2.5       Applications of MC-ICP-MS to radiogenic isotopes

 

            MC-ICP-MS is a more expensive technology than conventional TIMS, both to build and to operate. This is because the instruments have several complex engineering systems, involving the RF generator, the torch assembly with its argon supply, and the ion extraction system with its pumps, in addition to the magnetic sector analyser. Hence, MC-ICP-MS is most effectively applied to isotope systems where TIMS has encountered technical difficulties. A few of these systems will be described.

 

 

2.5.1    HfW

 

182W is the decay product of the short-lived nuclide 182Hf (t1/2 = 9 Myr). As an extinct nuclide 182Hf can place important constraints on the origin and early history of the Solar System, but the very high ionisation potential of tungsten (7.98 eV, similar to osmium) precludes its analysis as a positive ion by TIMS. The first high-precision W isotope measurements were made by negative ion TIMS, but MC-ICP-MS proved ideally suited to the analysis of this element. Following the establishment of the method (Lee and Halliday, 1995), these authors made numerous W isotope analyses of meteoritic and planetary samples, throwing new light on the timing of terrestrial core formation and the formation of the solar nebula (section 15.5.4).

 

 

2.5.2    LuHf

 

The LuHf isotope system was first exploited using positive TIMS analysis (section 9.1), but the high ionisation potential of hafnium (6.65 eV) has always rendered TIMS Hf analysis difficult,  requiring large sample size and high purity ion exchange separation in order to achieve good results. The ability of MC-ICP-MS to achieve excellent ionisation on impure sample solutions makes the method ideal for Hf isotope analysis. Whole-rock samples containing as little as 100 ng Hf can be analysed after pre-concentration only (Blichert-Toft et al., 1997), and zircons can be analysed in situ using a laser probe MC-ICP-MS (Thirlwall and Walder, 1995). Previously, TIMS analysis of Hf also required a very demanding chemical separation method (Patchett and Tatsumoto, 1980), Hence, for all of these reasons, MC-ICP-MS has effectively rendered TIMS analysis of hafnium obsolete.

 

 

2.5.3    UTh

 

Thorium is another element with a high ionisation potential (6.97 eV). It is routinely analysed by TIMS, but the poor ionisation efficiency is a significant problem, particularly for samples with large common thorium (232Th) contents (section 13.1). Such samples are well suited to simultaneous analysis on a Faraday and Daly collector. In this approach the small 230Th beam is analysed on a Daly or multiplier collector, while the large 232Th beam is analysed simultaneously on a Faraday collector (e.g. Luo et al., 1997). In order to calibrate the relative gain of the Daly and Faraday collectors, Luo et al. added uranium of known isotopic composition directly to the Th sample. The 235U/238U ratio measured on two Faraday collectors is used for mass fractionation correction of both U and Th, while the 234U/235U ratio is used to calibrate the Daly/Faraday collector gain. Results for the Table Mountain Latite standard showed excellent external (between run) precision, as well as internal (within run) precision. In more recent work, the method was used successfully to duplicate TIMS analyses of  carbonate samples (Shen et al., 2002) and igneous rock analysis (Pietruszka et al., 2002).

 

 

2.5.4    PbPb

 

Pb isotope analysis has long been performed by TIMS, but the existence of only one stable non-radiogenic isotope has always made mass fractionation the principal source of analytical error. Mass fractionation occurs in the plasma source, but it is almost completely independent of the chemistry of the species involved. Therefore, the two stable isotopes of thallium (202 and 205) can be used to make accurate fractionation corrections for Pb (Walder and Furuta, 1993).

 

            More detailed experiments (White et al., 2000) appeared to show small differences in the mass fractionation behaviour of Pb and Tl, although these could be corrected for. Some minor problems were also found by Thirlwall (2002) and attributed to subtle solution chemistry effects in the nebuliser. However, Collerson et al. (2002) observed coherent fractionation behaviour between Pb and Tl, demonstrated by plotting interference-corrected raw ratios for both elements on a log-log plot. Hence, they were able to obtain accurate fractionation-corrected Pb isotope data on several different types of sample, with an average reproducibility of ca. 300 ppm.

 

            It is concluded that MC-ICP-MS can achieve accuracies of Pb isotope analysis approaching  those produced by the much more experimentally demanding double spiking methods using TIMS (section 2.4.2). Therefore it can be expected that MC-ICP-MS will take over from TIMS as the preferred method for Pb isotope analysis where large samples suites must be analysed to high precision. This would apply to studies of igneous petrogenesis, and especially to Pb isotope analysis as a environmental tracer, such as in the study of seawater evolution from the analysis of ferromanganese crusts (Christensen et al., 1997).

 

 

2.5.5    UPb

 

Another area where MC-ICP-MS has been successfully applied is the in situ UPb analysis of zircons by laser ablation, for applications in geochronology. An infra-red or (more usually) an ultra-violet laser is used to ablate the sample inside a small chamber which is at atmospheric pressure. The atomic sample cloud in the chamber is carried to the plasma by the argon ‘sampler’ gas flow, and is then ionised in the plasma in the usual way (Fig. 2.25).

Fig. 2.25. Schematic illustration of the procedure for feeding laser ablated material into the ICP source. After Halliday et al. (1998).

 

            Walder et al. (1993a) used a glass standard to calculate the efficiency of laser ablation MC-ICP-MS for ion production. They found that the efficiency was comparable with ion microprobe analysis using the SHRIMP (section 5.2.3). However, because the volume of sample excavated by laser ablation can be larger than with the SHRIMP, laser ablation MC-ICP-MS can generate ion beams large enough for analysis by multiple Faraday collectors (Halliday et al., 1998). Hence the instrument is potentially capable of generating ages with higher precision than the SHRIMP. The instrument used by Halliday et al. (1998) was fitted with a wide flight tube to permit simultaneous analysis of U and Pb.

 

            Some problems remain in the accurate calibration of U/Pb ratios measured during the laser ablation process. However, Horn et al. (2000) proposed that 202Tl, 205Tl and 235U spike could be added by solution nebulization to the gas stream from laser ablation of the sample. Use of a zircon standard showed that elemental U/Pb fractionation during ablation could be quantified for a given laser power, spot size, and depth of excavation. This calibration procedure then allowed U/Pb fractionation during sample ablation to be calibrated. Pb mass fractionation during beam extraction from the plasma was also corrected. Horn et al. applied this procedure on a quadrupole ICPMS, whose ultimate precision is limited to ca. " 1% (2F) by the instability of the plasma. However, the use of this spiking technique in combination with MC-ICP-MS offers the possibility of matching the dating precision of ion microprobes such as the SHRIMP (section 5.2.3).

 

 

2.5.6    SmNd

 

Experiments to test the effectiveness of MC-ICP-MS for Nd isotope analysis were reported by Walder et al. (1993b) and Luais et al. (1997). Most analyses were made in static multi-collection mode, but a few multi-dynamic analyses gave similar results to static analysis. It was shown that Sm interference corrections could be made very accurately, so that Nd isotope ratio determinations could be made on bulk REE separates from a cation column, without secondary clean-up to remove Sm. In addition, the typical analysis time was only 20 minutes per sample.

 

            Disadvantages of the ICP method were the longer instrument setup times, the need to analyse more standards, and the slightly lower external (between run) reproducibility. This was found to be ca. 30 ppm over short periods, but 60 ppm over a period of a year. However, a more recent study (Vance and Thirlwall, 2002) suggests that this lower reproducibility was due to the inadequacy of the exponential law to correct for the large fractionation factors encountered with ICP, which are more consistent than TIMS fractionation effects, but usually more than an order of magnitude larger. Vance and Thirlwall showed that these problems could be solved using information from the fractionation of additional non-radiogenic ratios, therefore allowing MC-ICP-MS to generate reproducibilities comparable with TIMS. However, TIMS Nd analysis is simpler and cheaper, making it accessible to a wider range of users. Therefore, it appears that Nd isotope analysis will be a niche where TIMS will be applied for some time to come.

 

 

References

 

Arden, J. W. and Gale N. H. (1974). New electrochemical technique for the separation of lead at trace levels from natural silicates. Anal. Chem. 46, 2)9.

 

Aston, F. W. (1919). A positive ray spectrograph. Phil. Mag. (Series 6), 38, 707––14.

Aston, F. W. (1927). The constitution of ordinary lead. Nature 120, 224.

 

Barovich, K. M., Beard, B. L., Cappel, J. B., Johnson, C. M., Kyser, T. K. and Morgan, B. E. (1995). A chemical method for hafnium separation from high-Ti whole-rock and zircon samples. Chem. Geol. (Isot. Geosci. Sect.) 121, 303–8.

 

Blichert-Toft, J., Chauvel, C. and Albarede, F. (1997). Separation of Hf and Lu for high-precision isotope analysis by magnetic sector-multiple collector ICP-MS. Contrib. Mineral. Petrol. 127, 248–60.

 

Brooks, C., Wendt, I. and Harre, W. (1968). A two-error regression treatment and its application to Rb)Sr and initial Sr87/Sr86 ratios of younger Variscan granitic rocks from the Schwarzwald massif, Southwest Germany. J. Geophys. Res. 73, 6071)84.

 

Brooks, C., Hart, S. R. and Wendt, I. (1972). Realistic use of two-error regression treatments as applied to rubidium-strontium data. Rev. Geophys. Space Phys. 10, 551)77.

 

Cameron, A. E., Smith, D. H. and Walker, R. L. (1969). Mass spectrometry of nanogram-size samples of lead. Anal. Chem. 41, 525)6.

 

Cassidy, R. M. and Chauvel, C. (1989). Modern liquid chromatographic techniques for the separation of Nd and Sr for isotopic analyses. Chem. Geol. 74, 189)200.

 

Catanzaro, E. J. and Kulp, J. L. (1964). Discordant zircons from the Little Butte (Montana), Beartooth (Montana) and Santa Catalina (Arizona) Mountains. Geochim. Cosmochim. Acta 28, 87)124.

 

Chen, J. H. and Wasserburg, G. J. (1981). Isotopic determination of uranium in picomole and sub-picomole quantities. Anal. Chem. 53, 2060)7.

 

Christensen, J. N., Halliday, A. N., Godfrey, L. V., Hein, J. R. and Rea, D. K. (1997). Climate and ocean dynamics and the lead isotopic records in Pacific ferromanganese crusts. Science 277, 913–8.

 

Clayton, D. D. (1978). On strontium isotopic anomalies and odd-A p-process abundances. Astrophys. J. 224, L93)5.

 

Collerson, K. D., Kamber, B. S. and Schoenberg, R. (2002). Applications of accurate, high-precision Pb isotope ratio measurement by multi-collector ICP-MS. Chem. Geol. 188, 65–83.

 

Compston, W. and Oversby, V. M. (1969). Lead isotopic analysis using a double spike. J. Geophys. Res. 74, 4338)48.

 

Cotte, M. (1938). Recherches sur l’optique electronique. Ann. Physique 10, 333)405.

 

Crock, J. G., Lichte, F. E. and Wildeman, T. R. (1984). The group separation of the rare-earth elements and yttrium from geologic materials by cation-exchange chromatography. Chem. Geol. 45, 149)63.

 

Croudace, I. W. (1980). A possible error source in silicate wet-chemistry caused by insoluble fluorides. Chem. Geol. 31, 153)5.

 

Crumpler, T. B. and Yoe, J. H. (1940). Chemical Computations and Errors, Wiley, pp. 189)90.

 

Daly, N. R. (1960). Scintillation type mass spectrometer ion detector. Rev. Sci. Instrum. 31, 264)7.

 

David, K., Birch, J. L., Telouk, P. and Allegre, C. J. (1999). Application of isotope dilution for precise measurement of Zr/Hf and 176Hf/177Hf ratios by mass spectrometry (ID–TIMS/ID–MC–ICP–MS). Chem. Geol. 157, 1–12.

 

Davis, D. W. (1982). Optimum linear regression and error estimation applied to U)Pb data. Can. J. Earth Sci. 19, 2141)9.

 

Dawson, P. H. (1976). (Ed.), Quadrupole Mass Spectrometry and its Applications. Elsevier, 349 p.

 

DeBievre, P. J. and Debus, G. H. (1965). Precision mass spectrometric isotope dilution analysis. Nucl. Instrum. Meth. 32, 224)8.

 

Dempster, A. J. (1918). A new method of positive ray analysis. Phys. Rev. 11, 316-24.

 

DePaolo, D. J. and Wasserburg, G. J. (1976). Nd isotopic variations and petrogenetic models. Geophys. Res. Lett. 3, 249)52.

 

Dickin, A. P., Jones, N. W., Thirlwall, M. and Thompson, R. N. (1987). A Ce/Nd isotope study of crustal contamination processes affecting Palaeocene magmas in Skye, NW Scotland. Contrib. Mineral. Petrol. 96, 455)64.

 

Dodson, M. H. (1978). A linear method for second-degree interpolation in cyclical data collection. J. Phys. E (Sci. Instrum.) 11, 296.

 

Dodson, M. H. (1963). A theoretical study of the use of internal standards for precise isotopic analysis by the surface ionisation technique: Part I - General first-order algebraic solutions. J. Sci. Instrum. 40, 289)95.

 

Dosso, L. and Murthy, V. R. (1980). A Nd isotopic study of the Kerguelen islands: inferences on enriched oceanic mantle sources. Earth Planet. Sci. Lett. 48, 268)76.

 

Eberhardt, A., Delwiche, R. and Geiss, J. (1964). Isotopic effects in single filament thermal ion sources. Z. Natur. 19a, 736)40.

 

Edwards, R. L., Chen, J. H. and Wasserburg, G. J. (1987). 238U)234U)230Th)232Th systematics and the precise measurement of time over the past 500,000 years. Earth Planet. Sci. Lett. 81, 175)92.

 

Eugster, O., Tera, F., Burnett, D. S. and Wasserburg, G. J. (1970). The isotopic composition of gadolinium and neutron capture effects in some meteorites. J. Geophys. Res. 75, 2753)68.

 

Faul, H. (1966). Ages of Rocks, Planets, and Stars. McGraw-Hill, 109 p.

 

Gale, N. H. (1970). A solution in closed form for lead isotopic analysis using a double spike. Chem. Geol. 6, 305)10.

 

Galer, S. J. G. (1999). Optimal double and triple spiking for high precision lead isotopic measurement. Chem. Geol. 157, 255)74.

 

Habfast, K. (1983). Fractionation in the thermal ionization source. Int. J. Mass Spectrom. Ion Phys. 51, 165)89.

 

Halliday, A. N., Lee, D.-C., Christensen, J. N., Rehkamper, M., Yi, W., Luo, X., Hall, C. M., Ballentine, C. J., Pettke, T. and Stirling, C. (1998). Applications of multiple collector- ICPMS to cosmochemistry, geochemistry, and paleoclimatology. Geochim. Cosmochim. Acta 62, 919)40.

 

Hamelin, B., Manhes, G., Albarede, F. and Allegre, C. J. (1985). Precise lead isotope measurements by the double spike technique: a reconsideration. Geochim. Cosmochim. Acta 49, 173)82.

 

Hooker, P., O’Nions, R. K. and Pankhurst, R. J. (1975). Determination of rare-earth elements in U.S.G.S. standard rocks by mixed-solvent ion exchange and mass spectrometric isotope dilution. Chem. Geol. 16, 189)96.

Horn, I., Rudnick, R. L. and McDonough, W. F. (2000). Precise elemental and isotope ratio determination by simultaneous solution nebulization and laser ablation-ICP-MS: application to U–Pb geochronology. Chem. Geol. 164, 281–301. (Erratum = vol. 167, 405–25.)

 

Houk, R. S. (1986). Mass spectrometry of inductively coupled plasmas. Anal. Chem. 58, 97A–105A.

 

Houk, R. S., Fassel, V. A., Flesch, G. D., Svec, H. J., Gray, A. L. and Taylor, C. E. (1980). Inductively coupled argon plasma for mass spectrometric determination of trace elements. Anal. Chem. 52, 2283–9.

 

Ingram, M. G. and Chupka, W. A. (1953). Surface ionisation source using multiple filaments. Rev. Sci. Instrum. 24, 518)20.

 

Kalsbeek, F. and Hansen, M. (1989). Statistical analysis of Rb)Sr isotope data by the ‘bootstrap’ method. Chem. Geol. (Isot. Geosci. Section) 73, 289)97.

 

Krogh, T. E. (1973). A low contamination method for hydrothermal decomposition of zircon and extraction of U and Pb for isotopic age determination. Geochim. Cosmochim. Acta 37, 485)94.

 

Kuritani, T. and Nakamura, E. (2002). Precise isotope analysis of nanogram-level Pb for natural rock samples without use of double spikes. Chem. Geol. 186, 31–43.

 

Kurz, E. A. (1979). Channel electron multipliers. Amer. Lab. 11 (3), 67)74.

 

Lee D.-C. and Halliday, A. N. (1995). Precise determinations of the isotopic compositions and atomic weights of molybdenum, tellurium, tin and tungsten using ICP source magnetic sector multiple collector mass spectrometry. Int. J. Mass Spec. Ion Process. 146/147, 35–46.

 

Li, W. X., Lundberg, J., Dickin, A. P., Ford, D. C., Schwarcz, H. P., McNutt, R. H. and Williams, D. (1989). High-precision mass spectrometric uranium-series dating of cave deposits and implications for paleoclimate studies. Nature 339, 534)6.

 

Luais, B., Telouk, P. and Albarede, F. (1997). Precise and accurate neodymium isotopic measurements by plasma-source mass spectrometry. Geochim. Cosmochim. Acta 61, 4847)54.

 

Ludwig, K. R. (1980). Calculation of uncertainties of U)Pb isotope data. Earth Planet. Sci. Lett. 46, 212)20.

 

Ludwig, K. R. (1997). Isoplot. Program and documentation, version 2.95. Revised edition of U.S. Geol. Surv. Open-File report 91-445 (kludwig@bgc.org).

 

Lugmair, G. W., Scheinin, N. B. and Marti, K. (1975). Search for extinct 146Sm, 1. The isotopic abundance of 142Nd in the Juvinas meteorite. Earth Planet. Sci. Lett. 27, 79)84.

 

Luo, X., Rehkamper, M., Lee, D.-C. And Halliday, A. N. (1997). High precision 230Th/232Th and 234U/238U measurements using energy-filtered ICP magnetic sector multiple collector mass spectrometry. Int. J. Mass Spec. Ion Process. 171, 105–17.

 

McIntyre, G. A., Brooks, A. C. Compston, W and Turek, A. (1966). The statistical assessment of Rb)Sr isochrons. J. Geophys. Res. 71, 5459)68.

 

Manton, W. I. (1988). Separation of Pb from young zircons by single-bead ion exchange. Chem. Geol. (Isot. Geosci. Section) 73, 147)52.

 

Noble, S. R., Lightfoot, P. C. and Scharer, U. (1989). A new method for single-filament isotopic analysis of Nd using in situ reduction. Chem. Geol. (Isot. Geosci. Section) 79, 15)19.

 

Nier, A. O. (1940). A mass spectrometer for routine isotope abundance measurements. Rev. Sci. Instrum. 11, 212)16.

 

O’Nions, R. K., Hamilton, P. J. and Evensen, N. M. (1977). Variations in 143Nd/144Nd and 87Sr/86Sr ratios in oceanic basalts. Earth Planet. Sci. Lett. 34, 13)22.

 

O’Nions, R. K., Carter, S. R., Evensen, N. M. and Hamilton P. J. (1979). Geochemical and cosmochemical applications of Nd isotope analysis. Ann. Rev. Earth Planet. Sci. 7, 11)38.

 

Papanastassiou, D. A., Huneke, J. C., Esat, T. M. and Wasserburg, G. J. (1978). Pandora’s box of the nuclides. In: Lunar Planet. Sci. IX, Lunar Planet. Sci. Inst., Houston, Texas, pp. 859)61 (abstract).

 

Parrish, R. R. (1987). An improved micro-capsule for zircon dissolution in U)Pb geochronology. Chem. Geol. (Isot. Geosci. Section) 66, 99)102.

 

Parrish, R. R. and Krogh, T. E. (1987). Synthesis and purification of 205Pb for U)Pb geochronology. Chem. Geol. (Isot. Geosci. Section) 66, 103)10.

 

Patchett, P. J. (1980). Sr isotopic fractionation in Ca)Al inclusions from the Allende meteorite. Nature 283, 438)41.

 

Patchett, P. J. and Tatsumoto, M. (1980). A routine high-precision method for Lu)Hf isotope geochemistry and chronology. Contrib. Mineral. Petrol. 75, 263)7.

 

Pietruszka, A. J., Carlson, R. W. and Hauri, E. H. (2002). Precise and accurate measurement of 226Ra–230Th–238U disequilibria in volcanic rocks using plasma ionization multicollector mass spectrometry. Chem. Geol. 188, 171–91.

 

Potts, P. J. (1987). Handbook of Silicate Rock Analysis. Blackie, 622 p.

 

Powell, R., Hergt, J. and Woodhead, J. (2002). Improving isochron calculations with robust statistics and the bootstrap. Chem. Geol. 185, 191–204.

 

Powell, R., Woodhead, J. and Hergt, J. (1998). Uncertainties on lead isotope analyses: deconvolution in the double-spike method. Chem. Geol. 148, 95–104.

 

Richard, P., Shimizu, N. and Allegre, C. J. (1976). 143Nd/146Nd, a natural tracer: an application to oceanic basalts. Earth Planet. Sci. Lett. 31, 269)78.

 

Roddick, J. C., Loveridge, W. D. and Parrish, R. R. (1987). Precise U/Pb dating of zircon at the sub-nanogram Pb level. Chem. Geol. (Isot. Geosci. Section) 66, 111)21.

 

Russell, W. A., Papanastassiou, D. A. and Tombrello, T. A. (1978). Ca isotope fractionation on the Earth and other solar system materials. Geochim. Cosmochim. Acta 42, 1075)90.

 

Shen, C.-C., Edwards, R. L., Cheng, H., Dorale, J. A., Thomas, R. B., Moran, S. B., Weinstein, S. E. and Edmonds, H. N. (2002). Uranium and thorium isotopic and concentration measurements by magnetic sector inductively coupled plasma mass spectrometry. Chem. Geol. 185, 165–78.

 

Smythe, W. R. and Mattauch, J. (1932). A new mass spectrometer. Phys. Rev. 40, 429-

 

Tanaka, T. and Masuda, A. (1982). The La)Ce geochronometer: a new dating method, Nature 300, 515)18.

 

Thirlwall, M. F. (1982). A triple-filament method for rapid and precise analysis of rare-earth elements by isotope dilution. Chem. Geol. 35, 155)66.

 

Thirlwall, M. F. (1991a). High-precision multicollector isotopic analysis of low levels of Nd as oxide. Chem. Geol. (Isot. Geosci. Section) 94, 13)22.

 

Thirlwall, M. F. (1991b). Long-term reproducibility of multicollector Sr and Nd isotope ratio analysis. Chem. Geol. (Isot. Geosci. Section) 94, 85)104.

 

Thirlwall, M. F. (2000). Inter-laboratory and other errors in Pb isotope analyses investigated using a 207Pb204Pb double spike. Chem. Geol. 163, 299)322.

 

Thirlwall, M. F. (2002). Multicollector ICP-MS analysis of Pb isotopes using a 207Pb–204Pb double spike demonstrates up to 400 ppm/amu systematic errors in Tl-normalization. Chem. Geol. 184, 255–79.

 

Thirlwall, M. F. and Walder, A. J. (1995). In situ hafnium isotope ratio analysis of zircon by inductively coupled plasma multiple collector mass spectrometry. Chem. Geol. 122, 241–7.

 

Thompson J.J. (1913). Rays of Positive Electricity and their Application to Chemical Analysis, Longmans, Green and Co. Ltd.

 

Titterington, D. M. and Halliday, A. N. (1979). On the fitting of parallel isochrons and the method of maximum likelihood. Chem. Geol. 26, 183)95.

 

Todt, W., Cliff, R. A., Hanser, A. and Hofmann, A. W. (1996). Evaluation of a 202Pb –  205Pb double spike for high-precision lead isotopic analysis. In: Basu, A. and Hart, S. R. (Eds.) Earth Processes: Reading the Isotopic Code. Geophys. Monograph 95, American Geophysical Union, pp. 429–37.

 

Vance, D. and Thirlwall, M. (2002). An assessment of mass discrimination in MC-ICPMS using Nd isotopes. Chem. Geol. 185, 227–40.

 

Walder, A. J., Abell, I. D., Freedman, P. A. and Platzner, I. (1993a). Lead isotopic ratio measurement of NIST 610 glass by laser ablation-inductively coupled plasma-mass spectrometry. Spectrochim. Acta 48B, 397–402.

 

Walder, A. J. and Furuta, N. (1993). High precision lead isotope ratio measurement by inductively coupled plasma multiple collector mass spectrometry. Anal. Sci. 9, 675-80.

 

Walder, A. J., Platzner, I. And Freedman, P. A. (1993b). Isotope ratio measurement of lead, neodymium and neodymium–samarium mixtures, hafnium and hafnium–lutetium mixtures with a double focussing multiple collector inductively coupled plasma mass spectrometer. J. Anal. Atomic. Spectrom. 8, 19-23.

 

Wasserburg, G. J., Jacobsen, S. B., DePaolo, D. J. McCulloch, M. T. and Wen, T. (1981). Precise determination of Sm/Nd ratios, Sm and Nd isotopic abundances in standard solutions. Geochim. Cosmochim. Acta 45, 2311)23.

 

Wendt, I. and Carl, C. (1991). The statistical distribution of the mean squared weighted deviation. Chem. Geol. (Isot. Geosci. Section) 86, 275)85.

 

White, W. M., Albarede, F. and Telouk, P. (2000). High-precision analysis of Pb isotope ratios by multi-collector ICP-MS. Chem. Geol. 167, 257)270.

 

York, D. (1966). Least-squares fitting of a straight line. Can. J. Phys. 44, 1079)86.

 

York, D. (1967). The best isochron. Earth Planet. Sci. Lett. 2, 479)82.

 

York, D. (1969). Least-squares fitting of a straight line with correlated errors. Earth Planet. Sci. Lett. 5, 320)4.