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Ore Geology Reviews 35 (2009) 423–435
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Ore Geology Reviews
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Mineral assemblages of the Francisco I. Madero Zn–Cu–Pb–(Ag) deposit, Zacatecas,Mexico: Implications for ore deposit genesis
Carles Canet a,⁎, Antoni Camprubí b, Eduardo González-Partida c, Carlos Linares a, Pura Alfonso d,Fernando Piñeiro-Fernández e, Rosa María Prol-Ledesma a
a Instituto de Geofísica, Universidad Nacional Autónoma de México, Ciudad Universitaria, Delegación Coyoacán, 04510 México D.F., Mexicob Departamento de Geoquímica, Instituto de Geología, Universidad Nacional Autónoma de México, Ciudad Universitaria, Delegación Coyoacán, 04510 México D.F., Mexicoc Centro de Geociencias, Universidad Nacional Autónoma de México, Campus Juriquilla, Boulevard Juriquilla 3001, 76230 Santiago de Querétaro, Qro., Mexicod Departament d'Enginyeria Minera i Recursos Minerals, Universitat Politècnica de Catalunya, Avinguda Bases de Manresa 61-73, 08242 Manresa, Catalunya, Spaine Industrias Peñoles, S.A. de C.V., carretera a Francisco I. Madero n°1, Cieneguillas, 98170 Zacatecas, Mexico
⁎ Corresponding author. Tel.: +52 55 56224133.E-mail address: [email protected] (C. Canet
0169-1368/$ – see front matter © 2009 Elsevier B.V. Aldoi:10.1016/j.oregeorev.2009.02.004
a b s t r a c t
a r t i c l e i n f oArticle history:
The Francisco I. Madero dep Received 31 May 2008Received in revised form 12 February 2009Accepted 13 February 2009Available online 24 February 2009Keywords:SkarnMassive sulfidesGeothermobarometryMineral chemistryGuerrero TerraneNorth American Cordillera
osit, central Mexico, occurs in the Mesozoic Guerrero Terrane, which hosts manyore deposits, both Cretaceous (volcanogenic massive sulfides) and Tertiary (epithermal and skarn deposits). Itis hosted by a 600 m-thick calcareous-pelitic unit, of Lower Cretaceous age, crosscut by porphyritic dikes thatstrike NW–SE. A thick felsic volcanic Tertiary sequence, consisting of andesites and rhyolitic ignimbrites,unconformably overlies the Cretaceous series. At the base, the mineralization consists of several mantosdeveloped within calcareous beds. They are dominantly composed of sphalerite, pyrrhotite and pyrite withminor chalcopyrite, arsenopyrite and galena. At the top of the orebody, there are calcic skarns formedthrough prograde and retrograde stages. The resulting mineral assemblages are rich in manganoanhedenbergite (Hd75–28Di40–4Jh40–20), andraditic garnets (Adr100–62Grs38–0), epidote (Ep95–36Czo60–5Pie8–0),chamosite, calcite and quartz. The temperature of ore deposition, estimated by chlorite and arsenopyritegeothermometry, ranges from 243° to 277 °C and from 300° to 340 °C, respectively. The pressure estimatedfrom sphalerite geobarometry averages 2.1 kbar. This value corresponds to a moderately deep skarn andagrees with the high Cu content of the deposit. Paragenesis, P–T conditions and geological characteristics arecompatible with a distal, dike-related, Zn skarn deposit. Its style of mineralization is similar to that of manyhigh-temperature carbonate replacement skarn deposits in the Southern Cordillera.
© 2009 Elsevier B.V. All rights reserved.
1. Introduction
The Francisco I. Madero (FIM) Zn–Cu–Pb–(Ag) deposit is located~20 km west of the city of Zacatecas, in central Mexico (Fig. 1). Itwas explored between 1976 and 1994 by the Mexican GeologicalSurvey (formerly Consejo de Recursos Minerales), using geophysicalmethods and drilling. The deposit was acquired by ServiciosIndustriales Peñoles in 1994, which performed 130,000 m ofdiamond drilling. Mining operations started in 2001 with a7000 t/day processing plant. Historical production up to 2005 is9.6 Mt of ore containing 4.74 MOz silver, 30.28 kt of lead and309.7 kt of zinc (González and López-Soto, in press).
The FIM deposit is an ore deposit whose genesis has beencontroversial since its discovery. The orebodies are stratabound, arehosted byMesozoic marine sedimentary rocks deposited in a back-arcenvironment, and the only intrusive rocks observable near the ores area few Tertiary, post-Laramide dikes. For that reason, syngeneticsubmarine exhalative models, either sedimentary exhalative (SEDEX)
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l rights reserved.
or volcanogenic (VMS), have been suggested (Gómez-Caballero, 1986;Clark, 1999; Góngora-Flemate, 2001; Miranda-Gasca, 2003; Gonzálezand López-Soto, in press). On the other hand, the predominance ofcalc-silicate assemblages and replacement textures that developedselectively along limestone beds, and the absence of exhalites orunderlying structures attributable to feeder zones, suggest a manto ordistal skarn model (Caddey, 2003). In addition, lead isotope composi-tions of the FIM ores suggest that this deposit is Tertiary in age and,thus, epigenetic and related to the later continental arc magmatism(Mortensen et al., 2008). The aim of this study is to elucidate thenature and ore genesis of the FIM deposit through the detailed studyof its paragenesis and mineral chemistry.
2. Geological setting
The FIM deposit is located in the Mesa Central physiographicprovince (Central Plateau or Mexican “Altiplano”) in central Mexico,which contains several economically and historically importantmining districts, such as Zacatecas, Fresnillo, Guanajuato and Real deCatorce (Clark et al., 1982; Nieto-Samaniego et al., 2007). This deposit
Fig. 1. Location and detailed geological map of the Francisco I. Madero deposit. The schematic stratigraphic section (right) is based in González and López-Soto (in press). Circles A, Band C indicate the location of the geological cross-sections shown in Fig. 2.
424 C. Canet et al. / Ore Geology Reviews 35 (2009) 423–435
is hosted in the Guerrero Composite Terrane, which is a unit product ofcomplex subduction-related processes influenced by major transla-tion and rifting during the Mesozoic along the western margin ofMexico (Campa and Coney, 1983; Centeno-García et al., 2008). TheGuerrero Composite Terrane consists mainly of metavolcanic-sedi-mentary sequences and is partially covered by the Tertiary felsicvolcanics of the Sierra Madre Occidental.
The base of the host sequence of the FIM deposit is a Mesozoicmetapelitic unit composed of shales, meta-siltstones and -subarkoses(Fig.1). This unit is probably Upper Jurassic to Lower Cretaceous in age(González and López-Soto, in press), although no radiometric orpaleontological dating is available. It is conformably overlain by an upto 600 m thick Lower Cretaceous (González and López-Soto, in press)calcareous-pelitic series. These rocks are fine-grained and changeprogressively from black shales at the base to micritic limestones at
Fig. 2. Schematic geological section of the Francisco
the top; the latter host the ores. Up to ~300 m thick volcanosedi-mentary sequence is deposited on the above rocks. It consists ofbasaltic pillow lavas and submarine tuffs interlayeredwith sandstonesand shales. K–Ar dating of the volcanic rocks yielded an UpperCretaceous age (94 Ma; González and López-Soto, in press). A smallgabbroic stock, of probably Cretaceous age, intruded the Mesozoicsequence (Fig. 1).
The Mesozoic sequence was deformed during the Laramideorogeny (Late Cretaceous to Paleocene) and metamorphosed underlower greenschist facies conditions (e.g., Salinas-Prieto et al., 2000).During the Late Cretaceous, a compression event produced thecollision of several volcanic arcs, included those that formed theGuerrero Composite Terrane (Tardy et al., 1994; Centeno-García et al.,2008). In the FIM district, the Laramide compression led to theformation of large, open NW folds, with both limbs dipping about 20°.
I. Madero deposit (location shown on Fig. 1).
425C. Canet et al. / Ore Geology Reviews 35 (2009) 423–435
Subsequently, an ENE–WSWpost-Laramide extension event producednormal faults and developed horst and graben systems (González andLópez-Soto, in press).
A N1000 m thick felsic volcanic Tertiary sequence associated withthe SierraMadre Occidental volcanic province unconformably overliesthe Mesozoic series. It consists of andesites at the base and rhyoliticignimbrites at the top, with interlayered beds of continental volcanicconglomerates. K–Ar dating of the earliest rocks of such sequence inthe vicinities of the FIM district yielded an Eocene age (42 Ma;González and López-Soto, in press). A suite of meter-thick porphyriticdikes, associated with the Tertiary volcanics and ranging in composi-tion from diorite to tonalite and granite, crosscuts the Mesozoicsequence. Such dikes mostly strike NW–SE, were emplaced alongpost-Laramide normal faults, and produced an intense marmorizationof the Mesozoic limestone beds. Additionally, minor granitoid stockscrop out locally in the FIM district.
The Guerrero Composite Terrane hosts a large number ofCretaceous and Tertiary ore deposits (Miranda-Gasca, 2000). Tertiarydeposits include precious- and base-metal epithermal deposits,
Fig. 3. Photographs showing representative textures from the Francisco I. Madero deposit. (Amainly of fine-grained pyrrhotite, pyrite and sphalerite, and a later coarse-grained massivebanded ore, with fine-grained pyrrhotite and pyrite; (C) massive ore, composed by coarse-grbanded calc-silicate assemblage with calcic garnet (dark), and quartz with calcite and chlorichlorite with epidote (dark green), showing complex replacement textures; (F) banded chbrecciated vein, with fragments of black shale (dark) and banded chlorite-epidote with dissegalena; Grt — garnet; Hd — clinopyroxenes (hedenbergite); Po — pyrrhotite; Py — pyrite; Q
porphyry-copper deposits and skarns, whereas Cretaceous depositsare mostly of VMS type (Clark, 1999; Miranda-Gasca, 2000).
3. Structure of the orebodies
The FIM deposit extends over an area of ~6 km2, at depths between60 and 550 m below the present surface. It consists of several roughlystratiform orebodies hosted by a Mesozoic calcareous-pelitic series(Fig. 1). The thickness of the mineralization including non-economicportions changes abruptly from a few tens of meters up to ~170m. 3 to60 m thick individual ore lenses occur within calcareous beds. As ageneral feature, the mineralized unit is a large dome-shaped structurewhose flanks are cut by NW normal faults (Fig. 2). Thus, the marginalportions of the mineralizationwere downthrown. Many of such faultshost porphyritic dikes. Paterson (1995) found magnetic and gravi-metric anomalies suggesting the presence of a deep magmaticintrusion.
At its base, the mineralization consists of sulfide-rich (60 to 75modal % sulfides)mantos, withmajor pyrite and pyrrhotite, andminor
) Photograph showing the irregular, replacive contact between a banded ore composedore mostly composed by pyrrhotite, sphalerite and galena. Slabbed core samples: (B)ained sphalerite, galena, and pyrrhotite, accompanied by calcite and minor chlorite; (D)te (light); (E) irregular calc-silicate assemblage with calcic clinopyroxene (brown), andlorite-epidote assemblage, with coarse grained galena; (G) late quartz-calcite (white)minated sulfides (grey). Abbreviations: Cal— calcite; Chl— chlorite; Ep— epidote; Gn—
— quartz.
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sphalerite, galena and chalcopyrite, accompanied by quartz and pyrite.Locally, dm-thick Cu-(Ag-) and Pb- and Zn-rich lenses occur. Bothbanded and massive ores are observed (Fig. 3). Moderately silicifiedblack shale beds with disseminated pyrite occur interlayered with theores.
The banded ore is mostly fine grained (up to 0.5 mm) and is veryrich in pyrrhotite (~50modal %) and pyrite (~20modal %), withminorsphalerite and chalcopyrite (Fig. 3B). Towards the bottom of thebanded ores, the pyrite content and grain size increase, and accessoryarsenopyrite is present. The mm-scale layering of banded ores isdefined by alternating sulfide- and chlorite-rich layers. Massive oresare coarse grained (up to 5 mm) and form irregular, replacive bodiescomposed of sphalerite and pyrrhotite (total ~50 modal %), withminor galena, chalcopyrite, calcite, chlorite, sericite, quartz andepidote (Fig. 3C).
The upper part of themineralized structure consists mainly of calc-silicate rich assemblages that strongly vary in texture, composition andgrade. It contains, in order of abundance: (a) microcrystalline epidote-
Fig. 4. Episodes and sequence of crystalliza
chlorite, (b) almost-monomineralic macrocrystalline calcic clinopyr-oxene, and (c) banded calcic garnet-rich assemblages (Fig. 3D–F).Calcite, quartz, adularia, sericite, Ca-amphibole, stilpnomelane, tita-nite, rutile and apatite occur in variable amounts. Ore minerals are, inorder of abundance, sphalerite, galena, marcasite, pyrite, chalcopyrite,arsenopyrite andmagnetite; they attain up to 25modal %. Calc-silicaterich assemblages locally develop banded and fold-like patterns.
Calc-silicate- and sulfide-rich units show complex contact relation-ships, which include either sharp-replacive or gradual contacts.Decimeter-thick crustiform-banded undeformed veins and seldombreccias crosscut the above assemblages (Fig. 3G). These occur aroundfelsic porphyritic dikes, and are lined by essentially calcite and quartz.Calcite mostly occurs as bladed crystals and quartz as chalcedony. Suchveins also contain fluorite, chlorite and dolomite, and are locallyenriched in Au and Ag (González and López-Soto, in press). In addition,Yta et al. (2003) reported for these veins a complex assemblage of Ag-,Bi-, Pb- and Cu-tellurides, sulfides and sulfosalts, including hessite,matildite, tetradymite, bismuthinite, tsumoite, aikinite andwittichenite.
tion in the Francisco I. Madero deposit.
Table 1Chemical composition and structural formulas of selected silicates (anhydrous) fromthe Francisco I Madero deposit (electron-microprobe data).
Grt Grt Px Px Px Kfs Kfs
#1 #2 #3 #4 #5 #6 #7
SiO2 wt.% 38.78 37.29 49.65 50.56 47.56 64.62 63.95Al2O3 1.19 3.92 0.27 0.04 0.28 18.82 19.19TiO2 0.00 0.04 0.00 0.00 0.05 0.02 0.04CaO 32.35 34.94 22.56 22.23 25.32 0.01 0.03Na2O 0.00 0.00 0.09 0.02 0.03 0.25 0.39K2O 0.19 0.01 n.a. n.a. n.a. 15.39 16.07BaO n.a. n.a. n.a. n.a. n.a. 0.72 0.56MnO 0.17 0.18 11.35 9.03 10.94 0.00 0.00Fe2O3 25.37 25.73 – – – – –
FeO 2.60 0.00 16.26 17.28 8.90 0.07 0.13MgO 0.30 0.03 0.72 1.94 6.86 0.10 0.00ZnO n.a. n.a. 0.04 0.04 n.a. n.a. n.a.Cr2O3 0.00 0.00 n.a. n.a. n.a. n.a. n.a.Total 100.95 101.64 100.95 101.14 99.95 100.06 100.39Si Apfu 3.201 3.028 2.008 2.022 1.905 2.986 2.959Al 0.116 0.375 0.013 0.002 0.013 1.025 1.047Ti 0.000 0.003 0.000 0.000 0.002 0.001 0.001Ca 2.860 3.039 0.978 0.952 1.087 0.000 0.001Na 0.000 0.000 0.007 0.001 0.002 0.023 0.035K 0.020 0.001 – – – 0.907 0.948Ba – – – – – 0.013 0.010Mn2+ 0.012 0.012 0.389 0.306 0.371 0.000 0.000Fe3+ 1.576 1.572 – – – – –
Fe2+ 0.179 0.000 0.550 0.578 0.298 0.003 0.005Mg 0.037 0.004 0.043 0.116 0.410 0.007 0.000Zn – – 0.001 0.001 – – –
Cr 0.000 0.000 – – – – –
Apfu: atoms per formula unit. Grt: Ca garnets (structural formula based on 12 O);andradite. Px: Ca clinopyroxenes (structural formula based on 6 O); manganoheden-bergite. Kfs: K feldspars (structural formula based on 8 O); adularia.n.a.: not analyzed.
Table 2Chemical composition and structural formulas of selected silicates (hydrated) fromthe Francisco I Madero deposit (electron-microprobe data).
Chl Chl Stl Stl Ms Ep Ep Ep
#1 #2 #3 #4 #5 #6 #7 #8
SiO2 wt.% 25.32 30.98 39.45 38.39 49.04 38.51 38.79 37.13Al2O3 20.60 17.82 9.52 10.54 35.29 25.15 27.71 26.80TiO2 0.00 0.03 0.14 0.15 0.26 0.12 0.02 0.06CaO 0.00 0.10 0.00 0.00 0.00 23.25 22.83 20.46Na2O 0.00 0.00 0.03 0.02 0.30 n.a. n.a. n.a.K2O 0.00 0.00 2.80 3.70 8.11 n.a. n.a. n.a.BaO n.a. n.a. 0.00 0.00 0.26 n.a. n.a. n.a.MnO 0.07 0.28 4.21 3.70 0.00 – – –
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However, they do not contribute significantly to the overall economicresource of the FIM deposit.
At the base of the orebody, cm-scale, irregular, metamorphicquartz veins, often with pyrite crystals but devoid of other metallicminerals, are hosted in the basal metapelites, which in the vicinities oforebodies are altered and contain chlorite and epidote.
Mn2O3 – – – – – 0.10 0.69 0.77FeO 40.10 14.26 30.32 29.87 1.27 – – –
Fe2O3 – – – – – 11.76 8.21 11.72MgO 3.51 24.65 7.26 7.33 1.07 0.00 0.01 1.65ZnO 0.00 0.03 0.12 0.13 0.03 0.02 0.03 0.01Cl− 0.02 0.00 0.03 0.01 0.00 0.00 0.02 0.01F− 0.82 0.87 c1.12 0.98 0.07 0.48 0.29 0.54H2O 10.39 11.80 5.12 5.18 4.58 1.70 1.80 1.59Total 100.83 100.82 100.13 100.01 100.28 100.65 100.13 100.26Si Apfu 2.815 3.043 9.206 8.987 3.190 3.027 3.017 3.033Al 2.700 2.063 2.619 2.908 2.706 2.331 2.540 2.580Ti 0.000 0.002 0.024 0.027 0.013 0.007 0.001 0.004Ca 0.000 0.011 0.000 0.000 0.000 1.958 1.903 1.791Na 0.000 0.000 0.013 0.010 0.038 – – –
K 0.000 0.000 0.834 1.105 0.673 – – –
Ba – – 0.000 0.000 0.007 – – –
Mn2+ 0.007 0.024 0.832 0.734 0.000 – – –
Mn3+ – – – – – 0.006 0.041 0.048Fe2+ 3.730 1.171 5.918 5.848 0.069 – – –
Fe3+ – – – – – 0.696 0.480 0.721Mg 0.582 3.609 2.527 2.559 0.104 0.000 0.002 0.200Zn 0.000 0.002 0.021 0.022 0.001 0.001 0.002 0.001Cl− 0.003 0.000 0.012 0.004 0.000 0.001 0.003 0.002F− 0.289 0.271 0.827 0.722 0.015 0.118 0.071 0.140OH−⁎ 7.708 7.729 2.766 2.873 1.985 0.890 0.932 0.869
Apfu: atoms per formula unit. Chl: chlorite group (structural formula based on 18 O,OH);analysis #1 chamosite, #2 clinochlore. Stl: stilpnomelane (structural formula based on32 O,OH; 2.4 H2O). Ms: muscovite (structural formula based on 12 O,OH). Ep: epidotegroup (structural formula based on 14 O,OH); epidote.⁎Only the hydroxyl group (combined water).n.a.: not analyzed.
4. Paragenetic sequence
Textural patterns suggest an epigenetic sequential mineraldeposition caused by a complex, multistage hydrothermal event.The sequence of crystallization of the FIM mineralization is shown inFig. 4. Based on paragenetic relationships, three main stages can beinferred, from early to late: sedimentation and regional metamorph-ism, epigenetic hydrothermal stage, and supergene alteration.
Replacement textures suggest that the mineralization formed forthe most part at the expense of the carbonate beds of the LowerCretaceous sequence, in an epigenetic, hydrothermal metasomaticstage. This stage formed a complex sequential replacive deposition ofminerals, and is characterized by three substages: (a) prograde, (b)retrograde, and (c) vein filling. During the prograde substage Ca-clinopyroxene and garnet, along with minor magnetite and titanite,formed. During the retrograde substage hydrous silicates (mainlyepidote and chlorite), sulfides and quartz formed. Such mineralassemblage occurs interstitially with respect to the clinopyroxenecrystals, and pseudomorphose garnet.
Although early banded ores and a later replacive massive ores canbe macroscopically differentiated, microscopic and compositionaldifferences between them are only slight. Intergrowths and textureswith curvilinear equilibrium grain boundaries prevail in both cases,indicating a relevant overlap in the crystallization of sulfides.
The latest hydrothermal substage produced veins, breccias andvoid-lining quartz and carbonates, accompanied byminor chlorite andfluorite. Finally, a supergene assemblage, consisting of goethite andcarbonates, is locally developed.
5. Analytical conditions
Seventy-three samples were taken from drill cores and 15 werecollected from the mine. The mineral associations have been studiedin 30 polished thin sections using a standard petrographicmicroscope.Bulk mineralogy was confirmed by X-ray diffraction (XRD) analyses,performed on 14 samples, using a Philips 1400 diffractometerequipped with a Cu anode tube X-ray source and directing thecollimated Cu Kα1,2 radiation (λ=0.15405 nm) towards a randomlyoriented sample. X-radiationwas generated at 40 kV and 20mA. Scanswere recorded from 4° to 70° (2θ) with a step-scan of 0.02° and 2 s/step.
Images and quantitative analyses were obtained from 16 selectedthin sections, with an electron probe microanalyzer (EPMA) JEOL JXA-8900XR. The samples were examined in backscattered electron (BSE)mode. Wavelength dispersive spectrometry (WDS) analyses werecarried out using following conditions: (a) for silicates: 20 keV, 20 nA,beam diameter of 1 μm, and a counting time of 30 s; the usedstandards were biotite (FeKα, SiKα, MnKα, KKα, TiKα, MgKα) andpyrope (MgKα), chlorite (AlKα) and albite (AlKα), sanidine(BaLα, KKα), plagioclase (CaKα), kaersutite (NaKα, CaKα, SiKα),diopside (CrKα), obsidian (FKα, ClKα), sphalerite (ZnKα) and ilmenite
Table 3Chemical composition and structural formulas of selected sulfides from the Francisco I.Madero deposit (electron-microprobe data).
Sp Sp Sp Py Po Apy
#1 #2 #3 #4 #5 #6
S wt.% 34.20 34.12 33.77 53.56 39.15 23.51As 0.01 0.02 0.00 0.05 0.01 41.76Zn 54.68 51.68 54.35 0.00 0.03 0.00Co 0.00 0.02 0.02 0.05 0.05 0.05Ni 0.00 0.01 0.00 0.00 0.00 0.00Fe 10.32 13.59 10.53 47.11 61.16 32.01Sb 0.00 0.02 0.00 0.00 0.00 1.62Cu n.a. n.a. 0.00 n.a. 0.03 0.00Cd n.a. n.a. 0.09 n.a. 0.00 n.a.Ag n.a. n.a. n.a. 0.00 n.a. 0.02Sn n.a. n.a. n.a. 0.00 n.a. 0.00Pb n.a. n.a. n.a. n.a. n.a. 0.05Bi n.a. n.a. n.a. n.a. n.a. 0.00Te n.a. n.a. n.a. n.a. n.a. 0.00Total 99.21 99.45 98.76 100.80 100.43 99.01S atom % 51.095 50.713 50.784 66.409 52.671 39.033As 0.004 0.015 0.000 0.026 0.008 29.674Zn 40.045 37.648 40.067 0.000 0.018 0.000Co 0.000 0.016 0.016 0.030 0.039 0.049Ni 0.000 0.005 0.000 0.000 0.000 0.000Fe 8.856 11.596 9.096 33.535 47.243 30.516Sb 0.000 0.007 0.001 0.000 0.000 0.708Cu – – 0.000 – 0.022 0.000Cd – – 0.036 – 0.000 –
Ag – – – 0.000 – 0.007Sn – – – 0.000 – 0.000Pb – – – – – 0.013Bi – – – – – 0.000Te – – – – – 0.000
Apy, arsenopyrite; Po, Pyrrhotite; Py, pyrite; Sp, Sphalerite.n.a.: not analyzed.
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(TiKα, MnKα); (b) for carbonates: 15 KeV, 10 nA, beam diameter of1 μm, and a counting time of 30 s; the used standards were kaersutite(KKα, NaKa, MgKa), dolomite (MnKa, SrLa, FeKa), calcite (CaKa),sphalerite (ZnKα) and plagioclase (BaLα); and (c) for sulfides: 20 KeV,20 nA, beam diameter of 1 μm, and a counting time of 30 s; the usedstandards were skutterudite (NiKα, AsKα, FeKα, CoKα), sphalerite(ZnKα, SnLα), cuprite (CuKα), marcasite (SKα), stibnite (SbLα), Ag(AgLα) and crocoite (PbMα). The number of analyzed points is:chlorite, 75; muscovite, 16; stilpnomelane, 12; epidote, 87; Ca-pyroxene, 24; Ca-garnet, 19; feldspar, 6; sphalerite, 104; arsenopyrite,7; pyrrhotite, 15; carbonates, 56.
6. Mineral chemistry, geothermobarometry and paragenesis
Ore-bearing mineral assemblages are calc-silicate rich and showreplacement textures that suggest sequential mineral deposition.Details on mineral chemistry and textural features of the majormineral phases are provided in Tables 1–3, and in Figs. 5 and 6,respectively.
6.1. Calcic clinopyroxenes
Calcic clinopyroxenes occur mostly in almost-monomineraliclayers, as euhedral, randomly oriented prismatic crystals, a few tensof µm to 5 mm long. Quartz, calcite and minor epidote and sulfides(sphalerite, galena and pyrite) are interstitial to clinopyroxene crystals(Fig. 5C). Reddish weathering patinas of iron oxyhydroxides occuralong cleavage and cracks in clinopyroxene crystals. These belong tothe diopside-hedenbergite series (Hd75–28Di40–4Jh40–20; Table 1). As adistinctive feature, most of the analyzed clinopyroxenes have highcontents of Mn (ranging from 5.76 to 11.35 wt.% MnO) and can beclassified as manganoan hedenbergite (Fig. 7; Morimoto et al., 1988).
The highest Mn values were obtained from microcrystalline clinopyr-oxenes occurring in upper part of the mineralized structure, nearbythe calc-silicate-limestone contact. The Zn content is up to 0.4 wt.%ZnO.
6.2. Calcic garnets
Calcic garnets develop in roughly banded aggregates, associatedwith quartz, calcite, chlorite, muscovite, pyrite, and minor epidote,hedenbergite, chalcopyrite, titanite, rutile (altered to leucoxene) andapatite. Garnets constitute ~15 modal % of the total assemblage, andoccur as up to 2 mm subhedral crystals (Fig. 6D). They are partiallyreplaced by an assemblage of quartz, chlorite and sulfides, and arecrosscut by calcite veinlets. They belong to the grossular-andraditeseries (Adr100–62Grs38–0; Fig. 8), and their Mn content is very low(b0.5 wt.% MnO; Table 1). Their chemical composition is very variable,as reflected in their concentric zoning, where crystal rims are richerthan cores in the grossular end-member and in Mn (Fig. 9A).
6.3. Epidote
Epidote is a major component of the mineralization as it occurs inall the calc-silicate assemblages, in the sulfide mantos and in thefootwall altered metasedimentary rocks. Its main occurrence is asmicrocrystalline epidote–chlorite assemblages (up to 60 modal % ofepidote) with quartz and calcite, and minor amphiboles of theactinolite–tremolite series, calcic garnet and clinopyroxene, titanite,stilpnomelane and sulfides (galena, sphalerite, pyrite, marcasite andchalcopyrite). In such associations epidote crystals are 20 to 400 µmlong, randomly oriented subhedral prisms (Fig. 6C). In the sulfidemantos, epidote occurs as up to 2.5 mm euhedral prismatic crystalsthat are embedded into a sulfide groundmass. Such crystals showconcentric zonation, reflecting changes in chemical composition (Fig.9B). At a deposit scale the epidote end-member (Ep95–36Czo60–5Pie8–0)is dominant, and the Mn content is very low, between 0.10 and1.46 wt.% Mn2O3 (Fig. 10; Table 2). The highest Mn contents in epidotecorrespond to crystals in the orebodies, whereas the Mn content inepidote from the basal metasediments is almost negligible (Fig. 10).
6.4. Sheet silicates
Chlorite is very abundant, both in the mineralization and thefootwall altered metapelites. In the calc-silicate rich units, it occurs asup to 500 μm-wide platelets that can form spherulitic aggregates,commonly in association with quartz and epidote (Fig. 6B). Chloritemay form pseudomorphs, probably after clinopyroxene. In the sulfide-rich mantos, chlorite usually occurs disseminated within sulfidegroundmasses of pyrrhotite, sphalerite and galena. In the crustiform-banded veins and breccias chlorite is scarce and forms aggregates offine-grained crystals (up to 10 μm across).
EMP analyses of chlorite crystals indicate that they are trioctahe-dral (Type “I” of Zane and Weiss, 1998) and belong to the clinochlore-chamosite series (Fig. 11; Table 2). Chlorites from the orebodies arericher in the Fe2+ end-member (chamosite), whereas those from thefootwall metapelites plot close to the Mg end-member (clinochlore).In both cases, theMn content is almost negligible (Table 2). Octahedralvacancies per formula unit (□) based on Σ(O,OH)=18 vary between0.03 and 0.40, showing a progressive variation with depth. Thus, thelowest values correspond to the footwall metapelites (clinochlore),and the highest to the orebody (chamosite).
Two generations of muscovite were identified. The first generationis formed by diagenetic to low-grade metamorphic processes, and isan essential mineral of the host metapelites. The second generation, ofhydrothermal origin, occurs associated to chlorite in subordinateamounts. The Ba content in muscovite is negligible (Table 2); Cr wasnot detected.
Fig. 5. Photomicrographs (plane polarized light) of mineral assemblages from the Francisco I. Madero deposit. Intergrowths and curvilinear equilibrium grain boundaries betweensulfides (reflected light): (A) galena, pyrite and sphalerite, and (B) sphalerite, pyrrhotite and chalcopyrite; note that sphalerite lacks chalcopyrite blebs. (C) Replacement of calcicclinopyroxenes by an assemblage of bladed calcite, quartz and minor chlorite; (D) late vein filling of calcite and chalcedony (transmitted light, crossed nicols). Abbreviations: Cal —calcite; Chd — chalcedony quartz; Ccp — chalcopyrite; Gn — galena; Po — pyrrhotite; Px — calcic clinopyroxenes; Py — pyrite; Q — quartz; Sp — sphalerite.
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Stilpnomelane,with an approximate structural formula K(Fe2+,Mg,Mn2+)9(Si,Al)12 (O,OH)32·nH2O, occurs as small platelets, up to 75 μmacross, and is sparsely distributed in the chlorite-rich assemblages(Table 2; Fig. 6B).
6.5. Sulfides
Pyrrhotite is the most common sulfide in the ore mantos, but isscarce in the calc-silicate rich assemblages. It formsmosaic aggregateswith curvilinear equilibrium grain boundaries, in association withsphalerite and minor chalcopyrite. These aggregates contain minorinterstitial, fine-grained (up to 30 μm) pyrite. The grain size ofpyrrhotite crystals is up to 2mm. The Fe contents in pyrrhotite crystalsrange from 46.9 to 47.8 at.% (Table 3). The average Fe per formula unit(based on 1 S) is 0.897, and thus its composition approaches Fe9 S10.According to Lusk et al. (1993) and Lynch and Mengel (1995), suchcomposition is distinctive of the 5H polytype (hexagonal) pyrrhotite.
Pyrite is widespread in the mineralized zone, in a large variety oftextures and grain sizes. At the bottom of the orebody, the pyritecontent is up to 75 modal %, occurring as coarse grained aggregates ofeuhedral crystals (up to 1 cm in diameter) with interstitial calcite,chlorite and quartz. These crystals contain numerous inclusions ofpyrrhotite and sphalerite, and are accompanied byminor arsenopyrite(Fig. 6A). In contrast, in the banded ore pyrite occurs mostly asanhedral grains, up to 2 mm across, forming intergrowths andcurvilinear equilibrium grain boundaries with sphalerite and galena(Fig. 5A). In the calc-silicate rich assemblages, pyrite occurs inter-stitially and as pseudomorphs after garnet (Fig. 6D).
Arsenopyrite occurs in subordinate amounts in the coarse-grainedpyrite basal aggregates and in the garnet-rich rocks. It forms up to100 μm long euhedral, diamond-shaped, occasionally twinned crystals
(Fig. 6A). The arsenopyrite shows relatively low arsenic contents, from29.0 to 29.7 at.%; the Co content is b0.1 at.% (Table 3).
Sphalerite is the second metallic mineral in abundance (afterpyrrhotite) in the deposit, and occurs all through the mineralizedzone. It develops anhedral grains, up to few mm across, withcurvilinear equilibrium grain boundaries, forming mosaic aggregatesand intergrowths with galena, pyrrhotite, pyrite and seldom chalco-pyrite (Fig. 5A, B). In general, sphalerite grains lack “chalcopyritedisease”. The analyzed Fe contents in sphalerite show a wide range ofvariation, between 15.3 and 24.6 mol% FeS (Fig. 12; Table 3). Thisvariation meets up with the different paragenetic relationships.
6.6. Carbonates
Carbonate minerals occur: (a) in the host sedimentary rocks; (b)interstitially in the calc-silicate rich assemblages; and (c) in late veinsand breccias. In the calc-silicate assemblages, manganoan calcite(Ca0.91–0.82Mn0.09–0.16CO3) is abundant, and develops (i) anhedral,poikilitic patches up to 5 mm across, (ii) bladed crystals up to 1 mm indiameter, and (iii) microcrystalline pseudomorphs, in associationwithchlorite, probably after clinopyroxene. In the late veins, carbonatesrange from pure calcite to manganoan calcite, from 0.6 to 16.8 mol %MnCO3, and form mosaic textures associated with chalcedony (Fig.5D). In addition, mm-sized euhedral dolomite crystals occur as latebreccia cement.
6.7. Quartz
In the sulfide mantos quartz generally forms up to 1 mm longsubhedral to euhedral crystals, embedded in a sulfide groundmass.Such crystals are rich in inclusions of epidote and calcic amphiboles. Inthe calc-silicate assemblages quartz crystals occur in mosaic
Fig. 6. SEM-BSE images of mineral assemblages in the Francisco I. Madero deposit. (A) euhedral arsenopyrite and pyrite crystals, and a late marcasite–siderite assemblage; (B) stilpnomelaneassociated to quartz, chlorite and epidote; (C) euhedral titanite crystals associated to epidote, with interstitial quartz, calcite and sphalerite; (D) pseudomorphic replacement of andradite by asulfide assemblage (pyrite and chalcopyrite), calcite andquartz. Abbreviations: Adr— andradite; Apy— arsenopyrite; Cal— calcite; Ccp— chalcopyrite; Chl— chlorite; Ep— epidote;Gn— galena;Mrc—marcasite; Ms—muscovite; Po— pyrrhotite; Py— pyrite; Q— quartz; Sd— siderite; Sp— sphalerite; Stp — stilpnomelane; Ttn— titanite.
Fig. 7. Composition of calcic clinopyroxenes (manganohedenbergite) from the Francisco I. Madero deposit plotted on a johannsenite (Jh)— diopside (Di)— hedenbergite (Hd) diagram. Filleddiamonds indicate microcrystalline (up to 50 μm) manganohedenbergite disseminated within an epidote-quartz assemblage; open diamonds indicate coarse-grained (up to 1 cm) almost-monomineralic manganohedenbergite. Dashed areas indicate the pyroxene composition range for Zn skarn deposits summarized by Meinert et al. (2005).
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Fig. 8. Composition of calcic garnets from the Francisco I. Madero deposit (pyralspite-grossular-andradite diagram). Dashed areas indicate the garnet composition range for Zn skarndeposits summarized by Meinert et al. (2005).
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aggregates associated with chlorite, calcite and minor muscovite.Quartz also occurs in the late veins and breccias forming (a) earlyeuhedral crystals normal to the wall rock, and (b) late chalcedonyaggregates of up to 300 μm long fibrous crystals (Fig. 5D).
6.8. Geothermobarometry
A wide range of composition and a non-stoichiometric behaviormake the minerals of the chlorite group attractive for geothermo-metry (de Caritat et al., 1993). Many studies are based on an empiricalobservation stating that, in geothermal systems, SiIV and, hence, □VI
decrease with increasing depth. Thus, equations relating temperatureand chlorite composition have been deduced from microprobechlorite analysis and microthermometric data from fluid inclusions(Cathelineau and Nieva, 1985; Kranidiotis and MacLean, 1987;Cathelineau, 1988). However, besides temperature, many otherparameters such as fO2, pH and the Fe/(Fe+Mg) ratio in the hostrock could affect chlorite composition (de Caritat et al., 1993).Although the empirical chlorite geothermometry must be interpretedwith caution, it can be used satisfactorily in geologic settingscomparable to those where the calibration was performed and fortemperatures below 350 °C, since they consider, not explicitly, manythermodynamic variables (de Caritat et al., 1993). Using the empirical□-T plot for chlorites of Cathelineau and Nieva (1985), we obtainedtemperatures between 270° and 277 °C for chlorites at the footwallmetapelites (hydrothermally altered) and the bottom of orebodies,and between 243° and 262 °C at the central and upper parts oforebodies.
Arsenopyrite displays a significant solid solution range in the Fe–As–S system that is sensitive to temperature, which allows it to beused as a geothermometer (Kretschmar and Scott, 1976; Sharp et al.,1985). The estimated pressure effect on the composition of arseno-pyrite in equilibrium with pyrite is irrelevant (Kretschmar and Scott,1976). Arsenopyritewith b0.5 at.% Co can be used for geothermometry(Sharp et al., 1985). However, arsenic contents below 30.0 at.% As donot allow to use the fS2 vs. T equilibria established by Kretschmar andScott (1976), which has been applied in the study of several
metamorphosed ore deposits (e.g., Lynch and Mengel, 1995; Lentz,2002).
In this study, petrographic and scanning electron microscopeobservations suggest that arsenopyrite formed in the retrogradehydrothermal substage of the mineralizing event, together with pyrite(Figs. 4 and 6). Therefore, a coprecipitation under equilibriumconditions can be assumed. Thus, we obtained, from the arsenopyr-ite–pyrite stability field of the pseudobinary T–X diagram ofKretschmar and Scott (1976), temperatures that range between 300°and 340 °C (Fig. 13).
The Fe content in sphalerite is largely affected by pressure and,consequently, it can be used for geobarometry (Scott and Barnes,1971;Hutchison and Scott, 1981). The sphalerite geobarometer can beapplied with confidence in several skarn deposits, in view of theirsulfide assemblages and range of temperature and pressure conditions(Shimizu and Shimazaki,1981). To estimate the pressure fromXFeS it isrequired equilibrium of sphalerite with pyrite and hexagonal pyr-rhotite in order to buffer the sulfur fugacity. XFeS in sphaleritecrystallized along the pyrrhotite–pyrite equilibrium ranges between10 and 20% (Scott and Barnes, 1971). Sphalerite rich in chalcopyriteblebs is not suitable for geobarometry calculations (Hutchison andScott, 1981).
In this work, sphalerite crystals with XFeSN20% are mostly inparagenesis withmarcasite, whichmay be secondary; thesewere thusrejected for geobarometry purposes. On the other hand, sphaleritegrains with XFeS b20% mostly coexist with pyrite and minor pyrrhotite(without marcasite; Fig. 12). Thus, they are suitable for pressurecalculations. The estimated pressures from sphalerite within suchassemblages range from 0.8 to 4.2 kbar, with average of 2.1 kbar,corresponding to a depth of ~8 km.
7. Discussion
The ore-bearing rocks of the FIM deposit are composed largely bycalc-silicates (manganoan hedenbergite, andraditic garnet, epidote,titanite), which are accompanied by other silicates (quartz, chlorite),carbonates (manganoan calcite), oxides (magnetite), and sulfides
Fig. 9. Zoning patterns showing variations in Fe2O3, Al2O3 and Mn2O3 contents (electron microprobe data) for (A) calcic garnet, and (B) epidote crystals. SEM-BSE images (right)indicate the position of electron microprobe profiles.
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(sphalerite, pyrrhotite, pyrite, marcasite, chalcopyrite, galena andarsenopyrite). According to Einaudi et al. (1981), Delgado et al. (1997)and Meinert et al. (2005) such mineralogy and the association oforebodies with limestones allow us to categorize the FIM deposit as askarn.
Skarn deposits form by metasomatism, through a succession ofreplacive mineralizing events triggered by a magmatic-hydrothermalsystem, generally including a prograde (high temperature) stage, anda subsequent retrograde (lower temperature) stage (e.g., Einaudi et al.,1981). In the FIM deposit, the succession of prograde and retrogradestages resulted in a large exoskarn characterized by overprinted andrecrystallized paragenesis (Fig. 4).
The prograde stage caused the extensive occurrence of manganoanhedenbergite and minor andraditic garnet in the FIM deposit. In calcicskarns of the Zn–Pb type (Einaudi et al., 1981), calcic clinopyroxenespredominate over garnets. Besides, the highest pyroxene to garnet ratiosare found in skarns that are distal to the causal magmatic sources(Meinert et al., 2005). The highmanganese contents in pyroxenes (Mn/Fe ratio: 0.3–1.2) of the FIM deposit agree with the johannsenite-rich
composition of pyroxenes from most Zn–Pb skarns deposits (Einaudiet al.,1981;Nakano,1998).Nakano (1998) found in Japanese skarns, thattheMn/Fe ratio is N0.2 in Zn–Pb deposits, ranges between 0.2 and 0.1 inWdeposits, and is b0.1 in Cu–Fe deposits. According to the same author,an association of high Mn/Fe pyroxenes and andraditic garnet indicatesoxidizing conditions. Such conditions agreewith the early occurrence ofmagnetite at the FIM deposit. Zoning in garnet crystals reflectsoscillations in the composition of metasomatic fluids (Fig. 9A; Jamtveitet al., 1993).
The FIM retrograde skarn assemblage is largely made up ofepidote, chlorite (chamosite) and quartz, and is accompanied by anextensive deposition of base metal sulfides. Fe-rich members of theepidote-clinozoisite series are relevant minerals in retrogradeassemblages of many Zn–Pb skarn deposits (Einaudi et al., 1981),and their composition generally depends on the composition of theprotolith and the fO2 (Delgado et al., 1997). In addition, epidote andchlorite (clinochlore) occur in the footwall metapelites due to thehydrothermal alteration by metasomatic fluids. Thus, these rockscan be considered periskarns (as defined by Zharikov, 1970).
Fig. 10. Composition of epidote from the Francisco I. Madero deposit. Filled diamonds indicate crystals from the orebody; open squares indicate crystals from the altered metapelitesof the basal series. Abbreviations: Pie — piemontite; Czo — clinozoisite; Ep — epidote.
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The temperature of formation of the retrograde skarn, estimatedthrough the arsenopyrite and chlorite geothermometers, ranges from300° to 340 °C, and from 243° to 277 °C, respectively. Thesetemperatures may reflect a cooling path in the retrograde skarnstage, as arsenopyrite predates chlorite (Fig. 4). The arsenopyritetemperature range could represent the temperature for ore deposi-tion. This temperature range agrees with that of sulfide-rich skarndeposits (250° to N500 °C; Megaw, 1998), although it is notably lower
Fig.11. Classification of chlorites from the studied deposit. Chlorite diagram after Zane andWcrystals from the altered metapelites of the basal series.
than most data after fluid inclusion microthermometry in theprograde, pre-sulfide skarn stages (Einaudi et al., 1981, and referencestherein).
The average pressure estimated from the sphalerite geobarometryis 2.1 kbar. Pressure estimates for skarn deposits range from 0.3 to3 kbar, although pressure for most of Zn-rich skarn deposits rangefrom 0.5 to 1.8 kbar (Einaudi et al., 1981, and references therein).According to Shimazaki (1975), the depth of emplacement of skarn
eiss (1998). Filled diamonds indicate crystals from the orebody; open diamonds indicate
Fig. 13. Arsenopyrite geothermometry based on the pseudobinary T–X diagram ofKretschmar and Scott (1976). Abbreviations: Apy — arsenopyrite; As — native arsenic;L — liquid; Lo — löllingite; Po — pyrrhotite; Py — pyrite.
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deposits determine their base metal contents. Thus, shallow skarns(Pb1 kbar) are typically Zn- and Pb-rich, whereas deep skarns(PN1 kbar) are Cu-rich. In view of that, the high pressure valuesestimated for the FIM deposit agree with the high copper contentsthat it bears.
Considering the relationship and nature of causative magmatism,as well as the morphology of the orebodies, the FIM deposit is a distal,dike-related skarn deposit (Einaudi et al., 1981). According to Meinertet al. (2005) most Zn-rich skarns occur distally with respect toassociated igneous rocks. In Japan, near 70% of the Zn–Pb skarndeposits occur in close proximity to dikes, but distal to the unobservedplutons (Nakano et al., 1990). According to Einaudi et al. (1981), thesedikes act as pathways for metasomatic fluids that come from a deeper,cogenetic, plutonic body. Such conditions are in accordancewith thoseobservable at the FIM district.
Megaw (1998) defined Carbonate Replacement Deposits (CRD),based on the abundant base-metal distal skarn deposits of theSouthern Cordillera (northwesternMexico and southwestern USA), as“epigenetic, intrusion-related, high-temperature (N250 °C), sulfide-dominant Pb–Zn–Ag–Cu–Au-rich deposits that typically form lensesor elongate to elongate-tabular bodies referred to as mantos orchimneys”. The FIM deposit fulfills all geological and mineralogicalcharacteristics of this particular kind of skarn deposit. These include:(a) relatively large deposits (N50 Mt for the largest CRD deposits); (b)dome-like, fault-controlled deposits; (c) mineralization associatedwith dikes; (d) lack of exposed plutons or stocks; (e) the occurrence ofvolcanic capping rocks contemporaneous with the intrusions; (f)orebodies mostly shaped as lenses or mantos; (g) textural evidencefor replacement; (h) sequential formation of the deposits, includingprograde and retrograde mineralization stages; (i) occurrence of lateveins (typically rich in quartz and fluorite) adjacent to the dikes; and(j) the ore (sphalerite, galena, pyrrhotite, pyrite, chalcopyrite andarsenopyrite) and (k) gangue (dominantly pyroxene and garnet)mineralogy. The adscription of the FIM deposit to CRD-style skarndeposits significantly enlarges the prospective area for these inMexico towards the south, thus increasing the regional potential forbase metal exploration.
Most of the CRD-style skarn deposits, as well as the FIM deposit,are blind or poorly exposed (Megaw,1998). Therefore, the exploration
Fig. 12. Histogram showing mol% FeS in sphalerite (electron microprobe data) from theFrancisco I. Madero deposit. Abbreviations: Cal — calcite; Chl — chlorite; Dol —
dolomite; Ep — epidote; Gn — galena; Gt — garnet; Mrc — marcasite; Po — pyrrhotite;Py — pyrite; Q — quartz; Sp — sphalerite.
for such deposits is complex and should be supported by geophysicaltechniques (Megaw, 1998).
8. Conclusions
The petrography andmineral chemistry of themineral associationsallowed us to properly characterize the deposit model of acontroversial, and metallogenetically and economically importantdeposit. The FIM deposit is a distal, dike-related, Zn skarn akin to theCarbonate Replacement Deposits, a style of skarn mineralization thatis relatively common in the Southern Cordillera of North America.Prograde and retrograde mineralizing stages produced overprintedand recrystallized paragenesis. The prograde stage caused theextensive occurrence of manganoan hedenbergite and minor andra-ditic garnet, whereas the retrograde assemblage consists essentially ofepidote, chamosite and quartz, and is accompanied by an extensivedeposition of base metal (Zn–Cu–Pb) sulfides, pyrrhotite, pyrite andminor arsenopyrite.
Temperature of formation of the retrograde skarn, estimated fromarsenopyrite and chlorite geothermometry, ranges from 300° to340 °C, and from 243° to 277 °C, respectively. The average pressureestimated from the sphalerite geobarometry is 2.1 kbar, correspondingto a moderately deep skarn, and is in agreement with the high Cucontents in this deposit. The classification of the FIM deposit as a CRD-style skarn may increase the expectative for regional exploration ofbase metal deposits.
Acknowledgements
This project was sponsored by Industrias Peñoles, SA de CV.We aregrateful to the IGCP Project 502 (2004–2008). The SEM-EDS andWDSanalyses and BSE images were obtained at the Laboratorio Universi-tario de Petrología (LUP), and petrography studies were performed inthe Laboratorio de Yacimientos Minerales, both located in the InstitutodeGeofísica, Universidad Nacional Autónoma de México (UNAM). RufinoLozano Santa Cruz and Teresa Pi Puig are thanked for the XRD analysesthat were carried out in the Instituto de Geología (UNAM). JavierGarcía-Fons, Lepoldo González (Industrias Peñoles, SA de CV) and J.Richard Kyle are thanked for their assistance and comments during
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fieldwork. J.A. Saunders, Z. Chang, S.I. Franco, N.J. Cook and ananonymous reviewer are thanked for their comments, which allowedus to improve this paper.
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