Accurate high-precision 40Ar/39Ar ages are limited, in part, by the degree of accuracy and precision of the measurement of the 36Ar atmospheric Ar contamination correction and the mass spectrometer mass fractionation bias (mass discrimination) correction. To improve the measurements of the low-level 36Ar signals, we have implemented digital ion-counting and multicollector data acquisition methods. The switch to the digital ion pulse counting method results in a tenfold improvement in the signal-to-noise ratio relative to analog electron multiplier measurements that are in general use in most 40Ar/39Ar laboratories. The use of ion pulse counting significantly improves low-level signal (36Ar) measurements. The improvement in low-level 36Ar measurements, however, comes at the cost of a reduced dynamic range of the electron multiplier detector, thus requiring the use of an alternate detector at times, such as a Faraday cup or analog multiplier for large signals. In turn, this requires accurate intercalibration of the detectors. Here we present a protocol that addresses these issues, one that closely tracks changes in the mass spectrometer mass discrimination and the detector intercalibration (IC) factor(s) during the time frame of an experiment, thereby improving measurement accuracy. A major advantage of our protocol is that the procedure uses the same aliquots of atmospheric Ar to monitor mass discrimination and detector IC factors, saving a significant amount of measurement time. In addition, this IC protocol may address the cause of reported inaccuracies in the measured isotopic ratio data on the “new” generation multicollector mass spectrometers. Further, we present a “time series protocol” that monitors any temporal drift in the mass spectrometer mass fractionation bias that can occur due to laboratory environmental changes.
Accurate high-precision 40Ar/39Ar ages are limited, in part, by the degree of accuracy and precision of the measurement of (1) the 36Ar atmospheric Ar contamination correction and (2) the mass spectrometer mass fractionation bias (mass discrimination) correction. These two corrections have a direct influence on the accuracy of the value of the neutron flux monitor “J” (which is obtained from mass spectrometric measurements of the Ar isotopes of a mineral standard) and on the ages of sample unknowns. The accuracy and precision of the 36Ar measurement have significant impacts on determining both of these corrections. When measurements on background/blanks are taken, 36Ar is often at or near baseline values. Hence, 36Ar must be accurately resolved from baseline noise. Any variation or noise in baseline values will adversely affect the quality of the 36Ar measurement. In contrast, 40Ar and 39Ar signals are typically significantly above baseline and background values and are thus less affected. However, experiments on low-radiogenic and geologically young samples, as well as samples of small size and/or low gas yields, may also see adverse affects on 40Ar, 39Ar, 38Ar, 37Ar, and 36Ar measurements due to baseline noise.
The 36Ar measurement, because of its small size, is also a limiting factor in determining the accuracy and precision of the mass spectrometer mass fraction bias, which is any mass-dependent bias introduced by the ionization of the sample gas in the mass spectrometer ion source and detector conversion efficiency. This correction is commonly referred to as the mass discrimination correction. The mass discrimination correction is determined by comparing the measured value of a standard with a known isotopic ratio to the accepted value. In the case of 40Ar/39Ar dating, the isotopic reference standard is generally atmospheric Ar (typically delivered via an online pipette system) with an accepted 40Ar/36Ar ratio of 295.5. (Lee et al.  have recently reevaluated the isotopic ratio of atmospheric Ar and obtained a 40Ar/36Ar value of 298.56 ± 0.31 and a 38Ar/36Ar value of 0.1885 ± 0.0003. The impact of this change in the atmospheric 40Ar/36Ar ratio on 40Ar/39Ar ages is minor if atmospheric Ar was used as the reference standard for determining the mass spectrometer mass discrimination and in the calculation of the irradiation parameter “J” [see Renne et al., 2009a].) The 1 amu mass discrimination (d1amu) is obtained from the following power law relationship:
where Δm is the mass difference between the two isotopes of interest, in this case the mass difference between 40Ar and 36Ar, Ra is the accepted 40Ar/36Ar ratio of atmospheric Ar, and Rm is the measured 40Ar/36Ar ratio of air. If there is no mass bias, the d1amu mass discrimination correction is unity (1). If mass bias enriches the light isotope, then the d1amu mass discrimination correction is greater than unity (e.g., 1.003). Conversely, if the mass bias enriches the heavy isotope, then the d1amu mass discrimination correction is less than unity (e.g., 0.997). Typically, the values for d1amu range from 1.000 ± (0.000–0.006) (±0 to 6‰). This value is used to correct the mass bias for all Ar isotope ratio measurements.
The mass discrimination correction is significant for all samples. However, the correction has the greatest influence on samples with low concentrations of radiogenic 40Ar because the measured 36Ar/39Ar ratio is multiplied by 1/(d1amu)Δm(39Ar−36Ar). (In 40Ar/39Ar dating, the Ar isotopic data are generally reported as ratios normalized to the measured 39Ar signal. Recently, however, new data reporting norms have been suggested by the 40Ar/39Ar in which the relative abundances of argon isotopes (40Ar, 39Ar, 38Ar, 37Ar, and 36Ar), their uncertainties, and the mass discrimination and other data necessary are reported to facilitate better evaluation of published data [see Renne et al., 2009b].) Hence, for every 1‰ variation in mass discrimination correction, there is a 1‰ change in the 40Ar/39Ar ratio and a 3‰ change in the 36Ar/39Ar ratio. The mass discrimination corrected 36Ar/39Ar ratio is then used to correct for atmospheric Ar contamination, based on an accepted 40Ar/36Ar ratio of 295.5 for atmospheric Ar. Thus, any drift in the mass discrimination can have a profound effect on the calculated 40Ar/39Ar age.
Variations and uncertainties in mass discrimination may be unknowingly incorporated within the irradiation monitor measurements used to calculate “J.” This is especially true if both standards and unknowns are of similar radiogenic 40Ar yield and measured closely in time (ideally, an appropriate mineral standard would be interspersed with similar unknowns). However, this is generally not the case; unknowns are measured at different times under different operating conditions or even by different methods. For example, irradiation monitor minerals are generally measured using laser total fusion methods at a different time and under different measurement parameters, such as getter cleanup times, than sample unknowns. In contrast, sample unknowns are typically measured using laser incremental heating or resistance furnace heating methods with longer getter cleanup times. Hence, we suggest that the regular measurements of atmospheric Ar standards delivered via an online pipette system interspersed with sample unknowns can be used to monitor and correct any potential instrumental drift, thus improving the overall quality of the measurements (as discussed in detail below).
As discussed, the 36Ar measurement is used, in part, to determine the mass discrimination correction as well as the atmospheric contamination correction. Consequently, any improvement in the 36Ar measurement will benefit the accuracy and precision of the calculated apparent age of all samples. Thus, a reduction in the signal-to-noise ratio of low-level 36Ar signals would be a direct way to improve the 36Ar measurement.
As part of our effort to improve the quality of 36Ar measurements, we compare a Pfeiffer Vacuum SEM 217 electron multiplier operated in both the analog and digital ion pulse counting modes. In our comparison, the digital ion pulse counting method offers a tenfold improvement in the signal-to-noise ratio relative to analog electron multiplier measurement (Figure 1). This improvement in low-level signal measurement, however, comes at the cost of a reduced dynamic range of the electron multiplier measurement than is typical while operating in the conventional analog mode. Whereas an electron multiplier operated in the analog mode can measure an ion beam as large as 10−12 amps, the same multiplier in the ion pulse counting mode is limited to approximately 10−13 amps (or ∼1.5 × 106 ions per second or less) ion beams. This poses a significant obstacle because the ion beam for the major isotope of Ar, 40Ar, often straddles or exceeds this value (in addition, 39Ar can be too large also when long neutron irradiation times are employed). Under these circumstances, an alternate detector, such as a Faraday cup or possibly an analog multiplier, must be used. This, in turn, requires accurate intercalibration of the various detectors. Because large signals cannot be measured in ion pulse counting mode, the use of the same sample gas for direct intercalibration of the detectors is not possible.
In addition to reporting on the advantages of ion counting for 36Ar measurements, we also present an intercalibration protocol for noble gas mass spectrometers that yields an accurate intercalibration between a Faraday cup detector and an ion pulse counting electron multiplier. This protocol is equally applicable to systems fitted with more than two detectors. A major advantage of our protocol is that the procedure uses the same aliquots of air measured to monitor mass discrimination, saving a significant amount of measurement time. The mass discrimination and detector intercalibration are applied to all measurements that require the use of multiple detectors during the measurement interval. The protocol also addresses a previously unrecognized error invoked with a commonly used procedure for the intercalibration of multiple detectors. The erroneous protocol uses the residual gas, following routine analysis to intercalibrate the different detectors.
Several “new generation” multicollector noble gas mass spectrometers are now becoming available for Ar and other noble gas measurements [e.g., Cosca, 2007; Story et al., 2007; Turrin and Swisher, 2007]. These multicollector mass spectrometers employ one or more ion pulse counting detectors for measuring low Ar isotopic abundances. For ion beam intensities that are too large for the ion pulse counting detectors, the ion beam is measured on a conventional Faraday cup(s). The principle advantages of these multicollector mass spectrometer systems are twofold:
1. Ion pulse counting detectors significantly improve the signal-to-noise ratio relative to the analog electron multipliers. However, upgrading existing noble gas mass spectrometers from an analog electron multiplier to the ion pulse counting system will achieve the same improvement in signal-to-noise ratio as the “new generation” mass spectrometers.
2. Multicollector mass spectrometers have the ability to collect more isotopic abundance data in a shorter period of time, improving the measurement statistics on low-level ion beams. However, some of this advantage is offset by the necessity to then accurately intercalibrate detectors. In some cases, it has been reported that the intercalibration process can lead to inaccuracies as great as 1.5% to 2% in the measured isotopic ratio data [Cosca, 2007; Story et al., 2007; Turrin and Swisher, 2007].
2. Modifications of the MAP 215-50 for Ion Pulse Counting
The initial ion-counting hardware setup described here is a Mass Analyzer Products (MAP) factory configuration, consisting of an Ortec Model 9301 Fast Preamplifer directly connected to the electron multiplier output. The pulse signal output from the Model 9301 Fast Preamplifier is then fed into an Ortec Model 9302 Amplifier/Discriminator before being counted by an Ortec Model 994 Dual Channel Counter/Timer. In parallel to the Model 994 Dual Channel Counter/Timer is an Ortec Model 661 Analog Rate Meter. These components, with the exception of the Model 9301 Fast Preamplifier, are housed in an Ortec Model 4001A Bin. The only change we made to the system was upgrading from a Johnston Laboratories focused mesh electron multiplier to a Pfeiffer Vacuum SEM 217 electron multiplier. We have provided the necessary parts list and drawings to the mass spectrometer multiplier housing (Appendix A and Figure A1) and the performance specifications for the SEM 217 (Figure A2). Once installed, the SEM 217 electron multiplier was characterized in both the analog and ion pulse counting modes using an air pipette system that delivers ∼1 × 10−13 moles Ar and minerals the standards Alder Creek and Fish Canyon sanidines.
Electron multipliers operated in the ion pulse counting mode are typically set up using a procedure similar to the following. Most electron multipliers will start to produce some pulses at about 1.5 to 1.8 kV, so the electron multiplier is preset to a gain corresponding to the ∼2 kV setting. An ion beam of about 10–20 fA is then put on the electron multiplier. The next step is to determine the gain plateau curve for the electron multiplier. This is done by plotting the count rate of the electron multiplier as a function of high voltage/gain. Starting at an unsaturated high voltage/gain (∼1.5–1.8 kV), the count rate will increase until electron multiplier saturates, and the count rate will plateau and define an inflection point, commonly referred to as the “knee” (Figure 2). This plateau region can be as wide as 100 V or as narrow as about 20 V, depending on the discriminator and the characteristic and/or type of the particular electron multiplier. In Figure 2 the “knee” of this particular electron multiplier is about 85 V, 2.0–2.08 kV. Further increasing of the high voltage/gain past the inflection point will result in an increase in count rate with increasing high voltage/gain, indicating that the electron multiplier gain is in the oversaturated region of the gain curve. The electron multiplier is operated in the stable region “knee” of the gain curve. Typically, the analog gain value is on the order of 106 to 107 in the saturated region of the gain curve. However, the actual analog gain value is pretty much meaningless since the electron multiplier detects the actual incident of single incoming ions. For a more detailed discussion on the application of ion pulse counting, see Nelms .
3. Dead Time Correction
The “dead time” (dt) for the ion detection system is governed by the pulse width (in seconds) of the output signal produce by the electron multiplier by an incident ion plus any delays in the preamp, discriminator, and the counter electronics. In a perfectly linear system, any incident ions that strike the front dynode of the electron multiplier do not produce a corresponding pulse, during the time period of the pulse width. Thus, high count rates are lower than indicated. The observed/measured signal is “dead time” corrected using the following standard equation:
where cpsDTc is the dead time corrected electron multiplier signal in counts per second (cps), cpsm is the measured signal in cps, and dt is the dead time in seconds. The stated pulse width specifications are 10 ns for the SEM 217 electron multiplier. The risetime for the Ortec Model 9301 Fast Preamplifer is less than 1.5 ns, approximately 3 ns for the Ortec Model 9302 Amplifier/Discriminator. And the pulse resolution for the Ortec Model 994 Dual Channel Counter/Timer is less than 10 ns. To determine the cumulative dead time for all of these components, the pulse width was measured sequentially on the output end of each component on an HP/Agilent high-speed oscilloscope.
Direct measurement of the detection system dead time correction has been applied in thermal ionization mass spectrometry [Richter et al., 2001] and in multicollector inductively coupled plasma mass spectrometry [Hoffmann et al., 2005]. The advantage of examining the signal output from the various components with an oscilloscope is the ability to check the signal quality. No significant reflections (ringing) were detected in the signal cabling or detector system for this study. The measured pulse width for combined ion detection system that produced the data for this study was 12.3 ± 2 ns.
Another method that is used to determine the dead time correction employs the measurement of the isotopic ratio of a standard over a range of increasing concentrations. When the appropriate dead time correction is applied to the measured apparent ratio, the ratios converge, within error, to a constant isotopic ratio over the range of increasing concentrations [Fahey, 1998]. This approach only works if the electron multiplier has a linear response over the range of concentrations used to determine the dead time correction. It is well documented, however, that electron multipliers do not necessarily have a linear response [Bayer et al., 1989; Richter et al., 2001; Hoffmann et al., 2005]. So we consider the direct measurement approach to be the best method to determine the detection system dead time correction.
In the analog configuration, the electron multiplier was operated at 1.4 kV, which produced a 1.2 × 104 gain of the ion beam. Again, this is a fairly standard configuration for 40Ar/39Ar measurements that employ electron multipliers operated in the analog mode. The electron multiplier analog output current was measured directly on a Keithley Model 617 Programmable Electrometer. The preamp settling time for the Keithley 617 is scale/input dependent. At the pA and nA scales, the 1% settling times are 2.5 s and 15 ms, respectively, so for each peak jump there is a 3 s delay built in before any data are collected. The analog data points shown in Figure 1a consist of three measurements integrated for 0.35 s for a total integration time of 1.05 s.
The baseline “noise” associated with high-gain analog amplifiers is derived from three sources. The first source of noise is internally produced, for example, “flicker noise” caused by irregularities in the circuit such as impurities in a conductive channel, generation and recombination of internal noise in a transistor due to base current, and Johnson-Nyquist noise (thermal noise) of the electronic components generated within the electronic components themselves.
The second source of noise is from what the amplifier receives at the input channel. This includes “shot noise,” the statistical fluctuation of the ion beam, electronic noise (RF) picked up from nearby equipment, and/or noise from the power grid that “leaks” through the signal line shielding. An additional source of noise is the “capacitance” of the mass spectrometer flight tube frame and the path to ground. For a more detailed discussion on the technology on low-level signal measurements, see Horowitz and Hill .
The third source of “noise” is the background natural radioactivity and cosmic rays. However, in the 40Ar/39Ar application, radioactive decay of implanted radioactive isotopes, 37Ar and 39Ar, is the major cause of this high baseline noise. The primary source of this “decay noise” is from 37Ar because of its relatively short half-life of 35 days. Careful attention to minimize the 37Ar concentrations of the sample(s) being measured can keep the 37Ar decay counts to a minimum, but the baseline counts will still show a resultant increase. Figure 3 shows the effect of 37Ar ion implantation on a new SEM 217 electron multiplier in the ion pulse counting mode. The new electron multiplier baseline values averaged 0.69 cps. Samples were loaded into the extraction line and were baked overnight. A series of air pipettes and blanks were measured to characterize the mass discrimination, and then laser step heating experiments were started. Almost immediately, the baselines show a systematic increase. This occurred even though the 37Ar counts were limited to less than four 1 s integrations per cycle and less than 1 × 104 total cps (the points plotted in blue were measured on the Faraday cup and converted to cps using the beam intensity ratio intercalibration described below). This phenomenon of increasing base lines because of 37Ar ion implantation can be observed in the analog mode as well.
4. Ion Pulse Counting Mode Compared to Analog Mode
In Figure 1a the low-level 36Ar signal (plotted in orange) and the multiplier baseline (green circles) are of similar magnitude. The noise on the analog detector baseline has a range of 90 fA. The lowest level of noise that we have been able to obtain on the analog detector is about 20–30 fA, the same magnitude as the low-level 36Ar signal. Thus, the signal-to-noise ratio for the analog detector is ∼1:1.
In contrast, the same SEM 217 multiplier operated in the ion pulse counting mode has a factor of ∼10 better signal-to-noise ratio compared to the analog mode. Figure 1b shows the same the SEM 217 multiplier operated in the ion pulse counting mode. The low-level 36Ar signal (orange triangles) starts at about 100 cps and increases to about 450 cps during the course of the measurement, a time period of ∼1700 s. The multiplier baseline (dark circles in Figures 1b and 1c) is about 4 ± 2 cps during the same time period. This is a factor of ∼10 improvement over the analog detector mode.
On samples with higher-intensity 36Ar signals, such as those encountered when measuring the 40Ar/39Ar age of young, low radiogenic/high atmospheric materials, the improvement is not as dramatic. Nonetheless, there is still improvement in the precision of measured 40Ar/36Ar ratio data. For example, baseline noise of about ±20–30 fA limits the precision of the measured 40Ar/36Ar ratio to about 3 to 6‰. In contrast, the measured 40Ar/36Ar ratio from a similar volume of Ar measured using ion pulse counting shows as much as a 25% improvement in measurement precision (see Table 1 for examples). The measured 40Ar/36Ar ratio for an air pipette sample (A2/3-636) measured just prior to the electron multiplier detector upgrade to ion pulse counting was 284.12 ± 1.13 (±4‰). After the installation of the digital ion pulse counting hardware and software, an air pipette sample of virtually identical size (A2/3-648) yielded a 40Ar/36Ar ratio of 294.22 ± 0.8 (±2.6‰), almost a doubling of precision. In summary, a search of our analog detector air pipette data, collected over several years, indicates that the best overall results obtained for a single air pipette measurement are on the order of 2.5‰. This is compared to the best overall results from the ion pulse counting air pipette data of 2‰, consistent with an approximately 25% improvement in large-signal data acquisition.
Table 1. A Comparison of Ar Isotopic Data Collected on an Analog Detector and an Ion Pulse Counter Detector
23 Nov 2006
16 Nov 2006
Isotopes (nA) ±1σ
1.429603 ± 0.000912 (±00.06%)
1.431533 ± 0.000671 (±00.05%)
0.000906 ± 0.000027 (±02.98%)
0.000908 ± 0.000006 (±00.63%)
0.004907 ± 0.000019 (±00.39%)
0.004859 ± 0.000013 (±00.26%)
0.000010 ± 0.000002 (±17.79%)
0.000038 ± 0.000002 (±06.34%)
Background (240 s)
0.021499 ± 0.000059 (±00.30%)
0.003704 ± 0.000036 (±01.00%)
0.000003 ± 0.000026 (±742.9%)
0.000003 ± 0.000003 (±101.5%)
0.000013 ± 0.000003 (±19.40%)
0.000038 ± 0.000004 (±10.00%)
284.12 ± 1.13 (±00.40%)
287.29 ± 0.76 (±00.26%)
1559 ± 47.0 (±03.02%)
1556 ± 10 (±00.65%)
Ion Pulse Counter Detector
30 Nov 2006
24 Feb 2008
Isotopes (cps) × 106 ±1σ
0.518977 ± 0.002403 (±00.05%)
1.269548 ± 0.000485 (±00.04%)
0.000331 ± 0.000002 (±00.59%)
0.000807 ± 0.000005 (±00.62%)
0.001745 ± 0.000005 (±00.26%)
0.004316 ± 0.000009 (±00.20%)
0.029418 ± 0.000010 (±00.04%)
0.000007 ± 0.000000 (±06.77%)
0.000002 ± 0.000000 (±21.64%)
0.000968 ± 0.000006 (±00.64%)
Background (240 s)
0.002403 ± 0.000016 (±00.70%)
0.003744 ± 0.000067 (±01.80%)
0.000004 ± 0.000001 (±17.60%)
0.000018 ± 0.000001 (±07.10%)
0.000016 ± 0.000001 (±06.40%)
0.000105 ± 0.000004 (±03.40%)
0.000081 ± 0.000007 (±08.30%)
294.22 ± 0.8 (±00.26%)
294.14 ± 0.6 (±00.20%)
1561 ± 9 (±00.60%)
1572 ± 10 (±00.62%)
5. Detector Intercalibration Protocols
We tested three different methods for intercalibrating multiple collectors on a Mass Analyzer Product 215-50 mass spectrometer using an optic axis ion pulse counting multiplier upgrade and a standard high-mass Faraday cup detector. The first we refer to as the postanalysis intercalibration (PA-IC) method. As implied by the name, the intercalibration (IC) factor is measured at the end of the mass spectrometer analysis on residual gases. The second is the isotopic reference ratio intercalibration (IR-IC) method. A reference gas, typically air Ar, with a known isotopic ratio is used to determine the IC factor. The third we refer to as the beam intensity ratio intercalibration (BI-IC) method, which compares the beam intensity of a single isotope measured across the two detectors to determine the IC factor.
5.1. Postanalysis Intercalibration Method
The PA-IC method of intercalibrating two different detectors is the usual approach for an analog electron multiplier and Faraday cup. (This method is typically applied to instruments with the electron multiplier in the analog mode for the occasional sample with an Ar ion beam intensity too high to measure on the multiplier. There are two conditions that require switching from the analog electron multiplier to the Faraday cup detector. The first condition occurs when the intensity of the 40Ar beam is high enough to damage to the electron multiplier. The second condition occurs when the 37Ar ion beam exceeds a preset threshold value. This is typically done in an effort to minimize the exposure of the electron multiplier to ion implantation of radioactive 37Ar. As discussed above, ion implantation of 37Ar on the first dynode of the electron multiplier can cause a significant increase in the electron multiplier baseline (Figure 3). In these cases, the large 37Ar beams are measured on the Faraday cup or by waiting, up to several months, for the 37Ar to decay to an acceptable level prior to measurement.) The PA-IC compares the ion pulse counting to the Faraday cup signals on the residual gas at the end of a typical isotope data collection run. In the analog mode, an electron multiplier can measure larger signals for a brief period and not sustain damage. Thus, in the case where the signal is not too large, the 40Ar can be quickly measured on the electron multiplier and on the Faraday at the end of the run, to obtain an IC. In another variation of this method, the gas is partially pumped out of the mass spectrometer until the 40Ar signal intensity is within an acceptable range of both the Faraday and electron multiplier detectors. Once the 40Ar signal is optimized, the signal is measured on both detectors. The ratio of the multiplier signal over the Faraday signal is the IC factor. The advantage of the PA-IC method is that intercalibration of detectors is accomplished on the unknown in which abundances are being determined. In the ion pulse counting mode, however, this method is generally not feasible because of the variable intensity of the 40Ar signal; the signal is either too large for the multiplier or too small for accurate Faraday measurement and is rarely “just right.” In addition, the partial “pump out” method described above would defeat the operational consistency obtained by fully automated extraction systems because of the variability in process timing.
We tested the accuracy of the PA-IC method on air Ar aliquots that produce optimum signals for measurement on both the Faraday cup and ion pulse counting detectors. The advantage of using an optimized air Ar aliquot to determine the detector IC factor is that the same gas sample can be also used to determine the mass spectrometer mass discrimination.
In our tests of the PA-IC method, 40Ar for the twofold, threefold, and fourfold air pipettes was measured on the Faraday cup. At the end of the measurement the 40Ar beam was put into the electron multiplier to intercalibrate the Faraday cup and electron multiplier by the PA-IC method. The Faraday cup 40Ar signal was then multiplied by the PA-IC, and the 40Ar/36Ar ratios were calculated. All of the ratios are compared as raw ratios (not mass discrimination corrected). The PA-IC corrected 40Ar/36Ar ratios are too large for the twofold, threefold, and fourfold air pipette shots compared to the 40Ar/36Ar ratios of the onefold pipette(s) (Figure 4). The measured intercalibration factors were consistently too high. The miscalibrated ratios are not likely due to a too low dead time correction for the electron multiplier detector because higher 40Ar/36Ar ratios of twofold, threefold, and fourfold air pipette shots are opposite of what one would expect from too low of a dead time correction. For example, without a dead time correction, a twofold air pipette would yield a 40Ar count rate of about 9.988 × 105 cps on the electron multiplier and 20.8 mV on the Faraday cup, for an IC factor of approximately 4.75 × 104 cps/mV. With a 12.3 ns dead time correction, the same 40Ar count rate increases to about 1.00 × 106 cps while the Faraday stays the same at 20.8 mV, increasing the IC factor to approximately 4.81 × 104 cps/mV. So increasing the dead time correction would only increase the disparity between 40Ar/36Ar ratios of the onefold air pipettes compared to the twofold, threefold, and fourfold air pipettes. In addition, it is not likely that the dead time for the electron multiplier detection system is less than the measured dead time of 12.3 ns.
A more likely cause is that the relative gain between the two detectors changed independently during the course of the analysis, resulting in different IC values measured on the residual gas after a run compared with those at T0 (T-zero). The isotope intensity value at T0 is typically determined by a regression of the measured isotope data to a point 2/3 of equilibration time following introduction of the sample gas into the mass spectrometer. To test for this phenomenon, we examined how the IC factor behaves during the course of a typical analysis. Figures 5a and 5b show the typical 40Ar signal intensity evolution during measurement of an air aliquot on the Faraday cup and on the ion pulse counting detector, respectively. Since we are measuring the same 40Ar air aliquot essentially through the same time span, the IC factors of the two detectors should be constant. However, the calculated detector IC factor increases nonlinearly, by about 1.5%, from 46.82 to 47.55 during the course of the analysis (Figure 5c). In other words, the relative gain between the two detectors shows different evolutions during the same measurement time period. In fact, similar nonlinear behavior for electron multipliers has been reported in other studies [e.g., Bayer et al., 1989; Richter et al., 2001; Hoffmann et al., 2005]. The exact cause of this nonlinear behavior is not well understood and is discussed by Richter et al.  and Hoffmann et al. . We concur with Richter et al.  and Hoffmann et al.  that this nonlinear change in the work function (ion to pulse conversion rate) of the electron multiplier during the course of a run is due to internal heating of the secondary electron multiplier and space charge effects. Our concern is that in most cases, Ar abundances are determined by extrapolation of periodically measured signals to T0, and in this case, the PA-IC factor may be invalid. Variation in curvature as a result of this evolution will result in differences in extrapolations to T0. As a result, applying a PA-IC factor to our air standard produced 40Ar/36Ar ratios about 1.6% too large (Figure 4). Thus, the PA-IC determination of the IC factor fails to accurately intercalibrate the two detectors.
5.2. Isotopic Reference Ratio Intercalibration Method
The IR-IC factor is obtained by dividing the atmospheric 40Ar/36Ar ratio (295.5) by the ratio of Faraday cup 40Ar measurement signal (in mV) to the 36Ar ion pulse counting signal (in cps):
Air aliquots are interspersed with sample “unknowns” which can be then used to monitor any changes in the detector IC factors and mass discrimination through time (Figure 6). These values can be then time averaged or regressed over the period of the experiment and then applied to unknowns. The IR-IC method produces IC factors that correctly intercalibrate the two detectors if the measured 40Ar/36Armeasured ratio (no mass discrimination correction is applied to the measured ratio) is used instead of using “accepted” mass discrimination corrected atmospheric 40Ar/36Ar ratio of 295.5. However, several problems still persist with the IR-IC method for determining detector IC factors. One issue is that the measured 40Ar/36Ar ratio may drift with time, as discussed below and depicted in Figure 8. However, this can be addressed by time series regression or averaged value. A second and more significant issue with the IR-IC method is that the IC factors have a larger associated measurement uncertainty because both 36Ar and 40Ar isotope measurements are required. The low 36Ar concentration and hence low count rate adds significant dispersion to the measured IC factors. The IR-IC method highlights a problem associated with all detector intercalibration methods, which is, “What is the correct first-order mass discrimination to use when calculating the isotopic ratios from a multicollector system?” We discuss this in section 5.3.
5.3. Beam Intensity Ratio Intercalibration Method
The third method of detector intercalibration is an extension of the PA-IC method in that aliquots of atmospheric Ar from an air pipette are used to determine the IC factors. As in the PA-IC method, the pipette volume is optimized for both detectors. The BI-IC method measures the optimized 40Ar beam in both the Faraday cup and the ion pulse counter detectors (see Figures 5a and 5b). By definition, the 40Ar beam intensity projected to T0 for both detectors has to be the same within measurement error. Thus, the ratio of the two 40Ar beam intercepts is the best determination of the IC factor. In addition, the optimized size of the 40Ar ion beam optimizes the IC factors. Applying the BI-IC method to the air standard data produces uniform 40Ar/36Ar results (Figure 6b).
A significant advantage of the BI-IC method is the way the mass spectrometer mass discrimination/fractionation for two detectors is handled. In the BI-IC method, the IC factor converts the Faraday signal (in mV) to ion pulse counting units (cps). These measurements are raw in that no mass discrimination/fractionation correction is applied. As described above, the T0 for both detectors are the same within measurement error. Hence, the Faraday signal (mV) is converted to raw ion pulse counting units (cps) and then the ion pulse counting mass discrimination/fractionation correction is applied to the results.
A variant to the BI-IC method can also be applied to mass spectrometers with more than just two detectors (e.g., a mass spectrometer with a combination of Faraday cups and ion pulse counting electron multipliers or multiple Faraday cups, or multiple ion pulse counting electron multipliers). We refer to this variant as the simultaneous ratio intercalibration (SR-IC) method. This method measures all of the isotopes on all of the various detectors, taking into consideration appropriate signal intensities for the various detectors. Thus, a direct ratio of all of the signals is made continuously throughout the analysis period. These results could then be compared directly without extrapolation to T0 or could be regressed to T0. This method may become cumbersome using more than two detectors and may offset some of the advantage of reducing the measurement time cited for multidetector systems. However, if the evolution of the signal/beam intensity varies on the different detectors, the regression of the combined ratios would, in effect, result in a higher-order, nonlinear fit, thus increasing the associated uncertainty with the IC factor.
5.4. Mass Discrimination and Multiple Detectors
As discussed above, an additional challenge with multidetector systems is applying the correct mass discrimination to the isotopic measurements. We address this issue here by using a protocol that converts all multidetector measurements to a single detector, in our case the ion pulse counting detector, and then applying the corresponding ion pulse counting mass discrimination. Interspersing these air pipette aliquots with sample “unknowns” at a frequency of about 0.1 to 0.2 days (∼2–4 h) produces a time series for both the detector IC factors and mass discrimination (Figures 6a, 7, and 8). The detector IC factors are applied first, and then the mass discrimination corrections are applied to samples.
5.5. Time Series Protocol
Figure 7 shows the measured mass discrimination measured on two different days. The point of Figures 7 and 8 is that you cannot detect variations in mass discrimination with frequencies that are higher than your sampling rate. The data in blue show the typical mass spectrometer mass discrimination variability encountered on a MAP-215-50. The data in red, however, display a particularly interesting variation in the mass spectrometer mass discrimination. Variations in mass discrimination are not unique to our mass spectrometer/extraction system (e.g., variations between ±3 and 4‰ have been reported [Brown et al., 2009]). What is unique is that we advocate measuring mass discrimination at a much higher frequency then is common in most 40Ar/39Ar facilities.
While the cause of temporal variation the mass discrimination is not fully understood, we consider that the main cause of the variation is due to variations in the temperature and relative humidity. Generally, we see the greatest variations in the mass discrimination during the spring and fall on the east coast, when the HVAC system changes from the cooling mode during the day to the warming mode during the evening hours when the outside temperatures decrease. Changes in mass discrimination are not unique to a MAP-215-50. Temporal drift in mass discrimination is a known characteristic of all mass spectrometers and has been documented for a VG5400 mass spectrometer that is used to make He isotopic concentration measurements [Bayer et al., 1989; Turrin et al., 2008] (Figure 8). Similarly, these variations in the mass discrimination are greatest in the spring and fall, accompanying swings in temperature and humidity.
As demonstrated in Figures 7 and 9, these “variations or drifts” can have a profound effect on data and must be accounted for in order to produce 40Ar/39Ar ages with uncertainties approaching 1‰ of the measured age. Typically, a mass discrimination value is measured prior to an unknown incremental heating experiment and one at the end of the experiment. In our example, a mass discrimination value of ∼1.005 was measured prior to the start of the experiment (an incremental heating experiment takes about 1 day). At the end of the incremental heating experiment, the mass discrimination was measured again, and a similar value of ∼1.0045 was obtained. One might conclude that the mass discrimination had not changed, at least outside the measurement error. However, the mass discrimination was measured approximately every 2.5 h and shows a ∼1.7‰ drift over the time period of the incremental heating experiment.
The incremental heating experiment shown in Figure 9b demonstrates the impact that a 2‰ drift (shown in Figure 7) can have on an age measurement. At first glance one might conclude that the sample yielded a disturbed release pattern indicative of alteration or perhaps due to 39Ar recoil during irradiation. This particular sample is a very young (∼66 ka) low-K tholeiite; hence, the 40Ar/36Ar ratio is only slightly above that of atmosphere (295.5). The apparent ages for the low-temperature increments start out positive and monotonically decline until about 55% of the 39ArK is released. The last 45% of the 39ArK released actually produce a negative age plateau. However, had this sample been significantly older the 40Ar/36Ar ratio of the sample would be much greater than atmosphere Ar and the plateau would not be a negative age. This release pattern would then be considered typical of 39Ar recoil.
However, during the course of this particular incremental heating experiment, we closely measured the mass discrimination. From the measured air pipettes, we are able to determine that the mass discrimination had actually drifted approximately 1.7‰ during the period of the experiment as shown in Figure 7. Applying the appropriate time series corrected mass discrimination, the “disturbed” release spectra become essentially an undisturbed concordant release spectra (Figure 9a).
The mass discrimination correction also has an impact on samples with high radiogenic 40Ar concentrations as well. In the case of our example in Figure 7, the approximately 2‰ variation in the 1 amu mass discrimination would result in an at least 2‰ effect on the age of a highly 40Ar radiogenic sample because the 40Ar/39Ar ratio is multiplied by the 1 amu mass discrimination and the 36Ar/39Ar ratio is directly multiplied by 1/(d1amu)Δm(39Ar-36Ar). Thus, the approximately 2‰ variation in the mass discrimination would change the 40Ar/39Ar age by at least 2‰. For example, for a typical Fish Canyon sanidine standard (e.g., FC = 28.02 Ma) these two corrections would result in a 58 ka (a 2‰) difference in age. In some instances this variation may be incorporated in the J determination if measured at the same time under the same conditions. However, this is not always the case if the standards and unknowns are measured at different times and by various methods (i.e., laser total fusion versus resistance furnace incremental heating).
Close examination of the distribution of errors shows that the precision in the 36Ar isotopic measurement is the limiting factor in the overall precision of 40Ar/39Ar ages for samples with either high or low concentrations of radiogenic 40Ar. Thus, improving the ultimate accuracy and precision of the 36Ar isotopic measurements will improve the accuracy and precision of an age. Moreover, from our ion pulse counting and multiple collector systems experiments, we point to the following observations.
1. Upgrading the electron multiplier to ion pulse counting, for example, using a Pfeiffer Vacuum SEV 217 and installing Ortec ion pulse counting electronics, can significantly improve the low-level performance of first generation low-background, high-sensitivity mass spectrometers (e.g., MAP-216, MAP-215, MAP-215-50, VG/MM5400, and VG/MM3600). Specifically, the measurement of 36Ar benefits the most with the use of ion pulse counting.
2. Because of the variability in the electron multiplier detector characteristics through time due to changes in temperature/humidity, short-term drift of the work function on the electron multiplier, and general “aging” of the electron multiplier, a simple detector intercalibration on residual gas at the end of a run on a multicollector system may lead to errors in the measured isotopic ratios.
3. Because signal size limitation of the different types of detectors may prevent intercalibration using gas volumes from sample unknowns, using an air pipette of an appropriate volume interspersed with sample analyses provides not only accurate mass discrimination monitoring but can also provide accurate intercalibration between multiple detectors.
4. We have shown that the PA-IC method of multiple detectors is inherently flawed. Second, because of issues surrounding the mass discrimination of multiple detectors, we also conclude that the IR-IC method may also yield incorrect intercalibration values. For intercalibration of various detectors with signals that prevent simultaneous measurement on each detector, we consider the BI-IC to yield the most accurate means of multiple detector intercalibration.
In conclusion, if any drift in the mass spectrometer mass discrimination, even at the 1–2‰ level, is not closely monitored and accounted for, the goal of the EarthTime initiative (http://www.earth-time.org/intro.html) (“sequencing Earth history through the integration of high-precision geochronology and quantitative chronostratigraphy with uncertainties approaching 0.1% of the radioisotopic ages”) cannot be achieved.
The parts list for electron multiplier housing to refit a MAP 215-50 Mass Spectrometer with an ion pulse counter capable Pfeiffer Vacuum SEV 217 electron is as follows: (1) Pfeiffer Vacuum SEV 217 electron multiplier, (2) a 4-5/8 inch Con-Flat flanges or equivalent, and (3) A 3-3/8 inch Con-Flat flanges or equivalent. Additional illustrations and specifications are provided in Figures A1 and A2.
We would like to thank Matt Heizler, Michael Cosca, Duane Champion, and an anonymous reviewer for their constructive reviews and comments. This work was supported in part through NSF grants EAR0203388 and EAR0507924.