High-Pressure and High-Temperature Phase Transitions in Fe₂TiO₄ and Mg₂TiO₄ with Implications for Titanomagnetite Inclusions in Superdeep Diamonds

Abstract

Phase transitions of Mg₂TiO₄ and Fe₂TiO₄ were examined up to 28 GPa and 1600 °C using a multianvil apparatus. The quenched samples were examined by powder X-ray diffraction. With increasing pressure at high temperature, spinel-type Mg₂TiO₄ decomposes into MgO and ilmenite-type MgTiO₃ which further transforms to perovskite-type MgTiO₃. At ~21 GPa, the assemblage of MgTiO₃ perovskite + MgO changes to 2MgO + TiO₂ with baddeleyite (or orthorhombic I)-type structure. Fe₂TiO₄ undergoes transitions similar to Mg₂TiO₄ with pressure: spinel-type Fe₂TiO₄ dissociates into FeO and ilmenite-type FeTiO₃ which transforms to perovskite-type FeTiO₃. Both of MgTiO₃ and FeTiO₃ perovskites change to LiNbO₃-type phases on release of pressure. In Fe₂TiO₄, however, perovskite-type FeTiO₃ and FeO combine into calcium titanate-type Fe₂TiO₄ at ~15 GPa. The formation of calcium titanate-type Fe₂TiO₄ at high pressure may be explained by effects of crystal field stabilization and high spin–low spin transition in Fe²⁺ in the octahedral sites of calcium titanate-type Fe₂TiO₄. It is inferred from the determined phase relations that some of Fe₂TiO₄-rich titanomagnetite inclusions in diamonds recently found in São Luiz, Juina, Brazil, may be originally calcium titanate-type Fe₂TiO₄ at pressure above ~15 GPa in the transition zone or lower mantle and transformed to spinel-type in the upper mantle conditions.

1. Introduction

Titanomagnetite (Fe_3–xTi_xO₄), one of the important magnetic minerals in igneous and metamorphic rocks, is a solid solution between Fe₃O₄ magnetite (x = 0) and Fe₂TiO₄ ulvöspinel (x = 1), formed by replacement of Fe³⁺ by Ti⁴⁺. Fe₂TiO₄ ulvöspinel has an inverse spinel structure where tetrahedral sites are occupied by Fe²⁺ and octahedral sites are occupied randomly by Fe²⁺ and Ti⁴⁺ [1,2]. Mg₂TiO₄ qandilite is one of endmembers of spinel solid solution in the system Fe₂TiO₄–Mg₂TiO₄–Fe₃O₄–MgFe₂O₄, and is important in industrial ceramics. Mg₂TiO₄ qandilite also has the inverse spinel structure [3]. High-pressure phase transitions of A₂BO₄ and AB₂O₄ spinels have received much attention in geophysics and mineral physics, because they provide valuable information on post-spinel transitions of spinel-structured Mg₂SiO₄ ringwoodite which occurs at 660 km depth in the mantle and on stability of aluminous phases with the AB₂O₄ stoichiometry in the deep mantle.

Phase transitions of Fe₂TiO₄ spinel at room temperature and high pressure have been studied in detail [2,4,5,6]. The studies indicated that at room temperature Fe₂TiO₄ cubic spinel (space group Fd-3m) first changes into tetragonal spinel (I4₁/adm) at 9 GPa due to a Jahn-Teller effect of Fe²⁺ in the tetragonal site. At 12 GPa, the tetragonal spinel transforms to CaTi₂O₄-type structure (Cmcm), in which octahedral sites are occupied by disordered Fe²⁺ and Ti⁴⁺ and eight-fold sites by Fe²⁺. The CaTi₂O₄-type Fe₂TiO₄ further transforms at 53 GPa to another high-pressure polymorph (Pmma) with ordered Fe²⁺ and Ti⁴⁺ in the octahedral sites. Yamanaka et al. [4] reported that the high spin-low spin transition in Fe²⁺ in the octahedral sites of the CaTi₂O₄-type Fe₂TiO₄ started to occur above about 15 GPa at room temperature and that all of Fe²⁺ in the octahedral sites were in the low spin state in the Pmma phase, while Wu et al. [6] reported that the spin transition in Fe²⁺ initiated at around 40 GPa.

In contrast, studies on high-pressure and high-temperature transitions of Fe₂TiO₄ and Mg₂TiO₄ spinels have been limited. Phase transitions of the spinels were examined only up to 5 GPa at 800–1600 °C by Akimoto and Syono [7]. They reported that both Fe₂TiO₄ and Mg₂TiO₄ spinels decompose into ATiO₃ ilmenite and AO with rock-salt structure (A = Mg, Fe). The phase transitions at high temperature and high pressure above ~5 GPa, however, have not been well examined so far. Changes in elastic properties associated with the phase transitions in Fe₂TiO₄ and Mg₂TiO₄ shown above were investigated by Liebermann et al. [8]. The physical basis of elastic properties at high pressure and high temperature is described in detail by Anderson [9].

In this study, we have investigated phase transitions in Fe₂TiO₄ and Mg₂TiO₄ up to 28 GPa and 1600 °C, using a Kawai-type multianvil apparatus. We have found that the transition sequences in Fe₂TiO₄ at high pressure and high temperature are substantially different from those at high pressure and room temperature. Based on the results on Fe₂TiO₄ and Mg₂TiO₄, we discuss the difference in the transition behaviors between Fe₂TiO₄ and Mg₂TiO₄ from a crystal–chemical point of view. In addition, we discuss stability and possible origin of Fe₂TiO₄-rich titanomagnetites which were found as inclusions in superdeep diamonds from Juina area, Brazil [10,11].

2. Experimental Methods

Starting materials for high-pressure and high-temperature experiments of Mg₂TiO₄ and Fe₂TiO₄ were synthesized as follows. Spinel(Sp)-type Mg₂TiO₄ (qandilite) was synthesized from a 2:1 mixture (molar ratio) of MgO (>99.9% purity, Wako Co., Osaka, Japan) and TiO₂ (>99.9%, Wako Co.) by heating at 1300 °C for 20 h. Sp-structured Fe₂TiO₄ (ulvöspinel) was synthesized from a 1:1 mixture of Fe₂O₃ (>99.9%, Wako Co.) and TiO₂ by heating at 1270 °C for 27 h in controlled oxygen fugacity with mixed gasses of CO₂, H₂ and Ar (3:2:5 volume ratios). Powder X-ray diffraction measurements and composition analyses using a scanning electron microscope (SEM) with an energy-dispersive X-ray spectrometer (EDS) indicated that the synthesized samples were single-phase Sp-type Mg₂TiO₄ and Fe₂TiO₄ with the stoichiometric compositions. The lattice parameters determined by powder X-ray diffraction were a = 8.4398(1) Å for Mg₂TiO₄ Sp and a = 8.5375(3) Å for Fe₂TiO₄ Sp, which were in good agreement with those by Wechsler et al. [3] and Wechsler et al. [1], respectively. For high-pressure and high-temperature experiments of Fe₂TiO₄, 5 wt % metallic iron (>99.9 %, Johnson Matthey Co., London, UK) was added to the above synthesized Fe₂TiO₄ Sp to keep iron in the Fe₂TiO₄ samples in ferrous state.

High-pressure and high-temperature experiments were performed with the quench method using a Kawai-type 6-8 multianvil apparatus [12] at Gakushuin University. Tungsten carbide anvils with 2.5 mm truncated edge-length were used as the second-stage anvils. A 5 wt % Cr₂O₃-doped MgO octahedron of 7 mm edge length was used as the pressure medium. A cylindrical Re heater was placed in the central part of the octahedron. For the experiments of Mg₂TiO₄, the powdered starting material was directly put into the Re heater. For thermal insulation, a LaCrO₃ sleeve was placed between the heater and the MgO octahedron along with two LaCrO₃ plugs in both ends of the furnace. Two Pt discs were placed between the sample and the plugs to avoid any reaction between them. For the experiments of Fe₂TiO₄, the mixture of 95 wt % Fe₂TiO₄ and 5 wt % Fe was put into an Fe capsule which was placed in the central part of the Re heater. A BN sleeve was inserted between the Fe capsule and Re heater for electrical insulation. Temperature was measured at the central part of the outer surface of the furnace with a Pt/Pt-13%Rh thermocouple. Effect of pressure on emf of the thermocouple was ignored.

Pressure was calibrated at room temperature using pressure-fixed points: Bi I-II (2.55 GPa), Bi III-V (7.7 GPa), ZnS (15.6 GPa), and GaAs (18.3 GPa) in Ito [12] and GaP (23 GPa) by Dunn and Bundy [13]. The pressure was further corrected at 1200 and 1600 °C, using transition pressures of Mg₂SiO₄ olivine–wadsleyite–ringwoodite [14,15] and MgSiO₃ akimotoite–bridgmanite [16] and decomposition pressure of Mg₃Al₂Si₃O₁₂ pyrope to MgSiO₃-rich bridgmanite + Al₂O₃-rich corundum [16]. Uncertainties of pressure and temperature were estimated to be ±0.3 GPa and ±20 °C, respectively. In each run, pressure was raised to a targeted pressure of 11–28 GPa at a constant rate during about 2–4 h, and then temperature was raised to a targeted temperature of 1000–1600 °C at a rate of about 100 °C/min. The samples were kept for 60–120 min at the pressure-temperature conditions, and then quenched under pressure, slowly decompressed, and recovered to ambient conditions.

The recovered samples were pulverized and examined by a powder X-ray diffractometer (Rigaku, RINT2500, Tokyo, Japan) operated at 45 kV and 250 mA with a rotating Cr anode. Monochromatized CrKα radiation was used for identification of phases in the run products and determination of lattice parameters. High-purity Si powder was used to calibrate 2θ angle of the powder X-ray diffractometer. The lattice parameters were refined by the least squares method. By using some parts of run products which were mounted on slide-glass plates with epoxy resin and polished flat, phase identification and chemical analysis were made using a SEM (JEOL, JMS-6360, Tokyo, Japan) in combination with an EDS (SGX Sensortech Sirius SD-10133, High Wycombe, UK). The SEM was operated with acceleration voltage of 15 kV and probe current of 0.55 nA. Natural forsterite and synthetic fayalite and MnTiO₃ provided by JEOL were used as standard materials for Mg, Fe and Ti, respectively.

3. Results

3.1. Phase Transitions in Mg₂TiO₄

Table 1. Results of high-pressure and high-temperature experiments in Mg₂TiO₄.

Run No.	Pressure (GPa)	Temperature (°C)	(min)	Run Product
O160915	21	1000	120	Pe, Ln
O161025	23	1000	90	Pe, α
O161017	21	1300	90	Pe, Ln
O170116	22.5	1300	50	Ln, Pe, α
O161128	23.5	1300	60	Pe, α, Ln(tr)
O160909	24.5	1300	60	Pe, α
O160924	28	1300	90	Pe, α
O161106	28	1400	90	Pe, α, Ln(tr)
O170219	22	1500	90	Ln, Pe, α
O170202	25	1500	60	Pe, α
O170126	28	1500	60	Pe, α
O161021	21	1600	90	Pe, Ln
O161124	22	1600	60	Pe, Ln
O161209	23.5	1600	60	Ln, Pe, α
O160903	24.5	1600	60	Pe, α, Ln(tr)

Abbreviations are as follows: Ln, LiNbO₃-type MgTiO₃; Pe, MgO periclase; α, αPbO₂ type TiO₂; tr, trace.

summarizes results of phase transition experiments in Mg₂TiO₄ at 21–28 GPa and 1000–1600 °C. The previous study showed that at pressure below 1–2 GPa spinel (Sp)-type Mg₂TiO₄ first dissociates into ilmenite (Ilm)-type MgTiO₃ + MgO periclase (Pc) [7]. Figure 1a shows a powder X-ray diffraction pattern of the run product (No. O161021) quenched from 21 GPa and 1600 °C. The diffraction pattern exhibits MgO Pe and a phase with very similar diffraction peaks to MgTiO₃ Ilm (space group R-3). However, some diffraction peaks such as 003 and 101 of MgTiO₃ Ilm in 2θ range of 20–30° are absent. Almost all the peaks were indexed with hexagonal symmetry, and refined cell parameters were a = 5.0774(5) Å, c = 13.716(2) Å, giving c/a = 2.701. This c/a value is considerably smaller than 2.750 of MgTiO₃ Ilm [3]. The diffraction data in Figure 1a and the lattice parameters are consistent with those of LiNbO₃ (Ln)-type MgTiO₃ (R3c) [17]. Linton et al. [17] reported that Ilm-type MgTiO₃ transforms at about 15–20 GPa to the perovskite (Pv) phase, which is converted to the Ln-type phase on decompression. Therefore, our results in Table 1 and Figure 1a reveal that MgTiO₃ Pv + MgO Pe are stable at 21 GPa and 1600 °C and that MgTiO₃ Pv transforms to the Ln-type on release of pressure.

Figure 1b shows a powder X-ray diffraction pattern of the run product (No. O160924) quenched from 28 GPa and 1300 °C, in which diffraction peaks of MgO Pe and αPbO₂ type TiO₂ are observed. Broad diffraction peaks of αPbO₂ type TiO₂ in Figure 1b suggest that the phase was a retrograde transformation product from a high-pressure phase. Previous studies on TiO₂ indicated that at about 800–1000 °C TiO₂ rutile transforms to αPbO₂ type at about 6–8 GPa, which further transforms to baddeleyite (Bd)-type TiO₂ (akaogiite) [18,19] at about 15–20 GPa [20,21,22]. The Bd-type TiO₂ transforms to orthorhombic-I (OI) type TiO₂ at about 25–30 GPa at 1200–1500 °C [23,24]. These studies also showed that both of Bd- and OI-type TiO₂ phases back-transform to αPbO₂ type TiO₂ on release of pressure. Therefore, based on the experimental pressure range and the broad X-ray diffraction peaks, we conclude that the αPbO₂ type TiO₂ found in the run products of 28 GPa and 1300 °C was the retrograde transition product from Bd- or OI-type TiO₂ synthesized at the P, T conditions. This leads to the conclusion that MgTiO₃ Pv stable at 21 GPa decomposes to the constituent oxides at higher pressure.

Figure 2 shows the phase diagram of Mg₂TiO₄. Our experimental results at 21–28 GPa and 1000–1600 °C indicate that the transition boundary of MgTiO₃ Pv + MgO Pe to 2MgO Pe + Bd-type TiO₂ which is the decomposition boundary of MgTiO₃ Pv is located at 21–23 GPa and 1000–1600 °C with a small positive dP/dT slope. Figure 2 also includes the dissociation boundary of Mg₂TiO₄ Sp to MgTiO₃ Ilm + MgO Pe below ~1–2 GPa [7], as well as the Ilm-Pv transition boundary of MgTiO₃ at ~ 15–20 GPa [25]. The assemblage of MgO and TiO₂ is stable to at least 35 GPa at 1400 °C in our preliminary study on phase transitions in MgTiO₃ [25].

Molar volumes of high-pressure phases in the systems MgO-TiO₂ and FeO-TiO₂ are listed in

Table 2. Molar volumes of phases in the systems MgO-TiO₂ and FeO-TiO₂.

Comp.	Structure	V0 (cm3/mol)	Ref.	Comp.	Structure	V0 (cm3/mol)	Ref.
MgO	rock-salt	11.24	a	FeO	rock-salt	12.17	i
MgTiO3	ilmenite	30.86	b	FeTiO3	ilmenite	31.72	j
MgTiO3	perovskite	29.31	c	FeTiO3	perovskite	30.34	k
MgTiO3	LiNbO3	30.71	d	FeTiO3	LiNbO3	31.34	j
Mg2TiO4	spinel	45.25	e	Fe2TiO4	spinel	46.84	e
TiO2	αPbO2	18.41	f	Fe2TiO4	CaTi2O4	42.41	e
TiO2	baddeleyite	16.90	g
TiO2	OI	16.83	h

V₀: molar volume at ambient conditions. Ref. a: Hazen [31], b: Wechsler and Von Dreele [3], c: Linton et al. [17], d: Linton et al. [32], e: This study, f: Kojitani et al. [22], g: Al-Khatatbeh et al. [24], h: Nishio-Hamane et al. [33], i: McCammon [34], j: Akaogi et al. [26], k: Leinenweber et al. [27].

. Using the data in Table 2, for the following transitions in Mg₂TiO₄:

Mg₂TiO₄(Sp) → MgTiO₃(Ilm) + MgO(Pc) → MgTiO₃(Pv) + MgO(Pc) → 2MgO(Pc) + TiO₂(Bd) → 2MgO(Pc) + TiO₂(OI),

we obtain molar volume changes at ambient conditions of −3.15, −1.55, −1.17 and −0.07 cm³/mol, respectively, which are −7.0, −3.7, −2.9 and −0.2%, respectively.

3.2. Phase Transitions in Fe₂TiO₄

Results of high-pressure transition experiments in Fe₂TiO₄ are summarized in

Table 3. Results of high-pressure and high-temperature experiments in Fe₂TiO₄.

Run no.	Pressure (GPa)	Temperature (°C)	Time (min)	Run Product *
M150109	12.5	1000	60	Ilm, Wu
M150107	12.5	1100	60	Ilm, Wu
M140806	13	1100	60	Ilm, Ln, Wu
M150115	14	1100	60	Ln, Wu
M141128	15.5	1100	60	Ln, Wu
M140707	16	1100	60	CT
M150218	17	1100	60	CT
M150603	20	1100	60	CT
M150226	23	1100	60	CT
M150516	24	1100	60	CT
M150127	12.5	1200	60	Ilm, Ln, Wu
M150416	18	1200	60	CT
M150707	11	1300	60	Ilm, Wu
M150725	12	1300	60	Ilm, Wu
M140728	13	1300	60	Ln, Wu
M150625	14	1300	60	Ln, Wu
M150202	15	1300	60	CT
M140626	15	1300	60	CT, Ln, Wu
M140701	18	1300	60	CT
M140710	18	1300	60	CT
M150227	20	1300	60	CT
M150606	22	1300	60	CT

* Metallic iron coexisted in the run products. Ilm: ilmenite-type FeTiO₃, Wu: FeO wustite, Ln: LiNbO₃-type FeTiO₃, CT: CT-type Fe₂TiO₄.

. Phase identification was made mostly by powder X-ray diffraction method. Metallic iron in the samples was identified by the SEM-EDS analysis and/or powder X-ray diffraction. Fe₂TiO₄ ulvöspinel first dissociates into Ilm-type FeTiO₃ and FeO wustite (Wu) at 4–5 GPa and 1000–1300 °C [7]. Figure 3a shows a powder X-ray diffraction pattern of the run product (No. M150115) synthesized at 14 GPa and 1100 °C. The diffraction pattern of Figure 3a is composed of FeO Wu, metallic iron, and the other phase whose diffraction peaks agree with those of Ln-type FeTiO₃ by Akaogi et al. [26]. The Ln-type FeTiO₃ phase is interpreted to be the retrograde transition product from Pv-type FeTiO₃ [27]. Natural occurrences of Ln-type FeTiO₃ were reported in shocked meteorites, and the new mineral was recently named wangdaodeite [28,29].

Figure 3b shows a powder X-ray diffraction pattern of the run product (No. M140710) synthesized at 18 GPa and 1300 °C. The diffraction pattern is similar to calcium titanate (CaTi₂O₄), and the peaks were indexed with orthorhombic symmetry (Figure 3b). The Miller indices were consistent with extinction rules of CaTi₂O₄(CT)-structured phase (Cmcm). The lattice parameters refined using twenty nine diffraction peaks of the Fe₂TiO₄ phase were a = 2.9473(5) Å, b = 9.6448(2) Å, c = 9.9085(2) Å, V = 281.663(7) ų. The cell parameters agree well with those extrapolated to ambient pressure of CT-type Fe₂TiO₄ at 38–50 GPa and room temperature by Yamanaka et al. [4]. These results indicate that the Fe₂TiO₄ phase in the run product synthesized at 18 GPa and 1300 °C is the CT-type phase. This is consistent with the results in the previous studies that Fe₂TiO₄ CT is quenchable at ambient conditions [5,30]. Compositions of coexisting Fe₂TiO₄ CT and FeTiO₃ Ln with very small grains of FeO Wu in the run product (No. M140626) at 15 GPa and 1300 °C were analyzed using the SEM-EDS: Fe_1.97(1)Ti_1.01(1)O₄ for CT-type phase and Fe_0.95(2)Ti_1.02(1)O₃ for Ln-type phase, indicating almost stoichiometric compositions within the analytical errors.

Figure 4 shows the phase diagram of Fe₂TiO₄. Our experimental results indicate that at 1000–1300 °C the assemblage of FeO Wu + FeTiO₃ Ln which was Pv at high P, T was observed in the run products synthesized at 12.5–15.5 GPa, while FeO Wu + FeTiO₃ Ilm was observed at 11–12.5 GPa. The Ilm-Pv transition boundary has a small negative slope. The Ilm-Pv transition pressure in this study is generally consistent with that obtained by extrapolation of the boundary determined at 500–900 °C by Ming et al. [35]. We found that the assemblage of FeTiO₃ Ln (Pv at high P, T) and FeO Wu changes to Fe₂TiO₄ CT in the run products at 15–16 GPa at 1100–1300 °C with a small negative slope boundary. Therefore, the stability field of FeTiO₃ Pv and FeO Wu is limited in a narrow pressure interval of about 2 GPa. This study indicates that Fe₂TiO₄ CT is stable up to at least 22–24 GPa at 1100–1300 °C. In our previous study in FeTiO₃ composition, we found that Fe₂TiO₄ CT coexists with OI-type TiO₂ up to about 33 GPa, above which it decomposes into FeO Wu + TiO₂ OI [26]. Therefore, the upper stability pressure of Fe₂TiO₄ CT is about 33 GPa.

The results in Figure 4 combined with those by Akaogi et al. [26] indicate that the following transitions occur in Fe₂TiO₄ with increasing pressure:

Fe₂TiO₄(Sp) → FeTiO₃(Ilm) + FeO(Wu) → FeTiO₃(Pv) + FeO(Wu) → Fe₂TiO₄(CT) → 2FeO(Wu) + TiO₂(OI),

where molar volume changes at ambient conditions are −2.95, −1.38, −0.10 and −1.24 cm³/mol, which are −6.3%, −3.1%, −0.2% and −2.9%, respectively, using the data in Table 2.

4. Discussion

Our results indicate that Fe₂TiO₄ Sp undergoes phase transitions to FeTiO₃ Ilm + FeO Wu and subsequently to FeTiO₃ Pv + FeO Wu at high pressure and high temperature (Figure 4). The decomposition of Fe₂TiO₄ Sp to FeTiO₃ Ilm + FeO Wu is consistent with the result by Akimoto and Syono [7]. However, at room temperature and high pressure, the transition behavior is different: Fe₂TiO₄ cubic Sp is distorted to tetragonal Sp at ~9 GPa due to the Jahn-Teller effect of Fe²⁺ at the tetrahedral site [2]. The difference may arise from kinetic hindrance to decomposition into FeTiO₃ Ilm + FeO Wu at room temperature. In the experiments at room temperature and high pressure, tetragonal Sp transforms to Fe₂TiO₄ CT at ~15 GPa [4,6]. The pressure is generally consistent with transition pressure to Fe₂TiO₄ CT at room temperature extrapolated from the results at 1000–1300 °C, considering the uncertainty of the boundary slope (Figure 4).

Here, we compare the transitions in Mg₂TiO₄ and Fe₂TiO₄. As shown in Figure 2 and Figure 4, both of Sp-type Mg₂TiO₄ and Fe₂TiO₄ dissociate into ATiO₃ Ilm and AO (A = Mg, Fe) at pressures below ~5 GPa, and both of the ATiO₃ Ilm transform to ATiO₃ Pv at ~13–15 GPa. At higher pressure, however, the transition behaviors are different between Mg₂TiO₄ and Fe₂TiO₄. In Mg₂TiO₄, the assemblage of MgTiO₃ Pv + MgO Pe changes into 2MgO Pe + TiO₂ Bd due to decomposition of MgTiO₃ Pv. However, in Fe₂TiO₄ the assemblage of FeTiO₃ Pv + FeO Wu changes at ~15 GPa to CT-type Fe₂TiO₄ which is stable up to ~33 GPa.

Figure 5 illustrates the CT-type structure (Cmcm). The structure consists of double chains of edge-sharing octahedra running parallel to the a-axis, and tunnel spaces are formed by four corner-sharing double chains [37,38]. In the structure of CT-type Fe₂TiO₄, Fe²⁺ and Ti⁴⁺ are randomly distributed in the octahedral sites and only Fe²⁺ in the eight-fold sites in the tunnel spaces. Compared with Mg₂TiO₄, crystal-field effect of Fe²⁺ in the octahedral sites may stabilize the CT-type phase of Fe₂TiO₄ composition. Using effective ionic radii by Shannon [39], the difference of ionic radii between Fe²⁺ (0.78 Å in high-spin state) and Ti⁴⁺ (0.605 Å) in octahedral site is larger than that between Mg²⁺ (0.72 Å) and Ti⁴⁺. However, the ionic radius of Fe²⁺ in low-spin state in the octahedral site is 0.61 Å, which is much closer to that of Ti⁴⁺ compared with Mg²⁺. When we adopt that the high-spin to low-spin transition of Fe²⁺ in the octahedral site of Fe₂TiO₄ CT starts to occur at pressure of ~15–20 GPa at room temperature and proportion of low-spin Fe²⁺ increases with pressure [4], it is suggested that the very similar ionic radii of low-spin Fe²⁺ and Ti⁴⁺ is more favorable for the CT-type structure. Although the high-spin state and low-spin state would be mixed at high temperature such as 1000–1300 °C [40], it is likely that both of the crystal-field effect and the high-spin to low-spin transition of Fe²⁺ may facilitate the stability of Fe₂TiO₄ CT above ~15 GPa.

Sp-type titanomagnetites were found as inclusions in diamonds from some localities in Juina, Brazil, and the diamonds were interpreted to be derived from the deep mantle [10,11]. Two different occurrences of titanomagnetites as the diamond inclusions have been reported: one was a titanomagnetite-bearing mineral composite, and the other was separate single-phase inclusions of titanomagnetite. As the former-type inclusion, Walter et al. [10] discovered a ~30 μm-sized composite consisting mostly of orthopyroxene together with olivine and titanomagnetite (called “ulvöspinel” in their study) in a diamond from the Juina-5 kimberlite, Brazil. The analyzed composition of the titanomagnetite was approximately 36 mol % Fe₂TiO₄⋅36 mol % Fe₃O₄⋅28 mol % Mg₂TiO₄. Walter et al. [10] interpreted that the three-phase composite was originally a homogeneous Mg-rich bridgmanite in the lower mantle, and that the diamond was transported to the upper mantle at a depth range of ~150–200 km where immiscibility into the three phases occurred before eruption of the kimberlite. Based on the experimental data on NaAlSiO₄-MgAl₂O₄ [42,43], Walter et al. [10] estimated the depth range of ~150–200 km using nepheline–spinel composite inclusions which were interpreted to be originally calcium ferrite (CF)-type phase and hexagonal aluminous (NAL) phase in the lower mantle and the unmixing occurred at the depth range. Figure 1 and Figure 3 and the results of Woodland et al. [44] indicate that the upper bound of stability field of Sp-type Mg₂TiO₄, Fe₂TiO₄ and Fe₃O₄ increases in the order of ~1, ~4 and ~10 GPa, respectively. Using the pressures, we roughly estimate the upper limit of stability field of the titanomagentite inclusion of the above composition to be ~5–6 GPa. The pressure is compatible with the estimated depth range of ~150–200 km from the CF and NAL inclusions.

The other kind of titanomagnetites was separate single-phase inclusions in superdeep diamonds. By a new combined method of synchrotron microtomography and single-crystal X-ray diffraction with fast, non-destructive methodology, Wenz et al. [11] discovered ~10–20 μm-sized inclusions of separate titanomagnetite crystals and powders in diamonds from São Luiz, Juina, Brazil. They observed that titanomagnetite inclusions were relatively abundant next to (Mg,Fe)O magnesio-wustite and Fe_2−xTi_xO₃ titanohematite, and determined lattice parameters of the titanomagnetites embedded in the diamonds to be 8.511–8.405 Å by in situ X-ray diffraction method. Wenz et al. [11] assumed that compositions of the titanomagnetites were on the join Fe₂TiO₄-Fe₃O₄, because chemical analysis of the titanomagnetites was not made in the study. However, it is likely that the titanomagnetites contained minor amounts of Mg₂TiO₄ and MgFe₂O₄ components, as that found by Walter et al. [10]. At ambient conditions, cell parameters of Fe₂TiO₄ Sp and Fe₃O₄ Sp are 8.5375(3) Å (this study) and 8.3984(8) Å [4], respectively, while Mg₂TiO₄ Sp and MgFe₂O₄ Sp are 8.4398(1) Å (this study) and 8.391 Å [45], respectively. Therefore, there is large uncertainty in estimating compositions of the titanomagnetites in the diamonds only from the lattice parameters determined by the in situ measurements. It should also be considered that remnant pressure probably remained in the titanomagnetites embedded in the diamonds. When we use measured bulk modulus of Fe₂TiO₄ Sp of 121 GPa [8,46] or 147 GPa [47], the pressure dependence of cell parameter is calculated to be −0.023 or −0.019 Å/GPa, respectively.

We suggest, however, that the remnant pressure and possible presence of Mg₂TiO₄ and MgFe₂O₄ components, if any, decrease the lattice parameter of titanomagnetite from that in the Fe₂TiO₄–Fe₃O₄ system at 1 atm. When we assume that the titanomagnetites in the diamonds are Mg-free solid solutions in the system Fe₂TiO₄–Fe₃O₄ and the remnant pressure is negligibly small, we can estimate 81 mol % of Fe₂TiO₄ component for the titanomagnetite with the largest cell parameter (a = 8.511 Å). Because this is the lower bound for the Fe₂TiO₄ component, as discussed above, it is probable that the titanomagnetite composition was more Fe₂TiO₄-rich, possibly almost pure Fe₂TiO₄. Such titanomagnetites of very high Fe₂TiO₄ content probably could not be directly incorporated at a depth where the diamonds were formed, because the graphite–diamond transition boundary [36] is placed by ~1 GPa at higher pressure than the upper bound of the stability field of Fe₂TiO₄ Sp (Figure 4). Therefore, the above estimate would suggest that the Fe₂TiO₄-rich titanomagnetites were originally CT-type phases which are stable above ~15 GPa in the transition zone and the lower mantle conditions, and that they back-transformed to the Fe₂TiO₄-rich titanomagnetites in the diamonds after being transported to the upper mantle. The decomposition into FeTiO₃ Ilm (or Pv) + FeO Wu might have been kinetically hindered. Further experimental studies, particularly compositional analysis of the titanomagnetites, would be required to better clarify the origin of the titanomagnetites in the superdeep diamonds.