Enthalpy and entropy of perovskite formation from simple oxides (calculated per 1 mol of compound).
The present work is devoted to the review of experimental data on thermodynamic properties of perovskite in the condensed state, as well as the gas phase components over perovskite and its melts at high temperatures.
Calcium titanate (CaTiO3) or perovskite was found by Rose  in the Ural Mountains in 1839 and named after the Russian Statesman Count Lev Perovski. Perovskite is a relatively rare mineral, which is a promising material for use as matrices for safe long-term storage of actinides and their rare earth analogs that are present in radioactive waste . It is of particular interest for petrology and cosmochemical research as a mineral which is a part of refractory Ca-Al inclusions often found in carbonaceous chondrites, which are the earliest objects of the solar system with unusual isotopic characteristics [3, 4, 5].
In addition to perovskite, two more calcium titanates, Ca3Ti2O7  and Ca4Ti3O10 , melting incongruently, were found in the CaO-TiO2 system. The other calcium titanates, Ca4TiO6 , Ca3TiO5 , Ca8Ti3O14 [8, 10], Ca2TiO4 , Ca5Ti4O13 , Ca2Ti3O8 , CaTi2O5 [12, 13], CaTi3O7 , Ca2Ti5O12 , and CaTi4O9 , are mentioned in the literature. They also seem to be unstable, which does not exclude their possible existence . Compiled in this paper on the basis of data [7, 18], as well as the results of recent studies by Gong et al. , the phase diagram of the CaO-TiO2 system in the high-temperature region is shown in Figure 1.
2. The thermodynamic properties of perovskite solid phase
Thermochemical data on perovskite [20, 21, 22, 23, 24] are based on calorimetric measurements of entropy of perovskite formation Δ
Naylor and Cook  determined the enthalpy of perovskite phase transition: 2.30 ± 0.07 kJ/mol at 1530 ± 1 K. The overlapping phase transitions in perovskite observed by Guyot et al.  (Figure 2) were explained as consequences of a structural change, i.e., a transition from orthorhombic (
Panfilov and Fedos’ev  determined the enthalpy of the reaction with a calorimetric bomb by burning stoichiometric mixtures of rutile TiO2 and calcium carbonate CaCO3 (here and below, the square brackets denote the condensed phase; the parentheses denote the gas phase):
They then calculated the enthalpy of perovskite formation Δ
|HF/HCl solution calorimetry||298||1.05 ± 0.21|||
|HF/HCl solution calorimetry||298||−40.48 ± 0.42||1.86 ± 0.71|||
|Bomb calorimetry||298||−41.84 ± 1.88|||
|Adiabatic calorimetry||298||−40.48 ± 1.65||2.40 ± 0.35|||
|Adiabatic calorimetry||298||−47.11 ± 1.41||2.72 ± 0.23|||
|Na6Mo4O15 solution calorimetry||298||−42.98 ± 1.96|||
|EMF||888–972||−37.05 ± 3.28||4.62 ± 3.54|||
|EMF||900–1250||−40.07 ± 0.05||3.15 ± 0.05|||
|Pb2B2O5 solution calorimetry||973||−38.73 ± 1.34|||
|Na6Mo4O15 solution calorimetry||975||−42.25 ± 1.05|||
|Na6Mo4O15 solution calorimetry||975||−41.88 ± 1.36|||
|Na6Mo4O15 solution calorimetry||976||−42.86 ± 1.71|||
|Pb2B2O5 solution calorimetry||1046||−42.38 ± 1.82|||
|(Li,Na)BO2 solution calorimetry||1068 ± 2||−40.45 ± 1.15|||
|Pb2B2O5 solution calorimetry||1073||−40.43 ± 1.87||4.37 ± 1.23|||
|Pb2B2O5 solution calorimetry||1074||−43.78 ± 1.73|||
|Pb2B2O5 solution calorimetry||1078||−42.83 ± 3.12|||
|EMF||1180–1290||−26.88 ± 8.05||11.07 ± 6.44|||
|Raman spectroscopy||1300||2.82 ± 1.29|||
|Thermochemical calculations||1600–1800||−37.19 ± 0.14||5.85 ± 0.09|||
|Thermochemical calculations||1600–2100||−38.23 ± 0.04||5.00 ± 0.02|||
|Thermochemical calculations||1600–2100||−37.47 ± 0.03||5.60 ± 0.02|||
|DTA||1740 ± 20||−37.55 ± 3.76|||
|Knudsen mass spectrometry||1791–2241||−39.98 ± 0.54||3.15 ± 0.28|||
|Knudsen mass spectrometry||2241–2398||7.73 ± 1.76||24.39 ± 0.76|||
by solution calorimetry in a mixture of hydrofluoric and hydrochloric acids. The reactions of dissolution were more complete than combustion reaction (1).
Navrotsky et al. [19, 26, 34, 37, 38, 39, 40, 41, 42, 43] performed a number of studies by various calorimetric methods, using adiabatic calorimetry  and solution calorimetry in the (Li, Na)BO2 , Pb2B2O5 [37, 42, 43], and Na6Mo4O15 [19, 34, 38, 39, 40] salts in the temperature range 973–1074 K. They determined the value of Δ
The data obtained by Sato et al.  using adiabatic calorimetry deviate negligibly (by as much as 7 kJ/mol) in the enthalpy values of (
Golubenko and Rezukhina  studied the heterogeneous reaction using a solid electrolyte galvanic cell (EMF method) in the temperature range of 1180–1290 K:
A mixture of FeO and Fe (or NbO and Nb) was used as the reference electrode, and a mixture of La2O3-ThO2 crystals was used as the solid electrolyte. The Gibbs energy of perovskite Δ
Taylor and Schmalzried  (at 873 K) and Jacob and Abraham  (at 900–1250 K) also determined the perovskite Gibbs energy via EMF using the same solid electrolyte. The obtained Δ
Klimm et al.  used differential thermal analysis (DTA) to determine the enthalpy of reaction (2) at 1740 ± 20 K. The obtained value is consistent with the results of thermochemical calculations, although it has a significant error.
Banon et al.  (at 2150 K) and Shornikov et al. [48, 53, 56] (at 1791–2398 K) determined the values of CaO and TiO2 activities (Figure 4) and Δ
As it is seen in Figure 4, the values of oxide activities in perovskite determined via Knudsen effusion mass spectrometric method agree with one another in the investigated temperature range. As the temperature grows, there is a slight trend toward the higher activities of calcium and titanium oxides in the crystalline perovskite phase. This trend is less noticeable in the area of the liquid phase. The activities of titanium oxide calculated based on studying of equilibria in slags [54, 55] are fairly approximate but not inconsistent with the results in [48, 52, 53].
The values of Gibbs energy of perovskite formation determined at 800–1200 K via EMF [35, 36, 51] and solution calorimetry  correlate satisfactorily with the obtained via Knudsen effusion mass spectrometric method [48, 52, 53, 56]. Figure 3 shows a good agreement between these data and the results from thermochemical calculations performed by Woodfield et al. . The difference between our findings and the thermochemical data calculated by Bale et al.  is large in the perovskite melting area, but is still less than 3 kJ/mol.
3. Melting of perovskite
The data characterizing the melting of simple oxides [23, 24, 57, 58, 59, 60] are quite rough (Table 2). According to different thermochemical data, perovskite’s melting temperature lies in the range of 2188 to 2243 K.
|3200 ± 50||79.50||24.84|||
|3210 ± 10||55.20||17.20|||
|2220 ± 20||56.65 ± 11.33||25.52 ± 5.10|||
|2241 ± 10||47.61 ± 1.84||21.24 ± 0.81|||
|2130 ± 20||66.94 ± 16.70||31.43 ± 7.84||[23, 58]|
|2185 ± 10||68.00 ± 8.00||31.12 ± 3.66|||
Shornikov  based on his own data (Table 1) has obtained more accurate values, characterizing the perovskite melting (Table 2). They coincide satisfactorily with the experimental data obtained by Klimm et al.  and the thermochemical estimates made by Bale et al. . The enthalpy of perovskite melting estimated using Walden’s empirical rule  is also close to the result obtained by Shornikov : Δ
4. The thermodynamic properties of perovskite melts
Thermodynamic information about the CaO-TiO2 melts is quite scarce and limited by the results of only a few experimental studies. Consider the available experimental data, obtained by the Knudsen effusion mass spectrometry.
Banon et al.  investigated the evaporation of 24 compositions of the CaTiO3-Ti2O3-TiO2 system from molybdenum containers at 1900–2200 K. The synthesized compositions contained up to 90.2 mol% Ti2O3 and up to 42 mol% TiO2 as well as CaTiO3 compound. Based on the partial vapor pressures (Ca), (TiO), and (TiO2) over melts at 2150 K, the authors calculated the Ti, TiO, Ti2O3, TiO2, and CaTiO3 activities, as well as mixing energies in the melts. In the case of the CaTiO3-TiO2 melts, the TiO2 and CaTiO3 activities were calculated by extrapolation from the data relating to the CaTiO3-Ti2O3-TiO2 system and thus had, according to the authors themselves, low accuracy, which apparently was caused by inconsistency with different versions of the CaO-TiO2 phase diagram [7, 9, 11, 18]. Nevertheless Banon et al. , interpreting the obtained high values of TiO2 activities in the region close to titanium dioxide (Figure 5), assumed the presence of immiscibility of the CaO-TiO2 melts in this region.
Stolyarova et al.  investigated the properties of the gas phase over 14 compositions of the CaO-TiO2-SiO2 system and also determined the values of oxide activity and melt mixing energy by high-temperature mass spectrometry during the evaporation of melts from tungsten effusion containers at 1800–2200 K. The synthesized compositions contained up to 70 mol% CaO, up to 69 mol% SiO2, and up to 40 mol% TiO2. As it is shown in Figure 5, one of the two studied compositions of the CaO-TiO2 system at 2057 K was in the “CaO + liquid” region, and thus its value should be close to 1. The second composition was in the region of “Ca4Ti3O10 + liquid,” according to the information presented in [7, 18], or in the region of “Ca3Ti2O7 + liquid,” as follows from the data presented by Tulgar . However, the calculated values are quite close (Figure 5), which contradicts the CaO-TiO2 phase diagram (Figure 1). A possible reason for the discrepancies seems to be a significant error in the measurements of CaO activities in the melt, which may be, in our opinion, more than 50%.
Shornikov  investigated the evaporation from molybdenum containers of more than 200 compositions of the CaO-TiO2 system containing from 34 to 98 mol% TiO2 at 2241–2441 K. The studied compositions were the CaO-TiO2-SiO2 residual melts containing up to 1 mol% SiO2 that was lost during high-temperature evaporation. The determined composition of the gas phase over the CaO-TiO2 melts allowed to conclude that evaporation reactions are typical for individual oxides predominate.
The oxide activities in the CaO-TiO2 melts were calculated according to Lewis equations :
in which the ratio of the oxide activities in the melt could be easily converted to the ratio of the partial pressures, proportional to the ion currents (
and thus to evade the needs in additional thermochemical data, used in Eq. (5).
Values of chemical potentials (Δμ
which are related to the corresponding integral thermodynamic mixing functions:
and are represented in Figure 6.
The results presented by Banon et al.  correlate with the data found in . Some difference in values, as mentioned above, is probably due to the procedures for extrapolating information obtained by Banon et al.  for compositions of the CaTiO3-Ti2O3-TiO2 triple system, which could reduce their accuracy. The observed behavior of TiO2 activity in melts in the concentration region close to rutile may indicate some immiscibility of the melt, which follows from the observed inflection of the concentration dependence (Figure 5, line 3). However, in our opinion, the behavior of TiO2 and CaTiO3 activities (Figure 5, lines 4 and 6) are close to the ideal. The maximum value corresponds to the area of compositions close to perovskite (Figure 5, lines 5 and 6). Differences with values obtained by Stolyarova et al.  (Figure 5, points 1), are caused, apparently, by the low accuracy of the latter.
The partial and integral thermodynamic regularities presented in Figure 6 characterizing the CaO-TiO2 melts are symbate. The enthalpy and entropy of melt formation are positive. The extreme values of the integral thermodynamic properties of the melts are in the concentration ranges close to perovskite, which confirms its stability in the melt. Some displacement of the extremum of integral thermodynamic functions can be caused by the presence of oxide compounds with a large amount of CaO in comparison with perovskite CaTiO3 in the melt. A comparison of mixing energies in the CaO-TiO2 melts at 2300 K with those for the CaO-SiO2  and CaO-Al2O3  melts (Figure 6d) indicates a stronger chemical interaction in the CaO-TiO2 melts than the CaO-Al2O3 melts, but smaller than in the CaO-SiO2 melts. It manifests in more positive values of the mixing energy of the melts.
5. The gas phase over perovskite
The gas phase over calcium oxide consists of the molecular components (O), (O2), (O3), (O4), (Ca), (Ca2), and (CaO) possibly formed by the following reactions:
The gas phase over titanium oxide contains similar vapor molecular forms (O), (O2), (O3), (O4), (Ti), (Ti2), (Ti3), (TiO), and (TiO2) formed by similar reactions:
Balducci et al.  detected (Ti2O3) and (Ti2O4) molecules in the gas phase over cobalt titanate CoTiO3 at 2210–2393 K by the Knudsen effusion mass spectrometric method, which can be involved in the following equilibria:
Note that the predominant components of the gas phase over these oxides are (Ca), (CaO), (TiO), (TiO2), (O), and (O2); the content of other vapor species does not exceed 1% of the total concentration at 1700–2200 K.
The properties of the gas phase over perovskite were studied in less detail. The experimental conditions and results of high-temperature studies of perovskite evaporation we will consider below.
Zakharov and Protas  studied ion emission from the perovskite surface under the action of laser radiation and identified the ion of a complex molecule (CaTiO3) in addition to the ions of simple oxides (O+, Ca+, CaO+, Ti+, TiO+) in the mass spectra of the vapor. They explained the presence of this ion by the similarity of high-temperature evaporation of alkaline-earth oxide titanates, which is confirmed by the composition of the observed condensates (BaTiO3, SrTiO3, and CaTiO3) formed under similar conditions [74, 75]. The intensity ratio of ion currents in the mass spectra of vapor over perovskite obtained at laser pulse duration of 800–1000 μs at a wavelength of 6943 Å and energy of 3–5 J was as follows:
is 4890 ± 70 K, which is approximate, but does not contradict the conditions of similar laser-impact mass spectrometry experiments in the range 4000–6000 K.
Banon et al.  studied the evaporation of the CaTiO3-Ti2O3-TiO2 melts from molybdenum Knudsen effusion cells at 1900–2200 K by differential mass spectrometry. The mass spectra were recorded at a low ionizing voltage of 13 eV in order to avoid possible fragmentation of the TiO2+ molecular ion into Ti+ and TiO+ fragmentation ions, which were also molecular ions.
Atomic calcium was the dominant component of the gas phase over the composites. The complex gaseous oxide (CaTiO3) was not detected. The partial pressures of the (Ca), (TiO), (TiO2), and (O) vapor over perovskite at 2150 K were calculated using the thermochemical data of  and are shown in Figure 7 as a function of the inverse temperature (for easily understanding, the temperature scale was scaled appropriately).
Gaseous perovskite was also not detected in the mass spectrometric studies of high-temperature evaporation of various compositions of the CaO-TiO2-SiO2 system from molybdenum and tungsten Knudsen effusion cells at 1700–2500 K [53, 63, 82, 83] presumably because the sensitivity of the equipment used in [63, 83] was insufficient for determining the CaTiO3+ ion or because this was not the purpose of the study [53, 82].
Lopatin and Semenov  studied the evaporation of a mixture of calcium carbonate and titanium dioxide from tungsten cells by the Knudsen effusion mass spectrometry method in the temperature range 2100–2500 K. The following ions were detected in the mass spectra of vapor over the mixture: Ca+, CaO+, Ti+, TiO+, TiO2+, and CaTiO3+. The energies of ion appearance in the mass spectra allowed the authors to determine the molecular origin of the Ca+, CaO+, TiO+, TiO2+, and CaTiO3+ ions. The TiO+ ion also contained a fragment component of the TiO2+ ion, and the Ti+ ion was completely fragmentary. The energy of appearance of the CaTiO3+ molecular ion was determined to be 9 ± 1 eV (the energy of appearance of the gold ion was used as a standard). The partial pressures of vapor species (
and subsequently calculate the enthalpies of formation (Δ
|(CaTiO3) = (CaO) + (TiO2)||2287–2466||545 ± 8||284 ± 44||28 ± 19|||
|2000||—||298 ± 30||—|||
|1956–2182||—||287 ± 12||18 ± 6|||
|[Ca] + [Ti] + 3/2(O2) = (CaTiO3)||2287–2466||−826 ± 26||—||—|||
|1956–2182||—||−760 ± 10||−242 ± 5|||
|(CaTiO3) = (Ca) + (Ti) + 3(O)||2287–2466||2225 ± 26||—||—|||
|2000||—||1983 ± 81||—|||
|1956–2182||—||1993 ± 15||396 ± 7|||
|[CaTiO3] = (CaTiO3)||2000||—||1030 ± 22||—|||
|1956–2182||—||1027 ± 10||297 ± 5|||
Zhang et al.  studied the isotope fractionation of calcium and titanium during the evaporation of a perovskite melt suspended on an iridium wire in a vacuum furnace at a temperature of 2278 K (according to Langmuir method). The change in the composition of the residual perovskite melt during evaporation suggested that the component that evaporated predominantly from the melt was its calcium component. The total vapor pressure over perovskite could be evaluated from the data obtained (Figure 7).
The TiO2+, Ca+, TiO+, and O+ ions prevailed in the mass spectra of vapor over perovskite and its melts at the ionizing electron energy of 20 eV, as well as other ions characteristic of the mass spectra over individual oxides [57, 58, 71]. A small amount of CaTiO3+ ion was observed, which was fragmented into CaTi+, CaTiO+, and CaTiO2+ ions (::: = 6:10:13:100). The ratio of the ion current intensities in the mass spectra of vapor over perovskite at 2182 K was the following:
The ratio of the ion current intensities in the mass spectra of vapor over perovskite melt containing 57.81 ± 0.15 mol% TiO2 at 2278 K was the following:
The presence of MoO
as well as the interaction of perovskite with the cell material (:
Note that Berkowitz et al.  found that during evaporation of titanium oxide from a molybdenum liner inserted into a tantalum crucible at 1881 K, was initially 10–102 times higher than . The value gradually decreased and became comparable with the value, which is significantly different from the other results [52, 53, 56, 64, 77, 82]. The high observed in  probably was due to poor quality of the molybdenum liner material (or its alloy). Possibly it was made using powder technology from MoO3 reduced to metal molybdenum at ∼1300 K. It could lead to such an excess of partial pressure of (MoO3) and its decrease as it evaporates from the surface layers of the liner material.
The appearance energies of ions in the mass spectra of vapor over perovskite were determined by the Warren method  and corresponded to the accepted values of the ionization energies of atoms and molecules . The appearance energy of CaTiO3+ ion in the mass spectra of vapor over perovskite was equal to 8.5 ± 0.6 eV (the appearance energy of silver ion was used as a standard) and corresponded to obtained by Lopatin and Semenov .
The established molecular composition of the gas phase over perovskite allowed us to draw a conclusion on the predominant evaporation of perovskite according to the reactions (17), (18), (20), (23), (24), and (25), typical for evaporation of simple oxides [57, 71, 78, 86]. The presence of a small amount of (CaTiO3) molecules in the gas phase over perovskite is probably due to the reaction:
The partial pressure values of vapor species in the gas phase over perovskite were determined by the Hertz-Knudsen equation, written in the following form :
The Clausing coefficient is associated with the collision of vapor species inside the effusion orifice channel of effusion cell and their reverse reflection from the channel walls. Its value does not exceed 1 and depends on the ratio of the diameter of the effusion hole to its thickness.
Taking into account predominance of typical for CaO and TiO2 vapor species in the gas phase over perovskite and small amounts of CaTiO3, the α
The partial pressure of atomic oxygen determined using the relationships (38) and (39) agrees satisfactorily with those calculated using the thermochemical data  on
It should be noted that the
As it follows from Figure 8a, the defined partial pressures of vapor species over perovskite can be represented as linear logarithmic dependence vs. the inverse temperature:
which allows to determine the enthalpy () and entropy () of a reaction.
The partial pressures of the predominant vapor species of the gas phase over perovskite (Ca, TiO, TiO2 and O) are compared in Figure 7 with the results on evaporation of simple oxides (CaO and TiO2) under similar redox conditions caused by the interaction of oxygen with molybdenum [79, 81], tungsten , and tantalum  effusion cells or in chemically neutral conditions (in the absence of this interaction) for alundum cell .
We used the TiO and TiO2 activities as well as the Gibbs energy of perovskite obtained by Banon et al.  and thermochemical data  on equilibriums (17), (18), (23), and (24) to estimate the partial pressure of vapor species over the perovskite at 2150 K. Therefore, the obtained values characterized by the evaporation of perovskite were not under reducing conditions (from molybdenum cell), but, in contrary, under chemically neutral conditions (in the absence of interaction of perovskite with the cell material).
Figure 7 also shows the partial pressures of vapor species over calcium and titanium oxides calculated using thermochemical data . By comparison of the experimental data obtained in [71, 77, 78, 79, 80, 81] and the calculated results, we can see the effect of reducing properties of cell materials on gas phase composition: tantalum , molybdenum [79, 81], tungsten , and alundum . As we noted earlier , the greatest effect of cell materials on the vapor composition are observed with the oxygen-“deficient” species such as atomic calcium (Figure 7a), titanium monoxide (Figure 7b), and atomic oxygen itself (Figure 7d). There are no differences in the partial pressure of gaseous titanium dioxide (Figure 7c) determined in evaporation experiments using molybdenum  and tungsten  cells.
The total vapor pressure over the perovskite melt at 2278 K obtained by Zhang et al.  is consistent with the extrapolated values of partial pressures of the predominant vapor species of the gas phase—atomic calcium and titanium dioxide (Figure 7a and c) found in .
Similar slopes of lg
The enthalpy and entropy of reactions involving CaTiO3 gaseous complex oxide calculated by the relationship (46) are given in Table 3. They are in a good agreement with those found by Lopatin and Semenov  and our earlier estimates .
The concentration dependences of partial pressures of vapor species over perovskite melts show a sharp decrease in
The thermodynamic properties of perovskite determined by different calorimetric approaches and EMF method agree with the results obtained via Knudsen effusion mass spectrometry at high temperatures. The resulting values of oxide activities in perovskite, as well as the Gibbs energy, the entropy and enthalpy of the formation of perovskite from simple oxides, and the melting enthalpy of perovskite are consistent with each other. The enthalpy of perovskite formation is constant throughout the temperature range, and the entropy of perovskite formation tends to increase slightly.
The oxide activities in perovskite melts were determined by mass spectrometric Knudsen effusion method. The thermodynamic properties of melts (chemical potentials of oxides and mixing energies, as well as partial and integral enthalpies and entropies of melt’s formation) were calculated based on the experimental data. The obtained experimental information testifies to the symbate behavior of thermodynamic functions characterizing the melts. The extreme values of the integral thermodynamic properties of melts are in the concentration region close to perovskite, which confirms its stability in the melt. The displacement of the extremum of the integral thermodynamic functions in the CaO-TiO2 melts can be caused by the presence in the melt of oxide compounds with a large amount of CaO compared to perovskite. A comparison of mixing energies in the CaO-TiO2 melts with those for the CaO-SiO2 and CaO-Al2O3 melts indicates a stronger chemical interaction in the CaO-TiO2 melts than the similar CaO-Al2O3 melts, but smaller than in the CaO-SiO2 melts.
The evaporation of perovskite and its melts from a molybdenum cell at high temperature was studied by the Knudsen effusion mass spectrometric method. The molecular components typical of simple oxides and the (CaTiO3) gaseous complex oxide were identified in the gas phase over perovskite. The partial vapor pressures of the molecular components of the gas phase over perovskite were determined. A comparison of these values with the available experimental data and with the values corresponding to simple oxides showed that the character of perovskite evaporation is mainly affected by the calcium component of perovskite. The observed concentration dependences of the partial pressures of vapor species over the perovskite melts correspond to those characterizing the condensed phase.
This study was financially supported by the Presidium of the Russian Academy of Sciences (Program No. 7 “Experimental and Theoretical Studies of Solar System and Star Planetary System Objects. Transition Processes in Astrophysics”) and by the Russian Foundation for Basic Research (Grant No. 19-05-00801A “Thermodynamics of Formation Processes of Substance of Refractory Inclusions in Chondrites”).
I am grateful to Oleg Yakovlev (Vernadsky Institute of Geochemistry and Analytical Chemistry of the Russian Academу of Sciences) for his constant interest in this study and useful discussions and to Mikhail Nazarov (Vernadsky Institute of Geochemistry and Analytical Chemistry of the Russian Academу of Sciences) for his support during this work. I express my special gratitude to Marina Ivanova (Vernadsky Institute of Geochemistry and Analytical Chemistry of the Russian Academу of Sciences; National Museum of Natural History of Smithsonian Institution) for her help in working on the manuscript.
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