A calculation method based on isotope ratios for the determination of dead time and its uncertainty in ICP-MS and application of the method to investigating some features of a continuous dynode multiplier Andrea Held and Philip D. P. Taylor* Institute for Reference Materials and Measurements, European Commission-JRC, B-2440 Geel, Belgium. E-mail: taylor@irmm.jrc.be Received 20th November 1998, Accepted 27th April 1999 A method for the determination of dead time (and its uncertainty) of the ion-counting detection system of ICP-MS instruments is presented.It is based on isotope ratio measurements, which are more precise than ion current measurements and will result in values for the dead time with a measurable uncertainty. The suggested method allows us to estimate the uncertainty associated with the dead time. Typical relative uncertainties of the dead time values were found to be in the range of 10–20%. This method has been applied to monitoring the dead time for a detection system over the lifetime of a particular electron multiplier.The dead time was found to be an important criterion for replacing an old electron multiplier when optimum isotope ratio measurements are required. The dependence of the dead time on the mass of the measured isotopes has been investigated. No mass dependence of the dead time could be concluded within the measurement uncertainty on this particular instrumental set-up. It is therefore easily applicable for routine monitoring of dead Introduction time.Furthermore it can also deliver a reliable estimate of the The dead time of the ICP-MS detection system is an important combined uncertainty associated with the dead time value parameter for the reliable determination of isotope ratios when according to published guides on uncertainty evaluation.12,13 using an ion counting detection system1–4 If not corrected for, This method has been applied to monitoring dead time during it deteriorates the linearity of the instrument over a range of the lifetime behaviour of a Channeltron electron multiplier isotope ratios, the eVect being greater for larger isotope ratios.and to investigate a possible dependence of the dead time on Furthermore, the uncertainty associated with the determi- the mass of the incident ions. nation of the dead time aVects the uncertainty related to ratio measurements, as has been shown by Hayes and Schoeller,1 Instrumentation and reagents and consequently the uncertainty of isotope dilution analysis results.5,6 Ageing of the electron multiplier, which is part of A VG Instruments PQ2+ ICP-MS (VG Elemental, Winsford, the ion counting detection system, significantly changes the Cheshire, UK), equipped with a Channeltron continuous apparent dead time.Continuous monitoring of the dead time dynode electron multiplier (Galileo Electro-Optics Corpis therefore necessary. Frequently applied methods for the oration, Stunbridge, MA, USA), was used.Typical operdetermination of dead time for ICP-MS instrumentation ating conditions are given in Table 1. Further information on involve checking the linearity of the relation between measured Channeltron electron multipliers can be found in the ion current and concentration of the measured solution as a literature.14,15 function of dead time, deducing dead time from isotope ratio Water and nitric acid used for preparation of solutions in measurements by ‘trial-and-error’ methods, in which usually this work have been purified by sub-boiling distillation.the dead time is varied until the observed isotope ratio does A solution of NIST SRM 982 Pb was prepared by dissolving not vary with the concentration any more,3,6,7 or using the an appropriate amount of the metal in dilute nitric acid and eVect of dead time on isotope ratios measured at diVerent further dilution to the required concentrations with 0.14 M concentration levels systematically to calculate a dead time, which has been used by Vanhaecke et al.,2 Hayes et al.8 and in this work.Table 1 Typical operating conditions for the ICP-MS used in this work, equipped with a V-groove nebuliser In this article a simple method for the determination of dead time is described. It is based on isotope ratio measure- Parameter Typical setting ments as these are very sensitive to dead time eVects and can be measured with small uncertainties.Similar methods have Gas flows (Ar): Cooling 15 L min-1 been applied for the determination of dead time for secondary Auxiliary 2 L min-1 Nebuliser 0.8 L min-1 ion mass spectrometry (SIMS).9,10 We suggest applying this Forward power ICP generator 1400W method to ICP-MS. It can easily be implemented as a spread- Reflected power <5 W sheet using commercially available spreadsheet software as it Sample solution flow 1 mL min-1 is entirely based on straightforward calculations.It does not Spray chamber temperature 4 °C require iterative procedures as other workers have suggested.11 J. Anal. At. Spectrom., 1999, 14, 1075–1079 1075HNO3. Note that SRM 982 is slightly radioactive and neces- the certified 204Pb5208Pb ratio.) sary precautions have to be taken when working with this material. R(1E/2E)dt= Idt(2E) Idt(2E) = [1-Idt(1E)·t]·Itrue (1E) [1-Idt(2E)·t]·Itrue(2E) For the other elements investigated in this work, commercially available standard solutions from diVerent suppliers were used.= [1-Idt(1E)·t] [1-Idt(2E)·t] ·E(1E/2E)true (2) Bottles for sample storage were cleaned by leaching with 5% HNO3 for a minimum of one day. Various types of PE The equation is further rearranged to yield a linear expression and FEP bottles were used. R(1E/2E)true R(1E/2E)dt = (1-Idt(2E)·t (1-Idt(1E)·t) (3) Theoretical background R(1E/2E)true[1-Idt(1E)·t]=R(1E/2E)dt[1-Idt(2E)·t] (4) It is well known that ion counting systems show dead time R(1E/2E)true-R(1E/2E)true·R(1E/2E)dt·Idt(2E)·t eVects.This means that a minimum time diVerence between the impact of two ions is necessary to identify those as two =R(1E/2E)dt-R(1E/2E)dt·Idt(2E)·t (5) individual events. This eVect is partly due to processes taking Division of equation (5) by R(1E/2E)dt and rearranging yields place in the electron multiplier and is partly caused by eVects equation (6). in the counting electronic device connected to the multiplier.This leads to an observed count rate that is smaller than the true one. Counting systems can be divided into two fundamen- R(1E/2E)true R(1E/2E)dt =1+[R(1E/2E)true-1]·t·Idt(2E) (6) tally diVerent types, ‘paralysable’ and ‘non-paralysable’ counters. 1,16 Paralyzable counters will not count an incoming ion Plotting R(1E/2E)true/R(1E/2E)dt over Idt(2E) then yields a B that arrives within the dead time t of a previous ion A, but straight line, the slope being m¾=[R(1E/2E)true-1]·t.The dead the counter will be ‘dead’ for a new time span of t after the time can thus be calculated from the slope of such a plot. As arrival of ion B. Non-paralyzable counters would completely a basic requirement for linear regression it is assumed that the ignore a second ion B arriving within the dead time of ion A, relative uncertainty on the abscissa values is non-existent.22 In without any extension of the time that it will be ‘dead’ for practice, it is assumed to be negligible compared to the relative other incoming ions.Fortunately, both types can be described uncertainty of the ordinate, when the uncertainty of a typical using the same formula to a good approximation [eqn. (1)]. ordinate value compared to the range of the ordinate values Therefore, count losses occurring in any real counting system is bigger than the uncertainty of a typical abscissa value which might be in between those two types can be described compared to the full range of the abscissa values.23 This using Equation (1).relationship has been checked for the current problem and this criterion is fulfilled. Idt=(1-Idt·t)·Itrue (1) For any real measurement, the measured isotope ratio R(1E/2E)dt is not only aVected by dead time, but also by mass with Idt being the observed rate of events (i.e., aVected by bias eVects. A correction has to be applied to take these eVects dead time losses), Itrue the true rate of events and t the into account.In order to achieve lowest possible uncertainties apparent dead time. on the resulting dead time values, the mass bias correction is More refined models for the description of real counting carried out for each measured data point. When measuring a systems have been developed, including models where series suitable element or isotopic reference material, a ratio of paralysable and non-paralysable counters are con- R(3E/4E)mb of a second pair of isotopes 3E and 4E can be sidered.17,18 Sometimes, dead time is modelled for diVerent measured and used for the mass bias correction (indicated by parts of the counting system and pulse overlap is taken into the subscript mb) if that ratio is close to unity and therefore account17,19 or where dead time is assumed to have a distri- not aVected by dead time eVects.(In the example of measurebution itself.20,21 Here, only the simplest model [eqn. (1)] ments of NIST SRM 982, the isotopes 206Pb and 208Pb can be is used.used as 3E and 4E, respectively.) We define a mass bias For isotope ratio measurements with a combined relative correction factor k(3E/4E) as the ratio of the known to certified uncertainty uc<0.5%, the impact of dead time eVects on isotope ratio of the sample R(3E/4E)true and the measured one isotope ratios is significant. As the eVect increases with the R(3E/4E)mb, which is aVected by mass bias intensity of the ion beam hitting the counter, it causes a nonlinear response of the counting system.For isotope ratio k(3E/4E)= R(3E/4E)true R(3E/4E)mb (7) measurements this means that the measured ratio changes with the intensity of the ion beams measured. This unwanted eVect can, on the other hand, be used to determine the dead By applying, for example, the linear law,24 which is suYcient to correct for mass bias eVects within the measurement uncer- time, allowing a correction of all measurement data. A similar approach has been used by Hayes et al.,8 who also used tainties achievable on a quadrupole based ICP-MS, we can calculate from the mass bias k(3E/4E) the mass bias per mass isotope ratio measurements for the determination of dead time, but applied a more complex model, taking into account unit, e, [eqn.(8)] and further derive the mass bias for the ratio R(1E/2E) [eqn. (9)]. discriminator eVects for overlapping pulses. The present work focuses on a simple but nevertheless suYciently accurate k(3E/4E)=1+e·Dm(3E/4E) (8) method for the determination of dead time, as well as on the estimate of the uncertainty associated with the dead time.k(1E/2E)=1+e·Dm(1E/2E) (9) Applying eqn. (1) to a dead time aVected isotope ratio R(1E/2E)dt of two isotopes 1E and 2E (2E is the higher with Dm(1E/2E) and Dm(3E/4E) being the mass diVerence between the isotopes 1E–2E and 3E–4E, respectively. abundant isotope) yields eqn. (2). (As an example, in this work the NIST SRM 982 Pb isotopic reference material was In eqn.(6) we can replace R(1E/2E)dt by the actually measured ratio of 1E and 2E, R(1E/2E)meas, which is aVected used for the measurements. In this case 1E would refer to 204Pb and 2E would refer to 208Pb, Rtrue would correspond to by dead time and mass bias, multiplied by the mass bias 1076 J. Anal. At. Spectrom., 1999, 14, 1075–1079correction factor k(1E/2E), yielding eqn. (10) This lead material was chosen because it oVers a unity ratio of 206Pb5208Pb for the mass discrimination correction and a 1520 (204Pb5207Pb) and a 1540 ratio (204Pb5208Pb).In this R(1E/2E)true k(1E/2E)·R(1E/2E)meas =1+[R(1E/2E)true-1]·t·Imeas(2E) case the 204Pb5208Pb ratio was used for dead time determi- (10) nation. A set of solutions was prepared from this material with concentrations ranging from 5 ng g-1 to 100 ng g-1. Of As without dead time correction, the dead time is calculated these solutions a set of 4–10 were selected according to the from the slope m¾=[R(1E/2E)true-1]·t of a linear regression instrument’s sensitivity, such that for the major isotope, count line of R(1E/2E)true/[k(1E/2E)·R(1E/2E)meas] versus Imeas(2E).rates between 50 000 and 800 000 s-1 were obtained. It was The resulting dead time is given by eqn. (11) found that a set of four solutions was suYcient, if each solution was measured repeatedly. For each sample, the iso- t= m¾ [R(1E/2E)true-1] (11) topes 204Pb, 206Pb and 208Pb were measured.Further, the contribution of 204Hg to the measured ion current on m/z= This equation can also be used to estimate the uncertainty 204 needed to be taken into account. Therefore the 202Hg ion associated with the dead time. As the biggest source of current was monitored, and if any mercury above blank levels uncertainty in eqn. (11) is the slope, m¾, of the regression line, was detected, the respective ion current originating from the combined uncertainty12,13 of the dead time is estimated mercury on m/z=204 was calculated using the respective from the uncertainty on that slope m¾.The uncertainty of the abundances of 202Hg and 204Hg and subtracted from the ratio R(1E/2E)true is negligible compared with the uncertainty measured ion current on m/z=204. of the slope, and is therefore disregarded. The uncertainty of The software of most of the commercially available the dead time can then be included in uncertainty budgets for instruments automatically applies a dead time correction. isotope ratio measurements.Furthermore, the uncertainty of Therefore, it is necessary to set the dead time in the software the dead time can be used to calculate optimum measurement set-up to zero before starting the measurements. In the case conditions, such as the maximum admissible count rate and of the instrument used for this work this is not possible, as minimum measurement time required for a minimal contrithe software does not allow any value smaller than 1 ns for bution of the dead time, and counting statistics to the combined the dead time.During the dead time determinations the dead uncertainty of a ratio measurement1 or to optimise measuretime is thus set to 1 ns. This introduces a deviation of the ments by isotope dilution mass spectrometry.5 dead time values calculated, which was found to be negligible within the uncertainty of the determination, typically in the Experimental order of 2–5 ns. To achieve a variation in the intensity of the major isotope, Possible errors diVerent concentrations of an element in solution are used.In general any poly-isotopic element with 3 isotopes could be As the dead time in this work has been determined by used for dead time determinations: in practice, however, a measuring the 204Pb5208Pb ratio, the possible influence of solution with a suYciently small isotope ratio, Rt<0.05, is background, blanks and interferences (e.g., 204Hg) needs to be preferably used.If the isotope ratio is too close to unity, the discussed. The elimination of background contributions in the eVect of the dead time will be very small and hidden in the determination of dead time by an iterative procedure has been scatter of the measured ratios. Furthermore, the quality of the described by Hayes et al.8 In ICP-MS measurements, such a measurements can be improved by choosing another isotope procedure is not necessary as background can usually be ratio of the same element to calculate a mass bias correction measured and appropriately corrected for.In any case, such a within each sample rather than determining the mass bias background would be visible from a larger spread of measured correction in a separate measurement. Mass bias correction is ratios and therefore result in an increased uncertainty of the also important as it changes the ratio R(1E/2E)true/R(1E/2E)dt dead time. Another relevant source of error could also be a in eqn.(6) by a multiplicative factor that would consequently significant contamination of the solutions used to measure also change the value for the dead time [see eqn. (10)]. The dead time by material of diVerent isotopic composition. When isotope ratio for the mass bias correction should then be as material with natural isotopic composition is used to prepare close as possible to unity, as dead time has a minimal influence these solutions this risk is, of course, eliminated.on unity ratios. This limits the suitable elements to those with Contamination would result in a significant error in the at least three isotopes, with two isotopes having approximately determined dead time without being accounted for by an the same abundance. Possibilities are solutions of, e.g., Mg, increased uncertainty of the dead time and should therefore Zr, Ru, Cd, Dy, Os or Pt, of natural isotopic composition. be avoided at all cost. Another option is the use of isotopic reference materials, such as the IRMM-072 series, which oVers a 235U5238U ratio very Results close to unity and a 233U5238U ratio ranging from unity to 2×10-6, certified to an uncertainty of 0.03%.(This material Fig. 1 shows a typical example of the data resulting from a is radioactive and therefore not easily accessible for every dead time determination on an ICP-MS. The dead time as user.) In this case a Pb isotopic reference material, NIST calculated from the regression line for the dead time uncor- SRM 982, was used.This reference material has an isotopic rected data using eqn. (11) corresponds to 17.4±1.9 ns. The composition as given in Table 2. uncertainty of the dead time has been estimated from the uncertainty of the slope of the regression line. Using the instruments software the same data has been reintegrated Table 2 Isotopic composition of NIST SRM 982 using this dead time value (Fig. 2). A regression line fitted with these dead time corrected data points no longer shows a Isotope Relative isotope abundance (×100) significant variation of the isotope ratios with the intensity of 204Pb 1.0912±0.0012 the major isotope.This is also a verification of the dead time 206Pb 40.0890±0.0072 correction algorithm used in the instruments software. 207Pb 18.7244±0.0032 There is a residual oVset in the regression lines of Fig. 1 208Pb 40.0954±0.0077 and Fig. 2. The regression lines in both graphs should cross J.Anal. At. Spectrom., 1999, 14, 1075–1079 1077Fig. 4 Dead time determined using diVerent elements in solution (Mg, Fig. 1 Typical graph obtained for dead time determination on the Zr, Dy, Pb SRM 982) on one day. Uncertainty bars represent the ICP-MS. The resulting dead time is 17.4±1.9 ns, X= estimated uncertainty of the dead time (coverage factor k=1), broken R(204Pb/208Pb)true/[k(204Pb/208Pb)·R(204Pb/208Pb)meas]. lines represent the standard uncertainty (k=1) of the average value (continuous line).even showing apparently negative dead time (on day 329, indicated by the arrow in Fig. 3), although the gain was still high. Adjusting the voltage (increased to -2500 V from initially -2375 V on day 235, further increased to -2625 V on day 328) applied accross the multiplier did not improve its behaviour. The multiplier was finally replaced on day 353. As can be seen from Fig. 3, the dead time of the detection system should have been monitored more frequently in order have a valid value available at any time.The useful life of this particular multiplier ended when the observed dead time values started to scatter unpredictably. It should have been replaced earlier than was actually done, although its gain (the usual criterion for replacing a multiplier) was still unaVected. Regular monitoring of the multiplier’s dead time can give Fig. 2 Same data as displayed in Fig. 1, after correction for 17.4 ns valuable information to help decide when a multiplier needs dead time, X=R(204Pb/208Pb)true/[k(204Pb/208Pb)·R(204Pb/208Pb)meas]. replacing.Another concern regarding the dead time was the possible mass dependence of the dead time as the multiplier gain can the abscissa at a value of 1 if mass bias has been corrected for depend on the energy and m/z of a given ion.14,15,25 Vanhaecke appropriately. This residual oVset was due to an instrumental et al.2 have observed an increase of the dead time by 50% problem which was only discovered very recently and can be when going from Mg to Pb as the element used for dead time ignored for discussion of the proposed method as such.The determination using a Perkin-Elmer SCIEX ELAN 5000 determination of the dead time was carried out at regular ICP-MS equipped with a Channeltron continuous dynode intervals on this instrument to assess whether the dead time electron multiplier, whereas they did not observe a significant would stay constant over time.Fig. 3 shows the behaviour of variation of dead time with analyte mass on a Finnigan-MAT one multiplier over its lifetime. Although only a few determi- Element ICP-MS equipped with a conversion dynode and a nations of the dead time have been carried out, it shows a secondary electron multiplier with discrete dynodes. On our rather uniform increase over the first 220 days; after that, the instrument, which is equipped with a Channeltron multiplier dead time of the multiplier started to be rather unpredictable, similar to the Elan 5000 set-up used by Vanhaecke et al., no significant trend of the dead time with m/z could be observed within the uncertainty of the dead time measurement.In this work, dead time was determined using the Pb SRM 982 and Mg, Zr and Dy of natural isotopic composition to cover a wide mass range (Fig. 4). These results show that a similar type of multiplier can exhibit diVerent behaviour of dead time depending on the type of instrument in which it is installed.Therefore, dead time as a function of analyte mass needs to be determined on diVerent types of instrumentation. Conclusion A straightforward method for the determination of dead time and its associated uncertainty on ICP-MS instrumentation was presented. It can easily be implemented in commercial spreadsheet software for routine application. Compared to other methods it requires only few calculations and is not based on Fig. 3 Behaviour of dead time over the lifetime of the multiplier, the arrow indicates a negative dead time value. ‘trial-and-error’ methods. The dead time can be calculated 1078 J. Anal. At. Spectrom., 1999, 14, 1075–10797 I. S. Begley and B. L Sharp, J. Anal. At. Spectrom., 1997, 12, 395. with suYciently small uncertainties, typically in the range of 8 J. M. Hayes, D. E. Matthews and D. A. Schoeller, Anal. Chem., 10–20% relative. The dead time of the continuous dynode 1978, 50, 25.multiplier system used in this work varies constantly over time 9 Y. A. Liu and R. H. Fleming, Rev. Sci. Instrum., 1993, 64, 1661. and needs to be monitored frequently to ensure best possible 10 A. J. Fahey, Rev. Sci. Instrum., 1998, 69, 1282. isotope ratio measurements. The usual criterion for replacing 11 J. I. Garcia Alonso, F. Sena, Ph. Arbore, M. Betti and L. Koch, J. Anal. At. Spectrom., 1995, 10, 381. a multiplier, its loss in gain, should not be the only criterion 12 Guide to the Expression of Uncertainty in Measurement, when one is interested in isotope ratio measurements.It is International Organization for Standardization (ISO), Geneva, advisable to replace a multiplier when it shows unpredictable Switzerland, 1st edn., 1993. changes in dead time. 13 Quantifying Uncertainty in Analytical Measurement, Furthermore, a mass dependence of the dead time as EURACHEM Working Group on Uncertainties in Chemical observed by Vanhaecke et al.2 for a similar type of electron Measurement, Teddington, UK, 1st edn., 1995. 14 ChanneltronA Electron Multiplier Handbook for Mass multiplier could not be supported by results presented in this Spectrometry Applications, Galileo Electro-Optic Corporation, work. This should be considered when using ICP-MS for Sturbridge, MA, USA, 1991. isotope ratio measurements and renders this method for dead 15 E. A. Kurz, Am. Lab., March 1979, 67. time determination very useful. 16 G. F. Knoll, Radiation Detection and Measurement, John Wiley & Sons, Chichester, Sussex, UK, 1979, pp. 95–103. 17 J. A. Williamson, M. W. Kendall-Tobias, M. Buhl and M. Seibert, Acknowledgement Anal. Chem., 1988, 60, 2198. 18 J. W. Mu� ller, Nucl. Instrum. Meth., 1973, 112, 47–57. The authors would like to thank C. Quetel, who greatly helped 19 J. D. Ingle and S. R. Crouch, Anal. Chem., 1972, 44, 777. to refine this manuscript. 20 T. Stephan, J. Zehnpfennig and A. Benninghoven, J. Vac. Sci. Technol., 1994, A12, 405. References 21 S. K. Srinivasan, J. Phys. A: Math. Gen., 1978, 11, 2333. 22 K. DoerVel, Statistik in der analytischen Chemie, Deutscher Verlag 1 J. M. Hayes and D. A. Schoeller, Anal. Chem., 1977, 49, 306. fu� r GrundstoYndustrie, Leipzig, Germany, 1990, pp. 159–164. 2 F. Vanhaecke, G. de Wannemacker, L. Moens, R. Dams, 23 P. R. Bevington, Data Reduction and Error Analysis for the Ch. Latkoczy, T. Prohaska and G. Stingeder, J. Anal. At. Physical Sciences, McGraw-Hill Inc., New York, USA, 1969, Spectrom., 1998, 13, 567. p. 98. 3 S. R. Koirtyohann, Spectrochim. Acta, Part B, 1994, 49, 1305. 24 P. D. P. Taylor, P. De Bie`vre, A. J. Walder and A. Entwistle, 4 P. G. Russ and J. M. Bazan, Spectrochim. Acta, Part B, 1987, J. Anal. At. Spectrom., 1995, 10, 395. 42, 49. 25 E. Zinner, A. J. Fahey and K. D. McKeegan, Springer Ser. Chem. 5 A. G. Adriaens, W. R. Kelly and F. C. Adams, Anal. Chem., 1993, Phys., 1986, 44 (Second. Ion Mass Spectrom., SIMS 5), 170. 65, 660. 6 A. A. van Heuzen, T. Hoekstra and B. van Wingerden, J. Anal. At. Spectrom., 1989, 4, 483. Paper 8/09098J J. Anal. At. Spectrom., 1999, 14, 1075–1079