# Reassessing the thermal history of martian meteorite Shergotty and Apollo mare basalt 15555 using kinetic isotope fractionation of zoned minerals

Frank Richter, Lee M. Saper, Johan Villeneuve, Marc Chaussidon, E. Bruce

Watson, Andrew M. Davis, Ruslan A. Mendybaev, Steven B. Simon

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► To cite this version:

Frank Richter, Lee M. Saper, Johan Villeneuve, Marc Chaussidon, E. Bruce Watson, et al.. Reassessing the thermal history of martian meteorite Shergotty and Apollo mare basalt 15555 using kinetic isotope fractionation of zoned minerals. Geochimica et Cosmochimica Acta, 2021, 295, pp.265-285. 10.1016/j.gca.2020.11.002. insu-03590098

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# Reassessing the thermal history of martian meteorite Shergotty and Apollo mare basalt 15555 using kinetic isotope fractionation of zoned minerals

Frank Richter<sup>a*</sup>, Lee M. Saper<sup>b</sup>, Johan Villeneuve<sup>c</sup>, Marc Chaussidon<sup>d</sup>, E. Bruce

Watson<sup>e</sup>, Andrew M. Davis<sup>a</sup>, Ruslan A. Mendybaev<sup>a</sup>, Steven B. Simon<sup>f</sup>

<sup>a</sup> The University of Chicago, 5734 South Ellis Avenue, Chicago, IL 60637, USA

<sup>b</sup> California Institute of Technology, Pasadena, CA, USA

<sup>c</sup> CRPG, Université de Lorraine, Nancy, France

<sup>d</sup> Institut de Physique du Globe de Paris, Paris, France

<sup>e</sup> Rensselaer Polytechnic Institute, Troy, NY, USA

<sup>f</sup> University of New Mexico, Albuquerque, NM, USA

October 27, 2020

## Abstract

Elemental abundance and isotopic fractionation profiles across zoned minerals from a martian meteorite (Shergotty) and from a lunar olivine-normative mare basalt (Apollo 15555) were used to place constraints on the thermal evolution of their host rocks. The isotopic measurements were used to determine the extent to which diffusion was responsible for, or modified, the zoning. The key concept is that mineral zoning that is the result of diffusion, or that was significantly affected by diffusion, will have an associated diagnostic isotopic fractionation that can quantify the extent of mass transfer by diffusion. Once the extent of diffusion was determined, the mineral zoning was used to constrain the thermal history. An isotopic and chemical profile measured across a large zoned pigeonite grain from Shergotty showed no significant isotopic fractionation of either magnesium or lithium, which is evidence that the chemical zoning was dominantly the result of crystallization from an evolving melt and that the crystallization must have taken place at a sufficiently fast rate that there was not time for any significant mass transfer by diffusion. Model calculations for the evolution of the fast-diffusing lithium showed that this would have required a cooling at a rate of about ~ 150°C/h or more. Measurable isotopic fractionation across a zoned olivine grain from lunar mare basalt 15555 indicated that the chemical zoning was mainly due to crystallization that was modified by a small but quantifiable amount of diffusion. The results of a diffusion calculation that was able to account for the amplitude and spatial scale of the isotopic fractionation across the olivine grain yielded an estimate of 0.2°C/h for the cooling rate of 15555. The results of an earlier study of zoned augite and olivine grains from martian nakhlite meteorite NWA 817 were reviewed for comparison with the results from Shergotty. The isotopic fractionations near the edges of grains from NWA 817 showed that, in contrast to Shergotty, the lithium zoning in augite and of magnesium in olivine was due entirely to diffusion. The isotopic fractionation data across zoned minerals from the martian meteorites and from the lunar basalt were key for documenting and quantifying the extent of mass transfer by diffusion, which was a crucial step for validating the use of diffusion modeling to estimate their cooling rates.
# 1. INTRODUCTION

Compositional zoning, which is a common feature of many igneous minerals, can develop when crystallization proceeds at a sufficiently fast rate that the mineral cannot maintain bulk equilibrium with the evolving melt from which it is crystallizing. Here, such zoning will be referred to as crystallization zoning. Mineral zoning can also arise from, or be modified by, diffusion during or after crystallization. Establishing the extent to which diffusion caused or modified a given instance of mineral zoning is critical when zoning is used to constrain the thermal history and chemical evolution of a mineral grain. A number of approaches have been developed to determine the role of diffusion in connection with igneous mineral zoning. An often applied method involves comparing the zoning of two or more elements with significantly different diffusion rates with the expectation of how their initial profiles would evolve to different degrees if diffusion was the operative process (for examples, discussion, and mathematical formulation, see Costa et al., 2008 and Watson and Cherniak, 2015). In the case of minerals such as olivine, where the diffusion rate of major and trace elements depends on crystallographic orientation, the ratio of the length scale of the zoned portions in different directions can be used to test whether the profiles are consistent with having been produced by diffusion (see, for example, Costa and Dungan, 2005). The work presented here takes a different approach by determining the extent of diffusion in a zoned mineral based on two key concepts: (1) crystallization in igneous systems occurs at a sufficiently high temperature that equilibrium isotope fractionation between minerals and melts can be regarded as negligible (Tomascak et al., 1999; Teng et al., 2008); and (2) mass transport by diffusion in silicate systems produces diagnostic kinetic isotopic fractionations that can be used to quantify the extent of diffusion (Richter et al., 2003). Laboratory experiments by Richter et al. (2014, 2017) and by Sio et al. (2018) demonstrated and quantified isotope fractionations by diffusion in pyroxene and olivine that serve as “fingerprints” of the extent of diffusion in these igneous minerals. It is, of course, possible that a given instance of isotopic zoning of an igneous mineral can arise by crystallization from a melt that was itself evolving in isotopic composition, for example, by crustal contamination. However, such zoning is unlikely to have the diagnostic spatial correspondence between elemental and isotopic zoning documented by the laboratory experiments. Once the degree to which diffusion caused or affected mineral zoning is determined, it can be used to constrain the timescales of magmatic processes and cooling. In what follows, we review the results of laboratory experiments that documented isotopic fractionation by diffusion in minerals and use the results to specify parameters used to model the isotopic fractionation by diffusion of pigeonite from the basaltic martian meteorite Shergotty and from an olivine grain from the lunar low-Ti mare basalt 15555. The extent that diffusion affected the zoning of these minerals was used to constrain their thermal history. In a final section, the zoned pyroxenes from Shergotty are compared to those from an earlier similar study by Richter et al. (2016) of the martian nakhlite meteorite Northwest Africa 817 (NWA 817). While the magnesium elemental zoning of pyroxenes from these two meteorites is very similar their distinctly different isotopic fractionation provides a clear indication that the zoning resulted from different processes: fractional crystallization of pyroxene in Shergotty and diffusion out of initially homogeneous pyroxene grains in the case of NWA 817.
## 2. LABORATORY EXPERIMENTS AND MODEL CALCULATIONS OF ISOTOPE FRACTIONATION BY DIFFUSION

Laboratory experiments that quantify the rate of diffusion and the associated kinetic isotopic fractionation provide the foundation for modeling diffusive transport in pyroxene and in olivine. Diffusion experiments involving minerals often focus on lithium because it is a very fast diffuser and the expectation that the large mass ratio of ⁷Li/⁶Li (1.17) would result in measurable kinetic isotope fractionation. The results of laboratory experiments involving diffusion of lithium in olivine (Dohmen et al., 2010) and in pyroxene (Richter et al., 2014) are surprisingly complicated. For example, many of the experiments by Richter et al. (2014) in which lithium diffused into augite and diopside resulted in remarkable concentration profiles in which lithium propagated into the pyroxenes as a steep-fronted step rather than the usual smoothly declining profile. Panel (a) in Fig. 1 shows an example of such a stepped profile along with the associated lithium isotopic fractionation (panel b) reported in the usual permil notation $\delta^{7}\text{Li} (\text{‰}) = 1000 \times [(^{7}\text{Li}/^{6}\text{Li})_{\text{sample}}/(^{7}\text{Li}/^{6}\text{Li})_{\text{standard}} - 1]$. Dohmen et al. (2010) had previously reported similar step-like propagation of lithium in olivine and interpreted it as being the result of lithium occurring in two different sites: fast-diffusing interstitial lithium and slow-diffusing lithium in metal sites. The lithium in the two sites is assumed to be subject to an exchange reaction involving vacancies written as $Li^{*} + V \leftrightarrow Li_{M}$ where $Li^{*}$, V, and $Li_{M}$ represent the abundance of interstitial lithium, of vacancies, and of lithium in metal sites, respectively. The exchange is governed by an equilibrium constant, $K = [Li_{M}]/([Li^{*}] \times [V])$, with the square brackets indicating concentration. Dohmen et al. (2010) showed that lithium will propagate into the mineral as a step when there are a sufficiently large number of vacancies and the equilibrium constant K is sufficiently large. The reason for this is that when the fast-diffusing interstitial lithium encounters a vacancy, it will “jump” into a slow-diffusing metal site and lithium does not penetrate further into the grain until all the vacancies at a given distance from the grain edge are filled. Figure 1b shows that a negative lithium isotopic fractionation develops in that portion of the grain with elevated lithium as a result of ⁶Li having diffused into the grain faster than ⁷Li. Further into the grain interior the isotopic composition jumps abruptly back to unfractionated values because an insignificant amount of lithium diffused into the grain beyond the abrupt concentration step. The relative diffusion of ⁶Li compared to ⁷Li used to fit the isotopic fractionation data in Fig. 1b was calculated using a mass dependence of the interstitial lithium diffusion coefficients parameterized as $D_{6Li}/D_{7Li} = (7/6)^{\beta}$ with $\beta = 0.27$. For a detailed discussion of the two-site lithium diffusion model for olivine, see Dohmen et al. (2010), and for its application to account for the concentration and isotopic fractionation profiles of lithium diffused in pyroxene, see Richter et al. (2014, 2016).
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<figure><img src="image_3.png" /></figure>

Figure 1. Panel (a) shows the lithium concentration normalized by the average value in the interior across a 700 µm wide Templeton augite grain from experiment LiPx8 by Richter et al. (2014). Panel (b) uses filled and unfilled circles to show the measured lithium isotopic fractionation relative to the unfractionated interior measured along two parallel transects across the same grain as in (a). Comparing the isotopic fractionation from the two transects provides a realistic measure of the uncertainty of the isotopic measurements. The panels on the right show the normalized lithium concentration (c) and isotopic fractionation (d) from one edge to the interior of an augite grain from experiment LiPx20 by Richter et al. (2014). The calculated profiles shown as continuous black curves that fit the lithium concentration and isotopic data were calculated using a two-species lithium model (see text for details). Figure 1 is a modified version of Figs. 4 and 7 of Richter et al. (2014).

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Richter et al. (2014) found that in some experiments lithium diffused into pyroxene along a smoothly declining profile rather than as a step. An example of this is shown in panels (c) and (d) of Fig. 1 from an experiment run under more reducing conditions ($\log fO_2 = -15$) than the experiment shown in panels (a) and (b) that was run with $\log fO_2 = -12$. A point worth noting is that lithium-zoned pyroxene grains from both terrestrial (Parkinson et al., 2007, Jeffcoate et al., 2007) and martian rocks (Beck et al., 2006; Richter et al., 2016) all have smoothly varying profiles of lithium concentration and isotopic fractionation, not step-like profiles.

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The model curves shown in panels (a) and (b) of Fig. 1 were calculated assuming the initial concentration of vacancies in the interior is the same as the lithium in metal sites at the boundary but with the interstitial lithium at the boundary being very much less. Profiles such as the ones shown in panels (c) and (d) in Fig. 1 result when the interstitial lithium
concentration at the grain edge is comparable to or greater than the vacancy concentration in the grain interior. The profiles in panels (c) and (d) were calculated assuming that the initial vacancy concentration was equal to the lithium concentration at the grain edge (V=Li*). The same value of $\beta$ = 0.27 was able to fit the isotopic fractionation data from the two experiments shown in Fig 1 despite their very different profiles. However, when the concentration of vacancies in the model calculation is negligible (i.e. V<<Li*) lithium is effectively in only one type of site and a fit similar to that shown in panel (d) of Fig. 1 required a larger value of $\beta$ = 0.44 (see Fig. 7 and discussion in Richter et al., 2014). Estimates of $\beta$ for lithium diffusing in pyroxenes can also be obtained from natural zoned samples. Richter et al. (2014) were able to fit the lithium isotopic fractionation data from terrestrial clinopyroxenes reported by Parkinson et al. (2007) using $\beta$ = 0.25, and data from Jeffcoate et al. (2007) with $\beta$ = 0.30. Richter et al. (2014) also derived an estimate of $\beta$ = 0.27 for lithium diffusing in augite from martian nakhlite MIL 03346 using data reported by Beck et al. (2006). Subsequently, Richter et al. (2016) measured and fit the lithium isotopic fractionation of ten additional augite grains from nakhlites MIL 03346 and NWA 817 using values of $\beta$ from 0.28 to 0.40. The overall conclusion based on these estimates is that when the measured isotopic fractionation of lithium in natural pyroxenes can be fit using $\beta$ = 0.35±0.10 it can be taken as evidence of lithium transport having been dominantly by diffusion. The uncertainty as to the value of $\beta$ one should expect for the relative diffusion of lithium isotopes in a given pyroxene grain is a reflection of the complex multisite diffusion of lithium in pyroxene. While the uncertainty in the choice of $\beta$ translates into a similar uncertainty in the calculated amplitude of isotopic fractionations, the spatial distribution of the isotopic fractionations in relation to the concentration profile of their parent element is an equally important indicator of whether diffusion was the cause of the fractionations.

To our knowledge, there have not yet been experiments directly quantifying magnesium isotopic fractionation by diffusion in pyroxene minerals. There is no reason to assume that the value of $\beta_{Mg}$ should be similar to $\beta_{Li}$, in fact, in the case of diffusion in a silicate liquid, $\beta_{Li}$ is about four times larger than $\beta_{Mg}$ (Richter et al., 2003, 2008). The same is true for lithium diffusion in olivine where Richter et al. (2017) reported $\beta_{Li}$ =0.4±0.1 compared to $\beta_{Mg}$ =0.09±0.05 estimated by Sio et al. (2018). For lack of more direct evidence, we will assume that this difference between $\beta_{Mg}$ and $\beta_{Li}$ also applies to pyroxenes, yielding an estimate of $\beta_{Mg}$ ~ $\beta_{Li}/4$ ~ 0.1.

The only laboratory study to date of isotopic fractionation associated with Fe-Mg interdiffusion in olivine is by Sio et al. (2018) who reported a value of $\beta_{Fe}$ = 0.16±0.09. The diffusion couple used in their experiment juxtaposed olivine with a magnesium number mg# = 83.4 (mg# = Mg/(Mg+Fe) atomic) with olivine with mg# = 88.8. The high magnesium content diluted the kinetic isotope fractionation of magnesium to the extent that they were not able to directly resolve $\beta_{Mg}$. They did however make an estimate of $\beta_{Mg}$ using the anticorrelation of the isotopic fractionation of magnesium and iron in olivine of $\beta_{Mg}$ ~ $\beta_{Fe}/2$ derived from earlier studies of natural samples (Sio et al., 2013; Oeser et al., 2015) to estimate a value of $\beta_{Mg}$ = 0.09±0.05. These values of $\beta_{Fe}$ and $\beta_{Mg}$ are reasonably consistent with values reported by Oeser et al. (2015) based on the iron and magnesium isotopic fractionation of seven zoned terrestrial olivine grains that gave an average estimate of $\beta_{Fe}$ = 0.161±0.071 and $\beta_{Mg}$ = 0.084±0.019 (uncertainty of $1\sigma$ calculated from data in their Table 1). Given these results, we will use $\beta_{Mg}$ = 0.1 to calculate the relative mobility of magnesium isotopes in olivine.
### 3. PARAMETERS FOR CALCULATING THE DIFFUSION RATE IN PYROXENE AND OLIVINE

The one-dimensional mass conservation equation for calculating transport by diffusion in a mineral grain can be written as

$$ \frac{\partial \rho}{\partial t} = \left(\frac{1}{r^n}\right) \frac{\partial}{\partial r} \left( r^n D_{(T,X)} \frac{\partial \rho}{\partial r} \right) $$

(1)

where $\rho$ is molar density, $D_{(T,X)}$ is the diffusion coefficient that depends on temperature $T$ and composition $X$, $n = 0$ makes it applicable to a slab, $n = 1$ for a cylinder, and $n = 2$ for a sphere. The complete mathematical problem requires initial and boundary conditions, a temperature history $T(t)$, and a constitutive equation for the dependence of the diffusion coefficient on mineral composition and thermodynamic state. The diffusion coefficients in the various applications of Eqn. (1) are specified using the following parameterizations. For the magnesium diffusion coefficient in pyroxene we use $D_{Mg} = 2.77 \times 10^{-3} e^{-E/RT}$ cm$^2$s$^{-1}$ with $E = 320$ kJ, the gas constant $R = 8.314$ J mol$^{-1}$ K$^{-1}$ and $T$ the absolute temperature (Muller et al., 2013). The diffusion coefficient in olivine is calculated as $\log[D_{Fe-Mg}] = -5.21 - 201000/2.303RT + 3(X_{Fa} - 0.1) + (1/6)\log(fO_2/10^{-7})$, taken from Dohmen and Chakraborty (2007b,c) where $D_{Fe-Mg}$ is in units of cm$^2$ s$^{-1}$, $R$ and $T$ as above, $X_{Fa}$ is the mole fraction fayalite, and $fO_2$ is the oxygen fugacity in Pascals. This parameterization is for magnesium diffusing along the c-axis of olivine. The diffusion coefficients along the a- and b-axes are equal and smaller than along the c-axis by a factor of about six (Dohmen et al., 2007a). The lithium diffusion coefficient in pyroxene minerals is calculated using $D_{Li} = 2.4 \times 10^5$ e$^{-E/RT}$ cm$^2$ s$^{-1}$ with $E=330$ kJ and $R$ and $T$ as above. This parameterization was derived from experiments run at $\log fO_2 \sim -12$ with $fO_2$ in bars (for details see Richter et al. 2014). Figure 2 shows the diffusion coefficients for lithium and magnesium in pyroxene as a function of temperature calculated using these parameterizations and that of magnesium in olivine for three choices of the mole fraction fayalite. The lithium diffusion coefficient as a function of temperature plotted in Fig. 2 is for an oxygen fugacity of $10^{-12}$ bars.

<figure><img src="image_4.png" /><figcaption>Figure 2. Summary of diffusion coefficients of lithium in pyroxene and of magnesium (i.e., Fe-Mg exchange) in pyroxene and olivine as a function of temperature. The line representing the diffusion coefficient of lithium in pyroxene is a best fit to the combined data from experiments by Coogan et al. (2005) and Richter et al. (2014) run at $\log fO_2 = -12$ and experiments by Caciagli-Warman (2010) run at $\log fO_2 = -10.3$. The diffusion coefficient of</figcaption></figure>
magnesium in pyroxene was calculated using the parameterization given by Muller et al. (2013). The magnesium diffusion coefficient along the c-axis of olivine as a function of temperature for three different fayalite contents was calculated using the parameterization given by Dohmen and Chakraborty (2007b,c) with the oxygen fugacity corresponding to the FMQ buffer.

## 4. ANALYTICAL METHODS

A variety of methods were used to analyze the major element and lithium composition, along with the magnesium and lithium isotopic fractionation across pigeonite grains from Shergotty and the magnesium isotopic fractionation across a large olivine grain from Apollo sample 15555.

A backscattered electron (BSE) image of a large pigeonite grain (SH3) from Shergotty and quantitative color maps of MgO, FeO, and Na₂O concentration were obtained with a TESCAN LYRA3 scanning electron microscope equipped with two Oxford 80 mm² silicon drift x-ray detectors. A 256×256 quantitative map was made using Oxford AZtec software and exported to Wavemetrics Igor software for further processing. In the case of the MgO and FeO maps only data from pyroxene points were plotted. In order to reduce noise, smoothing was done by averaging each pixel with the surrounding eight pixels. Major element profiles across pigeonite grains from Shergotty were also measured with a Zeiss Evo 60 SEM operated at 20kV and equipped with an Oxford Instruments Aztec XMax 50 silicon drift detector. The data were reduced with AZtec software and have a precision of 1% relative.

The lithium abundance along with the lithium and magnesium isotopic composition was measured along traverses across a number of pigeonite grains from Shergotty using the CAMECA 1270 ion probe at the Centre de Recherches Pétrographiques et Géochimiques, Nancy, France. The analytical methods used for these ion probe measurements are the same as described in Richter et al. (2016). Lithium and magnesium isotopic compositions measured by secondary ion mass spectrometry can have significant instrumental mass fractionation (IMF) effects that depend on composition. The IMF of lithium and magnesium as a function of pyroxene composition (Figs. B1 and B2 in Appendix B) was determined by measuring the isotopic composition of a set of pyroxenes that were synthesized for this purpose as described in Appendix B. In the case of lithium the uncertainty of the IMF correction as a function of composition is much the same as the 2σ error of the individual isotopic measurements (see Fig. B1 in Appendix B) and therefore no IMF correction other than subtracting a constant 36.9 ‰ (i.e., the average of measured lithium isotopic composition of the synthetic pyroxenes). Subtracting 38.1‰ from the measured δ<sup>7</sup>Li at spots across Shergotty pyroxene grains makes average of the data set close to zero. Because we are only interested in changes in the isotopic composition along a transect (i.e., the isotopic fractionation) we are free to shift the data set by any fixed amount for convenience of presentation. When we report the 2σ uncertainty of lithium isotopic measurements across Shergotty pyroxene grains we use 2σ error of 50 repeated measurements made at each spot. In the case of the magnesium isotopes there is a resolved slope to the IMF as a function of the enstatite fraction of pyroxene (see Fig. B2 in Appendix B). The 2σ uncertainty bounds around the regression line is a function of the enstatite fraction and much larger than the uncertainty of the individual measurements. Accordingly, when we report the uncertainty of IMF-corrected δ<sup>26</sup>Mg data measured across pyroxene grains from Shergotty we use the 2σ uncertainty bound of the IMF as a function of the enstatite fraction at the spot where the magnesium isotopic composition is measured.
A FeKα map of the large zoned olivine grain and surrounding minerals from lunar basalt 15555 was made by Larry Taylor at the University of Tennessee using a CAMECA SX-50 electron microprobe (EMP). The olivine composition was measured along a transect across the large olivine grain using a JEOL JSM-5800LV scanning electron microscope equipped with an Oxford Link ISIS-300 energy dispersive X-ray microanalysis system (EDS) that gives a precision of better than 1% relative for the forsterite content. The magnesium isotopic composition was measured along the same transect using the CAMECA 1270 ion microprobe at Centre de Recherches Pétrographiques et Géochimiques in Nancy, France using analytical methods described in Chaussidon et al., (2017). The IMF of magnesium as a function of forsterite composition of olivine was determined by measuring the isotopic composition of a set of olivine grain that were synthesized specifically for this purpose as described in Appendix B. The slope and uncertainty of the magnesium IMF correction for the ²⁶Mg/²⁴Mg data as a function of the forsterite fraction of olivine is shown in Fig. B3. The uncertainty of the IMF correction is much larger than uncertainty of the individual isotopic measurements and therefore we use the 2σ uncertainty of the IMF correction as a function of the forsterite fraction of olivine as the measure of the uncertainty of the IMF-corrected δ²⁶Mg measured across the olivine grain from lunar basalt 15555.

# 5. LITHIUM AND MAGNESIUM-ZONED PYROXENE (PIGEONITE) GRAINS FROM SHERGOTTY

## 5.1. Previous studies of Shergotty

Shergotty is a basaltic meteorite from Mars described by Stolper and McSween (1979) as a pyroxene-rich cumulate (~70% pyroxene) with a foliated texture of preferentially oriented large pyroxene prisms with an average grain size of about 450 µm. It has a crystallization age of 165±4 Ma (Nyquist et al., 2001). A number of previous studies of Shergotty (see for example Laul et al., 1986; Udry et al., 2016) have focused on zoned pyroxene grains such as the one shown in Fig. 3. Stolper and McSween (1979) used laboratory experiments to interpret the major element zoning in terms of Mg-rich pyroxene cores that began to crystallize at about 1240°C and then developed zoned rims as the temperature dropped below about 1140°C. The cooling responsible for the Fe-Mg zoning could have been associated with shallow intrusion or extrusion (Lentz et al., 2001; McSween et al. 2001). These two papers noted an additional important aspect of the zoning of Shergotty pyroxenes: the lithium concentration measured in the rims was significantly lower than that in the cores. The lower lithium concentration in the rims is opposite of what one would expect for crystallization zoning given that lithium is generally assumed to be somewhat incompatible in pyroxene and thus in a closed system the concentration in the melt should increase as crystallization proceeds. Lentz et al. (2001) and McSween et al. (2001) suggested that the low lithium concentration in the rims might be the result of crystallization from a melt with initially about 2% water that lost lithium by partitioning into a water-rich fluid that exsolved from the melt during ascent and decompression. This required them to assume that lithium has a strong tendency to partition into aqueous fluids but they made no quantitative assessment of the partition coefficient that would be required. The general idea of lithium having been lost by fractionation into an aqueous fluid has also been suggested to explain lithium zoning of minerals from several other martian meteorites (see, for example, Udry et al., 2016) despite Treiman et al. (2006) having pointed out that in order for the required large amount of lithium to have been lost to an aqueous phase derived from a melt with 2% initial water, the partitioning of lithium from the melt into the aqueous phase would have to be thirty times
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larger than the experimentally constrained value. The inadequacy of even much larger initial amounts of water to account for the large loss of lithium from shergottite melts led Treiman et al. (2006) to suggest that the lithium zoning in pyroxenes in Shergotty very likely involved intracrystalline diffusion. Udry et al. (2016) also argued that post-crystallization diffusion played a role in producing the zoning of pyroxenes from Shergotty. These propositions that diffusion was responsible for some of the lithium zoning in pyroxene grains in Shergotty can be tested quantitatively, as shown below, by measuring the variation of the lithium isotopic composition across the grains.

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There have been several estimates of the time scales involved in the cooling and crystallization of Shergotty using a variety of approaches. Muller (1993) used clinopyroxene microstructure to infer a cooling rate for Shergotty of 2×10⁻³°C/h. Lentz and McSween (2000) compared crystal size distributions from Shergotty with those from experiments by McCoy and Lofgren (1999) to infer that the system cooled at a rate between 0.1 and 0.5 °C/h with the cores having grown between 11 and 53 days and the entire grain between 19 and 93 days (see their Table 2). Even a simple back-of-the-envelope calculation would show that these cooling rates are all much too slow for any lithium zoning to have been preserved.

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## 5.2. Elemental and isotopic zoning of a pigeonite grain from Shergotty

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A backscattered electron (BSE) image of a large pigeonite grain (SH3) from Shergotty and quantitative color maps of MgO, FeO, and Na₂O concentration are shown in Fig 3. The BSE image also shows the ion probe spots where magnesium isotopes were measured (the larger spots) and where both the lithium abundance and isotopic compositions were measured (the smaller spots). The Na₂O map allows one to see the distribution of maskelynite (transformed from plagioclase by shock) and devitrified glass around the pyroxene grain. Small areas of maskelynite and glass were also trapped within the large pyroxene grain. The extent of what was late-crystallizing plagioclase and melt suggests that the section of grain SH3 shown in Fig. 3 was surrounded by melt during its crystallization except for two small portions along the edge. The MgO and FeO maps show the continuity of the zoning along the entire edge of the grain. The FeO map includes two lines along which the major element data shown in Fig. 4 was measured. Similar data across other pyroxene grains from Shergotty are given in Appendix A.
<figure><img src="image_5.png" /></figure>

Figure 3. Top left: Backscattered electron image of Shergotty pigeonite grain SH3 and false color maps of Na₂O, MgO, and FeO with color scales in wt%. The larger light-colored spots in the backscattered electron image are ion probe spots from the magnesium isotopic measurements; the smaller spots are from the lithium abundance and isotopic measurements.

<figure><img src="image_6.png" /></figure>

Figure 4. The two panels show the wt% FeO (grey circles), MgO (black circles), and CaO (diamonds) measured along lines 3.1 and 3.2 across Shergotty pigeonite grain SH3 shown in the FeO map in Fig. 3.

The lithium abundance and both the lithium and magnesium isotopic composition was measured along traverses across a number of pigeonite grains from Shergotty using the CAMECA 1270 ion probe at the Centre de Recherches Pétrographiques et Géochimiques, Nancy, France. The analytical methods and instrumental mass fractionation are discussed in Section 4. The MgO concentration along line 3.1 of grain SH3 together with the magnesium
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isotopic fractionation, and the Li concentration and isotopic fractionation measured at the
spots running from the top left to lower right in the BSE image in Fig. 3 are shown in Fig. 5.

<figure><img src="image_7.png" /></figure>

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Figure 5. MgO and Li concentration and isotopic fractionation data measured across Shergotty pigeonite grain SH3 shown in Fig.3. The MgO concentration was measured along line 3.1 and the Li concentration along with the lithium and magnesium isotopic composition was measured at the ion probe spots that more or less follow line 3.1. The magnesium isotopic data shown as unfilled circles with error bars was corrected for the IMF as a function of the local enstatite fraction of the pigeonite whereas the black circles show the uncorrected values. The 2σ error of the δ<sup>6</sup>Mg IMF-corrected data reflects the uncertainty of the matrix corrections for the IMF (see Fig. B2 in Appendix B). The lithium isotopic fractionation did not require IMF correction (see Fig. B1 in Appendix B). The errors bars of the lithium isotopic data points are ±2σ, derived from the statistics of 50 repeated measurements at spot.

One might be inclined to argue that the Li and MgO concentration data shown in Fig. 5 already imply that the zoning of this pyroxene grain must be mainly the result of crystallization from an evolving melt with little or no diffusion. The argument would be based on the similar length scale of the Li and MgO zoning despite the orders of magnitude faster diffusion of lithium in pyroxene compared to magnesium (see Fig. 2) and therefore, had diffusion been important in causing the magnesium zoning, the faster diffusing lithium would have become uniform long before the iron-magnesium exchange had affected the outer 400 µm of the grain. There are several potential flaws in this line of reasoning. It could be that the lithium had in fact become uniform in terms of chemical potential and that the lithium zoning is due to the dependence of the activity coefficient of lithium on the major element zoning of pyroxene. This, however, can be ruled out based on experimental partitioning data (see Appendix C) that show that for the Li chemical potential to be uniform
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the Li concentration would increase with decreasing MgO in pyroxene, which is opposite to what is observed. Another possibility is that the lithium and magnesium zoning might be due to processes during different stages in the evolution of the system. For example, the elemental data on its own cannot rule out a two-stage evolution: Stage 1 with crystallization and/or diffusion producing the magnesium zoning on a time scale that was sufficiently long to have homogenized the much faster-diffusing lithium, followed by Stage 2 with a short duration sufficient to allow for the diffusive zoning of lithium but too short to have significantly affected the prior zoning of magnesium. The discussion in the next section shows how isotopic measurements are used to distinguish between otherwise possible scenarios for the thermal evolution of Shergotty.

## 5.3 Constraints on the thermal evolution of Shergotty from magnesium zoning and isotopic fractionation of pigeonite grain SH3

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Crystallization calculations using the alphaMELTS 1.8 front-end (Smith and Asimow, 2005) for the MELTS thermodynamic model (Ghiorso and Sack, 1995) hereafter referred to as “MELTS calculations” were used to explore the implications of pigeonite grain SH3 having a relative homogeneous core with similar ~20 wt% FeO and MgO. The initial melt composition used for the calculation is the bulk composition of Shergotty that Stolper and McSween (1979) used in their equilibrium crystallization experiments. The validity of the MELTS calculations was tested by comparing the minerals in equilibrium with the melt as a function of temperature predicted by MELTS with experimental data reported by Stolper and McSween (1979). The panel on the left of Fig. 6 shows the result of the calculation along with the temperature at which Stolper and McSween (1979) reported the first appearance of each major mineral. The MELTS calculation is in excellent agreement with the experimental data for the temperature of first appearance of the two pyroxenes (pigeonite and augite) and close to that for plagioclase.

<figure><img src="image_8.png" /></figure>

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Figure 6. The panel on the left shows the cumulative wt% of minerals in equilibrium with melt as a function of temperature calculated using MELTS assuming batch crystallization of a system with the same bulk composition used by Stolper and McSween (1979) in their equilibrium crystallization experiments. The temperature of first appearance of these minerals in the experiments quenched at different temperatures is shown by the arrows, which from right to left show the highest temperature at which pigeonite, augite, and plagioclase were found in the quenched material from the Stolper and McSween (1979) experiments (see their Table 4). The broad arrow for the first appearance of feldspar reflects that a range of temperatures rather than a specific temperature was reported. The panel on the right shows the results of a MELTS calculation for the evolution of the major oxide
concentration in pigeonite assuming batch crystallization (black lines) of a system with same bulk composition as used for the results shown in the panel on the left. At T=1135°C the concentration of FeO and MgO are both about 20 wt%, which is a good approximation to the measured composition of the core of pigeonite grain SH3 (see Fig. 5). The dashed lines show how the pigeonite composition evolves when MELTS is used to calculate perfect fractional crystallization for T<1135°C.

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The black lines in the panel on the right of Fig. 6 shows the results of a MELTS batch crystallization calculation for the composition of pigeonite in equilibrium with melt at temperatures from T = 1235 to 1055°C. Perfect batch melting, by definition, assumes that the bulk composition of all minerals are continuously in equilibrium with the melt and thus perfectly homogeneous. While this can account for the core of a grain like SH3, it cannot account for the zoned portion of the grain. For this reason, a second set of pigeonite compositions versus temperature was calculated using MELTS assuming batch melting down to T = 1135°C, which can explain the homogeneous core of grain SH3 with FeO = MgO ~ 20 wt%, followed by perfect fractional crystallization (dashed lines) to account for the increase of FeO and decrease of MgO in the outer portions of SH3. Batch crystallization requires that the system evolve sufficiently slowly in order for diffusion to continuously homogenize both the melt and the minerals and to maintain equilibrium between the pigeonite and the melt. Fractional crystallization, on the other hand, requires the system to evolve sufficiently fast that mass transport by diffusion within the mineral grains is negligible so that each increment of crystallization is isolated from any further exchange with the melt. The MELTS batch crystallization calculation shown in the right hand panel of Fig. 6 is interpreted as implying that pigeonite grain SH3 was in equilibrium with the melt at T = 1135°C with FeO = MgO ~ 20 wt% and then fractionally crystallized as it rapidly cooled to develop the zoned rims with increasing FeO and decreasing. The mass fraction of melt at T = 1135°C when the fast cooling begun is still large, about 65%.

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A lower bound for the duration of the slow crystallization or post-crystallization homogenization of the pigeonite core of grain SH3 can be estimated by the time $t > r^2/D$ required to homogenize a cylinder or a sphere of radius $r$ given a value for the diffusion coefficient $D$ (see Figs. 5.3 and 6.1 in Crank, 1975). Using $r=200 \ \mu m$ (0.02 cm) as the radius of the core of grain SH3 and $D = 3.7 \times 10^{-15} \ cm^2 \ s^{-1}$ at T=1135°C (from Muller et al., 2013) yields an estimate that the core of SH3 would be homogenized if it had been at T=1135°C for more than $10^{11}$ seconds (~3200 years). This calculation shows that the Lentz and McSween (2000) estimate that the core of Shergotty pyroxene grains grew for between 11 and 53 days is far too short a time to have produced even roughly homogeneous cores.

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The question of how the zoned portion of pigeonite grain SH3 might have been produced is explored using a numerical calculation to solve the mass conservation equation for the evolution of the magnesium concentration and isotopic fractionation. The conservation Eqn. (1) with $n = 2$ for a sphere written in terms of nondimensional variables is

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$$ \frac{\partial \rho_i}{\partial t'} = D'_{(t')} \left( \frac{\partial^2 \rho_i}{\partial r'^2} + \frac{2}{r'} \frac{\partial \rho_i}{\partial r'} \right) \quad (2) $$

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where $\rho_i$ is a measure of the concentration of an element or isotope $i$, $t'=(D_{To}/r_{gr}^2)t$ with $t$ the dimensional time in seconds, $r'=r/r_{gr}$ with $r_{gr}$ the final radius of the grain in centimeters, $D'_{(t')} =D_{(t')}/D_{To}$ with $D_{To}$ the diffusion coefficient in units of $cm^2 \ s^{-1}$ at the temperature $T_o$ when diffusion begins. $D_{(t')}$ is the diffusion coefficient at time $t'$ determined by the temperature $T(t')$ for the assumed cooling rate. When Eqn. (2) is used for the magnesium isotopes it is assumed

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that the diffusion coefficient of <sup>24</sup>Mg is larger than that of <sup>26</sup>Mg by a factor of (26/24)<sup>β</sup> with β = 0.1. Nondimensional variables are used here and in subsequent sections in order that the results of a given calculation can be used for the evolution of grains of different size r<sub>gr</sub>, and different reference diffusion coefficients D<sub>To</sub> corresponding to the temperature T<sub>o</sub> when diffusion is assumed to have begun. One can calculate the dimensional cooling rate for any particular grain by redimensionalizing time as t=t'(r<sub>gr</sub><sup>2</sup>/D<sub>To</sub>) where t' is the nondimensional time it took to fit zoning of the grain measured in units r'.

An issue that can be explored using the numerical model for the magnesium evolution of a pyroxene grain is whether the zoned rim of grain SH3 could be explained by diffusion of magnesium out of an initially homogeneous grain of fixed size. Such a case is specified by r' = 1 for all t', an initial condition ρ<sub>Mg</sub> = 20 wt% MgO (i.e., approximately the measured wt% MgO in the core of the grain) from r' = 0 to 1 at t'=0 and ρ<sub>Mg</sub> = 5 wt% MgO (i.e., the approximate wt% MgO at the grain edge) at r' = 0 and 1 for t'>0. The magnesium isotopic composition of the grain is assumed to be uniform (δ<sup>26</sup>Mg = 0 ‰) at r' from 0 to 1 and subject a boundary condition δ<sup>26</sup>Mg = 0‰ at r' = 0 and 1 for all t' > 0. This boundary condition assumes that there is no significant equilibrium isotopic fractionation of magnesium between pyroxene and melt and that there is a sufficiently large amount of melt that the isotopic composition of the melt is not significantly altered by the flux of isotopically fractionated magnesium out of the grain. The results of such a calculation run to t' = 0.01 with the temperature decreasing linearly by 100°C over the course of the calculation are shown in Fig. 7. The calculated magnesium isotopic fractionation is locally positive in the boundary layers, as a result of <sup>24</sup>Mg having diffused out of the grain faster than <sup>26</sup>Mg. The issue here is not so much the time scale but rather that a large isotopic fractionation has developed, which when compared to the measured data, makes it obvious that the magnesium zoning of the rim of grain SH3 could not have been the result of any significant amount of diffusion after the grain had grown to its present size.

<figure><img src="image_9.png" /></figure>

Figure 7. Results of a numerical calculation for the diffusive evolution of magnesium after a nondimensional time t' = 0.01 starting from a uniform grain with 20 wt % MgO (dashed line in the panel on the left) subject to a boundary condition of 5 wt% MgO at each edge of the grain. The measured wt% MgO along line 3.1 of Shergotty grain SH3 is shown by the black circles. The panel on the right shows the calculated magnesium isotopic fractionation associated with the diffusion of magnesium out of the grain calculated using β=0.1. The open circles show the matrix-corrected magnesium isotopic fractionation across line 3.1. The initial isotopic ratio of magnesium in the grain was taken as δ<sup>26</sup>Mg = 0 ‰, which was also used as the boundary condition at r' = 1.
A numerical calculation was also used to model a case where diffusion takes place while the zoned portion of a spherical grain is growing. The grain growth in the model starts with the grain already having a homogeneous core at $t' = 0$ with a radius $r' = 0.4$ (i.e., 40% of the final radius) and that for $t'$ between 0 and $t_{xtl}$ the grain grows from $r' = 0.4$ to 1 with the volume increasing linearly with time as shown in Fig. 8. Grain growth ends at $t' = t_{xtl}$, with diffusion continuing until $t' = 4t_{xtl}$, by which time the temperature is sufficiently low that diffusion has become negligible. The temperature is assumed to decrease linearly with time as $T(t') = T_0 - \Delta T t'$ where $T_0 = 1135°C$ and $\Delta T = 100°C$ is the temperature change over each nondimensional time interval $t_{xtl}$. Figure 8 shows the dimensional temperature as a function of time $t'$ used to calculate $D'(t')$ in the Muller et al. (2013) parameterization of the magnesium diffusion coefficient in pyroxene (see Fig. 2). The initial conditions at $t' = 0$ assumes uniform concentrations of $^{24}$Mg and $^{26}$Mg between $r' = 0$ and $0.4$ and $\delta^{26}$Mg = 0‰. The magnesium concentration ($^{24}$Mg + $^{26}$Mg) applied at the growing edge of the grain is assumed to decrease linearly as $C(r') = C_o - \Delta C t'$ with $C_o=20$ and $\Delta C$ is such that the concentration is reduced to 5 during the period of grain growth ($t' = 0$ to $t_{xtl}$) and $C = 5$ at $r' = 1$ for $t' > t_{xtl}$. The decrease of the magnesium concentration imposed at the growing edge of the grain is meant to reflect the decreasing magnesium concentration of material added to the grain during fractional crystallization as shown in Fig. 6. The isotopic composition at the grain edge is assumed to be the same as the initial value in the core (i.e., $\delta^{26}$Mg = 0‰ at $r'(t')$ for all $t'$ from 0 to $4t_{xtl}$).

<figure><img src="image_10.png" /></figure>

Figure 8. The panel on the left shows the linear cooling assumed in the magnesium evolution calculations of a growing spherical grain as a function of the nondimensional time $t'$ measured in units $t_{xtl}$. $t_{xtl}$ is the nondimensional time over which the grain grew to its final size. The panel on the right shows the growth of the fractional radius $r/r_{gr}$ ($r_{gr}$ is the final radius of the model grain) as a function of time. The grain growth corresponds to equal amounts of volume added per unit time. The portion of the grain from $r/r_{gr}=0$ to 0.4 (not shown) is assumed to be the core with an initially uniform elemental and isotopic composition.

The model of a growing grain was used to explore how fast the system must have cooled to account for the magnitude of magnesium isotopic fractionations measured in the rim of grain SH3. Figure 9 shows the calculated wt% MgO and the magnesium isotopic fractionation across a model grain that grew a rim with decreasing wt% MgO for the interval $t' = 0$ to 0.08 while the temperature decreased and the grain grew as shown in Fig. 8 for a nondimensional time $t' = 0.08$. The cooling and diffusion continuing until $t' = 0.24$.
<figure><img src="image_11.png" /></figure>

Figure 9. Panel on the left shows the calculated evolution of the wt% MgO (solid black curve) starting from a core having the extent and wt% MgO shown by the horizontal portion of the dashed line. The slopping dashed lines show the wt% MgO the grain would have if there had been no diffusion. The black circles show the wt% MgO measured along line 3.1 across Shergotty grain SH3. The panel on the right shows the calculated magnesium isotopic fractionation along with the matrix-corrected fractionation shown as open circles. The model grain crystallized over a nondimensional time $t' = 0.08$ with the temperature decreasing and the radius evolving as shown in Fig. 8. Diffusion continued to $t' = 0.24$ by which time the system had cooled to the point that diffusion had become negligible. The isotopic fractionation was calculated using $\beta = 0.1$ for an initially unfractionated grain.

The wt% MgO and isotopic fractionation profiles shown in Fig. 9 were calculated for a nondimensional time $t' = (D_{To}/r_{gr}^2)t = 0.08$ where $t$ is the dimensional time, $D_{To} = 3.7 \times 10^{-15}$ cm$^2$ s$^{-1}$ is the magnesium diffusion coefficient from Muller et al. (2013) for T = 1135°C, the temperature $To$ when diffusion was assumed to have begun, and $r_{gr} = 0.05$ cm is the final radius of the grain. The dimensional time $t$ corresponding to $t' = 0.08$ is then $t = 0.08$ ($r_{gr}^2/D_{To}) = 5.4 \times 10^{10}$ seconds (~1700 years). Given that Fig. 9 shows that the core is no longer homogeneous and that the magnesium isotopic fractionation is as large as the measured data would allow, it follows that the grain must have grown the rim in less than about 1700 years and that the cooling rate must have been faster than 0.05°C y$^{-1}$.

Because lithium diffuses in pyroxenes many orders of magnitude faster than magnesium, one can anticipate that modeling the lithium zoning of grain SH3 in the same way as done for magnesium will result in a much shorter bound on the duration for the crystallization of the rim and a correspondingly faster cooling rate. However, it is precisely the sluggishness of magnesium diffusion in pyroxene that led to the conclusion that a very long time at high temperature was required for grain SH3 to have a homogeneous core.

## 5.4 Constraints on the thermal evolution of Shergotty from lithium zoning and isotopic fractionation of pigeonite grain SH3

Lithium diffuses much faster than magnesium or any other major element in pyroxene, therefore the fact that the core of grain SH3 is relatively uniform in major element abundances (see Fig. 4) implies that it must have also been uniform in lithium. While the major element zoning of the pigeonite rim of SH3 can be explained by fractional crystallization of a closed system (see Fig. 6), the same cannot be the case for lithium, which being somewhat incompatible in pyroxene (Brenan et al., 1998 and data in Appendix C) would in a closed system increase rather than decrease toward the edge of the grain. Even accepting that the lithium budget of Shergotty was an open system, the fact that grain SH3 is
zoned in lithium already implies sufficiently rapid cooling that there was not time for lithium to have become homogenized by diffusion. An explicit estimate of how fast the parent rock must have cooled can be derived by modeling the effect of lithium diffusion in pigeonite grain SH3 compared to the measured isotopic fractionation. The numerical model used in the previous section to calculate the evolution of magnesium was modified by using the kinetic properties of lithium diffusion in pyroxene. A model calculation was first used to explore whether the lithium zoning could be due to lithium having diffused out of a grain that was initially uniform in lithium concentration and isotopic composition. As already noted, such a situation could have arisen if the growth of the grain had been sufficiently slow for lithium to have been first homogenized and the lithium zoning developing subsequently during rapid cooling by diffusion of lithium out of the fully-grown grain. Figure 10 shows the results of a model calculation for the lithium zoning after a nondimensional time $t' = 0.04$ of a grain with initially 6 ppm lithium and 1 ppm lithium at the boundary. If one only focused on modeling the lithium abundance data, it would seem that diffusion could be viable explanation of the zoning. The fact that the measured lithium concentration data are somewhat scattered around a smooth curve (i.e., the calculated profile in Fig. 10) is not particularly troubling because it is commonly observed that lithium measurements in minerals from martian meteorites tend to be quite “noisy” (see Figure 7 in Richter et al., 2016). The important point, however, is that the calculated lithium isotopic fractionation of the grain, modeled assuming an initial and boundary value of $\delta^{7}\text{Li} = 0\text{‰}$ and $\beta = 0.35$ clearly shows that by $t' = 0.04$ the calculated isotopic fractionation is obviously inconsistent with the measured data. The point to emphasize is that the lithium isotope measurements provide the key evidence that diffusion of lithium out of an initially uniform grain cannot be the process responsible for the lithium zoning of grain SH3.

<figure><img src="image_12.png" /><figcaption>Figure 10. Results of a numerical calculation for the lithium abundance and isotopic fractionation due to diffusion after a nondimensional time $t' = 0.04$ starting from initially uniform grain interior with 6 ppm Li (dashed line) subject to a boundary condition of 1 ppm at each edge of the model grain. Distance across the grain is normalized by the grain size (i.e., $r' = r/r_{gr}$). The panel on the left shows the calculated lithium concentration profile along with black circles showing the measured lithium concentration in Shergotty grain SH3 along line SH3.1. The panel on the right shows the lithium isotopic fractionation calculated for a grain with $\delta^{7}\text{Li} = 0\text{‰}$ for both the initial and boundary conditions, and using $\beta = 0.35$ to calculate the relative diffusion coefficient of the lithium isotopes. The calculated positive $\delta^{7}\text{Li}$ ‰ in the grain interior is due to about 50% of the lithium having diffused out of the grain with $^{6}\text{Li}$ having been lost faster than $^{7}\text{Li}$.</figcaption></figure>

Having shown that very little, if any, of the lithium zoning of pigeonite grain SH3 can have been the result of diffusive loss from a fully-grown grain that was initially uniform in
lithium, new calculations were used to model situations where a grain was assumed to simultaneously cool and grow as shown in Fig. 8. For this calculation, the nondimensional time $t'$ is defined as $t' = (D_{To}/r_{gr}^2)t$, where $t$ is the dimensional time, $D_{To}$ is the lithium diffusion coefficient corresponding to the temperature $T_o = 1135°C$ at the time ($t' = 0$) when the rim growth began and $r_{gr}$ is the final radius of the grain. The lithium abundance at the growing edge of the grain was assumed to decrease linearly with time from an initial 5.5 ppm to 1 ppm over the period of grain growth and remaining constant thereafter. A value of $\beta = 0.35$ was used to calculate the relative diffusivity of the lithium isotopes. Figure 11 shows the results of a calculation run to $t' = 0.05$. Had the grain cooled for longer than $t' = 0.05$ the calculated lithium isotopic fractionation would have become unacceptably large. The conclusion is that the lithium isotopic fractionation measured across grain SH3 implies that the grain rim must have grown in less than about $t' = 0.1$. Using a radius of 0.05 cm for pigeonite grain SH3 and $D_{To} = 1 \times 10^{-7} \text{ cm}^2 \text{ s}^{-1}$ for the diffusion coefficient of lithium at $T = 1135°C$ (see Fig. 2) when diffusion began, the rim of grain SH3 must have grown on a timescale of less than 2500 seconds (~40 minutes). Assuming that the temperature drop during the crystallization of the rim was of the order of 100°C, the cooling rate must have been faster than 150°C/h (~2°C per minute). Because lithium diffusion in clinopyroxene depends on $fO_2$ (see Fig. 11 in Richter et al., 2016) an important point is that the value of the diffusion coefficient of lithium used here to dimensionalize time comes from diffusion experiments run at $\log fO_2$ between -10.3 and -12, which is comparable to the estimates of the $fO_2$ of Shergotty at magmatic temperatures of $\log fO_2 \sim -11$ by Papike (2000) and $\log fO_2 \sim -12$ by Wadhwa (2001).

<figure><img src="image_13.png" /><figcaption>Figure 11. Calculated diffusive evolution as function of nondimensional time of the lithium concentration (left-hand panel) and the isotopic fractionation (right-hand panel) of an idealized spherical pyroxene grain with an initially homogeneous core (horizontal portion of the dashed lines) with subsequent growth of the rim from $t' = 0$ to 0.05 as the temperature dropped by 100°C as shown in Fig. 8. The slopping dashed lines are the zoning due to the decreasing boundary concentration had there been no diffusion. The lithium isotopic fractionation was calculated assuming a value of $\beta = 0.35$. The black circles show the measured lithium concentration and the open circles the lithium isotopic fractionation across Shergotty grain SH3, which for comparison with the calculated profile was increased by 2‰ from the values plotted in Figs. 5 and 10.</figcaption></figure>

It follows from the modeling and discussion above that both the magnesium and lithium zoning of the pigeonite grain SH3 from Shergotty was dominantly due to crystallization. The lack of isotopic evidence for any significant diffusion of lithium provides the more stringent lower bound on the rate of cooling rate of grain SH3.
# 6. CONSTRAINTS ON THE EVOLUTION OF MARE BASALT 15555 FROM MAGNESIUM ZONING AND ISOTOPIC FRACTIONATION OF OLIVINE.

## 6.1 Previous studies

The Apollo 15 mission returned a 3.3-billion-year-old olivine-normative mare basalt (15555) that because of its large size is often referred to as Great Scott (named after astronaut David Scott, who collected it). Bulk chemical analyses of Apollo 15 olivine-normative basalts were reported by Ryder and Schuraytz (2001). Basalt 15555 is a coarse-grained, porphyritic rock with about 12% rounded olivine phenocrysts, about 50% subhedral zoned pyroxene phenocrysts and a matrix dominated by poikilitic plagioclase. Schnare et al (2008) made a detailed study of the mineral modes, major-element and trace-element composition of olivine grains in the polished section 15555,257. Several early studies reported experimental data on the crystallization of a plausible parental melt of 15555 (Kesson, 1975; Walker et al., 1977). Taylor et al. (1977) modeled the Fe-Mg zoning of olivine grains as being due to diffusive exchange of iron and magnesium across an initial sharp composition contrast and estimated a cooling rate of 5°C/day. There was not, however, any independent evidence for the assumption that the Fe-Mg zoning was due to diffusion, which motivated the present study of the magnesium isotopic fractionation across the same olivine grain from 15555 as a way of determining the degree, if any, to which the zoning can be attributed to diffusion.

## 6.2. Magnesium zoning and isotopic fractionation of an olivine grain from 15555

A false color iron abundance image of zoned olivine grains from polished section 15555,172 is shown in Fig. 12. The variation of MgO and FeO measured along the white line segments across the grain on the left in Fig. 12 is shown in Fig. 13.

<figure><img src="image_14.png" /></figure>

Figure 12. Fe Kα image of a large zoned olivine grain from mare basalt 15555 and surrounding minerals labeled as cpx for clinopyroxene, plag for plagioclase, and ilm for ilmenite. The yellow to red colors surrounding the olivine's green core reflect increasing amounts of iron. The white line segments across the grain on the left show the transect along which the major element composition and magnesium isotopic composition was measured.
<figure><img src="image_15.png" /></figure>

Figure 13. Weight percent MgO and FeO along the transect shown by the white line segments in Fig. 12. The local increase (decrease) of FeO (MgO) around 450 µm suggests that two initially separate olivine grains grew into each other while the iron-rich outer portions of the grains were still developing.

MELTS was used to calculate both batch and fractional crystallization of olivine from a parental melt composition for 15555 suggested by Ryder (2001). Figure 14 compares the results of the MELTS batch crystallization calculation for the fayalite fraction of olivine as function of temperature to that found in the equilibrium experiments by Walker et al. (1977). The good agreement validates our MELTS calculation. The measured core composition of olivine has about 30 wt% each of MgO and FeO, which corresponds to a fayalite fraction Fe/(Fe+Mg) atomic ≈ 0.36, which according to Fig. 14 requires that the entire core and melt were in equilibrium down to a temperature of about 1175°C. This implies that the initial crystallization of the olivine was sufficiently slow, or that the system was at 1175°C for a sufficiently long time for the olivine to be or become homogeneous and in equilibrium with the evolved melt. The time $t = r^2/D$ required for homogenizing magnesium in a 200 µm core is about 3 years using $D = 4×10^{-12} \text{ cm}^2 \text{ s}^{-1}$ for magnesium diffusion along the a-axis of olivine at T=1175°C. This value for the diffusion coefficient of magnesium was calculated using the Dohmen and Chakraborty (2007b,c) parameterization for a fayalite fraction of 0.36, with log fO₂ for lunar basalt corresponding to the iron-wüstite buffer minus one log unit (Jones, 2004) and taking into account that the diffusion coefficient along the a-axis of olivine is a factor of six smaller than along the c-axis. The zoned portions of the olivine grains must have resulted from a second stage of evolution where the temperature decreased from 1175°C sufficiently rapidly such that equilibrium could no longer be maintained between the melt and the interior of the grain. The transition from batch to fractional crystallization was further explored with MELTS calculations. Figure 15 shows the results of two MELTS calculations for the evolution of the olivine composition as a function of temperature with one assuming batch crystallization continuing to a temperature of 1050°C and a second one with fractional crystallization from 1175°C to 1020°C. Both calculations showed that there was no interval from ~1175°C to 1100°C with no net olivine crystallization but that in the batch crystallization case the composition of the olivine continued to change by maintaining equilibrium with the melt that was changing in composition due to the crystallization of other minerals (mostly pigeonite). When the MELTS calculation is switched from batch to perfect fractional crystallization for T<1175°C the hiatus in crystallization results in a gap in the olivine composition of FeO and MgO from about 30 wt% in the core to the much higher (lower) FeO (MgO) once fractional crystallization resumes. No such gap, which would appear as an abrupt drop (increase) in the MgO (FeO) concentration, is seen in the actual
zoning of the olivine grain. Diffusion could have smoothed such an abrupt change in olivine
composition, which can be tested by comparing the magnesium and/or iron isotopic
fractionation across the grain with the results of a model calculation for the isotopic
fractionation associated with the amount of smoothing by diffusion that would be required.
One should keep in mind the results shown in Fig. 15 are for an idealized situation where
perfect batch crystallization changes instantaneously to perfect fractional crystallization at
T=1175°C. In reality, the transition from a homogeneous core to a zoned rim would most
likely not have been an instantaneous change from bulk to perfect fractional crystallization,
but rather something intermediate involving partial exchange between the outer portion of the
grain and melt. Be this as it may, Fig. 14 shows that the core of the olivine grain with a
fayalite fraction of 0.36 would have been in equilibrium with the surrounding melt at
T~1175°C and that the zoning developed after the temperature cooled below 1175°C.

<figure><img src="image_16.png" /><figcaption>Figure 14. The black line shows the evolution of the atom ratio Fe/(Fe+Mg) (i.e., the fayalite fraction) of olivine calculated using the MELTS code assuming continuous equilibrium between olivine and melt (i.e. batch crystallization). The unfilled circles show the fayalite fraction as a function of temperature from olivine recovered from the equilibrium experiments reported by Walker et al. (1977). The agreement between the calculated and observed fayalite fraction of olivine as a function of temperature gives us confidence that the MELTS calculation is a realistic representation of the early high-temperature stage of the evolution of olivine in 15555.</figcaption></figure>
<figure><img src="image_17.png" /></figure>

Figure 15. Results from MELTS calculations for the evolution of the oxide concentrations in olivine assuming batch crystallization (solid lines) of a system with the bulk composition of 15555 given by Ryder (2001). The dashed lines for T < 1100°C show how the composition evolves when MELTS is used to calculate perfect fractional crystallization with decreasing temperature starting from 1175°C. There is a gap in the crystallization of olivine between 1175°C and 1100°C, which is why there is no composition of fractionally crystallized olivine until T = 1100°C.

Figure 15 suggests that the rapid decrease (increase) in the MgO (FeO) towards the rim of the olivine grain from lunar rock 15555 involved some degree of fractional crystallization. Determining the role, if any, that diffusion had in affecting the zoning of the olivine grain can be done by measuring the isotopic composition of magnesium (and/or iron) across the olivine grain. Figure 16 shows the IMF-corrected magnesium isotopic composition at spots along the white line segments shown in Fig. 12 measured with a CAMECA 1270 ion microprobe. The data show the interior of the grain to be quite uniform in magnesium isotopic composition and that there are well-resolved isotopic fractionations of +2‰ to about -4‰ close to both edges of the grain.
<figure><img src="image_18.png" /><figcaption>Figure 16. Matrix-corrected magnesium isotopic composition of olivine measured at spots along the white line segments in Fig. 12 plotted against distance from the left edge of the grain. The error bars reflect the overall uncertainty of the IMF matrix corrections for the instrumental mass fractionation as a function of olivine composition (see Fig. B3 in Appendix B).</figcaption></figure>

The isotopic data in Fig. 16 shows that the interior of the grain was relatively homogeneous in isotopic composition at the time diffusion began and that the isotopic fractionation due to diffusion was restricted to boundary layers near each edge of the grain. The fact that the isotopic composition at the grain edge is significantly lower than in the interior may at first sight seem surprising given that it has been shown that the isotopic fractionation of magnesium during crystallization of olivine from a basaltic liquid is negligible (Teng et al., 2008). This implies that the isotopic composition of melt at the grain boundary would be same as that in the grain core, not negative by several ‰. However, if the boundary condition at the grain edge were no-flux, then the isotopic fractionation at the grain edge would become negative once the diffusion flux from the interior reaches the edge (for an example see Fig. 7 in Richter et al., 2003). The reason for the negative fractionation is that when diffusion down a concentration gradient impinges on a no-flux boundary the faster diffusing lighter isotope ‘piles up’ there causing the isotopic fractionation to become increasingly negative. The most likely cause of an effectively no-flux boundary condition at the edge of the olivine grain is that pyroxene, in which magnesium diffuses orders of magnitude more slowly than in olivine (see Fig. 2), had already crystallized and had become juxtaposed with olivine. The conclusion regarding the nature of the boundary condition at the olivine grain edge is another instance where isotopes point to something that would not have been obvious from the parent element concentration profiles.

## 6.3 Magnesium isotopic constraints on the cause of major element zoning of olivine and implications for the thermal history of 15555

Given the limited extent of the lithium zoning, a conservation of mass equation in Cartesian coordinates for total magnesium or its isotopes (Eqn. 3) was used.

$$ \frac{\partial C_i}{\partial t'} = \frac{\partial}{\partial x'} \left( D'_{i(T, x_{FA}, fO_2)} \frac{\partial C_i}{\partial x'} \right) $$

(3)
810

$C_i$ is a measure of the abundance of species $i$, $x'$ is distance measured in units $l$ (the length of the modeled segment), $t'$ is time measured in units $l^2/D_{To}$ and $D'_i = D^*_{i(T,X_{Fa},fO_2)}/D_{To}$ where $D^*_{i(T,X_{Fa},fO_2)}$

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is the dimensional diffusion coefficient of magnesium species $i$ calculated using the parameterization by Dohmen and Chakraborty (2007b,c). $D_{To}$ is the value of the diffusion coefficient in the grain interior when diffusion began at $T = 1050°C$ with $X_{Fa} = 0.36$ and log $fO_2$ corresponding to the iron-wüstite buffer minus one log unit (IW-1). The diffusion coefficient for $^{24}$Mg can considered to be indistinguishable from that of the total magnesium and the diffusion coefficient of $^{26}$Mg relative to that of $^{24}$Mg calculated as $D_{26Mg}/D_{24Mg} = (24/26)^\beta$, with the value for $\beta$ to be determined by fitting the measured data.

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A remarkable coincidence arises when model calculations are used to test the proposition by Taylor et al. (1977) that the zoning of olivine grain from 15555 was due entirely to diffusion starting from an initial step in concentration. Figure 17 shows that such a calculation for the diffusive evolution of a step assuming a constant value for the Fe-Mg interdiffusion coefficient results in a very good fit to the measured Mg concentration data (thin black line in Fig. 17). But several things are wrong with this. To begin with, it ignores the well-documented dependence of the rate of Fe-Mg interdiffusion on the olivine composition, which when taken into account results in the profile becoming distinctly asymmetrical and no longer fits the measured data (heavy black curve in Fig. 17). The difference in the diffusion coefficient between the low fayalite interior and the higher fayalite composition at the grain edge is about a factor of 100, which accounts for asymmetry of the diffusion profile. The panel on the right of Fig. 17 shows a second flaw in that the Mg isotopic fractionation calculated assuming a fixed Fe-Mg interdiffusion coefficient results in a very poor fit to the measured isotopic fractionation data. Having used a no-flux boundary condition would not have changed this because the diffusive flux and associated isotopic fractionation in the constant diffusion coefficient model had not yet reached the edge of the grain.

<figure><img src="image_19.png" /></figure>

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Figure 17. The panel on the left shows wt% MgO (small circles) measured along the left portion of the transect across the 15555 olivine grain shown in Fig. 12 compared to a model calculation of the diffusive evolution of an initial step (dashed line) for a constant Mg diffusion coefficient (thin black line) and for the diffusion coefficient depending on the local composition of the olivine concentration (heavy black line) as parameterized by Dohmen and Chakraborty (2007b,c). The panel on the right compares the measured Mg isotopic fractionation to the fractionation calculated using $\beta = 0.15$ for the case with constant Mg diffusion coefficient.
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Once one realizes that there was measurable diffusive Fe-Mg exchange in the olivine 15555, the task becomes one of finding by trial and error the zoning due to crystallization that evolves by diffusion to fit both the magnesium zoning and isotopic fractionation. The simplest model for this assumes that diffusion began after the olivine grain had grown to its present size and was bounded by pyroxene to account for the no-flux boundary condition required by the negative magnesium isotopic fractionation at the edge of the grain. The effectively no-flux boundary condition is due to the diffusion of magnesium in pyroxene being very much slower than in olivine and thus when olivine is juxtaposed with pyroxene the flux of magnesium across the contact would be negligible while diffusion was taking place in the olivine grain. The diffusion coefficient of magnesium in olivine used in the calculations depends on temperature and the local fayalite composition of olivine as given by Dohmen and Chakraborty (2007b,c). Figure 18 shows the results of a calculation in which an initial zoning was prescribed such that the system evolves by diffusion to give a good fit to both the wt% MgO and the magnesium isotopic fractionation data. The calculations that yielded the fits to the data shown in Fig. 19 for the left and right edge of the olivine grain were run for nondimensional times of $t' = 0.0015$ and 0.0008 over which the temperature dropped 200°C starting from 1050°C (the temperature corresponding to 5 wt% MgO in Fig. 15). The dimensional times $t = (l^2/D_{To})t'$ are 65 and 35 days for $l = 0.03$ cm and $D_{To} = 2.4 \times 10^{-13}$ cm$^2$ s$^{-1}$ calculated using $T = 1050$°C, a fayalite fraction of 0.36, and $fO_2 = 1.5 \times 10^{-15}$ bars (IW-1) in the Dohmen and Chakraborty (2007b,c) parameterization for the magnesium diffusion coefficient along the c-axis of olivine reduced by a factor of 6 to account for the diffusion being along the slower a-axis. These times result in estimates for the cooling rate of lunar rock 15555 of 3 and 6°C per day, which are much the same as that given more than 40 years ago by Taylor at al. (1977) but now with the added confidence provided by the magnesium isotopic fractionation across the olivine grain determining the extent of magnesium diffusion.

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The magnesium isotopic fractionation in panel (b) of Fig. 18 was fit with $\beta_{Mg} = 0.14$ and that in panel (d) with $\beta_{Mg} = 0.16$. That somewhat different run durations and $\beta_{Mg}$ values had to be used to fit the boundary layer at each edge of the olivine grain provides a measure of the uncertainty inherent in using necessarily simplified assumptions regarding the initial and boundary conditions to model the diffusive evolution of an olivine grain from a natural setting. The $\beta_{Mg}$ values (0.14 and 0.16) used to fit the isotopic fractionation data shown in Fig. 18 are somewhat larger than the average $\beta_{Mg} = 0.084$ reported by Oeser et al. (2015) based on modeling the magnesium isotopic fractionation of a set of eight terrestrial olivines. This difference may be due to the fact that the terrestrial olivines are much more magnesium rich than the lunar olivine studied here.
<figure><img src="image_20.png" /></figure>

Figure 18. Panels (a) and (b) compare model calculations with the measured wt% MgO (unfilled circles) and magnesium isotopic fractionation (circles with error bars) in 15555 olivine from the edge to 300 µm along the left side of white line segment shown in Fig. 12. Panels (c) and (d) are for data as a function of distance from the edge along the white line segment ending at the right edge of the grain. The initial condition for these calculations is shown by the dotted line in panel (a) and (c) with a no-flux boundary condition at the edge of the grain. The temperature at the start of the calculation was 1050°C and then cooled linearly by 200°C over the course of the calculation. The isotopic fractionation was modeled assuming that it was initially uniform and evolved with a mass-dependence of the magnesium diffusion coefficients given by $\beta = 0.14$ for the calculated fractionation shown in panel (b) and with $\beta = 0.16$ for the fractionation shown in panel (d). The nondimensional run time $t'$ for the results shown in panel (a) and (b) is 0.0015 and 0.0008 for that in panel (c) and (d).

## 7. RESULTS AND DISCUSSION

Lithium and magnesium isotopic measurements across zoned pigeonite grains from Shergotty showed little isotopic fractionation in either the relatively homogeneous core of the grains or in the zoned rims (see Fig. 5 and additional data in Appendix A). The lack of significant isotopic fractionation is evidence that the lithium and magnesium concentration variations of the zoned portions of the grains was not caused by, or significantly affected by, diffusion. Therefore, the dominant process that determined the distribution of lithium and magnesium in the grains must have been crystallization from a melt of evolving composition. MELTS calculations were used to model the major element evolution of pigeonite crystallized from a plausible Shergotty parental melt (Fig. 6), leading to the conclusion that the uniform core of the pigeonite grains with approximately equal amounts of FeO and MgO can be explained by batch crystallization down to a temperature of 1135°C. Batch crystallization implies that the crystallizing grains are uniform and in equilibrium with the evolving melt composition as the system cools. For this to be the case, the crystallization must have been sufficiently slow for diffusion to have sufficient time to homogenize the grains. This line of reasoning leads to an estimate that the core of the pigeonite grain SH3 from Shergotty would
maintain equilibrium with the evolved melt if it had been at T=1135°C for more than 3200 years. Batch crystallization, however, does not produce zoned minerals, thus at about T=1135°C grain SH3 must have begun to cool sufficiently rapidly that it grew by fractional crystallization sufficiently fast that there was not enough time for there to have been any significant mass transport by diffusion as evidenced by the limited isotopic fractionation. Bounds on the cooling rate of this second stage of the thermal evolution of grain SH3 were determined by numerical calculations of the magnesium isotopic fractionation of a cooling grain growing a rim around an initial core as a function of the cooling rate. Comparing the calculated magnesium isotopic fractionation with the measured data (see Fig. 9) required that the rim must have grown in less than 1700 years. When the same approach was used to model much faster diffusing lithium in grain SH3 (see Fig. 11), the lack of significant lithium isotopic fractionation associated with the lithium concentration gradient led to an estimate of time over which the rim must have grown for only 40 minutes corresponding to a cooling rate of about 150°C/h.

The major element and magnesium isotopic zoning of a large olivine grain (Figs. 13 and 16) from mare basalt 15555 was used to document a two-stage thermal history. The core composition of the olivine grain has a composition with a fayalite fraction of 0.36 (Fig. 13), which is consistent with a MELTS batch crystallization calculation down to T=1175°C (Fig. 15), suggests that it must have cooled sufficiently slowly for it to be uniform in composition and in equilibrium with the evolved melt composition at T=1175°C. The local increase in FeO and decrease in MgO in the center of the grain is interpreted to be the result of two partially crystallized olivine grains growing into other. The homogenization time of the olivine of the 200 µm grain cores at T=1175°C was estimated to be about three years. The zoned edges of the grain, where the MgO concentration decreases to ~5 wt% and FeO increases to ~60 wt%, implies that the cooling rate must have increased sufficiently for the crystal to grow by fractional crystallization. The magnesium isotopic composition across the olivine grain (Fig. 16) shows well-resolved fractionations at the edges that indicated that a small but resolvable amount of diffusion modified the zoning. The locally heavy δ²⁶Mg (~+2‰) in the zoned part of the grain is the result of the faster diffusion of ²⁴Mg down the magnesium concentration gradient leaving behind magnesium slightly enriched in ²⁶Mg. The light δ²⁶Mg (~-4‰) at the edges of the grain was interpreted as being due to the faster ²⁴Mg that diffused down the concentration gradient "piling up" at an effective no-flux boundary due to the olivine being bounded by pyroxene. Pyroxene provides a no-flux boundary because the rate of diffusion of magnesium in the pyroxene is many orders of magnitude slower than in olivine (Fig. 2). The duration of the fast cooling stage of lunar rock 15555 (~45 days at about 0.2°C/h) was estimated based on the time required to diffuse an amount of magnesium indicated by the isotopic fractionation in the zoned portions of the olivine grain.

Table 1 lists the estimates of the durations, and corresponding cooling rates where applicable, of two distinct stages of the crystallization of Shergotty and of mare basalt 15555. The estimated second-stage cooling rate of Shergotty of greater than 150°C/h is certainly extraordinarily fast but not unprecedented. First and Hammer (2016), for example, recently proposed a multistage thermal history for another shergottite, Yamato 980459, with a final cooling rate of 100°C/h. Saper and Stolper (2020) used diffusion modeling of MgO gradients in glassy inclusions in olivine from Yamato 980459 to estimate a cooling rate of 383±43 °C/hr. The 150°C/h cooling rate of Shergotty inferred in the present study is, however, much faster than what was proposed in previous studies such as that by Lentz and McSween (2000), who argued that the total time of pigeonite growth was between 19 and 93 days. Had this been the case diffusion would have had more than enough time to erase any lithium zoning of the pyroxene grains. Lentz and McSween (2000) also estimated that the pyroxene
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cores grew for a time between 11 and 53 days. This is orders of magnitude too short a time to
homogenize pigeonite cores, which because of the very slow diffusion of magnesium in
pyroxene, we estimated would have required several thousand years.

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Table 1 also lists for comparison with Shergotty the two-stage thermal history of another
martian meteorite, NWA 817, that was studied by Richter et al. (2016) using the same
isotope-based methods as used here. NWA 817 is similar to Shergotty in that it is a pyroxene-
rich cumulate (~70% augite), however it is much older than of Shergotty being a nakhlite, a
class of martian meteorites that have a common crystallization age of 1340±40 Ma (Udry and
Day, 2018) while Shergotty has an age of 165±4 Ma. There are several other significant
differences between these two martian meteorites. The augite grains from NWA 817 are
zoned, with the lithium abundance increasing towards the grain edge, which is expected for
closed system crystallization, given that lithium is somewhat incompatible in pyroxene (see
lithium partitioning data in Appendix A). The lithium zoning of the pigeonite grains in
Shergotty, on the other hand, have the lithium decreasing towards the edges of the grains
(Fig. 5). Another significant difference is that while the zoning of pyroxene grains in
Shergotty was shown here to be dominantly due to fractional crystallization, the zoning of
NWA 817 was shown by Richter et al. (2016) to be explicable entirely by diffusion from
initially homogeneous grains.
**Table 1.** Summary of results derived from modeling the zoning and isotopic fractionation of minerals from Shergotty, nakhlite NWA 817, and from mare basalt 15555. The temperature of Stage 1 is derived from MELTS batch crystallization calculations that match the proportions and composition of minerals in the grain cores. The duration and cooling rates for Stage 2 were derived from model calculation related to the zoned portion of the mineral grains. The depth below the cold surface of a partially molten layer corresponding to the reported cooling rates is taken from in Fig. 19.

Stage 1

<figure><img src="image_21.png" /></figure>

Stage 2

<figure><img src="image_22.png" /></figure>

<figure><img src="image_23.png" /></figure>

<figure><img src="image_24.png" /></figure>

<figure><img src="image_25.png" /></figure>

<figure><img src="image_26.png" /></figure>

<table><thead><tr><th>Sample</th><th>Temperature and duration</th><th>Duration</th><th>Cooling rate</th><th>Growth rate</th><th>Burial depth</th></tr></thead><tbody><tr><td>Shergotty</td><td>1135°C for >3200 y</td><td>&lt; 1 h</td><td>&gt;150°C/h</td><td>&gt;200 µm/h</td><td>&lt;10 cm</td></tr><tr><td>constraint:</td><td>homogeneous pigeonite cores</td><td>no lithium isotope fractionation</td><td></td><td>zoning extent and duration</td><td></td></tr><tr><td>15555</td><td>1175°C for &gt; 3 y</td><td>~1000 h</td><td>~ 0.2°C/h</td><td>~0.2 µm/h</td><td>~400 cm</td></tr><tr><td>constraint:</td><td>homogeneous Mg olivine cores</td><td>extent of Mg isotopic fractionation</td><td>extent of Mg isotopic fractionation</td><td>zoning extent and duration</td><td></td></tr><tr><td>NWA 817</td><td>1100°C for &gt; 2000 y</td><td>~1000 h</td><td>~ 0.2°C/h</td><td></td><td>~ 400 cm</td></tr><tr><td>constraint:</td><td>homogeneous Mg augite cores</td><td>Mg zoning and isotope fractionation</td><td>Mg zoning and isotope fractionation</td><td>not constrained</td><td></td></tr></tbody></table>

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Table 1 includes values for the distance from a cold surface at -50°C (close to average surface temperature of the Moon and Mars) that can account for the estimated cooling rates for each of the three rocks listed. The distance estimates were made using the cooling curve shown in Fig. 19 calculated with the error function solution to the heat equation given by

$$T(t,z) = -50 + 1150 \operatorname{erf} \left( \frac{z}{2\sqrt{kt}} \right)$$ with T in °C, z in cm, t in seconds, and with a thermal diffusion

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coefficient k = 0.006 cm² s⁻¹ as used by Peck et al. (1977) to model the measured temperature versus depth in a Hawaiian lava lake. The curve in Fig. 19 corresponds to the temperature change with time T(t) at a distance z = 10 cm from the cold surface, but it can be used for T(t) at any other distance by expanding or contracting the time scale by (z/10)². Note that the cooling has an initial period of constant temperature when the cooling from the cold surface has not yet arrived at the distance z.

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The most obvious interpretation of the distance of a sample from cold surface listed in Table 1 is that it represents an emplacement depth below the surface. In the case of 15555, which comes from basalt erupted onto the lunar surface, such an interpretation is not particularly problematic. Recall however that 15555 was already highly crystalline at the time cooling began and that in order for any partially molten material silicate material to flow onto the surface it must not have had much more than 40% crystals. At crystal fractions higher than this the effective bulk viscosity of the crystal-laden melt increases very rapidly and the mixture develops yield strength (see Saar et al., 2001, and Mueller et al., 2010) that inhibits flow. It seems likely that the originally erupted material had a crystal fraction of no more than about 40% and that the crystallinity at a depth of 400 cm increased by a combination of crystal settling during the relatively isothermal portion of the cooling curve and further crystallization during subsequent cooling. For a sample at about 400 cm below the surface the isothermal portion of the cooling curve would have lasted for about 500 hours with subsequent crystallization of pigeonite continuing for an additional 1000 hours as the temperature decreased by about 100°C.

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The remarkably fast cooling of highly crystalline Shergotty (>150°C/h) and the implied emplacement within 10 cm of a very cold surface requires a special setting for the last stage of the thermal evolution of this meteorite. First and Hammer (2016) suggested that their inferred final cooling rate of 100°C/h of a similar shergottite, Yamato 980459, could be explained by a breakout from a pahoehoe-like flow erupted onto the surface of Mars. In the case of Shergotty there is not a problem transporting the melt plus the homogeneous cores of pigeonite and augite grains because as the MELTS batch crystallization calculation shows, the melt volume fraction would have been about 65% when the pigeonite had equal wt% MgO and FeO. The rims of the pigeonite grains would have had to have grown to their final size and the melt fraction reduced to about 20% in a matter of minutes, perhaps in a thin pahoehoe flow as proposed by First and Hammer (2016). This, however, does not account for the large crystal fraction of Shergotty or for the foliated texture with large preferentially oriented pyroxene grains described by Stolper and McSween (1979). A slightly different setting that could have produced both the high crystal fraction and the foliated texture along with the final very rapid cooling is a thicker pahoehoe flow with perhaps up to 40% crystals, which then had the melt break out rapidly, leading to deflation and rapid cooling of the
crystals that were left behind. While this scenario could account for both the texture and very rapid cooling of Shergotty, it does not explain the open system behavior of lithium evidenced by the decrease in lithium concentration between the pigeonite cores and rims. The open system behavior of lithium during the crystallization of Shergotty remains, as far as we are concerned, an unsolved puzzle.

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<figure><img src="image_27.png" /></figure>

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Figure 19. Thermal evolution of a sample at a depth z in a partially molten silicate layer based on parameters derived from the cooling with depth at Kilauea Iki lava lake, Hawaii. The curve in the figure corresponds to the thermal evolution at a depth z = 10 cm. For the cooling curve at any other depth, the time scale is stretched or shortened by a factor (z/10)² with z centimeters.

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The work presented here along with the earlier results by Richter et al. (2016) for NWA 817 show three distinct types of zoning: pyroxene grains from Shergotty with no significant evidence of diffusion, zoned olivine from mare basalt 15555 showing limited but resolvable post-crystallization mass transport by diffusion, and pyroxene grains from nakhlite NWA 817 where the zoning can be explained in terms of diffusion from an initially homogenous grain. In each of these cases, the isotopic fractionation data allowed for quantifying the extent of mass transport by diffusion, which in turn was key for constraining their thermal history. Figure 20 illustrates the importance of the isotopic fractionation data by comparing magnesium abundance and isotopic fractionation profiles from Shergotty and NWA 817. Aside from different spatial scales, the magnesium abundance profiles are remarkably similar, which could have led one to assume that they were the result of the same process. However, the isotopic fractionation data clearly shows that this was not the case. The isotopic fractionation measured across the pigeonite grain SH3 from Shergotty is opposite to what it would be if there had been significant diffusion down the magnesium concentration gradient. It is possible that the magnesium isotopic differences across SH3 are due to inadequate correction of matrix effects. The fractionation across the augite grain 11 from NWA 817, on the other hand, was almost perfectly modeled by Richter et al. (2016) as having been caused by the diffusive loss of magnesium from a grain initially uniform in magnesium abundance and isotopic composition. In the case of the olivine grain from the 15555, the isotopic fractionations document and quantify the limited but resolvable extent that diffusion
modified the distribution of magnesium and that it must have taken place after pyroxene had crystallized. The process or processes responsible for the zoning of Shergotty, NWA 817, and 15555 would have been hard to document and quantify without the isotopic fractionation data.

<figure><img src="image_28.png" /></figure>

Figure 20. Comparison of the magnesium zoning and isotopic fractionation at the edge of pigeonite grain SH3 from Shergotty and that at the edge of an augite grain from nakhlite NWA 817 reported Richter et al. (2016). The calculated isotopic fractionation of lithium in SH3 calculated assuming that the lithium zoning was due to diffusion out of an initially homogeneous grain is shown by the solid curve and is clearly inconsistent with the measured fractionations shown by the open circles. This is in marked contrast to the magnesium evolution of the augite grain from NWA 817 where the measured data is reproduced by a calculation in which both the wt% MgO profile and the magnesium isotopic fractionation are due entirely to diffusion of magnesium out of an initially homogeneous grain. The dashed lines in these figures show the initial conditions assumed for the diffusion calculations.

## ACKNOWLEDGEMENTS

The work reported here was supported by NASA grants NNX13AH09G S01 (FMR), 80NSSC17K0251 (AMD), NNX16AI26G and NNX17AI43G (SBS), and NNX17AE84G (RAM). Support from Europlanet 2020 Project 16-EPN2-014 (FMR) and Programme National de Planétologie from INSU-CNRS and l'Agence Nationale de la Recherche grant ANR-18-CE31-0010-01 (JV) is also gratefully acknowledged. We thank Yan Liang of Brown University for helping us find the published data we list in Appendix C and Thomas Stephan of the University of Chicago for implementing the Mahon (1996) data analysis
1094 algorithm. We also thank three anonymous reviewers and the associate editor for their many
1095 suggestions that improved the manuscript.

1096 References
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