Application of thermodynamic modelling to natural mantle xenoliths: examples of density variations and pressure–temperature evolution of the lithospheric mantle

In this paper, we show how the results of phase equilibria calculations in different mantle compositions can be reconciled with the evidence from natural mantle samples. We present data on the response of bulk rock density to pressure (P), temperature (T) and compositional changes in the lithospheric mantle and obtain constraints on the P–T evolution recorded by mantle xenoliths. To do this, we examine the mantle xenolith suite from the Quaternary alkali basalts of Pali-Aike, Patagonia, using phase equilibria calculation in six representative compositions. The calculations were done subsolidus and in volatile-free conditions. Our results show that the density change related to the spinel peridotite to garnet peridotite transition is not sharp and strongly depends on the bulk composition. In a depleted mantle composition, this transition is not reflected in the density profile, while in a fertile mantle it leads to a relative increase in density with respect to more depleted compositions. In mantle sections characterized by hot geothermal gradients (~70 mW/m2), the spinel–garnet transition may overlap with the lithosphere–asthenosphere boundary. Phase equilibria calculations in peridotitic compositions representative of the Pali-Aike mantle were also used to constrain the origin and evolution of the mantle xenoliths. Our results indicate that the mineral modes and compositions, and the mineral zonation reported for the low-temperature peridotites (spinel and spinel + garnet harzburgites and lherzolites), are linked to a cooling event in the mantle which occurred long before the eruption of the host basalts. In addition, our phase equilibria calculations show that kelyphitic rims around garnets, as those observed in the high-temperature garnet peridotites from Pali-Aike, can be explained simply by decompression and do not require additional metasomatic fluid or melt.


Introduction
Combining the petrological and geochemical evidence of mantle xenoliths and peridotitic massifs with phase equilibria experiments and thermodynamic modelling is essential to further our understanding of the nature of the upper mantle. While there is a plethora of experimental information on the melting behaviour of upper mantle rocks (e.g. Green and Falloon 1998;Falloon et al. 2001), there is relatively little experimental information on subsolidus phase relations in complex upper mantle compositions (e.g. Ringwood 1967, 1970;O'Hara et al. 1971;). This is probably due to the fact that experiments in complex compositions are characterized by slow reaction rates, slow crystal growth rates and general sluggishness to equilibrate. Therefore, experiments in complex compositions are especially difficult to conduct and experimental results are often difficult to interpret (e.g. Green and Ringwood 1967;Brey et al. 1999; Girnis and Brey 1999;Girnis et al. 2003;Borghini et al. 2009;Fumagalli et al. 2014).
Perhaps this is one of the reasons why most experiments relevant to upper mantle processes were conducted Abstract In this paper, we show how the results of phase equilibria calculations in different mantle compositions can be reconciled with the evidence from natural mantle samples. We present data on the response of bulk rock density to pressure (P), temperature (T) and compositional changes in the lithospheric mantle and obtain constraints on the P-T evolution recorded by mantle xenoliths. To do this, we examine the mantle xenolith suite from the Quaternary alkali basalts of Pali-Aike, Patagonia, using phase equilibria calculation in six representative compositions. The calculations were done subsolidus and in volatilefree conditions. Our results show that the density change related to the spinel peridotite to garnet peridotite transition is not sharp and strongly depends on the bulk composition. In a depleted mantle composition, this transition is not reflected in the density profile, while in a fertile mantle it leads to a relative increase in density with respect to more depleted compositions. In mantle sections characterized by hot geothermal gradients (~70 mW/m 2 ), the spinel-garnet transition may overlap with the lithosphere-asthenosphere boundary. Phase equilibria calculations in peridotitic compositions representative of the Pali-Aike mantle were also used to constrain the origin and evolution of the mantle xenoliths. Our results indicate that the mineral modes and compositions, and the mineral zonation reported for the Communicated by Jochen Hoefs. in simplified chemical compositions, so-called simple systems. Many experiments in systems MgO-Al 2 O 3 -SiO 2 (MacGregor 1974;Danckwerth and Newton 1978;Gasparik and Newton 1984), CaO-MgO-Al 2 O 3 -SiO 2 (Kushiro et al. 1967;O'Hara et al. 1971;Akella 1976;Obata 1976;Jenkins and Newton 1979;Perkins and Newton 1980;O'Neill 1981;Gasparik 1984a, b;Sen 1985;Adam 1988;Gudfinnsson and Presnall 1996;Milholland and Presnall 1998;Walter et al. 2002) or Na 2 O-CaO-MgO-Al 2 O 3 -SiO 2 (Walter and Presnall 1994) have been performed to investigate processes in the upper mantle. Figure 1a depicts experimentally derived phase relations in the system CaO-MgO-Al 2 O 3 -SiO 2 , based on reversal experiments of O'Neill (1981), Klemme and O'Neill (2000a), Adam (1988) and Milholland and Presnall (1998). See also a recent review paper (Fumagalli and Klemme 2015) for details on garnet to spinel peridotite reactions and related reactions in simple systems. The garnet to spinel peridotite transition in CaO-MgO-Al 2 O 3 -SiO 2 is univariant and has a steep Clapeyron slope (dT/dP) of about 40 °C/ kbar (Walter et al. 2002) at temperatures above 1200 °C.
However, it has been known for a long time that minor elements, especially Cr and Fe 3+ , have a strong effect of phase relations (O'Neill 1981;Nickel 1986;Webb and Wood 1986;Brey et al. 1999;Girnis and Brey 1999;Klemme and O'Neill 2000a;Klemme 2004;Borghini et al. 2009;Klemme et al. 2009). While Cr (and other minor elements) probably does not affect phase relations in the deeper upper or the lower mantle much, Cr is known to partition very unevenly between upper mantle mineral phases and it is well known to strongly stabilize spinel relative to garnet (O'Neill 1981;Asimow et al. 1995;Klemme 2004). This is particularly important for depleted mantle compositions (e.g. harzburgite), which are characterized by Al depletion and relatively high Cr/[Cr + Al] bulk compositions (Fig. 1b).
As mentioned above, experiments in Cr-rich bulk compositions are difficult to conduct and even more difficult to interpret, especially at temperatures <1100 °C (very relevant for the uppermost mantle). However, the recent advances in thermodynamic modelling techniques and refinements of thermodynamic databases may help to investigate subsolidus phase relations in simple (e.g. Klemme 2004;Green et al. 2012) and complex (Asimow and Ghiorso 1998;Klemme et al. 2009, Ziberna et al. 2013, Jennings and Holland 2015 mantle compositions. In two previous papers, Klemme et al. (2009) and Ziberna et al. (2013) focused more on methods and calibration of a thermodynamic model for Cr-bearing mantle rocks, so the aim of this paper is to show how this thermodynamic model may be applied to investigate processes in the upper mantle.
As a case study, we used the compositions of mantle xenoliths from Pali-Aike, Patagonia (Skewes and Stern 1979;Stern et al. 1999;Wang et al. 2008) to address two different petrological problems. First, we calculate the response of density to changes in bulk compositions of subcontinental mantle, using different bulk compositions taken from the Pali-Aike mantle xenolith suite. Furthermore, we use phase equilibria calculations to explore possible P-T paths recorded in the peridotite xenoliths from the same suite and to investigate kelyphite-forming reactions around garnets.

Petrological background and sample selection
The Pali-Aike volcanic field is located in Southern Patagonia and is the southernmost volcanic exposure of the Late  Ziberna et al. (2013) for a depleted peridotite (man-tle xenolith JSL261 from Van Achterbergh et al. 2001). In (b) olivine, orthopyroxene and clinopyroxene are always present in all the calculated mineral assemblages. The calculated mineral assemblage for the white field is spinel-and garnet-free Cenozoic Patagonian Plateau lavas (Fig. 2). It belongs to the Deseado Massif, a geologic unit that records different stages of rifting and subduction from the Neoproterozoic to the Early Cambrian (Pankhurst et al. 2006). Geological evidence and zircon ages suggest that the basement and the lithospheric mantle beneath Pali-Aike may be part of a Phanerozoic accretionary prism (Pankhurst et al. 2006). Two following tectonic events that affected this area were subsidence and sedimentation in Jurassic-Cretaceous and mantle upwelling in Neogene that produced, among others, the alkali basalts of the Pali-Aike volcanic field (Wang et al. 2008 and reference therein). The mantle xenoliths considered here have been sampled by these alkali basaltic lavas and pyroclastic rocks, which are Pliocene to Pleistocene in age (see D'Orazio et al. 2000 for a review in regard to dating of these rocks).
The majority of mantle xenoliths include harzburgites and lherzolites, which contain spinel, spinel + garnet or garnet as aluminous phases (Stern et al. 1999). Overall, this peridotitic suite shows a broad range of compositions, from fertile lherzolites to depleted harzburgites, with Mg# = 0.89-0.93, Al 2 O 3 = 0.5-4.6 wt%, CaO = 0.4-4.0 wt% (see Fig. 5 in Stern et al. 1999 or our Table 1 for some representative compositions). This within-suite variability, together with the high abundance of vein-free and unaltered samples with no evidence of melt infiltration and no hydrous minerals like amphibole or phlogopite (cf. Stern et al. 1999;Wang et al. 2008), makes this a good case study to test our thermodynamic model. Note that our model does not account either for melting or for the presence of fluids and volatile-bearing phases.
The selection of samples for phase equilibria calculations was based upon the petrological problems to be addressed. In all cases only compositions from xenoliths were selected that were described as fresh and vein-free (Stern et al. 1999). The first application of our model aims to investigate how the predicted density profiles change with changing bulk composition within the range recorded by mantle xenoliths. We therefore selected four representative peridotite compositions (LS1, PA3, TM16 and BN4; Table 1) that encompass the entire range of Mg#, Cr# and Ca# of the mantle xenolith suite from Pali-Aike (Stern et al. 1999). The second application aims to investigate the P-T history of the mantle recorded in the xenoliths by comparing the textures, mineralogy and phase compositions of the xenoliths with the results of phase equilibria calculations. We therefore selected the samples that represent the mineralogical variability of the xenoliths and for which some descriptions on textures and compositional zoning are available in the literature. This selection included a spinel harzburgite (sample LS2), a spinel-garnet lherzolite (sample BN4) and a garnet lherzolite (sample LS33) ( Table 1).

Methods
We used the Perple_X set of computer programs (Connolly 1990;Connolly and Petrini 2002), which enables to calculate mineral modes, mineral compositions and bulk physical properties (Connolly and Kerrick 2002) as a function of temperature pressure and, perhaps most importantly, bulk composition. Following Ziberna et al. (2013), we calculate subsolidus phase relations for several water-and carbonate-free bulk compositions, ranging from fertile lherzolite to depleted harzburgite ( Table 1). The calculations were performed in the system The thermodynamic data used here for phase equilibria calculations in subsolidus mantle compositions are based on the internally consistent dataset of Holland and Powell (1998), complemented for the most relevant Cr-bearing phases in the upper mantle. Among the available sets of endmember properties and solution models for Cr-bearing phases (e.g. Klemme et al. 2009;Ziberna et al. 2013, Jennings andHolland 2015), we adopted the model suggested by Klemme et al. (2009) which was later on refined by Ziberna et al. (2013). This model shows good agreement with the available experimental data in both Cr-poor and Cr-rich mantle    Nickel 1986;Webb and Wood 1986;Walter 1998;Brey et al. , 1999Brey et al. , 2008 and is therefore considered to be more appropriate for an application to a set of natural mantle xenoliths such those from Pali-Aike (bulk Cr# = 0.05-0.30). We would like to caution the reader that the values reported as enthalpies of formation in Table 2 of Klemme et al. (2009) and supplementary table of Ziberna et al. (2013) are actually free energies of formation and that the Cr-bearing clinopyroxene end-member used in the calculations is CaCr 2 SiO 6 and not MgCr 2 SiO 6 . The entire set of end-member thermodynamic properties and solution models used for the calculations is available at http://www.perplex. eth.ch or can be obtained from the authors upon request.

Density variations in the subcontinental mantle
Understanding the vertical and lateral variation of density in the upper mantle is critical to our understanding of the tectonic and magmatic evolution of the lithosphere (Podladchikov et al. 1994;Kaus et al. 2005;Simon and Podladchikov 2008;Sakamaki et al. 2013). Moreover, a sound understanding of the nature of density variations is crucial to interpreting the structure of the mantle from geophysical information, such as seismic tomography or gravity anomalies (e.g. Stixrude and Lithgow-Bertelloni 2005;Afonso et al. 2013a, b). It is well known that density and seismic properties of mantle peridotites are related to the modes, compositions and elastic properties of their constituent minerals (i.e. olivine + orthopyroxene ± clinopyroxene ± aluminous phase) and melts, which in turn depend upon pressure, temperature and bulk composition (Ringwood 1975;Green and Liebermann 1976;Podladchikov et al. 1994;Suzuki and Othani 2003). Phase equilibria calculations based on thermodynamic data are commonly used to predict how phase relations and therefore the physical properties of rocks in the Earth's interior vary with depth (e.g. Connolly and Kerrick 2002;Stixrude and Lithgow-Bertelloni 2005;Afonso et al. 2008;Jones et al. 2014) (for a critical assessment on the application of phase equilibria calculations to rock physics and geodynamic modelling the reader is referred to Connolly 2009).
In this context, it is important to understand how bulk composition affects mineral phase assemblage and density in the uppermost mantle, which is known to be heterogeneous in both chemical and mineralogical composition, mainly due to localized metasomatism and melt extraction processes (Menzies and Hawkesworth 1987;Carlson et al. 2005;Pearson and Wittig 2008). Petrological studies of peridotite massifs and mantle xenoliths, integrated with geophysical observations and thermodynamic constraints, may help to understand how chemical composition, thermal state and density of the uppermost mantle are related to each other in a variety of geological settings. Thanks to the advances in computer programming and modelling techniques, it is now possible to integrate these methodologies in single, self-consistent models, which are able to predict even two-and threedimensional variations of density in the uppermost mantle (e.g. Afonso et al. 2008;Fullea et al. 2009).
In most previous studies, however, the calculations were made in Cr-free bulk composition (i.e. CFMAS or NCF-MAS; Afonso et al. 2008;Fullea et al. 2009Fullea et al. , 2010Fullea et al. , 2012Fullea et al. , 2014Jones et al. 2014). Notably, the recent studies of Klemme et al. (2009) and Ziberna et al. (2013) show that phase relations in Cr-bearing, near-natural peridotite compositions change considerably with respect to the Cr-free system. These changes may also affect the density profiles of the uppermost mantle peridotite. In this section, we set out to investigate whether and how the addition of Cr and resulting phase stability fields of spinel and garnet affect density profiles in a more realistic (i.e. Cr-bearing) uppermost mantle compositions in different thermal regimes.
The calculations for the four selected Pali-Aike peridotites (LS1, PA3, TM16, BN4; Table 1) were made for a P-T range 1.0-8.0 GPa and 500-1400 °C, and density profiles were calculated for two different geothermal gradients: 70 mW/m 2 , which is similar to that predicted for the mantle beneath Pali-Aike (Stern et al. 1999;Wang et al. 2008), and 50 mW/m 2 , which is representative of colder, off-craton, lithospheric sections. These gradients were derived from the preferred geotherm family of Hasterok and Chapman (2011), which are based on mantle xenolith thermobarometry, heat production measurements and tectonothermal constraints. Following Hasterok and Chapman (2011), here we also assume that the transition from a conductive to an adiabatic geotherm corresponds to the lithosphereasthenosphere boundary (LAB). This definition has no direct link to rheology, seismology or electrical conductivity, but is used here only to discuss the combining effects of phase transitions and changes in thermal gradient on the density profile. Moreover, it is important to emphasize that our calculations assume no volatile-bearing phases and only subsolidus conditions (and hence do not consider the possible presence of melt at the LAB or the presence of hydrous phases; cf. Green et al. 2010;Sakamaki et al. 2013;Stern et al. 2015). Figure 3 depicts these geothermal gradients together with two examples of predicted density distribution in P-T space. In agreement with previous calculations (cf., Afonso et al. 2008;Simon and Podladchikov 2008), increasing depletion of the rock (i.e. decreasing Al 2 O 3 , CaO, NaO and increasing Mg#) leads to an overall decrease in density (Fig. 4a, c) in the mantle. This is mainly caused by bulk Al 2 O 3 , which increases the modes of spinel and garnet, the densest mineral phases in peridotite assemblages (Fig. 4b, d) (see also e.g. Wood and Yuen 1983;Lee 2003), and by bulk Mg#, which relates to the Fe content in minerals (which in turn has a strong control on mineral densities; Lee 2003). However, here we show that the density profile across the spinel-to-garnet peridotite transition is not sharp and its shape strongly depends on bulk composition, other than geothermal gradient. If we consider a geotherm of 50 mW/m 2 and depleted compositions (LS1 and PA3 in Table 1), the density in the mantle remains virtually constant from ca. 30 km to ca. 120 km (Fig. 4a). In other words, the spinel-to-garnet transition is not reflected in the density profile of the mantle at all, with implications for interpreting seemingly contrasting geophysical datasets. However, things are very different if more fertile compositions are considered (TM16 and BN4 in Table 1). Here the density shows a relatively rapid increase when garnet becomes stable (at ~40 km depths for these compositions and this geotherm). This increase becomes progressively less pronounced, until density returns to be virtually constant at ~ 80 km (Fig. 4a, b).
In a mantle characterized by hot conductive geotherms (70 mW/m 2 , Fig. 4c,d), the slope of the P-T gradient is such that the effect of temperature on the bulk density is higher than the effect of pressure (Fig. 3), leading to a decrease in density with depth in the lithosphere (Fig. 4c). For depleted compositions (LS1, PA3) and identical geothermal gradients, the spinel-garnet transition is very narrow and occurs in proximity to the LAB (Fig. 3a). The rapid change of temperature gradient at the LAB and the low modes of spinel and garnet for these compositions hide the effect of the spinel-garnet transition on the density profile. For more fertile composition (BN4), the conductive geotherm enters the spinel + garnet stability field long before the LAB (Fig. 3b). The rapid increase in garnet modes (Fig. 4d) therefore leads to a relative increase in density with respect to the other compositions. Moreover, the interaction of temperature gradient and garnet and spinel mode variations result in a smooth density profile across the LAB (Fig. 4c), which in fact overlaps with the spinel-garnet transition.
The density profiles shown here are different from the results of recent geodynamical modelling studies, which show in all compositions a step-like change in density at the spinel-garnet transition (c.f. Fullea et al. 2014). The differences can be easily ascribed to (1) the absence of Cr in the Fullea et al. (2014) thermodynamic model (Cr is known to broaden the spinel + garnet stability field and, therefore, smooths the density contrast between spinel and garnet peridotites) and (2) the absence of depleted (e.g. poor in Al 2 O 3 and relatively enriched in Cr 2 O 3 ) or harzburgitic bulk compositions in their calculations. A step forward in the application of these integrated geophysical-petrological methodologies would be, therefore, to extend the thermodynamic model used by Fullea et al. (2014) to Cr-bearing systems.
In summary, our results show how the spinel-garnet transition affects the density variations in realistic nearnatural, and Cr-bearing, upper mantle compositions. It is worth noting that in a depleted mantle (bulk Cr# >0.20) the spinel-garnet transition is not reflected in the density profiles, while in a fertile mantle the transition clearly affects the density profile. This contrast can be explained by the lower bulk Cr# and higher Al 2 O 3 content of the peridotites typical in the fertile mantle. The former decreases the width of the spinel-garnet transition, while the latter increases  Stern et al. 1999). The two dashed curves represent a 50 (higher curve) and a 70 mW/m 2 (lower curve) conductive geotherms both joining the 1300 °C adiabat (Hasterok and Chapman 2011). The solid red curves delimit the stability fields predicted by the thermodynamic model (ol olivine, opx orthopyroxene, cpx clinopyroxene, grt garnet, sp spinel, esk eskolaite). It is worth noting that garnet modes (isopleths marked by grey squares) have the major control on density variations across the spinel-garnet transition. The smoother density variation at the spinel-garnet transition in (a) is indeed related to the very low modes of garnet (<3.0 wt%) for composition BN4 (see text) the modes of spinel and garnet, which therefore will have a stronger control on the density variations. In case of hot geotherms (ca. 70 mW/m 2 ), the spinel-garnet transition may overlap with the LAB. Such results may also help to interpret the origin of the Hales discontinuity or Hales gradient zone, a seismic impedance increase commonly attributed to the spinel-garnet transition (Hales 1969;Revenaugh and Jordan 1991;Ayarza et al. 2010).
The Pali-Aike lithospheric mantle is inferred to be composed by depleted harzburgites at shallow depths (ca. 30-60 km) and fertile lherzolites at greater depths (ca. 50-90 km; Stern et al. 1999). A possible origin for this layering is magma extraction in a mid-oceanic ridge setting occurred during the late Proterozoic, prior to the accretion of this mantle section to the western margin of Gondwanaland during the Palaeozoic (Stern et al. 1999). An estimated density profile for such a layered mantle is represented in Fig. 4c. Despite this being a simplified stratigraphic model, it shows how the compositional layering of the lithospheric mantle, which typically varies from depleted to fertile compositions, may have a strong effect on density structure of the upper mantle.

Evolution of garnet-spinel peridotites from Patagonia
Studying texture, mineralogy and geochemistry of mantle xenoliths is important if we are to constrain the nature and the evolution of the lithospheric mantle. The Pali-Aike mantle xenoliths suite includes lherzolites, harzburgites and minor pyroxenites that show a range of textural and  (Table 1) along a 50 mW/m 2 steady state geotherm (a, b) and a 70 mW/m 2 geotherm (c, d). The solid grey curve in (c) represents a possible density profile beneath Pali-Aike based on the compositional layering observed by (Stern et al. 1999). For sake of simplicity, the depth values shown on the right axes were calculated assuming constant density (i.e. depth = P(GPa) 9.8 m/s 2 · 3.0 kg/cm 3 ) mineralogical variations, which potentially record several processes that occurred in the mantle (Skewes and Stern 1979;Stern et al. 1999;Wang et al. 2008). Stern et al. (1999) and Wang et al. (2008) used this xenoliths suite to interpret the geochemical and tectonic history of the mantle beneath the southernmost South America. They suggested that the mantle section beneath Pali-Aike underwent two different tectonothermal events: (1) early cooling and/ or pressure increase (i.e. accretion) followed by (2) more recent heating and decompression (Stern et al. 1999;Wang et al. 2008).
Based on Stern et al. (1999), there are two pieces of evidence that support an early cooling and pressure increase. Firstly, spinel in spinel + garnet peridotites (e.g. BN4 in Table 1) is commonly fully enclosed in garnet, which led Stern et al. (1999) to interpret the spinels as relics of the reaction spinel + pyroxene = garnet + olivine. Secondly, in low-T spinel peridotites (<970 °C; e.g. LS2 in Table 1) the core of orthopyroxenes is homogeneous but close to the rim Al and Ca decrease. Similar but less prominent zoning was also observed for clinopyroxenes (no data are available instead for spinel and garnet). Based on consideration on element diffusion scales and thermometric estimates, Stern et al. (1999) interpret this zonation as a result of cooling. Stern et al. (1999) discussed two pieces of evidence also for the scenario of recent heating and decompression. Firstly, the high-T spinel and garnet peridotites contain orthopyroxene showing Al and Ca increase progressively from core to rim. In the garnet lherzolites recording the highest temperatures (e.g. LS33 in Table 1), the zonation in Ca is absent, which was interpreted as an effect of more rapid element diffusion at higher temperature (Stern et al. 1999). Then, garnet is often surrounded by a spinel + pyroxenes (+ occasional amphibole) kelyphitic rim, which is a reaction product commonly interpreted to be driven by heating and/or decompression (e.g. Godard and Martin 2000;Obata 2011).
Here we tested their proposed scenarios by calculating phase relations for the three selected peridotitic compositions (BN4, LS2 and LS33 in Table 1), which allowed investigating the effect of temperature or pressure variation on mineral modes and compositions. We focused in particular on the reaction spinel-to-garnet peridotite and on the formation of kelyphitic rims around garnet. Figure 5 shows how the calculated modes of the peridotitic assemblage and Al 2 O 3 content of pyroxenes vary with temperature (at constant pressure) and with pressure (at constant temperature). Generally, the model predicts that at P-T conditions where both garnet and spinel are stable, a temperature decrease results in a pronounced increase in modal garnet and decrease in orthopyroxene. Less pronounced decrease in modal clinopyroxene and increase in spinel are also evident (Fig. 5c, e). This is in line with the well-known reaction describing the spinel-to-garnet transition: spinel + pyroxene = garnet + olivine, with the reaction products being stabilized at lower temperatures (Green and Ringwood 1967;O'Neill 1981;Klemme and O'Neill 2000b). Al 2 O 3 contents in pyroxenes decrease constantly with decreasing temperature and generally increase with decreasing pressure, in accordance with experimental observations (cf. Green and Ringwood 1970;Nickel 1989;Brey et al. , 2008. However, the P dependence of Al 2 O 3 in pyroxenes is not linear. Al 2 O 3 is constant in the spinel stability field, it steeply decreases with pressure in the spinel + garnet field and then smoothes at higher pressures where spinel is not stable (Fig. 5b, d, f), and the reaction MgAl 2 SiO 6 + Mg 2 Si 2 O 6 = Mg 3 Al 2 Si 3 O 12 (Green and Ringwood 1970) is not as significant as at high temperatures. It is important to note, however, that the Al 2 O 3 contents in clinopyroxenes may be slightly overestimated by our model, as they generally show slightly higher values relative to the available phase equilibria experiments at comparable temperatures (e.g. Green and Ringwood 1970;Nickel 1989;Brey et al. , 2008. Further development of the model should include a better thermodynamic mixing model and better end-member data for the tschermakite end-members of clinopyroxene solid solution.

From spinel to garnet peridotites: cooling, pressure increase or both?
Based on the textural evidence of the reaction spinel + pyroxene → garnet + olivine, Stern et al. (1999) suggested early cooling of the mantle, perhaps in the Jurassic period (for details refer to Stern et al. 1999). This scenario is supported by Ca decrease in orthopyroxenes from core to rim in low-T spinel peridotites, which correspond to a T decrease of about 150-200 °C when applying the Ca-in-opx thermometer of . To explain the occurrence of relic spinel in garnet peridotites, Wang et al. (2008) on the other hand suggested a pressure increase driven by subduction or accretion of oceanic lithosphere, but they do not provide any petrological evidence to support this hypothesis.
To test the scenarios inferred by Stern et al. (1999) and Wang et al. (2008) on low-T peridotites (here represented by the composition LS2), we considered the cooling to be isobaric, with the fixed pressure values corresponding to the thermobarometric estimates of Stern et al. (1999) (see their Figs. 2 and 9). Given the likely uncertainties of these estimates (ca. 30-80 °C and 0.2-0.4 GPa depending on the adopted formulation and only if equilibrium of the assemblage is assumed; see Nimis and Grütter 2010 for a review), these values were used just as an approximate estimation of the P-T conditions of the xenolith, which were sufficient enough for the purpose of modelling. For the composition LS2, the predicted mineralogy at the estimated P-T conditions of the xenolith corresponds to a spinel harzburgite (Figs. 5a,b). A temperature decrease from 950 to 800 °C (as estimated by Stern et al., 1999 for the sample LS2) does not affect the mineral assemblage and results in a progressive decrease of Al 2 O 3 content in pyroxenes (Fig. 5a). Consistently, the xenolith LS2 (1) is a spinel harzburgite, (2) shows no textural evidence of replacement reactions and (3) contains orthopyroxenes characterized by decreasing Al 2 O 3 from core-to-rim (Stern et al. 1999). No Fig. 5 Temperature and pressure dependence of mineral modes and Al 2 O 3 wt% in ortho-and clinopyroxenes calculated for three different Pali-Aike mantle compositions. LS2 is a spinel-harzburgite, BN4 a garnet-spinel lherzolite and LS33 a garnet lherzolite xenolith (Stern et al. 1999). The thermobarometric estimates for each xenolith, reported in Stern et al. (1999), were used as reference P and T values for the calculation. The red arrows show the possible P-T evolution paths based on the thermobarometric estimates of the mantle xenoliths data about zoning of clinopyroxenes are reported by Stern et al. (1999) or Wang et al. (2008). On the other hand, a pressure increase in the range 1.0-2.0 GPa, a typical range for spinel peridotites, results in Al 2 O 3 decrease in orthopyroxene only when garnet become part of the assemblage. Given that there is no evidence of garnet in this xenolith, a pressure increase at constant temperature is therefore not supported by our calculations.
For the xenolith BN4, which was selected here to represent the Pali-Aike garnet-spinel lherzolites (with spinel present as inclusions in garnets), Stern et al. (1999) estimated the pressure and temperature to be 1.9 GPa and 1000 °C. If a temperature decrease from 1150 to 1000 °C is considered, the model predicts a transition from spinel to spinel-garnet peridotite, with garnet modes being ca. 6-7 wt% and spinel modes ca. 1-2 wt% at about 1000 °C (Fig. 5c). This is in good agreement with the mineral assemblage in the xenolith BN4 and the textural evidence of the reaction spinel + pyroxene = garnet + olivine observed for this and other garnet-spinel peridotites xenoliths from Pali-Aike. In this case, also a pressure increase from ca. 1.5 to 2.0 GPa would produce the same mineralogical variation (Fig. 5d).
Phase equilibria calculations therefore indicate that a temperature decrease of about 150 °C best reproduces the mineral assemblage and mineral zoning observed in the low-temperature spinel peridotites and garnet-spinel lherzolites. Although minor pressure variations may have also occurred, our thermodynamic modelling results indicate that progressive cooling from Palaeozoic to late Cenozoic may be the most likely scenario in this portion of the Pali-Aike mantle section.

Kelyphite formation around garnets: heating, decompression or both?
The formation of kelyphite rims is often explained as a reaction of garnet and other mantle minerals with volatilebearing infiltrating agents derived from the host magma (Dawson 1980;Hunter and Taylor 1982;Garvie and Robinson 1984). However, here we focus on an alternative kelyphite-forming process, which is linked to P-T change (Reid and Dawson 1972;Godard and Martin 2000), as suggested for the Pali-Aike garnet peridotites (e.g. Stern et al. 1999).
Based on element diffusion systematics and thermobarometry, Stern et al. (1999) suggested that the high-T garnet peridotites from Pali-Aike recorded only a last stage of heating and decompression related to the quaternary magmatism that sampled the xenoliths. They suggested that the core-to-rim CaO and Al 2 O 3 increase in orthopyroxenes and the occurrence of kelyphitic rims surrounding garnets support this scenario. The garnet lherzolite xenolith LS33 was selected here as representative for our calculations. Our model shows that heating from about 1050-1150 °C (the temperature increase estimated by Stern et al. 1999) results in a gradual decrease in modal garnet, increase in orthopyroxene and clinopyroxene and increase in Al 2 O 3 in orthopyroxene (Fig. 5e). The latter is in agreement with the observed zoning of the primary orthopyroxenes in the xenoliths. A pressure decrease from 2.5 to 2.0 GPa would result in a similar mineralogical variation, with garnet modes decreasing from 15 to 8 wt% (Fig. 5f).
The development of kelyphitic rims around garnets, which are typically composed of orthopyroxene + clinopyroxene + spinel, could be, at first approximation, modelled by our predicted decrease in garnet and increase in pyroxenes modes shown in Fig. 5e, f, driven by either heating or decompression. However, kelyphites around garnets in peridotites have been interpreted to be a product of the reaction between garnet and the surrounding olivine or orthopyroxene (Mukhopadhyay 1991;Godard and Martin 2000;Obata 2011), being therefore a reaction occurring in a discrete volume of the peridotite. Obata (2011) in particular, reported the textural evidence for such localized reactions. This means that the system to be considered for phase equilibria calculations should not be the bulk peridotite, but rather a local domain enclosing the garnet-olivine interface.
Therefore, to test the conditions of kelyphite formation in the case of garnet completely surrounded by olivine, we constructed a composition from the modal proportions 50 % olivine and 50 % garnet using the mineral composition reported for the sample LS33 (Wang et al. 2008). The resulting bulk composition is reported in Table 1 (LS33kel), and the results of the calculations are reported in Fig. 6.
The calculated mineralogical and compositional variations in Fig. 6 clearly show a predominant effect of pressure on the mineral assemblage. At T = 1100 °C and P > 2.5 GPa, garnet + olivine is the stable assemblage, in accordance with the xenolith evidence. Considering isothermal decompression, garnet modes rapidly decrease starting from ca. 2.3 GPa, while orthopyroxene, clinopyroxene and spinel modes increase, consistently with the typical assemblage found in kelyphites. Moreover, the variation of mineral modes agrees well with what is commonly observed in kelyphites, i.e. orthopyroxene being the dominant phase, while clinopyroxene and spinel modes are lower (Obata 2011). Furthermore, the very high Al 2 O 3 content typically observed in pyroxenes in kelyphites (5-15 wt%; cf. Mukhopadhyay 1991;Foley et al. 2006;Špaček et al. 2013) is also reproduced by our model (Fig. 6b).
Similar results were obtained considering different bulk compositions constructed from garnets and olivines from the other xenoliths from Pali-Aike, and different T and P values for the isothermal and isobaric calculations, respectively. The calculations therefore show how the formation Page 11 of 14 16 of kelyphites at the garnet-olivine interface is most likely related to decompression and can be isochemical (i.e. does not require additional components from metasomatic melts or fluids).

Conclusions
We present results from phase equilibria calculations in near-natural, Cr-bearing peridotitic compositions representing the Pali-Aike mantle. The results show that the interplay between thermal gradient and bulk composition exerts the major control on the density variation in the lithospheric mantle. Focusing on shallower mantle around the spinelgarnet transition, our results indicate that (1) in depleted bulk compositions (i.e. harzburgite) the density profile is such that the spinel-garnet transition does not show in the density profile and (2) in fertile bulk compositions (i.e. lherzolite) the density change across the garnet spinel transition on a warm geotherm is not abrupt but rather more gradual and may overlap with the density change related to the lithosphere-asthenosphere transition.
The comparison between the mineral assemblages in the mantle xenoliths and the calculated phase relations for the same rocks were used to infer the P-T evolution of the mantle beneath Pali-Aike. The results indicate that the spinel + garnet peridotite xenoliths, which exhibit textural evidence of the reaction spinel + pyroxene = garnet + olivine, are more likely a result of cooling rather than pressure increase. In addition, phase equilibria calculations showed that the kelyphitic rims around garnets in peridotites may form simply due to an isochemical reaction driven by decompression rather than heating.  Table 1), using the mineral compositions of the sample LS33 from Wang et al. (2008). At conditions 2.5 GPa and 700-1300 °C (a), the model does not predict clinopyroxene to be stable, while orthopyroxene is stable until ca. 900 °C and shows a progressive increase in Al with temperature