Performance of second generation ICP-TOFMS for (multi-)isotope ratio analysis: A case study on B, Sr and Pb and their isotope fractionation behavior during the measurements

The second generation ICP-TOFMS is subject to IIF that does not follow the known mass dependent fractionation laws and is possibly caused by non-mass dependent fractionation and/or multiple fractionation processes with varying contributions.


Introduction
Within the last decades, the analysis of systematic variations in the isotopic composition of B, Sr and Pb has been applied in a wide range of scientic disciplines, such as geosciences, 1,2 environmental sciences, [3][4][5] nuclear and forensic sciences, 6 (food) provenance studies, 7,8 anthropology and archaeology. 9,10e natural variation in their isotope abundances is the result of either radiogenic ingrowth or small differences in the efficiency with which their isotopes participate in physical, chemical, biological, biochemical, metabolic and climatic processes, and has very different causes. 11,12The magnitude and direction of the variation in the abundance of B isotopes (i.e., 10 B, 11 B) are controlled by the large relative difference in mass of the two isotopes (so called mass dependent fractionation). 11,13,14As a light element, B is highly sensitive to mass dependent fractionation. 13The magnitude and direction of the variation in the abundance of Sr and Pb isotopes are governed by factors such as ratio of radioactive parent and daughter nuclides (i.e., 87 Rb to 87 Sr; 238 U, 235 U and 232 Th to 206 Pb, 207 Pb and 208 Pb, respectively), decay constants and time. 13,15The potential mass dependent fractionation of the radiogenic isotopic signatures of Sr and Pb are considered to be small during geochemical and biochemical processes. 13Even though the relative variation in the isotopic composition of B, Sr and Pb may seem small, they are signicant, robust and measurable, when using appropriate instrumentation and calibration strategies. 14Typically, the isotope ratio analyses of B, Sr and Pb are performed by either multiple collector thermal ionization mass spectrometry (MC TIMS) or multiple collector inductively coupled plasma mass spectrometry (MC ICP-MS).Under optimal conditions, MC TIMS and MC ICP-MS instruments provide isotope ratio precisions of #0.001% RSD (in low resolution). 16,17evertheless, different types of single collector ICP-MS instruments have been applied for isotope ratio applications that could work with rather modest isotope ratio precisions.ICP-MS systems with different mass separation devices, a quadrupole lter (Q), a double-focusing sector eld (SF), and a time-of-ight (TOF), are already commercially available. 18raditionally, these single collector instruments are equipped with an electron multiplier as detector to enable (ultra-)trace analysis.This detector shows its highest sensitivity in pulse counting mode where almost every incoming ion is detected but dead time has to be taken into account. 19At high ion beam intensity, the electron multiplier is used as an analog ampli-er. 17Depending on the isotopic system, with 'traditional' quadrupole-based ICP-MS, the isotope ratio precision is limited to $0.1% RSD under optimal conditions. 17][22] The isotope ratio precision achievable with sector eld ICP-MS under optimal conditions (i.e., only one isotope pair is monitored) is at #0.05% RSD in low resolution.In medium resolution with its rather triangular peak shape the isotope ratio precision of ICP-SFMS (RSD $0.1%) is comparable to 'traditional' ICP-QMS. 16,174][25] The isotope ratio performance of the rst generation ICP-TOFMS is therefore comparable to collision-cell ICP-QMS and ICP-MS/MS instruments, and under optimal conditions even comparable to ICP-SFMS instruments which is attributed to the simultaneous handling of ions formed at the same time in the plasma. 17These rather modest isotope ratio precisions as compared to MC TIMS and MC ICP-MS are the result of the combination of ICP as a rather 'noisy' ion source and the use of only a single detector, which allows only monitoring of a single isotope at a given time. 26s the TOF mass separator accepts all ions at the same time 26 like an ion trap, it is capable of measuring all isotopes of the full elemental mass range quasi-simultaneously with a micro channel plate (MCP) that enables detection of multiple isotopes. 27The MCP detector itself as a whole does not have a dead time. 28In 1993, Myer and Hieje have described and designed a prototype ICP-TOFMS instruments with a MCP. 29heir preliminary isotope ratio analysis achieved a isotope ratio precision of <0.6% RSD. 26,30The second generation of ICP-TOFMS (i.e., employing a MCP as detector to measure a m/z range of approx.1-260) are now commercially available by the manufacturers TOFWERK 31 and Nu Instruments. 32Initial studies reported isotope ratio precision between <0.6% RSD and $0.02% RSD. 27,33This is comparable to the performance of the rst generation of ICP-TOFMS despite the multi-elemental detection capability of the MCP.However, the unique feature of the second generation ICP-TOFMS is multi-ion-counting which enables multi-isotope ratio analysis (i.e., quasisimultaneous detection of multiple isotope systems). 27o matter which of these ICP-MS instrument is used for the isotope ratio analysis, the different efficiency of sample introduction, ion formation, ion extraction, ion transmission, ion separation and ion detection of the ICP-MS itself may result in signicantly biased isotope ratios with respect to the true value. 17,34This phenomenon is referred to as instrumental isotopic fractionation (IIF, aka mass bias, mass discrimination) and has to be corrected for. 34IIF includes all discrimination effects, and it is mainly determined by mass dependent effects but mass independent fractionation has also been observed for ICP-MS.The potential occurrence of mass independent IIF has signicant impact on the choice of the IIF correction model to determine reliable isotope ratios. 35The understanding of the factors that cause IIF phenomena within the ICP-MS is still very limited, and appropriate correction remains a challenge. 12,34,36A number of different strategies to calibrate an ICP-MS measurement for the effect of IIF have been proposed over the years. 35,37For the present study, the following three approaches for IIF correction of B, Sr, and Pb isotope ratios measured by ICP-TOFMS are of interest: (i) In case of Sr, the R con ( 87 Sr/ 86 Sr) (hereinaer referred to as conventional 87 Sr/ 86 Sr isotope ratio) is corrected for IIF internally using the 86 Sr/ 88 Sr isotope ratio (= 0.1194 (ref.38)) by convention assuming that there is no natural fractionation of the 86 Sr/ 88 Sr isotope ratio.Here, a IIF correction factor f is calculated based on empirical fractionation laws and applied under the assumption of a constant IIF correction factor f for both 86 Sr/ 88 Sr and 87 Sr/ 86 Sr isotope ratios. 37This internal IIF correction model can correct for mass dependent IIF but not for any mass independent IIF. 35ii) The internal inter-elemental correction model uses another element similar in mass to the isotopic system of interest to calculate the IIF correction factor f in accordance with empirical fractionation laws, e.g., 205 Tl/ 203 Tl for Pb. 35,39his IIF correction factor f is subsequently applied to the isotopic system of interest assuming a constant IIF for both elements. 37The internal inter-elemental IIF correction model can correct for mass dependent IIF but not for any mass independent IIF. 35iii) The most straight forward approach is the direct comparison of the isotope ratio of the sample and a reference material with known isotopic composition.This method is also referred to as the correction factor method.The standardsample bracketing (SSB) is a special case of the correction factor method where the IIF is monitored in possibly short time intervals by measuring the reference material (bracketing standard) before and aer every sample.The SSB approach is used for calculating delta values, 37 e.g., for B isotopes, 40 and absolute isotope ratios, e.g., B, Sr and Pb. 35,37This external IIF correction model can correct for mass dependent and mass independent IIF. 35aking a closer look at IIF, 34,41 previous studies using the rst generation of ICP-TOFMS reported that the IIF per mass unit is substantial for light elements (e.g., Li has −13%) whereas for high mass elements the IIF per mass unit is signicantly lower (e.g., Pb has 0.2%). 24This is similar to observations from MC ICP-MS and ICP-QMS measurements, where the IIF typically varies systematically from about −13% to −15% for Li to −0.2% for U. 34 Moreover, the rst generation ICP-TOFMS instruments with their different geometry (i.e., orthogonal, axial) reported comparable IIF. 25 However, sudden shis in the IIF per mass unit occurred that indicated non-linear response and have not been explained yet. 24This odd IIF behavior required regular calibration with isotopic reference materials using 42 e.g., the SSB approach.In previous applications of isotope dilution mass spectrometry (IDMS) using second generation ICP-TOFMS, the internal inter-elemental IIF correction model was applied. 43,44owever, the IIF behavior and the applicability of different IIF correction models have not yet been investigated in detail for isotope ratio analysis using second generation ICP-TOFMS.With this background, the present study investigated the performance of a second generation ICP-TOFMS with a MCP detector in terms of isotope ratio precision, isotope ratio trueness and IIF for (multi-)isotope ratio analysis of B, Sr and Pb.These are three isotopic system that cover almost the full mass range, for which different IIF correction strategies are commonly applied and both relative and absolute isotope ratios are reported.

Experimental
Throughout the present study, measurement precision under different specied conditions of measurement are considered: 45 (i) isotope ratio precision (aka internal precision), expressed as RSD, refers to the standard deviation of M runs averaged to one measurement result, (ii) repeatability is the standard deviation of N measurements taken within a short time period, and (iii) intermediate precision is the standard deviation of N measurements over several days and used here as a measure for long-term stability.
Mixtures of NIST SRM 951a, NIST SRM 987, and NIST SRM 981 were prepared volumetrically with dilute nitric acid (w(HNO 3 ) = 2%) to optimize the mixture ratios.These mixtures covered the following mass concentration ranges: B mass concentrations of 100 mg L −1 to 5000 mg L −1 , Sr mass concentrations of 100 mg L −1 to 500 mg L −1 , and Pb mass concentrations of 100 mg L −1 to 2000 mg L −1 .

Instrumentation
The B, Sr and Pb isotope ratio analyses of the single-element solutions and a mixture were conducted using an ICP-TOFMS (icpTOF 2R, TOFWERK, Thun, Switzerland).The ICP-TOFMS analysis was carried out with the standard sample introduction system that consists of a concentric nebulizer and a cyclonic spray chamber.
The instrument was optimized in a daily routine for sensitivity and mass calibration using a tuning solution, containing B, Sr and Pb to maintain a reliable day-to-day-performance.In addition, the instrument was optimized in a weekly routine for mass resolution using the same tuning solution.General instrumental settings for the multi-isotope ratio measurements are described in ESI Table S2.†

Measurement routines, data processing and uncertainty budget
Data collection for samples, isotope reference materials and standards was accomplished with an averaged spectrum acquisition rate of 1.98 Hz (averaged mass spectra are composed of data summed from 11 000 full mass spectra extraction frequency = 21.739kHz), that came up to a spectral averaging time of 0.5 s.Blank correction was performed by subtracting background levels of dilute nitric acid (w(HNO 3 ) = 2%) measured before each sample, isotope reference material, and standards from all isotopes of interest.Data collection for the blank was accomplished over a period of 50 s.For an extended integration time, 33 signals and isotopic ratios were averaged across a time window of 10 s.This divided the total of 400 data points acquired into 20 runs (M).The samples and corresponding isotope reference material and standards were introduced into the plasma in the following sequence: standardsamplestandard, to enable correction for IIF via classical SSB. 34,46Mass concentrations of sample and SSB standard were matched within 10%.All isotope ratio measurements were carried out with ve replicates per sample (N = 5).
The IIF per mass unit for B, Sr, and Pb were calculated in accordance with Heumann et al. 41 and Irrgeher & Prohaska: 34 where IIF is the IIF per mass unit in percent (%), R true is the true/certied isotope ratio of the heavier isotope over the lighter isotope, R measured is the measured isotope ratio of the heavier isotope over the lighter isotope and Dm is the difference in mass between the heavier isotope and the lighter isotope.Throughout this study, isotope ratios of heavier isotope over lighter isotope were considered, and the masses recommended by IUPAC/CIAAW 47,48 were used.For B isotopes, d 11 B SRM951a values were calculated relative to the average isotope ratio of the isotope standard (NIST SRM 951a) from the SSB in accordance with standard protocols. 49,50or Sr isotopes, conventional 87 Sr/ 86 Sr isotope ratios were calculated as commonly agreed on: 51 (i) correction for residual 87 Rb interference via peak stripping 52 of the simultaneously measured 85 Rb and using the natural n( 87 Rb)/ n( 85 Rb) (= 0.3856) ratio recommended by IUPAC/CIAAW, 47,48 without correction of IIF (see discussion in section 3.

5). (ii)
The measured 87 Sr/ 86 Sr isotope ratio was corrected for IIF by applying an IIF correction factor f which was obtained from the measured 86 Sr/ 88 Sr isotope ratio and the conventional 86 Sr/ 88 Sr isotope ratio dened as 0.1194 (ref.38) by using the Russell law. 53A constant IIF correction factor f for both 86 Sr/ 88 Sr and 87 Sr/ 86 Sr isotope ratios was assumed It should be noted that this step is the main difference between the conventional 87 Sr/ 86 Sr isotope ratio and the absolute isotope ratio n( 87 Sr)/n( 86 Sr), since isotope variations are neglected, and an insufficiently accurate value is used for the 86 Sr/ 88 Sr isotope ratio.The commonly accepted value for the conventional 87 Sr/ 86 Sr isotope ratio of the NIST SRM 987 is 0.71025. 54ote, unfortunately this IIF correction model failed for 87 Sr/ 87 Sr isotope ratios measured by ICP-TOFMS (see discussion in Section 3.5).
Furthermore, absolute n( 87 Sr)/n( 86 Sr) isotope ratios were calculated following the classical SSB approach: 35,37,55 (i) correction for residual 87 Rb interference via peak stripping 52 of the simultaneously measured 85 Rb and using the natural n( 87 Rb)/n( 85 Rb) (= 0.3856) ratio recommended by IUPAC/ CIAAW, 47,48 without correction of IIF (see discussion in section 3.5).(ii) A correction factor k was calculated based on the observed bias between the measured 87 Sr/ 86 Sr isotope ratios of the NIST SRM 987 solution and its accepted values (0.71025 (ref.54)).The measured 87 Sr/ 86 Sr isotope ratio of the sample was corrected for IIF via the average correction factor k of the same isotope ratio measured in the NIST SRM 987 solution introduced before and aer each sample.As the same isotope pair from the SSB standard is used to correct IIF in the sample, potential mass independent IIF can be accounted for. 35,56Note, the accepted value of conventional 87 Sr/ 86 Sr isotope ratios for the NIST SRM 987 was used as the anchor point to enable comparison to MC TIMS measurements.
For Pb isotopes, absolute n( 208 Pb)/n( 204 Pb), n( 207 Pb)/n( 204 Pb), n( 206 Pb)/n( 204 Pb) and n( 208 Pb)/n( 206 Pb) isotope ratios were calculated following the classical SSB approach: 35,37,55 (i) correction for residual 204 Hg interference via peak stripping 52 of the simultaneously measured 202 Hg and using the natural n( 204 Hg)/n( 202 Hg) (= 0.2293) ratio recommended by IUPAC/ CIAAW, 47,48 without correction of IIF (see section 3.5).(ii) A correction factor k was calculated based on the observed bias between the measured Pb isotope ratio of the NIST SRM 981 solution and its true certied value.The measured Pb isotope ratio of the sample was corrected for IIF via the average correction factor k of the same isotope ratio measured in the NIST SRM 981 solution measured introduced before and aer each sample.As the same isotope pair from the SSB standard is used to correct IIF in the sample, potential mass independent IIF can be accounted for. 35,56The certied values of Pb isotope ratio of the NIST SRM 981 were used as the respective anchor points.
In addition, the internal inter-elemental IIF correction approach for Pb isotopes using an external standard (= Tl) was investigated.The absolute n( 208 Pb)/n( 204 Pb), n( 207 Pb)/n( 204 Pb), n( 206 Pb)/n( 204 Pb) and n( 208 Pb)/n( 206 Pb) isotope ratios were calculated as follows: 35 (i) correction for residual 204 Hg interference via peak stripping 52 of the simultaneously measured 202 Hg and using the natural n( 204 Hg)/n( 202 Hg) (= 0.2293) ratio recommended by IUPAC/CIAAW, 47,48 without correction of IIF (see section 3.5).(ii) The measured Pb isotope ratios were corrected for IIF by applying a IIF correction factor f which was obtained from the measured n( 205 Tl)/n( 203 Tl) ratio and the natural n( 205 Tl)/n( 203 Tl) ratio recommended by IUPAC/ CIAAW 47,48 by using the Russell law. 53A constant IIF correction factor f for all Pb and Tl isotope ratios is assumed.Note, unfortunately this IIF correction model failed for Pb isotope ratios measured by ICP-TOFMS (see discussion in Section 3.5).
For the single measurement of each sample, the total combined uncertainties for B, Sr, and Pb isotope ratios were calculated using a simplied Kragten approach. 57The standard uncertainties (u = SE) of the sample and both bracketing standards were considered as major contributors to the uncertainty.For the mean B, Sr, and Pb isotope ratios of each sample (N = 5), the total combined uncertainties were calculated using error propagation considering the combined uncertainty of the single measurement and the standard deviation of the mean (u = SE) of the ve replicates.

Mixture of elements
Since overloading of the MCP detector of the ICP-TOFMS occurs at high mass concentrations (total ion intensities >10 7 s −1 ), the composition of the mixture for simultaneous multi-isotope ratio analysis of B, Sr and Pb was optimized.Fig. 1 shows the isotope ratio precision of 11 B/ 10 B, 87 Sr/ 86 Sr and 208 Pb/ 206 Pb for different elemental mass concentrations.The 11 B/ 10 B isotope ratio reached an RSD of about 0.1% at a mass concentration of 5000 mg L −1 .The 87 Sr/ 86 Sr isotope ratio already reached an RSD of about 0.1% at a mass concentration of 500 mg L −1 .This is also the case for 88 Sr/ 86 Sr isotope ratio (see Fig. S1 in ESI †).In case of Pb isotopes, maximum precision of about 0.1% for the 208 Pb/ 206 Pb isotope ratio was reached at a mass concentration of 1000 mg L −1 .Furthermore, it can be observed that RSDs of about 0.1% for 207 Pb/ 206 Pb and <0.3% for x Pb/ 204 Pb were reached at a mass concentration of 1000 mg L −1 (see Fig. S1 in ESI †).Consequently, for maximum precision of all B, Sr and Pb ratios in a mixture the mass concentrations were set to 5000 mg L −1 for B, to 500 mg L −1 for Sr and to 1000 mg L −1 for Pb.At this concentration levels, the observed sensitivity was for B about 270 s −1 (mg L −1 ) −1 , for Sr about 4200 s −1 (mg L −1 ) −1 and for Pb about 1900 s −1 (mg L −1 ) −1 .The mixture of B, Sr and Pb came up to a total of less than 6.5 × 10 6 s −1 for all measured isotopes which did not overload the MCP detector of the second generation ICP-TOFMS.Further, linearity of the MCP detector was seen for B, Sr and Pb over the concentration range of 100 mg L −1 till 5000 mg L −1 (see Fig. S2 in ESI †).

Isotope ratio precision and long-term stability
Table 1 summarizes the precision, the repeatability and the intermediate precision of B, Sr and Pb isotope ratios measured by second generation ICP-TOFMS in 30-40 discontinuous measurements over ve days.This is the rst time, that an isotope ratio precision, expressed as RSD, is reported for an element lighter than m/z = 14 (i.e., B) measured by second generation ICP-TOFMS.The reported precision of 11 B/ 10 B isotope ratios is slightly better than reported in previous studies using rst generation ICP-TOFMS for B 58 and Li 24 isotopes (see Table S1 in ESI †).The reported precision of 88 Sr/ 86 Sr and 87 Sr/ 86 Sr isotope ratios is slightly higher than reported in previous studies 18,24 using rst generation ICP-TOFMS.Nevertheless, the reported isotope ratio precision of Sr is comparable to the previously reported precision of Cu and Ag isotopes measured by second generation ICP-TOFMS. 27,33In case of Pb, the isotope ratio precision reported here is better than reported in most previously studies using rst and second generation ICP-TOFMS 24,27,39,42,59 except for one study using rst generation ICP-TOFMS that reported comparable results 18 (see Table S1 in ESI †).A previous study using second generation ICP-TOFMS investigated the relationship between integration time and isotope ratio precision and showed that the isotope ratio precision can be as good as 0.02% when extended integration times of 100 s are used. 33This isotope ratio precision is comparable to the performance of ICP-SFMS.The same authors pointed out that the isotope ratio precision on second generation ICP-TOFMS is limited by dris in isotope ratios which affects the RSD more at long integration times. 33Overall, this shows that the performance in terms of isotope ratio precision is comparable between rst and second generation ICP-TOFMS, despite the multi-elemental detection capability of the MCP.
The long-term stability for 15 discontinuous measurements of 11 B/ 10 B intensity ratios of NIST SRM 951a, 87 Sr/ 86 Sr intensity ratios of NIST SRM 987 and 208 Pb/ 206 Pb intensity ratios of NIST SRM 981 over a period of eight hours is shown in Fig. 2. The measured intensity ratio values are relatively stable for a period of several hours (e.g., 11 B/ 10 B between 10 : 15 and 14 : 30) where the repeatability is < 0.2% for B, Sr and Pb.However, as previously reported for rst generation ICP-TOFMS, 24,42 sudden shis occur (e.g., 11 B/ 10 B drops approx.1.3% between 14 : 30 and 15 : 30) also for the second generation ICP-TOFMS for reasons that are not clear yet.For isotope ratio measurements, this means that regular calibration ($2 standards h −1 ) with an isotopic reference material is required to monitor and correct for such changes. 24The repeatability of the 15 discontinuous measurements which are shown in Fig. 2 is 0.62% for 11 B/ 10 B, 0.44% for studies 24,42 using the rst generation ICP-TOFMS, the observed variation of isotope ratio values between days is higher than the within day variation (see Table 1).

IIF per mass unit for B, Sr and Pb
In case of B, an IIF per mass unit of −11.3% ± 1.7% (2 s, N = 40) for 11 B/ 10 B intensity ratio was observed for 40 discontinuous measurements of NIST SRM 951a on four days of measurement.This corresponds to an RSD of IIF per mass unit of 8% (see Fig. 3a and Table S1 †).The within day variation (expressed as RSD of IIF per mass unit) ranged between 3.2% and 5.7%.This indicates within and between day instability of the IIF per mass unit for B. The extent and algebraic sign (direction) of IIF per mass unit observed for B using second generation ICP-TOFMS is comparable to IIF per mass unit observed for Li using rst generation ICP-TOFMS. 24n case of Sr, an IIF per mass unit of 2.2% ± 3.7% (2 s, N = 30) for 87 Sr/ 86 Sr intensity ratio was observed for 30 discontinuous measurements of NIST SRM 987 on three days of measurement.This corresponds to an RSD of IIF per mass unit of 85% (see Fig. 3b and Table S1 †).The within day variation (expressed as RSD of IIF per mass unit) ranged between 17% and 26%.This indicates within and between day instability of the IIF per mass unit for Sr which is signicantly higher than observed for B. To the authors knowledge, this is the rst study to report IIF per mass unit for 87 Sr/ 86 Sr isotope ratios using ICP-TOFMS.Previous studies using second generation ICP-TOFMS reported IIF per mass unit for similar masses (Cu, Ag 27,33 ) of <−3% whereas previous studies using rst generation ICP-TOFMS reported IIF per mass unit for similar masses (Rb 23,24 ) of −1.2%.In the present study, only IIF per mass unit reported for day 1 (see Fig. 3b, day 1) are of comparable extent and algebraic sign (−1.4% ± 0.5% (2 s, N = 5)) as reported in the previous studies.For the following measurements (see Fig. 3b, day 2 tillday 5), the present study reports IIF per mass unit of reverse algebraic sign (direction) between 2.4% and 3.6%.Furthermore, similar instability for the IIF per mass unit were also observed for 88 Sr/ 86 Sr (−0.2% ± 3.3% (2 s, N = 5)) for 30 discontinuous measurements of NIST SMR 987 on three days of measurement.This corresponds to an RSD of IIF per mass unit of > 100% (see Fig. S3 and Table S1 in ESI †).The within day variation (expressed as RSD of IIF per mass unit) ranged between 2% and >100%.The observed IIF per mass unit, especially on day 2 (see Fig. S3 in ESI †), is comparable to a previous study on rst generation ICP-TOFMS which reported IIF per mass unit for 88 Sr/ 86 Sr of −0.2%. 24The IIF( 87 Sr/ 86 Sr) per mass unit divided by IIF( 88 Sr/ 86 Sr) per mass unit ranges from about 40% (day 1) to >200% (day 2 till day 5) (compare Fig. 3b and S3 in ESI †).Consequently, the two isotope pairs of Sr (i.e., 87 Sr/ 86 Sr and 88 Sr/ 86 Sr) have signicantly different IIF per mass unit values, no matter whether they were measured in singleelement solution or in a mixture of B, Sr and Pb.This contradicts the observations and assumptions made in MC ICP-MS measurements of constant IIF factors for the isotope pairs within an isotopic system.This issue will be further discussed in Section 3.5.
In case of Pb, an IIF per mass unit of 4.8% ± 1.4% (2 s, N = 30) for 208 Pb/ 206 Pb intensity ratio was observed for 30 discontinuous measurements of NIST SRM 981 on three days of measurement.This corresponds to an RSD of IIF per mass unit of 16% (see Fig. 3c and Table S1 in ESI †).The within day variation (expressed as RSD of IIF per mass unit) ranged between 2.3% and 3.4%.Similar to B, this indicates a lower within and between day instability of the IIF per mass unit for Pb as compared to Sr. Previous studies using second generation ICP-Table 1 Isotope ratio precision, isotope ratio repeatability, and isotope ratio intermediate precision 45  TOFMS reported IIF per mass unit for 208 Pb/ 206 Pb of approx.1% 27 whereas previous studies using rst generation ICP-TOFMS reported IIF per mass unit for 208 Pb/ 206 Pb between −0.2% and −2.2%. 18,24,42The observed IIF per mass unit of the present study has the same algebraic sign (direction) but signicantly higher value than previously reported values from studies using second generation ICP-TOFMS.Furthermore, similar instability, extent and algebraic sign (direction) was observed for the IIF per mass unit of 207 Pb/ 206 Pb (1.9% ± 1.3% (2 s, N = 30)) (see Fig. S4b  As already observed for Sr, this is at odds with the assumption of constant IIF factors for the isotope pairs within an isotope system.This issue will be further discussed in Section 3.5.Overall, it could be observed that the IIF per mass unit of second generation ICP-TOFMS has a negative value for B (a light mass), a value around zero for Sr (a medium mass) and a positive value for Pb (a heavy mass), when measured in singleelement solutions and in a mixture of all three elements.Further, different pairs of isotopes from the same element (i.e., Sr, Pb) showed signicantly different IIF per mass unit, when measured in single-element solutions and in a mixture of B, Sr and Pb.To the authors knowledge, this is the rst study using a second generation ICP-TOFMS that compared the IIF per mass unit of different isotope pairs of the same element.Nonetheless, previous studies using rst generation ICP-TOFMS also reported different IIF per mass unit for different isotope pairs of the same element (i.e., Mg, 23 Zr, 30 Cd, 24,30 Nd, 30 Ba, 24 Pt, 23,24 Hg, 60 Pb 24,42 ) using rst generation ICP-TOFMS (see Table S1 in ESI †).In contrast, in previous studies of the authors using sector eld (MC) ICP-MS equipped with an ion counter or Faraday cups as detectors, highly reproducible and always negative values for IIF per mass unit were observed for all isotope pairs of an isotopic system (i.e., B of about −13% (as obtained from raw data of the ERM-AE101a certication study), Sr of about −2.1% and Pb of about −0.6% (as obtained from raw data of Retzmann et al. 55 )).The nature of the odd IIF is further investigated in the following section.Potential causes for the observed (sudden) shis and bias in the B, Sr and Pb isotope ratios when using second generation ICP-TOFMS will be discussed in detail in Section 3.6.

Potential non-mass dependent fractionation in ICP-TOFMS
The observation of signicantly different IIF per mass unit values for different isotope pairs of a same isotopic systems is an odd IIF behavior, given that the ICP-TOFMS provides quasisimultaneously isotope detection.The three-isotope plots can be used to investigate the IIF behavior in more detail: The slope, b exp., obtained from a three-isotopes plot is compared to the expected "theoretical" slope of common mass dependent fractionation functions, such as the Russell's law, b theo-Russell . 53,61hen b exp.agrees with the expected "theoretical" b theo-Russell , it indicates mass dependent fractionation which can be corrected for using all common IIF correction model (e.g., internal IIF correction and SSB).When b exp.differs signicantly from the expected "theoretical" b theo-Russell it indicates mass independent fractionation. 35,61,62Fig. 4 shows the three-isotope plots of the natural logarithm of 88 Sr/ 86 Sr vs. 87 Sr/ 86 Sr isotope ratios from six measurements of pure NIST SRM 987 single-element solution over two hours.Fig. 5a shows the three-isotope plots of the natural logarithm of 208 Pb/ 206 Pb vs. 207 Pb/ 206 Pb from six measurements of pure NIST SRM 981 single-element solution over two hours.The reported b exp.do not agree with the expected "theoretical" b theo-Russell , this is neither the case for the three Sr isotopes nor for the three Pb isotopes.This is also observed for measurements when Sr and Pb isotopes ratios were measured simultaneously from a mixture of B, Sr and Pb (see Fig. S7 and S8 in the ESI †).Further, there is no agreement with other mass dependent fractionation functions (i.e., equilibrium law, compare b theo-Equilibrium (Sr) = 0.5065 and b theo-Equilibrium (-Pb) = 0.5026 with Fig. 4 and 5a).In addition, Fig. 5b shows the four-isotope plot of the natural logarithm of 205Tl/ 203 Tl vs. 208 Pb/ 206 Pb isotope ratios from two discontinuous measurements of NIST SRM 981 and Tl single-element standard over 30 minutes.The four-isotope plot of Tl and Pb also does not show the expected slope.
The three-isotope plots of Sr and Pb as well as the four-isotope plot of Tl-Pb do not show mass dependent IIF but indicate nonmass dependent fractionation (see Fig. 4 and 5).This means that the IIF factor is not the same for different isotope pairs of a same or adjacent isotopic systems and possible mass independent IIF takes place during the ion formation, ion extraction, ion transmission, ion separation and ion detection in ICP-TOFMS.Consequently, mass dependent correction models such as internal IIF correction applying the Russell law cannot be used to correct the potential mass independent IIF 35,61,62 observed for Sr and Pb isotope ratio analysis using second generation ICP-TOFMS (see Section 3.5).The applicability of IIF correction models are described in more detail in the section 3.5.Comparing the correlation quality of IIF trends for different mass spectrometer in three-isotope plots, highly correlated mainly mass dependent IIF for MC TIMS and MC ICP-MS instruments is typically observed (see Fig. 4).For second generation ICP-TOFMS, the correlation coefficients for the IIF trends for single-element solutions of Sr and Pb in Fig. 4 and 5 are very low (R 2 < 0.4), indicating that the single datapoints are not well correlated with each other, and mainly non-mass dependent correlations between the individual isotopes of an element were observed.Similar, it can be observed that the correlation coefficients for the IIF trends of mixtures of B,  Sr and Pb in Fig. S7 and S8 † (in ESI) are very low (R 2 < 0.6).If the experimental data of the three-isotope plot are not correlated, instrumental artefacts are possibly the reason for the observed offsets. 61Other reasons could be caused by the observed unstable IIF over time (i.e., two hours), the large scatter of the ICP-TOFMS measurement (possibly related to the short integration time), and/ or multiple IIF processes occurring during ion formation, ion extraction, ion transmission, ion separation and ion detection that could be contradictory and/or of varying contributions.Further, the presence of potential non-mass dependent fractionation limits the applicability of IIF correction models are described in more detail in the Section 3.5.

Applicability of the internal IIF correction model
In case of Sr, the conventional 87 Sr/ 86 Sr isotope ratio which is corrected for IIF internally using the 86 S1 in ESI †), internal normalization appears to be working for day 2 but not for day 4 and day 5. Similar to Sr, when the IIF per mass unit and consequently the IIF factors are signicantly different, as it is the case for 208 Pb/ 206 Pb and 206 Pb/ 204 Pb (see Table S1 in ESI †), the internal IIF correction model fails no matter whether measured in a single-element solution or a mixture of B, Sr and Pb.This observation supports the assumption that non-mass dependent IIF occurs during ion formation, ion extraction, ion transmission, ion separation and ion detection of second generation ICP-TOFMS.Additionally, internal inter-elemental IIF correction using Tl isotopes which is added to the sample for this purpose has been a popular approach to determine absolute Pb isotope ratios based on the assumption of identical IIF correction factors for Pb and Tl.However, more recent studies using MC ICP-MS recognized that different elements can be isotopically fractionated and consequently the derived isotope ratios can be erroneous. 62It can be seen in Fig. 6 that this IIF correction approach fails for 208 Pb/ 206 Pb isotope measurements using second generation ICP-TOFMS.The determined 208 Pb/ 206 Pb isotope ratio of NIST SRM 981 is 2.1738 ± 0.0042 (2 s, N = 3) for a mixture of B, Sr, Tl and Pb.This value does not overlap within uncertainty with the certied 208 Pb/ 206 Pb value of the NIST SRM 987 (= 2.1681 ± 0.0008, U, k = 2).The determined 208 Pb/ 206 Pb isotope ratio of ERM-AE142 is 1.8556 ± 0.0038 (2 s, N = 3) for a mixture of B, Sr, Tl and Pb.This value does not overlap withing uncertainty with the certied 208 Pb/ 206 Pb value of the ERM-AE142 (= 1.8874 ± 0.0010, U, k = 2).Previous studies using rst generation ICP-TOFMS and internal inter-elemental IIF correction using Tl successfully determined Pb isotope ratios, 39 but failed to determined reliable Hg isotope ratios. 60Consequently, only correction models that do not rely on empirical fractionations functions and that can correct for mass dependent IIF as well as potential mass independent IIF, like the SSB approach (incl.external normalization-SSB), 35 are recommended to be used for isotopic analysis using second generation ICP-TOFMS.In addition, it was observed that the internal intra-elemental normalization (i.e., 86 Sr/ 88 Sr for 87 Sr/ 86 Sr, 207 Pb/ 206 Pb and 206 Pb/ 204 Pb for 208 Pb/ 206 Pb) and the internal inter-elemental normalization (i.e., Pb and Tl) signicantly harmonizes and reduces the IIF per mass unit (see Fig. 3b and 6).This is seen as an indication that change in IIF throughout a ICP-TOFMS measurement is approximately the same for all the different isotopes, even if the fractionation laws do not apply: i.e., the IIF for 206 Pb/ 204 Pb changes to the same extent as that for 208 Pb/ 206 Pb; so, both IIF per mass unit increase or decrease accordingly, but do not agree with respect to the mass dependent fractionation.Assuming a parameter such as plasma power changes, it has the same effect on both isotope ratios, but without changing the ratio to each other.
The internal intra-elemental normalization for isotope pairs with similar IIF factors (i.e., 208 Pb/ 206 Pb and 207 Pb/ 206 Pb) and the internal inter-elemental normalization applied for Pb works more efficiently as it reduces the IIF per mass unit to <1% than the internal intra-elemental normalization applied for isotope pairs with signicantly different IIF factors of Sr and Pb (i.e., 208 Pb/ 206 Pb and 206 Pb/ 204 Pb) which only reduces the IIF per mass unit to about 2.5% (see Fig. 3b and 6).Thus, perhaps the application of the combination of internal inter-elemental IIF correction and external IIF correction (i.e., external normalization-SSB, aka combined standard-sample bracketing and internal normalization isotopic fractionation correction model) in accordance with standard protocols 34,35,56 could lead to more precise and more true isotope ratios.

Potential source of odd IIF behavior within ICP-TOFMS
In ICP-MS, IIF represents the sum of effects in the instrument that occur during sample introduction, ion formation, ion extraction, ion transmission, ion separation and ion detection which lead to a difference between the true isotope ratio and the measured isotope ratio.IIF includes all discriminating effects within the ICP-MS instrument and describes mass dependent as well as mass independent effects.The extent of IIF differs signicantly between MS techniques and can be expressed by IIF per mass unit (see eqn (1)). 34However, external parameters such as analyte contamination, interferences and matrix effects can also introduce bias into isotope ratio measurements using ICP-MS or even affect the IIF occurring within the instrument.
3.6.1 Analyte concentration, contamination, and interferences.No consistent trend was observed that could indicate a correlation between mass concentration and the extent of the IIF per mass unit for B, Sr and Pb isotope ratios measured using second generation ICP-TOFMS (see Section 1 in ESI †).Nonetheless, the data suggests that the sample and standard must be at the same analyte concentration (<10%) for SSB to work.
If signicant amounts of analyte are present during the ICP-MS measurement (in absence of the sample), the isotope result is potentially biased. 12This is negligible for the present study, as blank corrections were performed as part of the data reduction and blank contributions were #0.15% for all isotopes under investigation.
Interferences can alter, modify or disrupt the isotope measurement signal of an ICP-MS. 52There are two groups of interferences: (i) the spectral interferences include bias based on isobaric, polyatomic and doubly-charged ions. 12,52As all analyses of the present study were performed with pure isotope certied reference materials either as single-element solution or as mixture of B, Sr and Pb, isobaric interferences can be neglected.Further, none of the analytes in the mixture (B, Sr, Pb) poses a problem to create doubly-charged or polyatomic interferences for one of the other analytes. 55(ii) The non-spectral interferences refer mainly to systematic bias introduced by variable matrix (i.e., matrix effects), e.g.isobaric and polyatomic interferences, signal instability, varying instrumental isotopic fractionation effects and loss of sensitivity due to signal suppression and material deposition. 64urther, noticeable space charge effects were observed for ICP-MS when heavy ions were added to lighter analytes. 36,65,66The odd IIF behavior of B, Sr and Pb isotopes when measured by second generation ICP-TOFMS occurred no matter whether the isotope ratios were measured in a single-element solutions or a mixture of B, Sr and Pb (see Fig. 3).Even repeated measurements of the same mixtures of B, Sr and Pb showed different IIF on different days (compare day 2 and day 5 in Fig. 3).Same is true for the threeisotope plots of Sr and Pb where the correlation is poor no matter whether the isotope ratios were measured in a singleelement solutions or a mixture of B, Sr and Pb (see Section 3.4).In addition, previous studies by the authors have shown no matrix effect of Pb on Sr isotope ratio measurements and vice versa. 55onsequently, potential matrix effects attributable to the mixing of B, Sr and Pb are not considered here as the driving force for the odd IIF behavior observed for second generation ICP-TOFMS.
3.6.2Instrumental noise and bias.The understanding of the causes for the IIF phenomenon (incl.mass independent IIF) within the ICP-MS is still limited but possible sources include supersonic expansion, space charge effects, ionization efficiency, diffusion repulsion, absolute isotope mass, ion density nuclear eld shi and magnetic isotope effect. 34,35IIF is usually most pronounced during sample introduction, ion formation and ion extraction (interface region) of ICP-MS instruments and the effects in this region are supposed to be the major determining factors regarding IIF (see Fig. 7). 3436]67 In accordance to eqn (1), this should report a negative IIF per mass unit value.The sample introduction and interface region of the ICP-TOFMS (by TOFWERK) is essentially the same as of the ICP-QMS (by Thermo Fisher). 31,33Consequently, the IIF effect in this region of the ICP-TOFMS should be the same as observed for other ICP-MS instruments.However, for isotopic measurements of Sr and Pb using second generation ICP-TOFMS, IIF behavior favoring lighter isotopes over heavier ones was observed in this study.Accordingly, the sample introduction and interface region are not the only regions with major determining factors regarding IIF for ICP-TOFMS.
The second generation ICP-TOFMS used in the present study applies a notch lter 33,68 (i.e., quadrupole) before the TOF analyzer to selectively excite and remove ions of four m/z regions (e.g., eliminate 40 Ar) from the spectra. 27Additional IIF may occur in the quadrupole mass lter used due to mass scale shis which would favor lighter isotopes over heavier ones. 69If this IIF effect would be more pronounced than the IIF effects of the sample introduction and interface region, a positive IIF per mass unit would be reported in accordance to eqn (1).Hence, it may be assumed that the notch lter contributes to the partially reverse IIF behavior observed for the second generation ICP-TOFMS.Although in ICP-QMS also a normal IIF caused by discrimination of the lighter ions is observed 41,69 which disproves this assumption.Considering that the front section (incl.notch lter) of the ICP-TOFMS (by TOWERK) is basically a normal ICP-QMS 31 (see Fig. 7) it is less likely that potential mass scale shis in the notch lter are a major cause for the odd IIF behavior which only leaves the TOF analyzer.
The TOF analyzer is positioned behind the notch lter, and its working principle is signicantly different to quadrupole-based and sector eld-based (MC) ICP-MS instruments.The TOF analyzer consists of an extractor and a ight region (see Fig. 7). 33,70For the ion separation, the ions are accelerated by the electric eld of the extractor which should give all ions a similar kinetic energy into the TOF chamber. 70Then the ion beam passes through two plates to which a voltage pulse is applied that creates a deection eld. 29This pulsed eld creates a sweeping action across the slit ahead of the ight region which sends an ion pulse (i.e., ion package) to dri through the ight region (= eld free region). 29At the MCP detector, the time between the ion extraction at the extractor and the collision with the detector is recorded which is a function of the ions mass and subsequent velocity. 70Remaining variation of kinetic energy at the extractor would mean that ions of different mass in the ion pulse leave the extractor at slightly different angles. 67his would cause somewhat different paths through the ight region and result in IIF. 29,67It seems likely that this causes the instability in the IIF behavior within the ICP-TOFMS.Since both negative and positive IIF per mass units are reported for ICP-TOFMS, it can be assumed that the contributions of IIF caused by sample introduction and interface in relation to the contribution of IIF caused by the TOF analyzer are almost equal: For the light mass B, sample introduction and interface predominate the IIF behavior, for the medium mass Sr, the IIF effects balance each other out, and for the heavy mass Pb, the TOF analyzer predominates the odd IIF behavior.Furthermore, different IIFs per mass unit were observed for different isotope pairs of the same and adjacent isotopic system (i.e., Sr, Pb, Tl) using second generation ICP-TOFMS to measure single-element solutions and mixtures.With respect to sector eld (MC) ICP-MS measurement, the authors observed previously that the IIF per mass unit ratios of several isotope pairs of the isotopic systems Sr and Pb agreed within 5% which legitimates the assumption of constant IIF factors.Previous studies that investigated several isotope pairs of the isotopic systems Mg, 23 Zr, 30 Cd, 24,30 Nd, 30 Ba, 24 Pt, 23,24 Hg, 60 Pb 24,42 using rst generation ICP-TOFMS have also reported not constant IIF per mass units for different isotope pairs of the same element (see Table S1 in ESI †).Consequently, it is deduced here that the observed odd IIF effect of ICP-TOFMS is possibly caused by the generation of ion packages in the TOF mass separator.The same logic can be applied to the sudden shis 24 already reported for the rst generation ICP-TOFMS.This assumption is further supported by a study applying a thermal ionization cavity (TIC) source with a TOFMS that reported different IIF factors for different isotope pairs of the same element despite the prediction of mass dependent IIF originating from the TIC source. 71inally, detector dead time and counting statistics may create a noise or bias to the isotope ratio measurements.According to the manufacturer of the ICP-TOFMS, the MCP detector itself as a whole does not have a dead time. 28Potential contributions by counting statistics can only be minor as the odd IIF and sudden shis 24 have been reported in previous studies applying rst generation ICP-TOFMS which used a SEM detector instead of MCP detector (see Table S1 in ESI †).Note, intensities are reported as average of a dened number of extractions per integration time.Future studies might take a closer look into the isotope ratios per single extraction which might help rening the isotope ratio precision.
3.6.3Causes of non-mass dependent IIF.Nuclear eld shi (aka nuclear volume effect) and magnetic isotope effect (aka nuclear spin effect) are oen attributed as causes for non-mass dependent IIF in ICP-MS but they are still under discussion. 35In case of Sr, magnetic isotope effect can arise from interaction of the spin-spin coupling in magnetic nuclei such as 87 Sr (I = 4.5).Non-mass dependent IIF has been reported for 87 Sr in a study using MC ICP-MS. 56In general, this could explain the observation of the present study that IIF per mass unit and consequently IIF factors of 87 Sr/ 86 Sr and 86 Sr/ 88 Sr do not agree and internal IIF correction fails.In case of Pb, non-mass dependent IIF based on nuclear eld shi and magnetic isotope effect ( 207 Pb: I = 0.5) is expected for 207 Pb, but previous studies using MC ICP-MS also reported non-mass dependent IIF for 204 Pb which cannot be expected from nuclear eld shi or magnetic isotope effect ( 204 Pb: I = 0.0). 35In the present study, the IIF per mass unit and consequently the IIF factors of 208 Pb/ 206 Pb and 207 Pb/ 206 Pb are comparable and enabled internal IIF to some extent (see section 3.5) whereas the values for 206 Pb/ 204 Pb are signicantly different (see Table S1 in ESI †).This contradicts the expectation of non-mass dependent IIF for 207 Pb, but it supports the observation of non-mass dependent IIF for 204 Pb although nuclear eld shi and magnetic isotope effect do not indicate this.Further investigation on the causes of the odd IIF occurring during isotopic measurements using second generation ICP-TOFMS is required.

Determination of d-values and absolute isotope ratios by ICP-TOFMS using SSB
Since potential non-mass dependent IIF was observed in this study, only isotopic results based on SSB approach are reported as successful here.If mass independent IIF is stable over time, it has no effect on the accuracy of the SSB as IIF correction model as it used the same isotope pair for IIF correction in the SSB standard and the sample, 35 but non-stable IIF within the ICP-MS leads to decreased accuracy and precision of the isotope data, 62 as observed here.Furthermore, since possible mass independent IIF would also affect the applicability of mass dependent IIF correction models to correct for isobaric interferences (i.e., Rb, Hg), the interference corrections were performed without IIF in the present study.
Table 2 reports the determined d 11 B SRM951a , conventional 87 Sr/ 86 Sr isotope ratios, and absolute n(  2 and Fig. S9 in ESI †).This is regardless of whether the analysis was performed in a single-element solution or in the mixture of all three elements.Consequently, simultaneous multi-isotope analysis is truly possible using second generation ICP-TOFMS and the SSB approach.Nonetheless, future studies using second generation ICP-TOFMS for n( 87 Sr)/n( 86 Sr) and Pb isotope ratio measurements should consider the application of the external normalization-SSB approach 34,35,56 for IIF correction.
Reported relative uncertainties range from 3%-8% for d( 11 B/ 10 B), about 0.10% for absolute 87 Sr/ 86 Sr isotope ratio and between 0.04% and 0.16% for absolute Pb isotope ratios.These are signicantly worse (i.e., approx. 1 to 2 orders of magnitude) than for MC ICP-MS and MC TIMS.This is likely be explained by non-stable IIF.

Conclusion
The present study of B, Sr and Pb (multi-)isotope ratios using second generation ICP-TOFMS has shown that the performance in terms of isotope ratio precision is comparable between rst and second generation ICP-TOFMS, despite using an MCP instead of SEM providing multi-elemental detection capability.The measured isotope ratios are stable for a period of several hours for B, Sr and Pb showing repeatability of <0.2% but consistent with other studies using rst generation ICP-TOFMS, sudden shis in IIF occur for reasons that are not clear yet but presumably originate from the TOF analyzer.The general trend, extent, and algebraic sign (direction) of IIF per mass unit observed for B, Sr and Pb using second generation ICP-TOFMS is mostly comparable to IIF per mass unit observed in previous studies using rst and second generation ICP-TOFMS.However, different IIFs per mass unit were observed for different isotope pairs of the same isotopic system (i.e., Sr, Pb) and adjacent isotopic systems (i.e., Pb vs. Tl) using second generation ICP-TOFMS no matter whether measured in a single-element solution or a mixture of B, Sr and Pb.These odd IIF effects possibly origin from TOF mass analyzer, in particular the extractor, and/ or notch lter.This observation and the observations from three-isotope plots for Sr and Pb showed that the IIF occurring during ion formation, ion extraction, ion transmission, ion separation and ion detection of second generation ICP-TOFMS does not follow the known mass dependent fractionation laws.Since this odd IIF behavior occurred when measuring singleelement solutions as well as a mixture of B, Sr and Pb, it is not linked to interferences or matrix effects.Furthermore, the IIF behavior is possibly caused by mass independent fractionation, and/or multiple (contradictory) fractionation processes with varying contributions this should be further investigated by future studies.Consequently, the internal IIF correction model was proven to be unsuitable for Sr and Pb isotope ratio analysis using ICP-TOFMS because it relies only on mass dependent behavior of IIF.Isotope ratio analysis using ICP-TOFMS require IIF correction models that can also correct for the possible mass independent fractionation such as the SSB approach that has proven its applicability in the present study.
In addition, the internal normalization has shown that it signicantly harmonizes and reduces the IIF per mass unit.Therefore, future studies should investigate the external normalization-SSB model for more reliable isotope ratios using second generation ICP-TOFMS.It was shown that reliable d 11 B values, and absolute B, Sr and Pb isotope ratios can be determined in single-element solutions as well as a mixture of all three elements, measured simultaneously, using second generation ICP-TOFMS and the SSB approach.The precision, uncertainty and the required analyte mass concentration is typically more than one order of magnitude worse than for measurement procedures using MC ICP-MS or MC TIMS.Nevertheless, second generation ICP-TOFMS in combination with SSB approach is a suitable tool for (multi-) isotope ratio analysis applications that could work with rather modest isotope ratio precisions like provenance studies that have signicantly different endmembers (e.g., B, 49 Sr, 72 Pb 10 ) or geochronology. 73Furthermore, the second generation ICP-TOFMS has the distinct advantage that it allows simultaneous multi-isotope analysis of short transient signals (e.g., LA-ICP-MS) which cannot be achieved by ICP-QMS, ICP-SFMS, and MC ICP-MS.It reduces effort for multi-isotope ratio analysis (does not require multiple analyses for multiple isotope systems) and provides true simultaneous multi-isotope data for the same data point.
Having an isotope ratio performance that is in the range of ICP-QMS and ICP-SFMS, second generation ICP-TOFMS should be a suitable tool for IDMS.In this context, particular attention should be paid to the unique feature of the second generation ICP-TOFMS of multi-isotope analyses, which allow multi-IDMS as already shown in a previous study. 27However, care must be taken to ensure that all isotope ratios are measured within the same analytical sequence so that IIF correction factors will cancel out in the IDMS calculations. 37In view of the obtained results it is highly recommended to use the SSB approach and calculate the IDMS results with already IIF corrected isotope ratios.Especially for long sequences such as in double or triple IDMS or when applying isotope dilution in hyphenated techniques the SSB correction is deemed reasonable.

Fig. 1
Fig. 1 Isotope ratio precision of 11 B/ 10 B, 87 Sr/ 86 Sr and 208 Pb/ 206 Pb, expressed as RSD (%), for an acquisition time of 10 s per run (M) and M = 20, obtained for different elemental mass concentrations.The data shown are from the measurement of a mixture in which B, Sr, and Pb were detected simultaneously.

Fig. 2
Fig. 2 Long-term stability of 11 B/ 10 B, 87 Sr/ 86 Sr and 208 Pb/ 206 Pb isotope ratios over eight hours for 15 discontinuous measurements of NIST SRM 951a, NIST SRM 987 and NIST SRM 981.Error bars correspond to 2 s (acquisition time of 10 s, M = 20).The data shown are from the measurement of a mixture in which B, Sr, and Pb were detected simultaneously.

Fig. 3
Fig. 3 (a) 11 B/ 10 B intensity ratios, (b) 87 Sr/ 86 Sr intensity ratios and conventional 87 Sr/ 86 Sr isotope ratios, and (c) 208 Pb/ 206 Pb intensity ratios over a period of five days for 30-40 discontinuous measurements of NIST SRM 951a, NIST SRM 987 and NIST SRM 981.The reported data are from measurements of both a single-element solution (,) and a mixture (-) of B, Sr and Pb.For Sr and Pb, additional internal normalized values ( , ) are reported.Error bars correspond to 2 s (acquisition time of 10 s, M = 20).

Fig. 4
Fig. 4 Three-isotope plot for Sr from measurements over several hours of NIST SRM 987 using ICP-TOFMS (integration time 0.5 s, M = 2000), MC TIMS (integration time 24 s, M = 443) and MC ICP-MS (integration time 42 s, M = 238).Solid lines represent experimentally determined slopes (b instrument ) and predicted mass dependent fractionation line (b theo-Russell ).All data points were taken from measurements of pure NIST SRM987 single-element solution.

Fig. 5
Fig. 5 (a) Three-isotope plot for Pb arising from six measurements over two hours of a pure NIST SRM 981 single-element solution (integration time 0.5 s, M = 2000), and (b) four-isotope plot for Tl-Pb arising from two discontinuous measurements over 30 minutes of mixture of NIST SRM 981 and Tl single-element standard (integration time 0.5 s, M = 800).Solid lines represent experimentally determined slope (b exp. ) and predicted mass dependent fractionation line (b theo- Russell ).
Sr/ 88 Sr isotope ratio (= 0.1194 (ref.38)) is commonly reported in MC ICP-MS and MC TIMS measurements.It is clear from Fig. 3b that the application of this internal IIF correction model fails for 87 Sr/ 86 Sr isotope ratio measurements using second generation ICP-TOFMS.The determined conventional 87 Sr/ 86 Sr isotope ratio of NIST SRM 987 is 0.69405 ± 0.00097 (U, k = 2, N = 5) in a single element solution and 0.69199 ± 0.00059 (U, k = 2, N = 25) in the mixture of B, Sr and Pb.This is signicantly different from the commonly accepted value for conventional 87 Sr/ 86 Sr isotope ratio of the NIST SRM 987 (= 0.71025 (ref.54)) no matter whether measured in a single-element solution or a mixture of B, Sr and Pb.This observation supports the assumption that non-mass dependent IIF occurs during ion formation, ion extraction, ion transmission, ion separation and ion detection of second generation ICP-TOFMS.Furthermore, the conventional 87 Sr/ 86 Sr isotope ratio obtained by ICP-TOFMS is outside the range for terrestrial 87 Sr/ 86 Sr values. 63Fig. 3c shows the 208 Pb/ 206 Pb isotope ratios of the NIST SRM 981 normalized to the certied isotope ratios of 207 Pb/ 206 Pb and 206 Pb/ 204 Pb.As the IIF per mass unit and consequently the IIF factors of 208 Pb/ 206 Pb and 207 Pb/ 206 Pb are quite similar (see Table

Fig. 6
Fig. 6 208 Pb/ 206 Pb intensity ratios and absolute 208 Pb/ 206 Pb isotope ratios (internal inter-elemental IIF correction using Tl) for three measurements of NIST SRM 981 and ERM-AE142.Error bars (smaller than symbols) correspond to 2 s (acquisition time of 10 s, M = 20) and are smaller than the symbols.The data shown are from the measurement of a mixture in which B, Sr, Tl and Pb were detected simultaneously.

Fig. 7
Fig. 7 Schematic illustration of the second generation ICP-TOFMS highlighting potential sources for instrumental noise and instrumental bias.