The MELTS algorithm, the most commonly used tool for calculating crystallization of basaltic magmas, uses thermodynamic parameters calibrated by experiments on select compositions, and thus, its use on newly discovered extraterrestrial compositions requires extrapolation across ranges where its applicability has not been evaluated in detail. To apply MELTS to Martian compositions, we undertook a systematic examination of the original MELTS calibration and the pMELTS revision as applied to Martian magmas. We find that the algorithm is effective in predicting the crystallization paths and conditions of Martian magmas, with some issues. The algorithm consistently overestimates the stability of spinel and underestimates pressures of multiple saturation compared to experiments. The pMELTS calibration comes close to fitting multiple-saturation pressures but cannot be used at low pressures. Both calibrations model crystallization temperatures with similar variances to those observed for terrestrial compositions. Both calibrations reproduce important compositional details of crystallizing magmas and coexisting minerals with errors similar to those observed on terrestrial compositions. We calculate several crystallization paths which predict high-FeO, high-density magma compositions that could be a mechanism for cumulate formation. Low-FeO compositions in recent Mars volcanism may be an expression of this density barrier. However, the composition of a high-FeO rock called “Et-Then” discovered by the rover Curiosity is strikingly similar to compositions calculated by the MELTS algorithm and could represent one of these high-FeO volcanic rocks.
 Since its formulation [Ghiorso and Sack, 1995], the MELTS algorithm has become one of the most widely used programs for simulating basaltic melt crystallization. When combined with routines for subsolidus phase relations [Asimow and Ghiorso, 1998], the pMELTS calibration for melting at higher pressures [Ghiorso et al., 2001], routines for trace elements and water [Asimow et al., 2004], the AlphaMELTS (formerly Adiabat_1ph) front end [Smith and Asimow, 2005], and the Rhyolite-MELTS calibration for silicic systems [Gualda et al., 2012], the MELTS calculator can effectively model the production and evolution of a wide variety of terrestrial basaltic magmas and a variety of new and unique insights have resulted from its application [e.g., Asimow et al., 2004; Boudreau, 2008; Armitage et al., 2008; Hebert et al., 2009].
 The MELTS algorithm calculates solid-liquid relations based on calibrated thermodynamic properties of the phases and components. It does not rely on a previous experiment on the exact composition of interest but instead calculates phase stabilities and compositions based on free energies of the components calibrated from the available experimental literature. The thermodynamic basis allows for projection from well-calibrated conditions and compositions into ranges where the thermodynamic parameters are not well calibrated, without any obvious signal that the calculation has moved outside the well-calibrated range. In many ways, this ability to project is an advantage; for example, a smooth crystallization path starting at a well-calibrated composition can provide information on the evolution of the melt throughout its crystallization. However, there is a concern as well; without a clear signal that the algorithm has moved beyond well-calibrated conditions, the user is left with no means to evaluate the accuracy of the calculation (in particular if there is no experimental check).
 Applying the MELTS algorithm to Mars relies on the applicability of the underlying thermodynamics and experimental calibrations to Martian magma compositions. Martian basalts, such as those represented by the available meteorites, in general resemble terrestrial basalts in their major element compositions; however, there are important differences, such as higher iron, lower calcium and aluminum, and elevated CaO/Al2O3 at a given melt fraction in Martian basalts [e.g., Lodders, 1998]; all of which could impact magma crystallization. In the original calibration database of Ghiorso and Sack , there is only one study [Longhi and Pan, 1989] devoted to Martian compositions. A number of extraterrestrial samples are included, but most involve lunar compositions which are not an exact match to Martian magmas. Outside of Longhi and Pan , application of the MELTS algorithm to samples from Mars (or other extraterrestrial bodies such as Vesta and other asteroids, Mercury, or Venus) relies on the applicability of calibrations from simplified systems, terrestrial compositions, and lunar compositions to the body of interest.
 There has been substantial application of the MELTS algorithm to Martian compositions, with mixed results. The most common application has been modeling the crystallization paths of newly-discovered Martian meteorites or rocks analyzed by rovers on the surface [e.g., Taylor et al., 2002; Xirouchakis et al., 2002; Thompson et al., 2003; Lin et al., 2005; Stockstill et al., 2005; McSween et al., 2006; Monders et al., 2007; Symes et al., 2008; Basu Sarbadhikari et al., 2009; Hui et al., 2011; Basu Sarbadhikari et al., 2011]. Other common uses are in evaluating the oxygen fugacity states of magmas [e.g., Ghosal et al., 1998; Hale et al., 1999; Treiman and Irving, 2008; Balta et al., 2013] or as the petrologic basis for more complex modeling endeavors [e.g., Elkins-Tanton et al., 2005; Hirschmann and Withers, 2008; Symes et al., 2008; Francis et al., 2011; Baratoux et al., 2013; Balta et al., 2013]. The studies which apply the MELTS algorithm to a newly-discovered composition tend to follow the format of conducting calculations based on a measured composition and evaluating whether the calculated crystallization sequence fits that inferred from textures and mineral compositions. A close fit between calculated and inferred crystallization paths is generally considered evidence that the presumed crystallization conditions are accurate, while a poor fit can lead to suggestions that the MELTS algorithm may be inapplicable to the system in question [e.g., Monders et al., 2007] or that simple fractional crystallization models may be a poor fit for that particular system [e.g., McSween et al., 2006; Francis et al., 2011].
 Continued discovery of new Martian meteorites and analyses of rocks by rovers on Mars have produced a wealth of new igneous compositions in the years since the MELTS and pMELTS calibrations were published. Furthermore, there have been multiple estimates of Martian parental magma compositions [e.g., Musselwhite et al., 2006; McSween et al., 2006; Monders et al., 2007; Gross et al., 2011; Filiberto et al., 2010; Filiberto and Dasgputa, 2011; Basu Sarbadhikari et al., 2011; Balta et al., 2013] and experimental studies of magma crystallization [Musselwhite et al., 2006; Monders et al., 2007; Filiberto et al., 2008; McCubbin et al., 2008; Filiberto and Treiman, 2009b; Filiberto et al., 2010]. These studies provide motivation to evaluate the applicability of the MELTS algorithm to Mars in a new way; rather than evaluating individual crystallization scenarios, we can compare MELTS calculations to the actual crystallization paths and compositions of Martian basalts in aggregate. By doing so, we will not only evaluate the applicability of the MELTS model to individual Martian compositions or even to Mars in general, but we will also look for systematic trends in Martian magma evolution that may have gone previously unnoticed.
 Using the AlphaMELTS front end for the algorithm and the MELTS and pMELTS calibrations, supplemented by additional calculations using Rhyolite-MELTS, we conducted a series of several hundred calculations on a variety of Martian magma compositions. Based on these calculations, we find that the MELTS algorithm generally reproduces Martian basalt crystallization paths and can be reliably applied to model Martian magma evolution. However, we note several issues which should be understood by future users, including the appearance of an error in a particular published composition and issues with its application to the stability of the mineral spinel. We further show that the MELTS and pMELTS calibrations each have benefits and drawbacks in predicting the stabilities and compositions of common minerals in Martian compositions. After characterizing both the problems and successes of the model, we outline our suggestions for how to use and interpret MELTS calculations on Martian compositions. Using these outlined constraints, we apply the algorithm to understanding the density and eruptability of the magmas, giving insights into the compositions of the Martian volcanoes, the evolution of the Martian crust, and a newly-discovered rock found by the rover Curiosity at Gale crater. This work will establish a framework for future authors to apply MELTS to Martian compositions (or other planetary magmas) and serve as a basis for comparison with future updates of the MELTS and pMELTS calibrations.
 We began by conducting a large series of crystallization calculations on Martian compositions using the AlphaMELTS front end for the MELTS algorithm [Smith and Asimow, 2005]. Initial calculations were conducted on four proposed parental melt compositions. For the Yamato 980459 shergottite (hereafter Y-98), we used the bulk rock composition [Musselwhite et al., 2006], and for shergottites LAR 06319 and NWA 1068 we used compositions corrected for olivine fractionation and mixing [Filiberto et al., 2010; Balta et al., 2013]. We also included a proposed parental Gusev crater basalt composition analyzed by the Spirit rover [McSween et al., 2006]. Although this composition may not be a primary mantle melt, it has been used in experiments where it behaves as a magma of that composition would, making it a useful inclusion. Figures 1-4 show example calculated crystallization paths under various conditions with conditions chosen to demonstrate various properties of the calculations and to allow for comparison between the different compositions. To supplement calculations on proposed parental magmas, we also included compositions of melt inclusions from chassignite NWA 2737 [He et al., 2013], the EETA 79001 lithology-A (hereafter EET-A) composition of McSween and Jarosewich , several proposed nakhlite parental melt compositions [Stockstill et al., 2005; Sautter et al., 2012], and the measured bulk rock compositions for shergottites NWA 1068 and DAG 476 [Koizumi et al., 2004; Filiberto et al., 2010]. These selections generally reflect the majority of the basalt types currently sampled from Mars: mildly alkaline basalts observed by rovers, nakhlites (which may also be related to chassignites [Nyquist et al., 2001; Beck et al., 2006; McCubbin et al., 2013]), and shergottites with a variety of tholeiitic compositions (although all tested shergottites were olivine-phyric as their compositions are the closest available representation of mantle-derived magmas [Filiberto and Dasgupta, 2011]).
 The original MELTS calibration and the recent Rhyolite-MELTS revision are recommended for use in calculating magmatic crystallization at pressures below 1.0 GPa. Using the MELTS calibration, we began by calculating a large series of isobaric crystallization paths. We began with calculations at 1 atm pressure, starting above the liquidus and cooling in small temperature increments (typically 1°C but occasionally up to 5°C) until either the calculation became unstable or reached a lower temperature limit outside of the calibrated range (typically ~800°C). We then repeated the isobaric calculations using the MELTS calibration for pressures from 0.1 GPa to 1 GPa keeping the same temperature settings. Figure 1 illustrates the effect of pressure on the Y-98 composition (in addition Figures 1-4 typically show both calibrations to illustrate the properties of each). We also varied initial water contents, increasing in steps of 0.25 wt. % H2O, with up to and occasionally greater than 2 wt. % H2O. Figure 2 illustrates the effect of water contents on the LAR 06319 composition, which Balta et al.  argued contained >1 wt. % H2O.
 Once this database had been established, we attempted comparisons between MELTS-calculated results, natural samples, and experiments on similar compositions to evaluate the accuracy of the calculations. We investigated the compositions of minerals and melts as well as phase relations and in particular focused on fixed points in pressure-temperature space which could be directly compared between experiments and calculations. However, it rapidly became clear as discussed below that the MELTS calibration calculations were unable to fit the pressure of the olivine-pyroxene multiple-saturation point, the single pressure where both olivine and a pyroxene are simultaneously on the liquidus. As this point is the best available single point for comparison between experiments and calculations at elevated pressures and has been used as a proxy for the last depth of equilibration between Martian magmas and the mantle [e.g., Musselwhite et al., 2006; Filiberto et al., 2010], this lack of agreement posed a major difficulty. However, we noted that many Martian multiple-saturation pressures were within the range of pressures where the pMELTS calibration could be applicable, and previous authors have used pMELTS calibration calculations to analyze multiple saturation in terrestrial magmas [Asimow and Longhi, 2004]. Consequently, we conducted a set of calculations using the pMELTS calibration on each of the liquid compositions in this study, again employing variable water contents. The pMELTS calibration is not designed for use on either evolved compositions or at pressures below 1.0 GPa; however, to test its utility we conducted select calculations outside of the recommended pressure range in addition to calculations above 1.0 GPa. For the purposes of illustration, we show calculations with both the MELTS and pMELTS calibrations on the NWA 1068 parental magma composition at a variety of pressures in Figure 3 and the Gusev basalt composition in Figure 4. Plotted pressures were chosen to highlight key differences, such as the MELTS calibration placing pyroxene as the liquidus phase at low pressures while the pMELTS calibration retains olivine on the liquidus. Because pMELTS can be employed to higher pressures, we continued the pMELTS calibration calculations to higher pressures, up to ~2 GPa.
 We also performed calculations using both equilibrium/batch crystallization and fractional crystallization modes. Figure 4 also demonstrates the results of those changes on the Gusev basalt composition.
 We also attempted selected calculations with variable oxygen fugacity. Shergottites generally have oxygen fugacities between FMQ-1 and FMQ-4 [Wadhwa, 2008] and thus typically fall within the tested ranges, although the liquid lines of descent were typically not strongly affected by redox state (A. Udry et al., Exploring fractionation models for Martian primary magmas, submitted to Journal of Geophysical Research, 2013). Nakhlites and chassignites are typically more oxidized than shergottites, but it has also been proposed that the oxidation of nakhlites occurred due to late brine assimilation (a scenario difficult to test with this setup [McCubbin et al., 2013]), and thus, their crystallization is also generally represented by the tested oxygen fugacities. In the original computational routines for the MELTS algorithm, imposing oxygen fugacity can lead to computational instabilities. Consequently, on occasions when the algorithm could not proceed close to full crystallization, we conducted a single calculation to set the Fe2+/Fe3+ ratio at the desired oxygen fugacity and then ran the calculation unbuffered from that point (Balta et al.  showed that this change does not significantly alter the Fe2+/Fe3+ ratio of the liquid and this step typically allows the algorithm to proceed closer to completion). The recent Rhyolite-MELTS release includes the same calibrations for mafic phases as the original MELTS calibration and also includes updated calculation routines which improve stability. Thus, selected calculations were redone using Rhyolite-MELTS where appropriate.
 We supplemented these calculations on parental melt crystallization paths with isobaric crystallization calculations on the NWA 2737 chassignite melt inclusion composition [He et al., 2013] to try to fit the mineralogy observed in those inclusions. We also performed a set of isobaric and adiabatic crystallization calculations on the EET-A composition to fit melt inclusion mineralogy in that meteorite [Liu et al., 2013]. As discussed previously, these supplemental calculations were conducted using both the MELTS and pMELTS calibrations, again at a variety of water contents. Finally, in several cases we performed select additional calculations to allow for direct comparisons with experimental conditions.
 These choices of pressures, volatile contents, and redox conditions were meant to cover the range of plausible crystallization conditions on Mars, from beneath the crust [e.g., Wieczorek and Zuber, 2004; Musselwhite et al., 2006; Filiberto et al., 2010] to the surface and from dry to moderately hydrous magmas. Previous authors have argued that Martian parental magmas may contain up to ~2 wt. % H2O [e.g., McSween and Harvey, 1993; Dann et al., 2001; Lentz et al., 2001; Balta et al., 2013] and as such fall within the range tested here. Other authors have proposed that instead of H2O, Martian basalts may instead contain significant amounts of other volatiles, such as Cl [Filiberto and Treiman, 2009] or CO2 [Hirschmann and Withers, 2008]. Although the MELTS algorithm does not currently include these components, other studies have evaluated their effects on magmatic crystallization paths, and as such, calculations across a range in water contents allows for general estimation of the effect of these volatiles on magmatic evolution.
3 Results and Discussion
3.1 Liquidus Phase and Spinel Stability
 Across the variety of compositions, pressures, volatile contents, and redox states we tested, we consistently found the liquidus phase to be a chromium-rich spinel. In some cases, particularly at low pressures, spinel appears on the liquidus only tens of degrees before other phases, but as pressure increases, the MELTS algorithm calculates that spinel begins to crystallize much earlier in the sequence. For example, at 1.0 GPa, anhydrous, and FMQ-2.5, the NWA 1068 liquid is calculated to begin crystallizing spinel at 1575°C, while the next phase does not appear until 1432°C (Figure 3). Particularly at elevated pressure, the same results are found when using either calibration.
 Perhaps the closest match is found for the LAR 06319 bulk rock composition. MELTS calculations by Basu Sarbadhikari et al.  placed olivine on the liquidus before spinel. However, Filiberto and Dasgupta , Basu Sarbadhikari et al. , and Balta et al.  suggest that LAR 06319 has accumulated olivine, and as such the bulk rock composition crystallizes olivine earlier than the actual parental magma would have. Calculations using the LAR 06319 parental composition of Balta et al.  place spinel as the liquidus phase (Figure 2). Based on petrography, Basu Sarbadhikari et al.  suggested that chromian spinel does not appear as inclusions in the cores of the highest Mg # (and therefore earliest-crystallized) olivines, and as such olivine was interpreted as the liquidus phase, leaving MELTS calculations still in disagreement with observations, but only narrowly in this case.
 Experimental studies also diverge from the MELTS calculations. Three of these compositions have been tested in experimental crystallization studies, and two, Y-98 [Musselwhite et al., 2006] and NWA 1068 [Filiberto et al., 2008], do not show spinel crystallization under near-solidus conditions. The Gusev basalt studied by Monders et al.  shows spinel crystallization under all conditions, but those authors note their starting material was overenriched in Cr2O3. Hui et al.  indicated that MELTS-calculated spinel to be the first phase to appear on the liquidus for shergottite NWA 5298 when petrography suggested that clinopyroxene was the actual liquidus phase and suggested that the mismatch may be due to the presence of volatiles.
 We consider it more likely that the high-temperature appearance of spinel is actually an incorrect calibration in the MELTS algorithms. Issues with the stability of chromian spinel in the MELTS algorithm have been noted previously, and efforts have been made to improve calibrations for that phase [Hamecher et al., 2013]. We conclude that both the MELTS and pMELTS calibrations significantly overestimate the stability of chromian spinel in Martian magmas, leading to calculated spinel crystallization at temperatures substantially above the actual liquidus and here attempt to constrain the magnitude of this issue for Martian magmas. A similar conclusion was reached by Asimow and Longhi  for calculations on terrestrial compositions.
 Many authors have established that spinel stability is a strong function of oxygen fugacity, increasing in stability with increasing oxygen fugacity [e.g., Roeder and Reynolds, 1991], but the redox settings for our calculations do not significantly vary from those used in the experiments or estimated for the meteorites in question. The mismatch between calculations and experiments appears largest at either elevated pressures or under reducing conditions, which is particularly problematic for extraterrestrial samples where reducing conditions are common [Wadhwa, 2008].
 Although the spinel crystallization intervals are large (Figures 1-4), the amounts of spinel produced during each step are small and the effect on the liquid line of descent is minimal. For comparison, we conducted an independent calculation subtracting equilibrium olivine and spinel at a fixed ratio, with olivine compositions calculated using the KD of Filiberto and Dasgupta  and a measured spinel composition. For the Y-98 composition, we show the CaO/Al2O3 ratio (on a weight percent basis), which would be increased by removal of excess aluminum, and the Cr2O3/TiO2 ratio, which would be decreased by removal of excess chromium, calculated in this manner and by the MELTS algorithm a function of wt. % MgO in Figure 5. The CaO/Al2O3 ratio is increased slightly in the MELTS calculation initially due to the formation of spinel, but the effect on components other than Cr2O3 is much smaller than the changes associated with pyroxene and plagioclase crystallization. This excess spinel produces errors in calculated liquid line of descent less than a tenth of a weight percent for components other than Cr2O3. Errors on calculated Cr2O3 contents of several tenths of a weight percent are represented by early depletion of that component; these variances should be considered if better precision in the Cr2O3 component is required in any particular calculation.
 Overall, we caution against direct interpretation of spinel-liquidus relations in Martian magmas based on the current MELTS and pMELTS calibrations. While the mismatch may be small in some calculations, it should be expected and taken into account when interpreting MELTS results.
3.2 Olivine-Pyroxene Crystallization Pressure
 Next we focus on modeling the olivine and pyroxene liquidus surfaces in Martian magmas. In basaltic magmas, there is a well-established change between olivine and low-calcium pyroxene as the primary liquidus mineral at elevated pressures. This “multiple-saturation point” has been observed experimentally in Martian liquids as well, in the Gusev basalt composition at ~1 GPa [Monders et al., 2007] and ~1.3 GPa [Filiberto et al., 2008], in NWA 1068 at ~ 1.7 GPa [Filiberto et al., 2010], and in Y-98 at ~1.2 GPa (shown in Figure 6, [Musselwhite et al., 2006]). This point is tantamount to olivine being replaced by pyroxene as a product of the melting reaction at elevated pressure or to a “tie-line flip” in multicomponent space [e.g., Kinzler, 1997]. In simplified systems, it is a function of the silica activity of the liquid, with high silica contents and silica activities leading to low multiple-saturation pressures [Ghiorso et al., 1983; Balta and McSween, 2013]. As it is a fixed point in P-T space for each composition, we attempted to use it to evaluate the effectiveness of the MELTS algorithm.
 In all cases, calculations using the MELTS calibration place this multiple-saturation point at unreasonably low pressures. For example, the Y-98 calculations showed multiple saturation close to 0.3 GPa (Figure 6) and all of the calculated liquids reach their multiple-saturation point at < 0.4 GPa. This issue would affect any effort to model Martian crystallization paths using the original MELTS algorithm at moderate, crustal pressures.
 Because of this discrepancy, we repeated the calculations using the pMELTS calibration and found it to give more accurate estimates of multiple-saturation pressures. In Y-98, the multiple-saturation point was calculated at 1.10 GPa, just below the 1.2 GPa measured in experiments by Musselwhite et al. . For the Gusev basalt we calculated multiple saturation at 1.21 GPa, while experiments placed it at 1.0 [Monders et al., 2007] and 1.3 GPa [Filiberto et al., 2008]. However, unlike these liquids which are well matched, the multiple-saturation point in the NWA 1068 liquid is calculated at 1.24 GPa, a significantly lower pressure than the 1.7 GPa found in the experiments of Filiberto et al. . There is also a mineralogical difference worth noting for the Gusev composition; the experiments of Monders et al.  place orthopyroxene as the liquidus phase above the multiple-saturation pressure while the experiments of Filiberto et al.  produced pigeonite. Anhydrous pMELTS calculations using the Gusev composition calculated pigeonite as the liquidus phase above the multiple-saturation pressure, consistent with the results of Filiberto et al.  and indicating that our calculations matched those experiments particularly well.
 Based on these results, we recommend the pMELTS calibration be used in any calculation effort that could be impacted by whether olivine or pyroxene is the earliest crystallized phase or for any estimation of crystallization depth within or below the Martian crust (which corresponds to ~1 GPa [e.g., Monders et al., 2007]). If the MELTS calibration pressures are used, a correction consistent with the multiple-saturation comparisons performed here would be to multiply the calculated pressure by a factor of 4, although we cannot guarantee that the correction in olivine-pyroxene multiple-saturation pressures applies to all calculated phases based on the available data. Outside of the experiments on the NWA 1068 composition by Filiberto et al. , the pMELTS calibration fits multiple-saturation pressures in Martian magma compositions to within an error of less than 0.2 GPa.
 The disagreement between the measured NWA 1068 multiple-saturation pressure and that calculated pMELTS allows us to illustrate how to interpret disagreements between calculated results and experiments. Both experiments and calculations can have problems, and as demonstrated in this paper, there are documented issues within the MELTS algorithm. On its own, a single-model calculation should not be given weight over a set of experiments. However, in this case we are not simply comparing a single calculation to experimental results; instead, we have verified that the pMELTS calibration calculations successfully reproduce the multiple-saturation pressures of the other experiments to within a reasonable error and the calculated multiple-saturation pressure for NWA 1068 is within the range of the other Martian liquids. Comparison of the NWA 1068 bulk rock composition to the other compositions offers no explanation for why its multiple-saturation pressure would be elevated. Compared to Y-98, NWA 1068 has a similar XSiO2, lower Mg #, and lower XMgO + XFeO/XSiO2 (the components of olivine and orthopyroxene). Therefore, it is not surprising that the pMELTS calculations place the NWA 1068 multiple-saturation pressure at similar values to Y-98 and slightly above the Gusev basalt multiple-saturation pressure; the calculations are showing a smooth relationship between multiple-saturation pressure and composition. If the multiple-saturation pressure for NWA 1068 is elevated relative to the calculations, the reason for it is not apparent based on the compositions. In this case this variation requires either some experimental issue or a previously uncharacterized behavior in this composition. The latter possibility cannot be ruled out solely from the calculations, requiring additional experiments to confirm the previous results and possibly to explain the properties which lead to an elevated multiple-saturation pressure in that composition.
3.3 Temperature Calibration Issues
 Next we will consider an issue with the application of the MELTS algorithm that is well established in the literature; both calibrations have been reported to overestimate liquidus temperatures. In general, this error is larger when applying the MELTS calibration than the pMELTS calibration; for terrestrial compositions, a linear decrease of 20–40°C in calculated liquidus temperatures from the pMELTS calibration and of 50–100°C in the MELTS calibration is sufficient to correct for this error [e.g., Asimow and Longhi, 2004].
 Based on the experiments discussed here, this issue appears more complicated. Gross et al.  reported that pMELTS calculations for the Y-98 composition underestimated the temperature of olivine-orthopyroxene multiple saturation by 100°C compared to experiments from Musselwhite et al. , a result our calculations reproduce. For NWA 1068, our calculations give a multiple-saturation temperature that underestimates the experimentally produced temperature of Filiberto et al.  by a similar amount (100°C). This estimate is likely impacted by the elevated multiple-saturation pressure discussed previously; however, even at 1.7 GPa, pMELTS calculates a liquidus temperature 50°C lower than reported in the experiments. The typical misfit discussed previously required reducing the calculated temperatures by 20–40°C; using that correction would lead to estimates for the multiple-saturation temperature 100–150°C below these experiments.
 Despite these mismatches, calculations reproduce temperatures in the other available experiments with similar corrections to those used for terrestrial compositions (Figure 7). For the MELTS calibration, the 1 atm liquidus is a reasonable P-T point for comparison across compositions, and calculations are able to reproduce the 1 atm liquidus for the Gusev basalt of Monders et al.  to within 30°C, the 1 atm liquidus for EET-A tested by Longhi and Pan  to within 30°C, and the 1 atm liquidus for DAG 476 of Koizumi et al.  to within 25–50°C. MELTS calibration results are also able to reproduce some details from these two studies, including the 1 atm liquidus for Y-98 of Musselwhite et al.  within 10°C and the 1 atm liquidus for NWA 1068 to within 20°C. pMELTS calibration calculations also reproduce other experiments; for the Gusev composition pMELTS gives a temperature estimate for the multiple-saturation point that is 30–40°C higher than measured experimentally by Monders et al. . Similarly, calculations give estimates 40–50°C too high for the wet and dry 0.93 GPa liquidus temperatures measured by McCubbin et al. . In all of these cases except for the two highlighted studies, calculated temperatures overestimate experimental results to a degree similar to terrestrial compositions in both calibrations. We do not consider MELTS calculations at elevated pressures due to the olivine-orthopyroxene multiple-saturation issue discussed above, and we do not consider pMELTS calculations at atmospheric pressure as it is outside the intended range for pMELTS.
 Overall, the temperature mismatches for MELTS and pMELTS are similar to those seen for terrestrial compositions with the exceptions of the pMELTS-calculated Y-98 and NWA 1068 multiple-saturation temperatures. As with before when there was a disagreement between the MELTS algorithm results and specific experimental results, we can suggest two possible explanations: either there is some behavior in Martian liquids related to the stability of the liquidus minerals that has not been previously characterized or there is an issue with the experimental temperature calibration. Although this temperature mismatch happens in two distinct studies, both studies were done using a similar piston-cylinder device, so a common experimental issue could be indicated. Filiberto et al.  performed experiments on a similar composition to Monders et al.  and reported a liquidus temperature 50°C higher, but that difference was attributed to the presence of water in the experiments of Monders et al. . The multiple-saturation temperature of Filiberto et al.  is closer to the predictions made by pMELTS than the other two studies, but could be slightly elevated.
 We attempted several other comparisons to evaluate this disagreement. Multiple-saturation points have been measured experimentally for many terrestrial compositions. Temperatures over 1500°C were found by Maaløe, 2004 for Hawaiian basalts, but only at pressures above 2 GPa, significantly higher than either of these studies. Kinzler and Grove  compiled a series of multiple-saturation points from terrestrial liquids which fall in similar pressure ranges to these experiments but reported temperatures typically in the range 1200–1350°C, again consistent with the expectation from pMELTS calculations. Beattie et al.  presented an olivine-liquid thermometer based on experiments but calibrated independently from MELTS. We inputted the compositions from these studies into that calibration and again found that the estimated temperatures were well below those reported in the experiments, although the estimates are ~25°C higher than those calculated by pMELTS.
 We thus can find no obvious comparison from the literature to explain why these temperatures are so much higher than predicted by pMELTS. Additional experiments may be necessary to understand whether these temperatures are reproducible and whether they give new insight into the properties of Martian basalts.
3.4 Why Not pMELTS?
 Given the issue highlighted previously with the MELTS calibration being unable to predict the multiple-saturation points of Martian magmas while the pMELTS calibration can, an obvious question to ask is why the pMELTS calibration should not simply be used for all Martian crystallization calculations even outside the recommended pressure range of >1.0 GPa. Here we provide two examples of how the pMELTS calibration is unable to match actual compositions outside of the recommended range.
McCubbin et al.  produced plagioclase in their crystallization experiments and measured compositions between An36 and An46 at pressures of 0.93 GPa. When we calculated plagioclase compositions for the same conditions, we found higher sodium contents corresponding to a composition of An32. While the calculations are accurate at elevated pressure, pMELTS continued to calculate high sodium contents in plagioclase even when used at lower pressures. Monders et al.  measured An75 plagioclase in their 1 atm experiments, but at similar pressures pMELTS still calculates sodium-rich feldspars with An40 compositions. On the other hand, the original MELTS calibration calculates that the initial feldspars to crystallize from that composition would be An72, accurately fitting the experimental results.
 In addition, we note that pMELTS continues to calculate the presence of feldspar at extreme pressures; we ran a test calculation up to 2 GPa and still found feldspar present. This feldspar was K rich, with composition Or90Ab10. In this case, the algorithm may be calculating the presence of feldspar solely because of the limited set of phases in which potassium can be placed, an issue briefly noted by Balta et al. [2011a].
 Similarly, there is a well-established change in the composition of clinopyroxenes with increasing pressure; the CaO content of clinopyroxene declines and substitution of other species increases as pressure increases [e.g., Balta et al., 2011a]. pMELTS is able to simulate this effect, as CaO contents of clinopyroxenes do decrease with increasing pressure. However, when used at pressures outside the recommended range, pMELTS continues to predict reduced CaO contents in clinopyroxene. Calculations show that clinopyroxenes calculated using the pMELTS calibration can contain up to 5 wt. % less CaO than that calculated by the MELTS calibration at comparable pressures. As clinopyroxene can represent >10% of Martian rocks, using pMELTS outside of its range will introduce additional errors in the calculated liquid lines of descent.
3.5 Compositions of Olivine and Pyroxenes
 Using our calculated olivine and pyroxene compositions, we can estimate the variance between calculated liquid lines of descent and observed experimental results. Filiberto and Dasgupta  examined experimental measurements of olivine-liquid KD values from Martian compositions and determined that a KD of 0.34 adequately fits most Martian samples close to the liquidus. At the liquidus, the MELTS calibration gives KD values outside this range (~0.25), while the pMELTS calibration accurately calculates KD values close to 0.34. In the MELTS calibration, despite the early variance the calculation rapidly converges to a KD within error of the Filiberto and Dasgupta  value; less than 10% olivine crystallization is required for this convergence. In batch crystallization mode, the early-crystallized olivine simply reequilibrates to the correct KD; in fractional crystallization mode this variance produces a slight compositional error on the order of 0.5 wt. % FeO or MgO by the point pyroxene saturation is reached (Figure 8). Overall, that is the error expected on liquid lines of descent in the MELTS calibration due to olivine compositions, while in the pMELTS calibration the errors are negligible.
 Pyroxene compositions are more difficult to put into context as Martian pyroxenes display significant zoning and possibly diffusive or shock reequilibration [e.g., Balta et al., 2013] and most of the available experiments do not proceed to low enough melt fractions to crystallize significant augite. The pyroxene compositions calculated using the MELTS calibration however do resemble the patterns actually measured in shergottite meteorites. Calculated pyroxene compositions from batch and fractional modes are shown in Figure 9 along with fields representing pyroxenes from the meteorites Shergotty (which shows a small range in pyroxene compositions) and Y-98 (which shows a larger range in pyroxene compositions). The batch crystallization case does not match the highest Mg content, but that is due to additional olivine calculated to crystallize prior to pyroxene crystallization, which changes the composition of the equilibrium pyroxene slightly. Overall, the pyroxene major element abundances calculated by MELTS show a generally good match to the pyroxene compositions measured in shergottite meteorites if some degree of mixing and equilibration between augite and pigeonite accounts for the intermediate compositions. It is more difficult to estimate errors on the liquid lines of descent from the pyroxenes due to the lack of a comparable simple crystallization model, but in all of the major cations in pyroxene the composition alone is unlikely to create errors greater than the level of 1 weight percent on any oxide.
 Pyroxene also hosts minor elements including Al2O3 and TiO2. MELTS and pMELTS calibration results both reproduce the pyroxene Al2O3 abundances reported in experiments and measured in natural samples. Calculations show Al2O3 contents of approximately 1.0 wt. % in calculated orthopyroxenes, increasing slightly to just over 2 wt. % in augites. Similarly, experimental pyroxenes show 1–2 wt. % Al2O3 [e.g., Musselwhite et al., 2006; Monders et al., 2007; Filiberto et al., 2010], and measured pyroxene compositions are similar as well [e.g., Balta et al., 2013]. Thus, Al2O3 contents of pyroxenes are a good match to observations. TiO2 contents of experimental pyroxenes cluster below 0.1 wt. % [Musselwhite et al., 2006; Monders et al., 2006; Filiberto et al., 2010]. Calculations using both the MELTS and pMELTS calibrations give pyroxene compositions within this range close to the liquidus but also predict elevated TiO2 contents in later-crystallized pyroxenes with > 0.5 wt. % TiO2 in some augites. Augites measured by McCubbin et al.  contain up to 0.25 wt. % TiO2. Thus, the MELTS algorithm in both calibrations does an adequate job of fitting early-crystallized pyroxene TiO2 contents but may overestimate compatibility of TiO2 late in crystallization.
3.6 Crystallization of Distinct Phases
Liu et al.  presented a phase diagram for EET-A based on pMELTS calculations which showed augite only appearing subsolidus; however, augite was found to be a magmatic phase in the actual sample. This calculation is an example of a situation where the accuracy of the algorithm is sufficient to calculate that the augite stability field is close when the solidus is crossed but not precise enough to place the augite saturation curve at the appropriate temperature. If augite were calculated to begin crystallizing 50°C higher than found in the actual calculations, similar to the temperature correction discussed previously, its appearance would seem reasonable relative to the calculated solidus. In all previous cases we estimated that the errors on the calculated liquid lines of descent would be at the level of <1 wt. %; however, those estimates were based solely on the composition of the minerals. A difference of 50°C between the calculated saturation point for a phase and the actual saturation point can cause larger errors in the calculated liquid composition, but it is difficult to estimate the occurrence or magnitude of such errors as few experiments report temperatures where phases begin crystallizing far below the liquidus. For the Y-98 composition MELTS calculates orthopyroxene saturation within 20°C of the temperature observed in the experiments of Musselwhite et al.  at 1 atm, a successful reproduction of some details far from the liquidus. Similarly, after augite formed in the EET-A calculations its modal abundance increased rapidly to a level consistent with the abundances reported in that sample [Liu et al., 2013], which again could suggest that this type of error could be minimal for some compositions or conditions. Thus, in the next section we give recommendations for how to use MELTS calculations for modeling Martian compositions and how to improve the calibrations in the future.
4 Applications of the Calculations to Martian Compositions
 We have focused on characterizing specific issues with the use of the MELTS algorithm for Martian magmas and interpretation of calculated results. However, as we have also attempted to detail, the MELTS algorithm, using both the MELTS and pMELTS calibrations, can be successful in modeling many details of magmatic crystallization, including compositions of the major minerals olivine, pyroxene, and feldspar, as well as the distribution of minor elements and the abundances of crystallized phases. Thus, the current calibrations for the MELTS algorithm have the ability to supply substantial insight into Martian (and other extraterrestrial) compositions if the properties of the model are understood. Here we will suggest how future users can best interpret MELTS calculations when applied to these compositions and outline experimental paths for the future.
4.1 Multiple Saturation
 Perhaps the most disappointing result of this examination is that neither calibration accurately calculates the olivine-orthopyroxene phase equilibria across a wide range in pressures. Calculations using the MELTS calibration are able to reproduce the crystallization temperatures of olivine and pyroxene at 1 atm pressure as well as their compositions and the composition of plagioclase. Similarly, calculations using the pMELTS calibration are able to reproduce the pressure of multiple saturation. We previously noted that the MELTS calibration is recommended for use below 1.0 GPa while the pMELTS calibration was recommended for use above that pressure; however, the MELTS calculations performed here significantly miss the olivine-pyroxene relationship at 0.3 GPa. Thus, there is no simple way to perform a MELTS calculation at pressures that could be representative of the Martian crust. The correction noted previously, multiplication of MELTS calibration pressures by a factor of 4, is consistent with the available data and could allow for liquid lines of descent to be calculated effectively in the range up to 1.0 GPa. However, we cannot guarantee that the same correction works for all phases because the available experiments typically do not proceed to plagioclase saturation, making complete comparisons impossible. Thus, the pMELTS calibration should be considered as a possible supplement in the case of characterizing phase relations.
 For constructing phase equilibria of Martian basalts at the liquidus, we recommend the pMELTS calibration be used. Although the recommendations are to only apply pMELTS above 1.0 GPa due to the issues discussed previously, pMELTS calculations produce generally reasonable changes in multiple-saturation pressures with composition. To construct phase equilibria for crystallizing magmas and characterize the relationship between olivine and pyroxenes in the lower Martian crust or upper mantle, the pMELTS calibration should be used. While we cannot recommend pMELTS be used outside of its calibrated range, for compositions that reach multiple saturation at pressures below 1.0 GPa, it is difficult to judge whether the factor-of-four correction required for the MELTS calibration or calculations using the pMELTS calibration will be more accurate. This issue with calculations at these pressures can be dealt with, but it must be understood by users of the algorithm and characterized in future usage.
 As the pMELTS calibration also accurately calculates compositions of coexisting liquids and minerals at Martian mantle pressures and the multiple-saturation point of magmas, we anticipate that pMELTS calculations will reproduce properties of Martian magmatism if used to represent partial melting of the mantle rather than crystallization as we have done here. Issues such as the partitioning of potassium referred to previously should be taken into account in those efforts, but otherwise, application of the pMELTS calibration to Martian mantle compositions is a fertile path for additional research.
4.2 Known Issues
 As discussed previously, there are two known issues that should be taken into account by users which we highlight again. First, the two calibrations of the MELTS algorithm both overestimate liquidus temperatures by ~50°C and all calculations should take this error into account. Similarly, spinel begins crystallizing earlier in calculations than in reality, depleting the magma in Cr2O3. Spinel is the main phase which takes up Cr2O3, and thus, it cannot be ignored or suppressed in calculations, but we caution against drawing conclusions from the presence or absence of chromian spinel. We recommend that users include spinel in their calculations but do not treat spinel saturation points as liquidus temperatures and expect small errors, on the order of 0.1–0.3 wt. % Cr2O3 in liquid lines of descent.
4.3 Technique Suggestions
 The algorithm in the available calibrations is able to reproduce the compositions of pyroxenes, olivine, plagioclase, and other phases such as garnet and oxides other than Cr-spinel, to a good degree of accuracy if the constraints noted above are considered. When we propagate the variances between measured and calculated compositions, we estimate that they produce changes in liquid lines of descent smaller than 1 wt. % on the major oxides, which we consider to be a success.
 However, there are larger possible errors associated with the order of crystallization of phases, and from the available data the magnitude of these errors is difficult to assess. For an example, if crystallization of a phase such as plagioclase is calculated to begin 50°C below where it actually does, this mismatch could produce significant errors in liquid lines of descent. The examples noted above, orthopyroxene crystallization in Y-98 and clinopyroxene crystallization in EETA 79001A, suggest that these errors are small, but we cannot constrain them fully.
 Our best suggestions for interpreting calculated crystallization paths are as follows. First, expect that errors of up to 1 wt. % on the major oxides are possible as melt fractions decrease. Second, note the known errors discussed in section 4.2. Third, do not rely on a single liquid line of descent calculation performed under one condition as fully representative of the calculated results. If attempting to fit a specific property observed in an actual sample, perform a series of calculations while varying parameters such as pressure, water content, oxidation state, and bulk composition in order to test not only whether MELTS calculations can fit the parameter of interest but also to understand the sensitivity to those variables as well. By performing multiple calculations, as done here, users will be better equipped to evaluate whether the calculated results fit the property of interest under most circumstances or only in certain cases and will be able to assess the sensitivity of the calculated results to small changes in mineral saturation.
 Finally, we also recommend that users be cognizant of experimental results where applicable and always attempt to compare calculated results to some sort of “ground truth”, whether they be experimental results or measurements of actual samples. This recommendation of course is not solely for the MELTS algorithm but also should be considered in most modeling efforts.
4.4 Future Experimental Work
 The results of this study suggest that significant improvements in modeling capability can be achieved if suitable experiments are performed. The lack of a single MELTS calibration capable of fitting crystallization at pressures between 0.1 GPa and 1 GPa has to our knowledge not been previously described, but this pressure range on Mars covers a much greater depth range than on Earth. Consequently, the accuracy of multiple-saturation pressures calculated by the MELTS calibration may not have been examined in this level of detail. Several authors have noted that this pressure range falls into a gap between 1 atm and gas pressure media and solid-state/piston-cylinder apparatus pressures [e.g., Villiger et al., 2007; Neave et al., 2013], a possible cause for this issue. This pressure range needs additional experimental exploration to allow for refinement of future versions of the MELTS calibration.
 Second, there are a number of variables we were unable to assess from the current experiments. While there are reasonable numbers of experiments at the liquidus, few experiments produce compositions close to the solidus in Martian compositions at crustal pressures, limiting our ability to assess these phases. Presumably, this lack of data would impact future efforts to improve the MELTS calibration as well. We hope that future experimental efforts on Martian compositions will consider producing samples at lower melt fractions to more fully characterize crystallization paths.
 Third, we note that the models for minor elements and possibly trace phases contain some of the largest relative errors observed here, such as the issues discussed for TiO2 and Cr2O3. Experiments measuring the behavior of these elements under a wider set of conditions would help expand both the available database and improve future calibrations of the MELTS model. We also note that we have not considered minor phases such as apatite or sulfides in this description; as experiments improve on those phases, the ability to model them will also improve.
 Finally, for Martian compositions other volatile elements, such as CO2, Cl, and F have been proposed as contributors and some have been tested experimentally. A long-term goal should be to include these elements in the phase relations of future MELTS calibrations, but the experiments on these elements are in their infancy. We will attempt to estimate their impact below based on the available experiments but hope that more detailed examinations of their impact on all phases become available in the future.
5 Applications of Our Database of MELTS Calculations
5.1 Previous MELTS Modeling of the Gusev Basalts
Monders et al.  performed calculations using the MELTS calibration on their Gusev crater experimental composition at atmospheric pressure and noted that the compositions fit the olivine-spinel portion of the crystallization path but seriously missed the late portions. Consequently, they suggested that the MELTS algorithm produced a poor fit for that composition and judged that using it for similar Martian compositions was risky. Similarly, Francis  argued that the Columbia Hills basalts represented an exhumed layered intrusion based in part on his inability to fit the crystallization of Gusev basalts using the MELTS algorithm. These arguments contrast with the conclusions of McSween et al.  and Udry et al. (submitted manuscript, 2013) that MELTS calculations reproduce significant compositional details of the Gusev basalts.
 We repeated the calculations of Monders et al.  and observed the same deviant calculated compositions, with up to 50 wt. % FeO and as low as 25 wt. % SiO2. On detailed examination, we noted an actual error in this sequence; when the MELTS algorithm attempts to calculate plagioclase saturation, it calculates a huge amount of plagioclase crystallization in a 1° step, producing a large composition break. The calculated melt drops from >41 wt. % SiO2 to 26 wt. % SiO2 in a single 1° step, inconsistent with smooth crystallization. However, when we simply increase the pressure to 0.1 GPa using the same composition, this error vanishes and the MELTS algorithm produces a smooth compositional path throughout the full temperature range (Figure 10). Similarly, using the modern calculation routines in rhyolite-MELTS produces a smooth crystallization path at 1 atm. This comparison illustrates the utility of multiple calculations; the study of Monders et al.  moved into an area which produces an error, but the error is easily removed by what is effectively a small change in settings.
 Although much of the analysis by Francis  is not based on MELTS, we can comment on the analysis of MELTS calculations in that work. For example, that work shows a discontinuous increase in measured TiO2 with decreasing MgO (and thus, increasing crystallization) in the fractionating Gusev basalts but argues that it is difficult to fit. However, a discontinuous increase in TiO2 is readily demonstrated in MELTS calculations; TiO2 increases slowly while MgO decreases rapidly in an olivine-spinel crystallization region, whereas TiO2 increases much more rapidly once pyroxene and plagioclase crystallization begins (Figure 11). The calculations shown in Figure 11 proceed to low melt fractions, and consequently, the calculated abundance of TiO2 is a strong function of its partioning into pyroxene, which as we noted previously has a possible variance of several tenths of a weight percent. In this case, therefore, the MELTS algorithm is able to do a better job than previously described at fitting the measured compositions if the margin of error is taken into account.
Francis  argued that fitting the Fe-Mg crystallization paths happens best at extremely high oxygen fugacities, which would produce high-Mg # olivine instead of the ~ Fo60 olivine actually measured. Like that work, we can find no single crystallization path which fits all of the observed compositions perfectly, but several additional insights can be made. Francis  suggested that typical terrestrial compositions do not show FeO enrichment with increasing crystallization; however, substantial FeO enrichment has been produced experimentally for Martian compositions by McCubbin et al.  and appears in MELTS calculations as well. The highest MgO points shown by Francis  could also be produced by olivine accumulation. The Fo60 olivine measured at Gusev crater is readily produced in our calculations if we thus allow for equilibration between olivine and liquid during crystallization, and much of the suite of Gusev compositions can be produced by a combination of crystallization and mixing. These processes are common in active magmatic systems and can produce a variety of bulk compositions without the requirement of a layered igneous intrusion. We do note that we cannot fit all of the compositions seen in Gusev crater (in particular the extremely high-P2O5 contents), requiring some additional process or incorporation of nonmagmatic material [Usui et al., 2008], but we find that crystallization models based on the MELTS calculations are more able to explain the geochemical trends than argued by Francis .
5.2 High-FeO Basalts and the Rocks of Gale Crater
 The study of McCubbin et al.  produced a trend of FeO enrichment and SiO2 depletion when the Gusev basalt composition was crystallized at elevated pressure without water, with melts containing up to 22 wt. % FeO. In this and other work [Nekvasil et al., 2009] several possible results of this process were presented, including the formation of lower crustal cumulates and selective eruption of evolved compositions late in Martian history.
 With our database of calculated crystallization paths, we are able to build upon these conclusions with more specific constraints regarding the impacts of water on the density. As we noted previously, it is advantageous to use MELTS and pMELTS calculations in coordination with available experiments as a way of both confirming the calculated trends and expanding the experimental results to additional conditions. In the pMELTS calculations the elevated FeO is driven by the identity of the liquidus phase; if olivine is on the liquidus, FeO contents begin slowly decreasing and decrease as long as olivine crystallization continues. However, we find substantial FeO enrichment when pyroxene is calculated as the liquidus phase, which occurs at elevated pressures and in dry magmas (Figure 12). Little olivine is calculated to form late in crystallization after plagioclase saturation, and consequently plagioclase crystallization also leads to buildup of FeO in the magma. This scenario repeats in Martian compositions across a variety of pressures and compositions, is supported by experimental results, and is not strongly impacted by the exact saturation point of any particular phase; thus, more detailed examination of these scenarios meets all of the standards we set previously. McCubbin et al.  hypothesized that decreasing water contents in the Martian mantle with time could lead to the formation of cumulates at the base of the Martian crust. As the MELTS algorithm includes calibrations for the partial molar volumes of the various components, we are able to build upon those results by characterizing how a wider variety of compositions evolve and how their densities evolve.
 As shown in Figure 12, the highest FeO contents are produced by fractional crystallization at pressures below the base of the Martian crust. The MELTS calibration calculates FeO to behave as an incompatible element at crustal pressures due to the lack of olivine (Figure 10). Consequently, we again focus on pMELTS calculations for interpretations of crystallization under lower crustal conditions.
 Using gravity data, Wieczorek and Zuber  estimated that the density of the Martian crust was in the range 2.7–3.1 g/cc. This range is particularly important as pMELTS calculates the anhydrous density of these Martian magmas at the pressure of the base of the crust to be ~2.9 ± 0.4 g/cc (Figure 13). Therefore, within the range of possible Martian crustal densities, anhydrous magmas at the base of the crust could be inherently negatively buoyant and unable to erupt. Furthermore, as these magmas fractionally crystallize, they produce minerals with greater density than the liquid concomitant with an increase in their own density due to the increasing FeO content. As both liquid and solid increase in density with crystallization, the volume of the combined material must decrease with cooling. Decreasing volume would counteract overpressure due to continued supply of magma pressure from below; consequently, a prediction based on pMELTS is that anhydrous magmas are very likely to stagnate at the base of the Martian crust and may never erupt at the surface. pMELTS also calculates the density of the solid phases formed from crystallization of these stagnant magmas, and at pressures above 1.0 GPa, garnet is calculated to be stable. Garnet is a high-density phase, and if substantial garnet is formed, the solid density could exceed the 3.55 g/cc upper limit for the mantle density estimated by Wieczorek and Zuber . Thus, for anhydrous crystallization at the base of the Martian crust, complete stalling and crystallization followed by delamination and sinking of the cumulate deeper into the mantle is plausible [e.g., Parmentier and Hess, 1992]. The negative buoyancy of eclogitic cumulates could impose a limit on the allowable thickness of the Martian crust; if enough basaltic material were added to the crust to allow the formation of garnet in the lower crust, it would delaminate and sink. Papike et al.  hypothesized that pyroxene-rich or eclogite bodies could contribute to Martian magmatism despite the lack of subduction. If such bodies do exist, stagnation at the bottom of the crust followed by delamination is a likely mechanism for generating that type of heterogeneity.
 Basaltic volcanism has continued on Mars up to geologically recent periods, so trapping of all magmas within the planet cannot be the only plausible result. The first possible solution to this problem simply is that erupted Martian magmas may all be hydrous; the addition of ~ 1 wt. % water to any of these Martian compositions reduces the calculated density below 2.7 g/cc, enough to allow for density-driven migration upward through the Martian crust. Furthermore, the addition of water also promotes olivine crystallization, which removes FeO from the melt and prevents the density increase, as seen both in these calculations and in the experiments of McCubbin et al.  (Figure 13).
 Several alternative possibilities are worth considering as well. First, simple batch crystallization helps limit iron enrichment as FeO is transferred to the solid. This effect alone reduces the calculated maximum FeO by 2 wt. %. However, this effect is most notable at high levels of crystallinity and lower temperatures; high levels of crystallinity (>50%) could again leave magmas at risk of stagnating.
 Other volatile elements including Cl and carbon-rich species have been postulated to be present in Martian magmas as well [Filiberto and Treiman, 2009a; McCubbin et al., 2012; Stanley et al., 2012; Wetzel et al., 2013]. The MELTS algorithms are not calibrated to account for these species, but we can speculate based on the available literature. We noted previously that water stabilizes olivine relative to pyroxenes. This effect can be observed graphically in Figure 14 where we show calculated liquidus curves for NWA 1068; when water is added, the curves move down in temperature and the multiple-saturation point shifts toward higher pressures, enlarging the olivine-only field. Filiberto and Treiman [2009b] performed experiments with Cl present to evaluate its effect on liquidus temperatures, but their experiments also showed decreasing multiple-saturation pressures and expansion of the pyroxene-only fields. Cl therefore has the opposite effect of water in basaltic melts in terms of mineral stability, destabilizing olivine and stabilizing pyroxenes (Figure 15). CO2 dissolved in magmas has long been known to have a similar effect; it polymerizes the melt and thus stabilizes pyroxene relative to olivine [e.g., Mysen et al., 1976]. Although the presence of CO2 or Cl could enhance eruptability through lowering the bulk density of the liquid [Lange, 1994], by reducing the stability of olivine, these elements would also be expected to enhance magmatic FeO with crystallization. Volatiles other than water therefore could promote passage through the crust, but if magma does stagnate, the density trap caused by increased FeO may remain.
 Other volatile substitutions, such as C-O-H fluids [Mysen et al., 2011; Steele et al., 2012] and iron-carbonyl groups [Wetzel et al., 2013], could impact these conclusions, but current data are insufficient to speculate about the petrologic results of their presence. However, we can speculate on one final detail; water also is well known to destabilize plagioclase [e.g., Beard and Lofgren, 1989], similar to the effect we illustrated for pyroxenes. If the behaviors of CO2 and Cl are analogous, then we would expect that those components would serve to enhance plagioclase stability. The resulting liquid line of descent in a system with CO2 or Cl as the dominant volatile would therefore show early formation of pyroxene and plagioclase at the expense of olivine, exacerbating the effect of increasing FeO of the magma until it began crystallizing Fe-Ti oxides.
5.3 Application to Orbital Composition Measurements
McCubbin et al.  speculated that dehydration of the Martian mantle over time would lead to the youngest surface compositions becoming SiO2 poor and FeO rich. However, Baratoux et al.  compiled compositional data from the orbiting Gamma-Ray Spectrometer on Mars Odyssey and showed that there is a slight depletion in FeO in younger volcanoes. Balta and McSween  argued that other geochemical trends measured from orbit are consistent with dehydration as argued by McCubbin et al.  but did not model the FeO depletion. An alternative possibility is that the FeO depletion measured in the recent volcanoes may not be a consequence of the melting conditions but of density. The most recent volcanoes include Olympus Mons, which rises to a height of 22 km [Plescia, 2004]. The height of these volcanoes could impose an additional requirement such that only magmas that have reduced FeO during crystallization have enough buoyancy to reach the surface. Eruption could therefore require a combination of equilibrium crystallization, shallow level olivine crystallization, or partial melting and assimilation of crustal material; all of which could reduce FeO in magmas erupted at the volcanic summits.
 On Sol 86 of the Curiosity rover mission in Gale Crater, a rock known as “Et-Then” was examined and analyzed for bulk rock composition by the Alpha-Particle X-ray Spectrometer (APXS). The rover was simultaneously conducting other analyses, and consequently, the APXS measurement was conducted at a standoff distance of 6 cm with no rock surface preparation. This lack of preparation led to a high margin of analytical error and a possibility of surface dust contamination. The rock appears fine grained in images but does not show obvious textural indications of whether it is igneous or sedimentary. Despite these uncertainties, the APXS-measured composition resembles the compositions predicted from our MELTS calculations, particularly in the FeO content.
 Et-Then is a low-SiO2 (43.6 ± 4 wt. %), high-FeO (27.5 ± 1.3 wt. %) rock (Table 1). If we assume it is volcanic, its composition would be classified as a tephrite/hawaiite, within the alkali basalt field. Given the variances in the MELTS calibrations and the APXS measurement, there are several paths in MELTS calculations which produce similar compositions. The most depleted composition tested here, that of Y-98, produces similar FeO contents when crystallization takes place at pressures above the multiple-saturation point. For example, at 16 kbar and dry, the calculated liquid produced by fractional crystallization of Y-98 reaches 27 wt. % FeOTotal with 3.4 wt. % MgO, 2.9 wt. % Na2O, 43.9 wt. % SiO2, and 1.7 wt. % TiO2; all of which are within error of the measured Et-Then composition. There are some differences: Al2O3 and CaO are too high in the calculated liquid, K2O is very low as it is virtually absent (0.02 wt. %) in the Y-98 starting composition, and the volatiles are not included, but overall, the compositions of many oxides are similar. The FeO/MnO ratio of Et-Then differs from some measured Martian basalts, but large degrees of fractional crystallization or the formation of garnet, both of which are suggested by our MELTS calculations, have been shown to alter FeO/MnO ratios in terrestrial magmas and may do so here as well [Qin and Humayun, 2008; Balta et al., 2011b]. The other magmas tested all reach similar values of FeO enrichment when crystallization takes place above the multiple-saturation pressure, but the calculated liquids are too high in CaO and Al2O3 to perfectly match Et-Then. All of these compositions are observed late in crystallization, following 50–80% crystallization of the initial magma, requiring substantial crystallization at depth followed by separation of the groundmass magma. As they are high in FeO, they would be expected to be denser than the Martian crust. Eruption of these magmas is therefore difficult, but their low-SiO2 contents would render them low viscosity, and so separation could still be possible. These compositions could also be impacted by the presence of volatiles; although water would prevent the FeO increase, Cl or CO2 would promote it, possibly reaching high FeO earlier in crystallization and also reducing the density and viscosity [Lange, 1994]. The CaO and Al2O3 excesses in the calculations could also be explained by those volatiles if they promote plagioclase or garnet crystallization to a degree greater than calculated by MELTS as discussed previously. Cl and SO3 were measured in Et-Then, although it cannot be determined to what degree those components are present in the bulk rock versus a dust coating.
Table 1. Et-Then Compared With Calculated Compositions
 One additional calculated scenario using the MELTS calibration produces compositions resembling Et-Then at low pressures. Calculations for low-pressure (<0.15 GPa nominal, <0.6 GPa corrected) crystallization of the Gusev basalt and NWA 1068 give compositions within error of Et-Then for many oxides after ~60–70% crystallization. From these starting compositions CaO is still elevated relative to Et-Then, but in this case Al2O3 is well matched. The remaining Martian magmas did not show this degree of FeO enrichment at low pressures, such that if Et-Then were produced by low-pressure crystallization, it would require a unique starting magma which crystallizes only limited amounts of olivine, possibly caused by elevated alkali elements (consistent with the alkaline Et-Then composition).
Stolper et al.  argued that another alkaline basalt analyzed by Curiosity, Jake Matijevic, could be produced by suppression of plagioclase, which Udry et al. (submitted manuscript, 2013) argued could be produced by crystallization at elevated pressures with water present. This high-pressure crystallization possibility is similar to the mechanisms we suggest for Et-Then, although suppression of olivine rather than plagioclase is required in the latter case. Even though this rock cannot be guaranteed to be igneous, its chemistry is predicted as a normal product of Martian crystallization by the MELTS algorithm. If CO2 or Cl were involved in the suppression of olivine, those elements could degas and generate pyroclastic eruptions which could produce fine grain sizes or sedimentary textures as well.
 We conducted hundreds of calculations using the MELTS algorithm and the pMELTS calibration of the crystallization of a variety of Martian magma compositions and conditions. We find that the calculations are generally able to reproduce a number of features of Martian compositions, but there are also some issues which should be considered by any researcher applying these models to Martian compositions.
 The MELTS algorithm is poorly calibrated for the stability of chromian spinel, depleting the liquid in the Cr2O3 component earlier than occurs in reality.
 The MELTS calibration significantly underestimates the olivine-orthopyroxene multiple-saturation pressure. However, the pMELTS calibration is much more accurate, giving pressure estimates that are within 0.2 GPa of experimental studies performed on the same compositions. We recommend that the pMELTS calibration be used to determine pressures that are above 1.0 GPa. Pressures calculated by the MELTS algorithm can be roughly corrected by multiplying by a factor of 4.
 The MELTS and pMELTS calibrations have previously been shown to overestimate crystallization temperatures for terrestrial magmas; a correction of 50°C is found to be appropriate for Martian magmas. However, selected experiments report temperatures much higher than estimated by the MELTS calculations, an issue requiring further experimental characterization.
 Both calibrations simulate compositions of major minerals well when used under the appropriate pressure conditions. Generally, liquid lines of descent can be calculated in Martian compositions with variance from experimental results on the order of ~1 wt. % or less for most major oxides. However, we have limited ability to confirm that the algorithms accurately reproduce the crystallization temperatures of minerals which form near the solidus. Thus, we recommend that future users perform multiple calculations and continue to compare with experiments to evaluate the sensitivity of calculated results to particular phases and verify their accuracy.
 The MELTS and pMELTS calculations consistently produce high-FeO magma compositions when water is not present. Volatiles such as Cl and CO2 could exacerbate FeO enrichment, leading to high-density magmas that may not be able to be erupted and FeO-rich cumulates which may sink within the Martian mantle. We suggest that the low-FeO magmas erupted in recent volcanoes may be a consequence of the elevated FeO and density, and also note that a high-FeO rock measured by the Curiosity rover is similar to compositions predicted by the MELTS calibration and may represent one of the simulated high-FeO magmas.
 This work was supported by NASA Cosmochemistry grant NNX13AH86G to HYM. The MSL-M-APXS-2-EDR-V1.0 data set was obtained from the Planetary Data System (PDS). We thank David Baratoux for editorial handling, and detailed, helpful reviews were provided by Mark Ghiorso and Dave Draper.