Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectrometry

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectrometry (IDMS)

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectrometry (IDMS)

Co-ordinating Editors Mike Sargent and Rita Harte Laboratory of the Government Chemist, Teddington, UK

Chris Harrington De Montfort Universip, Leicester, UK RSC Analytical Methods Committee Sub-committee on High Accuracy Analysis by Mass Spectrometry (HAAMS)

RSeC ROYAL SOCIETY OF CHEMISTRY

Setting standards in analflical science

VALIDANALYIICAL MEASUPEMENT

The work described in this book was supported under contract with the Department of Trade and Industry as part of the National Measurement System Valid Analytical Measurement (VAM) Programme.

A catalogue record for this book is available from the British Library ISBN 0-85404-418-3 OLGC Limited, 2002 Published for Laboratory of the Government Chemist by The Royal Society of Chemistry, Thomas Graham House, Science Park, Milton Road, Cambridge CB4 O W , UK Registered Charity Number 207890 Typeset by Keytec Typesetting Ltd. Printed and bound by Athenaeum Press Ltd, Gateshead, Tjne & Wear

Preface

This guide provides a general introduction to the use of the isotope dilution mass spectrometry (IDMS) technique for high accuracy measurements* but, more importantly, it describes two specific methodologies for applying the technique. These methodologies, one for inorganic mass spectrometry and the other for organic mass spectrometry, have been developed and tested through a series of collaborative studies carried out by a sub-committee of The Royal Society of Chemistry's Analytical Methods Committee. The Sub-committee on High Accuracy Analysis by Mass Spectrometry (HAAMS) was formed in 1997 to assist in the development by LGC of robust IDMS procedures which could be used in the certification of standards and reference materials or in other applications requiring high accuracy. The IDMS technique is well known and widely reported in the literature. Its application can, however, present considerable difficulties and without extensive development for a specific application may well give less accurate data than conventional calibration. The aim of the work encapsulated in this Guide was to make available simplified and robust IDMS methodology together with adequate guidance to enable laboratories applying the technique to obtain reliable data for specific applications without the need to embark on major analytical development projects. It must be emphasised, however, that the necessity remains to carefully validate each application of the methodology described here. There is a fhdamental difference between organic and inorganic IDMS. For organic IDMS the natural sample contains negligible amounts of the isotopically labelled analogue (conversely, the isotopically labelled analogue will contain negligible amounts of the analyte compound). In the case of inorganic IDMS the isotopically enriched analogue (isotopic spike) will often be present in significant amounts in the natural sample, e.g. 'natural silver is lo7Ag 51.84% and lo9Ag 48.16%. An enriched silver spike might be "'Ag 80% and lo9Ag20%. In other words the natural and spike materials would both be mixtures of the same isotopes, but in different proportions. The conceptual complications that arise from this aspect of inorganic IDMS have prompted the inclusion of a more detailed, graphical explanation for inorganic IDMS. LGC has prepared this guide in association with the Sub-committee as part of an extensive programme on high accuracy analysis that is being carried out for the Department of Trade and Industry Valid Analytical Measurement (VAM) *For the purpose of this guide high accuracy methods are considered to be those that provide measurements closest to the true value.

vi

Guidelines for Achieving High Accuracy in Isotope Dilution Mass SpectromeQ

Programme. The principal contributors from LGC were Tim Catterick, Ben Fairman, Mike Sargent, Ken Webb and Celine Wolff Briche. We are gratefbl to the Sub-committee Chairman, Gerry Newman, and members for their invaluable help and advice.

Members of AMC Sub-committee on High Accuracy Analysis by Mass Spectrometry During the Preparation of this Guide: Dr Peter Ash Dr David Blundell Dr Jim Carter Dr Tim Catterick Dr Jim Crighton Dr Mike Cullen Dr Trevor Delves Dr Hywel Evans Dr Ben Fairman Mr Steve Gardner Dr Colin Hamlett Dr Howard Handley Miss Rita Harte Dr Simon Hird Dr Ed Houghton Dr Neil Hudson Dr John Lewis Dr Andrew Midwood Professor John Monaghan Dr Gerry Newman Dr Gavin O’Connor Dr Marina Patriarca Dr Chris Pickford Dr Mike Sargent Ms Christine Sieniawska Dr Jim Startin Dr Jason Truscott Dr Ken Webb Dr Mark White Mr John Wilson Dr Ckline Wolff-Briche Mr David Wood

Johnson Mathey Technology Centre Johnson Mathey Technology Centre University of Bristol LGC BP Chemicals LGC University of Southampton University of Plymouth LGC Eclipse Scientific RHM Technology Ltd. Dynamco Scientific Services LGC Secretariat Central Science Laboratory Horseracing Forensic Laboratory Ltd. South East Water Ltd. Central Science Laboratory MLURI University of Edinburgh Chairman LGC University of Edinburgh AEA Technology LGC University of Southampton Central Science Laboratory University of Plymouth LGC Health and Safety Laboratory RSC LGC Scientific Analysis Labs. Ltd.

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Mike Sargent Manager, VAM High Accuracy Analysis Programme LGC January 2002

Contents

1 Introduction 1.1 Advantages and Disadvantages of IDMS 1.1.1 Advantages 1.1.2 Disadvantages of IDMS

2 The Principles of IDMS

3

3 Critical Stages and Sources of Error 3.1 Introduction 3.2 Sample Preparation 3.2.1 Inorganic IDMS 3.2.2 Organic IDMS 3.3 Selection of the Isotopic Analogue 3.4 Addition of the Isotopic Analogue 3.5 Characterisation of the Isotopic Analogue 3.6 Blank Correction 3.7 Instrumental Analysis 3.7.1 Instrumentation for organic mass spectrometry 3.7.2 Instrumentation for inorganic mass spectrometry 3.8 Calibration Procedures 3.8.1 Graphical method 3.8.2 Bracketing method 3.8.3 Single point calibration 3.8.4 Exact signal matching method 3.8.5 Approximate signal matching method 3.9 Isotopic Interferences 3.10 Isotopic Discrimination 3.10.1 Isotopic fractionation 3.10.2 Mass discrimination (mass bias) 3.10.3 Detector dead time (ICP-MS) 3.11 Aspects of Achieving High Accuracy Measurements 3.1 1.1 Precision 3.1 1.2 Sensitivity 3.1 1.3 Specificity

4 4 5 5 6 6 6 7 8 8 8 9 10 10 11 11 11 12 12 14 14 15 15 15 15 16 16

The Structured Approach to IDMS analysis 4.1 The ‘Exact signal matching’ Method for Organic IDMS

17 17

4

...

Vlll

5

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectrometry

4.1.1 Preparation of solutions - first iteration 4.1.2 Preparation of solutions - second iteration 4.2 The ‘Approximate signal matching’ method for Inorganic IDMS 4.2.1 Calculation of analyte concentration 4.2.2 Calculation of mass bias correction 4.3 A Diagrammatic Overview of Inorganic IDMS 4.3.1 Checking for interferences 4.3.2 Measurement of isotopic abundances 4.3.3 Estimating the concentration in the unknown sample 4.3.4 Establishing the spike concentration (reverse IDMS) 4.3.5 Preparing ‘signal matched’ blends 4.3.6 The h a 1 IDMS run 4.3.7 Spreadsheets

17 18 19 19 20 22 25 26 27 27 28 28 29

Optimised Spiking for Inorganic IDMS Analysis 5.1 Introduction 5.2 Key Parameters 5.2.1 Error propagation factor 5.2.2 Mass spectrometry precision 5.2.3 Ion counting uncertainty 5.2.4 Background signal 5.2.5 Linear dynamic range 5.2.6 Dead time

30 30 30 30 33 33 34 34 34

Annex 1: References and Additional Reading References Additional Organic IDMS Publications Additional Inorganic IDMS Publications Annex 2: Glossary of Terms and Abbreviations Annex 3: Standard IDMS Equations

35 35 36 38 41 46

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectrometry (IDMS)

1 Introduction The technique of isotope dilution mass spectrometry (IDMS) was initially developed during the 1950s for elemental analysis.’ With readily available and user-friendly instrumentation, the number of applications for which elemental IDMS was used developed rapidly. IDMS was extended into the field of organic ~ the range of applications for which isotopically compounds in the 1 9 7 0 ~and labelled organic compounds are available continues to grow. IDMS applications range from routine survey work, such as residue analysis of dioxin^,^ to use as a reference technique.2 In mass spectrometry, unlike spectrophotometric techniques, there is no fixed relationship between the amount, and concentration, of a particular substance and the instrument response. Sensitivity for a particular compound or ion varies with, for example, time and instrumental tune parameters. These variations are in addition to those caused by, for example, sample introduction and chromatography. To achieve even moderately accurate quantification requires the use of an internal standard. An advantage of mass spectrometry lies in its ability to use isotopically enriched analogues (inorganic mass spectrometry) or isotopically labelled analogues (organic mass spectrometry) as internal standards. Indeed, in some instances IDMS is referred to as ‘stable isotope internal standardisation’. Provided the isotopic analogue is added to the sample at the very beginning of the analytical method and it comes into equilibrium with the analyte without losses or isotopic fractionation, it enables exact compensation to be made for errors at all stages of the analysis, from sample digestiodpreparation through to the final instrumental measurement. Initially, IDMS of inorganic analytes was most frequently performed using thermal ionisation mass spectrometry (TIMS). More recently, inductively coupled plasma mass spectrometry (ICP-MS) based IDMS has become more prevalent, because it requires much less sample preparation prior to analysis, and can provide results of the required accuracy and precision. The inorganic sections of this guide are concerned only with the use of ICP-MS for high accuracy IDMS measurements. IDMS of organic analytes can equally well be carried out using the fill range of sample inlet systems available, such as GC-MS, LC-MS and the newer technique of capillary zone electrophoresis-mass spectrometry (CZEMS). Tandem mass spectrometers (MS-MS) can also be used. In some instances, however, the inlet systedmass spectrometer type can have an influence on IDMS analysis. The use of a GC split injector, for example, can cause isotopic fra~tionation.~

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Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectrometry

The advent of compact and economic instrumentation, such as quadrupole and ion trap mass spectrometers, has led to the increasing use of mass spectrometry in the field of analytical chemistry. As a result, IDMS is playing an increasingly important role in trace a n a l y s i ~ . ~This . ~ is also due to its greater accuracy than other calibration methods and its ability to compensate for matrix effects. Notwithstanding this, there are several reasons why, in spite of the unrivalled accuracy and precision possible with the IDMS technique, it is not more widely used. In principle, the method is simple and allows for knowledge or control of all the variables that can lead to error. In practice, achieving accurate results requires careful design of the experiment and considerable attention to detail and is hence quite time consuming. Such factors have led to a slow acceptance of the technique. It has become popular, however, in some analytical fields where the sample matrix makes sufficiently accurate quantification difficult, e.g. clinical analysis.’ A theoretical discussion on the influence of some instrumental parameters on the precision of IDMS measurements has been

1.1 Advantages and Disadvantages of IDMS The use of IDMS has a number of advantages and disadvantages, which the prospective user should consider.

1.1.1 Advantages Providing the sample is homogeneous and isotopic equilibrium has been reached, the advantages of IDMS include:

1. It is a definitive method because of its precision, accuracy and provision of definable uncertainty values. 2. Once equilibration of the spike and analyte isotopes has been achieved, the total recovery of the analyte is not required, because the determined value is based on measuring the ratio between the analyte and the isotopic analogue (spike). 3. The accuracy of the method is determined by the precision of this ratio measurement. 4. Analyte transformation (e.g. breakdown) during sample preparation (most applicable to organic analysis) is compensated for by use of the isotopic analogue as internal standard. 5 . The methodology is less time consuming and can provide greater accuracy than standard additions. This guide aims to provide a structured approach to the use of IDMS to achieve high accuracy analytical measurements in both organic and inorganic IDMS. The approach outlined in Sections 4 and 5 has the advantage over normal IDMS of:

The Principles of IDMS

3

1. Negating the need to accurately characterise the isotopic analogue in terms of isotopic abundance and concentration (most applicable to inorganic analysis). 2. Providing a logical framework of understanding, which allows the analyst to identify specific problems, related to their application. 3. Providing a lower uncertainty value. 4. Simplifying the equations used for organic analytes.

1.1.2 Disadvantages of IDMS 1. The cost and availability of suitable isotopic materials. 2. The cost of the mass spectrometry instrumentation required. 3. Training of the analyst is of the utmost importance; otherwise less accurate results are often achieved. 4. Isotopic equilibration needs to be shown to have been achieved. 5. Differences in the physical (e.g. solvation) and chemical properties (e.g. pK, value) between the analyte and the isotopic analogue, can affect the ions generated in the mass spectrometer (most applicable to organic analysis).

2 The Principles of IDMS The underlying principle of IDMS’ is that an isotopically enriched analogue (inorganic MS) or an isotopically labelled analogue (organic MS) of the analyte compound is used as an internal standard in quantification by mass spectrometry. An accurately known amount of the isotopic analogue is added to the sample. The consequent ratio of the amounts of the two isotopes (one resulting from the analyte and the other from the isotopic ‘spike’) is measured on a portion of the sample using a mass spectrometer, so enabling the analyte concentration to be calculated. In summary the stages are: 1. Characterisation of the isotopic analogue (see Section 3.5) using a traceable natural standard by ‘reverse IDMS’. If a certified isotopic analogue is used this information is provided in the certificate. This step applies primarily to inorganic analytes. 2. An accurately known amount of the isotopic analogue is then added to an accurately measured portion of the sample (see Section 3.4). This step is widely referred to as ‘spiking’ the sample. 3. The mixture is equilibrated for an appropriate time. For inorganic analysis destructive digestion is necessary for solid samples (see Section 3.2.1). With organic analysis sample preparation often involves extraction and purification steps. In some cases a chemical reaction is necessary to free any bound form of the analyte (e.g. conjugates) present in the sample.’0 For analysis by gas chromatography a derivatisation step may be necessary to confer thermal stability to the analyte and spike compounds. 4. An aliquot of the spiked sample is introduced into the mass spectrometer either

4

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectrometry

directly (inorganic MS) or after chromatographic separation from other compounds (organic MS) (see Section 3.7). 5. The ratio of the signal responses for the ions resulting from the mixture of the analyte and isotopic analogue is accurately measured in the spiked sample using a mass spectrometer (see Section 3.8). From this ratio the concentration of analyte is calculated by comparison with the same ratio measured for the same ions in a standard calibration mixture. The calibration mixture contains the spike used in the sample and a certified standard of the analyte. 6. Corrections need to be made for instrumental effects, such as mass bias and detector dead-time (see Section 3. lo). Using the signal matching procedures outlined in this guide this can be achieved by running an alternating sequence of standards and samples. 7. Blank analysis is still required when using IDMS because any isotopic contribution to the mixture (from reagents, contamination etc.) will affect the isotopic abundance ratio and ultimately lead to a systematic bias (see Section 3.6).

3 Critical Stages and Sources of Error 3.1 Introduction IDMS analysis can provide results of great accuracy, but to achieve that accuracy it is necessary to consider the critical stages in the experimental procedure and to understand the potential sources of error. All the general precautions associated with mass spectrometry and trace analysis apply equally well to IDMS based procedures. Issues such as sampling, sample homogeneity, contamination and losses prior to analysis will play their part in influencing the accuracy of the reported result. The purpose of this guide is to highlight the specific points pertinent to the use of IDMS for accurate measurement. Therefore, issues related to sampling etc. will not be directly addressed in this guide. For guidance on general trace analysis the following references may serve as a starting point."-l3 A useful summary of critical parameters in ICP-MS instrumentation has been p~b1ished.l~ There are a number of critical stages in the IDMS procedure where errors may occur including: 1. Sample preparation (a) Sample digestion and isotopic equilibration (inorganic analysis) (b) Extraction, clean up, derivatisation (GC-MS) and isotopic equilibration (organic analysis) 2. Selection of the most appropriate isotopic internal standard (often termed the 'spike' and in this guide generically referred to as the isotopic analogue) (a) An isotopically enriched analogue (inorganic analysis) (b) An isotopically labelled analogue (organic analysis) 3. Addition of the isotopic analogue

Critical Stages and Sources of Error

5

4. Characterisation of the isotopic analogue 5 . Blank correction

6. 7. 8. 9.

Instrumental analysis Calibration procedure Calculation of the result Estimation of the uncertainty

There are a number of important sources of error in the IDMS procedure including: 1. Less than complete isotopic equilibration will lead to significant systematic errors 2. Presence of interfering ions (a) Isobaric and polyatomic interferences (inorganic MS) (b) Natural analyte ion signal overlap with isotopic analogue ion (organic MS) 3. Isotopic discrimination (mass fractionation, detector dead-time, mass bias) It should be noted that errors occurring during sub-sampling, addition of the isotopic analogue, sample preparation and isotopic equilibration are not compensated for by the use of isotope dilution analysis. However, these errors can be assessed by analysis of a suitable certified reference material or an ‘in-house’ prepared standard, analysed alongside the sample. The critical stages and sources of error summarised above are dealt with in greater detail in the following sections.

3.2 Sample Preparation With IDMS it is particularly important that full equilibration between the analyte and the isotopic analogue is achieved. This will ensure identical behaviour during the analytical procedure. Sufficient time for equilibration must be allowed but, even so, it is often difficult to ensure that full equilibration has taken place. Particular attention must also be paid, for example, to the chemical forms of the analyte and the isotopic analogue, e.g. oxidation state (inorganic MS), analyte form present (organic MS) etc.

3.2.I Inorganic IDMS It is advantageous to add the isotopically enriched analogue at the earliest point of the analysis. For solid samples, there will be a period during the digestion phase when the analyte is in a different form from the added enriched isotope. An example of this is the analysis of trace metals in glass. The natural metal has to be released from its silicate matrix to achieve dissolution. During this period the analyte isotope may behave differently from the added analogue isotope before true equilibration is achieved. Thus, losses due to incomplete dissolution or volatile species generation can result in errors, which are unaccounted for by the IDMS procedure. Also, any contamination during the sample digestion stage will

6

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectromehy

add to the final error in an IDMS analysis (this is easily corrected for by analysis of a suitable blank solution). It is essential to ensure that both isotopes are in the same chemical form. This can be achieved, for example, by an oxidation or reduction step.

3.2.2 Organic IDMS Analyte extraction, sample clean-up and derivatisation steps may also introduce errors prior to the benefits of the isotopic spike being realised. A good example of this is the analysis of cholesterol in serum using IDMS with GC-MS measurements. Even though the serum can be spiked at an early stage with the isotopically labelled analogue this does not guarantee equilibration. In fact, the natural cholesterol is mainly bound to proteins or other lipid materials. Thus, a saponification step is required before the two forms of cholesterol are equivalent and approach equilibration. Even vigorous shaking of the unspiked sample is to be avoided, as there is evidence that foaming is linked to unwanted conversion of the indigenous cholesterol. However, it is essential that all the natural cholesterol is released, otherwise the subsequent derivatisation step for GC-MS analysis will introduce a bias between the isotopically labelled analogue and the natural form.

3.3 Selection of the Isotopic Analogue For organic analytes, selection of the isotopically labelled analogue may have an effect on the analysis. If deuterium (D) is labelled onto an OH group, for example, then isotopic exchange may take place. Consequently the isotopic label should be introduced into a stable position of the analogue. To avoid discrimination during the various steps of the analytical procedure the label should not be in a position that affects solvation properties, pK, values or derivatisation kinetics (where applicable). When using chemical ionisation GC-MS or atmospheric pressure chemical ionisation LC-MS, if ion formation differs between the isotopic analogue and the analyte, a significant error could occur. For inorganic analytes there are usually a limited number of options when selecting an isotopically enriched analogue for use in a given IDMS analysis. Where there is a choice, consideration should be given to possible isobaric or polyatomic interferences during the ICP-MS measurement that might be linked with a particular sample (e.g. cadmium in the presence of tin because of the isobaric interferences at mlz values of 112, 114 and 116).

3.4 Addition of the Isotopic Analogue In general, to achieve an isotopic ion abundance ratio measurement with the best precision,* the ratio of analyte concentration to isotopic analogue concentration

*The better the precision of the isotopic abundance ratio measurement the less will be the uncertainty of the result.

7

Critical Stages and Sources of Error

should be such as to produce equal ion abundan~es.’~ The solution for analysis should, therefore, contain similar amounts of the two isotopes. However, if measurements are to be made near the detection limit of the analyte, it is often better to use more isotopic analogue so that this response at least can be measured with greater precision. This approach may be inappropriate for inorganic IDMS, where other situations may apply. In the case of silver, its two natural isotopes actually exist in proportions close to 1:l (51.8% and 48.2%). Thus, the optimum spiking regime 4 minimise the propagation of errors. requires a h a 1 concentration ratio of ~ 1 : to A fuller explanation of this particular issue is given in Section 5. In the case of organic analytes there may be some circumstances where the isotopic analogue has only a small mass difference from the natural analyte, for example, if only one carbon or hydrogen atom has been labelled. In such cases, where the isotopic analogue has a mass of only ( M l), the analyte itself may have a significant ( M 1) abundance due to the natural isotopic composition of the analyte (contribution from 13C or 2H in the analyte). Under these circumstances a large addition (say 5 to 1) of the isotopic analogue compared to the analyte will reduce the relative concentration of the natural ( M 1) abundance compared to the ( M 1) abundance arising from the isotopic analogue. This will reduce non-linear effects arising from the natural ( M 1) abundance, and can also be particularly important where the bracketing or single point method of calibration is used (see Section 3.8). The relative molecular mass of the analogue should, wherever possible, be increased by at least three mass units, which should avoid interference of the natural isotopes of the analyte on the isotope being measured for the labelled analogue. In certain circumstances sensitivity can be improved by using a large excess of isotopic analogue to reduce adsorptive losses of the analyte during GC-MS (the ‘carrier effect’).16 This can have the effect of decreasing the precision of the analysis. It is, therefore, preferable that, whenever possible, experimental conditions which eliminate or minimise adsorptive losses are selected rather than the use of a ‘carrier’.

+

+

+

+

+

3.5 Characterisation of the Isotopic Analogue In inorganic IDMS, prior to spiking the sample with the isotopic analogue it needs to be fully characterised. If a certified isotopic analogue is available the certificate will provide information on the solution concentration and isotopic abundance. Alternatively, a process known as reverse IDMS can be used to determine the concentration. In this case the analogue is calibrated against a high purity solution of the natural analyte isotope, prepared from a gravimetric solution of a suitable reference material. If the abundance of the isotopic analogue is unknown this needs to be determined by carrying out a separate measurement, commonly referred to as an abundance run.For high accuracy work both of these measurements need to be corrected for instrumental mass bias effects (Section 3.10.2). In organic IDMS analysis an assumption is made that the sample contains a negligible amount of the isotopically labelled analogue and the spike contains a

8

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectrometry

negligible amount of the sample isotope. In this way the equations used for organic IDMS are significantly simplified.

3.6 Blank Correction Ideally an analyte-free matrix material should be used to establish blank levels. In the absence of such a material (e.g. it is not possible to obtain cholesterol free serum), a full reagent blank, subjected to all sample preparation steps, should be used to evaluate possible blank contributions. The way in which blank corrections are made can cause problems in IDMS, especially where a digestion stage has proved to be necessary during sample preparation for an inorganic analyte. There are two possible approaches that can be followed: 1. If there is no digestion stage, or when the digestion blank gives no appreciable signal above either the diluent blank or in comparison with the samples, then a simple blank subtraction can be performed on the individual instrumental measurements. 2. If the digestion blank does contain significant amounts of analyte then separate quantification of the blank level, by IDMS if possible, should be the preferred option.

3.7 Instrumental Analysis In order to achieve the highest level of accuracy, special care must be taken in setting up mass spectrometric instrumentation prior to measurement of isotopic ion abundance ratios, as a long stabilisation period may be necessary in order to achieve the highest precision. A major source of imprecision is the instability of the instrument and the electronic signal level must be correctly set and not be subject to drift. In the case of the latest computer controlled instruments such checks can be carried out automatically.

3.7.1 Instrumentationfor organic mass spectrometry For organic analytes, the instrumental measurement stage of the IDMS procedure typically involves the use of a chromatography-MS combination. Ideally, the analyte and labelled analogue should have the same retention time in order that the relevant ions can be monitored simultaneously under the same mass spectrometric conditions. The transient signal peak can be assessed either by height or area. The factors that affect the isotopic precision have been assessed and peak area measurements shown to offer the most precise ratios.” In the case of GCMS, if a capillary column is used there may be a considerable separation between the analyte isotope and the isotopic analogue even if there is only a small difference in mass. It should be noted that retention time differences can be significant for deuterated compounds (several seconds, depending on the degree of deuteration) whilst in the case of 13C labelling such differences are consider-

Critical Stages and Sources of Error

9

ably less. In the case of LC-MS, some care may be necessary if adduct ion formation occurs because this could affect sensitivity and possibly introduce an unexpected effect on the isotopic ion abundance ratio measurement. The selection of the ions to be monitored is of the utmost importance because it will influence both the specificity and sensitivity of the analysis. Normally, for greatest specificity, the molecular ion will be monitored if it is sufficiently abundant and in this context the optimal mode of ionisation should be used. In the case of LC-MS, for example, the use of electrospray ionisation (ESI) should ensure a relatively abundant protonated molecule in many cases, with atmospheric pressure chemical ionisation (APCI) being considered only as a possible alternative because it can generate adduct, rather than molecular ions. In the case of GC-MS, chemical ionisation may be better than electron ionisation. If fragment ions are monitored, they should be at high mass values to minimise interferences from instrumental background, column bleed, and co-eluting sample components. If the molecule ion signal of the analyte is of low relative abundance, and there are no suitable fragment ions to monitor, an alternative approach is to form a high molecular weight derivative. Also in GC-MS, if a temperature programme is used then the analyte should elute at an isothermal stage of the programme. This will ensure that any background due to column bleed, carrier gas flow, etc. remains relatively constant. In IDMS applications, the ions characteristic of the analyte and isotopically labelled analogue are normally detected by selected ion monitoring (SIM). SIM is the continuous monitoring of an ion of a single mass to charge value or rapid switching between ions of different mass to charge values. Quantitative analyses are also possible by repetitive scanning of the full, or partial, mass interval during analyses. With magnetic sector and quadrupole instruments, this is less satisfactory than SIM because sensitivity and precision are reduced (sensitivity by up to a factor of 1000). The sensitivity, and hence precision, of other types of instrumentation such as ion traps, Fourier transform spectrometers (FTMS) or time-of-flight analysers are not adversely affected in this way.

3.7.2 Instrumentationfor inorganic mass spectrometry It is important that a stabilisation period of 45-60 minutes is allowed prior to measurement in order to permit the instrumentation to settle. At the point of sample introduction the nebuliser and spray chamber should ideally deliver a steady, stable spray. Although a ratio of two signals is being measured, the reproducibility of the measurement will still in part depend on the quality of the nebulisation. Advances in design have produced nebulisers capable of extremely consistent results, usually at lower flow rates (E 0.2 mL min-I). The scan parameters of the mass spectrometer need careful optimisation. In order to achieve an optimum precision for the ratio measurement a compromise has to be reached between the need to monitor several masses in quick succession, while still maintaining adequate signal levels (counts s-l). This will also be governed by the amount of sample available and how much is consumed during the measurement.

10

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectrometry

It is important in order to achieve good precision that the signal from the electron multiplier detector is at a high count level, typically 105-106 counts s-l, whilst avoiding operating at ion abundances where the multiplier will become saturated, that is at greater than lo6 counts s-I. In practice, matching the ion abundances obtained from the mass bias solutions and the isotopically spiked samples can greatly reduce errors arising from lack of an accurate knowledge of detector ‘dead time’ and linearity (see Section 3.10). Variations in the instrument response to different signal levels are negated if the solutions being compared have very similar abundances.

3.8 Calibration Procedures Several different approaches to calibration are available for IDMS measurements, as described below. In order to obtain very accurate results, particular attention must be given to the choice of calibration procedure. For example, the graphical method using a calibration curve is most usehl for analysing a number of samples of varying concentration. However, it is not likely to prove as accurate as the bracketing or ‘exact signal matching’ techniques for individual samples. When using a manufacturer’s application programmes or other commercial software for inorganic IDMS, especially those that perform the IDMS calculations on-line, care must be taken to validate the data produced by the software before relying on it. Caution is also required to ensure that the software is used correctly. For example, when measuring peak areas in organic analysis by GC-MS, which are normally calculated automatically, care must be taken to ensure that baselines are being assigned correctly and the peak area measurements are valid.

3.8.1 Graphical method In this procedure’8 a range of calibration solutions are prepared containing different amounts of the natural analyte calibration standard and a fixed amount of the labelled analogue material. Ion abundance ratio measurements of these mixtures together with those of the sample mixture enable a graphical evaluation to be made of the analyte concentration in the sample. Accuracy and precision are improved when the calibration data are fitted to an equation from which the concentration can be predicted. Linear regression analysis can only be applied in those cases where the calibration graph is truly linear, which is not always the case. The graphical approach has been applied mainly to organic IDMS. This method of calibration has the disadvantage that drift in instrumental response may cause significant errors because the calibration and sample measurements are made some time apart. It has been widely used for organic IDMS but is less attractive for inorganic IDMS where several isotopes may be present at significant levels in both the sample and the spike material. In such instances the calculation of calibration data will be more difficult. This is because both the natural and the spike materials will often contain both isotopes of interest for the IDMS measurement. This in turn leads to a non-linear relationship between the signals observed and the amounts used to create a blend of the natural and spike materials.

Critical Stages and Sources of Error

11

3.8.2 Bracketing method This procedure19 involves making measurements on each sample between measurements on two calibration standards prepared such that their ion abundances fall just above and below the ion abundances of the sample. Analyte concentration is calculated by linear interpolation between ‘bracketing’ standards and good precision and accuracy can be achieved using this procedure. This is a specialised version of the graphical method and, again, is mostly used for organic IDMS.

3.8.3 Single point calibration This procedureZouses only one calibration standard. To achieve good accuracy the ion abundances of the standard should be as close as possible to those of the sample. This method has been used for both organic and inorganic IDMS, especially using thermal ionisation mass spectrometry (TIMS).

3.8.4 Exact signal matching method The ‘exact signal matching’ method is a recent developmentz1and involves an iterative adjustment procedure culminating in the preparation of calibration and sample solutions which have exactly the same concentration of analyte isotope* in the spiked sample and the spiked calibration standard. It is not necessary to match the concentrations of natural and isotopic analogue in either the spiked sample or the spiked calibration solutions. Although this procedure can be time consuming, the ‘exact matching’ method is capable of very high accuracy. It can also produce very low uncertainties because systematic errors in the determination of the isotopic ion abundance ratios are cancelled out under exact matching conditions. This approach is applicable to both organic and inorganic IDMS measurements. In practice this procedure involves a number of preparations of the spiked calibration mixture until a match is produced: 1. Initially, an estimate of the concentration of the analyte in the sample is made. This can be made by using either a conventional IDMS analysis (calibration, graph or bracketing) or by some alternative method such as conventional GCMS or ICP-MS analysis with an internal standard. 2. The sample is then gravimetrically spiked with an isotopic analogue of the analyte (this analogue is termed the spike) such that the spike concentration matches the prior estimate of the natural analyte concentration in the sample. To prepare a sample solution blend, extraction (organic analysis) or acid mineralisation (inorganic analysis), followed by any clean-up stages necessary is carried out. 3. A calibration standard is then gravimetrically prepared with concentrations of *The analyte isotope in organic IDMS is usually I2C, ‘Hor I4N.Any of the inorganic isotopes can be used as the analyte isotope in inorganic IDMS. The choice will depend on considerations such as which isotope is available as the enriched isotopic analogue (this is used as the spike isotope) and the detection limit required (which limits the use of lower abundance isotopes).

12

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectrometry

natural analyte and isotopic analogue, which are the same as those estimated in the spiked sample solution blend. 4. Using appropriate ions of the natural analyte and the spike, the isotope amount ratios for the spiked sample and the spiked calibration standard are determined. It is suggested that alternating measurements of the isotope amount ratio are made on these two solutions (repeated measurement of the calibration blend allows mass bias correction to be performed for inorganic IDMS (see Section 3:10), repeating each five times. The mean value of the five measurements will minimise the effects of any instrument drift. An improved estimate of the natural analyte concentration in the sample can then be calculated from the data. 5. Steps (3) and (4) are repeated using the latest value for the concentration of the natural analyte. This iterative procedure is continued until the determined concentration value converges towards a limiting value. A flow diagram illustrating this iterative procedure is shown in Figure 1. In practice, it has been found that after only two iterations the difference in isotope amount ratio between the sample and calibration solutions changes sign randomly between repeat measurements indicating the condition of ‘exact matching’. When this occurs, taking the mean of each of the five sets of isotope amount ratios suggested at (4) above should produce very similar values for the sample and calibration solutions. The mean value can then be used to make the final definitive calculation of the analyte concentration. This is particularly true for inorganic IDMS where the varying concentrations of multiple isotopes may need to be taken into account for many analytes. The approximate matching technique (see below) provides a less onerous alternative to ‘exact matching’ whilst retaining many of its advantages.

3.8.5 Approximate signal matching method Many of the benefits of ‘exact signal matching’ can be achieved by an approximate signal matching technique,” which is essentially the same except that only one iteration is carried out. It is important, however, that the spiked sample and calibration solutions should have isotopic amount ratios within 5% and produce similar counts s-l within 5% of each other. The two approximately matched solutions are then run alternately to provide a series of replicate measurements which can be averaged as with the ‘exact matching’ technique. This method is recommended for achieving high accuracy measurement in inorganic analysis (a diagrammatic description of this approach is given in Section 4.3) but is also applicable to organic analytes.

3.9 Isotopic Interferences Often the ion current, at a given mass to charge ratio, is not the result of a single ionic species, but is subject to interference from an ion of similar mass leading to an enhanced signal. Depending on the mass difference and resolution available,

Critical Stages and Sources of Error

13

Make initial estimate of analyte concentrationin sample

Check for isotopic interferences

Spike sample with isotopic analogue to match estimated concentration of analyte in sample

Carry out extraction

and clean-up of sample blend if necessary

I

Prepare calibration standard blend of analyte and isotopic analogue to match analyte concentrationto that estimated in sample blend L

If necessary derivatise sample and calibrationblends to confer thermal stability for analysis by GC-MS

Do the isotope ratios indicate exact signal matching has been

No

Definitive result

Figure 1 Schematic representation of the ‘exact signal matching’ IDMS procedure, as applied to organic analysis

14

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectrometry

organic and inorganic mass spectrometry instrumentation can differentiate between these ions. Unless this is feasible, or corrections can be made, IDMS determinations may be subject to a significant bias. With inorganic mass spectrometry (ICP-MS) the generation of ions at the same mass as the target ions can be overcome to some extent by tuning the instrument parameters so that the formation of polyatomic and oxide interferences are minimised. Where it is necessary to make corrections for isobaric overlap, for example, the isobaric interference of Hg when performing Pb IDMS measurements, additional isotope measurements will have to be included. Thus, '02Hg may be monitored to compensate for 204Hgcontributions to the '04Pb signal when determining the isotopic ion abundance of '04Pb. Other advances in instrumentation, such as the advent of double focusing sector field ICP-MS instrumentation, have given analysts the option of resolving many of the polyatomic interfering species found in the mass to charge range mlz 20- 100. This has proved extremely useful, especially for the first row transition element isotopes. However, by increasing the resolving power of the instrument some loss in precision is observed, because the peak shapes are no longer flat topped. It is important to check for the presence of isotopic interferences, for example, by comparing spiked and unspiked standards or samples. There are various ways to overcome problems caused by coincident ion interferences:

1. It is often useful to monitor more than one characteristic ion of both the natural analyte and isotopic analogue. This may allow detection of interferences by a change in the apparent natural to analogue ion abundance ratio obtained using the different channels. This is usually applied to organic IDMS and is generally at the expense of sensitivity and precision, because more ion signals must be monitored. 2. It may be more satisfactory to initially run the sample without the isotopic analogue present in order to detect the presence of interferences at the massto-charge value of the analogue. 3. Interferences can often be overcome by operation of the mass spectrometer at higher resolution settings, sufficient to separate the interfering signal from that of the analyte or isotopic analogue. 4. An alternative method of overcoming interferences in organic analysis is to utilise tandem mass spectrometry (MS-MS). This technique is now popular, particularly in the LC-MS field, and offers the means to overcome interferences without recourse to the expensive and increasingly rare high resolution instrumentation. By utilising MS-MS in the multiple reaction monitoring (MRM) mode IDMS can readily be carried

3.10 Isotopic Discrimination 3.10.1 Isotopic fractionation For organic analytes care must be taken to ensure that isotopic fractionation does not occur or, if unavoidable, is minimised or corrected for. Any clean-up,

Critical Stages and Sources of Error

15

evaporation and derivatisation stages can be particularly prone to fractionation if care is not taken. Up to the present time this type of fractionation has not been identified as an issue in IDMS of inorganic analytes using ICP-MS, because the behaviour of the two isotopes in the sample introduction system tends to be similar.

3.10.2 Mass discrimination (mass bias) When an instrument produces a different response for ions of different mass, this systematic error is termed mass bias. In ICP-MS applications mass bias is related to the kinetic energy of the ion, so sampling of the ions from the plasma, ion transmission and ion detector can impart a mass dependent bias. This is typically 1% per mass unit at m/z 100 irrespective of the instrument, and particularly significant at the lower end of the mass range, e.g. lithium or boron analysis. Mass discrimination or bias can be readily corrected in both organic and inorganic measurements by use of external calibration. Using the methods outlined in this guide mass bias correction is achieved by bracketing the sample blend with measurements made on the calibration blend.

3.10.3 Detector dead time (ICP-MS) The detector dead time is the time taken for a detection system to recover from an ion pulse. If a second ion hits the detector before it has recovered it will not be recorded. This will bias the count rate, which will appear lower than it really is. The dead time for the usual electron multiplier detectors favoured in MS instrumentation is the order of 15 to 100 ns. The detector dead time can be determined quite easily, but the IDMS methodologies described below (Section 5) can compensate for this effect and so it is necessary only to establish this value periodically and not for each determination.

3.1 1 Aspects of Achieving High Accuracy Measurements Having considered the critical stages in IDMS analysis, it is useful to review those aspects of IDMS that affect precision, sensitivity and specificity. In many cases it will be necessary to adopt a compromise between conflicting requirements. A general point is the recommendation that all procedures are carried out by gravimetric and not by volumetric procedures. In addition, it is important to apply recognised best practice in making all analytical measurements as well as addressing the issues highlighted here for IDMS.

3.11.1 Precision 1. The level of the target analyte should be significantly above the limit of quantification to ensure a good signal-to-noise ratio. With ICP-MS measurements the instrumental response should be 105-106 counts s-' (for each ion). For organic IDMS the signal-to-noise ratio should be at least 10:1.

16

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectrometry

2. The steady state signals generated with inorganic IDMS should be accumulated for several minutes. With organic IDMS the chromatographic separation will generate a transient peak. Sufficient isotopic ion abundance ratios should be measured across the chromatographic peak to give the required precision. This will be dictated by the chromatographic system and the scan speed available with the MS instrumentation. 3. In organic determinations, a specific ion of high abundance should be used, which is not subject to interference from column bleed ions or from other sources. 4. The instrument should be operated under conditions that ensure maximum stability. 5 . The optimum mass spectral resolution should be used.

3.11.2 Sensitivity 1. 2. 3. 4.

The number of masses monitored simultaneously should be minimised. Optimum mass spectral resolution should be selected. Ions selected for measurements should be of high abundance The optimum mode of ionisation should be chosen. 5 . Dwell time should be long enough for maximum sensitivity but not too long to compromise precision. In addition, where chromatographic separations are used:

1. There should be an absence of adsorption on the GC column or elsewhere. 2. Adduct ion formation in LC-MS should be minimised.

3.11.3 SpeciJicity 1. Known sources of interference should be removed or corrected for. 2. High purity standards and reagents should be used, and should be characterised where appropriate. 3. There must be full equilibration between the labelled analogue and the analyte. 4. The mass-to-charge ratio of the specific ions monitored should be high, where a choice exists (specifically for organic IDMS). 5 . Several ions should be monitored where this is possible (specifically organic IDMS). 6 . Clean-up procedures should be used to minimise the amount of matrix material and possible interferences in the measured solutions. 7. The sample should be analysed in the absence of the isotopic analogue to show that interferences do not occur at the mass-to-charge of the analogue isotope. 8. Field blanks, or at the very least procedural blanks, processed using the isotopic analogue must be analysed to demonstrate absence of uncorrected interferences.

The Structured Approach to ZDMS Analysis

17

9. Isotopes that are free from instrumental interferences should be selected wherever possible.

4 The Structured Approach to IDMS Analysis This section includes worked examples of the recommended calibration procedure as applied to organic and inorganic IDMS, together with a graphical overview of the procedure for inorganic IDMS. The equations used for each measurement step are given in a simplified form. A more extensive derivation and explanation of the equations used in IDMS is given in Annex 3.

4.1 The ‘Exact signal matching’ Method for Organic IDMS The procedure described in Section 3.8.4 is illustrated using the determination of p,p’-DDE in 2,2,4-trimethylpentane. This example shows how the sample and calibration solutions may be prepared so that the natural and isotopically labelled analogue concentrations and their isotope amount ratios are as close to being identical as possible. Additionally, to obtain high accuracy the measured isotopic ion abundance ratios should be as close to unity as possible. For the highest accuracy to be achieved, all solutions should be prepared gravimetrically except where identified below. Conventional volumetric techniques will limit the accuracy attainable by this IDMS method. The symbols used in this example should be read in conjunction with Equation 11 (Annex 3) which was used for the calculation of results.

4.1.1 Preparation of solutions

- first

iteration

The estimated concentration of p,pr-DDE from a preliminary analysis of the sample by GC-MS with an external standard was 4.1 1 pgg-I. In order to prepare analytical solutions with isotope amount ratios as close to 1 as possible, the mass spectrometer assigned for this work was used to measure the ratio for a solution prepared with accurately known amounts of the natural isotope and labelled isotopic analogue. It was then possible to calculate the amounts of analyte and spike necessary to produce a measured (observed) ratio of 1.O.

-

The sample blend was prepared by mixing known weights of the sample solution and a spike solution containing 7.79 pgg-’ of p,pr-DDE-I3Cl2.The solutions were weighed into a 25 ml volumetric flask

Sample solution (mx)10.16425 g (-14.7 ml). Spike solution (my)6.541 18 g (-9.4 ml). The resulting solution was bulked to 25 ml (-17.3 g) volumetrically because now the ratios are fixed and this dilution achieved a suitable signal-to-noise ratio. Based on the result of the preliminary analysis this solution had a concentration

18

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectrometry

of p,p'-DDE of -2.4 pgg-' and of P , ~ ' - D D E - ' ~ Cof~ ~-2.9 pgg-'. This produced an ion abundance ratio of -1.0 on the mass spectrometer used in this work. Analysts should note that even if provided with identical solutions they would need to adopt the above procedure in order to calculate the weights which will produce an ion abundance ratio of 1.O on their own instruments.

-

The calibration blend was prepared using an analyte standard solution containing 7.93 pgg-' of p,p'-DDE (cz) and the same spike solution as used above to prepare the sample blend. The solutions were again weighed into a 25 ml volumetric flask: Analyte standard solution ( m Z c )4.89140 g (-7.0 ml). Spike solution (myc)6.551 14 g (-9.4 ml). The resulting solution was again bulked to 25 ml (-17.3 g) volumetrically. This solution had a concentration of p,p'-DDE of -2.2 pgg-' and of p,p'DDE-I3Cl2of -2.9 pgg-'. The sample solution had a concentration of p,p'-DDE of -2.4 pgg-' and of p,p'-DDE-13C12of -2.9 pgg-'. IDMS analysis of the sample blend was then carried out using replicate measurements as described for the 'exact signal matching' technique. Five replicate measurements were carried out using ions with mlz of 3 18 and 330. The mean ion abundance ratio of the sample blend (RB) was 0.98803 and that of the reference standard blend (RBc)0.95462. Equation 11 (Annex 3) produced a result (cx) for the first iteration of 3.944 pgg-' of p,p'-DDE in the sample solution.

4.1.2 Preparation of solutions - second iteration The concentration of p,p'-DDE in the original sample blend was recalculated to be -2.3 pgg-' using the revised analyte concentration (in the sample) of 3.944 pgg-'. For the second iteration the value of 3.944 pgg-' of p,p'-DDE in the sample solution was used to calculate the composition of a new calibration blend which would more exactly match the sample blend. This new calibration blend was prepared using the analyte and spike solutions as detailed above. The solutions were again weighed into a 25 ml volumetric flask. Analyte solution ( m Z c )5.04720 g (-7.3 ml). Spike solution ( m y c )6.52138 g (-9.4 ml). The resulting solution was again bulked to 25 ml (-17.3 g), volumetrically. This solution had a concentration of p,p'-DDE of -2.3 pgg-' and of p,p'DDE-'3C12 of -2.9 pgg-'. IDMS analysis of the sample blend using the new calibration blend was carried out, again using five ratio determinations obtained by alternate measurements of the sample and calibration blends. The mean ion abundance ratio of the sample blend (RB) was 0.97190 and that of the calibration blend (RBc) 0.97065. It was observed that the difference between sample and standard blend ratios changed

The Structured Approach to IDMS Analysis

19

sign randomly, indicating the condition of ‘exact signal matching’. Thus, using Equation 11, the result (cx) of this second iteration, 3.955 pgg-’ of p,p’-DDE in the sample solution, was regarded as the definitive value of the p,p’-DDE concentration in the sample solution.

Note: It is apparent that the mean ion abundance ratio of the sample blend for the second iteration is different from that obtained from the first iteration even though the same solution was used. This is due to long-term instrumental drift as the measurements for the first and second iterations were carried out several days apart. Such drift is negligible during the five alternating measurements required for each iteration and in any event is compensated for by the alternation of the measurements.

4.2 The ‘Approximate signal matching’ Method for Inorganic IDMS This is a variation of the ‘exact signal matching’ method, as noted in Section 3.8.5. Although the exact signal matching method can be applied to inorganic analytes it becomes a lengthy procedure in view of the multiple isotopes that need to be taken into account in the equations for most analytes. This also requires slight modification to the terminology used with organic IDMS. The isotope used to represent the natural isotope is generally the isotope of highest natural abundance while the spike isotope is generally taken as one of the minor isotopes in nature, and is usually selected to be close in mass to the natural isotope. Most of the elements in the periodic table (z80%) are amenable to isotope dilution, the only prerequisite being that the element has two or more stable isotopes or long-lived radioisotopes. The method is straightforward to apply but involves relatively complicated calculations, including one for the instrument mass bias correction factor, which is essential for accurate results.

4.2.1 Calculation of analyte concentration In this section we illustrate the calculation used in applying the approximate matching method to IDMS analysis of Pb, using 208Pbas the analyte isotope and 206Pbas the enriched analogue or spike isotope. The example is based on an IDMS calculation with Equation 5 (see Annex 3) using isotopic abundances (isotopic amount fractions). For clarity, the symbols used in the equation are shown in Table 1 together with the values assumed for the example. The isotope amount ratio was measured by ICP-MS using a blend (B) of the sample solution (X) and isotopically enriched analogue solution (Y). Substituting the values into Equation 5 (Annex 3) gives the concentration of the Pb in the sample solution.

20

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectrometry CX

= 30.7604 X

0.0991 207.218 (1.06965 X 99.76 - 0.03) - 0.2499

205.97

(52.70 - 1.06965 X 24.51)

= 49.435 pgg-I

If the isotope abundance (isotope amount fraction) of the sample is not known this must be determined experimentally via an isotopic abundance run.Otherwise, the only information required is the weight of the enriched isotopic analogue added (and hence the elemental concentration of the spike solution), the weight of the sample and the measured ratios. Modern analytical balances are capable of routinely weighing to 1 part in 50000, so that errors arising from the weights of the sample and spike should be minimal unless very small aliquots are taken.

Table 1 Symbols used in Equations Quantity

Unit

Enriched isotope

Analyte isotope

(Y)

@7

Symbol

Value

Symbol

Value

% fy(2E) Abundance (amount fraction) f x ( 2 E ) 24.51 99.76 ''Pb (205.97) YO fy('E) fx(lE) 52.70 Abundance (amount fraction) 0.03 20sPb(207.98) Relative molar mass of Pb Mx 207.218 My 205.97 Concentration of enriched Pg g-' CY 30.76 isotope in spike Pg g-' cx ? Concentration of natural isotope in sample Mass of spike Y added to the g my 0.0991 sample X Mass of sample X added to g mX 0.2499 the spike Y Measured isotope amount ratio* of 2osPb/206Pb in the sample blend B (= X + Y): R B = 1.06965

*After mass bias correction; see Section 4.2.2 for an example of calculating the mass bias correction.

4.2.2 Calculation of mass bias correction A solution containing a blend of the two isotopes is prepared so that the isotopic ion abundance ratio and the concentrations match as closely as possible the isotopic ion abundance ratio and concentration of the sample solution being measured. A known weight of a solution of known concentration of the natural isotope is added to a known weight of a solution of the enriched analogue isotope. Thus the true value of the isotope amount fraction ratio can be calculated from certificate values. The experimental value of the ratio for this solution is usually

The Structured Approach to IDMS Analysis

21

determined for each sample by analysing it before and after the unknown sample being measured. The mass bias correction factor is calculated using the equation: CF = t / e where CF = mass bias correction factor t = true ratio of the isotope amount fractions calculated from certificate values

e = experimental ratio of the isotope amount fractions obtained using the mass spectrometer This value of CF is then applied to the raw ratio data obtained from the samples. Calculation of the true (theoretical) ratio of 20ePb/2MPb for the mass bias solution is shown below (see Table 2). Calculated number of atoms 208Pbin mass bias solution 30.7604 100

= (0.6035 X = 0.0000270

) + (7.1235

0.03 205.97

X-

10.0417 100

52.347 207.215

+ 0.1807055

= 0.1807325

Calculated number of atoms 206Pbin mass bias solution 30.7604 100

99.76) 205.97

= (0.6035 X - = 0.0899128

+ (7.1235 X- 10.0417 100

22.144 207.215

+ 0.833468

= 0.173259

ratio Table 2 Data used in calculation of 208Pb/206Pb Quantity

Unit

Enriched isotope solution

Natural isotope solution

Weight of solution Concentration of Pb 20sPbisotopic abundance z06Pbisotopic abundance Relative molar mass of Pb

g Pug g-'

0.6035 30.7604 0.03 99.76 205.97

7.1235 10.0417 52.347 24.144 207.215

atom percent atom percent

22

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectrometry

True (theoretical) ratio 20sPbP06Pb

t = 1.04313 Measurement of the instrumental ratio of 208Pb/2MPbfor the mass bias solution is obtained by running the mass bias solution before and after analysis of a sample. This enables calculation of two values of CF using the value of t previously calculated for the solution (Table 3).

Table 3

Mass bias correction factor before and after analysis

Quantity *‘*Pb counts s-’ *06Pbcounts s-’ Measured ratio True ratio Mass bias correction factor

Symbol

e t CF

Leading solution

Trailing solution

27921 1 270490 1.03224 1.04313 1.0105

268098 259462 1.03328 1.04313 1.0095

Hence the mean mass bias correction factor to be applied to the sample is 1.0100.

4.3 A Diagrammatic Overview of Inorganic IDMS The following is a more detailed description and diagrammatic illustration of each step in the IDMS procedure. At each stage, suggestions are included which will help in the use of this guide. The diagrams are based on an element with two stable isotopes. The overall scheme is represented in the flow charts shown in Figures 2 and 3. This clearly illustrates that the actual isotope dilution analysis is dependent on additional information about the unknown sample and the isotopically enriched standard used to spike it. In particular: 1. It is considered good practice to know the concentration of the spike (although this is not strictly necessary as the IDMS measurement is actually based on a natural calibration standard of the analyte). If a certified spike standard is unavailable, the concentration of the spike is determined by a ‘reverse’ IDMS measurement using the natural calibration standard. 2. It is necessary to know the isotopic abundances of the two isotopes in the unknown sample. For a few elements (Li, B, Pb, U, Sr, 0 s ) these vary significantly in nature and hence must be determined for the actual sample. This can be done by carrying out an abundance run (Section 4.3.2). 3. The technique described here requires prior knowledge of the ‘approximate’ analyte concentration in the unknown sample.

.:: .:: :i

STANDARDISATION ACHIEVED

+

.. ... ...: .... : : .: .: : : :i .. ... ...:. ....:. . .

: using ~ t u r a l standard for massbias

abundancerun

Yes

r

SAMPLE IS READY FOR IDMS DETERMINATION

1 .

estimate of analyte concentration

vary in

Doisotopes

Figure 2 Establishing the viability of the materials used for the IDMS procedure prior to the dejinitive determination: (a) characterisation of the isotopically enriched analogue, (b) standardisation of the pure natural standard, (c)preliminary examination of the sample

(

STANDARDISATION ACHIEVED

7

Yes

W N

E;. I

8

sa

3

b

B

I

bias blend

I

L

Sample concentrationdetermined

Blank correct

Calculate result

Cany out isotope ratio measurements alternately on the mass bias and spiked sample blends

ISOTOPIC ANALOGUE STANDARD

Figure 3 Schematic detailing the steps in the definitive inorganic IDMS determination

NATURAL

I

Prepare spiked sample blend and digest/dissolveas appropriate

rc I

PROVISIONALLY CHARACTERISED SAMPLE (SOLID OR LIQUID)

N P

The Structured Approach to IDMS Analysis

25

4. IDMS will only give accurate results if the measured isotopic abundance ratio

is accurate. Hence it is essential to check both isotopes for isobaric or other isotopic interferences. Other effects due to the sample matrix or the instrument, should be evaluated. Note that for clarity, the sample blank has been omitted from Figure 2. It is essential to check the blank for contamination andor interferences and to resolve any problems. A graphical representation of the two isotope system is shown in Figure 4 for the three main components used in this description of the IDMS procedure.

Figure 4

The three main components in the IDMS procedure: (a) natural standard, (b) sample and (c) isotopically enriched spike

4.3.1 Checkingfor interferences The unknown sample and a pure standard should be run alternately to establish that both have the same isotopic abundance ratio (within ~ 0 . 5 %relative). While not foolproof, this approach provides a very good check for interferences. This is illustrated in Figure 5.

26

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectrometry Standard

Run sequence: Figure 5

Sample

Standard

+

The run sequence for checking that the sample has the same isotope ratio as the pure standard (i.e. interference free); for key see Figure 4

Technical tips: The solutions should be diluted so that they give comparable counts (i.e. within 5%), with >I0000 counts s-’ for the minor isotope. Typical analysis times per solution should be several minutes, resulting in a precision of 0.1-0.2% relative.

4.3.2 Measurement of isotopic abundances The isotopic abundance (isotope amount fraction) is usually obtained from the IUPAC standard tablesz4 However, if the abundance of the element varies in nature (e.g. Li, B, Pb, U, Sr, 0s) it must be determined experimentally on the actual material in use. In this case, the unknown sample and a pure ‘natural’ isotopically certified standard (e.g. SRM981, NIST for Pb), should be run alternately, so that the unknown sample is bracketed by the analyses of the standard. (The run sequence is the same as that used for checking for interferences, as shown in Figure 5 . ) This approach allows mass bias correction to be facilitated. The abundances for the unknown sample can then be determined, after allowance has been made for any mass bias effect. For the abundance run it is essential that all isotopes present are measured, not just those used for the IDMS determination. For the two-isotope system used here, it would appear that the interference check run is identical to the abundance run. In practice this will not be the case for an element with more than two isotopes. Thus, for lead all four isotopes (204, 206, 207 and 208) need to be measured to establish the abundances. As a result of the isobaric interference of Hg at mlz 204, another isotope of this element needs to be analysed to correct for the interference on 2MPb. Technical tips: The solutions should be diluted so that they give comparable counts (i.e. within 5%), with >I0000 counts s - I for the minor isotope.

The Structured Approach to IDMS Analysis

27

Typical analysis times per solution should be several minutes, resulting in a precision of 0.1-0.2% relative.

4.3.3 Estimating the concentration in the unknown sample As noted previously (Section 3.8) an initial estimate of the elemental concentration is needed so that suitable spiked calibration and sample solutions can be prepared. Conventional non-IDMS analysis should be used to establish this first estimate of sample concentration. This estimate can then be used in a subsequent calculation of the appropriate composition for the calibration and sample solutions.

Technical tips: Ifpossible thisjrst estimate should be accurate to within -5%. Analysis of an appropriate cert8ed reference material or gravimetrically prepared sample alongside the unknown will help to indicate that this has been achieved.

4.3.4 Establishing the spike concentration (reverse IDMS) This step is required if the spike solution of the isotopically enriched analogue only has an indicative concentration value. The spike solution is blended with a gravimetrically prepared solution of the pure reference isotope of known concentration. The concentration of the enriched isotope in the spike solution can then be calculated from a first reverse IDMS run of this blended solution. The revised value of the concentration can then be used to prepare a second blended solution. The first blend can be used as a mass bias standard, with the revised value for the concentration, and run alternately with the second blended spike solution. This second iteration should give an acceptable value for the spike concentration but if necessary a third iteration can be carried out. The run sequence for characterising the second blend is shown in Figure 6 . Technicaltips: The solutions should be blended so that both isotopes give >I00 000 countss-'. The proportions and countss-' should be within -5% for the mass bias standard and the next blended spike. All dilutions and blended solutions should be prepared gravimetrically.

A simple spreadsheet is invaluable for predicting the weight of solutions necessary to achieve this approximate matching. Typical analysis times per solution should be several minutes, resulting in a precision of 0.1-0.2% relative.

28

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectrometry

60 40

20

+

t

A

B

1. Blended Spike [Ist]

A

B

2. Blended Spike [2nd]

t

A

B

3. Blended Spike [lst]

Figure 6 Run sequence to characterise the spike, using reverse IDMS of the second blend with thejrst blend for mass bias correction; for key see Figure 4

4.3.5 Preparing ‘signal matched ’ blends Using all of the above information it should now be possible to prepare a blend of the unknown sample and the isotopic analogue and a blend of the pure calibration standard and the same isotopic analogue, which will have similar isotope amount ratios and display similar ion abundance. The same amount of isotopic analogue is used in both the sample blend and the calibration standard blend. A simple spreadsheet can be used to predicate the weights of the sample and standard that will produce an approximate match between the two blended solutions. More detailed guidance on spiking is given in Section 5. Technical tips: The solutions should be diluted so that they give comparable counts (i.e. within 5%), with >I00000 counts s-’ for the two major isotopes. Dpical analysis times per solution should be several minutes, resulting in precisions of 0.1-0.2% relative.

4.3.6 TheJinal IDMS run The two approximately matched blended solutions should be run alternately, so that the spiked unknown sample is bracketed on either side by the spiked natural standard. The run sequence for this determination is illustrated in Figure 7. This data should then be processed on a validated spreadsheet to give the final

The Structured Approach to IDMS Analysis

A

B

1.Blended Standard

A

29

B

2. Blended Unknown

A

B

3. Blended Standard

Figure 7 Thejinal run sequence to determine the concentration in the s p i k d sample with bracketing ‘matched’ mass bias standards; for key see Figure 4

concentration in the unknown sample. The final concentration in the sample is calculated by the equation described in Annex 3, as shown in Section 4.2. Technicaltips: The two spiked solutions should be blended so that they give comparable counts 0.e. within S%), with >I00000 counts s-l for the two major isotopes. Typical analysis times per solution should be several minutes, resulting in precisions of 0.1-0.2% relative. Blanks should be run with a reduced spike content to reflect their low analyte concentration. Blank blends will not normally be ‘matched’to a spiked standard. The inclusion of an IDMS analysis of an independent in-house gravimetrically prepared pure standard is highly recommended. It can provide an overall quality control check and supply invaluable information for realistic total uncertainty estimates.

4.3.7 Spreadsheets It is strongly recommended that a set of spreadsheets be developed for the calculations. This should include spreadsheets for the following steps: 1. Calculating elemental abundance for elements that vary in nature. 2. Predicting a suitable sample weight given an estimate of the concentration.

30

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectromehy

3. Calculating the concentration of the spike by reverse IDMS. 4. Calculating the final IDMS result for the unknown sample. It is important to validate these spreadsheets by independent means, such as a hand calculator, especially with regard to the spreadsheet used for the final IDMS calculation of the unknown sample.

5 Optimised Spiking for Inorganic IDMS Analysis 5.1 Introduction There are a number of key parameters which should be considered when selecting the proportion at which to spike the sample with the isotopically enriched analogue. These include: 1. Error propagation factor 2. Mass spectrometry precision 3. Ion counting uncertainty 4. Background signal 5 . Linear dynamic range 6 . Dead time

Some of these points will have conflicting requirements. For instance the natural abundances of the two silver isotopes are very similar. It is, therefore, not practicable to adhere to a matching procedure2'J2 which normally aims for isotope amount ratio measurements close to unity after spiking. To help clarify the different aspects, each is discussed below.

5.2 Key Parameters 5.2.I Error propagation factor There is a theoretical optimum for spiking samples to achieve the best precision for the ratio measurements. The error propagated by this measurement factor alters as one moves away from the theoretical optimum. This error propagation factor can be ~ a l c u l a t e d ~from ~ - ~ ~the isotope system being measured and is dependent on the isotopic abundances in the natural sample and the isotopically enriched (spike) material. The error propagation factor is therefore the theoretical factor influencing the precision of the ratio measurements, as a function of the closeness to the calculated optimum spike. This factor can be calculated for each specific combination of the natural (analyte) isotope and the enriched (spike) isotope abundances for the element of interest. The description of error propagation plots (see below) includes a number of examples showing how this factor varies as a hnction of the isotope amount ratios in the spiked sample. The isotope proportions in the unmixed natural and isotopically enriched materials heavily influence the shape of these plots. Thus for

31

Optimised Spiking for Inorganic IDMS Analysis

the 107Ag:'ogAg system, which has two isotopes of very similar natural abundance (48%:52%) the optimum concentration for the sample isotope and the enriched isotope in the blended solution is approximately 1:4. The error propagation factor should be minimised for optimum results. A number of error propagation plots have been calculated to illustrate how the error propagation factor may be minimised by adjustment of the amounts of the analyte and spike isotopes. Details of the chosen isotope systems and their IUPAC abundancesZ6are given in Table 4 (with the spike isotope listedjirst). The graphical plots for these systems in Figure 8 appear in the same order as in Table 4. The exact theoretical optimum, EPFop, can be calculatedz4~z7 from the following formula:

EPFopt=

Main Spike Abundance Minor Sample Abundance X Minor Spike Abundance Main Sample Abundance

Using the "'Cd: "*Cd system as an example, the optimum ratio in the spiked solution to minimise the error propagation factor is:

Table 4

Isotope systems used to study error propagation

Element

Isotope

Spike abundance

Natural abundance

Lithium

6 I 25 24 26 24 57 56 61 60 65 63 61 66 71 82 109 107 106 111 111 112 206 208

99.32 0.68 98.81 0.96 99.16 0.42 92.74 7.05 94.91 2.89 91.20 8.80 78.63 9.57 68.69 1.65 95.00 5.00 79.01 2.60 95.29 2.61 99.76 0.03

4.75 95.25 10.00 18.99 11.01 78.99 2.20 91.72 1.19 26.23 30.91 69.09 4.1 1 27.81 1.58 9.19 48.18 5 1.82 1.22 12.80 12.80 24.13 24.14 52.35

Magnesium Magnesium Iron Nickel Copper Zinc Selenium

Silver Cadmium Cadmium Lead

Optimum ratio* 2.7 3.6 5.7 0.6 2.2 2.2 1.1 5.9 4.2 1.7 4.4 39

*Optimum ratio for spiking the sample to achieve the best precision for the ratio measurement. The enriched isotopic analogue used to spike the sample is given fist for each element shown.

!I0K J qy-J g

1 0.1

1

10

01

100

10

1

'L1:'LI Ratio

%g?Mg

I00

Ratio

I

I I

01

10

1

%p:"M@ Ratio

loo

II

01

10

1 -F."F.

100

Rat10

gior- q-y-J I

I

,

j

L

1

01

1

10

01

EPFOp,=

1

10

-c""Cu

"NIP'NI Ratio

/=

95.29 2.61

12.80 24.13 = 4.40

The optimum ratios predicted by these error propagation plots are, as explained earlier, just one aspect in optimising IDMS measurements. In practice, irrespective of the predicted optimum the ratio should always lie between 4:l and 1:4 to retain reasonable counts for both isotopes. This range will usually be obtained when equimolar amounts of the sample and spike are mixed together. Hence, although the theoretical optimum ratio for Pb is 1:39, in practice this would result in unacceptably low counts for the lesser isotope.

Optimised Spiking for Inorganic IDMS Analysis

33

I

100

j ~~~

i l : : F

lo

1

1

0.1

10

1

100

0.1

1

I

0.1

Figure 8

10

1

"'Cd'%d

10

100

"'Cd?"Cd Ratlo

'p'Ag?aAg

RaUo

0.1

1

10

100

1000

loo00

*bLo"Pb

(continued)

5.2.2 Mass spectrometry precision The best mass spectrometry precision for measurement of a ratio is usually achieved with isotope amount ratio measurements close to unity. Hence silver was used by Begley and Sharpz8for their fundamental studies in order to exploit the advantages of a natural 1:l system. However, it is generally acknowledged that modest deviations, by a factor of 3 or 4, from this optimum are unlikely to degrade the overall performance by a significant degree.

5.2.3 Ion counting uncertainty The advantage noted above of working at close to unity assumes that both isotopes will be present in a reasonable amount. However, for samples with very

34

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectrometry

low analyte concentrations there is little to be gained from measuring an equally low level of the enriched isotopic analogue. In these circumstances it would be better to opt to overspike the samples.24

5.2.4 Background signal In the presence of a significant background signal, it would be desirable to increase the relevant isotope signal so as to minimise the effect of the background signal. Increased signal strength is also a way of improving the counting statistics.

5.2.5 Linear dynamic range Poisson counting statistics28ultimately limit signal-to-noise ratios in conventional ICP-MS instruments. The improvement achieved by increased intensity is directly proportional to the square root of the counts s-l. The temptation is, therefore, to work with ever-larger counts. However, the detectors (usually electron multipliers) will have a limit to their linearity and will ultimately saturate. Even over the normal linearity range, typically up to lo6 countss-’, there will be an influence from the detector’s ‘dead time’. There is no need to correct for ‘dead time’25if a ‘matching’ procedure is being adopted, but in other cases, for very accurate measurements, the multiplier will need to be characterised for dead time.

5.2.6 Dead time The use of approximate matching between the mass bias solutions and the spiked sample solutions removes the necessity for making dead time corrections provided, that the matching includes both the isotopic ion abundances and their ratios. Arranging for just the isotopic ion abundance ratios to be matched in the mass bias and spiked sample solutions is not sufficient.

Annexes

Annex 1: References and Additional Reading References 1. Reynolds, J.H., A mass spectrometric investigation of branching in &lCu,80Br,82Brand 1281,Phys. Rev., 79, 789-795 (1950). 2. Pickup, J.F. and McPherson, K., Theoretical considerations in stable isotope dilution mass spectrometry for organic analysis, Anal. Chem., 48, 1885-1890 (1976). 3. Telliard, W.A., McCarty, H.B. and Riddick, L.S., Results of the inter-laboratory validation study of USEPA method 1613 for the analysis of tetra- through to octachlorinated dioxins and furans by isotope dilution GC-MS, Chemosphere, 27, 4146 (1993). 4. Meier-Augenstein, W., Watt, P.W. and Langhans, C.D., Influence of gas chromatographic parameters on measurement of 13C/1zC isotope ratios by gas-liquid chromatography-combustion isotope ratio mass spectrometry, J. Chromatogr A, 752, 233-241 (1996). 5. Heumann, K.G., Isotope-dilution mass spectrometry of inorganic and organic substances, Fresenius’ Z. Anal. Chem., 325, 661-666 (1986). 6. De Bievre, F?, Isotope dilution mass spectrometry: what can it contribute to accuracy in trace analysis?, Fresenius’ Z. Anal. Chem., 337, 766-771 (1990). 7. Lawson, A.M., Gaskell, S.J. and Hjelm, M., Methodological aspects on quantitative mass spectrometry used for accuracy control in clinical chemistry, J. Clin. Chem. Clin. Biochem., 23,433-441 (1985). 8. Bjorkhem, I., in Stable Isotopes, Schmidt, H.L., Forstel, H. and Heinzinger, K. (eds.), Elsevier, Amsterdam, p. 593 (1982). 9. Schoeller, D.A., Model for determining the influence of instrumental variations on long-term precision of isotope-dilution analyses, Biomed. Mass Spectrom., 7, 457-463 (1980). 10. Wolff-Briche, C.S.L., Carter, D. and Webb, K.S. A comparison of GCMS and LCMS measurements for high accuracy analysis of cholesterol in human serum by isotope dilution mass spectrometry, Rapid Commun. Mass Spectrom, 16, 848-853 (2002). 11. Prichard, E., Trace Analysis: A Structured Approach to Obtaining Reliable Results, Royal Society of Chemistry, Cambridge, ISBN 0-85404-417-5 (1996). 12. Gorsuch, T.T., The Destruction of Organic Mutter, Pergamon Press, Oxford (1970). 13. Griepink, B. and Tolg, G., Sample digestion for the determination of elemental traces in matrices of environmental concern, Pure Appl. Chem., 61, 1139 (1989). 14. Report by the Analytical Methods Committee: Evaluation of analytical instrumentation. Part X. Inductively coupled plasma mass spectrometers, Analyst, 122, 393-408 (1997). 15. Colby, B.N., Rosecrance, A.E. and Colby, M.E., Measurement-parameter selection for quantitative isotope-dilution gas chromatography-mass spectrometry, Anal. Chem., 53, 1907-1911 (1981).

36

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectrometry

16. Dehennin, L., Reiffsteck, A. and Scholler, R., in Stable Isotopes, Schmidt, H.L., Forstel, H. and Heinzinger, K. (eds.) Elsevier, Amsterdam, p. 617 (1982). 17. Webb, K.S., VAM report on calibration and traceability for primary chemical methods; application of isotope dilution mass spectrometry (IDMS) to organic ultra-trace analysis (1994). 18. Schoeller, D.A., Mass spectrometry: calculations, J Clin. Pharmacol., 26, 396-399 (1986). 19. Yap, W.T., Schaffer, R., Hertz, H.S., White, YE,and Welch, M.J., On the difference between using linear and non-linear models in bracketing procedures in isotope dilution mass spectrometry, Biomed. Mass Spectrom., 10, 262-264 (1983). 20. Thienpont, L.M., Van Nieuwenhove, B., Stockl, D. and De Leenheer, A.P., Calibration for isotope dilution mass spectrometry - description of an alternative to the bracketing procedure, 1 Mass Spectrom., 31, 1119-1125 (1996). 21, Henrion, A,, Reduction of systematic errors in quantitative analysis by isotope-dilution mass spectrometry (IDMS): an iterative method, Fresenius ’ 2.Anal. Chem., 350, 657658 (1994). 22. Catterick, T.,Fairman, B. and Harrington C.F., Structured approach to achieving high accuracy measurements with isotope dilution inductively coupled plasma mass spectrometry, 1 Anal. At. Spectrom., 13, 1009-1013 (1998). 23. Furuta, N., Ohata, M., Ichinose, T., Shinohara, A. and Chiba, M., Isotope-dilution analysis of selenium in human blood serum by using high power nitrogen microwaveinduced plasma mass spectrometry coupled with a hydride-generation technique, Anal. Chem., 70,2726-2730 (1998). 24. Hoelzl, R., Hoelzl, C., Kotz, L. and Fabry, L., The optimal amount of isotopic spike solution for ultratrace analysis by isotope-dilution mass spectrometry, Accred. Qual. Assur., 3, 185-188 (1998). 25. Russ, G.P. 111, Isotope Ratio Measurements Using ICP-MS, in Applications of Inductively Coupled Plasma Mass Spectrometry, Date, A.R. and Gray, A.I. (eds.), Blackie, Glasgow (1993). 26. Rosman, K.J.R. and Taylor, P.D.P., Isotopic compositions of the elements, Pure Appl. Chem., 70, 217 (1998). 27. Webb, K.S. and Carter, D., The role of isotope-dilution mass spectrometry in the development of tandem mass spectrometry for quantitative organic analysis, Rapid Commun. Mass Spectrom., 11, 155-158 (1997). 28. Begley, I.S. and Sharpe, B., Occurrence and reduction of noise in inductively coupled plasma mass spectrometry, for enhanced precision in isotope ratio measurement, 1 Anal. At. Spectrom., 9, 171-176 (1994).

Additional Organic IDMS Publications Quantitative aspects De Bitvre, PJ. and Debus, G.H., Precision mass spectrometric isotope dilution analysis, Nucl. Instrum. Methods, 32, 224-228 (1 965). Bush, E.D. and Trager, W.F., Analysis of linear approaches to quantitative stable isotope methodology in mass spectrometry, Biomed. Mass Spectrom., 8, 21 1-2 18 (1981).

Annexes

37

Falkner, F.C., Comments on some common aspects of quantitative mass spectrometry, Biomed. Mass Spectrom., 8,43-46 (1981). Sabot, J.F., Ribon, B., Kouadio-Kouakou, L.P. and Pinatel, H., Comparison of two calculation procedures for gas chromatography-mass spectrometry associated with stable isotope dilution, Analyst, 113, 1843- 1847 (1988). Boyd, R.K., Quantitative trace analysis by combined chromatography and mass spectrometry using external and internal standards, Rapid Commun. Mass Spectrom., 7, 257-27 1 (1 993).

Statistical aspects Schoeller, D.A., A review of the statistical considerations involved in the treatment of isotope dilution calibration data, Biomed. Mass Spectrom., 3, 265 271 (1976). Jonckheere, J.A. and De Leenheer, A.P., Statistical evaluation of calibration curve nonlinearity, in isotope dilution gas chromatography/mass spectrometry, Anal. Chem., 55, 153-155 (1983). Moler, G.F., Delongchamp, R.R., Korfinacher, W.A., Pearce, B.A. and Mitchum, R.K., Confidence limits in isotope dilution gas chromatography/mass spectrometry, Anal. Chem., 55, 835-841 (1983).

Applications Bjorkhem, I., Bergman, A., Falk, O., Kallner, A., Lantto, O., Svensson, L., Akerlof, E. and Blomstrand, R., Accuracy of some routine methods used in clinical chemistry as judged by isotope dilution mass spectrometry, Clin. Chem., 27, 733-735 (1981). Moore, L.J., Kingston, H.M., Murphy, T.J. and Paulsen, P.J., Use of isotope dilution mass spectrometry for certification of standard reference materials, Environ. Int., 10, 169-173 (1984). Marlier, M., Lognay, G., Wagstaffe, J., Dreze, P. and Severin, M., Application of radiometric and isotope dilution-mass spectrometric techniques to the certification of edible oil and fat reference materials, Fresenius’ 2. Anal. Chem., 338, 419422 (1 990). De Leenheer, A.P. and Thienpont, L.M., Applications of isotope dilution-mass spectrometry in clinical chemistry, pharmacokinetics and toxicology, Mass Spectrom Rev., 11,249-307 (1992). Boenke, A., Certification of the mass concentration of three stilbenes in bovine urine reference materials by gas chromatographic-mass spectrometric methods. Sources of error and their control, Anal. Chim. Acta, 275, 3-8 (1993). Sabot, J.F. and Pinatel, H., Calculation of the confidence range in order to obtain

38

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectromem

a linear calibration graph in stable isotope dilution mass spectrometry: application to reference methods and pharmacological studies, Analyst, 118, 83 1-834 (1993). Bowers, G.N. (Jr), Fassett, J.D. and White, VE., Isotope dilution mass spectrometry and the national reference system, Anal. Chem., 65,475R-479R (1993). Thienpont, L.M., Stockl, D. and De Leenheer, A.P., Letter - Isotope dilution mass spectrometry and implementation of a common accuracy base for routine medical laboratory analysis: practice and prospects, J Mass Spectrom., 30, 772-774 ( 1995).

Liquid chromatography-mass spectrometry Brown, F.R. and Draper, W.M., Matrix effect in particle beam liquid chromatographylmass spectrometry and reliable quantification by isotope dilution, Biol. Mass Spectrom., 20, 515-521 (1991). Doerge, D.R., Burger, M.W. and Bajic, S., Isotope dilution liquid chromatography-mass spectrometry using a particle beam interface, Anal. Chem., 64, 1212-1216 (1992). Doerge, D.R., Exchange of comments on ‘Isotope dilution liquid chromatography-mass spectrometry using a particle beam interface’, Anal. Chem., 65, 1489- 1490 (1993).

General aspects Blom, K., Schuhardt, J. and Munson, B., Mass spectral analysis of monodeuteriolabelled compounds exhibiting significant (M - H)+ peaks, Anal. Chem., 57, 1986-1988 (1985). Gaskell, S., Hjelm, M. and Lawson, A., Letter to the Editor - Reference methodology involving isotope dilutiodmass spectrometry, Clin. Chem., 31, 167168 (1985). Blom, K.F., Average mass approach to stable isotope dilution mass spectrometry, Mass Spectrom., 22, 530-533 (1987). Roth, E., International Union of Pure and Applied Chemistry Technical Report Critical evaluation of the use and analysis of stable isotopes, Pure Appl. Chem., 69, 1753-1828 (1997).

Additional Inorganic IDMS Publications General background Webster, R.K., Mass Spectrometric Isotope Dilution Analysis, in Methods in Geochemiso, Smales, A. and Wagner, L.R. (eds.), Interscience, New York (1960).

Ann exes

39

De Bievre, P.J. and Debus, G.H., Precision mass spectrometric isotope dilution analysis, Nucl. Instrum. Anal. Methods, 32, 224-228 (1965). Heumann, K.G., Isotope Dilution Mass Spectrometry, in Inorganic Mass Spectrom e Q , Adams, F., Gijbels, R. and Van-Grieken, R. (eds.), J. Wiley & Sons, Chichester (1988). Fassett, J.D. and Paulsen, P.J., Isotope-dilution mass spectrometry for accurate elemental analysis, Anal. Chem., 61,643A-644A, 646A, 648A-649A (1989). Taylor, H.E., in Applications of Inductively Coupled Plasma Mass Spectrometry, eds. Date, A.R. and Gray, A.L., Blackie, Glasgow, p. 80 (1993).

Practical aspects Ingrahm, M.G., Brown, H., Patterson, C. and Hess, C.D., The branching ratio of

40Kradioactive decay, Phys. Rev., 80, 916 (1950). Crain, J.S., Houk, R.S. and Eckles, D.E., Noise power spectral characteristics of an inductively coupled plasma mass spectrometer, Anal. Chem., 61, 606 (1989). Colonder, D., Salters, V and Duckworth, D.C., Ion sources for analysis of inorganic solids and liquids by MS, Anal. Chem., 66, 1079A-1089A (1994). Watters, R.L. (Jr.), Eberhardt, K.R., Beary, E.S. and Fassett J.D., Protocol for isotope dilution using inductively coupled plasma mass spectrometry (ICP-MS) for the determination of inorganic elements, Metrologia, 34, 87-96 (1997). Lamberty, A. and Pauwels, J., How to correct for blanks in isotope-dilution mass spectrometry, Int. J Mass Spectmm. Ion Processes, 104, 45-48 (1991). Catterick, T., in Trace Analysis: A Structured Approach to Obtaining Reliable Results, Chapter 4.3, Elemental Mass Spectrometry, Prichard, E., Mackay, G.M. and Points, J. (eds.), Royal Society of Chemistry, Cambridge, ISBN 0-85404-4175 (1996). Wolff-Briche, C.S.J., Harrington, C.F., Catterick, T., and Fairman, B., Orhodox uncertainty budgeting for high accuracy measurements by isotope dilution inductively coupled plasma mass spectrometry, Anal. Chim. Acta, 437, 1 (2001).

Applications Heumann, K.G., Baier, K., Beer, F., Kifmann, R. and Schindlmeier, W., Mass spectrometric isotope dilution analysis of trace amounts of halides, Adv. Mass Spectrom., 8A, 318-324 (1980). Garbarino, J.R. and Taylor, H.E., Stable-isotope-dilution analysis of hydrologic samples by inductively coupled plasma mass spectrometry, Anal. Chem., 59, 1568-1575 (1987). Pin, C., Lacombe, S., Telouk, P. and Imbert, J., Isotope-dilution inductively

40

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectrometry

coupled plasma mass spectrometry: a straightforward method for rapid and accurate determination of uranium and thorium in silicate rocks, Anal. Chim. Acta, 256, 153-161 (1992).

Certification of reference materials Beauchemin, D., McLaren, J.W., Willie, S.N. and Bermann, S.S., Determination of trace metals in marine biological reference materials by inductively coupled plasma mass spectrometry, Anal. Chem., 60, 687-691 (1988). De Bievre, P., Laeter, J.R., Peiser, H.S. and Reed, W.P., Reference materials by isotope-ratio mass spectrometry, Mass Spectrom. Rev., 12, 143- 172 (1993). Catterick, T., Handley, H. and Merson, S., Analytical accuracy in ICP MS using isotope dilution and its application to reference materials, At. Spectrosc., 16, 229-234 (1995). Papadakis, I., Taylor, P.D.P. and De Bievre, P., Establishing an SI-traceable copper concentration in the candidate reference material MURST ISS A1 Antarctic Sediment using isotope dilution applied as a primary method of measurement, J. Anal. At. Spectrom., 12, 791-796 (1997). Papadakis, I., Taylor, P.D.P. and De Bievre, P., CCQM-1 interlaboratory study, measurement of lead amount content in water by a primary method of measurement: direct isotope dilution, Metrologia, 35, 715-721 (1998). Evans, P. and Fairman, B., High resolution ID-ICP-MS certification of an estuary water reference material (LGC 6016) and analysis of matrix induced polyatomic interferences, J. Environ. Monit., 3, 469 (2001).

Optimisation Ting, B.T.G. and Janghorbani, M., Optimization of instrumental parameters for the precise measurement of isotope ratios with inductively coupled plasma mass spectrometry, 1 Anal. At. Spectrom., 3, 325-336 (1988). Van Heuzen, A.A., Hoekstra, T. and Van Wingerden, B.J., Precision and accuracy attainable with isotope-dilution analysis applied inductively coupled plasma mass spectrometry: theory and experiments, J. Anal. At. Spectrom., 4, 483-489 (1989). Furuta, N., Optimization of the mass scanning rate for the determination of leadisotope ratios using an inductively coupled plasma mass spectrometer, J. Anal. At. Spectrom., 6, 199-203 (1991). Denoyer, E.R., Evaluation of spectral integration in ICP MS, At. Spectrosc., 13, 93-98 (1992). Patterson, K.Y., Veillon, C. and O’Haver, T.C., Error propagation in isotopedilution analysis as determined by Monte Car10 simulation, Anal. Chem., 66, 2829-2834 (1994).

Annexes

41

Annex 2: Glossary of Terms and Abbreviations This glossary attempts to provide helpful descriptions of key terms referred to in the Guide. It does not necessarily adhere to internationally recognised definitions of these terms.

Accuracy A quantity referring to the difference between the mean of a set of results or an individual result and the value that is accepted as the true value for the quantity measured.

Amount of Substance (amount) Base quantity in the SI system of units. It is the number of elementary entities divided by the Avogadro constant. Prior to 1969 it was simply referred to as the number of moles. The words ‘of substance’ may be replaced by the specification of the entity, e.g. amount of sodium chloride.

Amount of Substance (amount) fraction Amount of a constituent divided by the total amount of all constituents in the mixture. It is also called mole fraction.

Amount of Substance (amount) concentration Amount of a constituent divided by the volume of the mixture. Mole per litre (mol L-’)sometimes denoted by M (molarity).

Analyte The component of a sample which is ultimately determined directly or indirectly.

Bias Characterises the systematic error in a given analytical procedure and is the (positive or negative) deviation of the mean analytical result from the (known or assumed) true value.

Blank analysis A test procedure carried out without the sample, i.e. an analysis utilising the reagents or solvents required by the method which have, as far as possible, undergone the processes and treatments of the analytical method.

42

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectrometry

Calibration The set of operations which establish, under specified conditions, the relationship between values indicated by the analytical instrument and the corresponding known values of an analyte. In the case of IDMS, it is the instrumental measurement of ion abundance ratios of known mixtures of natural and isotopically labelled analogues in order to determine the concentration of the analyte in an unknown sample to which a precisely defined amount of the isotopically labelled analogue has been added.

Discrimination The extent to which the behaviour of the natural compound or element differs from the behaviour of the isotopically labelled analogue or enriched isotope during the analytical procedure, for example, during evaporation, derivatisation or chromatography.

Equilibration Incorporation of an isotopically labelled analogue (the spike) into the sample matrix, ideally in an identical manner to the natural compound (analyte), where further changes with time do not occur. Note: This is ideally carried out before sample digestion or extraction.

Error The difference between an analytical result and a ‘true’ value. Contribution from two components - systematic error (bias) and random error (precision).

Error, random Result of a measurement minus the mean that would result from an infinite number of measurements of the same measurand carried out under repeatability conditions. See also Precision.

Error, systematic Mean value that would result from an infinite number of measurements of the same measurand carried out under repeatability conditions minus a true value of the measurand. In the course of a number of measurements made under the same conditions, of the same value of a given quantity, such an error either remains constant in absolute value and sign, or varies according to a definite law when the conditions change. See also Bias.

Annexes

43

GC-MS The combination of gas chromatography and mass spectrometry, used for the separation and analysis of compounds.

IDMS - isotope dilution mass spectrometry A quantitative analysis based on the measurement of the isotopic abundance of an analyte after isotope dilution, and measured using a mass spectrometer.

Internal standard A compound, as similar in behaviour to the analyte as possible, added to a sample in known concentration to facilitate the quantitative determination of the sample components. Note that IDMS is theoretically the ideal form of internal standardisation.

Ion abundance Signal response of the mass spectrometer for a given characteristic ion of a compound.

Isotope amount ratio The ratio of the molar quantities of a characteristic ion of an analyte to the corresponding ion of its isotopic analogue.

Isotope dilution Mixing of a given nuclide with one or more of its isotopes.

Isotope dilution analysis A method of quantitative analysis based on the measurement of the isotopic abundance of a nuclide after isotope dilution with the test portion.

Isotopes Forms of an element (nuclide) where the numbers of neutrons are different leading to different atomic weights, for example I2C and 13C.

Isotopic abundance The relative number of atoms of a particular isotope in a mixture of the isotopes of an element, expressed as a fraction of all the atoms of the element.

44

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectrometry

Isotopic ion abundance ratio The ratio of the ion abundance of a characteristic ion of an analyte to the corresponding ion of its isotopic analogue.

Isotopically enriched analogue An internal standard comprising an isotope of the element of interest with an

altered abundance, such that it is greater than found in nature, for example, '06Pb natural abundance 0.03 atom percent, enriched abundance 99.76 atom percent.

Isotopically labelled analogue A compound which has had one or more atoms of its constituent elements replaced by a different isotope of that element, for example, "C replaced by I3C in '3C2H50Hand used as an internal standard.

LC-MS The combination of liquid chromatography and mass spectrometry, used for the separation and analysis of compounds.

Limit of detection The lowest amount of an analyte in a sample which can be detected with reasonable certainty for a given analytical procedure. For many purposes the limit of detection is taken to be a minimum of 3 X signal-to-noise ratio.

Limit of determination (quantification) The lowest amount of an analyte in a sample which can be quantitatively determined with suitable uncertainty. It can be taken typically as 1OX signal-tonoise ratio.

Mass bias Difference between the measured ion abundance ratio and the actual molar ratio for a compound and its isotopic analogue or two isotopes of the same element.

Mass concentration Mass of a constituent divided by the volume of the mixture.

Annexes

45

Mass discrimination - see Mass bias Mass fraction Mass of a constituent divided by the total mass of all constituents in the mixture.

MS-MS A mass spectrometric technique in which ions are subjected to two or more sequential stages of analysis according to the quotient madcharge. Can be useful to minimise interferences.

Precision The closeness of agreement between the independent results obtained applying the experimental procedure under prescribed conditions.

Reagent (solvent/process) blank Ideally a solution obtained by carrying out all steps of the analytical procedure in the absence of the sample.

Signal-to-noise ratio A measure of the relative influence of noise on a control signal. Usually taken as the magnitude of the signal divided by the standard deviation of the background signal.

Spike The isotopically enriched analogue of the analyte used for IDMS analysis.

Stable isotope internal standardisation - see IDMS Tandem MS - see MS-MS Uncertainty The characteristic dispersion of the measured values that could reasonably be attributed to the measurand.

Annex 3 Standard IDMS Equations This section will deal with the standard IDMS equations for calculating concentrations in the unknown sample in both organic and inorganic analysis. The principle of IDMS is based on the measurement of isotope amount ratios

46

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectrometty

that were modified in a sample by addition of an isotopic analogue (it can be the element enriched in one of its isotopes, or a compound with one, or more, atoms isotopically labelled). In this section, the following convention of notation is used to describe the different solutions and blends: Sample: Spike: Primary analyte standard: Sample blend, i.e. sample spike: Calibration blend, i.e. primary standard

+

+ spike:

index X index Y index Z index B = X Y index Bc = Y Z.

+ +

The following notations are used to described the different quantities:*

nx: amount of substance in sample X (mol) ny: amount of substance in spike Y (mol) cx: concentration of elemendanalyte in sample X (mol I,-') cy: concentration of elemenuanalyte in spike Y (mol L-') cz: concentration of elemenuanalyte in primary standard Z (mol L-') my:mass of spike Y added to the sample X to prepare the blend B (g or kg) mx:mass of sample X added to the spike Y to prepare the blend B (g or kg) mZc:mass of primary standard solution Z added to the spike Y to make calibration blend Bc (g or kg) myc:mass of spike Y added to the primary standard solution Z to make calibration blend Bc (g or kg) RB: isotope amount ratio of sample blend B RBc:isotope amount ratio of calibration blend Bc Rx: isotope amount ratio of sample X Ry: isotope amount ratio of spike Y Rz: isotope amount ratio of primary standard Z We have tried to adopt a consistent notation but alternatives will be found in the literature. The isotope amount ratio of a blend is defined for element (analyte) E as:

Equation 1

+

amount of isotope 1 of element E in B - n x ( ' E ) n y ( ' E ) n B ( Z E) amount of isotope 2 of element E in B nx(2E)+ ny(ZE)

RB=-- n B ( ' E )

*The concentration can be replaced by mass fraction (gkg-'), amount content (molkg-' or any appropriate quantity as long as it stays consistent throughout the equations.

47

Annexes

The ratio of amount of element E in the sample to spike is given by:

Equation 2 nx CX. -ny cy *

mx amount of element E in X - nx('E) m y amount of element E in Y - nY(lE)

+ nx(2E)- (Rx + 1) nx(2E) + ny(2E) - ( R y + 1 ) - ny(2E)

By combining and re-arranging Equation 1 and Equation 2, the IDMS equation, also sometimes called 'normal' IDMS, 'single' IDMS or 'one-way' IDMS, is obtained for a bi-isotopic element:

Equation 3

If the element has more than two isotopes the IDMS equation is written as:

Equation 4

where:

R,: isotope amount ratio of isotope i to the reference isotope in sample X . R N : isotope amount ratio of isotope i to the reference isotope in spike Y. If isotope abundances (isotope amount fractions) are used instead of isotope amount ratios, then the IDMS equation can be formulated as:

Equation 5

where:

Mx:molar mass of sample X My: molar mass of spike Y f x ( ' E ) : amount fraction of isotope 'E in sample X f X ( * E ) amount : fraction of isotope 'E in sample X

48

Guidelines for Achieving High Accuracy in Isotope Dilution Mass Spectrometry

f y ( ’ E ) : amount fraction of isotope ‘E in spike Y fy(’E): amount fraction of isotope 2E in spike Y When organic compounds are analysed by IDMS, they are usually labelled with 13C, ’H or ”N. For these elements, it is often considered that there is a negligible amount of the isotopically labelled analogue in the natural sample. Then Rx tends towards infinity and in this case the equation simplifies to:

Equation 6

A fi.uther simplification can be made if Rx tends to infinity and the isotopic analogue is of a high isotopic purity (i.e. contains a negligible amount of the natural isotope), in which case Ry tends to zero. For this case, the IDMS equation can be simplified to:

Equation 7

The same principle can be applied to characterise the concentration of a spike; in this case, the labelled analyte is blended with a primary standard solution Z , which is well characterised. This will give a ‘reverse’ IDMS equation:

Equation 8

If the concentration of the spike was determined by IDMS analysis, or if ‘reverse’ IDMS cannot be performed each time, a ‘double IDMS’ or ‘two-way’ IDMS can be performed, which eliminates the need for a well-known concentration of the spike. The ‘double’ IDMS equation can then be written as:

Annexes

49

Equation 9

I

I

For most elements, there is no variation in the isotopic composition in nature. As a consequence, Rx = Rz and Rix = RiZ.The equation can then be simplified as:

Equation 10

This equation can be used when the exact signal matching procedure is used as the calibration procedure as two blends are needed, one prepared with the sample and one with a primary standard, having matching isotope amount ratios RB = RBc. This approach also has the advantage of eliminating the quantity cy from the calculation, which is often not very well known, or might have a large standard uncertainty associated with it. In the case of an organic analyte, the same approximation can be made as for the ‘normal’ IDMS situation, leading to a simplified ‘double’ IDMS equation:

Equation 11

The measurement of isotope amount ratios is influenced by a number of factors including the mass bias of the mass spectrometer, the non-linearity or dead time of the detector, and mass spectral interferences at the selected isotope masses. It is common practice to compensate for the mass bias effect by bracketing the analysis of the spiked sample with a pure reference standard, of known isotopic composition. The ‘matching’ approach takes this a step further. The reference standard is replaced by the calibration blend. Under these circumstances many of the sources of error, of which mass bias is only one, are negated.