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In accord with abiogenic experimental studies showing that there should be a negative isotopic fractionation between reduced and oxidized copper minerals ...

Chemical Geology 243 (2007) 238 – 254

Copper isotope fractionation in sedimentary copper mineralization (Timna Valley, Israel) Dan Asael a,⁎, Alan Matthews a , Miryam Bar-Matthews b , Ludwik Halicz b a

Institute of Earth Sciences, Hebrew University of Jerusalem, 91904 Jerusalem, Israel b Geological Survey of Israel, 30 Malchey Israel St., 95501 Jerusalem, Israel

Received 22 March 2007; received in revised form 27 May 2007; accepted 11 June 2007 Editor: D. Rickard

Abstract Copper isotopes (65Cu/63Cu) are potentially powerful new geochemical proxies for oxidation–reduction processes and metallic cycling. This research presents a Cu-isotope study of mineralization in historically mined stratiform sediment-hosted copper (SSC) ore deposits of the Precambrian and Cambrian rocks of the Timna Valley, southern Israel. These deposits provide a natural laboratory for studying isotopic fractionations between Cu-sulphides and Cu(II) minerals (copper carbonates, hydroxides and silicates), formed during sequential cycles of low-temperature alteration of igneous copper porphyries, marine sedimentary diagenesis, and epigenetic mobilization in sandstones. Isotopic measurements were made using MC-ICP-MS after ion chromatographic separation of the copper from matrix elements. In accord with abiogenic experimental studies showing that there should be a negative isotopic fractionation between reduced and oxidized copper minerals, δ65Cu values of Cu-sulphides are significantly lower (− 3.4 to −1.2‰) than coexisting Cu(II) carbonates and hydroxides (− 1.2 to 0.5‰). Cu(II) silicates, which should only show a very small isotopic fractionation relative to parent Cu (II) solutions, give average δ65Cu values of 0.09 ± 0.24‰; consistent with the fact that the primary source of sedimentary copper was the Precambrian igneous rocks. Isotopic zoning profiles in Cu-sulphides of the Cambrian dolomites suggest they were formed through the interaction of small disconnected Cu solution reservoirs with H2S formed by bacterial reduction of sulphate containing pore waters. Mass-balance modeling, based on the measured Cu-isotope compositions and experimental fractionation factors, shows that the main copper reservoir is the Cambrian sandstone–shale sequence and that the Cu-sulphide reservoirs are relatively small. Thus, most of the copper transport occurred in relatively oxidized conditions. The calculated reservoir sizes are in agreement with field observations and confirm that copper isotopes are able to trace both the oxidation–reduction cycles and mass transfer during sedimentary copper mineralization. © 2007 Elsevier B.V. All rights reserved. Keywords: Copper isotopes; Stratiform sediment-hosted copper deposits; Redox isotopic fractionation; Metallic cycling; Cu-isotope reservoir effects; Timna

1. Introduction

⁎ Corresponding author. Tel.: +972 2 658 4758; fax: +972 2 566 2581. E-mail address: [email protected] (D. Asael). 0009-2541/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.chemgeo.2007.06.007

Transition metal stable isotopes (Fe, Cu, Mo) represent a new group of metallic isotopic proxies for paleoenvironmental research that are increasingly

D. Asael et al. / Chemical Geology 243 (2007) 238–254

recognized to be powerful tracers of geochemical oxidation–reduction (redox) processes and metallic element cycling. Theoretical calculations show that transition metal isotopes fractionate during redox processes because the differences in bond length (and hence strength) between oxidized and reduced species will lead to preferential incorporation of the heavy isotope in the oxidized species (Polyakov and Mineev, 2000; Schauble et al., 2001; Anbar et al., 2005; Tossell, 2005). Kinetic isotope fractionations and unidirectional reactions will also influence transition metal isotope processes (Matthews et al., 2001). Consequently, an important research field to which transition metal isotope systems can be applied is sedimentary and low-temperature hydrothermal metallic element redox cycling: where both abiogenic and biogenic redox processes potentially lead to significant isotope fractionations (Albarede and Beard, 2004; Anbar, 2004; Johnson et al., 2004a,b; Johnson and Beard, 2005; Dauphas and Rouxel, 2006). The first 65Cu/63 Cu measurements, made using Thermal Ionization Mass Spectrometry (TIMS) (Walker et al., 1958; Shields et al., 1965), showed large variations of up to 9‰ in natural samples, but also had large analytical errors of 1 to 1.5‰. MC-ICP-MS measurement of the isotopic variations of copper in natural samples with smaller analytical errors (2σ = 0.05‰) were first reported by Marechal et al. (1999) and confirmed a large range of isotopic compositions. These first MC-ICP-MS studies showed that primary igneous copper minerals exhibit a relatively restricted range of δ65Cu values (∼ 0 ± 0.5‰ relative to the SRM 976 copper standard) (Zhu et al., 2000). These observations were later confirmed in studies on copper porphyry igneous rocks and skarns, sea-floor hydrothermal spreading centers and exhalative (VHMS) systems (Zhu et al., 2000; Larson et al., 2003; Mason et al., 2005; Mathur et al., 2005). The most significant fractionations of Cu-isotopes have been observed in low-temperature supergene, hydrothermal, alteration and sea-floor oxidation of Cu(I) minerals (Rouxel et al., 2004; Mathur et al., 2005; Markl et al., 2006). The lowest negative δ 65 Cu values (− 2 to − 4‰) commonly occur in hydrothermal Cu(I)-sulphide minerals (Jiang et al., 2003; Markl et al., 2006), indicating that reduction leads to lighter isotopic compositions. Significant negative isotopic fractionations on forming Cu(I) from Cu(II) solutions at sedimentary temperatures are predicted by inorganic (abiogenic) experimental studies (Fig. 1). Ehrlich et al. (2004) studied the anoxic precipitation of covellite (CuS) from aqueous CuSO4. Their study showed fractionation factors varying from


of Δ65Cu(Cu(II)aq–CuS) = 3.47 ± 0.03‰ at 2 °C to 2.72 ± 0.04‰ at 40 °C. Similar copper isotope fractionation factors (3.02 ± 0.14‰ to 2.66 ± 0.11‰) were measured for Cu(I) sulphides formed by the reaction of pyrite and pyrrhotite crystals with CuSO4 solution under anoxic conditions at 40 °C and 100 °C (Asael et al., 2006). Dissolution experiments involving oxidation of chalcocite and chalcopyrite gave Cu(II) solutions that were isotopically heavier by ca 2.7 and 1.3‰, respectively (Fig. 1; (Mathur et al., 2005)). These probably kinetic fractionations of about 2.5 to 3.5‰ thus characterize redox processes among copper minerals and solutions at sedimentary temperatures. In contrast, where there is no redox reaction, such as during the precipitation of malachite or copper hydroxide from Cu(II) solutions, much smaller fractionations of 0 0.3‰ are measured (Fig. 1; (Marechal and Sheppard, 2002; Ehrlich et al., 2004)). Small fractionations ∼ 0.6‰ have been inferred for ligand-bond substitution (Marechal and Albarede, 2002).

Fig. 1. Summary of experimentally determined Cu(II)aq-Cu(solid) fractionation factors at temperatures of 2–100 °C. Sources and descriptions of the experimental data are given in the legend above the figure. The results are separated into two major groups indicated by grey shaded areas: 1. Experiments involving redox between Cu(II) solutions and Cu-sulphides, where large fractionations of ∼ 2.5 to 3.5‰ are observed; 2. Non-redox experiments involving precipitation of Cu(II) minerals from Cu(II) solutions, where very small fractionations are measured.


D. Asael et al. / Chemical Geology 243 (2007) 238–254

Biological fractionations are less studied. Zhu et al. (2002) observed − 1.5 to − 1.0‰ fractionation between the copper taken up by enzymes and the parent Cu(II) solution and considered this to reflect preferential incorporation of the lighter isotope. On the other hand, Mathur et al. (2005) found that isotopically heavy copper is adsorbed by iron-oxidizing bacterial cellular material. This work presents a first systematic study of the 65 Cu/ 63 Cu fractionation associated with sedimenthosted stratiform copper (SSC) mineral deposits. SSC ores are a world-class mineral deposit type and include the giant deposits of the Kupferschiefer of North Central Europe and the copper-belt of Central Africa (Robb, 2005). The historically-mined copper deposits exposed in the Cambrian sediments of the Timna Valley of southern Israel (Fig. 2a) represent a relatively small economic deposit of this type, but provide a natural laboratory for studying redox fractionations of copper isotopes because of the occurrence of coexisting Cu(I)sulphides and Cu(II) minerals. This study primarily

addresses the magnitude and mechanisms of the copper isotope fractionation associated with redox and nonredox processes at sedimentary temperatures. However, at Timna, in common with many multi-stage ore deposition systems, a major problem is accounting for the effects on fractionation of the amount of mass transfer among the various sources and sinks (‘reservoir affects’). Thus, to examine these reservoir effects using the isotopic data we have developed a flow diagram and massbalance model that partitions the isotopes among the various sources and sinks. The results show that copper isotopes can provide an effective tracer of metallogenic redox cycling. 2. Geological setting SSC deposits form where connate fluids in clastic sediments scavenge detrital copper in neutral mildly oxidizing conditions. These fluids then ascend or move laterally into a reducing sedimentary environment (e.g., carbonaceous shales, siltstones, carbonates), where they

Fig. 2. a. Map showing the location of the Timna Valley; b. A Stratigraphic section of the Timna valley (after Segev, 1986), showing the Precambrian and Cambrian rocks of the Timna valley. The symbols Cu indicates the rock sequences studied in this work for their Cu-isotope geochemistry. The following acronyms are given in the stratigraphic section and are used in the paper: TIC — Timna Igneous Complex, CMD — Cambrian Dolomite, and CMSS — Cambrian Sandstones and Shale.

D. Asael et al. / Chemical Geology 243 (2007) 238–254

precipitate a variety of copper minerals at the redox front, predominantly Cu-sulphides (covellite (CuS), chalcocite (Cu2S), chalcopyrite (CuFeS2), and bornite (Cu5FeS4)), depending on the concentration of ions in solution and Eh–pH conditions (Brown, 1992, 1997; Oszczepalski, 1999; Robb, 2005). The Timna Valley is a half-crater shaped valley, truncated in the east by the Dead Sea Transform (Fig. 2a). Its continuation across the transform is found approxi-


mately 100 km north at Feinan, Jordan (Freund et al., 1970; Bender, 1974). A stratigraphic section of the Precambrian–Cambrian rocks of the Timna Valley is given in Fig. 2b. The Timna Valley exposes copper porphyry granites and quartz porphyry dikes of the Precambrian Timna Igneous Complex (TIC) (Wurzburger, 1967; Beyth, 1987). Intense weathering of the Precambrian basement during the Late Precambrian and Early Cambrian provided the source of copper into the

Fig. 3. Photographs of hand specimens (3a, c, e) and SEM back-scattered electron images (3b, d, f) of the copper-bearing rocks studied in this work. a and b. Cu-sulphides, djurleite, (Dj) and anilite (An), with oxidized margins of malachite (Mal) hosted by the middle Cambrian Timna Formation dolomite (Dol); c. Cu-silicates mainly chrysocolla (Chr) in Timna Formation shale; d. Chrysocolla (Chr) replacing a quartz (Qtz) grain in the sandstone of the Timna Formation (Shlomovitch et al., 1999); e and f. Cu-sulphide, chalcocite (Clc), with oxidized margins of Cu(II) minerals in secondary veins in a quartz porphyry from the Timna Igneous Complex. Note the phase intergrowth of the Cu(II) and Cu(I) minerals in (f); the oxidized margins mostly consist of paratacamite whereas the oxidized minerals within the sulphides are mostly malachite.


D. Asael et al. / Chemical Geology 243 (2007) 238–254

Cambrian Timna basin. The TIC is unconformably overlain and onlapped by a sequence of sedimentary Cambrian rocks consisting of the fluvial sandstones [Amudei Shelomo (Solomon's Pillars) Formation], the Lower Cambrian Timna Formation, and Middle Cambrian continental sandstones of the Shehoret Formation. The Timna Formation consists of the lower Member (Hakhlil) overlain by the upper Member (Sasgon), which formed in a marine lagoonal–sabkha environment during a marine transgression. Copper mineralization predominantly occurs in the sandstones, dolomites and shales of the Sasgon Member (Fig. 2b), as well as in the Shehoret Formation sandstones (Bentor, 1956; Wurzburger, 1967; Garfunkel, 1970; Bartura and Wurzburger, 1974; Segev, 1986; Shlomovitch et al., 1999). Lower Cretaceous Formations, which unconformably overlie the Cambrian sediments, also feature minor copper mineralization, most probably derived by reworking of the Cambrian deposits (Kedar, 1984). These Lower Cretaceous cupriferous sandstones are not studied in this work, which is restricted to the Cambrian and Precambrian rocks. Intense erosion and peneplainization of the Timna igneous rocks has left few exposures of the copper porphyry rocks. Primary igneous copper minerals in the exposed rocks have undergone secondary temperature alteration (most probably supergene), and only minute relics of igneous chalcopyrite are found (Wurzburger, 1967). Sedimentary Cu-sulphides occur in dolomite rocks of the Timna Formation as dispersed mm to cm sized spherules (Fig. 3a and b). The dolomites are strictly mangano-dolomites with up to 2.8 wt.% manganese as Mn2+ in the dolomite lattice (Bar-Matthews, 1987; Segev and Sass, 1989). The Cu-sulphides are interpreted to have formed in reducing conditions during early diagenesis (Shlomovitch et al., 1999). These Cusulphides were then replaced by Cu(II) minerals in two stages: 1) alteration to malachite (Cu2(OH)2CO3), which armours and sometimes completely replaces the sulphide minerals and is the only time that this mineral formed in the Cambrian sedimentary sequence; 2) development of paratacamite (Cu2(OH)3Cl) as veins emanating from the sulphides and cross-cutting the dolomitic rocks. Copper silicates are principal minerals of the sandstones and shales of the Timna and Shehoret Formations. Optical microscope and scanning electron microscope (SEM) studies show that these minerals formed by the reaction of quartzo-feldpathic minerals with Cu(II) solutions (Charach et al., 1976; Shlomovitch et al., 1999; Fig. 3d). The high abundance of copper in sandy lithofacies of the Timna Formation has also been

attributed to in-situ copper pre-concentration resulting from karstic dissolution of the carbonate fraction of precursor sandy dolomites (Segev and Sass, 1989). Early studies proposed that deposition occurred through stratiform syngenetic sedimentation in lagoons (Bentor, 1956; Wurzburger, 1967; Bartura and Wurzburger, 1974). Charach et al. (1976) later proposed that weathering of the Precambrian porphyries transported copper into the lowermost clastic sandstone sequences, and that subsequent mobilization of copper into the overlying sediments was induced by migrating groundwater. Mixing of groundwater with saline marine water during the marine transgression would provide the solutions necessary for the transport of copper, either as Cu(II) chloride complexes in relatively oxidized conditions or as CuCl32− complex in intermediate redox conditions (Renfro, 1974; Rose, 1976; our own calculations using The Geochemist's Workbench version 4.03). The Cu-bearing rock samples studied in this work are: 1) Cambrian dolomites, containing spherules of Cusulphides, partially or completely altered to malachite and paratacamite (Fig. 3a and b); 2) Cambrian sandstones and shales, containing veins of Cu-silicates (Fig. 3c and d); and 3) copper porphyry from the TIC containing secondary supergene Cu-sulphides and Cu (II) minerals (Fig. 3e and f). Because primary copper minerals are not found in the Timna Valley igneous rocks, six Cu-sulphide samples (chalcopyrite, bornite, covellite) from the Copper porphyry ore deposits at Butte, Montana were analyzed for comparative purposes. 3. Analytical methods 3.1. Sample preparation Dolomite and copper porphyry samples were first sawn into thin slices in order to expose as many Cusulphides as possible. The rock slices were then drilled using a 1 mm diameter diamond drill in the dark sulphiderich cores and blue-green envelopes (Cu(II) minerals) (Fig. 3a and e). Other samples, such as paratacamite veins in dolomites, and veins of Cu-silicates, were separated from their host rock by crushing and hand picking. Mineral phase identification was performed using X-ray powder diffraction (XRD) using a Bruker D8 Advance Xray diffractometer at the Hebrew University Center for Nanoscience and Nanotechnology and by SEM at the Geological Survey of Israel (GSI) (JEOL-840 combined with LINK-10000 energy dispersive spectrometer). The elemental chemical composition of samples was determined at the GSI with a Perkin Elmer Optima Inductively

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Table 1 Mineralogy of the different Cu-bearing rocks studied in this work determined by X-ray diffraction Formation

Mineral type

Major minerals

Minor minerals


Cu sulphide Cu(II)


Cu sulphide Cu(II) Cu(II)

Chalcocite, Malachite Paratacamite Djurleite, Covellite Malachite Chrysocolla, Plancheite

Covellite, Paratacamite Malachite Paratacamite Paratacamite Bronchantite


in a helium atmosphere at 25 °C. The CO2 was then chromatographically separated from other gases and analyzed using the Gas Bench II preparation system and the Thermoquest Delta XL mass spectrometer at the Hebrew University. The malachite-water oxygen isotope analyses were corrected with the CO2-calcite acid fractionation factor of 1.01025 at 25 °C (Melchiorre et al., 1999). Dolomite analyses are corrected using an acid fractionation factor of 1.01103 (Northrop and Clayton, 1966). 3.3. Copper isotope measurement

Fig. 4. a. Calibration of solution matrix effects on the copper isotope analyses in this study. Measurements were conducted using sample standard bracketing and using internal Ni standard mass-bias correction. The δ65Cu values are plotted as a function of the [Cu]/[X] ratio in ppm where X represents the contaminating ion. The grey bar represents the analysis of a pure solution with δ65Cu = 0.10 ± 0.20‰ (i.e., a range considered acceptable for Cu-isotope analysis without chromatography); b. Results of experiments in which a copper solution prepared from malachite was contaminated with varying amounts of dolomite (indicated by the ratio [Cu]/[X] in ppm, where X = [Ca + Mg]). Two series of experiments were performed (see text): purified–solution purified using the chromatographic procedure of Marechal et al. (1999) and Ni mass-bias correction; non-purified solution analyzed without chromatographic purification. Diamonds represent solutions after chromatographic separation with 0.1‰ error bars where dots represent non treated solutions with 0.1‰ error bars. Grey bar indicates the pure malachite δ65Cu value of − 0.17 ± 0.05‰ (95% confidence level).

Isotopic compositions are reported in this work using the δ65Cu notation in permil relative to the SRM 976 standard and fractionations are given as: Δ65Cu(A − B) = δ65Cu(A) − δ65Cu(B). Sample powders were first dissolved: 1) Cu-sulphide and Cu-carbonate samples were dissolved in 10 ml of 0.1 N HNO3 and Cusilicates were dissolved in a 40% hydrofluoric acid mixed with 7 N HNO3; 2) the solution was chemically analyzed by ICP-OES, using Sc as an internal standard and the

Coupled Plasma Optical Emission Spectrometer (ICPOES). The typical error of these measurements is ±2% of the absolute concentration. 3.2. O and C isotopic measurements δ18O PDB and δ13C PDB values of malachite (replacing Cu-sulphides) and the host-rock dolomite were also determined using continuous flow procedures. CO2 was extracted off-line by phosphoric acid reaction

Fig. 5. δ18O and δ13C values of malachite and host-rock dolomite samples from the Timna Formation.


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Table 2 Copper isotope compositions measured in this study Sample




Precambrian Basement — quartz porphyry

Cu(II)-minerals Cu-sulphide Cu(II)-minerals Cu-sulphide Cu(II)-minerals Cu-sulphide Cu(II)-minerals Cu-sulphide Cu(II)-minerals Cu-sulphide Cu-sulphide Cu(II)-minerals Cu-sulphide Cu(II)-minerals Cu-sulphide Cu(II)-minerals Cu-sulphide Cu(II)-minerals Cu-sulphide Cu(II)-minerals Cu-sulphide Cu(II)-minerals Cu-sulphide Cu(II)-minerals Cu-sulphide Cu(II)-minerals Cu-sulphide Cu(II)-minerals Cu-sulphide Cu(II)-minerals Cu-sulphide Cu(II)-minerals Cu-sulphide Cu(II)-minerals Cu-sulphide Cu(II)-minerals Cu-sulphide Cu(II)-minerals Cu-sulphide Cu(II)-minerals Cu-sulphide Cu(II)-minerals Cu-sulphide Cu(II) -minerals Cu-sulphide Cu-silicate Cu-silicate Cu-silicate Cu-silicate Cu-silicate Cu-silicate Cu-silicate Cu-silicate Cu-silicate Cu-silicate Cu-silicate

Precambrian Basement — quartz porphyry Precambrian Basement — quartz porphyry Precambrian Basement — quartz porphyry Precambrian Basement — quartz porphyry Precambrian Basement — quartz porphyry Precambrian Basement — quartz porphyry Precambrian Basement — quartz porphyry Precambrian Basement — quartz porphyry Cambrian Timna Formation — dolomite Cambrian Timna Formation — dolomite Cambrian Timna Formation — dolomite Cambrian Timna Formation — dolomite Cambrian Timna Formation — dolomite Cambrian Timna Formation — dolomite Cambrian Timna Formation — dolomite Cambrian Timna Formation — dolomite Cambrian Timna Formation — dolomite Cambrian Timna Formation — dolomite Cambrian Timna Formation — dolomite Cambrian Timna Formation — dolomite Cambrian Timna Formation — dolomite Cambrian Timna Formation — dolomite Cambrian Timna Formation — sandstone and shale Cambrian Timna Formation — sandstone and shale Cambrian Timna Formation — sandstone and shale Cambrian Timna Formation — sandstone and shale Cambrian Timna Formation — sandstone and shale Cambrian Timna Formation — sandstone and shale Cambrian Timna Formation — sandstone and shale Cambrian Timna Formation — sandstone and shale Cambrian Timna Formation — sandstone and shale Cambrian Timna Formation — sandstone and shale Cambrian Timna Formation — sandstone and shale

δ65Cu(SRM-976)‰ I


0.39 − 1.70 0.30 − 1.83 0.10 − 3.41 0.04 − 3.32 − 0.35 − 2.52 − 1.72 − 0.77 − 1.63 0.22 − 2.43 0.47 − 2.26 − 1.22 − 1.74 − 1.02 − 3.26 − 1.18 − 1.39 − 0.56 − 1.82 − 1.10 − 1.22 − 0.89 − 1.24 − 1.16 − 2.82 − 1.16 − 2.80 − 0.82 − 2.52 − 0.21 − 2.06 − 0.38 − 2.20 − 0.64 − 1.83 − 0.56 − 2.06 − 0.69 − 2.22 − 0.46 0.06 − 0.20 0.05 0.09 0.12 0.12 0.07 0.27 0.23 0.35

0.52 − 1.57 0.44 − 1.75 0.07 − 3.47 0.13 − 3.43 − 0.28 − 2.46


− 0.77 − 1.65 0.28 − 2.40 0.36 − 2.30 − 1.23 − 1.73 − 0.91 − 3.10 − 1.22 − 1.45 − 0.71 − 2.00 − 1.19 − 1.32 − 0.89 − 1.22 − 2.51 − 1.16 − 0.66 − 2.53 − 0.26 − 2.04 − 0.11 − 2.22 − 0.66 − 1.75 − 0.57 − 2.06 − 0.79 − 2.22 − 0.47 − 0.26 0.09 0.08 0.07 0.12 0.13 0.34 0.31 0.26

− 2.81

− 0.10 0.09

Mean 0.45 − 1.63 0.37 − 1.79 0.09 − 3.44 0.08 − 3.37 − 0.31 − 2.49 − 1.72 − 0.77 − 1.64 0.25 − 2.42 0.41 − 2.28 − 1.23 − 1.73 − 0.96 − 3.18 − 1.20 − 1.42 − 0.64 − 1.91 − 1.14 − 1.27 − 0.89 − 1.24 − 1.19 − 2.66 − 1.16 − 2.80 − 0.74 − 2.62 − 0.24 − 2.05 − 0.25 − 2.21 − 0.65 − 1.79 − 0.56 − 2.06 − 0.74 − 2.22 − 0.47 − 0.10 − 0.20 0.07 0.08 0.03 0.11 0.10 0.31 0.27 0.31

Δ65Cu (Cu(II)– Cu(I)) 2.08 2.16 3.52 3.46 2.18

0.87 2.67 2.70 0.51 2.22 0.22 1.27 0.13 0.35 1.48 1.64 1.88 1.81 1.96 1.14 1.50 1.48

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Table 2 (continued) Sample



δ65Cu(SRM-976)‰ I

CMSS 12 CMSS 13 Butte 1 Butte 2 Butte 3 Butte 4 Butte 5 Butte 6

Cambrian Timna Formation — sandstone and shale Cambrian Timna Formation — sandstone and shale Pre-main-stage, Steward mine⁎ Main stage, Leonard mine⁎ Main stage, Leonard mine⁎ Mountain Con mine, level 4200⁎ Pre-main-stage, Leonard mine⁎ Pre-main-stage, Leonard mine⁎

Cu-silicate Cu-silicate Chalcopyrite Chalcopyrite + covellite Chalcopyrite + covellite Bornite + chalcopyrite Bornite Bornite

II 0.39 0.45 0.06 0.21 0.67 0.65 0.35 0.28

III 0.27 0.34


Δ65Cu (Cu(II)– Cu(I))

0.33 0.40


⁎Samples provided by the Montana Bureau of Mines.

appropriate amounts of copper in solution taken for plasma mass spectrometry. The copper isotope measurements were made on a Nu Plasma™ MC-ICP-MS at the GSI. Samples were introduced to MC-ICP-MS as 1 ppm solutions in 0.1 N HNO3, using an Aridus liquid sample introduction system with aerosol desolvation. The isotopic measurements were made using standard-sample-standard bracketing technique relative to the SRM 976 copper standard (Zhu et al., 2000). Early work on impure sample solutions showed that a major problem exists of mass discrimination and matrix effects especially when ions such as Ca2+, Na+ and K+ are present in the solution (Marechal et al., 1999; Albarede and Beard, 2004). Marechal et al. (1999) used ion-exchange purification of copper for natural silicate samples and Zn internal standard to give an accuracy of ± 0.04 (2σ), whereas Ehrlich et al. (2004) worked with a Ni internal standard and standard-sample–standard bracketing without ionexchange to get results with 1σ of ± 0.06‰ for synthetic samples. Archer and Vance (2006) improved analytical quality and stability by running both standard and the samples through chemical separation. For this study a working procedure was developed for the specific impure materials (i.e., malachite contaminated with dolomite; copper silicates with quartz and feldspar). 3.3.1. Calibration of the internal Ni standard matrix effect correction A series of experiments was made, in which pure copper solution with δ65Cu = 0.1 ± 0.06‰ was contaminated with different amounts of the ions: Ca, Mg, Fe, Si, Na and K. Fig. 4a displays the results of these experiments on a graph of δ65Cu versus the [Cu]/ [contaminant ion] ppm ratio. For most ions, it was found that the Ni internal standard correction gives reasonable values with 1σ limits set at 0.10‰ when the [Cu]/ [contaminating ion] ratio is greater than 0.1. For Na and

K, however, poor analyses are obtained even when the [Cu]/[contaminating ion] ratio is less than 1 and for other ions when this ratio is less than 0.1. Ni-mass bias correction by itself is therefore, of limited applicability. 3.3.2. Ion-exchange purification and Ni-matrix correction Six solutions were prepared from mixtures of pure malachite with δ65Cu = − 0.17 ± 0.06‰ (2σ) with different amounts of dolomite. A portion of each solution chromatographically purified using the method of Marechal et al. (1999) and the purified and non-purified solutions were measured several times on different days. The results (Fig. 4b) show a significant improvement of precision in the purified samples (2σ = 0.05‰) compared to samples that were not treated by chromatography (2σ = 0.12‰). The latter analyses also show a strong negative drift with decreasing [Cu]/[contaminant ion] ratio (Fig. 4b). Thus, both mass bias correction using Ni internal standard, as described by Ehrlich et al. (2004) and sample purification by chromatographic separation (Marechal et al., 1999), were used in the analyses. Recovery was 95 ± 5%. SRM 976 standard solution samples taken through the full protocol gave δ65Cu = 0.01 ± 0.06‰ (2σ). Almost all measurements were made with duplicate column chemistry extractions and MC-ICP-MS analyses. Long term mass spectrometric drift was independently monitored by running a separate pure Cu-solution (δ65Cu = 0.10 ± 0.06‰), prepared by dissolving copper wire in nitric acid, against the SRM 976 standard. 4. Results 4.1. Mineralogy and petrography Table 1 summarizes the mineralogy. Major sulphide minerals in the Cambrian dolomites are djurleite


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(Cu1.93S), anilite (Cu1.75S), both solid-solution minerals of the covellite–chalcocite series, together with covellite (Shlomovitch et al., 1999). Paratacamite sometimes appears in very small amounts in the sulphide separates and is attributed to cross-contamination during drilling. The main mineral of the oxidized envelope surrounding the Cu-sulphides is malachite with small amounts of paratacamite (Fig. 3a). No residual sulphide mineral was identified in these rim powders. The main minerals of the sulphide separates from the altered copper porphyries are chalcocite and covellite. However, XRD also indicates the presence of malachite in these powders. Paratacamite is the dominant mineral in the oxidized parts (Fig. 3e). Color differences evident in the hand specimens of the copper spherules in the Cambrian dolomites (Fig. 3a) are clearly shown by SEM-BEI where djurleite is overgrown by anilite in the sulphide part and malachite in the oxidized rim of the spherules (Fig. 3b). Replacement of silicate minerals by chrysocolla in the sandstones is shown in Fig. 3d. Secondary sulphides and Cu(II) minerals in the copper porphyries show more complex intergrowth relations (Fig. 3e); thus, accounting for the difficulty in obtaining pure sulphide separates by drilling. The presence of malachite rather than paratacamite (the dominant mineral of the oxidized parts) in the sulphide powders suggests that it is derived by atmospheric carbonation and hydration of chalcocite and covellite, as commonly observed in copper porphyries being open caste mined today. 4.2. C and O isotope composition of Cambrian malachites and dolomites The stable isotope measurements of the carbonate of dolomites and malachites are plotted on a δ13C versus δ18O diagram in Fig. 5. The δ18O values have similar ranges for both dolomites and malachites (ca − 9 to − 4‰), although δ13C values of the malachite are on average about 0.5‰ lower than those of dolomites. The majority of analyses fall within the range of δ180 and δ13C values (δ18O − 7 to 0‰; δ13C − 4.5 to − 0.5‰) determined for diagenetic dolomites by Bar-Matthews and Matthews (1989). 4.3. Copper isotope compositions The δ65Cu results for the sulphide and Cu(II) mineral separates are presented in Table 2 and summarized in Fig. 6a. The samples of primary igneous porphyry copper minerals from Butte, Montana analyzed during this work gave δ65Cu values averaging at 0.37 ± 0.24‰

(Table 2), and are consistent with other studies of igneous porphyries. The most notable aspect of the results is the significant difference between the low δ65Cu values of the Cu-sulphide minerals and the higher values of coexisting Cu(II) minerals (Fig. 6a). δ65Cu values of the Cu-sulphides range from − 3.5 to − 1.6‰ in the porphyries (TICS) and − 3.2 to − 1.3‰ in the Cambrian dolomite (CMDS), compared to − 0.8 to +0.4‰ in the oxidized rims of the copper porphyry (TICO) and − 1.2 to − 0.1‰ in the dolomites (CMDO). The copper silicate minerals of the Cambrian sandstones, which did not undergo any redox cycle, have δ65Cu values close to zero (0.09 ± 0.24‰). The isotopic fractionations between the coexisting sulphide and Cu(II) mineral phases are plotted on a δ65Cu (Cu-sulphide) vs. δ65Cu (Cu(II) minerals) diagram in Fig. 6b. Diagonal lines indicate different values of the fractionation factor Δ65Cu(Cu(II)mineral-Cusulphide). The measured fractionations vary between 0.2‰ and 3.5‰, with a mean value of 1.7 ± 0.9‰. The data do not show any linear distribution along a particular fractionation line (the equilibrium array), but the maximum measured fractionation factors are similar to those found in experimental studies (Fig. 1). In order to check if the δ65Cu variations of the Cusulphides could reflect isotopic zoning, we made a number of core to margin profiles on some of the larger spherules in the Cambrian dolomites. The results are given in Table 3 and plotted in Fig. 7. There are positive zoning trends toward higher isotopic compositions from core to margin of the Cu-sulphide, followed by a marked jump to the Cu(II) mineral envelope. 5. Discussion 5.1. Isotopic compositions and fractionations among reduced and oxidized copper phases The principal observation of this study is that copper isotopes are significantly fractionated between reduced Cu-sulphide minerals (djurleite, covellite, chalcocite, anilite) and coexisting oxidized copper minerals. It should be noted that despite contradictory views regarding the valency of copper in minerals such as covellite and chalcopyrite, the most recent mineralogical studies have shown that copper exists as the Cu(I) ion in all of these phases (Luther et al., 2002; Goh et al., 2006). Cross-contamination cannot account for the wide range of fractionation between Cu-sulphide and Cu(II) minerals. High resolution XRD studies indicate that the Cu-sulphide spherules in the Timna dolomites are

D. Asael et al. / Chemical Geology 243 (2007) 238–254


Fig. 6. a. Summary of the δ65Cu analyses of the copper minerals from the Timna Valley (data from Table 1). The sample locations are placed in their relative stratigraphic location indicated on the left of the figure. The δ65Cu range for igneous rocks shown by the vertical shaded rectangle is taken from published literature (i.e., 0 ± 0.5‰), the lines connect Cu(I)–Cu(II) mineral pairs. The term Cu(II) minerals covers all Cu(II) minerals formed by oxidation of Cu-sulphides (malachite, paratacamite, chrysocolla etc.); b. δ–δ diagram for Cu(II)–Cu(I) mineral pairs. Samples from the Timna Igneous Complex are shown by diamonds and samples from the Timna Formation dolomite — by open circles. Contours represent constant Δ65Cu (Cu(II)–Cu(I)) fractionation values. Fractionations vary from 0.2‰ to 3.5‰, with a mean value of 1.7 ± 0.9‰. There is no significant distribution parallel to fractionation lines that could indicate an approach to equilibrium (an equilibrium array).

either free of oxidized minerals (as also evident in Fig. 3b) or only contain minor amounts, and no Cusulphide was indicated in the Cu(II) mineral envelope. This was also true of the blue Cu(II) mineral (paratacamite) zones sampled in the TIC copper porphyry. However, the Cu-sulphides of these porphyries contain significant amounts of malachite, whose presence has been attributed to atmospheric carbonation

and hydration. Since there is no net mass transfer of copper in this in-situ alteration of the Cu-sulphides, it should not lead to isotopic fractionation. Thus, the Cusulphides of porphyries are believed to still retain their pre-malachite isotopic composition. Support for this conclusion comes from the fact that these Cu-sulphides have a similar range of values to those of the Timna dolomite spherules (Fig. 6).


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Table 3 Isotopic zoning profiles in copper sulphide spherules Sample



δ65Cu(SRM-976)‰ I



CMDO 15 CMDS 15a CMDS 15b CMDS 15c CMDS 15d CMDS 15e CMDO 16 CMDS 16a CMDS 16b CMDS 16c CMDO 17 CMDS 17a CMDS 17b CMDS 17c CMDS 17d

Cambrian Timna Formation — dolomite

Cu(II)-minerals Cu-sulphide Cu-sulphide Cu-sulphide Cu-sulphide Cu-sulphide Cu(II)-minerals Cu-sulphide Cu-sulphide Cu-sulphide Cu(II)-minerals Cu-sulphide Cu-sulphide Cu-sulphide Cu-sulphide

− 0.86 − 1.98 − 1.89 − 1.85 − 1.84 − 1.74 − 0.20 − 2.35 − 1.78 − 1.58 − 0.16 − 2.22 − 2.18 − 2.07 − 2.04

− 1.06 − 1.90 − 1.89 − 1.86 − 1.82 − 1.73 − 0.17 − 2.27 − 1.74 − 1.42 − 0.03 − 2.26 − 2.18 − 2.16 − 1.92

− 0.96 − 1.94 − 1.89 − 1.85 − 1.83 − 1.73 − 0.19 − 2.31 − 1.76 − 1.50 − 0.09 − 2.24 − 2.18 − 2.11 − 1.98

Cambrian Timna Formation — dolomite

Cambrian Timna Formation — dolomite

Our overall interpretation of the variable isotopic compositions and fractionations is that zoning and cross-contamination do not contribute a major part. This implies that the dominant effect is the ‘reservoir effect’, reflecting variable mass transfer of copper between the various sources and sinks. 5.2. Controls of isotopic composition in specific lithologies 5.2.1. Altered copper porphyry The alteration of the copper porphyry is not directly related to the formation of the Cu-sulphides in the dolomites. Following Wurzburger (1967), our view is that these minerals were formed during cycles of lowtemperature supergene alteration of the Cu-bearing porphyries. The timing of this alteration is not constrained. However, the intense erosion and weathering of the igneous rocks (key features of supergene alteration) that took place during the Late Precambrian– Early Cambrian would have resulted in vertical fluctuations of the water table and could have produced alternations in redox conditions, allowing both reduced and oxidized copper minerals to form. 5.2.2. Diagenetic dolomites C and O isotope compositions in Timna Formation dolomites were shown to be consistent with diagenetic dolomitization at temperatures of 25–55 °C (BarMatthews and Matthews, 1989). The isotopic properties of malachite have been shown to be similar to those of calcite (Melchiorre et al., 1999). Thus, at equilibrium with dolomite, malachite carbonate should have slightly

Δ65Cu (Cu(II)– Cu(I)) 0.98



lower δ18O values than the dolomite (Sheppard and Schwarcz, 1970; Matthews and Katz, 1977). The similar ranges found in this study are compatible with precipitation of malachite from pore fluids that had exchanged with dolomites at very low water/rock ratios. Lower δ18O values (− 10 to − 7‰) may suggest higher diagenetic temperatures. On the other hand, the slight carbon isotope fractionation between dolomite and malachite (Fig. 5) suggests that there was an overall equilibrium exchange between the two phases, possibly via the intermediary carbonate solution species. The correspondence in the C and O isotope composition of the

Fig. 7. Diagram illustrating the Cu-isotopic zoning in three samples of Cu-sulphides spherules from the Timna Formation dolomite. From right to left the samples are plotted according to their relative position of drilling. The grey shaded vertical bar identifies the copper isotope analysis of the malachite rim. Mild positive zoning is observed in the Cu-sulphides, but a sharp positive shift is always found between the copper sulphide margin and the malachite envelope.

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Cambrian dolomites and malachites shown in Fig. 5 favors the interpretation that they (and the Cu-sulphide spherules) were formed during the same diagenetic event, as also interpreted on textural grounds by Shlomovitch et al. (1999). The range of Cu-isotopic zoning in the sulphide varies from 0.2‰ to 0.8‰ (Fig. 7). Such positive zoning is consistent with enrichment of a solution in the heavy isotope when a low δ65Cu mineral is formed (i.e., a mild reservoir effect associated with a negative fractionation). However, the cores of the different sulphide spherules show a δ65Cu variation of more than 1‰ (Fig. 7), indicating that the Cu-sulphides initially formed with different δ65Cu values. The Cu-isotopic zoning and variability of δ65Cu values in Cu-sulphide spherules suggest that they formed from small disconnected Cu solution reservoirs. 34 δ S values of the spherules range from − 14.9 to − 13.7‰ (Shlomovitch et al., 1999) and were attributed to early diagenetic reduction of Cambrian marine sulphate. This suggests that bacterial sulphate reduction (BSR) in anoxic pore waters was main mechanism allowing the Cu(I)-sulphide minerals to form through the reaction of percolating limited volumes of Cu(II) solution with H2S. The degree of BSR and H2S pro-


duction must be relatively small compared to the mass of Cu transported through the system and only sufficient to partition a fraction of the Cu to sulphides. BSR has been suggested to be an important aspect of SSC deposition processes (Haynes, 1986a,b). The negative δ65Cu values of Cu-sulphides clearly represent an overall negative fractionation with respect to an original copper porphyry source with δ65Cu values of ∼ 0‰. In the classical models of SSC deposition, metals are leached from detrital minerals derived from the erosion of a metal-bearing basement assemblage (Brown, 1997; Robb, 2005). In this case the original ‘fertile’ basement was the copper porphyries of the TIC, but as noted in Section 5.2.1, it is considered likely that the secondary alteration predated the erosional transport of copper from the igneous complex. The formation of malachite and paratacamite requires a rise in Eh and carbonated and chloride aqueous fluids (Rose, 1976). Consequently, the formation of the malachite/paratacamite with significantly higher δ65Cu values requires the infiltration of a Cu(II) solution to the Cu-sulphide interface. The δ65Cu value of the malachite envelope therefore reflects both Cu(II)–Cu-sulphide fractionation and mass-balance between the Cu-sulphides and the infiltrating Cu(II) solution.

Fig. 8. Flow diagram used to calculate the mass–balance relationship between the various copper reservoirs in the Timna Precambrian–Cambrian system. All copper is considered to originate with a bulk earth value BE (i.e., that of primary igneous rocks). This provides the overall Cu(II) solution (SOL) that is partitioned among the various sources and sinks. See text and Fig. 6 for definition of symbols. Stages that do not involve redox (indicated by dashed arrows) are assumed zero fractionation; stages involving either reduction or oxidation (indicated by full arrows) are assumed a fractionation factor of Δ65Cu(Cu(II)–Cu(I)) = 2.5‰.


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5.2.3. Copper silicates in the Cambrian sandstones Copper silicates (mainly chrysocolla, plancheite) are the major ore minerals in the Timna valley. Since they occur in Shehoret sandstones overlying the dolomites, as well as the Timna Formation sandstones, their formation must at least partly post-date the diagenetic SSC processes in the dolomites. The mobilization of copper under oxidizing conditions implies that only part of the total available copper was mobilized during sulphide formation. Experimental data on the copper isotope fractionation during the formation of Cu(II) minerals from Cu(II) solutions (Fig. 1) suggest that the formation of the copper silicates should involve a very small fractionation. Thus, the δ65Cu values of 0.09 ± 0.24‰ for the copper silicates are close to the values of the Cu (II) solutions from which they formed. This provides the strongest evidence that the parent solutions for the copper mineralization in Timna had δ65Cu values close to the value of igneous rocks.

fractionation is assumed only to occur during redox processes, for which a fractionation factor of Δ65Cu(Cu (II)–Cu(I)) = 2.5‰ is taken for both the reduction and oxidation reaction (Fig. 1). All other processes (i.e., those not involving copper valency change) are assumed to occur with a fractionation factor of zero permil. An additional assumption is that there is no overall loss or gain of copper in the system: potential loss to Lower Cretaceous sandstones is not taken into account because of the relatively small amounts of copper present in these rocks. The calculation is made using Matlab software and provides a best fit match between calculated model δ65Cu values and the average measured δ65Cu values of the copper-bearing reservoirs: TICO = 0.02 ± 0.43‰; TICS = − 2.38 ± 0.71‰; CMDO + − 0.75 ± 0.39‰; CMDS = − 2.01 ± 0.43‰; and CMSS = 0.09 ± 0.24‰. Each copper reservoir is described by a vector consisting of two elements, where the first element contains the amount of 63Cu and the second the amount of 65Cu. The

5.3. Mass-balance modeling of copper isotope fractionation The critical processes leading to isotopic fractionation are those involving reduction to form low δ65Cu Cu-sulphides and the subsequent oxidation. The measured isotopic fractionations between reduced and oxidized phases (Fig. 6b) are, however, variable and smaller than those determined in experimental studies (Fig. 1). As indicated in Section 5.1, we consider this to be a reflection of mass-balance constraints during the transfer of copper from source to sink (reservoir affects). In order to address this problem we have created a massbalance calculation based on a model system involving transfer of copper isotopes to and from the various reservoirs. The model scheme is shown in Fig. 8. The flow diagram based on a source reservoir (SOL), which represents all the copper from the original igneous basement that is mobilized during the mineralization. This reservoir is assumed to have a δ65Cu value of 0‰ (i.e., the igneous or bulk earth value). This reservoir is then sequentially partitioned between the various sources and sinks: the TIC copper porphyry Cu (II) minerals and Cu-sulphides (TICO and TICS); the Cambrian Cu(II) solution (CMSL); the Cambrian dolomite Cu-sulphides and oxides (CMDS and CMDO) and finally the Cambrian sandstones (CMSS). The scheme allows for sinks to become sources (e.g., the TICO and TICS secondary minerals can also become a detrital source for the Cambrian copper solutions (CMSL) and the CMSL, CMDS and CMDO can provide the source of the CMSS). Copper isotope

Fig. 9. Results of the isotopic mass-balance calculation: a. Shows the fit between the calculated δ65Cu values given by the mass-balance model and the mean measured values (shown with their standard deviation). The shaded rectangle shows the range of δ65Cu values associated with igneous rocks. b. Shows the percentage size of each reservoir given by the mass-balance calculation; most notable are the dominance of Cu(II) minerals over Cu(I) sulphides and the overall dominance of the Cambrian sandstone reservoir (CMSS).

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Fig. 10. Three stages in the evolution of the Precambrian–Cambrian copper mineralization system in the Timna Valley, based on published field and petrographic data and the Cu, C, O isotope composition data of this study.

transfer of Cu from one reservoir to another is made using an external Matlab function, which takes as an input the fractionation factor and the size ratio between the two reservoirs. The output is the amount of each isotope (each vector element) that needs to be transferred. Each model run gives as an output a matrix with the different reservoir sizes, the predicted δ65Cu values of the different reservoirs, and the Δ65Cu(Cu (II)–Cu(I)) difference between coexisting phases (e.g., TICO–TICS and CMDO–CMDS). In order to evaluate the fitness of each run to the measured isotopic compositions, a comparison of this output matrix and a matrix of the measured values is conducted using a statistical objective function which sums the square of the differences between the calculated and the measured δ65Cu and Δ65Cu(Cu(II)–Cu(I)) values. A lower value of the function implies a better fit. The model results are given in Fig. 9. Fig. 9a shows the correspondence of the calculated δ65Cu values to the average measured values and Fig. 9b presents the % mass

of copper partitioned among the various reservoirs. The main observations of the mass-balance calculation are: 1) The δ65Cu values produced by the model are in agreement with the measured values and hence, show a very similar pattern, where the Cu(II) sinks have the higher isotope compositions (TICO = 0.12‰; CMDO = − 0.75‰ and CMSS = 0.09‰) and the Cusulphide sinks show lighter compositions (TICS = − 2.38‰ and CMDS = − 2.01‰). 2) The major reservoirs of copper minerals are the Cu(II) minerals, where the CMSS is markedly the largest (TICO = 9.5%, CMDO = 6.4% and CMSS = 81.9%). 3) The Cu-sulphide reservoirs contain only minor amounts of copper (TICS = 0.5% and CMDS = 1.7%) and each one is considerably smaller than its coexisting Cu(II) mineral phase. These observations are in accord with field observations, which show that copper silicates are the dominant


D. Asael et al. / Chemical Geology 243 (2007) 238–254

copper mineral reservoir of Timna Valley. Assuming that CMDO and TICO minerals are formed by oxidation reaction of Cu-sulphides with infiltrating copper solutions, the maximum amount of sulphide formed is b 18%. The Timna Cambrian mineralization is clearly a mildly oxidized Cu(II) dominated system and differs from giant SSC copper deposits such as the Kupferschiefer of Poland where sulphides are the major copper minerals, clearly operating under more reducing conditions. A schematic diagram, consistent with the isotopic modeling, illustrating the various stages of the copper mobilization from Precambrian igneous rocks to Cambrian sediments is given in Fig. 10. 6. Conclusions This study of the Precambrian–Cambrian Timna copper deposits shows that copper isotopes are powerful geochemical tracers of redox transformations and metallic cycling in sedimentary conditions. Well defined Cu-isotope fractionations are shown to occur during both oxidation and reduction reactions. The low δ65Cu values of the Cu-sulphides (among the lowest yet measured) reflect the negative fractionation that occurs during the reduction of Cu(II)aq to give Cu-sulphides, whereas the in-situ oxidation of the Cu-sulphides is associated with a positive fractionation giving Cu(II) minerals with δ65Cu values approaching 0‰. The variability in Δ65Cu(Cu(II)–Cu(I)) values of the natural samples is largely attributed to reservoir effects in open system conditions. The correspondence between the δ65Cu values of the silicates (0.09 ± 0.24‰) and the range of igneous porphyries supports the view that the primary source of copper is the Precambrian basement. Massbalance modeling of the isotopic system shows that the silicate reservoir constitutes 82% of the copper in the system, compared to the 3% of the all of the Cu-sulphides. Although the calculations in this study are based on a set of simple fractionation and mass transfer assumptions, and the fact that we have ignored isotopic zoning and cross-contamination, it does appear to show that complex multistage isotope systems can be realistically modeled using Cu-isotope data and fractionation factors. Moreover, the calculation shows that copper isotope fractionation can be explained in terms of experimental abiogenic fractionation factors. Thus, in contrast to iron isotope systems, where dissimilatory iron reducing bacteria may play an important role in the isotopic cycle (Crosby et al., 2005; Johnson and Beard, 2005; Yamaguchi et al., 2005; Archer and Vance, 2006; Severmann et al., 2006; Staubwasser et al., 2006),

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