Zircon-type crystal structure

The first studies concerning the crystal structure of zircon date back to the early 20^th century and were carried out independently by Vegard (Reference Vegard1916, Reference Vegard1926), Binks (Reference Binks1926), Hassel (Reference Hassel1926) and Wyckoff and Hendricks (Reference Wyckoff and Hendricks1928), in the framework of the pioneering works about the silicate’s structure determination, later gathered by Bragg (Reference Bragg1929) in his Atomic Arrangement in Silicates. After the first studies on zircon, its structural type has been described in several REE-bearing compounds, including xenotime-(Y) (Vegard, Reference Vegard1927) and the synthetic counterpart of chernovite-(Y), YAsO₄ (Strada and Schwendimann, Reference Strada and Schwendimann1934).

The zircon-type structure is characterised by a tetragonal I-centred lattice (space group I4₁/amd). The tetragonal zircon-type structure is constructed by infinite chains of polyhedra, developed along the [001] direction (Fig. 2a and 2d), as the result of the connection, along the polyhedral edges, between the eightfold coordinated A-site dodecahedron (AO₈ or REEO₈) and the TO₄ tetrahedra (Fig. 2c). The AO₈ polyhedron displays two independent A–O atomic distances (Fig. 2c), whereas the TO₄ is an undistorted tetrahedron defined by a single T–O bond distance. Each chain is in contact with four others on the (001) plane, through connecting edges along an AO₈ unit and the surrounding four (Fig. 2b). The atomic coordinates of the A- and T-sites are placed in special, fixed positions, both characterised by a 2m point symmetry. The oxygen atom is also at a special position (m), being its y and z coordinates the sole refinable parameters.

Figure 2.

Crystal structure of the zircon-type materials viewed (a) along the [010] and (b) [001] directions and showing (c) the chains running along the c directions and the bond distances configuration among the AO₈ polyhedron and (d) a side view of the overall crystal structure. Structure drawings have been made using the software Vesta3 (Momma and Izumi, Reference Momma and Izumi2011).

Monazite-type crystal structure

Parrish (Reference Parrish1939), within the first crystallographic studies on monazites, identified its correct space group as P2₁/n. The first description of the monazite-type structure has been reported by Mooney (Reference Mooney1948), who investigated the La, Ce, Pr and Nd phosphates as part of the Manhattan project and described the REE atomic site in eightfold coordination. The crystal structure of monazite with the REE site in ninefold coordination has been proposed by Ueda (Reference Ueda1953, Reference Ueda1967), but with non-reliable average P–O bond lengths of ∼1.6 Å. The structure was later described correctly by Beall et al. (Reference Beall, Boatner, Mullica and Milligan1981), Mullica et al. (Reference Mullica, Milligan, Grossie, Beall and Boatner1984) and Ni et al. (Reference Ni, Hughes and Mariano1995), whereas an exhaustive review of the monazite-structure type has been carried out by Boatner (Reference Boatner, Mottana, Paolo Sassi, Thompson and Guggenheim2002) and then by Clavier et al. (Reference Clavier, Podor and Dacheux2011). The monazite-type structure can be described as made by infinite chains running along the [001] direction (c-axis), comprising the alternation of the REE-coordination polyhedra and the T-hosting tetrahedra (Fig. 3).

Figure 3.

Crystal structure of monazite, viewed along (a) the [100] and (b) [010] directions; a chain-like unit is highlighted in blue; (c) coordination polyhedron of the REE-bearing A site, with 9 independent A–O bonds; and (d) general view of the monazite structure. Structure drawings have been made using the software Vesta3 (Momma and Izumi, Reference Momma and Izumi2011).

The REE-polyhedron coordination environment has nine corners (oxygen ligands, REEO₉, Fig. 3c). According to Mullica et al. (Reference Mullica, Milligan, Grossie, Beall and Boatner1984), the REEO₉ polyhedron can be described as an equatorial pentagon (sharing vertices with five TO₄ tetrahedra of five adjacent chains in correspondence of the O1_b, O2_b, O2_c, O3_b and O4_b oxygens), interpenetrated by a tetrahedron (made by the O1_a, O2_a, O3_a and O4_a oxygen atoms, see Fig. 3c), which is along the [001] direction in contact with two subsequent TO₄ tetrahedra, leading to the formation of the infinite chain units (Fig. 3a,b). The REE–O2_a bond length is significantly longer than the other REE–O bonds, contributing to a significant distortion of the REEO₉ polyhedron (Beall et al., Reference Beall, Boatner, Mullica and Milligan1981; Ni et al., Reference Ni, Hughes and Mariano1995; Clavier et al., Reference Clavier, Podor and Dacheux2011), which can be considered as 8+1 coordinated.

In situ high-pressure experiments

In situ high-pressure single-crystal synchrotron X-ray diffraction experiments have been conducted on chernovite-(Y), xenotime-(Y) and monazite-(Ce) at the P02.2 beamline (PETRA-III synchrotron at DESY, Hamburg, Germany) and ID15B beamline (European Synchrotron Radiation Facility, Grenoble, France) using different classes of P-transmitting fluids as shown in Table 2. For all the experiments, the crystals were loaded in membrane-driven diamond anvil cells (DAC), equipped with Boehler-Almax designed diamonds/seats. Metallic foils (steel or rhenium) were pre-indented to ca. 40–70 μm and then drilled by spark-erosion to obtain P-chambers. Ruby spheres were employed as pressure calibrants (pressure uncertainty ±0.05 GPa; Mao et al., Reference Mao, Xu and Bell1986; Chervin et al., Reference Chervin, Canny and Mancinelli2001). All data collections were based on a ω-rotation with 0.5° per step and 0.5 s (monazite and chernovite) or 1 s (xenotime) of exposure time per frame. At ID15B, X-ray diffraction (XRD) data were collected using an Eiger2 9M CdTe detector positioned at 179 mm from the sample with a monochromatic 30.2 keV (λ = 0.4099 Å) beam, whereas XRD patterns at P02.2 were collected on a Perkin Elmer XRD1621 detector at 373 mm from the sample and a monochromatic incident beam with E = 42.67 keV (λ = 0.2906 Å). Further details on the beamlines setups are presented in Merlini and Hanfland (Reference Merlini and Hanfland2013) and Poreba et al. (Reference Poreba, Comboni and Mezouar2022) for ID15B and Rothkirch et al. (Reference Rothkirch, Gatta, Meyer, Merkel, Merlini and Liermann2013), Liermann et al. (Reference Liermann2015) and Bykova et al. (Reference Bykova, Aprilis, Bykov, Glazyrin, Wendt, Wenz, H-P., Roeh, Ehnes, Dubrovinskaia and Dubrovinsky2019) for P02.2. Indexing of the X-ray diffraction peaks, unit-cell refinements and intensity data reductions were performed using the CrysAlisPro package (Rigaku Oxford Diffraction, 2020). Absorption effects, due to the DAC components, were corrected using the semi-empirical ABSPACK routine, implemented in CrysAlisPro.

Table 2.

Details pertaining to the in situ high-pressure and high-temperature experiments of this study

* SC-XRD: single-crystal X-ray diffraction; PXRD: powder X-ray diffraction

** He: helium (Klotz et al., Reference Klotz, J-C., Munsch and Le Marchand2009); Ne: neon (Klotz et al., Reference Klotz, J-C., Munsch and Le Marchand2009); m.e.w.: methanol:ethanol:water = 16:3:1 (Angel et al., Reference Angel, Bujak, Zhao, Gatta and Jacobsen2007)

*** See the text for further details

^# Institute of Mineralogy and Petrography, University of Innsbruck, Austria

Based on the experimental intensity single-crystal XRD data, the structure refinements were performed using the Jana2020 software (Petříček et al., Reference Petříček, Palatinus, Plàšil and Dušek2023), starting from the structural models reported by Pagliaro et al. (Reference Pagliaro, Lotti, Comboni, Battiston, Guastoni, Fumagalli, Rotiroti and Gatta2022a) for the mineral samples from the same locality. The site occupancy factors of the A (lanthanide-bearing) and tetrahedral sites were fixed according to the average chemical composition obtained from EPMA-WDS analysis (Table 1), disregarding the elements with a concentration lower than 0.03 atoms per formula unit and assuming a full occupancy for both the sites. In addition, for monazite-(Ce), the atomic displacement parameters (ADP) of the oxygen atoms were refined as isotropic. All the refinements converged with no significant correlations among the refined variables. Refined structural models are deposited as crystallographic information files (cifs) and are available as Supplementary material (see below).

For a chernovite-(Y) sample with a slightly larger amount of Ca and Th replacing Y and REE, an in situ high-pressure powder XRD experiment was conducted at the P02.2 beamline of PETRA III (Hamburg, Germany) with a wavelength of λ = 0.2906 Å (42.67 keV) and a Debye-Scherrer geometry. The sample was loaded into a DAC equipped with Boehler-Almax designed diamonds of 400 μm culet size along with the pressure-transmitting medium (see Table 2 for details) and ruby spheres for pressure determination (P – uncertainty ±0.05 GPa; Mao et al., Reference Mao, Xu and Bell1986; Chervin et al., Reference Chervin, Canny and Mancinelli2001). The data collection strategy at any pressure point consisted of a 30° rotation along ω, for an exposure time of 60 s. The X-ray diffraction signals captured by the Perkin Elmer XRD1621 flat panel detector have been finalised and integrated by means of the Dioptas software (Prescher and Prakapenka, Reference Prescher and Prakapenka2015), in order to remove the background noise due to DAC components and extract the 2θ-intensity pattern for any experimental dataset. The unit-cell parameters were determined by fitting the powder XRD data by means of the Rietveld full-profile method using the GSAS-II software (Toby and Von Dreele, Reference Toby and von Dreele2013): the unit-cell parameters, crystallite size, individual scale factor and profile parameters (pseudo-Voigt function) have been refined. Moreover, the background signal has been interpolated through a Chebychev polynomial function, with 4 to 15 terms.

In situ high-temperature experiments

In situ high-temperature single-crystal X-ray diffraction data were collected at the Institute of Mineralogy and Petrography of the University of Innsbruck, using a Stoe IPDS II diffractometer equipped with a Heatstream HT device, providing a continuous flow of hot N₂. The primary X-ray beam was generated by an X-ray tube (Mo-anode), operating at 50 kV and 40 mA. A plane graphite monochromator and a multiple pinhole collimator (0.5 mm) were used to guide the beam onto the sample. The image-plate detector was placed at a distance of 100 mm. The temperature calibration had been conducted previously using phase transitions of KNO₃, Ag₂SO₄, K₂SO₄ and K₂CrO₄ powders into glass capillaries. The samples, single crystals of monazite-(Ce), xenotime-(Y) and chernovite-Y (ca. 50–120 μm³) have been inserted into SiO₂ glass capillaries (0.1 mm in diameter). For all the samples, the data collection consisted in a 180° ω-rotation with a step size of 1° and variable exposure times. The temperature accuracy is ≤ 5°C. Further details about the experimental setting are reported in Krüger and Breil (Reference Krüger and Breil2009). Data collection and reduction has been performed using X-Area (Stoe and Cie, 2008). The indexed cell parameters were always compatible with either the unit cells of chernovite-(Y), xenotime-(Y) or monazite-(Ce).

Structure refinements were performed based on the single-crystal XRD data adopting the same procedure reported previously for the high-pressure data, and refined structural models are available as cifs (supplementary materials, see below). The thermal evolution of significant structural parameters (i.e. A–O bonds, A-coordination polyhedral and T-coordination polyhedral volumes) has been determined from the refined structure models, by means of the tools implemented in the VESTA3 software (Momma and Izumi, Reference Momma and Izumi2011).

In situ high-temperature X-ray powder diffraction experiments were performed on the chernovite sample relatively enriched in Ca and Th at the MCX beamline of the Elettra synchrotron (Basovizza, Trieste Italy), with a wavelength of λ = 0.7293 Å (17 keV) and a Debye-Scherrer setting. The sample, ground to powder in an agate mortar, was loaded in a SiO₂ glass capillary (0.3 mm as outer diameter). For any experimental point, the data collection strategy consisted of a 2θ-scan between 8° and 60°. A step size of 0.008° was applied and an equivalent counting time for 1 s/step used. The X-ray diffraction effects were collected by the high-resolution scintillator detector available at the beamline. During the data collection, the sample was spun at a rate of 1000 rotations per minute along the φ-axis. The sample was heated by an air blower, operating between 30 and 1000°C. Further details concerning the experimental setting are reported in Rebuffi et al. (Reference Rebuffi, Plaisier, Abdellatief, Lausi and Scardi2014) and Lausi et al. (Reference Lausi, Polentarutti, Onesti, Plaisier, Busetto, Bais, Barba, Cassetta, Campi, Lamba, Pifferi, Mande, Sarma, Sharma and Paolucci2015).

Compressional behaviour of the REETO₄ minerals

The evolution of the unit-cell parameters of the investigated samples with pressure is reported in Table S3 and shown in Figs 4 and 5. For monazite-(Ce), the evolution of unit-cell parameters vs. P shows no evidence of phase transformation in the entire P-range investigated. Both the zircon-type minerals, on the other hand, show the occurrence of a phase transition. Chernovite-(Y), at pressures higher than ∼10 GPa is no longer stable, undergoing a phase transition to several single-crystal fragments, for which, the position of the peaks in the XRD pattern is compatible with a tetragonal scheelite-type structure. Otherwise, at pressures exceeding ∼17 GPa, xenotime-(Y) undergoes a single-crystal to single-crystal phase transition towards a monazite-type structure. For any pressure ramp, the elastic behaviour of the mineral studied has been described by fitting an isothermal Birch-Murnaghan EoS (BM-EoS), truncated at the second or third order, to the P–V data (a comprehensive description of the BM-EoS formalism can be found in Angel, Reference Angel, Hazen and Downs2000) using the EoS-Fit7_GUI software (Gonzalez-Platas et al., Reference Gonzalez-Platas, Alvaro, Nestola and Angel2016). For monazite, similarly to what was observed for the isostructural gasparite-(Ce) by Pagliaro et al. (Reference Pagliaro, Lotti, Guastoni, Rotiroti, Battiston and Gatta2022b), a change in the compressional behaviour was detected at ∼18 GPa. The parameters refined by fitting the experimental data by BM-EoS are reported in Table 3, among them: the bulk modulus K_V = β_V ^–1 = –V*(∂P/∂V) and its pressure derivative K_V’ = (∂K_V/∂P)_T.

Figure 4.

High-pressure evolution of the unit-cell parameters (normalised to ambient conditions values) of (a) the investigated (Ca,Th)-poor and (b) (Ca,Th)-enriched chernovite-(Y) samples and (c) of their respective normalised unit-cell volumes with the refined Birch-Murnaghan equations of state. Empty symbols refer to data collected in decompression.

Figure 5.

High-pressure evolution of the unit-cell parameters (normalised to ambient-conditions values) of (a) xenotime-(Y) and (c) monazite-(Ce), (b) the normalised unit-cell volumes of the ambient-pressure and high-pressure polymorphs of xenotime-(Y) and (d) of the monoclinic β angle of monazite-(Ce).

Table 3.

Refined equations of state parameters from the fit to the experimental high-pressure and high-temperature unit-cell volume data (see text for further details)

* From Pagliaro et al. (Reference Pagliaro, Lotti, Guastoni, Rotiroti, Battiston and Gatta2022b).

α_V: volume thermal expansion coefficient at ambient conditions calculated on the basis of the Holland-Powell EoS.

a ₀ and a ₁ are two refinable variables in the Holland-Powell EoS (Holland and Powell, Reference Holland and Powell1998).

The evolution of significant structural parameters (i.e., A–O bonds, A-coordination polyhedral and T-coordination polyhedral volumes) with pressure has been determined, based on the refined structure models, by using the VESTA3 software (Momma and Izumi, Reference Momma and Izumi2011). The corresponding values are reported in Table S4.

The results of this study confirm that arsenates are always more compressible than the isostructural phosphates (Table 3), in agreement with the observed relationship that the larger the ionic radii of the A and T sites, the higher the bulk compressibility (e.g. Zhang et al., Reference Zhang, Zhou, Li and Li2008; Li et al., Reference Li, Zhang, Zhou and Cao2009; Lacomba-Perales et al., Reference Lacomba-Perales, Errandonea, Meng and Bettinelli2010; Errandonea et al., Reference Errandonea, Kumar, López-Solano, Rodríguez-Hernández, Muñoz, Rabie and Sáez Puche2011). The refined bulk moduli apparently suggest that monazite-structure type minerals are more compressible than those with a zircon-structure type (Table 3). However, internally consistent theoretical data (Zhang et al., Reference Zhang, Zhou, Li and Li2008; Li et al., Reference Li, Zhang, Zhou and Cao2009) show that there is a clear increase in compressibility along the lanthanoid series from Lu to La, with a discontinuity in the form of a stiffening when transforming from the zircon to the monazite structure type. Therefore, it can be concluded that, for the investigated minerals, the softening induced by the larger A site has a stronger impact than the stiffening induced by the monazite structure type.

The two minerals investigated, with the same zircon structure type, i.e. chernovite-(Y) and xenotime-(Y), undergo different phase transitions paths. Chernovite-(Y) experiences an irreversible transition, from a single-crystal to several crystal fragments, towards a scheelite-type polymorph between ca. 10.5 and 11 GPa. The same phase transition occurs, for synthetic YAsO₄ in a powder XRD experiment, in a broader pressure range between 8 and 12 GPa (Errandonea et al., Reference Errandonea, Kumar, López-Solano, Rodríguez-Hernández, Muñoz, Rabie and Sáez Puche2011). The apparent discrepancy between these two studies may be ascribed to: (1) a different kinetics of the phase transition between a single crystal and a polycrystalline material; and (2) slightly different chemical compositions, as a higher phosphorous content in the presently investigated mineral decreases the average radius of the T site; or a combination of both. In general, the same phase transition has already been observed to occur in other ATO₄ compounds, where the pressure of transition increases with the decrease of the A and T atoms ionic radii (Wang et al., Reference Wang, Loa, Syassen, Hanfland and Ferrand2004; Zhang et al., Reference Zhang, Wang, Lang, Zhang, Ewing and Boatner2009; Lacomba-Perales et al., Reference Lacomba-Perales, Errandonea, Meng and Bettinelli2010; Errandonea et al., Reference Errandonea, Kumar, López-Solano, Rodríguez-Hernández, Muñoz, Rabie and Sáez Puche2011). The relationship between the ionic radii of the A and T atoms and the type of structure stable at ambient and high-pressure conditions is well known and was first described by Fukunaga and Yamaoka (Reference Fukunaga and Yamaoka1979) and Bastide (Reference Bastide1987), and later discussed in other publications, e.g. in Lopez-Solano et al. (Reference López-Solano, Rodríguez-Hernández, Muñoz, Gomis, Santamaría-Perez, Errandonea, Manjón, Kumar, Stavrou and Raptis2010). As suggested by the Bastide diagram (Fig. 1) and already reported in the literature (Tatsi et al., Reference Tatsi, Stavrou, Boulmetis, Kontos, Raptis and Raptis2008; Zhang et al., Reference Zhang, Wang, Lang, Zhang, Ewing and Boatner2009; Lacomba-Perales et al., Reference Lacomba-Perales, Errandonea, Meng and Bettinelli2010; Musselman, Reference Musselman2017; Heuser et al., Reference Heuser, Palomares, Bauer, Rodriguez, Cooper, Lang, Scheinost, Schlenz, Winkler, Bosbach, Neumeier and Deissmann2018), xenotime-(Y) and isomorphous phosphates undergo a single-crystal to single-crystal phase transition towards a high-pressure polymorph, xenotime-(Y)-II, showing a monazite-type structure. The transition observed in our experiments occurs at a pressure (> 17 GPa) consistent with those reported for synthetic YPO₄ compounds (Zhang et al., Reference Zhang, Zhou, Li and Li2008; Lacomba-Perales et al., Reference Lacomba-Perales, Errandonea, Meng and Bettinelli2010). The reversibility of this phase transition is confirmed by this single-crystal study, even though with a significant hysteresis, as the tetragonal polymorph is recovered in decompression only between 6.3 and 1.3 GPa.

Despite a relative scattering between the published values of bulk compressibilities of zircon- and monazite-type phosphates and arsenates, determined on the basis of experimental and theoretical studies, the elastic parameters refined for the mineral species of this study (Table 3) are in agreement with those reported in the literature (Table S1). In the zircon-type minerals chernovite-(Y) and xenotime-(Y), the bulk compression is significantly anisotropic. Indeed, the structure is approximately two times more compressible within the (001) plane than along [001] (Figs 4 and 5, Table S5), which corresponds to the direction of the polyhedral chains evolution. Such a behaviour is strongly controlled by the high tetragonal symmetry, which limits the intra-chain deformation, as confirmed by the behaviour of the two independent A–O bond distances, where the A–O_a bonds, oriented parallel to [001] (Fig. 2), are the less compressible in both the minerals (Table S4). The bulk compression is therefore mainly accommodated by the AO₈ coordination polyhedron, as suggested by its bulk modulus, refined by modelling the polyhedral volume data obtained using Vesta3 with a II-BM equation of state by means of the EoS-Fit7-GUI software (Table 4). For both chernovite-(Y) and xenotime-(Y), bulk moduli values of the A-polyhedra are much lower than those obtained for the AsO₄ and PO₄ tetrahedra, which behave as quasi-rigid units (Table 4). The same conclusion can be drawn for monazite-(Ce) (Table 4) and gasparite-(Ce) (Pagliaro et al., Reference Pagliaro, Lotti, Guastoni, Rotiroti, Battiston and Gatta2022b), which, in addition, show that the AsO₄ tetrahedra are slightly more compressible than the PO₄ ones. As observed previously by Pagliaro et al. (Reference Pagliaro, Lotti, Comboni, Battiston, Guastoni, Fumagalli, Rotiroti and Gatta2022a), the structural features (and responses to external T and P stimuli) of these compounds are strongly controlled by the crystal chemistry, in particular of the T sites. Moreover, not only do PO₄ and AsO₄ tetrahedra have a different compressional behaviour, but the nature of the prevailing T site controls the size (i.e. the average ionic radius) at ambient conditions of the A polyhedron (Pagliaro et al., Reference Pagliaro, Lotti, Comboni, Battiston, Guastoni, Fumagalli, Rotiroti and Gatta2022a). This leads, given a similar chemical composition of the A site, to slightly larger compressibility for the more ‘expanded’ A-polyhedra of the arsenates among isostructural minerals. The control exerted by the crystal chemistry on the elastic response is also pointed out by the chernovite sample relatively enriched in Ca and Th studied here, which shows a slightly lower bulk modulus value (Table 3). The lack of structure refinements prevents an unambiguous derivation of the structural mechanisms responsible for this behaviour, but it can be suggested that the more ‘expanded’ A-polyhedron (due to the higher content of the larger Th and Ca ions, as reported in Table 1) is coherent with the previous observations that a larger average ionic radius of the A site generates a softer polyhedron.

Table 4.

Refined equation-of-state parameters pertaining to the A- and T-sites coordination polyhedra from the high-pressure (BM2 EoS) and high-temperature (Holland-Powell EoS, only A-site coordination polyhedron) experiments

* Due to the high uncertainties, these data should be considered as a qualitative estimation of the TO₄ units rigid behaviour

** From Pagliaro et al. (Reference Pagliaro, Lotti, Guastoni, Rotiroti, Battiston and Gatta2022b)

The description of the elastic anisotropy in monazite-(Ce) is less straightforward, as the monoclinic symmetry does not allow us to rely on the axial compressibilities alone, given the variation of the β angle with pressure. Therefore, the finite Eulerian unit-strain tensor of monazite-(Ce) between ambient-P and 18.39 GPa has been calculated using the Win_Strain software (Angel, Reference Angel2011) and with a geometric setting with X//a* and Y//b. The results show that the principal axes of maximum and minimum unit-strain do not correspond with any of the crystallographic axes, as described by the tensor values in the following matrix:

\begin{equation*}\left( {\begin{array}{*{20}{c}} {{\varepsilon _1}} \\ {{\varepsilon _2}} \\ {{\varepsilon _3}} \end{array}} \right)\left( {\begin{array}{*{20}{c}} {158.2\left( 2 \right)^\circ }&{90^\circ }&{56.2\left( 2 \right)^\circ } \\ {90^\circ }&{180^\circ }&{90^\circ } \\ {68.2\left( 2 \right)^\circ }&{90^\circ }&{33.8\left( 2 \right)^\circ } \end{array}} \right) \cdot \left( {\begin{array}{*{20}{c}} a \\ b \\ c \end{array}} \right)\end{equation*}

The analysis of the finite Eulerian unit-strain tensor allowed the determination of the mean compressibility values along the axes of the strain ellipsoid (with ε ₁>ε ₂>ε ₃): ε ₁ = 0.003030(11) GPa^–1, ε ₂ = 0.00200(2) GPa^–1, ε ₃ = 0.0014(12) GPa^–1. The directions of minimum and maximum compressibility are within the (010) plane and the anisotropic scheme is ε ₁:ε ₂:ε ₃=2.16:1.43:1. A comparison with the finite Eulerian unit-strain tensor reported for gasparite-(Ce) by Pagliaro et al. (Reference Pagliaro, Lotti, Guastoni, Rotiroti, Battiston and Gatta2022b) points out that these isostructural minerals share a similar elastic anisotropy. The shared compressional behaviour extends to the structural deformation mechanisms acting on the atomic scale: the nine independent A–O bond distances in monazite-(Ce) have different compressional evolutions, as shown in Fig. 6 (see also Table S4). A moderate scattering of the monazite-(Ce) unit-cell parameters can be observed between 10 and 18 GPa, which implied that we should fit the V–P data using a Birch-Murnaghan equation of state truncated to the II-order (Table 3). On the basis of the available experimental data and structure refinements, it is not possible to unambiguously detect a change in the compressional behaviour at P < 18 GPa. On the contrary, a change in the response to compression clearly occurs at pressures exceeding ∼18.4 GPa, as evidenced by the significant deviation in the high-pressure evolution of the monoclinic β angle (Fig. 5; Table S3), similar to gasparite-(Ce) (Pagliaro et al., Reference Pagliaro, Lotti, Guastoni, Rotiroti, Battiston and Gatta2022b). This behaviour has already been reported for synthetic monazite-type LaPO₄ and CePO₄ (Huang et al., Reference Huang, J-S., Kung and Lin2010), but not in another high-pressure investigation of CePO₄ (Errandonea et al., Reference Errandonea, Gomis, Rodríguez-Hernández, Muñoz, Ruiz-Fuertes, Gupta, Achary, Hirsch, Manjon, Peters, Roth, Tyagi and Bettinelli2018). The structure refinements performed in this study allows us to draw a relationship between the change in the elastic behaviour and the structural re-configuration. Figure 6 and Table S4 show that, at lower pressures, the O_3c atom is too far from the A site to be considered to effectively belong to its coordination sphere (Fig. 3). However, the A–O_3c interatomic distance shows a significant shortening under compression (Fig. 6; Table S4), so that, at a pressure consistent with the change in the compressional behaviour, the O_3c atom is close enough to the A site to enter its coordination sphere, as suggested by the individual bond valences calculated for selected structure refinements and reported in Table S6. As a consequence, the coordination number of the A site would increase from 9 (8+1) to 10 (8+2), even though with different contributions from the individual bonds, given the longer bond distances of the of A–O2_a and A–O3_c (Tables S4 and S6). As the same behaviour has already been independently described for gasparite-(Ce) (Pagliaro et al., Reference Pagliaro, Lotti, Guastoni, Rotiroti, Battiston and Gatta2022b) and is analogous to what is described to occur at 3.25 GPa in the monazite-type crocoite (PbCrO₄, Bandiello et al., Reference Bandiello, Errandonea, Martinez-Garcia, Santamaria-Perez and F.J2012; Errandonea and Kumar, Reference Errandonea and Kumar2014), we are inclined to believe that this is an intrinsic feature of the monazite structure type. Therefore, the known transition to a post-baryte-type polymorph at P higher than 26 GPa (Ruiz-Fuertes et al., Reference Ruiz-Fuertes, Hirsch, Friedrich, Winkler, Bayarjargal, Morgenroth, Peters, Roth and Milman2016) is accomplished through an intermediate structural configuration, still preserving the monazite symmetry and atomic arrangement, but characterised by an increase from 9 to 10 in the number of the oxygen atoms bonded to the lanthanide-bearing site. This intermediate structural configuration is accomplished, with no clear discontinuity, by a smooth approach of the O3_c atom to the A site (where O3_c corresponds to O3_a and O3_b in the coordination sphere of two further A atoms). It is worth noting, that the same configuration, with a 10-fold coordinated A-site, is also shared by the monazite-type high-pressure polymorph of CaSO₄ (Crichton et al., Reference Crichton, Parise, Antao and Grzechnik2005). The higher pressure at which the change of the elastic behaviour occurs in monazite-(Ce) (ca. 18.4 GPa, vs. ca. 15 GPa in gasparite-(Ce), Pagliaro et al., Reference Pagliaro, Lotti, Guastoni, Rotiroti, Battiston and Gatta2022b) is consistent with the higher P-stability expected for the isostructural phosphate with smaller average atomic radii.

Figure 6.

(a) Bulk moduli as a function of the A-site atomic radii for several REETO₄ (T = As,P,V) minerals, after Li et al. (Reference Li, Zhang, Zhou and Cao2009) and Zhang et al. (Reference Zhang, Zhou, Li and Li2008). (b) High-pressure evolution of the A–O interatomic bond distances in monazite-(Ce).

Despite being affected by larger experimental uncertainties, the same deformation mechanisms described for monazite-(Ce) and gasparite-(Ce) can be derived by the analysis of the refined structural models of the monazite-type high-pressure xenotime-(Y)-II polymorph (Table S4). In this case, the possible occurrence of a change in the compressional behaviour, according to the previous description, should be verified by investigations performed up to higher pressure values, though interatomic A–O3_c bond distances of ∼2.8–2.9 Å (Table S4) can suggest a 10-fold coordinated A site. A striking and anomalous feature shown by the experimental results of this study concerns the much larger refined compressibility if compared to what is reported in other studies for the same polymorph (K_V = 146(5) GPa in this study; K_V = 206 and 266 GPa in Zhang et al. (2009) and Lacomba-Perales et al. (Reference Lacomba-Perales, Errandonea, Meng and Bettinelli2010), respectively). The relatively high number of experimental data of this study leads us to the conclusion that the refined bulk modulus value we obtained is very reliable, implying a similar compressibility between the ambient and high-pressure polymorphs of the investigated xenotime-(Y). It is worth mentioning that a similar compressibility can also be found between the zircon- and monazite-type polymorphs of LaVO₄, with K_{V 0} = 93(2) GPa (Yuan et al., Reference Yuan, Wang, Wang, Zhou, Yang, Liu and Zou2015) and 95(5) GPa (Errandonea et al., Reference Errandonea, Pellicer-Porres, Martínez-García, Ruiz-Fuertes, Friedrich, Morgenroth, Popescu, Rodríguez-Hernández, Muñoz and Bettinelli2016), respectively. The thorough re-investigation of the zircon-to-monazite phase transition in xenotime and of the elastic behaviour of the xenotime-II polymorphs appear, therefore, mandatory for a comprehensive understanding.

Thermal behaviour of the REETO₄ minerals

The thermal unit-cell parameters evolution from the three in situ single-crystal high-T ramps on monazite-(Ce), chernovite-(Y) and xenotime-(Y) and from the powder ramp on chernovite-(Y), relatively enriched in Ca and Th, are reported in Table S7 and shown in Fig. 7. The thermo-elastic behaviour has been modelled according to the isobaric equation of state modified from Pawley et al. (Reference Pawley, Redfern and Holland1996) and Holland and Powell (Reference Holland and Powell1998) and implemented in the EoS-Fit7_GUI (Gonzalez-Platas et al., Reference Gonzalez-Platas, Alvaro, Nestola and Angel2016). The linear thermal expansion coefficients have also been refined using the TEV software (Langreiter and Kahlenberg, Reference Langreiter and Kahlenberg2015). The refined parameters and the calculated thermal expansion coefficients at ambient conditions α_V = 1/V*(∂V/∂T)_P are reported in Table 3.

Figure 7.

High-temperature evolution of the unit-cell parameters (normalised to ambient-conditions values) of (a) (Ca,Th)-poor and (b) (Ca,Th)-enriched chernovite-(Y), (c) xenotime-(Y) and (d) monazite-(Ce).

A comparison of the linear thermal expansion coefficients refined in this study for xenotime-(Y) and monazite-(Ce) and those already published for the same compounds reveal a good agreement with the literature data (see Table S2 and references therein). However, a significant discrepancy is observed between the values refined for chernovite-(Y) in this study and those reported previously by experimental investigations of YAsO₄ (Kahle, Reference Kahle, Schopper, Urban and Wüchner1970; Schopper, Reference Schopper, Urban and Ebel1972; Reddy et al., Reference Reddy, Satyanarayana Murthy and Kistaiah1988). As none of the cited references provide experimental unit-cell parameters, nor structure refinements, it is not possible to discuss such a discrepancy, but it is worth noting that the refined values for both the (Ca,Th)-poor and (Ca,Th)-enriched chernovites of this study are self-consistent and diverge from the literature data. With this in mind, future investigation of other natural or synthetic YAsO₄-type zircon compounds seems imperative.

A comparative analysis of the thermo-elastic behaviour of the investigated minerals shows that monazite-(Ce) is much more expansible than the two zircon-type compounds (Table 3). In the latter, the [001] direction, i.e. the least compressible at high-P, is found to be the most expansible at high-T. The thermo-elastic anisotropy of monazite-(Ce) cannot be directly described based on the unit-cell parameters behaviour, given its monoclinic symmetry. The thermal expansion of monazite-(Ce) has been modelled with the TEV software (Langreiter and Kahlenberg, Reference Langreiter and Kahlenberg2015) and at the temperature of 400°C (i.e. ΔT ∼ 380°C) its relationship with the unit-cell axes, with a geometric setting with X//a* and Y//b, is described by the following matrix:

\begin{equation*}\left( {\begin{array}{*{20}{c}} {{\alpha _1}} \\ {{\alpha _2}} \\ {{\alpha _3}} \end{array}} \right)\,\angle \,\left( {\begin{array}{*{20}{c}} {109.02^\circ }&{90^\circ }&{5.47^\circ } \\ {19.02^\circ }&{90^\circ }&{84.53^\circ } \\ {90^\circ }&{0^\circ }&{90^\circ } \end{array}} \right)\, \cdot \,\left( {\begin{array}{*{20}{c}} a \\ b \\ c \end{array}} \right)\,\end{equation*}

The mean thermal expansivity along the axes of the unit-strain ellipsoid, determined at 400°C, is: α₁ = 11.56·10^–6 K^–1, α₂ = 9.93·10^–6 K^–1 and α₃ = 7.39·10^–6 K^–1, leading to the anisotropic scheme α₁: α₂: α₃ = 1.56:1.34:1.

The structure refinements (thermal evolution of selected structural parameters is reported in Table S8) showed that for the zircon-type minerals xenotime-(Y) and chernovite-(Y), the coordination polyhedron hosting the lanthanides ions (A-polyhedron) has a paramount role in accommodating the bulk thermal expansion, its refined thermal expansivity being almost the double of the value referred for the unit-cell volume (Tables 3, 4), whereas the two independent A–O bond distances show a comparable behaviour, different to what is shown at high-P (Table S8). In monazite-(Ce) as well, the A-polyhedron plays a significant role in accommodating the thermal expansion, but of a lesser magnitude with respect to the tetragonal minerals (Tables 3, 4), given the larger degrees of freedom for structure deformation induced by the monoclinic symmetry. In all the cases, it is worth noting that the tetrahedra, being either PO₄ or AsO₄, appear to behave as rigid units in the temperature range investigated (Table 4).

As a general observation based on the experimental data of this study, xenotime-(Y) appears more expansible with temperature than chernovite-(Y). Even though the discrepancy between our data and the previously published thermal expansion behaviour of other YAsO₄ compounds (Kahle, Reference Kahle, Schopper, Urban and Wüchner1970; Schopper, Reference Schopper, Urban and Ebel1972; Reddy et al., Reference Reddy, Satyanarayana Murthy and Kistaiah1988) suggests caution in this regards. However, our observation is consistent with the results reported by Li et al. (Reference Li, Zhang, Zhou and Cao2009) for APO₄ and AAsO₄ (A = lanthanides) and based on theoretical calculations of lattice energies, where phosphates always show a larger expansibility than isostructural arsenates sharing the same A cation for both the zircon and monazite structural types.