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Solid-state plastic deformation in the dynamic interior of a differentiated asteroid
 

Solid-state plastic deformation in the dynamic interior of a differentiated asteroid

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    Solid-state plastic deformation in the dynamic interior of a differentiated asteroid Solid-state plastic deformation in the dynamic interior of a differentiated asteroid Document Transcript

    • LETTERS PUBLISHED ONLINE: 20 JANUARY 2013 | DOI: 10.1038/NGEO1710 Solid-state plastic deformation in the dynamic interior of a differentiated asteroid B. J. Tkalcec1 *, G. J. Golabek2,3 and F. E. Brenker1 Diogenite meteorites are thought to represent mantle rocks that formed as cumulates in magma chambers on 4 Vesta or a similar differentiated asteroid1,2 . Northwest Africa 5480 is a harzburgitic diogenite3,4 , composed mainly of heterogeneously distributed olivine and orthopyroxene. Here we present a microstructural analysis of olivine grains from Northwest Africa 5480, using electron backscatter diffraction techniques to quantify any preferred orientation of crystallographic lattice. We find that the preferred orientation in the olivine-dominated zones can be explained neither by cumulate formation nor by impact reprocessing near the asteroid’s surface. Rather, they represent high-temperature solid-state plastic deformation by the pencil-glide5 slip system. The detected type of preferred orientation is well known from dry ultramafic rocks on Earth, where it is typically formed by mantle shear5–7 at temperatures between 1,273 and 1,523 K. Numerical modelling indicates that our observations can be explained by large-scale downwelling inside the asteroid’s mantle, within the first 50 million years after formation of calcium–aluminium-rich inclusions. The discovery of solid-state plastic deformation in an asteroidal ultramafic rock represents compelling evidence of dynamic planet-like processes in asteroids. We conclude that longlasting enhanced mass exchange occurred in the dynamic interior of a differentiated asteroid such as Vesta, and enabled accelerated chemical, structural and thermal equilibration. Diogenites belong to the Howardite–Eucrite–Diogenite (HED) group of achondrites thought to have originated from the differentiated asteroid 4 Vesta, or a Vesta-like body1 . This study concentrates on the achondrite Northwest Africa (NWA) 5480, which is dominated by olivine (57 vol%) and orthopyroxene (42 vol%; ref. 2) and is classified a harzburgitic diogenite3,4 . Diogenites have so far been thought to represent ultramafic cumulate rocks formed at deep crustal or upper mantle levels of the parent body1,2 . Most studies of HEDs have concentrated on the geochemistry and petrology of these achondrites1–3 . In this investigation we focus on the structural and textural properties, performing quantitative structural analysis on the olivine grains of NWA 5480 using electron backscatter diffraction (EBSD) to measure the crystallographic orientation of all crystal axes and determine any lattice-preferred orientation7 (LPO). Within the Earth’s upper mantle, depending on conditions of pressure, temperature, water content, strain geometry and strain-rate, LPOs of olivine are formed during plastic deformation, preferentially via dislocation glide or dislocation creep. Slip is accommodated by (010)[100] (refs 7–9) and (001)[100] (refs 7–9) systems, a combination of both (pencil glide {0kl}[100]; ref. 7) or by (010)[001] (refs 7,9). The respective main slip systems active can be identified by the resulting LPO of olivine. Alternatively, compaction Zone B 1 mm Zone A Figure 1 | Stitched back-scattered electron image of NWA 5480 showing two distinct zones. Zone A is dominated by coarse-grained olivine; Zone B is dominated by orthopyroxene schlieren. White line indicates the approximated northeast–southwest direction of the foliation (relative to the bottom rim of the polished sample), based on the schlieren structure and main vein orientation. processes such as cumulate formation form a distinct LPO dominated by a shape-preferred orientation (SPO) of olivine7,10 . Thus, quantitative analysis of the LPO of olivine in NWA 5480 and comparison with that of terrestrial samples or experimental data should expand our knowledge of the origin and formation of harzburgitic diogenites. The results offer new insights into the complex, polyphase textural and microstructural evolution undergone during the thermal history of accretion, heating, differentiation, compaction, deformation and cooling of the HED parent body. The studied harzburgitic diogenite3,4 enables a unique, relatively undisturbed view into primary processes as, in contrast to most other diogenites1 , NWA 5480 shows no sign of brecciation. The distribution of olivine and orthopyroxene is very heterogeneous, with some areas exhibiting up to 90% of either of the two minerals, whereby some dominantly orthopyroxene regions exhibit schlieren-like patterns2 . The sample can be subdivided into two petrographically distinct regions (Fig. 1) for targeted analysis: Zone A, the olivine-dominated region, and Zone B, the orthopyroxenedominated schlieren region. Minor chromite, troilite and occasional metal iron grains are present throughout both zones as well as a couple of larger (500–1,000 µm) patches of chromite within the schlieren region. Throughout the sample there is a general 1 Geoscience Institute, Goethe University, Altenhöferallee 1, 60438 Frankfurt am Main, Germany, 2 ENS Lyon, Laboratoire de Géologie, 46 Allée d’Italie, 69364 Lyon Cedex 07, France, 3 ETH Zürich, Institute of Geophysics, Sonneggstrasse 5, 8092 Zürich, Switzerland. *e-mail: tkalcec@em.uni-frankfurt.de. NATURE GEOSCIENCE | VOL 6 | FEBRUARY 2013 | www.nature.com/naturegeoscience © 2013 Macmillan Publishers Limited. All rights reserved. 93
    • NATURE GEOSCIENCE DOI: 10.1038/NGEO1710 LETTERS a [100] Y [010] [001] Zone A [010] [001] Zone B XO b [100] 5 10 Equal area, upper hemisphere, half-width 10°, cluster size 20°, multiples of uniform density (m.u.d.) Figure 2 | Stereographic projections of EBSD data for NWA 5480. Contour plots (Supplementary Fig. S1) show the measured crystallographic orientations of olivine crystals from Zone A (a) and Zone B (b) according to the [100], [010] and [001] axes. Solid black line denotes the presumed northeast–southwest foliation (Fig. 1). Zone A reveals a well-developed LPO with [100] point maxima within the foliation and broad girdles of [010] and [001] perpendicular to the [100] direction. Zone B shows a weaker LPO with [100] point maxima around the centre and [010] and [001] as circumferential girdles perpendicular to the [100] maxima. northeast–southwest foliation (Fig. 1, white line) relative to the lower base of the polished sample, present mainly as veins in Zone A and as schlieren-features in Zone B. The olivine grains within Zone A are coarser (400–1,200 µm) compared to olivine grains (50–300 µm) within Zone B. The Mg/Fe ratio of olivine is similar in both zones, with an approximated Mg# value of 70. The FeO/MnO ratio of olivine with 40.8–44.5 confirms previous findings2 . Although using polarized light microscopy the olivine crystals show no SPO, the EBSD results reveal a well-defined preferred orientation of the main crystallographic axes [100], [010] and [001] in both zones (Fig. 2a,b and Supplementary Information S1 and Fig. S1). Yet, the measured LPOs of the olivine crystals from the olivine-dominated Zone A (Fig. 2a) and those of the olivine crystals from the orthopyroxene-schlieren region of Zone B (Fig. 2b) differ significantly in intensity and orientation. This indicates two distinct texture-forming events. In Zone A the [100] axes form point maxima within the foliation. The other two main crystallographic axes of olivine, [010] and [001], show pronounced broad girdles perpendicular to the [100] point maxima (Fig. 2a). The LPOs of Zone B show a similar pattern. Here the [100] axes again form point maxima within the assumed foliation but rotated roughly 90◦ along the foliation. As in Zone A, the two other crystallographic axes, [010] and [001], plot perpendicular to the [100] point maxima in broad circumferential girdles (Fig. 2b). These pronounced LPOs observed in both zones reveal the unexpected occurrence of plastic deformation on the HED parent body. To better understand the nature of the texture-forming processes the measured axes orientations are compared with compilations of observed LPOs from common terrestrial mantle rocks and experimental data. For ease of comparison, a schematic summary of the LPOs of NWA 5480 Zone A, using the assumed northeast– southwest foliation as the necessary reference frame, was compiled and rotated approximately 45◦ clockwise. In almost all cases of published LPOs, the [010] axes of olivine in olivine-rich natural rocks plot perpendicular to a given lineation6,7,9–11 . We use this general observation to set the orientation of the lineation (L) within the sample, plotting it horizontally within the foliation (Fig. 3). We have summarized the data schematically in Fig. 3a–g (Supplementary Information S1.1 and Table S1) depicting the axes-plots [100], [010] and [001] as spotted, striped and solid grey, respectively, and the foliation as a solid black line. Figure 3a summarizes the LPO from NWA 5480 Zone A. Figure 3b summarizes the olivine LPO from a wehrlite intrusion within the Oman ophiolite12 , showing a well-developed SPO fabric typical of compaction processes7,12 . The general observation for terrestrial cumulates and compacted olivine typically reveals strong point maxima of [010] normal to the foliation12 with the [100] and [001] axes as girdles along the foliation7,12 . Being the slowest growth direction for olivine, [010] represents the shortest axis. If close to euhedral in shape, any olivine crystals sinking to the bottom of a magma chamber will settle in the most stable position with the shortest axis [010] parallel to the direction of cumulation and perpendicular to any foliation. The other two axes, [100] and [001], will be randomly distributed within the foliation, perpendicular to the direction of cumulation. The obvious dissimilarity to the LPO of NWA 5480 Zone A (Fig. 3a) reveals that the latter was not caused by cumulation. According to studies of more than 100 naturally deformed peridotite samples7,10 over 95% show LPO patterns related to (010)[100] (Fig. 3c), the most active glide system during solid-state deformation in the Earth’s mantle7,10,13 . Figure 3d summarizes a common glide system (100)[001] (ref. 13) at low-temperature solid-state plastic deformation7 . Figure 3e5,7,10 summarizes the LPO generated by 94 NATURE GEOSCIENCE | VOL 6 | FEBRUARY 2013 | www.nature.com/naturegeoscience © 2013 Macmillan Publishers Limited. All rights reserved.
    • NATURE GEOSCIENCE DOI: 10.1038/NGEO1710 a LETTERS b c NWA 5480 zone A d LPO examples of terrestrial and experimental olivine L L e f g [100] [010] [001] Foliation Figure 3 | Sketches summarizing LPO patterns found in olivine crystals. Comparison with LPOs of typical terrestrial mantle rocks, schematically summarized and adapted from published literature as referenced (Supplementary Table S1). a, NWA 5480 Zone A (Fig. 2). b, Cumulate olivine from the Oman ophiolite12 showing the typical SPO pattern. c, One of the most common glide systems of olivine, (010)[100] (refs 7,10). d, A further common slip system in terrestrial olivines, the (100)[001] (ref. 13). e, The pencil glide system {0kl}[100] (refs 7,10), whereby multiple planes are activated to slip along the [100] direction. f, Olivine deformed under wet conditions14 . g, Olivine deformed with 6% melt17 . a Temperature (K) 500 1,000 1,500 Temperature (K) 2,000 500 240 1,000 1,500 Temperature (K) 2,000 500 240 1,500 2,000 240 260 Time = 8.65 Myr 260 280 T = 1,273 ¬ 1,523 K 280 280 300 300 320 260 Time = 30.12 Myr Z (km) Z (km) 300 Z (km) 1,000 320 Time = 50.12 Myr 320 340 340 340 360 360 360 380 380 380 400 240 260 280 300 320 340 360 380 400 400 240 260 280 300 320 340 360 380 400 400 240 260 280 300 320 340 360 380 400 X (km) b 0 X (km) Silicate melt fraction (%) 10 20 30 40 0 240 X (km) Silicate melt fraction (%) 10 20 30 40 0 240 240 Time = 8.65 Myr 260 280 d = 50 km ξ = 0.1 ¬ 4% 280 280 300 300 320 340 260 Time = 30.12 Myr Z (km) 300 Z (km) 260 Z (km) Silicate melt fraction (%) 10 20 30 40 320 340 Time = 50.12 Myr 320 340 360 360 360 380 380 380 400 240 260 280 300 320 340 360 380 400 400 240 260 280 300 320 340 360 380 400 400 240 260 280 300 320 340 360 380 400 X (km) X (km) X (km) Figure 4 | Comparison of experimental constraints and numerical results. Magnification of the temporal evolution of temperature (a) and silicate melt fraction (b) from a global numerical model of a Vesta-sized body with r = 265 km and tstart = 0.5 Myr. The white line in a and b depicts the surface of the body. Black lines in a show the temperature range where pencil glide is the dominant deformation mechanism5–7 . Yellow lines in b mark 0.1% and 4% of silicate melt, and the red line is the maximum excavation depth (d = 50 km) of vestan meteorites22 . NATURE GEOSCIENCE | VOL 6 | FEBRUARY 2013 | www.nature.com/naturegeoscience © 2013 Macmillan Publishers Limited. All rights reserved. 95
    • NATURE GEOSCIENCE DOI: 10.1038/NGEO1710 LETTERS dunites and peridotites plastically deformed in the solid state by pencil-glide5,7 , whereby multiple {0kl}[100] glide systems are activated. Whereas the LPOs of Fig. 3b–d bear no resemblance to the LPO of NWA 5480 (Fig. 3a), the LPO of Fig. 3e matches that of NWA 5480 Zone A, indicating the latter was deformed by the pencil-glide system. Figure 3f depicts the influence of water on olivine fabric14 , which can be neglected here as the resulting LPO bears no similarity to the axes orientations measured in NWA 5480 (Fig. 3a). Furthermore, low volatile abundances found in diogenites15,16 imply anhydrous mantle conditions in the HED parent body15,16 . Similarly, the influence of partial melt can be neglected here, as experimental studies17 yield olivine LPOs (Fig. 3g) distinct from the fabric from NWA 5480 Zone A. Thus, in comparison with the most common LPOs formed in natural olivine-dominated terrestrial rocks the LPOs measured in Zones A and B of NWA 5480 imply that the olivine crystals of NWA 5480 were plastically deformed at least twice under solid-state conditions in a temperature–pressure-strain rate regime where {0kl}[100] pencil-glide is the most active glide system. This may have occurred at depth within the mantle of the meteorite parent body. Experimental work suggests that deformation by pencil-glide is active at moderate strain-rates5 and dry14 , virtually melt-free17 conditions at temperatures between 1,273 and 1,523 K (refs 5–7), delivering a temperature constraint for the plastic deformation in NWA 5480. Therefore we draw our attention to the scenario of a solid-state deformation mechanism within the early stages after asteroid formation. To identify a feasible mechanism for this dynamic process we performed 2D numerical models18 (Supplementary Methods S3) of Vesta and its early evolution. The modelled conditions at 8.6, 30 and 50 Myr (Fig. 4) reveal that after core formation a thin thermal lid forms on top of the partially molten mantle. As the partially molten silicate layer beneath exhibits a low viscosity, this favours large growth rates of Rayleigh–Taylor instabilities19,20 . Assuming dry conditions, the resulting downwelling material is within the temperature range relevant for pencil-glide (Fig. 4a and Supplementary Movie). These downwellings exhibit no or only very small silicate melt fractions (Fig. 4b), in agreement with observations for the solid-state deformation of NWA 5480 and experimental studies17 revealing that the absence of melt bands in NWA 5480 constrains the silicate melt fraction to <4% (Fig. 4b, yellow contours). As the interior cools, the thickness of the rigid part of the thermal lid grows over time20 . Thus, part of the lid material experiences solid-state deformation without finally sinking towards the core–mantle boundary, thereby fossilizing the deformation pattern in these regions. In our model the downwellings occur within the first 50 Myr within a depth range (Fig. 4b, red line) from which later impact excavation via the Rheasilvia crater at the south pole of Vesta21 , the most likely source of HED meteorites1 , is feasible22 . Whereas the LPO of NWA 5480 documents solid-state plastic deformation in virtually melt-free conditions, deeper layers must have been partially molten to allow viscosities low enough to induce buoyancy-driven downwellings to develop within geologically relevant timescales. This has implications for the timing of solidification of the HED parent body, which is still a matter of keen debate. In line with our model, most geochemical data23–25 and numerical 1D models26,27 indicate that a considerable portion of Vesta’s interior must have been partially molten during the first 100 Myr after accretion. Recent isotopic data indicate solidification occurred after 3–4 Myr (refs 16,28). Other isotopic studies of zircons found in eucrites conclude magmatism occurred 7–24 Myr (ref. 29) after the formation of calcium–aluminium-rich inclusions (CAI). Although consolidation of these various data is necessary, our model remains valid for virtually all temporal scenarios (Supplementary Information S2 and Fig. S2), with downwellings beginning as early as 3–4 Myr after CAI formation (Supplementary Movie). 1. McSween, H. Y., Mittlefehldt, D. W., Beck, A. W., Mayne, R. G. & McCoy, T. J. HED Meteorites and their relationship to the Geology of Vesta and the Dawn Mission. Space Sci. Rev. 163, 141–174 (2011). 2. Irving, A. J., Bunch, T. E., Kuehner, S. M., Wittke, J. H. & Rumble, D. Peridotites related to 4 Vesta: Deep crustal igneous cumulates and mantle samples. Lunar Planet. Sci. 40, 2466 (2009). 3. Beck, A. & McSween, H. Y. Diogenites as polymict breccias composed of orthopyroxenite and harzburgite. Meteorit. Planet. Sci. 45, 850–872 (2010). 4. Wittke, J. H., Irving, A. J., Bunch, T. E. & Kuehner, S. M. A nomenclature system for diogenites consistent with the IUGS system for naming terrestrial ultramafic rocks. Meteoritics Planet. Sci. 46 (Meteoritical Society LXXIV), Abstr. 5223 (2011). 5. Carter, N. L. & Avé Lallement, H. G. High temperature flow of dunite and peridotite. Geol. Soc. Am. Bull. 81, 2181–2202 (1970). 6. Guegen, Y. & Nicolas, A. Deformation of mantle rocks. Annu. Rev. Earth Planet. Sci. 8, 119–144 (1980). 7. Tommasi, A., Mainprice, D., Canova, G. & Chasatel, Y. Viscoplastic self-consistent and equilibrium-based modeling of olivine lattice preferred orientations: Implications for the upper mantle seismic anisotropy. J. Geophys. Res. 105, 7893–7908 (2000). 8. Prior, D. J. et al. The application of electron backscatter diffraction and orientation contrast imaging in the SEM to textural problems in rocks. Am. Mineral. 84, 1741–1759 (1999). 9. Warren, J. M., Hirth, G. & Kelemen, P. B. Evolution of olivine lattice preferred orientation during simple shear in the mantle. Earth Planet. Sci. Lett. 272, 501–512 (2008). 10. Ismaïl, W. B. & Mainprice, D. An olivine fabric database: An overview of upper mantle fabrics and seismic anisotropy. Tectonophysics 296, 145–157 (1998). 11. Bystricky, M., Kunze, K., Burlini, L. & Burg, J-P. High shear strain of olivine aggregates: Rheological and seismic consequences. Science 290, 1564–1566 (2000). 96 NATURE GEOSCIENCE | VOL 6 | FEBRUARY 2013 | www.nature.com/naturegeoscience To conclude, the LPOs measured from both zones of NWA 5480 are most likely formed by deformation via the pencil-glide system {0kl}[100], indicating that NWA 5480 underwent at least two distinct solid-state plastic deformation events at temperatures between 1,273 and 1,523 K. Assuming a dry environment with low melt fractions, this result contradicts previous generalized ideas30 about texture-forming processes for diogenites, ruling out deformation as a cumulate rock in a magma chamber. Our numerical models reveal early downwellings of lid material on the HED parent body as a feasible explanation for the documented solid-state plastic deformation of NWA 5480, suggesting a dynamic asteroid mantle and a geologically active phase in the early evolution of planet-buildingblocks such as Vesta. This unexpected dynamic process in the solidified lid over a partially molten asteroid mantle will enable prolonged fast mass exchange, therefore providing an effective mechanism for late-stage chemical redistribution and homogenization. Methods A thick section (3 × 23 × 35 mm) of NWA 5480 was embedded in epoxy resin and polished with Syton polish. It was thinly coated with carbon and surrounded on all sides by a thin copper band to minimize ionic charging on the sample surface. Analysis was performed in the Nanoscience Laboratory of the Geoscience Institute at Goethe University Frankfurt using a Jeol Scanning Electron Microscope JSM 6490 equipped with an EBSD detector. The software used for imaging and mineral composition analysis included an Inca Energy Dispersive X-ray Spectroscopy system and HKL Channel 5 of Oxford Instruments and HKL Technology, respectively. The first 84 back-scattered electron-images were collected at low magnification and stitched together as an overview map. EBSD was performed with an acceleration voltage of 15 kV, a beam current of 35–40 µA, a working distance of 20 mm, a detector insertion of 176 mm and a Si-wafer as calibrant. Within Zone A, the olivine-dominated zone, a total of 1361 crystallographic orientation measurements of olivine were recorded manually over a total of 58 sample locations, each about 800 × 500 µm2 in size. Indexing was monitored manually and only those EBSD measurements with a mean angular deviation (MAD) of <1◦ were accepted and recorded. Within Zone B, the schlieren zone, a total of 148 crystallographic orientation measurements of olivine were recorded over a total of 20 sample locations (Supplementary Analytical Methods S1.1). Received 21 June 2012; accepted 17 December 2012; published online 20 January 2013 References © 2013 Macmillan Publishers Limited. All rights reserved.
    • NATURE GEOSCIENCE DOI: 10.1038/NGEO1710 12. Boudier, F. Olivine xenocrysts in picritic magmas. Contrib. Mineral. Petrol. 109, 114–123 (1991). 13. Frese, K., Trommsdorff, V. & Kunze, K. Olivine [100] normal to foliation: Lattice preferred orientation in prograde garnet peridotite formed at high H2 O activity, Cima di Cagnone (Central Alps). Contrib. Mineral. Petrol. 145, 75–86 (2003). 14. Jung, H., Katayama, I., Jiang, Z., Hiraga, T. & Karato, S. Effect of water and stress on the lattice-preferred orientation of olivine. Tectonophysics 421, 1–22 (2006). 15. Warren, P. H., Kallemeyn, G. W., Huber, H., Ulff-Møller, F. & Choe, W. Siderophile and other geochemical constraints on mixing relationships among HED-meteoritic breccias. Geochim. Cosmochim. Acta 73, 5918–5943 (2009). 16. Day, J. M. D., Walker, R. J., Qin, L. & Rumble, D. Late accretion as a natural consequence of planetary growth. Nature Geosci. 5, 614–617 (2012). 17. Holtzman, B. K. et al. Melt segregation and strain partitioning: Implications for seismic anisotropy and mantle flow. Science 301, 1227–1230 (2003). 18. Gerya, T. V. & Yuen, D. A. Robust characteristics method for modelling multiphase visco-elasto-plastic thermo-mechanical problems. Phys. Earth Planet. Int. 163, 83–105 (2007). 19. Ramberg, H. Fluid dynamics of layered systems in the field of gravity, a theoretical basis for certain global structures and isostatic adjustment. Phys. Earth Planet. Int. 1, 63–87 (1968). 20. Turcotte, D. L. & Schubert, G. Geodynamics 2nd edn (Cambridge Univ. Press, 2002). 21. Thomas, P. C. et al. Impact excavation on asteroid 4 Vesta: Hubble space telescope results. Science 277, 1492–1495 (1997). 22. Jutzi, M. & Asphaug, E. Mega-ejecta on asteroid Vesta. Geophys. Res. Lett. 38, L01102 (2011). 23. Righter, K. & Drake, M. J. Core formation in Earth’s Moon, Mars and Vesta. Icarus 124, 513–529 (1996). 24. Righter, K. & Drake, M. J. A magma ocean on Vesta: Core formation and petrogenesis of eucrites and diogenites. Meteorit. Planet. Sci. 32, 929–944 (1997). LETTERS 25. Greenwood, R. C., Franchi, I. A., Jambon, A. & Buchanan, P. C. Widespread magma oceans on asteroidal bodies in the early Solar System. Nature 435, 916–918 (2005). 26. Ghosh, A. & McSween, H. Y. A thermal model for the differentiation of asteroid 4 Vesta, based on radiogenic heating. Icarus 134, 187–206 (1998). 27. Gupta, G. & Sahijpal, S. Differentiation of Vesta and the parent bodies of other achondrites. J. Geophys. Res. 115, E08001 (2010). 28. Schiller, M. et al. Rapid timescales for magma ocean crystallization on the Howardite-Eucrite-diogenite parent body. Astrophys. J. Lett. 740, L22 (2011). 29. Misawa, K., Yamaguchi, A. & Kaiden, H. U–Pb and 207 Pb–206 Pb ages of zircons from basaltic eucrites: Implications for early basaltic volcanism on the eucrite parent body. Geochim. Cosmochim. Acta 69, 5847–5861 (2005). 30. Fowler, G. W., Shearer, C.K., Papike, J. J. & Layne, G. D. Diogenites as asteroidal cumulates: Insights from orthopyroxene trace element chemistry. Geochim. Cosmochim. Acta 59, 3071–3084 (1995). Acknowledgements We thank T. V. Gerya for providing the code 12MART. Funding to G.J.G. was provided by SNF grant PBEZP2-134461. Author contributions B.J.T. and F.E.B. conceived this project. B.J.T. carried out the EBSD measurements on the sample. B.J.T. and F.E.B. analysed and discussed the results of the EBSD measurements. G.J.G. designed and implemented the numerical model. B.J.T., G.J.G. and F.E.B. analysed and discussed the results. B.J.T. prepared the manuscript, which was then jointly edited by B.J.T., G.J.G. and F.E.B. Additional information Supplementary information is available in the online version of the paper. Reprints and permissions information is available online at www.nature.com/reprints. Correspondence and requests for materials should be addressed to B.J.T. Competing financial interests The authors declare no competing financial interests. NATURE GEOSCIENCE | VOL 6 | FEBRUARY 2013 | www.nature.com/naturegeoscience © 2013 Macmillan Publishers Limited. All rights reserved. 97