data for natural Cr 3+ -free kyanite (Liu et al. 2009;Friedrich et al. 2004;Yang et al. 1997a) ◂