Skip to main content
Log in

Mantle Pb paradoxes: the sulfide solution

  • Original Paper
  • Published:
Contributions to Mineralogy and Petrology Aims and scope Submit manuscript

Abstract

There is growing evidence that the budget of Pb in mantle peridotites is largely contained in sulfide, and that Pb partitions strongly into sulfide relative to silicate melt. In addition, there is evidence to suggest that diffusion rates of Pb in sulfide (solid or melt) are very fast. Given the possibility that sulfide melt “wets” sub-solidus mantle silicates, and has very low viscosity, the implications for Pb behavior during mantle melting are profound. There is only sparse experimental data relating to Pb partitioning between sulfide and silicate, and no data on Pb diffusion rates in sulfides. A full understanding of Pb behavior in sulfide may hold the key to several long-standing and important Pb paradoxes and enigmas. The classical Pb isotope paradox arises from the fact that all known mantle reservoirs lie to the right of the Geochron, with no consensus as to the identity of the “balancing” reservoir. We propose that long-term segregation of sulfide (containing Pb) to the core may resolve this paradox. Another Pb paradox arises from the fact that the Ce/Pb ratio of both OIB and MORB is greater than bulk earth, and constant at a value of 25. The constancy of this “canonical ratio” implies similar partition coefficients for Ce and Pb during magmatic processes (Hofmann et al. in Earth Planet Sci Lett 79:33–45, 1986), whereas most experimental studies show that Pb is more incompatible in silicates than Ce. Retention of Pb in residual mantle sulfide during melting has the potential to bring the bulk partitioning of Ce into equality with Pb if the sulfide melt/silicate melt partition coefficient for Pb has a value of ∼ 14. Modeling shows that the Ce/Pb (or Nd/Pb) of such melts will still accurately reflect that of the source, thus enforcing the paradox that OIB and MORB mantles have markedly higher Ce/Pb (and Nd/Pb) than the bulk silicate earth. This implies large deficiencies of Pb in the mantle sources for these basalts. Sulfide may play other important roles during magmagenesis: (1) advective/diffusive sulfide networks may form potent metasomatic agents (in both introducing and obliterating Pb isotopic heterogeneities in the mantle); (2) silicate melt networks may easily exchange Pb with ambient mantle sulfides (by diffusion or assimilation), thus “sampling” Pb in isotopically heterogeneous mantle domains differently from the silicate-controlled isotope tracer systems (Sr, Nd, Hf), with an apparent “de-coupling” of these systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Allègre CJ (1982) Chemical geodynamics. Tectonophysics 81:109–132

    Article  Google Scholar 

  • Allègre CJ, Brévart O, Dupré B, Minster J-F (1980) Isotopic and chemical effects produced in a continuously differentiating convecting Earth mantle. Philos Trans R Soc Lond A 297:447–477

    Article  Google Scholar 

  • Allègre CJ, Dupré B, Brévart O (1982) Chemical aspects of the formation of the core. Philos Trans R Soc Lond A 306:49–59

    Article  Google Scholar 

  • Asimow PD, Hirschmann MM, Ghiorso MS, O’Hara JJ, Stolper EM (1995) The effect of pressure-induced solid-solid phase transitions on decompression melting of the mantle. Geochim Cosmochim Acta 59:4489–4506

    Article  Google Scholar 

  • Asimow PD, Dixon JE, Langmuir CH (2004) A hydrous melting and fractionation model for mid-ocean ridge basalts: application to the Mid-Atlantic Ridge near the Azores. Geochem Geophys Geosyst 5:Q01E16. DOI 10.1029/2003GC000568

  • Ballhaus C, Ellis DJ (1996) Mobility of core melts during Earth’s accretion. Earth Planet Sci Lett 143:137–145

    Article  Google Scholar 

  • von Bargen N, Waff HS (1986) Permeabilities, interfacial areas and curvatures in partially molten systems: results of numerical computations of equilibrium microstructures. J Geophys Res 91:9261–9276

    Article  Google Scholar 

  • Barnes SJ, Mavovicky E, Makovicky M, Rose-Hansen J, Karup-Moller S (1997) Partition coefficients for Ni, Cu, Pd, Pt, Rh, and Ir between monosulfide solid solution and sulfide liquid and the formation of compositionally zoned Ni–Cu sulfide bodies by fractional crystallization of sulfide liquid. Can J Earth Sci 34:366–374

    Article  Google Scholar 

  • Barnes SJ, Peregoedova A, Baker D, Maier WD (2004) Incongruent melting of monosulfide solid solution and its implications for fractionation of the platinum-group elements during partial melting of the mantle (abstract). In: EOS, vol 85. AGU, p 508

  • Bézos A, Lorand J-P, Humler E, Gros M (2005) Platinum-group element systematics in Mid-Oceanic Ridge basaltic glasses from the Pacific, Atlantic, and Indian Oceans. Geochim Cosmochim Acta 69:2613–2627

    Article  Google Scholar 

  • Bockrath C, Ballhaus C, Holzheid A (2004) Fractionation of the platinum-group elements during mantle melting. Science 305:1951–1953

    Article  Google Scholar 

  • de Bremond d’Ars J, Arndt NT, Hallot E (2001) Analog experimental insights into the formation of magmatic sulfide deposits. Earth Planet Sci Lett 186:371–381

    Article  Google Scholar 

  • Brenan JM, McDonough WF (2005) Fractionation of highly siderophile elements (HSEs) by sulfide–silicate partitioning: a new Spin. EOS 86:52 (poster version and personal communication)

    Google Scholar 

  • Brenan JR, Cherniak DJ, Rose LA (2000) Diffusion of osmium in pyrrhotite and pyrite: implications for closure of the Re–Os isotopic system. Earth Planet Sci Lett 180:399–413

    Article  Google Scholar 

  • Carignan J, Ludden J, Francis D (1996) On recent enrichment of subcontinental lithosphere: a detailed U–Pb study of spinel lherzolite xenoliths, Yukon, Canada. Geochim Cosmochim Acta 60:4241–4252

    Article  Google Scholar 

  • Condit RH, Hobbins RR, Birchenall DE (1974) Self-diffusion of iron and sulfur in ferrous sulfide, in oxidation and metals, vol 8. pp 408–455

  • Dobson DP (2000) Fe and Co tracer diffusion in liquid Fe–FeS at 2 and 5 GPa. Phys Earth Planet Inter 120:137–144

    Article  Google Scholar 

  • Dobson DP, Crichton WA, Vocadlo L, Jones AP, Wang Y, Uchida T, Rivers M, Sutton ST, Brodholt JP (2000) In situ measurement of viscosity of liquids in the Fe–FeS system at high pressures and temperatures. Am Mineral 85:1838–1842

    Google Scholar 

  • Ebel DS, Naldrett AJ (1996) Fractional crystallization of sulfide ore liquids at high temperature. Econ Geol 91:607–621

    Article  Google Scholar 

  • Eggler DH, Lorand JP (1993) Mantle sulfide geobarometry. Geochim Cosmochim Acta 57:2213–2222

    Article  Google Scholar 

  • Eisele J, Sharma M, Galer SJG, Blichert-Toft J, Devey CW, Hofmann AW (2002) The role of sediment recycling in EM-1 inferred from Os, Pb, Hf, Nd, Sr isotope and trace element systematics of the Pitcairn hotspot. Earth Planet Sci Lett 196:197–212

    Article  Google Scholar 

  • Fleet ME, Tronnes RG, Stone WE (1991) Partitioning of platinum group elements in the Fe–O–S system to 11 GPa and their fractionation in the mantle and meteorites. J Geophys Res 96:21949–21958

    Article  Google Scholar 

  • Fleet ME, Crocket JH, Stone WE (1996) Partitioning of platinum-group elements (Os, Ir, Ru, Pt, Pd) and fold between sulfide liquid and basalt melt. Geochim Cosmochim Acta 60:2397–2412

    Article  Google Scholar 

  • Gaetani GA, Grove TL (1997) Partitioning of moderately siderophile elements among olivine, silicate melt, and sulfide melt: constraints on core formation in the Earth and Mars. Geochim Cosmochim Acta 61:1829–1846

    Article  Google Scholar 

  • Gaetani GA, Grove TL (1999) Wetting of mantle olivine by sulfide melt: implications for Re/Os ratios in mantle peridotite and late stage core formation. Earth Planet Sci Lett 169:147–163

    Article  Google Scholar 

  • Gao S, Luo T-C, Zhang B-R, Zhang H-F, Han Y-W, Zhao Z-D, Hu Y-K (1998) Chemical composition of the continental crust as revealed by studies in East China. Geochim Cosmochim Acta 62:1959–1975

    Article  Google Scholar 

  • Garuti G, Gorgoni C, Sighinolfi GP (1984) Sulfide mineralogy and chalcophile and siderophile element abundances in the Ivrea-Verbano mantle peridotites (Western Italian Alps). Earth Planet Sci Lett 70:69–87

    Article  Google Scholar 

  • Godard M, Kelemen P, Hart S, Jackson M, Hanghoj K (2005) High Pb/Ce reservoir in depleted altered mantle peridotites. Eos Trans 86:F1937

    Google Scholar 

  • Hart SR, Dunn T (1993) Experimental cpx/melt partitioning for 24 trace elements. Contrib Mineral Petrol 113:1–8

    Article  Google Scholar 

  • Hart SR, Ravizza G (1996) Osmium partitioning between phases in lherzolite and basalt. In: Basu A, Hart SR (eds) Earth processes: reading the isotopic code, vol, pp 123–134

  • Hart SR, Zindler A (1986) In search of a bulk-earth composition. Chem Geol 57:247–267

    Article  Google Scholar 

  • Hauri EH, Hart SR (1997) Rhenium abundances and systematics in oceanic basalts. Chem Geol 139:185–205

    Article  Google Scholar 

  • Hauri EH, Wagner TP, Grove TL (1994) Experimental and natural partitioning of Th, U, Pb and other trace element between garnet, clinopyroxene and basaltic melts. Chem Geol 117:149–166

    Article  Google Scholar 

  • Hirschmann MM (2000) Mantle solidus: experimental constraints and the effect of peridotite composition. Geochem Geophys Geosyst 1:2000GC000070

    Google Scholar 

  • Hofmann AW (1988) Chemical differentiation of the Earth: the relationship between mantle, continental crust, and oceanic crust. Earth Planet Sci Lett 90:297–314

    Article  Google Scholar 

  • Hofmann A (2003) Sampling mantle heterogeneity through Oceanic Basalts: isotopes and trace elements. In: Holland HD, Turekian KK (eds) Treatise on geochemistry, vol 2.03. pp 61–101

  • Hofmann AW, Jochum KP, Seufert HM, White WM (1986) Nb and Pb in oceanic basalts: new constraints on mantle evolution. Earth Planet Sci Lett 79:33–45

    Article  Google Scholar 

  • Ionov AD, Hoefs J, Wedepohl KH, Weichert U (1992) Content and isotopic composition of sulphur in ultramafic zenoliths from central Asia. Earth Planet Sci Lett 111:269–286

    Article  Google Scholar 

  • Ionov DA, Chazot G, Chauvel C, Merlet C, Bodinier J-L (2006) Trace element distribution in peridotite xenoliths from Tok, SE Siberian craton: a record of pervasive, multi-stage metasomatism in shallow refractory mantle. Geochim Cosmochim Acta 70:1231–1260

    Article  Google Scholar 

  • Jacobsen SB (2003) How old is planet Earth? Science 300:1513–1514

    Article  Google Scholar 

  • Jagoutz E, Palme H, Badenhausen H, Blum K, Cendales M, Dreibus G, Spettel G, Lorenz V, Wanke H (1979) The abundances of major, minor and trace elements in the Earth’s mantle as derived from primitive ultramafic nodules. In: Proceedings of 10th Lunar Planet Sci Conf, vol, pp 2031–2050

  • Jones JH, Hart SR, Benjamin TM (1993) Experimental partitioning studies near the Fe–FeS eutectic, with an emphasis on elements important to iron meteorite chronologies—Pb, Ag, Pd and Tl. Geochim Cosmochim Acta 57:453–460

    Article  Google Scholar 

  • Jugo PJ, Luth RW, Richards JP (2005) Experimental data on the speciation of sulfur as a function of oxygen fugacity in basaltic melts. Geochim Cosmochim Acta 69:497–503

    Article  Google Scholar 

  • Kelemen PB, Yogodzinski GM, Scholl DW (2004) Along-strike variation in lavas of the Aleutian island arc: genesis of high Mg# andesite and implications for continental crust. In: Eiler J (ed) Inside the subduction factory, vol 138. American Geophysical Union, Washington

  • Keshav S, Corgne A, Gudfinnsson GH, Bizmis M, McDonough WF, Fei Y (2005) Kimberlite petrogenesis: insights from clinopyroxene-melt partitioning experiments at 6 GPa in the CaO–MgO–Al2–SiO2–CO2 system. Earth Planet Sci Lett 168:287–299

    Google Scholar 

  • Kleine T, Münker C, Mezger K, Palme H (2002) Rapid accretion and early core formation on asteroids and the terrestrial planets from Hf–W chronometry. Nature 418:952–955

    Article  Google Scholar 

  • Kleine T, Mezoer K, Münker C, Palme H, Bichoff A (2004) 182Hf–182W isotope systematics of chondrites, eucrites, and martian meteorites: chronology of core formation and early mantle differentiation in Vesta and Mars. Geochim Cosmochim Acta (68):2935–2946

  • Klemme S, Blundy JD, Wood BJ (2002) Experimental constraints on major and trace element partitioning during partial melting of eclogite. Geochim Cosmochim Acta 66:3109–3123

    Article  Google Scholar 

  • Li C, Barnes S-J, Makovicky E, Rose-Hansen J, Makovicky M (1996) Partitioning of nickel, copper, iridium, rhenium, platinum, and palladium between monosulfide solid solution and sulfide liquid: effects of composition and temperature. Geochim Cosmochim Acta 60:1231–1238

    Article  Google Scholar 

  • Lorand J-P (1991) Sulphide petrology and sulphur geochemistry of orogenic lherzolites: a comparative study of the Pyrenean bodies (France) and Lanzo Massif (Italy). J Petrol Spec Lherzolites Issue:77–95

  • Lorand J-P, Alard O, Luguet A, Keays RR (2003) Sulfur and selenium systematics of the subcontinental lithospheric mantle: inferences from the Massif Central xenolith suite (France). Geochim Cosmochim Acta 67:4137–4151

    Article  Google Scholar 

  • Lundstrom CC, Shaw HF, Ryerson FJ, Williams Q, Gill J (1998) Crystal chemical control of clinopyroxene-melt partitioning in the Di–Ab–An system: implications for elemental fractionations in the depleted mantle. Geochim Cosmochim Acta 62:2849–2862

    Article  Google Scholar 

  • Mavrogenes JA, O’Neill HSC (1999) The relative effects of pressure, temperature and oxygen fugacity on the solubility of sulfide in mafic magmas. Geochim Cosmochim Acta 63:1173–1180

    Article  Google Scholar 

  • McCulloch MT, Bennett VC (1994) Progressive growth of the Earth’s continental crust and depleted mantle. Geochim Cosmochim Acta 58:4717–4738

    Article  Google Scholar 

  • McDonough WF, Sun S-S (1995) The composition of the Earth. Chem Geol 120:223–253

    Article  Google Scholar 

  • Meijer A, Kwon T-T, Tilton GR (1990) U–Th–Pb partitioning behavior during partial melting in the upper mantle implications for the origin of high Mu components and the “Pb Paradox.” J Geophys Res 95:433–448

    Article  Google Scholar 

  • Minarik WG, Ryerson FJ, Watson EB (1996) Textural entrapment of core-forming melts. Science 272:530–533

    Article  Google Scholar 

  • Moretti R, Ottonello G (2005) Solubility and speciation of sulfur in silicate melts: the conjugated Toop-Samis-Flood-Grjotheim (CTSFG) model. Geochim Cosmochim Acta 69:801–823

    Article  Google Scholar 

  • Mungall JE, Su S (2005) Interfacial tension between magmatic sulfide and silicate liquids: constraints on kinetics of sulfide liquation and sulfide migration through silicate rocks. Earth Planet Sci Lett 234:135–149

    Article  Google Scholar 

  • O’Neill H, Mavrogenes J (2002) The sulfide capacity and the sulfur content at sulfide saturation of silicate melts at 1400°C and 1 bar. J Petrol 43:1049–1087

    Article  Google Scholar 

  • O’Nions RK, Evenson NM, Hamilton PJ (1979) Geochemical modeling of mantle differentiation and crustal growth. J Geophys Res 84:6091–6101

    Article  Google Scholar 

  • Oversby VM, Ringwood AE (1971) Time of formation of earth’s core. Nature 237:463–465

    Article  Google Scholar 

  • Peach CL, Mathez EA (1993) Sulfide melt-silicate melt distribution coefficients for nickel and iron and implications for the distribution of other chalcophile elements. Geochim Cosmochim Acta 57:3013–3021

    Article  Google Scholar 

  • Peach CL, Mathez EA, Keays RR, Reeves SJ (1994) Experimentally determined sulfide melt-silicate melt partition coefficients for iridium and palladium. Chem Geol 117:361–377

    Article  Google Scholar 

  • Peucker-Ehrenbrink B, Hofmann AW, Hart SR (1994) Hydrothermal lead transfer from mantle to continental crust: the role of metalliferous sediments. Earth Planet Sci Lett 125:129–142

    Article  Google Scholar 

  • Pickering-Witter J, Johnston AD (2000) The effects of variable bulk composition on the melting systematics of fertile peridotitic assemblages. Contrib Mineral Petrol 140:190–211

    Article  Google Scholar 

  • Rose LA, Brenan JM (2001) Wetting properties of Fe–Ni–Co–Cu–O–S melts against olivine: implications for sulfide mobility. Econ Geol 96:145–157

    Article  Google Scholar 

  • Rudnick RL, Fountain DM (1995) Nature and composition of the continental crust: a lower crustal perspective. Rev Geophys 33:267–309

    Article  Google Scholar 

  • Ryzhenko B, Kennedy GC (1973) The effect of pressure on the eutectic in the system Fe–FeS. Am J Sci 273:803–810

    Article  Google Scholar 

  • Salters VJM, Longhi JE, Bizimis M (2002) Near mantle solidus trace element partitioning at pressures up to 3.4 GPa. Geochem Geophys Geosyst 3(7). DOI 10.1029/2001GC000148

  • Sattari P, Brenan JM, Horn I, McDonough WF (2002) Experimental constraints on the sulfide- and chromite–silicate melt partitioning behavior of rhenium and platinum-group elements. Econ Geol 97:385–398

    Article  Google Scholar 

  • Schmidt KH, Bottazzi P, Vannucci R, Mengel K (1999) Trace element partitioning between phlogopite, clinopyroxene and leucite lamproite melt. Earth Planet Sci Lett 168:287–299

    Article  Google Scholar 

  • Shimazaki K, MacLean WH (1976) An experimental study on the partition of zinc and lead between the silicate and sulfide liquids. Miner Deposita 11:125–132

    Article  Google Scholar 

  • Sims KWW, DePaolo DJ (1997) Inferences about mantle magma sources from incompatible element concentration ratios in oceanic basalts. Geochim Cosmochim Acta 61:765–784

    Article  Google Scholar 

  • Smith CS (1964) Some elementary principles of polycrystalline microstructure. Metall Rev 9(33):1–48

    Google Scholar 

  • Stacey JS, Kramers JD (1975) Approximation of terrestrial lead isotope evolution by a two-stage model. Earth Planet Sci Lett 26:207–221

    Article  Google Scholar 

  • Su Y, Langmuir CH (2003) Global MORB chemistry compilation at the segment scale. In: Department of Earth and Environmental Sciences, vol. Columbia University, New York

  • Sun S-S (1980) Lead isotopic study of young volcanic rocks from mid-ocean ridges, ocean islands and island arcs. Philos Trans R Soc Lond A 297:409–445

    Article  Google Scholar 

  • Szabo C, Bodnar RJ (1995) Chemistry and origin of mantle sulfides in spinel peridotite xenoliths from alkaline basaltic lavas, Nógrád-Gömör Volcanic Field, northern Hungary and southern Slovakia. Geochim Cosmochim Acta 59:3917–3927

    Article  Google Scholar 

  • Tatsumoto M, Basu AR, Wankang H, Junwen W, Guanghong X (1992) Sr, Nd, and Pb isotopes of ultramafic xenoliths in volcanic rocks of Eastern China: enriched components EMI and EMII in subcontinental lithosphere. Earth Planet Sci Lett 113:107–128

    Article  Google Scholar 

  • Terasaki H, Frost DJ, Rudie DC, Langenhorst F (2005) The effect of oxygen and sulphur on the dihedral angle between Fe–O–S melt and silicate minerals at high pressure: implications for Martian core formation. Earth Planet Sci Lett 232:379–392

    Article  Google Scholar 

  • Urakawa S, Kato M, Kumazawa M (1987) Experimental study of the phase relations in the system Fe–Ni–O–S up to 15 Gpa. pp 95–111 In: Manghnani MH, Syono Y (eds) High pressure research in mineral physics. American Geophysical Union, Washington

  • Vidal P, Dosso L (1978) Core formation: catastrophic or continuous? Sr and Pb isotope geochemistry constraints. Geophys Res Lett 5:169–172

    Article  Google Scholar 

  • Vollmer R (1977) Terrestrial lead evolution and formation time of the Earth’s core. Nature 270:144–147

    Article  Google Scholar 

  • Walter MJ (1998) Melting of garnet peridotite and the origin of Komatiite and depleted Lithosphere. J Petrol 39(1):29–60

    Article  Google Scholar 

  • Wasylenki LE, Baker MB, Kent AJR, Stolper EM (2003) Near-solidus melting of the shallow upper mantle: partial melting experiments on depleted peridotite. J Petrol 44(7):1163–1191

    Article  Google Scholar 

  • Witt-Eickscen G, O’Neill H (2005) The effect of temperature on the equilibrium distribution of trace elements between clinopyroxene, orthopyroxene, olivine and spinel in upper mantle peridotite. Chem Geol 221:65–101

    Article  Google Scholar 

  • Woodhead JD (1996) Extreme HIMU in an oceanic setting: the geochemistry of Mangaia Island (Polynesia), and temporal evolution of the Cook-Austral hotspot. J Volcánol Geotherm Res 72:1–19

    Article  Google Scholar 

  • Workman RK, Hart SR (2005) Major and trace element composition of the depleted MORB mantle (DMM). Earth Planet Sci Lett 231:53–72

    Article  Google Scholar 

  • Workman RK, Hart SR, Jackson M, Regelous M, Farley KA, Blusztajn J, Kurz M, Staudigel H (2004) Recycled metasomatized lithosphere as the origin of the enriched mantle II (EM2) end-member: evidence from the Samoan volcanic chain. Geochem Geophys Geosyst 5. DOI 10.1029/2003GC000623

  • Yang L, Kado S, Derge G (1959) Diffusion in molten sulfides. In: Kingery WD (ed) Kinetics of high temperature processes, vol. Wiley, New York, pp 79–80

  • Yoshino T, Walter MJ, Katsura T (2004) Connectivity of molten Fe alloy in peridotite based on in situ electrical conductivity measurements: implications for core formation in terrestrial planets. Earth Planet Sci Lett 222:625–643

    Article  Google Scholar 

  • Zartman RE, Haines SM (1988) The plumbotectonic model for Pb isotopic systematics among major terrestrial reservoirs—a case for bi-directional transport. Geochim Cosmochim Acta 52:1327–1339

    Article  Google Scholar 

  • Zindler A, Hart SR (1986) Chemical geodynamics. Annu Rev Earth Planet Sci 14:493–571

    Article  Google Scholar 

Download references

Acknowledgements

We are grateful to J. Brenan and an anonymous referee for thoughtful and constructive comments. As always, we are grateful to the Geochemistry Seminar at WHOI for their stimulation and enthusiasm, and their incitement to excess. Or to re-cast Einstein, “Every paper should be as daring as possible, but not more”. Our intemperance should not be blamed on the support we gratefully acknowledge from NSF: EAR-0125917 to SRH and OCE-0118198 to GAG.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. R. Hart.

Additional information

Communicated by: T. L. Grove

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hart, S.R., Gaetani, G.A. Mantle Pb paradoxes: the sulfide solution. Contrib Mineral Petrol 152, 295–308 (2006). https://doi.org/10.1007/s00410-006-0108-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00410-006-0108-1

Keywords

Navigation