2.3 Magnetic
sector mass spectrometry
In a typical ‘magnetic sector’ instrument (Fig.
2.1) the nuclides to be separated are ionised under vacuum and accelerated
through a high potential (V) before
passing between the poles of a magnet. A uniform magnetic field (H) acting on particles in the ion beam
bends them into curves of different radius (r)
according to the following equation:
m
2V
r2 = ) @ )) [2.4]
e
H2
where m/e = mass/charge for the ion in question.
Since most of the ions produced by TIMS or ICP sources are single-charged, the
different isotopes in the sample will be separated into a simple spectrum of
masses. The relative abundance of each mass is then determined by its
corresponding ion current, captured by a Faraday bucket or a multiplier
detector.
2.3.1 Ion optics
The ion optic properties of an instrument
determine how the cloud of ions generated in the source is accelerated,
focussed into a beam, separated by the magnetic field, and collected for
measurement. Correct ion optic alignment is essential to obtain reliable
results, because if part of the ion beam hits an obstruction, different masses
may be affected to different degrees, leading to a bias in the results.
Most
older mass spectrometers follow Nier’s (1940) design (Fig. 2.1). From the
filament (several kV positive), the beam traverses a series of focussing source
plates (the ‘collimator stack’). These plates are at progressively lower
potential and bring the beam to a principal focus at the source slit (zero
volts). Thereafter, the beam slowly diverges (Fig. 2.14). In the y direction, the magnet brings each
nuclide (isotope) beam back into focus at the primary collector slit, which is
wide enough to let the whole of one nuclide beam through into the collector.
This focussing effect of a sector-shaped magnet was already understood by Aston
(1919).
Fig. 2.14. Schematic diagram of the envelope of
a double nuclide beam from the source slit to the collector slit in a Nier-type
mass spectrometer.
To
bring a heavier nuclide into the collector, the magnetic field may be
increased, or the momentum of the ions may be reduced by lowering the high
voltage (HV) potential across the collimator stack. If the whole of one nuclide
beam is focussed into the collector slit in the y direction, an apparently flat topped peak is produced when
magnetic field or HV is varied to sweep the mass spectrum across the collector
slit (e.g. Fig. 2.15). In practice, the magnetic field rather than the HV is
normally switched to bring different nuclide beams into the collector, because
the field can be more precisely monitored and controlled, using a ‘Hall probe’.
This is used to sense the field strength and adjust the magnet power supply in
a feed-back loop (‘field control’). The magnet (whose pole pieces are
perpendicular to the beam) does not focus in the z direction, and in this direction the beam is ‘clipped’ by baffle
plates.
Fig. 2.15. The appearance of flat topped ‘peaks’
when strontium 88, 87 and 86 nuclide beams are swept across a triple (Faraday)
collector system by varying magnetic field strength.
This
type of magnet design has a disadvantage, because the process of switching from
one mass to another changes ‘fringing fields’ which are generated by the ends
of the magnet poles. The change in these fringing fields may cause slight
convergence or divergence of the beam, so that different amounts of different
nuclide beams are clipped by the collector slit. Hence, a slight bias is
introduced to the beam current reaching the collector, according to whether the
magnet is switching ‘up-mass’ or ‘down-mass’.
Fig. 2.16. The effect of different shaped pole
faces in generating fringing fields which cause focussing of the ion beam in
the y and z planes. a) exit pole piece perpendicular to beam yields short
focal length in the x direction but
no focussing in z. b) normal to exit
pole face (n) is at an angle , to the beam direction, yielding longer focal length in x, and also z focussing.
Instruments
built since 1980 feature refinements in the design of the magnet pole pieces,
based on theoretical work by Cotte (1938). If the pole pieces are set at a
slightly oblique angle to the beam, the fringing fields generated by the magnet
have the effect of focussing the beam in the z direction (Fig 2.16). However, the focussing effect in the y
direction is weakened, so the distance from the magnet exit pole to the
principal focus in the y plane is
increased. Therefore this design is referred to as ‘extended geometry’. Ion
optics in this type of machine are shown in Fig. 2.17. This configuration has
three advantages:
1.
Because the whole of the z-focussed beam can pass through the collector slit,
the transmission of the machine is improved (defined as the number of ions in
the source required to yield each ion at the collector).
2.
Small variations in fringing field do not cause signal bias, so accuracy is
improved.
3.
Extended geometry increases the distance between nuclide beams at the
collector, so that multiple Faraday buckets can be more easily accommodated.
Hence a magnet with 30 cm radius yields a beam separation equivalent to a
magnet with 54 cm radius.
Fig. 2.17. Schematic diagram of the ion optics
of an extended geometry machine between the source and collector slits (compare
with Fig. 2.14).
If
one of the magnet pole faces (e.g. the entry pole) is made slightly convex,
this changes the normally oblique focal plane of nuclide beams in the y direction into a flat plane
perpendicular to the beams (Fig. 2.18). This facilitates the installation of
multiple collectors, whose spacing can then be adjusted to fit ion beams one
atomic mass unit (a.m.u.) apart in any part of the spectrum. However, a more
complex adjustable multiple collector configuration can be constructed on the
oblique focal plane. At higher mass numbers the spacing of the collectors
becomes closer and closer until their outer grounded screens are actually
touching during uranium analysis.
Fig. 2.18. Effect of magnet entry pole face
shape. a) Flat pole face yields oblique curved focal plane at collector; b)
convex pole face yields flat focal plane perpendicular to flight path.
A
very high vacuum throughout the ion path is essential, otherwise the ion beam becomes
scattered, particularly to the low mass side, by inelastic collisions with air
molecules. Such beam scattering becomes serious at analyser pressures > 10!8 mbar. This causes the formation of a tail from
one peak which may interfere with the adjacent nuclide. The problem is
particularly severe in the case of a small peak down mass from a very large
peak. For example, interference by 232Th onto 230Th may
be severe in silicate rocks with 232/230 ratios approaching 106. The
magnitude of interference by a peak on a position one a.m.u. lower is called
the ‘abundance sensitivity’ of the instrument (measured in ppm of the peak
size). A typical specification for a single-focussing TIMS machine with
analyser vacuum < 5 H 10!9 mbar is
2 ppm at 1 a.m.u. from 238U.
If
a very high abundance sensitivity is essential, it can be obtained by adding a
type of ion energy filter between the magnet and collector, thereby creating a
double focussing machine. The ion energy filter has the effect of removing ions
with unusually high or low energy (= velocity). Thus, ions which have suffered
a collision, and therefore lost energy, should be weeded out. Three types of
filter which have been applied to this task are ‘electrostatic’, quadrupole,
and ion retardation types. They typically result in a 10)100 fold improvement in abundance
sensitivity.
2.3.2 Detectors
Ion beams in mass spectrometry normally range
up to ca. 10!10 amps.
For beams as small as 10!13 amps,
the most suitable detector is the Faraday bucket. This is connected to
electrical ground (Fig. 2.1) via a large resistance (e.g. 1011 ohm).
Electrons travel from ground through this output resistor to neutralise the ion
beam, and the potential across the resistor is then amplified and converted
into a digital signal. A typical ion beam of 10!11 amps then generates a potential of 1 volt,
converted to, say, 100 000 digital counts. Traditionally, an indefinite
life-time has been assumed for Faraday buckets. However, the very narrow
buckets in modern multi-collector arrays were found to quickly become coated
inside with sample debris if large beams were analysed. This degraded ion beam
measurements by allowing stray beams to escape from the Faraday. This is now
solved by putting absorbant charcoal blocks in the buckets.
For
ion beams smaller than ca. 10!13 amps, the electrical noise of the Faraday
amplifier becomes significant relative to the signal size, so that some form of
signal-multiplication is necessary. One of the most useful approaches was
pioneered by Daly (1960). In the Daly detector, ions passing into the collector
are attracted by a large negative potential (e.g. 20 kV). Collision of each ion
with the polished electrode surface (Fig. 2.19) yields a secondary electron
shower. When this impinges on a phosphor, the resulting light pulse is
amplified by a photo-multiplier (situated behind a glass window, outside the
vacuum system). In the analogue mode this system can have a gain (ie
amplification) about 100 times the Faraday cup. Because ions do not strike the
multiplier directly, the detector has a long life-time.
Fig. 2.19. Schematic diagram of a Daly detector
showing the means of amplification of an incoming positive ion beam. After Daly
(1960).
The
Daly detector can only be used with positive ion beams. On the other hand,
channel electron multipliers (CEM) can be used to amplify either positive or
negative ion beams. These devices are therefore used for Re and Os analysis by
negative molecular-ion TIMS (section 8.1). The negative ion enters the orifice
of the CEM at a potential near zero, releasing electrons when it strikes the
semi-conducting channel wall. These electrons are multiplied during further
collisions, as they are attracted to a positive HV collector. Because the
collector is at high voltage the signal cannot be amplified directly, but a
pulsed ion-counting signal can be transmitted through an isolating capacitor to
low voltage pulse-counting electronics (e.g. Kurz, 1979). The drawback of CEM
detectors is their tendency to suffer damage when struck by heavy ions.
Therefore signal sizes should be minimised to prolong their life.
2.3.3 Data collection
Depending on the size of the ion beam, it is
necessary to measure each nuclide signal for up to an hour to achieve high
precision data. To achieve this in a single collector TIMS machine the magnetic
field is ‘switched’ to cycle round a sequence of peak positions. On switching
to a new peak there is a waiting period of 1)2 s to allow the output resistor and
amplifier to reach a steady state in response to the new ion current. Then data
are collected for a few seconds. In practice, each peak must normally be
corrected for incomplete decay of the signal from previous peaks (termed
‘dynamic zero’, ‘tau’ or ‘resistor memory’ correction). The computer then
cycles round and round a series of peaks, baseline/background(s) and
interference monitor position(s), interpolating between successive measurements
of the same peak to correct for growth or decay of the beam size. A simple
linear time interpolation may be used (Fig. 2.20), but Dodson (1978) developed
a more sophisticated ‘double interpolation’ algorithm which can make better
allowance for non-linear beam growth or decay.
Fig. 2.20. Schematic illustration of the
principal of linear time interpolation for a strontium ion beam growing at an
(immense) rate of 30% per scan.
Before
isotope ratios can be determined from the different signals, background
electronic noise must be subtracted in order to determine net peak heights. In
TIMS analysis this is done by measuring a baseline position in each collector
channel at approximately 0.4 a.m.u. above a whole mass position, usually a few
a.m.u. away from the masses of interest. In plasma source analysis, background
are often measured under each peak (‘on peak zeros’) before the analysis starts
in order to remove the memory effects of previous samples from the nebuliser.
From
a single cycle of time-interpolated net peak heights, a set of net peak ratios
is extracted. These are often collected in blocks of 10 scans. The cycle time
round a set of peaks may be shortened by the measurement of backgrounds and
interferences ‘between blocks’ rather than ‘within-scan’. For a single
collector TIMS instrument, collecting 200 scans in about 3 hours might give a
statistical within-run precision of 0.004% (2F = 2 standard errors on the mean).
That is, the scatter of data around the mean suggests that one can be 95%
confident that the ‘correct’ answer lies within 0.004% (40 ppm) on either side
of the mean. For 87Sr/86Sr this is equivalent to 0.71000 " 0.00003 (2F).
Occasional
signal ‘spikes’ and other perturbations outside of normal random error are
inevitable in a long mass spectrometer run. It is generally regarded as acceptable
to run through the data a few times and test for outliers which are more than a
certain number of population standard deviations (SD) from the mean (Pierce and
Chauvenet, 1868; in Crumpler and Yoe, 1940). The cut-off level should depend on
the size of data set, so that only a minimal number of outliers resulting from
normal random variation are rejected. In practice the cut-off would normally be
between 2 SD and 3 SD.
Ideally,
a multiple collector machine can analyse isotope ratios in a ‘static’ mode
without peak jumping. However, this may be limited, firstly by the extent to
which each of the Faraday buckets is identical in terms of beam transmission
characteristics; and secondly by the extent to which the gain of each bucket’s
amplifier system can be calibrated. Until the 1990s, these problems did not allow static analysis
to achieve the highest levels of analytical precision, necessary for Sr or Nd
isotope analysis.
The alternative approach for high
precision analysis is double- or triple-collector peak-jumping (multi-dynamic
analysis). The simplest (double-collector) method is given below:
High collector:
87 88 91.4
-
Low collector:
86 87 90.4
85
Place
in sequence 1 2
3 4
After background subtraction, the 85Rb
monitor is used to correct both 87Sr peaks. The following algorithm
represents an approximation, assuming unit mass differences between the
isotopes:
87 | 87 87 1 |0.5
)) = | )) @
)) @ )))) | [2.5]
86true | 861 882 0.1194 |
where suffixes denote places in the scan
sequence. This equation cancels out beam growth or decay and amplifier bias, as
well as performing a power law mass fractionation correction, all in a single
calculation. To use the exponential law for Sr evaporation as the metal, the
function above is raised to the power of 0.5036 (Thirlwall, 1991b). Using
multi-dynamic analysis, within-run precision should reach 0.002% (2F) after 3 hours. Triple-collection
analysis allows a further improvement in efficiency. In this method, two
double-collector determinations on adjacent collectors are averaged to yield a
more precise result.
Unfortunately, while within-run
precision can be taken to lower and lower levels by more efficient sample
ionisation and data collection, between-run reproducibility often reaches a
limiting 2F value of about 0.004% (40 ppm), which is difficult to break through.
Thirlwall (1991b) attributed this phenomenon to imperfect centring of some
peaks during dynamic multiple collection. This occurs because mass separations
decrease as absolute masses increase, so the collectors are actually set
slightly different distances apart. Using the above example, if the three
collectors are set up with masses 86-87 perfectly centred (position 1 in the
sequence) then at position 2 the peaks will be slightly off-centre. This slight
miss-centring may amplify any non-idealities in the optical path of the beam,
so that slightly different source configurations (for different bead numbers)
yield small systematic variations in isotope ratio.
A
more recent development in multi-collector analysis obtains the best compromise
between static and multi-dynamic analysis by allowing the signal from each
Faraday to be switched in turn to each amplifier channel. This cancels out the
electrical gains of the different
amplifiers, without the problem of peak switching. Reproducibilities of 5 ppm
(2F) can then be
achieved on isotope ratio measurements (Finnigan MAT technical report, 2001).
Provided that the ion optic bias of each collector can be accurately
calibrated, this system offers a new level of precision and accuracy in isotope
ratio mass spectrometry. It should be particularly useful for applications such
as seawater Sr, 186Os and 142Nd, where isotopic variations
are at the limits of analytical measurement.
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,
Brooks, C., Hart, S. R. and Wendt,
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 (
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,
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,
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.
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
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
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,
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.
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
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.,
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.,
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 207Pb–204Pb 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
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,
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,
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.
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.