Post-Spinel Phases in the Earth’s Mantle

Abstract—

The post-spinel phases include compounds with stoichiometry ${{A}^{{2 + }}}B_{2}^{{3 + }}{{{\text{O}}}_{4}}$$\left( {A_{2}^{{2 + }}{{B}^{{4 + }}}{{{\text{O}}}_{4}}} \right)$ and structures of the calcium ferrite CaFe₂O₄, calcium titanate CaTi₂O₄, and marokite CaMn₂O₄ types. The structures with a centered Cmcm (Bbmm) and primitive Pnma (Pmcn) and Pbcm (Pmab) cells are distinguished in this family of topologically related compounds with a “marokite” channel formed by six octahedra. The sites A and B are occupied by various cations, in particular, Cr, Al, Mg, Fe, Ca, Ti, Fe, Na, and Si, which implies the formation of solid solutions of a wide compositional range. In nature, such high-pressure phases were found in meteorites, as inclusions in diamond crystals, and in rocks from some metamorphic complexes. This review provides a characterization of natural mineralogical finds, the results of an experimental study of post-spinel phases of various compositions and their solid solutions, as well as crystal chemical simulation and assessment of likely compositions and the areas of stability of compounds with a “marokite” channel. The discrepancy between the results of individual studies indicates the necessity to clarify the stability parameters and probable isostructural transitions, and, ultimately, to improve the classification of post-spinel phases.

INTRODUCTION

Spinel is a widespread mineral with a stoichiometry of ${{A}^{{2 + }}}B_{2}^{{3 + }}{{{\text{O}}}_{4}}$$\left( {A_{2}^{{2 + }}{{B}^{{4 + }}}{{{\text{O}}}_{4}}} \right)$, the study of which is of great importance in the earth sciences, due to the abundance of various geological formations in rocks. In addition, the spinel-type structure is of petrological and geochemical interest due to its ability to accommodate both tri- and divalent cations, such as Fe²⁺ and Fe³⁺. However, the stability of phases with the spinel-type structure is limited, since a phase transition and change in structure occur already under transition zone conditions.

Most spinels decompose to oxides at high pressure (Reid and Ringwood, 1969) or undergo structural phase transitions. Various researchers consider compounds with the structures of calcium ferrite CaFe₂O₄ (Decker and Kasper, 1957), calcium titanate CaTi₂O₄ (Rogge et al., 1998), and marokite CaMn₂O₄ (Giesber et al., 2001) as post-spinel phases. The spinel-type structure transforms into a CF-type structure at pressures above 9–12 GPa, followed by a transition to the CT-type structure at pressures above 20 GPa (Akaogi et al., 1999; Chen et al., 2008). In turn, CaMn₂O₄ transforms into the structural type of marokite at a pressure of ~30 GPa, and CaTi₂O₄ at 39 GPa.

It should be noted that not all spinel mineral phases have high pressure polymorphs. The r_B/r_A ratio, where r_B and r_A are the ionic radii of B and A, respectively, is one of the key criteria for the appearance of the CF-type structure. CF oxides with r_B/r_A <0.53 were not detected (Müller-Buschbaum, 2003). Structural compounds of the CT type are less studied due to the higher pressures of their synthesis.

The structure of post-spinel phases is formed by edge and angular octahedra with hollow channels parallel to the b axis (CF-type structure) and a axis (CT-type structure), respectively. These two structures contain eight-fold AO₈ and octahedra BO₆. There are two types of octahedral BO₆ sites in the CF-type structure and one type of octahedral BO₆ sites in the CT-type structure (Fig. 1). The structures with a centered Cmcm (Bbmm) and primitive Pnma (Pmcn), Pbcm (Pmab) cells are distinguished within this family of topologically related structures with a “marokite” channel formed by six octahedra.

Fig. 1.

Three structural types of post-spinel phases: (a) CaMn₂O₄ (CM); (b) CaFe₂O₄ (CF); (c) CaTi₂O₄ (CT). Mn, Fe, and Ti atoms are in the octahedron; Ca atoms are in the eight-fold coordination.

Unfortunately, at present, post-spinel phases, their properties, and the ability to form the series of solid solutions have not been sufficiently studied. It is necessary to expand the area of the experimental study of these phases and to refine our understanding of them. In this paper, we analyze and systematize the data on the structural patterns and phase transitions of post-spinel phases.

NATURAL POST-SPINEL PHASES

Natural post-spinel phases have been found as inclusions in diamonds, which supports their mantle origin.

A multiphase mineral inclusion in a diamond from the Juina area (Brazil) was described by Kaminsky et al. (2015). It contained iron carbide aggregate (Fe–N–Si–C), Fe-rich periclase (solid solution with magnesioferrite), graphite, as well as Mg–Cr–Fe oxide with the formula (Mg_0.90Mn_0.18)_Σ1.08(Cr_1.37V_0.11Al_0.05)_Σ1.92O₄ (orthorhombic) and Ca–Cr oxide with the formula (Ca_1.07Mg_0.02Mn_0.02)_Σ1.11(Cr_1.71V_0.06Ti_0.03Al_0.03)_Σ1.89O₄ (orthorhombic). In addition to the major elements, there are minor impurities, such as Mg, Al (~0.80 at %), Ti, V, and Fe (~1.93 at %) in Ca–Cr oxide; Al (~1.58 at %) and V, in Mg–Cr–Fe oxide.

Polymineral assemblages were found as inclusions in superdeep diamonds from the Juina-5 kimberlite (Brazil), which were formed during the crystallization of melt with the MORB composition under the lower mantle conditions (Walter et al., 2011). Several high-pressure phases have been described: a phase with a CF-type structure, new hexagonal alumina phase (NAL), Mg-perovskite enriched in Al, Ti, and Fe, and Ti-rich Ca-perovskite.

The composition of the polymineral inclusion in Ju5-20 diamond is similar to the CF phase, while the inclusions in Ju5-67 and Ju5-89 diamonds correspond to the NAL phase formed under the lower-mantle conditions. The synthetic phases are distinguished by significant concentrations of potassium in the NAL phase, while the natural CF phases do not contain potassium (Walter et al., 2011). The natural phase with the calcium ferrite-type structure (CF) contains up to 7.15 wt % Al₂O₃, 0.04 wt % CaO, and 2.11 wt % FeO. NAL phases contain 7.56 and 6.41 wt % Al₂O₃, 0.06 and 0.15 wt % CaO, 1.80 and 2.23 wt % FeO, respectively.

In addition to the findings of natural post-spinel phases as inclusions in diamonds, minerals with calcium ferrite- and calcium titanate-type structures were detected in meteorites and impact craters in a number of studies (Table 1).

Table 1. Natural post-spinel phases

Thus, maohokite (MgFe₂O₄), a post-spinel polymorph of magnesioferrite with the CF-type (Pnma) structure, was discovered in impacted gneiss of the Xuyan Crater in China (Chen et al., 2019). This phase coexists with diamond, reidite, TiO₂-II, as well as quartz and feldspar diaplect glass and was formed via the subsolidus decomposition of ankerite Ca(Fe²⁺, Mg)(CO₃)₂ at a pressure of 25–45 GPa and a temperature of 800–900°C. Xieite (FeCr₂O₄), a natural orthorhombic chromite polymorph with a calcium ferrite-type structure, was found in shock veins of the Suizhou meteorite (Chen et al., 2008). It was formed via the solid-phase transformation of chromite at high pressures and temperatures, in association with other high-pressure minerals, such as ringwoodite, majorite, etc. According to the phase diagram (Agee et al., 1995), the transformation of chromite into xieite occurs at 18–23 GPa and 1800–1950°C. Chenmingite (FeCr₂O₄) is a high-pressure mineral with a CF-type (Pnma) structure, which occurs in the form of lamellae in chromite grains in association with xieite and Fe, Cr-saturated ulvöspinel, near veins of melt impactites formed by the impact of the Tissint Martian meteorite. The areas of xieite are always in contact with the melt zones, and chenmingite lamellae are found in chromite only, a few micrometers from these zones. Such position suggests that chenmingite was formed at the same pressure as xieite, but at lower temperatures, which is consistent with the experimental studies (Ma et al., 2019). Tschaunerite (Fe²⁺)(Fe²⁺Ti⁴⁺)O₄ is a high pressure ulvöspinel polymorph. This mineral with the CT-type structure was found in the central part of altered ulvöspinel–ilmenite aggregates in the Tissint Martian shergottite (Ma and Prakapenka, 2018).

As a rule, the natural post-spinel phases are formed at high pressures. Nevertheless, some of them were formed at low pressures (Table 1). Among them are ellinaite (CaCr₂O₄), which was detected in gehlenite–rankinite paralavas in the southern part of Hatrurim Basin (Negev Desert, Israel) (Sharygin, 2019), marokite (CaMn₂O₄) found in the dumps of Vein 2 of the Tachgagalt deposit (Gaudefroy et al., 1963), harmunite (CaFe₂O₄, natural calcium ferrite CaFe₂O₄ found in larnite-bearing (high-temperature) metamorphic rocks) (Galuskina et al., 2014), wernerkrauseite (CaMn⁴⁺O₆, one more “low-pressure” mineral (Pnma) found in altered xenoliths of alkaline basalt from the Bellerberg Volcano, Eifel, Germany) (Galuskin et al., 2016).

Finds of post-spinel phases among inclusions in deep-seated diamonds, in particular their detection in intergrowth with other mantle minerals, illustrate their likely formation in diamond-forming chambers and their presence as accessory phases in the Earth’s mantle. A very wide compositional range of them indicates that they may accumulate aluminum, alkalis, and a number of trace elements at high temperatures and pressures corresponding to the transition zone and lower mantle of the Earth (Irifune and Ringwood, 1993; Kesson et al., 1994; Perrillat et al., 2006). In turn, the high concentrations of these elements may be geochemical indicators of the crustal matter in the Earth’s mantle.

EXPERIMENTAL STUDY OF POST-SPINEL PHASES

The conditions of the formation, boundaries of phase transitions (Table 2), and changes in the physical properties of post-spinel phases in various chemical systems were studied experimentally in a wide range of pressures and temperatures. A summary P–T diagram of the stability and phase transitions of post-spinel phases is shown in Fig. 2.

Table 2.   P–T parameters of the formation and phase transitions of post-spinel phases

Fig. 2.

P–T diagram of the stability and phase transitions of post-spinel phases. Solid and dashed lines are the boundaries of phase transitions; shaded areas show the stability fields of the phases; points indicate P–T parameters of the formation of individual phases.

CaFe₂O₄. Decker and Kasper (1957) reported the synthesis of the compound CaFe₂O₄ and refined its structure, which turned out to be isomorphous to the CaV₂O₄-type structure. The study of this phase by single crystal X-ray diffraction showed that, like many other iron oxides, a sharp decrease in its volume occurs at a pressure of ~50 GPa (Merlini et al., 2010). It was shown that a new high-pressure CaFe₂O₄ phase is formed at a pressure of 51 GPa (Yamanaka et al., 2008). The space group does not change upon the transition, but a shift occurs in every third cation layer. This results in change in the cell parameters: a = 10.0032(11) Å, b = 8.5046(7) Å, c = 2.8366(13) Å at a pressure of 50.2 GPa and a = 9.5834(9) Å, b = 8.2689(13) Å, c = 2.7895(18) Å at a pressure of 52.9 GPa. This was accompanied by a change in the volume of the phase from 241.3(4) to 221.1(6) ų. The density increased by 8.3% in the new phase. It was shown that this transition was associated with a change of the high-spin state of Fe³⁺ to the low-spin state (Greenberg et al., 2013).

MgFe₂O₄. It was shown experimentally that MgFe₂O₄ with a spinel-type structure begins to transform into a phase with a CaMn₂O₄-type (CM) structure at a pressure of ~ 17.7 GPa. The diffraction lines of magnesioferrite with a spinel-type structure remain clear up to 27.2 GPa, which indicates mixing of the low- and high-pressure phases between 17.7 and 27.2 GPa. With a subsequent increase in pressure up to 46 GPa, the high-pressure MgFe₂O₄ phase with the CM-type structure is stable. It was found that the behavior of MgFe₂O₄ depends on temperature: at T < 1600°C, MgFe₂O₄ decomposes to form Fe₂O₃ and MgO, while at T > 1600°C, the MgFe₂O₄ phase transforms directly into the high-pressure hp-MgFe₂O₄ phase. Such dual behavior is most likely explained by uneven conditions during diamond-cell experiments. It is believed that magnesioferrite is transformed from the hp-MgFe₂O₄ phase upon upwelling. However, the phase relations of MgFe₂O₄ exclude the probability of a direct transition from hp-MgFe₂O₄ to magnesioferrite. In addition, the stability of hp-MgFe₂O₄ is not confirmed under the conditions of P > 18 GPa and T = 1000–1500°C or higher. Although the phase is called “magnesioferrite,” compositional analysis shows that it is a solid solution (Mg_0.5Fe_0.5Fe₂O₄). At higher pressures, the system contains phases with different stoichiometry: Mg₂Fe₂O₅ and Mg₃Fe₄O₉ (Uenver-Thiele et al., 2017 and references therein). It was shown by Ishii et al. (2020) that the system contains the Mg₂Fe₂O₅ (Cmcm) + Fe₂O₃ assemblage at pressures of 12–19 GPa, the Mg₃Fe₄O₉ (C2/m) + Fe₂O₃ assemblage at pressures of 19–22 GPa, while with a further increase in pressure, the MgFe₂O₄ (Pnma) phase becomes stable. However, despite the same space group Pnma, the structure of the latter phase does not belong to the CF-type structure. The structure of the MgFe₂O₄ (Pnma) phase has a distorted Z-shaped framework composed of edge-connected (Mg, Fe)O₆ octahedra. Octahedra form the channels parallel to the b-axis, which contain two octahedral and one tetrahedral sites. Mg and Fe cations, which do not occupy the framework octahedra, are randomly distributed in the octahedral and tetrahedral sites of the channels, which results in a partial occupation of these three sites. It is assumed that the phase with such structure may be formed in impact craters and meteorites. The authors emphasize the need for careful identification of high-pressure phases by refinement of the crystal structure both in experimental studies and for natural samples, because of the crystallographic similarity of post-spinel structures.

Fe₃O₄ (Fe²⁺${\mathbf{Fe}}_{{\mathbf{2}}}^{{{\mathbf{3 + }}}}$O₄). Magnetite transforms into a high-pressure phase at ~25 GPa. Bassett et al. (1967) suggested that the high-pressure Fe₃O₄ phase should have monoclinic symmetry. In other studies, the high-pressure phase transition was registered in the range of 25–32.4 GPa, and its temperature dependence was studied. The magnetic properties and electrical resistance changed upon the phase transition as well. It was suggested that the high-pressure Fe₃O₄ phase crystallized in the CM structure type. Later, the structural type of CaTi₂O₄ (Bbmm) was suggested for this phase. According to the thermodynamic calculations, Fe₃O₄ should decompose into FeO and Fe₂O₃ at 13.3 GPa, and then transform into a high-pressure phase at 35 GPa (Lazor et al., 2004 and references therein).

ZnFe₂O₄. The ZnFe₂O₄ phase, which has a mineral name “franklinite,” was studied up to 37 GPa (Levy et al., 2000). A phase with a spinel-type structure is stable up to a pressure of ~25 GPa. The new Zn–Fe phase was detected at 24.4 GPa for the first time. The proportion of a phase with a spinel-type structure in a two-phase aggregate decreases with pressure (with a minimum amount at 36.6 GPa). Based on the results of comparison with other post-spinel structures, the authors suggested that franklinite underwent a transformation from a spinel-like structure to a structure of the CaTi₂O₄ or CaMn₂O₄ types.

CoFe₂O₄. The CoFe₂O₄ phase was studied up to a pressure of 93.6 GPa (Wang et al., 2003a). The compound has a spinel-type structure up to 32.5 GPa; with further increase in pressure, it transforms to a phase with a CF-type structure, which is stable up to ~94 GPa. The orthorhombic high-pressure phase is 14.7% denser than the tetragonal phase under the normal conditions.

MnFe₂O₄. The behavior of the jacobsite MnFe₂O₄ was studied up to a pressure of 39.55 GPa at room temperature (Ye et al., 2015). Spinel with the composition MnFe₂O₄ undergoes a phase transition at ~18 GPa with the formation of a denser polymorph with the CM-type structure. The high-pressure phase is stable up to 39.55 GPa being preserved after decompression.

MgCr₂O₄. Based on the data of X-ray diffraction and Raman spectroscopy at high pressure (Yong et al., 2012), it was shown that the symmetry of MgCr₂O₄ spinel changes from cubic to tetragonal at ~20 GPa and room temperature. According to other data (Ishii et al., 2015 and references therein), spinel of the MgCr₂O₄ composition transforms into an assemblage of a phase with a modified ludwigite-type structure Mg₂Cr₂O₅ and eskolaite Cr₂O₃ at pressures of 14–19 GPa and temperatures of 1000–1600°C. With a further increase in pressure and temperature, a transition to a phase with the CT-type structure is recorded (Fig. 2) (Sirotkina et al., 2018), which was first synthesized at 23 GPa and 1600°C and structurally studied by Bindi et al. (2014).

Based on Raman spectroscopy data, the coexistence of two phases was detected in a wide pressure range (14.2–30.1 GPa) (Wang et al., 2002a). The stability of the high-pressure phase was traced up to 76.4 GPa.

FeCr₂O₄. Chromite FeCr₂O₄ transforms into Fe₂Cr₂O₅ + Cr₂O₃ at ~14 GPa and 1200°C, and at higher pressures, into the CF or CT phase (Ishii et al., 2014). The Fe₂Cr₂O₅ phase, like Mg₂Al₂O₅, has the same structure, called the modified ludwigite-type structure (mLd) (Pbam), in which the edge and angular (Fe, Cr)O₆ (or (Mg, Al)O₆) octahedra are parallel to the c axes, while Fe²⁺ (or Mg²⁺) ions occupy the voids in the channels formed by octahedra (Enomoto et al., 2009; Ishii et al., 2014). A sample of natural chromite, similar in composition to the sample from the Suizhou meteorite, was studied at high pressure (Chen et al., 2008). It was shown that FeCr₂O₄ with a spinel-type structure transforms into the CF phase at 12.5 GPa, and then, into the CT phase at a pressure of >20 GPa.

β-CaCr₂O₄. There are two CaCr₂O₄ polymorphs (α and β), which are the high- and low-temperature ones, respectively. Unlike most of chromites with a spinel-type structure, α- and β-CaCr₂O₄ crystallize with the orthorhombic symmetry, Pmmn and Pnam space groups, respectively. The β-CaCr₂O₄ phase was studied up to 16.2 GPa. No phase transitions were detected in this range, and the CF-type structure was retained. In addition, it was noted that the structure is more compressible along the a axis than along the b and c axes, which shows an anisotropic elasticity for β‑CaCr₂O₄ (Zhai et al., 2016 and references therein).

CdCr₂O₄. The β-CdCr₂O₄ polymorph crystallizes with a calcium ferrite-type structure (Hill et al., 1956), with r_Cr/r_Cd ≈ 0.56. It was shown experimentally that CdCr₂O₄ spinel was completely transformed into the β-CdCr₂O₄ phase with the CF-type structure at 10 GPa and 1100°C (Arévalo-López et al., 2010).

ZnCr₂O₄. Wang et al. (2002b) showed that ZnCr₂O₄ with the spinel-type structure transforms into the post-spinel phase with the CF- or CT-type structure in the range of 17.5–35 GPa.

NiCr₂O₄. It was demonstrated experimentally that NiCr₂O₄ spinel decomposes into oxides Cr₂O₃ and NiO at 13.1 GPa, the presence of which was traced in situ to a pressure of 57.1 GPa (Wang et al., 2003b).

CaAl₂O₄. The areas of stability of two phases (low-temperature CA-III and high-temperature CA-IV) coexist in the CaAl₂O₄ system up to a pressure of 9–10 GPa (Ito et al., 1980; Akaogi et al., 1999). With increasing pressure, both phases transform into the phase with the CF-type structure. This phase was previously obtained by Iskrina et al. (2020) at 15 GPa and 1600°C in association with Ca₂Al₆O₁₁ compound. Comparison of the CF phase described by Akaogi et al. (1999) and the phase obtained by Iskrina et al. (2020), shows that all structural parameters in the latter work are somewhat lower. This results an underestimated value of the density of the CF-phase (ρ = 3.975 g/cm³) from in the study of Akaogi et al. (1999) in comparison with our value (ρ = 4.08 g/cm³) (Iskrina et al., 2020). Such differences are likely due to the different techniques structure refinement in the considered studies.

MgAl₂O₄. MgAl₂O₄ with the CF-type structure was synthesized at 25 GPa and 1600°C (Yutani et al., 1997). A direct transition from MgAl₂O₄ spinel to the CF phase was previously registered in experiments at pressures of >26 GPa. These parameters are most likely close to the lower limit of stability of MgAl₂O₄ with the CF-type structure, since in a number of studies, it was shown that with increasing pressure, MgAl₂O₄ spinel decomposes to form Mg₂Al₂O₅ with the modified ludwigite-type structure (mLd) and Al₂O₃ at ~20 GPa and 2000°C. (Enomoto et al., 2009; Kojitani et al., 2007 and references therein).

It was shown by Ono et al. (2006) that the MgAl₂O₄ phase with a spinel structure at a pressure of 30 GPa transforms into a phase with a CF structure. The ε‑MgAl₂O₄ phase, presumably with the orthorhombic symmetry, previously observed above 25 GPa, was obtained in the range of 40–45 GPa. It was found that ε-MgAl₂O₄ coexists with periclase and corundum. The diffraction peaks from ε-type MgAl₂O₄ cannot be identified within the orthorhombic structure. At the moment, the structure of the ε-MgAl₂O₄ phase and the exact area of its stability have not been determined (Ono et al., 2006 and references therein).

FeAl₂O₄. Hercynite FeAl₂O₄ is unstable at pressures of >12 GPa and 1000°C and decomposes to form corundum and wüstite. In later works, the upper limit of hercynite stability was lowered to 8.0 GPa at 1450°C. At 18 and 24 GPa and 1400 and 1600°C, respectively, the decomposition of hercynite occurred as well, but a new high-pressure phase was not detected. Thus, according to the experimental data, the high-pressure FeAl₂O₄ polymorph with the post-spinel-type structure is unlikely (Schollenbruch et al., 2010 and references therein).

CaMn₂O₄. The CaMn₂O₄ compound was synthesized at a pressure of 2.3 GPa and temperature of 600°C, and its structure was refined (Giesber et al., 2001). This phase was studied up to a pressure of 73.7 GPa. At a pressure of ~35 GPa, the transformation of the structure into the CT-type structure begins. In the range of 35–45 GPa, the coexistence of two phases was detected: initial CaMn₂O₄ and the high-pressure phase with the CT-type structure. With further increase in pressure up to 73.7 GPa, the polymorph with the CT-type structure remains stable. Yamanaka et al. (2008) studied the CaMn₂O₄ phase up to 75 GPa and specified that the transition to the CT structure occurred at 30 GPa with the decrease in the unit cell volume by 3.8%. In addition, a likely electron-spin transition of Mn³⁺ in the octahedral site was investigated at this pressure, since the high-spin state may change to a low-spin one. The symmetry of the octahedral MnO₆ site increases from “1” in the Pmab space group to “..m” in Bbmm, and then the octahedron becomes more highly symmetric with almost equivalent bonds (Yamanaka et al., 2008 and references therein).

MgMn₂O₄. The MgMn₂O₄ compound was studied up to 30 GPa (Malavasi et al., 2005). It was found that this phase had a tetragonal symmetry I4₁/adm up to 15.6 GPa. There was a phase transition at a higher pressure. The high-pressure compound crystallized with the orthorhombic symmetry and had the CM-type (Pmab) structure. This transition is very similar to the structural change that occurs with the Mn₃O₄ phase (Paris et al., 1992).

ZnMn₂O₄. The ZnMn₂O₄ compound was up to 52 GPa (Asbrink et al., 2006). The phase changes to tetragonal symmetry at 23 GPa and is retained up to 52 GPa. A compound with a post-spinel-type structure is not formed in this range, which differs from the behavior of phases with the different compositions. Spinel ZnMn₂O₄ with an active Mn³⁺ Jahn–Teller ion exhibits the first-order structural phase transition at high pressure. The c/a ratio in the tetragonal structure decreases sharply from 1.62 to 1.10 at a transition pressure of ~23 GPa. A high- to low-spin transition was proposed for ZnMn₂O₄ during the study by X-ray powder diffraction at 23 GPa and by calculation of the band structure; however, experimental results up to 100 GPa do not indicate any change in the electronic state or spin configuration up to 50 GPa (Choi et al., 2006 and references therein).

LiMn₂O₄. Experiments on the behavior of LiMn₂O₄ at a pressure of 6 GPa and temperatures up to 1500°C showed a transition to a high-pressure polymorph with the CF-type structure at temperatures above 1100°C (Yamaura et al., 2006).

MgMn₂O₄. Malavasi et al. (2005) studied the Mg_1‒xMn_2+xO₄ system at 0 ≤ x ≤ 1. It is noteworthy that MgMn₂O₄ spinel has a tendency to inversion, thus, some of magnesium ions may occur in the octahedral site even at room temperature. When most of the magnesium occupies the tetrahedral site, the tetragonal structure of spinel with the space group I4₁/adm transforms into the CM-type orthorhombic structure Pmab at a pressure of 15.6 GPa. With increasing amount of magnesium in the octahedra, the boundary of the phase transition from the tetragonal to the orthorhombic symmetry shifts to 14.4 GPa. In addition, it was found that due to an increase in the inversion, the compressibility along the c axis slightly decreases, while the compressibility along the a axis increases.

Mn₃O₄ (Mn²⁺${\mathbf{Mn}}_{{\mathbf{2}}}^{{{\mathbf{3}} + }}$O₄). Paris et al. (1992) studied the Mn₃O₄ phase up to a pressure of 38.7 GPa. It was shown that a transition from gaussmanite Mn₃O₄ to the phase with the CM-type structure occurred at 10–12 GPa, which was accompanied by the decrease in volume by 8.7%. However, the unit cell parameters of Mn₃O₄ (CM) are lower than those of isostructural marokite by 1.6–4.5%. Most likely, this is due to the smaller radius of Mn²⁺ compared to Ca²⁺. At 1 atm (10^–4 GPa), the Mn₃O₄ phase with the marokite-type structure is not stable, in contrast to the CaMn₂O₄ phase. Most likely, this is due to the fact that Mn²⁺ cation is too small for the site A^(VIII), and the structure is destabilized at low pressures.

ZnGa₂O₄. ZnGa₂O₄ spinel was studied up to 56 GPa at room temperature (Errandonea et al., 2009). At 31.2 GPa, there is a transition from the cubic spinel-type structure to the tetragonal structure. At 55 GPa, a second transition to the orthorhombic marokite-type (CM) structure occurs. It was shown that ZnGa₂O₄ is one of the least compressible spinels studied to date.

CaTi₂O₄. The study of the CaTi₂O₄ phase by powder X-ray diffraction up to a pressure of 80 GPa showed that a transition to the high-pressure polymorph occurred at 39.6 GPa (Yamanaka et al., 2008). The space group of the high-pressure phase remains the same, while the cell parameters change: a = 9.338(6) Å, b = 9.718(4) Å, c = 3.026(1) Å at a pressure of 29.8 GPa and a = 9.257(5) Å, b = 9.642(3) Å, c = 8.967(2) Å at a pressure of 39.8 GPa. The volume of the phase changes from 274.7(3) to 800.4(2) ų. The mechanism of the transition is very similar to the above-described transformation registered in CaFe₂O₄, but, nevertheless, it is simply a martensitic transformation with a rearrangement of atoms in the layer.

Zn₂TiO₄. The study of the Zn₂TiO₄ phase at pressures up to 80 GPa showed that Zn₂TiO₄ spinel initially transforms into the phase of the orthorhombic (CaTi₂O₄) symmetry at 23.7 GPa, and this phase transition is completed by 32.4 GPa. It was determined that the high-pressure phase of Zn₂TiO₄ has a higher value of the bulk elastic modulus of 205(6) GPa than that of the cubic spinel phase of 162(11) GPa. In this case, the Zn₂TiO₄ phase with an orthorhombic symmetry is 2.1% denser than the spinel phase. However, the difference in the density of the Zn₂TiO₄ (CT) and Zn₂TiO₄ (Sp) phases is ~10.0% (Zhang et al., 2017 and references therein).

Fe₂TiO₄. Based on the data of X-ray diffraction, Mössbauer, and Raman spectroscopy, it was shown that ulvöspinel Fe₂TiO₄ undergoes a series of phase transitions from cubic (Fd3m) to tetragonal (I4₁/amd) at ~9 GPa, and then to orthorhombic structure (Cmcm) at 12–16 GPa. In this case, the high-pressure Fe₂TiO₄ phase (Cmcm) is retained upon decompression to normal conditions. In all Fe₂TiO₄ polymorphs, iron cations are characterized by the high-spin state, which is supported by the data of Mössbauer spectroscopy (Wu et al., 2012). A new Fe₂TiO₄ high-pressure polymorph was discovered at 48 GPa, but its structure was not refined. With decreasing pressure, this phase transforms back to the Fe₂TiO₄ polymorph with an orthorhombic symmetry (Cmcm). The orthorhombic Fe₂Ti-O₄ phase is isostructural to CaTi₂O₄ (Kyono et al., 2011 and references therein; Wu et al., 2012).

Fe₂SiO₄. The study of the synthetic phase γ-Fe₂SiO₄ at pressures up to 66 GPa and at room temperature showed a structural phase transition at ~30 GPa. The high-pressure phase Fe₂SiO₄ belongs to the space group $R\bar {3}m$ (Z = 2) (Greenberg et al., 2011). Yamanaka et al. (2015) studied the transition from the cubic spinel structure to the body-centered orthorhombic phase I-Fe₂SiO₄ (Imma) at ~34 GPa. Laser heating of I-Fe₂SiO₄ up to 1227°C leads to its decomposition into rhombohedral FeO and stishovite SiO₂ (Yamanaka et al., 2015).

CuRh₂O₄. Along with the tetragonal phase CuRh₂O₄, Ohgushi et al. (2006) synthesized its orthorhombic analog at a pressure of 4 GPa and a temperature of 900°C. The density of the lower-symmetry phase was higher by 2%.

Co₂TiO₄. The Co₂TiO₄ phase with the spinel-type structure is stable up to 21 GPa; with further increase in pressure, it transforms into a high-pressure polymorph with the CM-type structure, and above 35 GPa, a phase with the CT-type structure becomes stable (Zhang et al., 2019).

SOLID SOLUTIONS OF POST-SPINEL PHASES

MgAl₂O₄–Mg₂SiO₄ system. The MgAl₂O₄–Mg₂SiO₄ solid solution was studied up to a pressure of ~27 GPa and T = 1600°C (Fig. 3a) (Kojitani et al., 2007). This system contains two assemblages in the pressure range up to 23 GPa: Cor + Per with a higher content of the Mg₂SiO₄ component, and Cor + Per + Grt with a higher content of MgAl₂O₄ in the starting composition. As the pressure increases, the CF phase appears in the samples, and the CF-free field Cor + Per gradually wedges out with increasing pressure to ~26.5 GPa. The coexistence of garnet and CF at 23 GPa suggests that the phase transition between the assemblages Grt + Per + Cor and Cor + Per + CF or Grt + Per + CF occurs just at this pressure. When the MgAl₂O₄ content exceeds ~23 mol %, CF becomes the only phase remaining in the system at a pressure of >26.5 GPa.

Fig. 3.

Phase diagrams for the systems of solid solutions: (a) MgAl₂O₄–Mg₂SiO₄ (Kojitani et al., 2007); (b) MgAl₂O₄–CaAl₂O₄ (Akaogi et al., 1999); (c) MgAl₂O₄–NaAlSiO₄ (Ono et al., 2009).

MgAl₂O₄–СaAl₂O₄ system. The MgAl₂O₄–CaAl₂O₄ solid solution was studied up to a pressure of ~26 GPa and T = 1200°C (Fig. 3b) (Akaogi et al., 1999). At a pressure of >8 GPa, the CA-IV phase transforms into a phase with the CF-type structure, while the MgAl₂O₄ phase continues to retain the spinel-type structure (Ito et al., 1980; Akaogi et al., 1999). The MgAl₂O₄ compound is transformed into a phase with the CF-type structure at 26–27 GPa and is associated with the hexagonal aluminum phase (Hex.P). The CaAl₂O₄ and MgAl₂O₄ phases have the different lattice parameters; therefore, despite the absence of immiscibility regions in the system, there is no complete series of solid solutions. However, the solubility of the Mg component in the CF phase increases with pressure. Consequently, magnesium can still enter the structure of calcium aluminates, but under the high-pressure conditions only.

NaAlSiO₄–MgAl₂O₄ system. The NaAlSiO₄–MgAl₂O₄ solid solution was studied up to a pressure of ~30 GPa and T = 1600°C (Fig. 3c) (Ono et al., 2009). At pressures of >17 GPa, the NaAlSi₂O₆ (Jd) phase decomposes with the formation of the NaAlSiO₄ phase with the calcium ferrite-type (CF) structure. This phase is stable up to the maximum pressure studied in this work (30 GPa) with the condition that an admixture of the Mg component does not exceed 30 mol %. With a higher content of magnesium in the structure of NaAlSiO₄, the CF phase is accompanied by the hexagonal aluminum phase Hex.P. It should be noted that Na/(Mg + Na) in the CF phase is higher than that in the coexisting Hex.P phase. This is because most of the magnesium, as was noted above, is redistributed into perovskite-like phases, while sodium begins to predominate in the residue, which, accordingly, stimulates the formation of Na-rich phase with the calcium ferrite-type structure in association with Mg- and Na-bearing hp-phase for the starting MORB composition. Guignot and Andrault (2004) confirmed an assumption that the NaAlSiO₄ component predominates in the phase with the calcium ferrite-type structure, while the MgAl₂O₄ component predominates in the hexagonal phase. Based on the fact that sodium prefers to enter the CF phase, it can be assumed that the formation of solid solutions and mixing (probably partial) of the NaAlSiO₄ and CaAl₂O₄ components are likely at high pressures.

Mg₂SiO₄–MgCr₂O₄ system. Bindi et al. (2018) synthesized chromium-bearing ringwoodite (4.23 wt % Cr₂O₃) with an inverse structure at a pressure of 20 GPa and a temperature of 1600°C in the Mg₂SiO₄–MgCr₂O₄ system. Inverse ringwoodite is characterized by the incorporation of silicon into the octahedral site and the disordered population of octahedra and tetrahedra with magnesium. Most likely, the inverse structure is stabilized by an impurity of chromium distributed over the octahedral and tetrahedral sites. Earlier, ringwoodite with an inverse spinel-type structure was detected in chromitite from ophiolite of the Luobusa region (Tibet, China) (Griffin et al., 2016). Mg(Mg,Cr,Si)₂O₄ with a distorted orthorhombic CT-type structure synthesized by Sirotkina et al. (2018) in a wide pressure range (13–18 GPa) in the model system Mg₂SiO₄–MgCr₂O₄.

In addition, a solid solution Mg[(Cr,Mg)(Si,Mg)]O₄ with a distorted CT-type structure and space group Cmc2₁, was obtained in the considered system at a pressure of 16 GPa and 1600°C (Bindi et al., 2015).

RESULTS OF COMPUTER SIMULATION OF POST-SPINEL PHASES

Using quantum chemical calculations, it was shown that a phase transition of CaAl₂O₄ with a change from the P2₁/m to the Pnma space group occurs at 7–8 GPa (Eremin et al., 2016), which is supported by the experimental data (Lazić et al., 2006). The results of semiempirical simulation by the method of interatomic potentials provided the higher values of the transition boundary (18–19 GPa). In addition, it was shown that the Pnam “marokite” phase is energetically more favorable under the conditions of the Earth’s mantle. Judging by the enthalpy value, the Bbmm phase with a base-centered cell is less preferable under the studied conditions. The same applies to the hypothetical monoclinic phase based on the “α-PbO₂” motif, which most likely appears at >130 GPa, but is less favorable than the structures with a “marokite” channel (Marchenko, 2019).

The equations of state of normal spinels MgCr₂O₄, MnCr₂O₄, and ZnCr₂O₄, as well as the reactions of their decomposition into oxides Cr₂O₃ (eskolaite) and MO (NaCl), were studied using the Hartree–Fock self-consistent field method (Catti et al., 1999). The predicted decomposition pressures for Mg-, Mn-, and Zn-bearing chromium spinels are 19, 23, and 34 GPa, respectively. The spinel-type structure becomes more stable with respect to component oxides as the atomic numbers of metals increase. This effect is especially noticeable for ZnCr₂O₄. This behavior is likely due to the higher relative stability of the tetrahedral (spinel) and octahedral (NaCl) coordination for Zn²⁺ than for other M²⁺ cations, which is consistent with the existence of the tetrahedral phase of wurtzite for ZnO only (Catti et al., 1999).

The MgAl₂O₄ phase was studied by Catti (2001). According to the results of ab initio modeling (LDA and B3LYP functionals), it was determined that with increasing pressure, the cubic spinel-type structure (Fd3m) transforms into the MgO + Al₂O₃ assemblage at pressures from 6.4–17.3 to 38.5–57.2 GPa (in each of the ranges, the first number was obtained by the LDA method and the second, by the B3LYP method, respectively), and then it is transformed into a phase with the CT-type structure. According to the experimental data, the range noted above is from 15 to >40 GPa (Irifune et al., 1991; Funamori et al., 1998). It should be noted that Catti (2001) did not consider the MgAl₂O₄ phase with the CF-type structure.

SIGNIFICANCE OF POST-SPINEL PHASES IN THE EARTH’S MANTLE

High-pressure minerals with the spinel-type structure containing transition elements are important constituents of the lower parts of the Earth’s mantle. Their abundance is a prerequisite for a comprehensive study of phase stability and structure under high pressures and temperatures, especially high-pressure polymorphs. Starting from the transition zone of the Earth, the spinel-type structure ceases to be stable and transforms into a set of simple oxides or into the structures with a “marokite” channel (CM, CF, CT). This is the main reason for both mineralogical and geophysical interest to high-pressure phases with post-spinel types of structures.

The CaFe₂O₄-type structure is considered as a high-pressure form of many spinels under the conditions corresponding to the transition zone and the upper boundary of the Earth’s lower mantle (Kesson, 1994; Kirby et al., 1996; Funamori et al., 1998). An experimental study of natural basalt samples (Perrillat et al., 2006 and references therein) showed the formation of two Al-rich phases with the CaFe₂O₄-type structure in association with bridgmanite, Ca-perovskite, and stishovite (Akaogi et al., 1999). The synthesis of similar post-spinel Al phases was carried out before (Gasparik et al., 2000; Litasov and Ohtani, 2005). The incorporation of Si and Na into Al-rich phases increases the stability of the CF-type structure (Irifune and Ringwood, 1993; Kesson, 1994), since NaAlSiO₄ has this structure at pressures of >18 GPa (Liu, 1977). The Al phases are the compounds accumulating alkaline elements, such as Na and K. Thus, these post-spinel mineral phases are considered as a likely geochemical reservoir for alkalis and other large cations in the Earth’s mantle.

Along with the most abundant minerals, such as olivine (wadsleyite and ringwoodite) and clinoenstatite (ilmenite), spinel (post-spinel) may contribute to seismic heterogeneities due to stagnation of the subducted lithosphere at the depths of the transition zone (Kirby et al., 1996). This depth range is characterized by a rapid increase in seismic velocities due to the mineral transformations into high-pressure phases in the upper mantle. This explains why the deep seismicity occurs only in the approximate depth range of the transition zone of the mantle, where the minerals of the subsiding slabs should acquire the structures of spinel and ilmenite. Even if the plate penetrates the lower mantle, the seismic heterogeneity should not appear at depths of ~700 km, since the key seismically sensitive phase transformations will be completed already (Kirby et al., 1996). Nevertheless, the study of various characteristics of the post-spinel phases is necessary, especially for understanding of the nature of local seismic heterogeneities in the lower mantle. Ab initio modeling of the elastic properties of the NaAlSiO₄, MgAl₂O₄, and (Mg,Fe)Al₂O₄ phases with the calcium ferrite-type structure made possible to estimate the velocities and density of the oceanic crust along various mantle geotherms (Wang et al., 2020). It may be assumed that the occurrence of the subducted oceanic crust at significant depths may be the reason for local seismic heterogeneities of the lower mantle due to the ongoing transformations of spinels into post-spinel phases. In addition, the formation of the post-spinel Mg₂SiO₄-CT phase at high pressure via the interaction of MgSiO₃ with the post-perovskite-type (PPv) structure and MgO with the NaCl-type structure was substantiated (Zhang et al., 2017). Due to the relatively small volume of our planet, the further high-pressure phase transition of the MgSiO₃(PPv) + MgO(NaCl) assemblage may not seem so important in the study of the Earth’s mantle. However, this may be of decisive importance for understanding of the internal dynamic processes in some exoplanets with masses of ten times higher than that of the Earth.

CONCLUSIONS

Post-spinel phases are a large group of more than 30 mineral phases, mainly with the stoichiometry A²⁺${\text{B}}_{2}^{{3 + }}$O₄. Most of them are synthetic, and their natural analogs have not yet been found. Nevertheless, in recent years, six new minerals with a “marokite” channel have been found in nature (harmunite, wernerkrauseite, tschaunerite, maohokite, chenmingite, and ellinaite). The stability fields of natural post-spinel phases are mainly located in high-pressure areas. The discovery of natural phases with the post-spinel-type structure in meteorites and inclusions in diamonds supports the assumption that these compounds are part of the phase composition of the mantle of the Earth and other planets of the solar system. Thus, the study of the formation conditions, likely systems of solid solutions of compounds with a “marokite” channel will allow us to understand the process of the evolution of the composition of matter of the terrestrial planets and, in particular, to assess the effect of subduction of the basaltic oceanic crust to depth on the heterogeneity of the transition zone and the lower mantle.