INTRODUCTION

Geodynamic, petrological, and geochemical processes are largely controlled by phase relations in peridotites. Information on peridotites is commonly inferred from data obtained (1) in experiments (Zhang and Herzberg, 1994; Robinson et al., 1998; Laportе et al., 2004; Brey et al., 2008; Keshav and Gudfinnsson, 2021) and by studying (2) xenoliths in deep magmas (Boyd et al., 1997; Kopylova et al., 1999; Rudnick et al., 2004; Griffin et al., 2009; Arai and Ishimaru, 2008; Liu et al., 2021), (3) peridotites in orogenic belts (Shmelev, 2011; Dobrzhinetskaya et al., 1996; Scambelluri et al., 2010; Medaris et al., 2018), and (4) abyssal peridotites (Silantyev et al., 2015). Petrological studies of metamorphic complexes are lately often carried out with the application of the Perple_X (Connolly, 2009) and THERMOCALC (Powell et al., 1998) software packages. Their usage, together with thermodynamic data on deep mantle minerals (Jennings and Holland, 2015; Holland et al., 2013; Stixrude and Lithgow-Bertelloni, 2011), opens new avenues for studying phase relations in peridotites and other lithologies in different mantle layers (e.g., Klein et al., 2017).

The chemical heterogeneity of the mantle (O’Neill and Palme, 1998; Hofmann, 2003; Frost et al., 2018) considerably complicates determining its average composition, which is employed in solving a broad spectrum of problems in geosciences (McDonough and Sun, 1995; Palme and O’Neill, 2004). The average compositions of the mantle currently most widely used by various researchers can be classified into the following three major groups (Table 1). The first one comprises model compositions of the so-called primitive mantle (Primitive Mantle or Bulk Silicate Earth) that had occurred during the early Earth’s evolution, before its crust was melted out. This group also includes the compositions of pyrolite, a hypothetical rock made up of dunite and basalt in a certain proportion (Ringwood, 1975). The second group consists of the model compositions of the depleted mantle produced after the mantle and core were segregated from one another. Because the crust makes up as little as 1% of the bulk silicate Earth (White, 2013), the major-component model compositions of the former two groups are closely similar (Table 1). However, differences in concentrations of some trace elements (for example, LREE and LILE) can be significant (Salters and Stracke, 2004). The third group is made up of the compositions of natural peridotites, which are the closest to the composition of the model primitive mantle. Fresh, slightly altered varieties of such peridotites are widely employed as starting compositions in experimental studies (Table 1). A composition nowadays used by many experimentalists is that of spinel lherzolite KLB-1 from the Kilbourne Hole volcanic crater, New Mexico, United States (Takahashi, 1986; Herzberg et al., 1990; Agee and Walker, 1993; Hirose and Kushiro, 1993; Takahashi et al., 1993; McFarlane et al., 1994; Zhang and Herzberg, 1994; Hirose and Kawamoto, 1995; Herzberg and Zhang, 1996; Hirose, 1997a, 1997b; Wang and Takahashi, 2000; Hirose, 2002; Hirose and Fei, 2002; Matsukage and Kubo, 2003; Yoshino et al., 2004) (Table 1). This lherzolite composition was recently applied in thermodynamic modeling (Holland et al., 2013, 2018; Klein et al., 2017).

Table 1. Chemical composition (wt %) of the mantle
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In this publication, we turn again to the thermodynamic modeling of phase relations in spinel lherzolite KLB-1 (Takahashi, 1986) to analyze the mineralogy of the various Earth’s mantle layers and boundaries between them during the early Earth’s evolution. In order to justify the key conclusions, we compare the results of thermodynamic modeling using different databases and models of solid solutions, and compare them with experimental data. The results are discussed in the scope of petrology and geodynamics.

MODELING PHASE RELATIONS

The phase relations were modeled with the Perple_Х program package ver. 6.9.0 (Connolly, 2009) for the composition of spinel lherzolite KLB-1 (Table 1) without K2O, P2O5, Cr2O5, and NiO (these components were not included in the models of the mineral solid solutions), at temperatures of 600–2000°C and pressures of 0–30 GPa (depths of 0–800 km). The simulations for the NCFMAS system were carried out using the thermodynamic database hp622ver.dat (Holland and Powell, 2011) and models of solid solutions specified in the program with the following symbols: Cpx(JH), Opx(JH), Hpx(H), Gt(H), Melt(JH), Mpv(H), O(JH), Ring(H), and Wad(H), where Hpx is high-pressure clinopyroxene, which replaces orthopyroxene in the upper mantle, Mpv is Mg-perovskite, which was named bridgmanite [Brd in (Tschauner et al., 2014)], JH is models for the upper mantle under pressures up to 6 GPa (Jennings and Holland, 2015), H is models for the deep mantle, including the transition zone and lower mantle (Holland et al., 2013). Garnet is the only mineral of the upper mantle that remains stable in the transition zone and occurs there as the high-density majorite phase, which can dissolve Na. Inasmuch as this component is not included in the Grt(JH) model, we applied the universal model Gt(H), which is applicable to the upper mantle and transition zone.

MODELING RESULTS

Phase relations simulated for spinel lherzolite KLB-1 are shown in a P–T diagram in Fig. 1. This diagram makes it possible to follow principal phase transformations occurring in this composition: the dry liquidus line, the boundaries between the depth facies of the lherzolite (the plagioclase, spinel, and garnet lherzolite facies) at pressures up to 2 GPa, phase transitions in the mantle, and its upper and lower boundaries.

Fig. 1.
figure 1

P–T phase diagram for the composition of spinel lherzolite KLB-1 in the NCFMAS system, calculated with the Perple_Х ver. 6.9.0 software complex (Connolly, 2009), database (Holland et al., 2011), and mixing models (Jennings and Holland, 2015; Holland et al., 2013). Phases: Aki is akimotoite, Cpv is calcic perovskite, NAl is an Al phase (CaMg2Al6O12–NaNa2Al3Si3O12), Brd is bridgmanite, and Fper is ferropericlase. Conductive geotherms are according to (Polack and Chapman, 1977) for the continental lithosphere and (Turkotte and Schubert, 1985) for the oceanic lithosphere. Mantle adiabats are for potential mantle temperatures Tр = 1300°C (modern) and Tр=1550°C (Archean). Peridotite solidus: violet line—this publication, white dashed line—data from (Katz et al., 2003), and white dotted line—data from (Zhang and Herzberg, 1994; Takahashi, 1986). Regular polygons show the mineralogical composition and P–T parameters of experiments (Takahashi, 1986; Zhang and Herzberg, 1994; Herzberg and Zhang, 1996; Hirose, 2002; Matsukage and Kubo, 2003). Experiments (Hirose, 2002) are characterized by a pressure uncertainty of ±(1.0–1.2) GPa. Experimental results by (Takahashi, 1986) at a pressure of <5 GPa are in good agreement with our data but are not shown because they overlap some fields of the phase diagram.

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Note that much of the diagram (at upper-mantle pressures) is covered by the field of the mineral assemblage of garnet wehrlite (Grt + Ol + Cpx)Footnote 1, which occurs between the modern adiabat (approaches it at 4–6 GPa and deviates farther from it at higher and lower pressures) and the dry liquidus line (Fig. 1). At lower temperature, garnet lherzolite is stable (its higher pressure variety contains high-pressure pyroxene, Hpx, instead of orthopyroxene, Opx), a typical fertile mantle peridotite.

Mineral assemblages with wadsleyite, an olivine polymorph, mark the upper boundary of the mantle transition zone by a line positively sloped in P–T diagram at T > 1100°C. The line intersects the modern adiabat at a depth of about 410 km (Fig. 1). Interestingly, the first an assemblage to be formed at lower temperatures and pressures is that with ringwoodite (ringwoodite is another olivine polymorph, which is stable at greater depths than wadsleyite). Mineral assemblages with ringwoodite (without wadsleyite) are indeed widespread on the modern adiabat at pressures corresponding to the lower part of the mantle transition zone, from ~19 GPa to the boundary between the lower mantle and transition zone. This boundary line is negatively sloped in P–T space at 1850°C and 23 GPa and crosscuts the modern adiabat at a depth close to 660 km. At higher temperatures, ringwoodite is absent, and the slope of the line becomes positive (Fig. 1). A positively sloped line divides the deeper and shallower mineral assemblages, Grt + Fper + Cpv and Grt + Brd + Cpv + Fper, respectively, in P–T diagram.

Transformations of mineral assemblages and modal relations of minerals were traced along various geotherms (Fig. 2). The oceanic geotherms were calculated according to (Turcotte and Schubert, 2002) for a 60-Ma plate and the modern mantle (the potential temperature Tр = 1300°C, ΔT = Tp – Tр, modern = 0) and the Archean mantle (Tр = 1550°C, ΔT = 250°C), respectively. For the modern mantle, we have also calculated the continental geotherm corresponding to a heat flow of 45 mW/m2 (Pollack and Chapman, 1977) and a thickness of the thermal lithosphere of about 200 km. We have not calculated the Archean continental geotherm because of the significant uncertainties in the thickness, inner structure, thermal state, and other parameters of the continental crust and its lithospheric mantle (Brown et al., 2020).

Fig. 2.
figure 2

Modal abundances of minerals and densities calculated for the bulk composition of spinel lherzolite KLB-1 at pressure varying along various geotherms (Fig. 1). (a) Variations in modal abundances of minerals along the modern continental geotherm at a heat flow of 45 mW/m2; (b) variations in modal abundances of minerals along the modern oceanic geotherm; (c) variations in modal abundances of minerals along the Archean oceanic geotherm at Tр = 1550°C (ΔT = 250°C); (d) variations in the density of mineral assemblages along the continental and oceanic geotherms.

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Note similar modal abundances of minerals in the continental and oceanic lithosphere for the modern geotherms (Figs. 2a, 2b). The significant differences in the mineralogical and modal compositions are clearly seen when the modern and Archean oceanic geotherms are compared. First of all, it is worth mentioning the absence of ringwoodite from the lower transition zone, because of which the garnet content is much higher and ferropericlase becomes stable. Moreover, the Archean mantle at pressures above ~3 GPa contains no orthopyroxene, i.e., the mantle mineralogy corresponds to that of wehrlite.

Pressure and temperature variations along the modern continental geotherm significantly affect not only the modal contents of the monoclinic and orthorhombic varieties of pyroxenes (which define the names of the peridotites and pyroxenites) but also the compositions of the minerals (Fig. 3). For example, a temperature increase to 1350oC along the geotherm (dominantly, the parameters of the lithospheric mantle) is associated with that Ca isopleths [ХCа = Cа/(Cа + Mg)] in the pyroxenes become more closely spaced, which is caused mostly by changes in the composition of the clinopyroxene, because it dissolves the enstatite end-member (Fig. 3). An analogous phenomenon is well known from the exsolution curves of En–Di solid solution in shallow-depth pyroxene (Lindsley, 1983). At higher temperatures and pressures above 3–6 GPa, the isopleths of the pyroxene deviate wider from one another again (Figs. 3a, 3b). The concentration of the jadeite end member in the clinopyroxene varies within the range of 8–14 wt % and only insignificantly depends on the P–T parameters. The jadeite content drastically increases (up to 19 mol %) only on the Archean geotherm in the upper mantle transition zone.

Fig. 3.
figure 3

Variations in the composition of pyroxenes in the enstatite–diopside solid solution for the composition of spinel lherzolite KLB-1 in the upper mantle calculated for the geotherms shown in Fig. 1 depending on (a) temperature and (b) depth (pressure).

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Variations in density were traced along the modern and Archean geotherms (Fig. 2d). The most significant density jumps were detected at the upper and lower boundaries of the mantle transition zone, where wadsleyite and bridgmanite, respectively, become stable. The jump at the lower boundary of the modern mantle is twice as great as at the lower one, is more rapid, and the curve shows a kink at the point where ringwoodite becomes unstable. The density change near the lower boundary is smoother. The density profiles obviously show that the transition zone was somewhat thinner in the Archean than nowadays (Fig. 2d).

The phase diagram in Fig. 1 also shows experimental data on the composition of spinel lherzolite KLB-1 (Takahashi, 1986; Zhang and Herzberg, 1994, Herzberg and Zhang, 1996; Hirose, 2002; Matsukage and Kubo, 2003) and currently widely used dry solidus lines (Zhang and Herzberg, 1994, Takahashi et al., 1993; Katz et al., 2003). The P–T parameters of most of the experiments lie in the high-temperature (T ≥ 1500°C) region of the upper mantle and transition zone, closer to its boundary with the lower mantle. The diagram is reasonably well consistent with experimental data for composition KLB-1. This pertains, for example, to the position of the dry liquidus and the stability field of the mineral assemblage of garnet wehrlite in subsolidus experiments under upper mantle pressures of >4 GPa. Note that the calculated dry solidus of average lherzolite (Katz et al., 2003) occurs at lower temperatures than the solidus based on our data, with the difference between the lines increasing from 20 to 80°C with increasing pressure (Fig. 1).

Experimental data (Zhang and Herzberg, 1994) are in good agreement with our data on the stability of garnet wehrlite in the subsolidus region and on the location of the solidus line (Fig. 1). However, the mineral assemblage of garnet lherzolite is stable in experiments at 5 GPa between the solidus and liquidus (Zhang and Herzberg, 1994, Table 2), but this assemblage is missing in our diagram (Fig. 1). It is worth mentioning that the diagrams in (Zhang and Herzberg, 1994; Herzberg and Zhang, 1996) are much better consistent with our data than the mineral assemblages listed in Table 2 according to experiments in (Zhang and Herzberg, 1994). It is also worth noting that differences with experimental data by (Takahashi, 1986) are insignificant. For example, lherzolite and wehrlite mineral assemblages were found out to contain spinel relics and metal, the stability field of garnet lherzolite extends to 1600°C at 5 GPa and 1500°C at 7.5 GPa, and this field is wider than according to our data in Fig. 1. Note that the modal abundancy of orthopyroxene in the experimental products is not reported by the authors, and this does not rule out the occurrence of the wehrlite mineral assemblage with accessory amounts of orthopyroxene.

Experimental data by (Hirose, 2002) at P–T parameters near the lower boundary of the transition zone, whose pressure is poorly constrained (uncertainty up to 1.2 GPa), are generally in good agreement with our model mineral assemblages, but the boundaries between the fields are not always strictly consistent. Note that the newly found aluminum–silicate phase NAl (Mookerjee et al., 2012) was not identified in the experimental products, but our diagram predicts its occurrence (Fig. 1), and bridgmanite was identified in the products of experiments at pressures above ~22 GPa, which corresponds to the mantle transition zone (Fig. 1).

We failed to find any experimental data on composition KLB-1 under the P–T parameters of the ringwoodite-free region, and the occurrence of this region thus calls for experimental verification.

DISCUSSION

Phase Diagrams for Spinel Lherzolite KLB-1

The thermodynamics of minerals stable in the deep mantle in the NCFMAS system was studied by two groups of researchers (Holland et al., 2013; Stixrude and Lithgow-Bertelloni, 2011, 2012), and we compared our results with their data. As has been shown above, our results are mostly consistent with published experimental data (Fig. 1).

Our calculated phase diagram is closely similar to that in (Holland et al., 2013, Fig. 1), as is expectable in view of that both were calculated using the same thermodynamic database and mixing models for deep minerals. The differences between the diagrams stem from the fact that the authors (Holland et al., 2013, Fig. 1) used the THERMOCALC program complex with lower P–T ranges (T = 1200–2000°C and P = 4–30 GPa) than in our work and also utilized somewhat different models for the solid solutions of pyroxenes and garnet in the upper mantle. Differences are seen, first of all, in relations between the fields of garnet lherzolite (Hрх that replaces Opx at high pressures is monoclinic, but its composition corresponds to that of orthopyroxene, and hence, we regard the mineral assemblage as lherzolitic). The boundary between the Opx + Cpx + Ol + Grt and Hpx + Cpx + Ol + Grt fields is shown in (Holland et al., 2013) at higher temperatures than in Fig. 1. Orthopyroxene occurs in mineral assemblages on the adiabat (asthenospheric mantle) in accessory amounts (no more than 3 vol %), the amounts of the high-pressure pyroxene (Hpx) replacing it at pressures of ~8 GPa vary within 4–8 vol %, and it becomes unstable in the mantle transition zone at ~14 GPa (Holland et al., 2013). Our data indicate (Fig. 2) that high-pressure pyroxene appears in very small amounts (no more than 1 vol %) at pressures of ~8–13 GPa. Orthopyroxene is almost absent from the asthenosphere (except its negligibly small amounts at pressures of 7–8 GPa), but its amount dramatically increases as the lithospheric temperature decreases from 5 GPa in the oceanic lithosphere and 6 GPa in the continental one, and reaches 10 vol % at 2 GPa in both (Fig. 2). The amount of orthopyroxene increases mostly at the expense of garnet and clinopyroxene in the oceanic lithosphere (Fig. 2a) and mostly at the sacrifice of clinopyroxene in the continental lithosphere (Fig. 2b).

Calculations in (Holland et al., 2013) also predict a ringwoodite-free area in the mantle transition zone and a related change in the slope of the boundary line between the transition zone and lower mantle. However, neither this mineralogical feature of the mantle nor related effects were discussed in (Holland et al., 2013).

It has been demonstrated (Stixrude and Lithgow-Bertelloni, 2011, 2012) that the field of garnet wehrlite occurs at T > 2000°C, which is ~700°C higher than our estimates. Because of this, the orthopyroxene content on the modern adiabat (in the asthenosphere) may, according to these authors, reaches 10 vol %. However, these calculations were made not for spinel lherzolite KLB-1 but for the pyrolite mantle according to the model (Workman and Hart, 2005) in the NCFMAS system (wt %: SiO2 = 44.93, Al2O3 = 4.37, FeOt = 8.56, MgO = 38.81, CaO = 3.19, and Na2O = 0.13). To eliminate the effect of the chemical composition of the system, we first exactly reproduced the phase diagram in (Stixrude and Lithgow-Bertelloni, 2011, Fig. 16) by using the composition of the system from this publication in simulations with the Perple_Х software complex [ver. 6.9.0, with thermodynamic database stx11ver.dat and models of solid solutions from stx11_solution_model.dat: Cpx, Gt, Pv, O, Opx, Ring, Wad, Wus, C2/c, and Aki (Stixrude and Lithgow-Bertelloni, 2011), where О is olivine, Pv is perovskite, and C2/c is clinopyroxene (HughJones et al., 1996)] and then calculated a phase diagram for composition KLB-1 (Table 1, Fig. 4). The configurations of fields with the Grt + Opx + Cpx + Ol mineral assemblage (generally speaking, garnet lherzolite) and Grt + Cpx + Ol (wehrlite) in this diagram are different and close to that in Fig. 1, with the boundary shifted for ~100°C toward higher temperatures. Because of this, almost the whole modern geotherm is constrained within the field of the four-phase mineral assemblage Grt + Opx + Cpx + Ol (Fig. 4). However, orthopyroxene occurs in accessory amounts (no more than 3 vol %) at the P–T parameters of the adiabat and is replaced by high-pressure pyroxene at pressures above 10 GPa. At this modal composition, the mineral assemblage corresponds to garnet wehrlite.

Fig. 4.
figure 4

Phase diagram in P–T space calculated for the composition of spinel lherzolite KLB-1 in the NCFMAS system with the Perple_X ver. 6.9.0 (Connolly, 2009) and with the thermodynamic database and mixing models (Stixrude and Lithgow-Bertelloni, 2011). Note the wide field of the mineral assemblage Grt + Cpx + Opx (garnet wehrlite) in the upper mantle and the absence of ringwoodite from the mantle transition zone at T ~ 1980°C.

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It is important to mention that this thermodynamic dataset also predicts that ringwoodite ceases to be stable, and the aforementioned change in the slope of the boundary line between the transition zone and lower mantle takes place (Fig. 4). However, the kink of the line occurs at T ~1980°C, i.e., at a higher temperature than one shown in Fig. 1.

Note that the thermodynamic database (Stixrude and Lithgow-Bertelloni, 2011) does not involve melting processes, i.e., it does not allow one to compare the results with the extensive massif of experimental data. Because of this, we did not consider this database as a preferable one.

Available thermodynamic data predict major effects for the composition of spinel lherzolite KLB-1 related to the broad stability of garnet wehrlite in the upper mantle and the occurrence of a ringwoodite-free mantle transition zone that can be formed at some temperatures.

Wehrlite Upper Mantle?

Wehrlites, including their garnet varieties, are relatively rare peridotite types in orogens, abyssal regions, and ophiolites (Fig. 5). These rocks are also scarce among mantle xenoliths entrained by arc volcanic rocks (Arai and Ishimary, 2008, Fig. 3). Xenoliths of mantle peridotites (both fresh and metasomatized) in kimberlites are also mostly lherzolites, harzburgites, and more rare dunites (Griffin and O’Reilly, 2009). With regard to this, the widespread occurrences of wehrlites in the asthenospheric mantle predicted by experimental data and thermodynamic simulations for the composition of spinel lherzolite KLB-1 (Figs. 1, 4) look like paradoxical and deserve discussion. The position of geotherms at Tp = 1550oC (ΔT = 250°C) in Р–T space indicates that wehrlites may have occur in the Archean mantle much more widely than these rocks are now found on the surface.

Fig. 5.
figure 5

Ol–Opx–Cpx triangular plot showing variations in the calculated modal abundances of these minerals along the geotherms shown in Fig. 1. The reason for the occurrence of accessory amounts of orthopyroxene at depths greater than 200 km is that the phase Hpx is there stable. Composition fields of natural peridotites are according to (Bodinier and Godard, 2003). The small red circle displays the modal composition corresponding to the chemical composition of spinel lherzolite KLB-1 (Table 1) at 1 GPa (~30 km) and 950°C (Perkins and Anthony, 2011). See text for details.

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If composition KLB-1 is indeed representative of the upper mantle, then the rarity of wehrlites among mantle rocks brought to the Earth’s surface may be explained by a valuable temperature change on the geotherms of the lithospheric mantle, which are contrastingly different from the small temperature changes (0.5°C/km) along the adiabat in the asthenospheric mantle (Fig. 1). For example, ascent to the surface along a continental geotherm with a heat flow of 45 mW/m2 shall be associated with an increase in the modal amount of orthopyroxene (Fig. 5). At ascent along a continental geotherm corresponding to 120 mW/m2, the modal orthopyroxene content shall increase even more significantly (Fig. 5), because the mineral reaction Ol + Grt → Opx + Spl consumes olivine and garnet with the transition from the depth facies of garnet lherzolites to that of spinel lherzolites.

The presented phase diagram and corresponding continental geotherms clearly indicates that peridotite xenoliths from kimberlite pipes cannot strictly represent the mineral assemblages of the Early Precambrian mantle when the protokeels were formed (e.g., Perchuk et al., 2020), because these xenoliths are brought to the surface by relatively young (Phanerozoic) magmas from anomalously cold mantle regions, which were conductively cooled over 2.5 Ga and longer (Eaton and Perry, 2013). The slow cooling of these rocks resulted in changes in the modal abundances of clinopyroxene and orthopyroxene and formed the lherzolitic mineral assemblages instead of the wehrlitic one in the mantle.

Another source of information on the composition of the mantle is deep off-arc magmas, first of all, those in oceanic hotspots (Sobolev et al., 2005; Herzberg et al., 2010). The composition of these volcanic rocks is controlled by the bulk chemical composition of the mantle source. However, by analogy with that Ni concentration in melt makes it possible to conclude that the mantle sources contained elevated amounts of pyroxenite (Sobolev et al., 2005), it cannot be ruled out that it will be sometimes possible to infer a wehrlite composition of a source from the concentrations of other trace elements.

Component Composition of the Model System

Results of thermodynamic simulations presented in this paper for the composition of spinel lherzolite in the six-component system NCFMAS can be further refined and specified by adding trace elements (Table 1). The availability of pertinent thermodynamic data now makes it possible to evaluate the effects of Cr (KLB-1: Cr2O3 = 0.31 wt %) and Fe3+ (Fe2O3 = 0.3 wt %) in the mineral assemblages of this lherzolite at pressures up to 6 GPa (Jennings and Holland, 2015). For example, the addition of up to 0.31 wt % Cr2O3 to the system (Cr is accommodated mostly in spinel, garnet, and clinopyroxene) almost does not modify the P–T parameters of the transition from spinel lherzolite to garnet lherzolite but diminishes the stability field of plagioclase lherzolite. For example, at 1000°C this takes place partly because of the extension (by ~1 kbar) of the stability field of spinel lherzolite, primarily because of the origin of a broad field in which both plagioclase and spinel are stable in lherzolite (Jennings and Holland, 2015, Fig. 3). Note that Cr concentrations in most orogenic, ophiolitic, and abyssal peridotites are lower than in spinel lherzolite KLB-1 (Bodinier and Godard, 2003) and is slightly higher in some model mantle compositions (Table 1).

Much attention is nowadays focused on oxygen fugacity in the mantle as an important thermodynamic parameter that significantly controls the composition of the minerals, mineral reactions, and rock melting (Woodland et al., 2006; Rohrbach et al., 2007; Foley, 2011; Frost and McCammon, 2011). One of the most important indicators of oxygen fugacity is Fe2O3 concentration in minerals (rocks). The Fe2O3 concentration of spinel lherzolites is controlled by spinel and pyroxenes, varies within 0.1–0.3 wt % (Woodland et al., 2006; Frost, McCammon, 2011), and reaches 0.3 wt % in spinel lherzolite KLB-1 (Jennings and Holland, 2011). Thermodynamic calculations for KLB-1 composition within 0.001–6 GPa and at temperature from 800°С to solidus showed that spinel peridotite stability field widens as the amount of Fe3+ increases (Jennings and Holland, 2015). For example, the boundary between spinel lherzolite and garnet lherzolite at 1100°C is raised to ~0.1 GPa, and the transition zone between spinel and plagioclase lherzolite occurs at a pressure lower by ~0.05 GPa. These changes are hardly discernible in the phase diagram, in which the pressure changes within the range of 0 to 30 GPa (Fig. 1). Nevertheless, these corrections shall be taken into account when processes in the shallow upper mantle are considered.

According to (Foley, 2011), oxygen fugacity in the upper mantle decreases with depth from FMQ-1 (fayalite–magnetite–quartz buffer minus 1 log unit) in the lithospheric mantle to FMQ-4 closer to the boundary with the mantle transition zone. In spite of the lower oxygen fugacity, the garnet may contain the high-pressure skiagite end-member (Fe2+3Fe3+2Si3O12), which can be formed by the redox reaction

$$\begin{gathered} 4{\text{F}}{{{\text{e}}}_{{\text{2}}}}{\text{Si}}{{{\text{O}}}_{{\text{4}}}}\left( {{\text{in}}\,\,{\text{olivine}}} \right) + {\text{F}}{{{\text{e}}}_{{\text{2}}}}{\text{S}}{{{\text{i}}}_{{\text{2}}}}{{{\text{O}}}_{6}}\left( {{\text{in}}\,\,{\text{pyroxene}}} \right) \\ + \,\,{{{\text{O}}}_{2}} = {\text{2Fe}}_{3}^{{2 + }}{\text{Fe}}_{2}^{{3 + }}{\text{S}}{{{\text{i}}}_{{\text{3}}}}{{{\text{O}}}_{{{\text{12}}}}}\left( {{\text{in}}\,\,{\text{garnet}}} \right). \\ \end{gathered} $$

In experiments with model mantle compositions and anomalously high FeO concentrations, the content of the skiagite end-member in garnet in equilibrium with metallic iron increases with increasing pressure starting at 7 GPa (Rohrbach et al., 2007, 2011). These authors interpret this phenomenon as evidence that the upper mantle contains metallic iron. The redox reaction responsible for the origin of metallic iron in the deep part of the upper mantle involves olivine decomposition and can be written as

$${\text{F}}{{{\text{e}}}_{{\text{2}}}}{\text{Si}}{{{\text{O}}}_{{\text{4}}}}\left( {{\text{in olivine}}} \right) = 2{\text{Fe}}\left( {{\text{metal}}} \right) + {\text{Si}}{{{\text{O}}}_{2}} + {{{\text{O}}}_{2}}.$$

It is thus suggested that Fe2+ is partially disproportionated to form metallic iron and Fe3+ in the skiagite end-member of the garnet solid solution. The presence of Fe3+ in the starting composition shall constrain the origin of the metallic iron at high pressures. The P–T–\(f{\text{O}}2\) parameters under which metallic iron and the skiagite end-member is formed can be quantified by modeling phase equilibria for the composition of KLB-1 (as an approximation of the upper-mantle composition Table 1) requires further consideration.

Geodynamic Effects Related to the Presence or Absence of Ringwoodite

It is well known from experiments in simple chemical systems that the line corresponding to the olivine–wadsleyite phase transition (upper boundary of the mantle transition zone) is positively sloped in P–T diagram (Katsura et al., 2004; Акаogi, 2007), and that of the ringwoodite–bridgmanite transition (lower boundary) is negatively sloped (Akaogi, 2007; Bina, 1994; Hirose, 2002). Results of thermodynamic simulations in a chemically more complicated system (KLB-1, Fig. 1) than FMS, which was employed to study this phase transition, are well consistent with data on the slope of the upper boundary but partially with the lower one. It has been emphasized above that the absence of ringwoodite from the lower mantle transition zone at 1820°C (Fig. 1) or at ~1980°C (Fig. 4) changes the slope of this boundary line from negative to positive.

Phase transitions in the mantle related to the olivine ↔ wadsleyite and ringwoodite ↔ bridgmanite transitions are widely applied in modeling geodynamic processes, because the slopes (Clapeyron slopes) of the corresponding lines in P–T space largely control the movements of subducted slabs (Davies, 1995) and the ascent of plumes (Davies, 1995; Schubert and Tackley, 1995; Brunet and Yuen, 2000). For example, the geotherms of subducted slabs are always colder than the corresponding mantle adiabat, and hence, at a positive slope of the olivine → wadsleyite transition line (the temperature increases with increasing pressure), denser (heavier) wadsleyite becomes stable in the peridotitic part of the slab earlier than in the ambient mantle, which makes the slab heavier and facilitates its sinking (Fig. 6a). Conversely, if the slope of the lower boundary of the transition zone in P–T space is negative (i.e., temperature decreases with increasing pressure), the reaction ringwoodite → bridgmanite + Fe-periclase in the slab shall proceed outside the mantle transition zone. In this case, the lighter peridotitic part of the slab shall be surrounded by denser lower-mantle rocks (Fig. 6b), i.e., the phase transition shall then hamper slab entry into the lower mantle.

Fig. 6.
figure 6

Effects of phase transitions at the boundaries of the mantle transition zone on (a) a subducted slab and (b) ascending mantle plume. Left in each row: schematic temperature–depth diagrams with boundaries of the mantle transition zone, adiabats (green dashed lines), slab or plume geotherms (green arrows) for the present time and Archean. Near them: schematic representations of descending slabs or plumes ascending from the lower mantle, with deviations of the boundaries of the mantle transition zone from the present time (left) and Archean (right). The Archean slab geotherm is hypothetical. Blue fields are the mantle transition zone. See text for details.

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Unlike the modern adiabat, the Archean one occurred in the region with a positive slope of the lower boundary of the mantle transition zone in P–T space (Fig. 1), and hence, the geotherms of the slabs were often cooler (by 300°C and more) than the adiabat temperature, and their crossing the positively sloped phase-transition line can be discussed only as hypothetically possible. In this situation, slabs should have been additionally accelerated at the lower boundary of the transition zone (Fig. 6a).

The temperatures of ascending mantle plumes can be 100–400°C higher than that of the surrounding mantle (e.g., Thompson and Gibson, 2000; Herzberg and Gazel, 2009), and hence, the plume and slab geotherms shall occur on different sides of the mantle adiabat. At a negative slope of the transition zone boundary, ringwoodite shall be formed in the mantle later than in the surrounding mantle, and this shall hamper the buoyant ascent of the plume (Fig. 6b). Wadsleyite shall be transformed into olivine in the plume below the lower boundary of the mantle transition zone, and this shall facilitate the ascent of the plume. The same effect should have pertained in the Late Archean to the upper boundary of the transition zone. At the lower boundary of the transition zone, whose slope in P–T space is positive (Fig. 1), bridgmanite replacement by majorite garnet in a plume starts beneath the mantle transition zone and imparts additional buoyancy to the ascending diapir (Fig. 6b).

Thus, the onset of ringwoodite instability and ensuing change in the slope of the mantle transition zone boundary in P–T space may have stimulated mantle diapirism in the early Earth’s surface. Nowadays this effect can occur only in plumes, in which temperatures are reached close to those in the Archean mantle.

CONCLUSIONS

Thermodynamic modeling allows us to accurately reproduce available experimental data on mineral assemblages within wide temperature and pressure ranges, as well as experimental data on the melting parameters of the composition of spinel lherzolite KLB-1. The thermodynamic data will be possibly further corrected for the accommodation of Cr and Fe3+ in the structures of the minerals.

The thermodynamic data indicate that the modern upper mantle (if its composition is of KLB-1 type) is dominated by a mineral assemblage like that of garnet wehrlite, which is almost absent in the samples brought to the surface by deep magmas or tectonic processes. This is explained by that the lherzolite–wehrlite phase transition occurs only under pressures greater than 5 GPa (Figs. 1, 2a), whereas most of the xenoliths were formed under lower pressures.

The bend of the lower boundary of the mantle transition zone, which was predicted using various thermodynamic databases and is related to ringwoodite replacement by majorite garnet and ferropericlase, awaits for further studying and testing. If the thermodynamic data are confirmed experimentally, this shall attract much attention to the topic of “Archean window” for lower-mantle plumes, and the hypothesis of overall mantle convection shall thus receive additional support.

The data presented in this publication can be applied in further studies of mantle processes, including numerical petrologic–thermomechanical simulations of subduction and collision. Our results pertain to the composition of spinel lherzolite KLB-1, which is nowadays widely employed by many researchers, but these data may not be performed to other mantle compositions.