Fe-Mg interdiffusion profiles in rimmed forsterite grains in the Allende matrix: Time temperature constraints for the parent body metamorphism

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1 Meteoritics & Planetary Science 50, Nr 9, (2015) doi: /maps Fe-Mg interdiffusion profiles in rimmed forsterite grains in the Allende matrix: Time temperature constraints for the parent body metamorphism Priscille CUVILLIER, Hugues LEROUX *, Damien JACOB, and Pierre HIREL Unite Materiaux et Transformations UMR 8207, Universite Lille 1 and CNRS, F Villeneuve d Ascq, France * Corresponding author. hugues.leroux@univ-lille1.fr (Received 26 November 2014; revision accepted 23 June 2015) Abstract The Allende matrix is dominated by micron-sized lath-shaped fayalitic olivine grains with a narrow compositional range (Fa ). Fayalitic olivines also occur as rims around forsterite grains in chondrules and isolated forsterite fragments in the matrix or as veins cross-cutting the grains. Allende is a type 3 CV carbonaceous chondrite having experienced a moderate thermal metamorphism. There is therefore a strong chemical disequilibrium between the large forsterite grains and the fayalite-rich fine-grained matrix. Chemical gradients at interfaces are poorly developed and thus not accessible using conventional techniques. Here, we used analytical transmission electron microscopy to study the microstructure of the fayalite-rich matrix grains and interfaces with forsterite fragments. We confirm that fayalitic grains in the matrix and fayalitic rims around forsterite fragments have the same properties, suggesting a common origin after the accretion of the parent body of Allende. Composition profiles at the rim/forsterite interfaces exhibit a plateau in the rim (typically Fa 45 ), a compositional jump of 10 Fa% at the interface, and a concentration gradient in the forsterite grain. Whatever the studied forsterite grain or whatever the nature of the interface, the Fe-Mg profiles in forsterite grains have the same length of about 1.5 lm. This strongly suggests that the composition profiles were formed by solid-state diffusion during the thermal metamorphism episode. Time temperature couples associated with the diffusion process during thermal metamorphism are deduced from profile modeling. Considering the uncertainties on the diffusion coefficient value, we found that the peak temperature in Allende is ranging from 425 to 505 C. INTRODUCTION Chemical zoning in olivines is frequently found in unequilibrated chondrites, both in carbonaceous chondrites and ordinary chondrites (e.g., Peck and Wood 1987; Hua et al. 1988; Weinbruch et al. 1990; Jones and Rubie 1991; Krot et al. 1997; Miyamoto et al. 2009). Typically, zoned olivines display forsteriterich cores and increasing fayalite concentration toward the rim. Zoned olivines are either found within chondrules or as isolated forsterite grains within the matrix. Studying chemical zoning in olivines may allow a quantitative approach to the determination of mineral thermal histories by calculating time temperature couples associated with the chemical zoning length and shape. This type of study thus opens an access to the maximum peak metamorphic temperature or the duration of the thermal event responsible for the zoning. Zoning of olivine within chondrules have been used to decipher chondrule formation history and, in particular, chondrule cooling rates (Miyamoto et al. 1986, 2009; Kaiden et al. 1997; Bejina et al. 2009). Fractional crystallization of the chondrule melt can account for a chemical zoning, termed igneous zoning. Indeed, in a rapid event such as chondrule formation and subsequent cooling, the cooling rate is not slow enough to maintain chemical equilibrium by diffusion. This results in a chemical gradient in olivine, established during crystallization, with a Mg-rich core and a Fe-rich outer rim. This effect is due to the large difference in solidus temperatures between Mg and Fe 1529 The Meteoritical Society, 2015.

2 1530 P. Cuvillier et al. endmembers of olivine (1890 and 1205 C at ambient pressure, respectively). Fe-Mg chemical zoning can also be due to a secondary solid-state process through a Fe- Mg interdiffusion mechanism, postdating the primary chondrule crystallization event and resulting from the interaction between the Fo-rich chondrules and an oxygen- and iron-rich environment (Miyamoto et al. 1986, 2009). It may develop at high temperature in the nebula during a recycling episode of chondrules, at the interface between a relict forsterite and a fayalitic-rich overgrowth (e.g., Ruzicka et al. 2008). It was also shown that thermal metamorphism on parent bodies at moderate temperature can be an efficient process for causing diffusion-driven zoning (Jones and Rubie 1991; Kaiden et al. 1997; Krot et al. 1997). Fe-Mg zoning in olivine and the surrounding fayalite-rich matrix have been extensively studied in the Allende CV3 chondrite. Nebular processes (before any accretion event) at high temperature (T > 1000 C) and enhanced oxygen fugacity were first suggested to explain the FeO enrichment in olivine (Peck and Wood 1987; Hua et al. 1988; Palme and Fegley 1990; Weinbruch et al. 1990; Weisberg and Prinz 1998). Alternatively, a secondary origin for the fayalitic olivines, occurring after the accretion of the Allende parent body, was proposed (e.g., Housley and Cirlin 1983; Kojima and Tomeoka 1996; Krot et al. 1997; Brearley 1999). Krot et al. (1997) emphasized that fayalitic olivines from the matrix and fayalitic olivine rims around chondrules and isolated forsterites are related (texturally and chemically), suggesting a common origin and thermal history. In this formation mechanism scheme, fayalitic olivines were formed through a fluid-assisted metamorphism process occurring in the parent body (e.g., Krot et al. 2004; Brearley 2012). Thus, chemical zoning of olivine occurred after accretion of the Allende parent body. Chemical zoning can be used to constrain the conditions of formation, such as the associated time temperature couple. Here, we present a study of the chemical interaction between chondrule fragments (isolated forsterite and diopside grains) and the FeOrich fine-grained matrix in which they are embedded. The study of contacts between matrix and chondrule fragments allows us to avoid features and contributions from chondrule formation histories, such as an eventual igneous zoning during crystallization, and thus study of only secondary modifications occurring after the accretion on the parent body can be performed. It was previously reported that the chemical zoning in olivine has a low extension, less than 3 lm (e.g., Weinbruch et al. 1994), making difficult their detailed study by conventional techniques such as electron microprobe. Here, we used analytical transmission electron microscopy (ATEM) to study the composition profiles Fig. 1. Backscattered electron image of the fine-grained matrix of Allende. The matrix is dominated by a porous aggregate of lath-shaped Fa-rich olivines (in light gray). The dark gray grains are pyroxenes. along zoned forsterite and diopside at nm scale (spot size 5 15 nm) on prepared electron transparent samples (100 nm thick). We quantified and modeled the measured composition profiles to determine precise characteristics of the event that affected Allende, such as its duration and maximum peak temperature. For forsterite, three types of interfaces were studied, namely the interface between forsterite fragments and external fayalitic rims, the interface between fayalitic veins crosscutting forsterite fragments, and grain boundaries in a polycrystalline forsterite. To fully understand the formation mechanism of small extended zoning profiles, we also performed analyses in two different mineral species (olivine and diopside). These two mineral species have different Fe-Mg interdiffusion properties (preexponential factor and activation energy) and the Fe- Mg interdiffusion rates in olivine are different along the different crystallographic axes. If used as speedometers, the cross-correlation between the deduced time temperature couples should give an access to the duration and metamorphic temperature at which the Fe-Mg profiles were established. SAMPLES AND METHODS Scanning electron microscopy (SEM) was used to identify forsterite and diopside fragments within the Allende matrix (Figs. 1 and 2). This matrix is mainly constituted of a porous aggregate of fayalite-rich (Farich) olivine grains with a composition range of Fa 40 50, as reported by number of previous studies (e.g., Green et al. 1971; Scott et al. 1988; Howard et al. 2010). Forsterite grains in contact with the matrix (either chondrules or isolated forsterites) are always rimmed by a Fa-rich rim contrary to the diopside grains (at least at the SEM scale). For the transmission electron

3 Fe-Mg interdiffusion profiles in Allende 1531 Fig. 2. a d) SEM-BSE images of the forsterite grains (dark gray) selected for the ATEM study. The grains are surrounded by a Fa rim (light gray). Focused ion beam sections (white lines) were extracted at the interface between the forsterite fragments and the matrix. microscopy (TEM) study, we selected one Ca-rich, Fepoor, pyroxene and four isolated forsterite grains with sharp boundaries with the matrix. They are likely fragments of broken type I chondrules. We also selected different rim thicknesses, from 1 to 5 lm thick. Among the four selected forsterite grains, three are cross-cut by Fa-rich veins and one is a polycrystalline forsterite (Fig. 2). We also selected random Fa-rich grains from the matrix to compare the olivine microstructure from rim and matrix. TEM samples, about 100 nm thick, were prepared by the focused ion beam (FIB) technique using an FEI Strata DB 235 at IEMN (University of Lille). Matrix and Carich pyroxene samples were prepared by the conventional argon ion milling technique. Analytical TEM was performed using a FEI Tecnai G2-20 (LaB 6 filament) operating at 200 kv and a Philips CM30 (LaB 6 filament) operating at 300 kv. Composition profiles were measured using energy dispersive X-ray spectroscopy (EDS). For the acquisition of the analytical data, we used the scanning transmission electron microscopy (STEM) mode with a beam diameter within the range 5 15 nm. The study of the microstructure was performed using bright and dark-field imaging in conventional TEM mode and annular bright and dark-field detectors in STEM. The crystallographic orientations of the grains were determined by selected area electron diffraction (SAED). For quantitative chemical analysis by EDS, calculations of element concentrations and atomic ratios were performed using calibrated k-factors and thin film matrix correction procedure. The k-factors for the major elements (O, Mg, Si, Ca, and Fe) were determined using standard specimens according to the parameter-less method of Van Cappellen (1990). The absorption correction procedure based on the electroneutrality principle has been applied (Van Cappellen and Doukhan 1994). Microstructure RESULTS Fa-Rich Olivine Grains in the Matrix The matrix in Allende is dominated by a porous aggregate of micron to sub micron-sized FeO-rich olivine grains (Fig. 3a). They exhibit a tabular morphology. Olivine grains contain frequent planar

4 1532 P. Cuvillier et al. carbon, spinels, and glass), voids, planar defects, and dislocations as for olivine grains from the matrix. Rim thicknesses are variable from approximately 0.7 to 10 lm. SAED patterns show that rims are in crystallographic continuity with the forsterite in contact. The interface between the forsterite grain and the rim is rounded and its neighboring part in contact with forsterite is commonly richer in defects (dislocations, inclusions, and voids) (Fig. 5b; see also Fig. 8a). Forsterite grains frequently contain fayalitic-rich veins (about 1 lm in thickness). A low magnification FIB cross-section containing a vein is shown on Fig. 6. The composition of the vein varies from Fa 40 close to the external rim to Fa 20 at 6 lm into the forsterite grain. The vein and each of the adjacent olivine parts have the same crystallographic orientation, suggesting that the veins are healed fractures involving a growth process into the forsterite grain interior. The size of the vein, about 1 lm, allows an estimation of a moving interface of about 0.5 lm on each side. Both forsterite grain and vein are cross-cut by few c screw dislocations. The vein contains the same type of inclusions (Al-Cr-Fe spinel, pentlandite, and glass) and voids as the fayalitic olivine from the rim and from the matrix except it has fewer of them (Fig. 6). Like the external rim, the interface between the vein and the forsterite grain is rounded and the Fa-rich border close to the interface with forsterite is richer in defects than the vein interior. Fig. 3. Microstructure of the Fe-rich olivine in the matrix. a) Low magnification TEM bright-field image of an Fe-rich olivine assemblage. Note the elongated shape of the olivine grains. b) Dark-field image showing a sub grain boundary and c screw dislocations. defects oriented along the (100) plane as well as dislocations sometime forming sub grain boundaries or in form of straight c screw segments (Fig. 3b). The grains contain number of inclusions and voids (Fig. 4). Inclusions comprise Al-Cr-Fe spinel, pentlandite, carbon and glassy phases. More rarely, some olivines are found with neither defects nor inclusions. The matrix mean compositional range varies from Fa 40 to Fa 50. No significant Fe-Mg zoning was detected across these Farich grains in the matrix. Fa-Rich Rims and Fa-Rich Veins As already reported by Krot et al. (1997), we confirm that Fa-rich rims around the forsterite fragments and Fa-rich olivine grains from the matrix have the same microstructure and compositional range (Fig. 5a). The rim composition spreads over the Fa range and contains numerous inclusions (pentlandite, Internal Microstructure of the Forsterite and Ca-Rich Pyroxene Fragments Forsterite grains are very defect-poor in comparison with the rims and the matrix grains. Only a few c screw dislocations have been observed (Fig. 6). The Ca-rich pyroxene grain composition is ranging from En 60 Wo 40 Fs 0 to En 80 Wo 20 Fs 0. One region near the edge contains some twins along (100) plane (Fig. 7a). For the area with a Wo content lower than Wo 35, the grain also contains diopside/pigeonite exsolution microstructure. The exsolution lamellae are oriented close to the (001) plane with a spacing of approximately equal to nm (Fig. 7b). The exsolution features are characteristic of a rapid cooling rates ( C h 1 ) from high temperature domain above 1200 C (see Weinbruch and M uller [1995] and Weinbruch et al. [2001] for details about the cooling rates determination in exsolved pyroxene grains). This confirms that the Capyroxene grain is a chondrule fragment. Composition Profiles Rim/Fo Interface Composition profiles were measured in four isolated forsterite grains (Fig. 2). For each sample, several

5 Fe-Mg interdiffusion profiles in Allende 1533 Fig. 4. Microstructure of a Fe-rich olivine in the fine-grained matrix. a) Low magnification TEM bright-field image showing that the olivine grains frequently contain a high density of defects, inclusions, and voids. b) High magnification showing an olivine grain containing a glassy inclusion, a spinel inclusion, and a void. Fig. 5. Microstructure of the Fe-rich rims around forsterite fragments. a) TEM bright-field image showing a representative rim microstructure. Rims have the same microstructure as the Fa-rich olivines from the matrix containing glassy, pentlandite, and spinel inclusions and voids. b) Scanning TEM image showing a rounded interface between a forsterite grain and its rim. The rim is rich in defects in comparison with the forsterite. The interface is richer in inclusions and voids. Note also the oriented texture in the rim. The sub domains are elongated along the b crystallographic axis and are separated by sub grain boundaries. profiles were recorded to ensure their representativeness. For a given grain or for the different selected forsterite grains, they all show the same tendency with a Fig. 6. TEM bright-field of a forsterite grain cross-cut by a Fe-rich vein whose iron content is decreasing from the rim (here from Fa 40 in the rim to Fa 20 deep inside the vein). Interfaces with the forsterite grain are rounded and richer in inclusions and voids.

6 1534 P. Cuvillier et al. Fig. 7. Microstructure of the Ca-rich pyroxene fragment. a) Twins along (100) planes and associated diffraction pattern. The mirror plane is highlighted by a dotted white line. b) Exsolutions of pigeonite along the (001) plane. The wavelength is within the range nm. The presence of h+k odd reflections on the diffraction pattern indicates the superposition of the P2 1 /c pigeonite exsolved phase in addition to the diopside C2/c matrix host. composition plateau in the Fa-rich rim (mean value between Fa for all the rims) and a chemical zoning restricted to the forsterite grain in contact, from typically Fa at the interface to lower values toward the forsterite core (Fig. 8). At interfaces between rims and forsterite grains, all the profiles display a compositional jump of about 10 Fa% (Fig. 8). Fe-Mg zoning lengths are close to 1.5 lm (along the a or b crystallographic axis), whatever the thickness of the fayalite-rich rim (roughly between 0.7 and 10 lm). Vein/Fo Interface Composition profiles were recorded across a fayalite-rich vein into a forsterite grain (Fig. 9). As shown on Fig. 6, the composition of the vein is variable depending on the distance from the external rim. However, all composition profiles recorded in the forsterite grain display the same shape and length. Whatever the location at which the profiles were recorded (deep inside the veins or close to the external rim), the Fe-Mg zoning length is close to 1.5 lm as for the other composition profiles measured within the isolated forsterite grains. Fo/Fo Grain Boundaries A FIB section was extracted from a polycrystalline forsterite about 50 lm in size (Fig. 10). It contains three forsterite grains whose estimated size is about 5 lm. The three forsterite grains exhibit well equilibrated grain boundaries with triple junctions at 120. Grain boundaries are decorated with numerous inclusions (spinels and pentlandite) and voids. On the FIB section, the two forsterite grains in contact with the matrix display Fa-rich rims in crystallographic continuity with the forsterite grain. The rim composition is close to Fa 40. Their microstructure (crystal defects, glassy and pentlandite inclusions, voids) is similar to that previously described. At the interface between forsterite grains and their rims, the composition profiles are similar to those previously shown in the other grains

7 Fe-Mg interdiffusion profiles in Allende 1535 Fig. 8. Composition profiles across the interface rim/forsterite (dashed line). a) TEM bright-field image of a fayalitic rim in contact with a forsterite grain. The dotted arrow shows the direction of the composition profile (b). c d) Other examples of Fa concentration (mol%) profiles recorded by energy dispersive X-ray spectroscopy across the interface between other forsterite grains and their associated rims. In the rim part, the profiles display a composition plateau close to the matrix mean value. At the interface between the forsterite and the rim, there is a compositional jump from typically Fa 45 (the value in the rim) down to Fa 35 when entering the forsterite. Chemical zoning is restricted to the forsterite grain. The profile length is about 1.5 lm, whatever the studied forsterite grain. (Fig. 8), with a composition plateau in the rim (mean value close to Fa 40 ), a compositional jump of about 10 Fa% when entering the forsterite grain, and a chemical zoning restricted to the forsterite part with a length of about 1.5 lm. The grain boundaries show significant Fe enrichment compared to the forsterite grain cores of the polycrystalline assemblage. Figure 11 shows a composition profile recorded across a grain boundary. The two forsterite grains (and so the rims) shown in Fig. 11a have a different orientation. The left side of the profile is oriented along the c-axis. As shown in Fig. 11b, the corresponding fayalite concentration is Fa 30 at the grain boundary and decreases to Fa 20, the mean value of the grain. The profile length is not fully accessible as the TEM foil is ending but is at least 3 lm. On the right side, the profile direction is oriented perpendicular to the c-axis (in the [a,b] plane). The Fe- Mg zoning starts from Fa 30 at the grain boundary and Fa content progressively decrease to Fa 10, the mean composition of the grain. The profile length is less extended than in the left grain and is close to 1.5 lm, the same value as for the other composition profiles measured in Allende.

8 1536 P. Cuvillier et al. Fig. 9. Composition profile across a Fa-rich vein and a forsterite grain. a) TEM bright-field image of a forsterite grain cross-cut by a Fa-rich vein whose iron content is about Fa 20 in this area. The dotted arrow indicates the location and direction of the composition profile. b) Corresponding Fa concentration (mole%) profile across the vein and host. The composition value at the interface is close to Fa 20. Zoning length in the forsterite grain is about 1.5 lm. Interfaces between the Diopside Grain and the Fa- Rich Matrix Grain boundaries between the pyroxene grain and the fayalitic grains are filled with poorly crystalline material, about 50 nm thick (Fig. 12a). In the diopside grain, the iron content is progressively decreasing from 2 atom% at the grain edge to approximately 0 atom%. The edge of the grain also displays a Ca enrichment up to 10 atom% while the Ca concentration in the diopside interior is lower. All the zoning lengths measured are very short and between 40 and 70 nm (Fig. 12b). DISCUSSION The discussion is first focused on the origin of the fayalite-rich olivines and the origin of the zoning profiles. The composition profiles are then modeled to Fig. 10. STEM bright-field image of a polycrystalline forsterite. The grain boundaries are filled with voids and inclusions and formed an equilibrated triple junction at the contact with the three forsterite grains. The rim is found in crystallographic continuity with the adjacent forsterite grains. determine their associated time temperature couples. The value of these time temperature couples and their implications concerning the Allende metamorphic event are discussed in the last part. Origin of the Fayalite-Rich Olivines in the Matrix of Carbonaceous Chondrites The fayalitic olivines in the matrices of CV chondrites have been widely studied. Two major scenarios were proposed to explain their properties. One favors a formation in the solar nebula, before accretion, while the other involves parent body transformation of the fine-grained matrix. For the solar nebula scenario, the fayalitic olivine would have formed by a direct condensation from a gas phase (MacPherson et al. 1985; Peck and Wood 1987; Hua et al. 1988; Palme and

9 Fe-Mg interdiffusion profiles in Allende 1537 Fig. 11. Composition profile across grains boundaries in the polycrystalline forsterite. (a) TEM bright-field image of the polycrystalline forsterite. The two forsterite grains have a different crystallographic orientation as revealed by the corresponding diffraction patterns. b) Composition profile measured across the two forsterite grains. The profile is oriented along the c-axis in the first grain (on the left side) and perpendicular to c-axis in the second grain (on the right side). The composition at the grain boundary is close to Fa 30. Fegley 1990; Weinbruch et al. 1990, 1993; Murakami and Ikeda 1994; Weisberg and Prinz 1998; Nozawa et al. 2009; Varela et al. 2012). This nebular model includes a direct condensation of iron-rich olivine grains from a gas phase with enhanced oxygen fugacity originated from a dust-rich or water-rich nebular region. However, Grossman et al. (2012) showed that even with a very high dust or water enrichment, the FeO-bearing olivine does not form until temperatures are relatively low and diffusion rates are too slow to make entire FeO-rich grains. The other scenario proposes a secondary origin for the fayalitic olivines in the parent body (Housley and Cirlin 1983; Brearley and Prinz 1996; Kojima and Tomeoka 1996; Brearley 1997, 1999; Krot et al. 1997, 1998, 2004; Imai and Yurimoto 2003; Watt et al. 2005; Howard et al. 2010). The most prevalent scenario implies a fluid-assisted alteration at low temperature followed by a metamorphic event (Brearley and Prinz 1996; Kojima and Tomeoka 1996; Krot et al. 1997, 1998, 2004; Brearley 1999; Imai and Yurimoto 2003). Our observations confirm that fayalitic olivines from the matrix exhibit the same microstructure as the olivines from rims and veins of the forsterite grains, as previously mentioned by Krot et al. (1997). They both contain voids, inclusions (Al-Cr-Fe spinel/pentlandite/ glassy/carbon), dislocations, and planar defects. The olivine compositional range, from Fa 40 to Fa 50, is the same for both the matrix and rims. These observations suggest a common origin and thermal history for the fayalitic olivine in the matrix and the fayalitic rim. It is well consistent with a thermal metamorphism episode on the parent body which imposed similar conditions to the whole assemblage. The Fa-rich grains microstructure is also compatible with a lowtemperature formation. The presence of pentlandite inclusions in Fa-rich olivines requires a temperature of formation lower than 610 C to be stable and thus implies a low-temperature formation for the Fa-rich olivine hosts (Brearley 1999). The presence of Fa-rich veins (healed fractures) cross-cutting chondrules is also a strong argument in favor of a formation process occurring after the accretion of the parent body. At last, the Fe-Mg zonings at the edge of the forsterite fragments in the matrix are also in agreement with a parent body origin. Whatever the nature of the interface (rims, grain boundaries, or veins) extensions of the zoning are in the same order of magnitude, close to

10 1538 P. Cuvillier et al. Fig. 12. Composition profile at the interface between a diopside grain and a Fa-rich olivine in the matrix. a) TEM bright-field image of the Ca-rich pyroxene in contact with a Fa-rich olivine grain. Boundaries of the interface are indicated by the dashed lines. The interface is filled with poorly crystallized material a few tens of nanometers thick. b) Composition profile measured across the pyroxene and the olivine. The iron content in the Fa-rich olivine is constant (11 atom%). The chemical zoning is restricted to the pyroxene grain with a length value between 40 and 70 nm, with an iron content ranging from about 2 atom% at the interface to 0 atom% in the pyroxene interior. At the edge, the diopside grain also displays a Ca enrichment and a Mg depletion. 1.5 lm (in the [a,b] crystallographic plane). Only the profile oriented along the c crystallographic axis (perpendicular to [a,b] plane) shows a larger length. This is due to a crystallographic anisotropy and discussed in the following. These comparable zoning length values strongly suggest a common and single event, compatible with a parent body process. The parent body process involving a fluid-assisted mechanism scenario for the formation of the fayalitic olivines (e.g., Krot et al. 1995, 1997) could account for the observed features. Krot et al. (1995, 1997) first attributed the formation of fayalitic olivine in Allende to the dehydration of phyllosilicates, after the suggestion of Kojima and Tomeoka (1996) concerning the fayalitic olivine in Allende dark inclusions. Later, Krot et al. (2004) gave up this scenario due to the high abundance of fayalitic olivines in aqueous altered and unmetamorphosed chondrites from the CV Bali subgroup (CVoxB) as well as the lack of oxygenisotopic evidence for a hydration-dehydration process in CV chondrites (Clayton and Mayeda 1999). Krot et al. (2004) then favored a fluid-assisted thermal metamorphism including various mechanisms such as the replacement of the primitive precursors (Fe,Ni metal, sulfides, crystalline and amorphous silicates) and direct precipitation of FeO-rich olivine from a fluid. In a fluid-assisted thermal metamorphism scenario, the fayalitic olivine in Allende formed at low temperature before the metamorphic event. The process includes the formation of new grains in the matrix but also an overgrowth on pre-existing grains, such as chondrule fragments. Part of rim thickness should also include replacement at the border of the initial forsterite grains. This fayalitic replacement is well illustrated by the thick (up to 1 lm) Fa-rich veins, which were likely formed on initial fractures (Fig. 6). Our TEM study also showed that the interface between the Fa-rich rims and the forsterite is rounded, confirming that the forsterite surfaces were smoothed during an alteration process. The thickness of the Fa-rich rims around forsterite grains is highly variable. The rims probably formed by a combination of a direct replacement of the edge of the forsterite grains and an overgrowth (Imai and Yurimoto 2003; Krot et al. 2004) whose thickness is controlled by a very local environment. Both of these mechanisms keep the crystallographic continuity between the rim and the forsterite. The narrow compositional range (Fa ) (e.g., Howard et al. 2010) of the fayalitic olivines, their homogeneous microstructure, and the similar zoning length in the whole matrix clearly indicate that a thermal homogenization, probably during the metamorphic event, occurred after the formation of the ferroan olivines. Origin of the Fe-Mg Zoning in Forsterite The forsterite edges, in contact with the Fa-rich rims, are strongly zoned. All the recorded profiles have a comparable width, close to 1.5 lm, regardless of the

11 Fe-Mg interdiffusion profiles in Allende 1539 studied forsterite grain or the nature of the interface (direct interface with an external rim, internal grain boundaries, or interface with veins crosscutting the forsterite). This reproducible zoning length supports a diffusion origin for composition profiles and disqualifies a chemical zoning due to crystal growth. Moreover, the studied profiles are also compatible with the diffusion anisotropy in olivine because of its orthorhombic symmetry (e.g., Buening and Buseck 1973; Misener 1974; Chakraborty et al. 1994; Dohmen et al. 2007). We had the opportunity to study the influence of the crystallographic orientation in the polycrystalline forsterite sample (Fig. 11). The different profile lengths can be directly interpreted as originated from an anisotropy of diffusion along the crystallographic axis. For one grain, the composition profile is oriented along the c crystallographic axis and for the other one, the profile is perpendicular to the c- axis (in the [a,b] plane). The zoning length in each of the grains is different, about 3 lm along the c-axis and 1.5 lm perpendicular to the c-axis. The Fe-Mg interdiffusion coefficient along c, D c, is six times faster than along a or b, for which the diffusion coefficient is equivalent (Dohmen and Chakraborty 2007). Therefore, the diffusion distance, approximately equal to x = 2 Dt, is 6 times larger along c than perpendicularly to c. As the profile in the first grain is incomplete (thus the diffusion distance cannot be fully measured), we used the angles between the slope at the origin of the profile and the interface. This angle is directly related to the diffusion distance. If composition profiles measured in Allende are diffusion-driven, the ratio between angles on each side of the grain boundary should be tana ab /tana c = 1/ 6. The calculated angle values for the profile along c-axis and perpendicular to c are, respectively, a ab = 37 and a c = 61 leading to tana ab /tana c = / 6. There is therefore a very good correlation between intrinsic properties of Fe-Mg interdiffusion and the observed profiles, thus confirming that the profiles developed by Fe-Mg interdiffusion and do not result from the growth process of the Fa-rich rim. Altogether, the microstructure of the fayalite-rich grains and rims and the chemical zoning in forsterite grains are compatible with a secondary process that occurred at moderate temperature, likely during the thermal metamorphism of the Allende parent body. Modeling of the Diffusion Profiles The measured diffusion lengths are below 2 lm in olivine and below 100 nm in diopside. Both the olivine and diopside grains measure several tens of lm. The 1D approximation for diffusion modeling is thus valid. This approximation is nevertheless not fully satisfactory for small grains with a profile length close to the grain size as it is the case for the polycrystalline assemblage. As a consequence, this sample was excluded for our diffusion modeling study. Composition profiles were modeled by solving the diffusion equation (also referred to as the Fick s second tþ=@t tþ ð@cðx; tþ=@xþþ (1) where C(x,t) is the concentration of the element for a given position x and time t and D is the Fe-Mg interdiffusion coefficient. In this expression, the dependence on temperature is contained within D. Diopside Grain As the bulk composition of the studied pyroxene is almost Fe-free (<0.5 atom%) and Al-rich (~2 atom%) we choose the f(o 2 )-independent Fe-Mg interdiffusion rate measured by M uller et al. (2013) in natural Al-rich (~0.1 atoms of Al per formula unit) pyroxenes. log½dðm 2 =sþš ¼ 6: =2:303RT (2) It was measured for temperature between 800 and 1200 C and we extrapolated its value to the lower temperatures expected for the Allende parent body. For modeling, fayalitic olivines from the matrix were assumed to act as an infinite source for iron diffusion into the pyroxene grain as we did not observe any compositional change in the adjacent fayalitic grain. The diffusion coefficient being not dependent on the iron content, the diffusion equation was resolved analytically. The profile shapes were thus modeled with an error function (erf), solution of the diffusion equation. This solution takes the following form: Cðx; tþ ¼C s þðc i C s Þerfcð x x c Þ (3) where x c = 2 D(T)t is the diffusion length which is a function of the temperature (via the interdiffusion coefficient D[T]) and the time t, C i is the initial concentration of iron in the diopside grain and C s the concentration of iron at the interface. This modeling shows a good fit with the experimental diffusion profile. The diffusion length can be determined as well as the time temperature pairs in the isothermal approximation (see last part). Olivine Grains Diffusion profiles at the rim/forsterite interface exhibit a very peculiar shape. They include a plateau in

12 1540 P. Cuvillier et al. the rim (Fa ), a compositional jump between forsterite and rims from Fa to Fa (the matrix mean value), and a concentration gradient in the forsterite. The composition plateau in the rim and the lack of gradient in the Fe-rich grains of the matrix show that diffusion is fast in Fe-rich olivine. This faster diffusion is likely related to the fact that diffusion in olivine becomes significantly more efficient when the iron concentration is increased (e.g., Misener 1974; Hermeling and Schmalzried 1984; Nakamura and Schmalzried 1984; Chakraborty 1997; Dohmen and Chakraborty 2007). It is also probably enhanced by the higher concentration of crystal defects in Fe-rich olivine. In contrast, the forsterite grain in contact with the rim is defect-free and displays a strong Fe-Mg zoning. Considering the high microstructure contrast, it would not be surprising that a significant diffusion coefficient discontinuity across the interface exists, likely linked with the observed compositional jump at forsterite/fa-rich rim interfaces. The compositional jump (from about Fa at the forsterite interface to Fa in the rim) reveals that interfaces between the forsterite grains and the Fa-rich rims are unequilibrated. This compositional jump could be due to a resistance at the interface. This resistance notion has been introduced by Crank (1975) to explain abrupt slowing down of the kinetic at interfaces, preventing the interface from reaching equilibrium. However, interface resistance is not known to occur at the contact between two olivine crystals, or olivines with two different compositions, in conditions where exchange between olivines has been observed in nature and in experiments (e.g., Chakraborty 1997; Dohmen et al. 2007). Therefore, the compositional jump points to the role of moving boundaries during the time of residence in the parent body. As the iron is diffusing into the forsterite grain, the boundary is progressively moving inward the forsterite grain. This is thus erasing a part of the initial zoning in the rim by progressively replacing it by a composition plateau as experimentally observed. For olivine, we used the interdiffusion coefficient described by Dohmen and Chakraborty (2007) for low f (O 2 )(<10 15 bar) or unknown oxygen fugacities: log½d c ðm 2 =sþš ¼ 8: =2:30RT þ nðx Fe 0:14Þ (4) and D a D b D c =6 (5) As the interdiffusion coefficient was only measured for T > 600 C, we extrapolated its value to lower temperatures corresponding to conditions expected for the Allende parent body. Contrary to what occurs in diopside, this coefficient is dependent on the iron content (X Fe ); the coefficient n describes the weight of this dependency (Dohmen et al. 2003; Dohmen and Chakraborty 2007). The value of n is determined experimentally by finding the best fit of experimental diffusion profiles with simulated ones. Many studies (e.g., Misener 1974; Hermeling and Schmalzried 1984; Nakamura and Schmalzried 1984; Chakraborty 1997; Dohmen et al. 2003; Dohmen and Chakraborty 2007) have found a value between 2 and 3. When the crystallographic orientation of the profile was unknown we used the mean value of the diffusion coefficient along the three crystallographic orientations. The Fe- Mg interdiffusion coefficient (equation 4), which is dependent on the iron content X Fe, varies along the profile. Therefore, the diffusion equation (equation 1) cannot be solved analytically and we solved it numerically using a finite difference method. In an attempt to account for the compositional jumps of the measured profiles, the model also implemented a velocity for the Fa-rich rim/forsterite boundary. The initial conditions of the model were first, the initial position of the rim/fo boundary which was adjusted to obtain the best fit of the concentration profile in the forsterite; second, the concentration in the Fa rim, which was fixed at the mean value of the rim, i.e., between Fa 40 50, mimicking an infinite reservoir; and third, the temperature, which was constant throughout a simulation (i.e., isothermal approximation, see next part). Each simulation was run until the least-squares procedure yielded the best fit to the experimental data in the forsterite part, thus allowing determination of the corresponding time temperature couple. Figure 13 shows four simulations that were run at 500 C, with a fixed or a moving boundary. Whatever the interface velocity, the concentration profile near the interface always decays as an error function, with slopes depending on the velocity. On one hand, a fixed or slow boundary results in a smooth composition profile that does not reproduce the observed compositional jump, as shown by the dashed black and light gray curves in Fig. 13 (the two curves almost overlaps). On the other hand, a fast boundary produces a sharper profile, but does not allow reproducing the profile tail in the Fo grain (dark gray curve). The best fit to the observed composition profile in the Fo grain is obtained by considering a fixed boundary (dashed black curve). The assumption that diffusion processes occurred while the boundary was moving does not allow reproducing the concentration profile in the Fo grain neither the compositional jump. Accordingly, the origin of the compositional jump remains unclear. A possibility could be to consider a moving boundary at lower temperature

13 Fe-Mg interdiffusion profiles in Allende 1541 Fig. 13. Concentration profiles as observed experimentally (black open squares) and as simulated (lines) under various conditions: fixed boundary corresponding to a time of yr (dashed black curve); boundary moving at 1, 10, and 100 lm/myr with a corresponding time of yr (light gray curve), yr (gray curve), yr (dark gray curve), respectively. The dashed black and light gray curves almost overlap. All simulations are performed at 500 C and the initial position of the boundary is placed at 2.5 lm. NB: The velocities of the interface used in this example are arbitrary and have been chosen to illustrate the variation of the shapes of the profiles for various conditions of mobility of the interface. during the retrograde step of metamorphism, with an interdiffusion process strongly slowed in the forsterite. The shape of the profile in the forsterite part would then not be significantly modified. Consequently, we chose to fit the concentration profiles only in the forsterite part, without modeling the plateau in the rim neither the compositional jump. Running several simulations at various temperatures allowed determining the time temperature couples. Figure 14 shows an example of a fit (continuous line) to the experimental data. Given the indetermination on n, i.e., the weight of the iron content dependency, two values were used for the interdiffusion coefficient: n = 2 or 3. The resulting uncertainty on the time temperature values will be taken into account for the estimation of the peak metamorphic temperature. Metamorphic Event of Allende: Time Temperature Constraints The data derived from the analysis of composition profiles are used to constrain the time temperature couple that prevailed during the metamorphic heating of Allende. The calculations were performed from profiles in forsterite and diopside. The Fe-profile at the Fig. 14. Example of profile modeling at a rim/fo interface: dark gray curve n = 2, light gray curve n = 3. The characteristic temperature is fixed here at 500 C, which corresponds to a time of yr for n = 2 and for n = 3. The initial concentration is adjusted at the mean value of the rim close to Fa 43. In this case, the best fit is obtained for an interface placed at x = 2.5 lm from the observed jump position. Only the profile in the forsterite part was considered in the least-squares fitting procedure. edge of the diopside grain is significantly shorter (40 70 nm) than for forsterite grains (few microns). This is due to the interdiffusion coefficient in pyroxene, about two orders of magnitude smaller than in olivine (e.g., Ganguly and Tazzoli 1994). Given that these two minerals have different diffusion coefficients, for the pre-exponential factor but especially for the activation energy, they could constitute a double marker whose characteristics should lead to determine the intensity and the duration of the metamorphic heating. For calculations, we assumed that most of the atomic mobility was generated during the peak metamorphic temperature and we thus used an isothermal modeling. Indeed, when the temperature decreased by 50 C, the timescales needed to obtain the best fit in the forsterite part drastically increased by one order of magnitude (10 4 yr at 550 C, 10 5 yr at 500 C, 10 6 yr at 400 C, and so on). The lower temperature contribution on the atomic mobility is thus negligible relative to the higher temperature value (corresponding here to the peak metamorphic temperature). In the framework of an isothermal approximation, the modeling allows us to deduce time temperature couples corresponding to the best fit with the experimental profiles. Chakraborty and Ganguly (1991) have shown that the temperature retrieved from such a modeling is a characteristic temperature T ch, that should be converted into the peak temperature T peak, using the relation T ch (K) = 0.97T peak (K), to obtain timescales closer to the

14 1542 P. Cuvillier et al. real ones. In the following, the time characteristic temperature couples given by calculations will be directly converted to time peak temperature couples. Allende was classified as CV3.2 by Guimon et al. (1995) and as a CV3.6 by Bonal et al. (2006). The value of the peak metamorphic temperature in Allende is still debated. It was estimated around 330 C by Rietmeijer and Mackinnon (1985) using ordering in graphitic material and by Bonal et al. (2007) using the structural grade of the organic matter in the matrix. Huss and Lewis (1994) estimate the peak temperature between 530 and 600 C by using presolar grain abundances. Busemann et al. (2007) and Cody et al. (2008) found the same range of values by using characterization of insoluble organic material. Weinbruch et al. (1994) also used the Fe-Mg interdiffusion into forsterite fragments to estimate the peak temperature in the Allende chondrite. The measured diffusion length was there about 2 lm. The authors used two different interdiffusion coefficients and found, assuming a timescale of yr, a peak temperature of 327 C with the Fe-Mg interdiffusion coefficient measured by Buening and Buseck (1973) and 477 C with the one measured by Nakamura and Schmalzried (1984). To use our data, we calculated the time temperature couples giving the best agreement between measured profiles and simulated ones for temperatures between 330 and 800 C. The results are shown on Fig. 15 on which are plotted the time temperature couples associated with the diffusion profiles measured in forsterite (dark gray area) and diopside (light gray area). In a case of a thermal metamorphism due to the Al 26 decay, the timescales are estimated between 1 and yr in type 4 ordinary chondrites (e.g., Trieloff et al. 2003; Kleine et al. 2008). They are of the same order of magnitude, or slightly lower, for type 3 ordinary chondrites (Miyamoto et al. 1981; Henke et al. 2011). Taking into account these estimated durations, between and yr, we found a peak metamorphic temperature comprised between 425 and 505 C if considering the profiles measured in forsterite curve and C if considering the diopside data. Figure 15 shows the T t intersection intervals for the two markers (forsterite and diopside). The intersection starts at a temperature of 535 C, which corresponds to a time of yr, and continuing toward higher temperature and shorter time scale. The timescales retrieved from this cross-correlation seem short for a parent body process. This is probably due to the value of the diffusion coefficients which are extrapolated to low temperature and thus induce uncertainty on the time temperature couples, in particular for diopside, which is much less constrained than for olivine. Finally, peak metamorphic temperatures lower than 425 C are Fig. 15. Extension of the time temperature couples calculated from the modeling of several composition profiles in Allende. Dark gray area is for forsterite profiles and light gray area is for diopside profiles. excluded as they would correspond to timescales above yr. CONCLUSION We have studied evidence of interaction between chondrule fragments (isolated forsterite and diopside) in the Allende matrix and the fayalitic olivines from the matrix to constrain the thermal history of the metamorphic episode of Allende. Analytical TEM observations show that Fa-rich olivines from matrix, rims, and veins have an identical microstructure suggesting a common origin and thermal history. The Fe-Mg profiles in forsterite grains have the same zoning lengths about 1.5 lm, whatever the forsterite fragments and the nature of the interface (contact with the external rim, veins cross-cutting the fragments, or grain boundaries). This strongly suggests that the composition profiles were formed during a single process by solid-state diffusion during the thermal metamorphism episode of the Allende parent body. The TEM analysis of chemical zoning at the nanoscale level revealed the presence of unequilibrated interfaces at the contact between isolated forsterite fragments and their Fa-rich rims whose origin remains unclear. Composition profile lengths measured at the edge of a diopside grain are restricted to nm only. Due to uncertainties concerning the interdiffusion coefficient value for diopside, the double marker olivine/ diopside should not be used to constrain both the time scale and the peak temperature as the cross-correlation gives timescales that seem too short (< yr) for a parent body process. This illustrates that the main

15 Fe-Mg interdiffusion profiles in Allende 1543 source of uncertainties is due to the diffusion coefficient values, especially in the case of Fe-Mg interdiffusion in diopside, which has been less studied than in forsterite. In addition, it is worth noting that the interdiffusion coefficients were extrapolated to low temperatures because experiment measurements were performed at temperature higher than those inferred for Allende. Relying on the results given by the forsterite solely, for which the interdiffusion coefficient values are better constrained, and considering a time scale for the peak metamorphic duration between 0.5 and yr, a range for the peak metamorphic temperature was estimated. This temperature is comprised between 425 and 505 C. Acknowledgements The authors thank J. F. Dhenin and A. Addad for their assistance at the Lille electron microscopy facility. They thank M. Roskosz and J. Ingrin for useful discussion on the composition profiles and diffusion data. They also thank D. Troadec for the preparation of high quality FIB sections. The TEM work has been done at the electron microscope facility at Lille University with the support of European FEDER and Region Nord-Pas-de-Calais. This work was partly supported by the French RENATECH network. S. B. Simon and S. Chakraborty are thanked for their detailed constructive reviews which led to major improvements to this manuscript. Editorial Handling Dr. A. J. Timothy Jull REFERENCES Bejina F., Sautter V., and Jaoul O Cooling rate of chondrules in ordinary chondrites revisited by a new geospeedometer based on the compensation rule. Physics of the Earth and Planetary Interiors 172:5 12. Bonal L., Quirico E., Bourot-Denise M., and Montagnac G Determination of the petrologic type of CV3 chondrites by Raman spectroscopy of included organic matter. 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