Sources of error in external calibration ICP-MS analysis of geological samples and an improved non-linear drift correction procedure

S ecnochlmrca

Ada.

Vol

P!8nted m Great Bntam

ow-8547/93 SfJal + 00 @ 1993 Pergamon Res.s Ltd

48B. NO 3. pp E467-E506, 1993

Sources of error in external calibration ICP-MS analysis of geological samples and an improved non-linear drift correction procedure*

MICHAELM. CHEATHAM,?WILLIAMF. SANGREYand WILLIAMM. WHITE Department

of Geological Sciences, Snee Hall, Cornell University, Ithaca, NY 14853-1504, U.S.A. (Received 25 August 1992; accepted 23 October 1992)

Ah&act-The pnmary factors hmitmg accuracy and precision using inducttvely coupled plasma mass spectrometry (ICP-MS) m matrix-matched external standardization are machme drift and variatton of the instrument response as a functton of mass. Because dnft 1s usually non-linear, the degree of dnft differs from one mass to the next, and the direction of drift can change frequently when analyzing over large mass ranges. Internal standardization results in minimal tmprovement of data quality. An analyttcal procedure and an off-line data reduction algorithm have been developed that correct for these vanattons and produce a signilicant improvement m analytical accuracy and precision. In thts techmque, a “drift correction” standard is analyzed after every four or five samples. A polynomial curve 1s fitted to each isotope analyzed, and a correction based on this curve is apphed to the measured intensity of the respecttve isotopes in the samples and standards. This data reduction algorithm has been developed mto a Microsoft Excel- 3.0 Macro that completely automates all calculations. This arttcle IS an electronic publication in Spectrochimica Actu Electronica (SAE), the electronic section of Spectruchrmica Acta Part B (SAB) The hard copy text is accompamed by a dtsk wtth the Excel macro for the Macintosh computer and sufficient mstructtons for its use The mam arttcle discusses the scientific aspects of the subject and explains the purpose of the macro.

1.

INTR~DU~ITON

GOALS generally sought in the development of new analytical procedures are maximum accuracy and precision with minimum effort and cost. Inductively coupled plasma mass spectrometry (ICP-MS) has promised improvements in reaching both these goals, although in actual implementation, one or the other is often sacrificed. Of the three methods of quantitative analysis available for the ICP-MS, external standardization, standard additions and isotope dilution, we have found that high precision is possible using standard additions and isotope dilution; unfortunately, considerable effort in sample preparation is required for these techniques. In the case of standard additions @A), the technique involves taking the sample, dividing it into equal aliquots, and adding to each increasing amounts of a reagent containing the element(s) under consideration [l]. The increments usually consist of equal volumes, and a minimum of four mixtures is required per sample. Therefore, a set of standard addition “spikes” must be prepared and calibrated in addition to the preparation of the sample. Thus, for each sample analyzed by standard additions, at least four solutions must ultimately be measured. Isotope dilution, while being a potentially extremely accurate technique, is also labor intensive and more costly than standard additions. Isotope dilution mass spectrometry (IDMS) is based on the addition of a known amount of enriched isotope (called the “spike”) to a sample. After equilibration of the spike isotope with the natural element in the sample, the ICP-MS is used to measure the altered isotope ratio. The difference between the isotopic ratio in the mixture and the natural isotope ratio can be used to accurately calculate the concentration of the element in the sample [2]. While the

* This article is an electronic pubhcatton in Spectrochrmrcu Actu Electronccu (SAE), the electromc section of Spectrochimicu Actu Port B (SAB). The accompanying disk is identified as “Drift Correcting Solution Excel 3.0 macro”, Spectrochimrcu Actu Electromcu 48B, E487-ES06 (1993), where E487 1s the 1st page of the text m this publication. Readers of this journal are pernutted to copy the contents of the disk for their personal use under the conditrons stated under ‘Copyright and Disclaimer” at the end of this article, and, generally, in the “Instructions for Authors”, published elsewhere m this issue. t Author to whom correspondence should be addressed. E487

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M M CHEATHAM et al.

addition of a spike is not particularly time consuming, the initial time spent in preparing the spike solution is. Additionally, the initial cost of purchasing the spike solution can be high. A further disadvantage of isotope dilution is that the concentration in the unknown is generally a non-linear function of the isotope ratio of the standard-spike mixture. This non-linearity leads to error magnification, which becomes a serious problem when the isotope ratio in the sample-spike mixture approaches that of either the natural value or the spike value. Avoiding error magnification requires some knowledge of the concentration before spiking. With both SA and IDMS there is the inherent risk of increasing the contaminant level of the sample simply by adding more steps in the sample preparation process. External standardization minimizes effort, but often sacrifices precision. In the external standard calibration (ESC) method, the blank-subtracted signal intensities for the element of interest in a group of standards are plotted against the known concentration of the element in those standards. A calibration curve is fitted to the data points. Typically, in the commercially available ICP-MS instruments, the linear dynamic range, the range over which the response of the instrument is linear with respect to analyte concentration, is greater than six orders of magnitude. As such, the curve fitted to the standard data should be linear. The slope of the line defined by the standards is proportional to the concentration in the standards. The unknown sample is run and its signal intensity is plotted against the curve to determine the concentration. This technique as outlined is not as labor intensive as SA or IDMS; however it is not as accurate. In our experience, using a straightforward classical approach, under optimal conditions of instrument tuning and maintenance, the ICP-MS produces results with a maximum precision for analysis of geological materials (i.e. complex matrices) in the range of 5-10%. In contrast, standard additions can routinely yield data that are better than 2%, and IDMS on the ICP-MS produces data better than 1%. 2.

SOURCES OF ANALYTICAL

ERRORIN ICP-MS

We undertook a systematic evaluation of errors associated with ESC that might be responsible for analytical precision being limited to 5-10%. We have explored three particular areas that frequently lead to poor precision: the linear dynamic range of the instrument, matrix effects, and drift. Non-linear response can be an important source of error in traditional instrumental techniques; in techniques such as calorimetry or atomic absorption, the linear dynamic range is typically limited to three or four orders of magnitude of analyte concentration. Manufacturers of commercial ICP-MS units claim the instruments, including the VG Plasmaquad 2+ used in this study, have at least six orders of magnitude linear dynamic range. We have found this to be true. In addition, since concentrations of the elements of interest in this study (Ba and the lanthanide rare earths) range by four orders of magnitude or less in the samples of interest to us (igneous rocks), linear dynamic range Senru strict0 (i.e. the ability of the detector system to respond linearly to varying ion beam intensities) does not significantly limit analytical precision. The role that the matrix plays is complex and varied [3-81, and can lead to dramatically diminished accuracy. Complex geological matrices generally result in a suppression of the analyte, although enhancements have been observed [9]. The details of matrix effects have been extensively discussed in the literature [5, 10-121, and one common suggestion is to match the matrices of the standards and unknowns. There are, of course, varying degrees to which an analyst can attempt to matrix match. How closely must the matrices of standards and samples be matched? We have found that it is necessary to matrix match standards and unknowns as exactly as possible. For example, we have found that using a suite of United States Geological Survey (USGS) standards encompassing the entire range of igneous rock compositions from basalt to granite (e.g. BIR-1, DNC-1, W-2, BHVO-1, AGV-1, GSP-1, and G2) results in non-linear calibration curves for the rare earth elements (REE). The

Error sources m ICP-MS analysisof geologicalsamples

E489

maximum range in concentrations in rare earths in this suite is less than four orders of magnitude, and thus is well within the linear dynamic range of the instrument. The non-linear portion of the calibration curves involves AGV-1, GSP-1 and G-2, the three non-basaltic members of this suite. The non-linearities are a result of differences of the major element concentrations in the standards. All the standards are similar in that they are all igneous rocks. Thus it seems necessary that basaltic rocks are analyzed against basaltic standards, granites against granitic standards, and so forth. We typically analyze basalts using the USGS standards BIR-1, DNC-1, W-2 and BHVO-I. This suite of basalt standards adequately matches the matrices in most of the unknowns that we analyze; however, we do analyze basalts that have light rare earth element concentrations (LREE) greater than those encountered in BHVO-1, and as such we have incorporated the GIT-IWG basalt BE-N into our repertoire of standards. BE-N extends the concentration range for the LREE by as much as a factor of five. While BE-N is classified as a basalt by GIT-IWG, its major element concentrations are different enough from the USGS basaltic standards that, for reasons that we do not fully understand, BE-N falls on the linear trend defined by the other standards for the REE in some runs and off it on others, Another source of error associated with the ESC method is drift. Drift can have a dramatic effect on all analyses performed using ICP-MS [13-151. Drift arises when an instrument response changes with time. Often, drift is associated with the effect of changes in ambient temperature on the stability of electronic circuits. During the early years of use of the original generation of commercially-available ICP-MS instruments, drift resulting from electronic instability was usually quite severe. Unfortunately, early instruments were often installed in environments without temperature and/or humidity regulation, resulting in even greater drift problems. Though subsequent generations of inst~mentation contained better electronics and were generally installed in laboratories with tight environmental controls, drift remains a limiting factor in obtaining high accuracy and precision ESC data by ICP-MS. These non-electronic-related drift problems appear to be directly dependent on the matrices of the solution introduced to the ICP-MS 14, 9, 16, 171. Typically, samples with moderate to high total dissolved solids contents will deposit salts on the cone orifices. This plating action results in a drop in sensitivity over time. Drift can also be a limiting factor with analyses where the matrix is considered simple. WANGEN et al. [13] attribute many drift-related phenomenon observed when analyzing multielement standards to machine malfunction, which can include faulty sample transport (nebulizer, peristaltic tubing), condition of the sample and skimmer cones, incorrect voltage settings for the lens stack, etc. WANGENet al. [13] have reviewed many of the techniques available for correcting for drift phenomenon, and have developed an additional technique utilizing the method of principal component factor analysis (PCFA). The PCFA method they have implemented relies on the use of internal standards, but the difference between this new approach and previous studies using an internal reference is one where the application of PCFA results in the prediction of what elements should be used as internal references in dependence on the elements to be determined. Their results show a signi~~ant improvement in the precision attainable in analyses that use internal references when PCFA is used to select the reference elements. While this approach shows considerable promise, it does suffer from two drawbacks. First, the technique requires a pre-analysis of the samples so that PCFA can be performed and the appropriate internal references selected. Secondly, all of the samples then have to be spiked with the appropriate internal references. As has already been outlined in the Introduction, the ECS method has the advantage over SA and isotope dilution in that nothing is added to the samples, thereby avoiding a potential source of contamination. Any technique that involves the use of internal reference falls prey to this drawback. If the drift were exactly linear as a function of time, as in Fig. 1, it could be easily corrected by re-analyzing the first sample in a series again in the last position of the analysis, as a recalibration solution or standard. If instrument response is a non-linear

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M. M.

CHEATHAM

el

al.

008

Fig. 1. Lmear drift as a function of time

function of time, but is independent of mass (e.g. Fig. 2), then an internal standard can be used to adequately correct for it [18, 191. Several recent papers [9, 161 have noted that machine response can vary both as a function of time and of mass as in Fig. 3. In this case, neither recalibration nor the use of a single internal standard will adequately compensate for curvilinear drift. It is our experience in the analysis of geological samples with complex matrices that instrument response is indeed a complex function of time and mass, and that neither simple recalibration nor internal standardization adequately corrects for it. So long as matrices of samples and standards are well matched, we have found that drift is the single most important factor limiting analytical precision in ICP-MS analysis. Since the drift we observe is virtually always in the direction of decreasing sensitivity, it is likely that it is due to the matrix, as mentioned above. In this case, one solution to reduce drift would be to remove the matrix. This may be necessary or beneficial for other reasons, for example, to remove an isobaric interference or to preconcentrate an analyte to achieve better sensitivity [20, 211. The simple spectrum and high sensitivity of the ICP-MS, however, means that matrix removal is not necessary for many or most elements. The chemical processing required for matrix removal is generally labor intensive; carrying it out when not otherwise necessary negates one of the principal advantages of ICP-MS, i.e. that it is not inherently labor intensive. Matrix removal also introduces two other potential sources of analytical error: blank and yield. We concluded that developing a method of correcting for drift was preferable to removing the matrix. We have developed an analytical procedure and an off-line data reduction algorithm that corrects for curvilinear drift as a function of mass and time. The algorithm results in a significant improvement in analytical accuracy and precision. In this technique, we analyze a “drift correction” standard after every four or five samples. We then fit

E491

Error sources m ICP-MS analysis of geological samples

/ 0.8

Fig. 2 Curvdmear drift as a function of time

a polynomial curve to each isotope analyzed, and apply a correction based on this curve to the measured intensity of the respective isotope in both sample and standard solutions. We now routinely employ this technique in the analysis of the rare earth elements in geological samples, in addition to the careful matrix matching mentioned above.

3. PROCEDURES This study was limited to the analysis of the lanthanide rare earth elements (BEE) and Ba in geological samples, m particular m basalts. Chemically, these rocks are composed of approximately 23 wt % Si, 9% Ca, 8% Fe, 7.5% Al, 4% Mg, 2% Na, 1% Ti and 0.5% K as major components (the remamder bemg mainly oxygen). Concentrations of the elements of interest range from well over 1000 ppm Ba and Ce m some cases, to less than 0.5 ppm for Tm and Lu. The mineralogy of basalts is usually simple, consisting of pyroxenes, feldspars, olivme, iron-titanium oxides, and glass. All these phases are readily digested in HF, with the exception of some oxide phases (which contain neghgible quantities of the elements of interest). Chemically resistant minerals, such as zircon and sphene, which would necessitate more complex digestion procedures, are not equilibnum phases of basalt. Fluxed fusion digestion, which is necessary for some geological materials [22], but has the disadvantage of dilutmg the elements of interest and increasing the matrix, can be avoided in favor of the simple digestion procedure described below. We normally prepare 250 ml of final solution for the ICP-MS. The solutions are m ~1% I-IN03 and contain less than 0.1% total dissolved solids. In preparing the sample, 250 mg of rock powder are weighed into a 50 ml PFA screw-top capsule. Fifteen milhliters of 28 N HF and 0.1 ml of 12 N HC104 are added to the sample. The capsule is closed to hand tightness and heated overnight on a hot plate at 120°C. The sample is uncapped and taken to dryness, followed by a temperature increase to drive off the Si as SLF.,, as well as any excess HF and HCIO.,. The sample is redissolved in 20 ml of 4.0 N HNOs. Once dissolved, the solution is transferred to a

E492

M M CHEATHAM et

al.

~0.6

Fig 3 Curvdmear drift as a function of mass and time

250 ml high density polyethylene (HDPE) bottle and diluted to final volume. Samples, blanks and standards are all prepared similarly. All reagents are purified by double sub-boiling distillation, except HC104, which we obtain pre-purified. The ICP-MS is a VG Fisons Instruments PlasmaQuad PQ2+ with diffusion pumps. The machine is run as purchased except for a shght modification to the lens stack that involved grounding the photon stop. The detector is a Galileo Channeltron channel electron multiplier. Solutions are sampled using a Gilson autosampler Mode1 221, and a Gilson Minipuls 3 peristaltic pump running at a setting of 20.3 with 0.63 mm i.d. PVC manifold tubing. The sample inlet system is composed of a Meinhard TR-30-A3 concentric glass nebuhzer and a Scott-type double pass spray chamber. A standard VG Fisons Instruments quartz torch is used. Gas flow rates are 13.75 standard liters per mmute (SLPM) for cool gas, 0.6 SLPM for auxiliary, and 0.725-0.760 SLPM for the nebulizer (set to minimize oxide levels). The spray chamber is cooled to 12°C. The sample and skimmer cones are nickel and have 1.0 mm and 0.75 mm diameter openings respectively. The instrument is imtrally tuned up on a 100 ppb solution of In, Mg and Pb. Typically the count rate is between 200 and 400 kHz for the l151n isotope. Mg and Pb are monitored on a daily basis to check for resolution and mass calibration. The operating pressure m the analyzer is nominally 2 x 10m6 mbar. The isotopes we are analyzing for Ba and the REE are listed m Table 1. Normal parameters for operation of the ICF-MS include the use of the autosampler with a 180 s wash time and a 90 s uptake time. Analyses are performed m peak jump mode, with a 10 240 us dwell time, 5 points per peak, 6 DAC steps and 100 sweeps per peak. A normal Ba and REE analysis includes 22 isotopes and requires 280 s of actual counting time per sample. A typical procedural run includes 5 or 6 calibration standards, lo-15 unknowns (including 3 or 4 standards run as unknowns), and 5-7 drift correcting solutions. Standards and unknowns are dispersed throughout the course of the run. The drift correcting solutron is an abundant inhouse standard, matrix-matched to the samples being analyzed (all tubes in an analysis are filled from a single stock solution). To minimize matrix effects, we are careful to matrix-match samples and standards. Thus we use solutions of basalt standards (USGS standards BIR-1, DNC-1, W2, BHVO-1, and the GIT-IWG standard BE-N) as external calibration standards. These basaltic

E493

Error sources m ICP-MS analysis of geologxal samples Table 1. Isotopes used in a typical element menu for the analysis of Ba and the lanthanides Element Ba Ba La Ce Pr Nd Nd Nd Sm Sm EU Eu Gd Gd

Isotope

Element

Isotope

Tb Gd DY DY DY Ho Er Er Er Tm Yb Yb Yb Lu

159 160 161 162 163 165 166 167 168 169 172 173 174 175

137 138 139 140 141 143 14.5 146 147 149 151 153 156 157

were chosen because their concentrations for barium and the lanthanides cover the concentration range in the samples of interest. rock standards

4. RESULTS One of our initial suspicions regarding the ESC poor precision was that the published values for the concentrations of the REE in the USGS standards we used were not accurate. The first indication that the values for these standards may be off was their “bumpy” nature when plotted on a standard chondrite-normalized REE plot (log of the chondrite-normalized concentration plotted vs atomic number). Accurate rare earth concentration data generally produces smooth patterns on such plots owing to the gradual change in the ionic radius of the REEs as a function of mass. Ionic radius is the principal factor governing rare earth distribution in igneous rocks. The gradual size difference results in gradual differences in the partition coefficients for the REEs between the melt and the solid as an igneous rock crystallizes. We re-analyzed these standards for Ba and the polyisotopic REEs by isotope dilution using thermal ionization mass spectrometry (TIM?&ID). Concentrations of monoisotopic rare earths were estimated by interpolation on chondrite-normalized rare earth plots on the assumption that the curves should be smooth. Use of these new values, which were significantly different from the recommended values in some cases, resulted in a clear improvement in our calibration curves, as well as smooth rare earth patterns. The averages of three TIM!XD analyses of these standards are compared with published values [23] in Table 2. The three analyses agree within 3% or better for all elements, and we believe the accuracy is also 3% or better. We use these revised values in all subsequent calculations in this study. Although adoption of the new values for the standards resulted in an improvement in the calibration curves and the precision of unknowns, we were still unsatisfied with the data quality of our analyses. Close examination of the calibration curves generated by the VG Fisons software “talcs” module and the reported statistics for each isotope led us to believe that the final solution concentration data may be calculated incorrectly. We transferred the data for the peak integrals to an Apple Macintosh computer and re-reduced the data using Microsoft Excel TM. With the selection of the appropriate statistical models, we were able to reproduce the VG Fisons data set. Having eliminated that suspicion, we surmised that the real problem resulting in such poor precision must lie elsewhere. This conclusion led us to closely monitor the raw data. It became evident that drift was the leading cause of the poor results obtained, yet adoption of an internal standardization technique similar to that of

M M CHEATHAM et al

E494

Table 2 Values for the USGS and GIT-IWG

Element

basalt standards determined by IDMS compared to pubhshed values (Publ.)

BIR-1 IDMS

Pub1

DNC-1 IDMS

Pub1

w-2 IDMS

Pub1

6.6 0.56 1 90 0.39 2 40 1 11 0 52 1.98 0 41 2.62 0 59 1 71 0.27 1 70 0 26

77 0.88 2.50 0.50 2.50 1.08 0.54 1.90 0.41 2.40 0.50 1.80 0.27 1.70 0.26

103.3 3.56 8.11 1.12 4.98 1.43 0.57 2.11 0.43 2 76 0.62 1.87 0 30 1 97 0 32

1140 3 80 10 60 1.30 4 90 1 38 0 59 2 00 0.41 2.70 0.62 2.00 0.10 2.01 0.32

171 6 10 07 22 79 3.04 12 90 3 24 1 10 3 73 0 68 3.83 0 80 2 17 0.33 1 98 0 30

182.0 11.40 24.00 5.90 14.00 3 25 1 10 3.60 0 63 3.80 0 76 2 50 0.38 2 05 0 33

Ba La Ce Pr Nd Sm Eu Gd Tb DY Ho Er Tm Yb Lu

THOMPSON

BHVO-1 IDMS 132 9 15 74 37 77 5.40 24.81 6 10 198 6 56 1 02 5.37 1.01 2.38 0.33 2.01 0.29

Pub1

BE-N IDMS

Pub1

139.0 15 80 39 00 5.70 25.20 6 20 206 6.40 0 96 5.20 0 99 2 40 0.33 2.02 0 29

1046.0 85.61 160.63 18.20 66 20 12 00 359 9 91 1 38 6.41 1 10 2 49 0 34 1 85 0 26

1025 0 82 00 152 00 70.00 12 00 360 9 50 1.30 6.40 1.10 2.50 0.36 1 80 0 24

and HOUK [24] and DOHERTY [18], using Cs and Re as internal standards to bracket Ba and the lanthanides resulted in only a moderate improvement in the accuracy of the results for the very lightest REEs and the very heaviest REEs. The accuracy of the middle REEs decreased. An experiment was performed in which 30 autosampler tubes were filled from one stock solution. The solutions were analyzed for Ba and the lanthanides. Significant drift was readily observed. Plotting the data as a three-dimensional surface resulted in Fig. 3. The shape of the curves varied smoothly over the mass range from 137 to 175. We repeated the experiment a number of times and found that, while the exact shape of the mass-time-intensity surface was not reproducible from one run to the next, it was always smooth. Confident of a smoothly varying surface, we devised an algorithm whereby a real data set of standards and unknowns could be corrected. We interspersed a number of tubes in the run that were filled from one stock solution to monitor drift. After the completion of the run, the integrals for those “drift correcting solutions” (DCS) were used to reduce the data and correct for drift. Our drift correction technique is described in greater detail in a subsequent section. Briefly, it involves analyzing a drift correcting solution after every fourth or fifth solution in the run. To correct the data set for drift, we fit a polynomial curve (intensity as a function of tube position) to each isotope analyzed in the drift correcting solution. We then apply a correction based on this curve to the measured intensity of the corresponding isotope in the samples and standards. Table 3 lists duplicate analyses of the USGS standard W-2. The table compares the concentration data reduced with VG Fisons software, the same data reduced off-line on the Macintosh using our “drift correction solution” (DCS) technique, and our TIMS-ID data for the standard. The linear regression performed on the peak integral data is obtained using a zero intercept in both the VG Fisons data set and the DCS data set. BONATE [25] has discussed the merits of both the “no-intercept” (O-intercept) and the “intercept” model in the use of linear regression to generate calibration curves; as he has pointed out, the “no-intercept” model usually provides more accurate estimates of unknown sample concentration than does the “intercept” model. The data obtained by ICP-MS meet the criterion for the use of the “O-intercept” model, where the blank level is so low that its subtraction from the data results in no significant change in the peak intensities. The percent relative error, calculated as ((true - unknown)/true) x 100, between the TIMS-ID values and the analysis values range from 0.17-24.1% for the VG Fisons reduced data. The lack of agreement between the TIM!+ID values and the analysis values is discouraging at best and

Error sources in ICP-MS analysts of geological samples

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Table 3 Comparison of two data sets reduced through (a) FISON’s/VG “talcs” module and (b) with the DCS macro. Each data set IS compared to our IDMS data or the USGS standards W-2 (a) Reduced wtth FISON’s “talcs” module w-2 IDMS uW2a Element Ba La Ce Pr Nd Sm Eli Gd Gd corrected Tb DY Ho Er Tm Yb Lu Mean Abs Dev.

%rel err

uW2b

%rel err

193.76 12 08 26.63 3 41 14 40 3 74 1 23 4 16 4.01 0.72 4.13 0.82 2.42 0.41 2 24 0.35

12.90 19.95 16.87 12.06 11 60 15 32 11 71 11 42 7.56 5 78 7 73 2 40 11 41 24.12 13 02 15 40 12 04

177 64 11 16 24 40 3 13 13 12 3 43 1 13 3 83 3.70 0 65 3 84 0 79 2 23 0 38 2 09 0 32

3 51 10 82 7 05 2 86 1 69 5.76 2.63 2 58 -0.93 -4.50 0 17 -1.34 2 67 15.04 5 46 5 51 4.60

uW2a

%rel err

uW2b

%rel err

0 68 3 83 0.80 2 17

172 47 10 51 22 78 2.98 12 94 3 27 1.07 3 89 3.76 0 67 3 82 0.78 2.12

0 50 4.36 -0 06 -1 84 0 27 0 86 -3 09 4.18 0.71 -0.88 -0 23 -2.25 -2 21

169.76 10.38 22.38 2.94 12.54 3.23 1.07 4.04 3.91 0 67 3 86 0.82 2 13

-1.08 3.05 -1.82 -3.26 -2.82 -0.34 -2.55 8 31 4.95 -1 91 0.86 2 12 -1.80

0 33 1 98 0 30

0.33 2.03 0.32

-1 52 2.27 4.62

0 34 2.04 0 31

2 42 3 18 3.30

171. 6 10.07 22.79 3.04 12.90 3.24 1.10 3.73 0.68 3 83 0 80 2 17 0 33 1 98 0 30

(b) Reduced with the DCS macro w-2 Element IDMS Ba La Ce Pr Nd Sm Eu Gd Gd corrected* Tb DY Ho Er Tm Yb Lu Mean Abs Dev

171 6 10 07 22 79 304 12 90 3.24 1 10

3.73

2.00

*Gd correcttons are calculated by subtractmg 1.0% of the Nd concentration concentratton Thus correction is based on an average oxide level of 1.0%.

2 59 from the Gd

alarming in the least. The two solutions of W-2 were filled from one stock solution, and yet there is poor agreement between the two analyses. In comparison, the data obtained using the DCS technique are in substantially better agreement with the TIMS-ID results. The average absolute deviation from the reference values improves by up to a factor of five (from 12% to 2.0% and 4.6% to 2.6% for the two aliquots, respectively). Large errors (4% and 8%) remain for Gd. This is due to an interference of iUNd160 with the lmGd peak. We apply an empirical correction for this by subtracting 1% of the intensity of the laNd peak from the laGd intensity. The Gd concentration so derived is listed as “Gd corrected” in Tables 3 and 4. The value of 1% reflects the average oxide level in routine analysis on our instrument. Oxide levels vary within and between runs, however, so this correction is still not entirely satisfactory. It is also apparent that the data for the less abundant REE, such as Lu, is somewhat poorer than for the more abundant elements. We believe this reflects poorer counting statistics at these low concentrations. The small spread in

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M. M. CHEATHAM et al. Table 4. Means and standard dewations of 15 rephcate analyses of W-2 analyzed since late 1990

Ba La Ce Pr Nd Sm Eu Gd Gd corRcted Tb DY Ho Er Tm Yb Lu

Ba La Ce Pr Nd Sm Eu Gd Cd eorreeted Tb DY Ho Er Tm Yb Lu

W2 unk

W2 unk

W2 unk

W2 unk

w-2 10/16/91

w-2 w-2(wfs) 10/16/91 (10/23/91)

w-2 10/29/91

w-2 10129/91

169.764 10.377 22.376 2.941 12.536 3.229 1.072 4.040 3.914 0.667 3.863 0.817 2.131 0.338 2.060 0.313

172 474 10.509 22.777 2.984 12.935 3268 1066 3.886 3.757 0.674 3 822 0.782 2.122 0 32.5 2 058 0 317

174.696 10.779 23.004 3.043 13.144 3.275 1094 3.978 3.847 0 672 3.920 0807 2.177 0.327 2069 0.313

178.640 11.037 23.725 3.071 13.467 3.303 1.125 3.974 3.839 0.676 3.955 0.819 2.240 0.342 2.159 0.327

171 244 10.456 22.269 2.950 13.024 3.336 1.066 3.876 3.745 0.695 3.990 0.812 2.176 0.346 2.077 0.301

167.909 10.182 22.010 2.893 12.602 3.191 1.062 3.774 3.648 0.651 3.807 0.777 2.117 0.320 1.989 0.307

161 105 10 669 23 323 3.002 12.588 3.125 1.048 3.611 3.485 0 653 3.728 0.799 2.154 0.333 2.124 0 322

179 030 11.478 24.457 3.236 13 574 3.472 1 125 4.015 3.879 0 688 4.101 0.859 2.378 0.379 2.267 0 339

W-2a 2114192

W-2b W-2unka W-2unkb 2114192 3-237 4129192

W2unk 4129192

W-2unk 4129192

Avg (15 analyses)

169.00 10 56 23.03 304 13 15 3.31 1.09 3 89 3.76 0 68 3.94 0 82 2 17 0.34 2.10 0 32

165 38 10 53 22.81 2.99 12.99 3 31 1 07 3 92 3.79 0 68 3 87 0.80 2 13 0.33 2.04 0 31

171 02 10.79 23 12 304 13.02 3 30 1.08 3 84 3.71 066 3.87 0 81 2 19 0 34 2 10 0.32

168.39 10 90 22.05 3.00 12.97 3 42 1.07 3 56 3.43 0.59 3.61 0.79 2.25 0.38 2.14 0.32

166 72 10.94 21.71 2.95 12.77 3 33 1.04 3.46 3.34 0.59 3.61 0 80 2.24 0.38 2.12 0.33

176.40 11.52 25.18 3 23 13.45 3.40 1.14 3.95 3.82 0.68 4.04 0.86 2.27 0.35 2.14 0.33

166.50 10 76 23.92 311 12 73 3 16 105 3 70 3.57 0 65 3 73 0 79 2 12 0.33 2.09 0 32

178.039 11.082 24.136 3.194 13.436 3 317 1.097 4025 3.891 0.696 4027 0.819 2 245 0 341 2 123 0 317

2xstd dev 10.79 0.76 2.00 0.21 0.69 0.19 0.06 0.36 0.36 0.07 0.30 0.05 0.15 0.04 0.13 0 02

concentrations of the heavy rare earths in the standards also probably limits data quality. Figure 4 shows two chondrite-normalized rare earth diagrams. This type of plot is generated by dividing the concentrations determined for the rock by the average concentration of the respective element in chondritic meteorites [26]. The log of this ratio is plotted against the atomic number. Plotting the raw element concentrations produces a sawtooth pattern due to the greater stability, and hence greater abundance, of even proton number nuclides. Normalizing the data eliminates these even-odd abundance differences and produces a smooth pattern. Figure 4(a) is the normalized plot of the DCS corrected data set for the USGS standard W-2. Figure 4(b) is the uncorrected data set from the VG Fisons software. This figure clearly demonstrates the improvement in the quality of data when our DCS method is applied. Means and standard deviations for 15 replicate analyses of W-2 are listed in Table 4. Precision is better than 2% for each element except Ba, which has an error of 10.8%. The implementation of the DCS macro allows us to obtain high quality results from data that would otherwise be unacceptable. There are two things we look for in the corrected data set to give us an indication of its overall quality. The first is the goodness of fit on the calibration curves, particularly on Ba and the LREE. When the standards show a clear spread in

E497

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concentration range for any given isotope, then the calibration curves should yield good “r-squared” values. In the case of the standards we normally use, we can obtain high quality calibration curves for Ba and the light rare earth elements (LREE). The second criterion is also based on the examination of the goodness of fit for the calibration curve, but in this case it is based 011 the HREE. It is typically more difficult to obtain high quality calibration curves for the heavy rare earth elements (HREE) because of the limited range of concentrations in available standards. It has been our experience however, that good “r-squared” values are attainable with the suite of standards that we use. We have found that when very high quality calibration curves are obtained on Ba and the LREE, but the calibration curves for the HREE are poor, it is usually an indication of contamination, poorly-prepared standards, or evaporative loss and/or concentration of the standard solutions.

5. A PROCEDUREFOR MULTIELEMENT DRIFT CORRECTIONAND ITS IMPLEMENTATIONIN A SPREADSHEETMACRO

In detail, the drift correction algorithm is as follows. If the number of drift correcting solutions is n, for example 5, we fit an n- 1 (4th) order polynomial curve to each analyzed isotope (Fig. 5(a)), where the x-values are the solution position in the run, and the y-values are the integrated counts for the isotope. Using the resulting equations, we calculate a “predicted” intensity for all tube positions and isotopes (Fig. 5(b)). For each isotope and each tube position, we calculate the ratio of the predicted intensity to the measured intensity of the first tube (Fig. 5(c)). The inverses of these values are the correction factors for every isotope and tube position. We then multiply the actual measured intensities by the appropriate correction factor. These corrections

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Tube position (Time) Rg. 5. Sequence of steps used ta correct peak Integral intensltresfor dnft usrng the DCS standards See text for d&a& are applied to all solutions in the run, including external calibration standards and unknowns. Generation of calibration curves for the external calibration standards, calculation of slopes and goodness of fit, and calculation of concentrations in the unknowns can then be performed with better accuracy and precision. It is important ta note that all of our quantitative analyses are performed using an autosampler. This allows us to substitute “tube position” for “time of data acquisition” in all of our computations because the time of acquisition and the time spacing between samples is uniform throughout an analysis. Wtitizing a true time function in the calculations would be a more exact approach, but it would also be a much more difficult one to implement in the macro. The calculations described above can easily become cumbersome and time-consuming. For example, a typical analysis of 20 sample and standard solutions for 30 isotopes involves calculation of 30 polynomial curves and generation of &Xl correction factors. Concentrations must then be calculated from the corrected peak intensities. Spreadsheet programs for persona1 computers are ideally suited for such repetitive, yet simple, calculations, The calculations can be further simplified through the use of macro commands. We have developed such a macro in Microsoft ExcelTM 3.0 for Macintosh. The macro automates the entire process from importing the raw peak integrals to calculation of final concentrations in the rock. The functioning af this macro, which we refer to as the “DCS macro”, is described in the following paragraphs, Further details, and instructions for its use, are given in the Appendix. A copy of the complete macro along with a sample data set is included on the relevant disk accompanying this journal. The Appendix also outlines a few changes that could be made to the macro that would allow data from other vendors’ ICP-MS instruments to be reduced. We use the DOS-based version of VG Fisons TCP-MS software “‘Issue 3.2.la”. It should also be possible to port the macro to Microsoft Excel for W~ndowsTM on I~~~~ompatible computers with little or no modification, though we have not attempted to do so.

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Use of the macro requires that the data be in a specified format. In the Appendix, we describe how the run procedure should be set up in VG Fisons ICP-MS software “Issue 3.2.la” so that it is stored in a suitable format for importing into the DCS macro. Certain naming conventions must be adhered to in order for the macro to identify drift correction, external calibration and unknown solutions. When the run procedure is properly set up, the VG Fisons software stores the data in an ASCII file, which is transferred to the Macintosh (we do this over a local area network). The remainder of the reduction process involves the Macintosh only. The DCS macro requires only three inputs: the full name of the file to be reduced; the name under which the reduced file is to be saved; and the name of the file where the concentratrons of the standards are stored. With this information, the DCS macro performs the following tasks: (a) the ASCII file is read in; (b) the stacked/listed text data file is transposed into a spreadsheet format with peak integrals in a sample-by-mass matrix. Masses filled by zeroes are stripped out (the masses filled by zeroes are a byproduct of the peak jump mode of data acquisition). The data are converted from text to numeric values; (c) a tube or run position number is assigned to each sample in the data set; (d) all DCS peak integrals are identified and moved to an open section of the worksheet; (e) an (n-1) degree ~lynomial is fit to the intensities of each isotope of the n DCSs using Lagrange’s formula [27]; (f) drift correctron factors are computed and applied to each tube position within the procedural run for each analyzed isotope; (g) the measured blank intensity is subtracted from all sample and standard intensities; (h) the macro identifies which tubes contained external calibration standards (based on the naming convention described above), and moves those drift-corrected integrals to a new section of the worksheet. It then opens the spreadsheet containing tbe concentrations in solution of each identified standard, and imports these concentrations for the appropriate isotopes. The Appendix describes how to create this “standards by isotope” worksheet; (i) calibration curves are generated for each isotope, and drift-corrected concentrations are calculated for the unknown solutions; and (j) a final output sheet is generated and saved to disk. This sheet contains the calibration graphs, slopes, r-squared values, and a listing of the solution concentrations of each tube in the run procedure. The macro then closes itself automatically. The macro is labeled ICP_DATA_REDUCTION(v3.1) and is on the accompanying disk. A listing of the DCS macro can be printed if needed. A detailed outline of the components of the DCS macro can be found in the Appendix.

6. CONCLUSION Instrument drift significantly limits data quality in external calibration ICP-MS analysis of samples with complex matrices. When inst~ment drift is properly corrected, it is possible to obtain results using the ESC technique comparable to those achievable by IDMS on a thermal ionization mass spectrometer. Certainly, the ability to obtain 1 or 2% data on Ba and the LREE is attainable by ESC using the DCS method. An improvement in the accuracy of HREE analyses is foreseen as the sensitivity of ICP-MS instruments improve and the selection of standards with a greater spread in concentration range than those used in this study.

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REFERENCES

[l] [2] [3] [4] [5] [6] [7] [8] [9] [lo] [ll] [12] [13] [14] [15] [16] [17] [lS] [19] [20] [21] [22] [23] [24] [25] [26] [27]

K. I. Ratzlaff, Anal. Chem. 51, 232 (1979). J. D Fassett and P. J. Paulsen, Anal. Chem 61, 643A (1989). J. S. Crain, R S. Houk and F. G. Smith, Specrrochrm Actu 43B, 1355 (1988) D. J. Douglas and L. A. Kerr, J. Anal. At. Spectrosc. 3, 749 (1988). Y. Ktm, H Kawagucht, T. Tanaka and A. Muulke, Spectrochrm. Acta 45B, 333 (1990). J. R Pretty, E. H. Evans, E. A Blubaugh, W.-L. Shen, J. A Caruso and T. M. Davtdson, J. Anal At. Spectrosc. 5, 437 (1990) C Vandecasteele, M Nagels, H. Vanhoe and R Dams, Anal. Chrm. Acta 211, 91 (1988) D. C. Gregotre, Specfrochim. Acfa 42B, 895 (1987). G. Horhck, Spectroscopy 7, 22 (1992). J. W. McLaren, A. P Mykytmk, S. N. Wdlie and S. S. Berman, Anal. Chem. 57, 2907 (1985) D. Beauchemm, J. W McLaren and S. S. Berman, Specrrochrm. Acta 42B, 467 (1987). D. C Gregoue, prog. Anal. Spectrosc. 12, 433 (1989) L. E Wangen, G. E Bently, K. P Coffelt, D L Gallimore and M V Phillips, Chemom Intell. Lab Systems 10, 293 (1991). G. E. Bently, V. T. Hamdton, E. J. Peterson and L. E. Wangen, Appf Spectrosc. 40, 949 (1986). A. Lorber, Z. Goldbart and M. Eldan, Anal. Chem 56, 43 (1984) B. S. Ross and G. M. Hieftje, Spectrochrm. Acru 46B, 1263 (1991). R. C. Hutton and A. N. Eaton, J. Anal. At. Spectrosc. 3, 547 (1988). W. Doherty, Specrrochim. Acra 44B, 263 (1989). F E. Ltchte, A. L. Meter and J. G. Crock, Anal. Chem. 59, 1150 (1987). Z Horvath, A. Laszttty and R. M. Barnes, Specrrochzm Actu Rev 14, 45 (1991) M Shabani and A. Masuda, Anal. Chem. 63, 2099 (1991) G. E. M. Hall and J. A. Plant, Chem. Geof 95, 141 (1992) K. Govmdaralu, Geostandards Newsl. 13, 1 (1989). J J. Thompson and R. S Houk, Appf. Specrrosc. 41, 801 (1987). P. L. Bonate, LC CC 10, 378 (1992) N. Nakamura, Geochrm. Cosmochim. Acta 38, 757 (1974) W. M. Press, B. P. Flanery, S. A. Teukolsky and W. T. VeHerling, Numerrcal Recipes: the Art of Scientrfic Computing, p.80. Cambridge University Press (1986).

APPENDIX

One disk accompanies the publication entitled “Sources of error in external calibration ICP-MS analysis of geological samples and an improved non-linear drift correction procedure” (Spectrochimicu Actu Electronica). This disk is for use on the Apple Macintosh family of computers. The current version of the DCS macro has been tested using Excel ~3.0 running under Apple’s System 7.0.1. The DCS macro will also run using Excel ~4.0. At least 3.0 Mb of RAM should be allocated to Excel in order to run the macro. The followmg files can be found on the disk:

I> II) III) IV) V)

“81291aa.asc” ICPDATA-REDUCTION(v3.1) Standardsby-Isotope TutDCS TestData.

The first file is the sample data set used in the paper. A more complete overview follows below. The second file is the fully implemented macro created in Excel ~3.0. This version can be opened and saved as an Excel ~4.0 macro for those runmng that version. File three IS the standards data file. We have included the concentrations of the standards identified in the file “81291aa.asc” as well as the concentrations found in the rock powder of the geological standards used in the paper. The fourth file is a version of the macro that has been modified to run as a tutorial. Please read the section Tutorial Guide before opening the file. The fifth file is an example test data set to be used with the tutorial. This data set was extracted from the file “81291aa.asc” mainly to streamline the tutorial. Working with only four isotopes rather than the full 22 will speed up the tutorial session. Two isotopes of Ba (137 and 138), La and l%e are used. The structure of the file is otherwise identical to the file “81291aa.asc”.

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Tutorial guide Step 1. Copy the contents of the disk entitled “Drift correcting Solution Excel 3.0 macro” to a folder of your choosing on your hard disk. It is important that you keep all of these files m the same folder. After you feel ~mfo~able with the use of the macro, you can delete the files TutDCS and TestData, if you wish to conserve space on your hard disk. Step 2. Allocate at least 3.0 Mb of RAM to Excel. Step 3. Open Excel. Use the Open command from within your File menu, and open the folder where you stored the DCS macro files. Open the file TutDCS. The macro does not run automatt~lly: you have to start It. To do so, press ~tion-Com~d-R. The first of many dialog or alert boxes opens. These alert boxes are intended to serve two purposes; the first two alerts (which you will find in the full implementation of the macro) are intended to give general Information and general constraints on the use of the macro, the other alert boxes have been inserted m key pomts in the macro and serve as convenient places of mterruption to explain what has occurred in the previous step in the macro and what is to follow. Step 4. After you have read the first alert box, which is a genera1 description of what the macro is all about, hit the return button or click in the OK box. Another alert box immediately follows. Again, after reading this alert box, which contains the general constraints on the functioning of the macro, hit return or click OK. Step 5. The next three dialog boxes require mput from you. The first Dialog box asks for the name of the file you wish to reduce. Your input should contain no blank spaces, and the name should exactly match the file stored on your hard disk. It is very important that the file that you wish to reduce be located in the same folder as this tutorial (or full DCS macro). The structure of the data file IS described m the section of the Appendix entitled “Overview of tbe tile 81291aa.a~~“. For the purposes of this tutorial enter “TestData” (without the quotes) then hit return or click OK. Step 6. Another Dialog box immediately follows. This dialog box offers you the option of selectmg the name of the final output file. The macro defaults to a final name that utilizes the input data file name from Step 5 with a small suffix appended. If you do not wish to use the default, simply type over it. Press return or click OK. Step 7. The last dialog box now opens. This dialog box asks for the name of the file where all the solution concentration data for the standards are stored. For a complete overview on the structure of this file see the section in the Appendix entitled “Standard by Isotope Spreadsheets”. For the purposes of this tutorial enter “Standardsby_Isotope” (without the quotation marks, but with the underline symbols). Press return or chck OK. Step 8. An alert box opens notifying you that the selected data file wdl now open. Step 9. The opening of the data file IS a quick process. Once it is open, a new alert box pops up informmg you that the data file will now be converted into a spreadsheet format. This section of the macro involves a significant amount of time to complete. The macro loops through the data file retrieving the information needed for each sample and placing it in the appropriate section of a spreadsheet. The peak integrals are in a space-delimited format in the ASCIIINT file. The Integral data begins at row 67. Row 67 contains the integrals for masses 1 through 7. All subsequent rows contain peak integrals for 8 masses. As such, the full spectrum mass range from AMUl to AMU IS contained m rows 67 through 98. These data are first parsed on a row by row nature. Then the cells containing the parsed values are read and copied, and then pasted in a separate section of the spreadsheet in a column format. Step 10. All the necessary data from the ASCIIINT data file has been read in and digested. The Excei spreadsheet is almost in a usable form for the real number crunching steps in the macro, but there are a few more steps that need to be completed. The next section of the macro completes the formattIng of the spreadsheet. It will remove all spurious columns from the parse. The actual data for the ASCIIINT file begins in column 2. Column 1 will now be filled with the mass numbers corresponding to the appropriate isotopes found in columns 2 on out. This section of the macro will also remove all lmes (i.e. masses) for which no data were collected, I.e. all rows that contain zero values are deleted from the spreadsheet. The last step in this section IS to save the spreadsheet under the name you input to the second dialog box in Step 6 above. For those of you who wish to utihze the macro with data sets collected from other instrumentation other than a VG Fisons Plasmaquad, you should have their data in the form that is saved at this step in the macro. Further instructions on how to do this are described towards the end of the Appendix. Step 11. Now that the spreadsheet is cleaned up, the actual drift correction can begin. The current alert box informs you that a search and copy operation will begm in the next section where the solutions that have been identified as drift correcting solutions will have their integrals

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copied and pasted to another section of the sheet. Before the copy and paste operation can begin, the tube positions for all solutions m the data set are assigned. It is assumed that the data were collected with the use of an autosampler such that the timing of all functrons such as wash times, uptake times and data collectron times are the same for each tube. Since all times are equal for each tube, a simple integer value 1s assigned to each tube denoting rts position in the run. These values are used as the “x” values in all ensuing calculations. Once the tube positrons are assigned, the copy and paste operation for the DCS solutrons proceeds. When all DCS solution integrals have been moved, polynomial curves are fitted to the integrals (using Lagrange’s formula) for each mass (isotope) in the run, where the integral is the “y” value and the tube position is the “x” value. This part of the macro 1s described in detail both in the paper and later in the Appendix. Without repeating all of it again, suffice rt to say, that when this section of the macro is completed, all of the integrals for the entire run will have been corrected for drift both as a function of time and mass. Step 12. The current alert box informs you that the integrals for the blank will now be subtracted from the corrected integrals for all other tubes m the data set. Step 13. The next section of the macro identifies the solutions that you coded as being standards. The corrected and blank subtracted integrals are copied and pasted to a new section of the spreadsheet. The macro then opens the Standard by Isotope worksheet that you identified in the third dialog box as described in Step 7 previously. The macro seeks a match between the names of the standard solutions in the spreadsheet and the Standards by Isotope sheet. When matches are made, the Standard by Isotope sheet 1s scanned for each standard and the concentration data for each required isotope is copied and pasted mto the working spreadsheet. Once all the concentratrons have been pasted, calibration curves are generated for each isotope, and the slopes of the lines as well as the goodness of fit (3 values) are calculated. Next, the solution concentrations for all tubes in the run are calculated using the slopes, the corrected integrals, and an intercept of 0. Step 14. The graphs of the calibration curves for each isotope are now moved to the correct position on the spreadsheet in preparation for the generation of the final output sheet. Step 15. The final output sheet 1s now generated. Lines 2-12 are hidden. These lines contam the equations and data required to generate the cahbratron curves. Lines 1342 contam the graphs for each isotope. Lines 43-50 contain information about the sample, such as the name, mode of acquaitron, data and time of acqursrtron, etc. The actual solution concentratron for each isotope analyzed follow, starting at line 51. Step 16. The final output sheet is now saved to disk using the name you provided m the second dialog box, then the spreadsheet 1s closed. Step 17. The macro itself then closes. Excel itself remains resident m RAM, but no active wmdows are present. Overview of the file 81291aa.usc

This is an ASCII text file generated on a Compaq computer. It was created using VG Fisons “list data” module. The “list data” module will stack all the samples run as a procedure mto a single stacked file. For each sample within the run, 98 lines of text are saved in the file. For the DCS macro, the important information 1s contained as follows: line 1 contains the sample name, lines 2 and 3 give mformatron on the data collection method, lure 5 contains the date and time of analysis, and lines 67-98 contam the integral counts of each isotope from 1 to 263. The remaining informatron 1s not utilized in the data reduction procedure. This is the data set used as an example in the hard copy paper. The file can be opened from within Excel. Using the DCS macro with data from VG Fzsons ICP-MS

software v3.2.la In order to utilize the DCS software that accompanies this paper, the multielement analysis procedure module of the Plasmaquad software must be set up m a specrfic manner. The first solutron must be a blank, and rts name should begin with a lower case “b”. The blank name should be kept to six letters or less. The next solution should be a drift correcting solution, and its name should begin with a lower case “p”. To satisfy constraints imposed by DOS and the VG Fisons software (explained below) and the functioning of the macro, the DCS name should be more than one but less than SIXcharacters long. We routmely analyze a DCS every fourth or fifth tube, a larger spacing between DCSs could be implemented but we have noticed a degradation in the quality of the results. There is a limit of seven DCSs in an analysis procedure. This 1s a hmrtation rooted in the Microsoft Excel DCS macro, and is specifically limited by the available RAM and the speed of the Macintosh computer that was used to develop the macro. The remammg solutions m the analysis procedure are standards and

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unknowns. The standard names must begin urlth a lower case “‘s”, and they must exactly match the names used m the “standards-by-isotope” file (see Appendix). Additionally, the name should not exceed six characters. The DCS software will treat any other solution m the run as an unknown, but we recommend that unknowns begm with a lower case “u” for ease in readmg the files. Agam, the convention of limiting sample names to six characters or less should be mamtained. The normal DOS naming convention allows for up to eight characters m a file name. One convention implemented in the VG Fisons procedure set-up modules, is the ability to acquire data multiple times sequentially on the same solution over the course of the analysis. In order that each sequential data aquisition does not overwrite the previous aqutsition when stored to disk, an integer is appended to the sample name that represents the position m the multiple analysis acquisition. This utility restricts the usual DOS naming constraint of eight characters to seven. We further limit the number of characters that can be used for sample names to SIX, in order to skirt a VG Fisons software “bug”. The “bug” results when data for solutions are acquired only once rather than multiple trmes. VG Fisons wnvention of appending the aqmsition number to the sample name is still utihzed in “Single Aquisinon” mode; however, the abihty to read and use the data files collected in “Single Acquisition” mode will fail durmg any of the followmg operations: reduction of isotope ratio data using the Isotope Dilution module, reduction of multielement data usmg the Standard Additions module, and data export using the List Data module. Our DCS macro requires that the exported data file be in the form that is output from the List Data module. We have found that the easiest way to skirt the “bug” in the VG Fisons software is to create two nearly identical multielement procedure files. Create the actual data acquisition file as outlined above and save the file. After the file is saved, rename each sample m the procedure by appendmg a “1” to each sample name, then save the “changed” file under a new name. After the multielement analysis is completed, enter the Con~guration File, and change the output parameter from printer to file, then save the Configuration File. Next, enter the List Data module, where two options are presented: “List Procedure” or “List File”; choose “List Procedure” Enter the name of the file under which you want the listed data to be stored. The subsequent screen will then ask for the name of the file to list; enter the second file name that you created as described above. The module will then ask whether you want to list “Integrated” or “Raw” data, respond “Integrated” The module will read each sample in the order created using the file name supplied. The newly created file will contain each subsequent sample m a listed or stacked structure. This newly created file is also m ASCII format, which is ideally smted for export to other computer software, or to other computer platforms. The DCS macro has been written to read this listed file. The structure of this ASCII data tile has been discussed previously. The next step is to export the file in ASCII format to a Macintosh computer. We normally do this over a local area network (LAN) using TOPS. Overview of the file ICPllATA-REDUCTION(v3.1) The macro entitled ICP~AT~~DUCTION(v3.1) is a program written within Microsoft Excef’m ~3.0 to reduce data collected by ICP-MS. The data is corrected through the use of dnft correction solutions (DCS) and Lagrange’s formula [27] for generating a polynomial curve to fit multiple X-Y data points. The program follows a series of steps that convert an ASCII text file into a corrected and reduced Excel worksheet containing solution concentrations as well as graphs of the regression curves used to calculate the concentrations. Initially, the program identifies itself and asks the operator to input three pieces of information: the name of the ASCII file to be reduced, the name of the file to be created for the reduced data output, and the name of the file containing the standard concentrations listed by isotope. After getting this information, the program opens the raw data sheet, and turns off the screen updating feature. From this point, the computer screen will not change until the macro has completed the data analysis. If the operator desires to watch the macro work, enter the ICP-DATA_REDUCTION(v3.1) file and change cell B9 from “=ECHO(False)” to “ECHO(False)“. Removal of the ‘I=” causes the program to omit that line of code, thereby retaining the screen update function. The total runtime for a typical analysis of rare earth elements (REE) as we outhned in the Procedures section of the body of the paper is about half an hour on a Macintosh Plus equipped with an accelerator with a 68030 processor running at 20 MHz and the 68882 floating point co-processor. After opening the ASCIIINT file, the macro proceeds to convert the ASCII text file into an Excel file. To accomplish this, the integrated counts are parsed m order to separate the counts for each isotope (see below for descnption of structure of an ASCIIINT data file), then the data is copied to a new location on the sheet. Then each mdividual sample wrll have its name, acquisition method, and date of acquisition translated and moved to the new location on the

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spreadsheet. Finally the text data IS deleted, and the next sample is processed. The final step of the ASCII conversion is a deletion of the formatting contained within cells outside the range now occupied by the organized data. The next step of the program is the drift correction using the DCS data. The drift correction is accomplished by separating and isolating the DCS data, then fitting a polynomial curve to the data for each isotope in those solutions using Lagrange’s formula [27]. Once the curve IS generated, predicted counts are made for each isotope at every tube position as if each tube were a DCS. Using these predicted counts, a correction factor is calculated and applied for each isotope in every sample to compensate for curvilinear drift. From this point, the data reduction continues with a blank subtraction procedure, which subtracts the raw counts for the first sample (if it IS identified as a blank) from the remaining raw counts of the data set. Additional cosmetic changes are made to the data sheet at this time as well. Once the data is corrected, the program generates standard regression curves and calculates the concentration of the solutions based on the counts of the standards within the analytical procedure. As before, the peak integrals (counts) for the standards are identified and moved to a new location on the spreadsheet. The macro then opens the file that the user identified as containing the concentration data for the standard solutions for each isotope for which counts were found in the original parse, and imports them into the working spreadsheet. From here, the program calculates the slope of a regression line forced through the origin, gives the rsquared value, and generates a graph of the curve for each isotope. The program generates graphs as long as more than three standards are included in the analytical run. Using the slope of the line, concentrations are calculated for each isotope of each sample. Finally, the program formats an output sheet containing the graphs stacked three high above the concentration data. Also on this sheet, hidden in lines 2-11, are the data used to generate the graphs. While the data are not important for the results, they cannot be deleted as they are linked to the graphs and must be present to maintain the graphs. The last steps of the macro involves savmg the output sheet and closing the file ICP-DATA-REDUCTION(v3.1). Naming conventions and the use of identification codes

A summary of the identification codes that preface each sample name during the creation of the run procedure m the ICP-MS software is listed below. These codes are the letter expected to be the first character of the sample name. If these are not included, the macro will not run correctly: “b’‘-identifies “p’‘-identifies “s’‘-identifies

blank in tube position No. 1; Drift Correction Solution samples anywhere within the data set; standards anywhere within the data set.

Any other character found as the first character of a name is assumed to be an unknown. For additional information about the nammg of standards, which is critical for correctly reducing the data, be sure to refer to the section titled “Instructions for S-b-1” found below. Outline and description of the macro procedures

The following outline lists the procedures within the macro, as well as a brief description of the purpose of the procedure. The indenting of the procedures indicates the nesting of the routines, with those further indented being accessed from within those less indented. ICPDATA-CRUNCH Make-sheet Form-Completer DCS-Correction DATE-reduced DCS-Separation DCS_Move DCS-Regression DCSIII DCSIV DCSV DCSVI

Mam Body of data reduction program Converts ASCII text file to Excel spreadsheet Formats new Excel spreadsheet as required by macro Normalizes data using the DCS and the Lagrange formula Adds today’s time and date to header Isolate DCS data m preparation for Lagrange function Move individual DCS sample data Normalizes all sample data using isolated DCS Subroutme for Lagrange with 3 DCS Subroutine for Lagrange with 4 DCS Subroutine for Lagrange with 5 DCS Subroutme for Lagrange with 6 DCS

Error sources m ICP-MS analysis of geological samples

DCSVII DC%OUTPUT-FILE Blank-Subtraction STD-Analysis STD-Separation STD_Move MOVE-STDname STD_prep STD-Import GET-STD MissingSTD Rcurve STDII STDIII STDIV STDV STDVI STDVII STDVIII STDIX STDX FEWSTD SLN_gen Graph-Mover Final-Form

ES05

Subroutine for Lagrange with 7 DCS Removes spurious material from spreadsheet Subtracts blank data from raw data counts Calculates regression curves and concentrations Isolate standard data in preparation for hnear regression Moves and transposes data for standards Moves standard name to regression part of spreadsheet Adds spaces for importation of standard values Imports standard values from Standards-by-Isotope Imports individual isotope values from S-b-1 sheet Removes standard data if standard not found in S-b-I Linear regression of standards Subroutine for regression with 2 standards Subroutine for regression with 3 standards Subroutme for regression with 4 standards Subroutine for regression with 5 standards Subroutine for regression with 6 standards Subroutine for regression with 7 standards Subroutine for regression with 8 standards Subroutine for regression with 9 standards Subroutine for regression with 10 standards Outlet if too few or too many standards Calculates concentrations from regression line Relocates regression graphs for final output sheet Formats final output spreadsheet

Parameters needed for the ICP-DATA-REDUCTION(v3.1) macro to reduce data Initial data sheet input (as received from VG Fkons hst procedure). No more than 44 samples to reduce at one time. File structure is assumed to be in VG Fisons ASCIIINT style. Initial set-up parameters .for Macintosh. Microsoft Excel ~3.0 must have 3.0 Mb of available random access memory (RAM). Names of solutions (this is very important for the MACRO to run correctly). All drift correction solutions (DCS) start with a small “p” (i.e. “pPALa”). The blank starts with a small “b” (i.e. “bBLK”) and is located at tube position No. 1. All standards start with a small “s” and characters 2 through ? (up to 5) exactly match the standard names on your standard sheet (i.e. “sWSO9”). If it is necessary to change standard solution names in order to avoid an overwrite of a sample by DOS on the Compaq computer, concatenate additional letters after the standard identifier, as the MACRO will not read them during execution (i.e. “sWSO9a”). Standard by isotope spreadsheets The Excel 3.0 worksheet containing the concentrations of the elements in the standard solutions listed by individual isotopes is set up according to the following parameters. (1)

The top row of the spreadsheet starting in column 3, consists of the names of the standards (4 or 5 characters preferably, although the data reduction macro will identify longer names). The names of the standards in the ASCIIINT data file should exactly match the names found m this row of this spreadsheet. This excludes the first character in the name m the ASCIIINT file, which is used to identify whether the sample is a DCS solution, an unknown, or a standard. In effect, the names are the same except for the initial “s” which identifies the standards for the macro. Name must be continuous with no blanks. (ii) Column 1 contains mass numbers, starting at row 2, from 1 to 256 in ascending order (i.e. cell Al contains the number 1 (corresponding to AMU l), cell A2 contains 2 (corresponding to AMU 2), and so on). It is important that these are values, not text, as the macro uses a mathematical identification for mass. (iii) Column 2 contains element name(s) corresponding to mass numbers in Column 1. Beginning at Column 3, individual concentrations for standard solutions are listed next to the corresponding mass number. These vaiues must be in the form of values, not formulas, as the copying to the active sheet during the execution of the macro will negate formulas. (iv) The list can include all mass numbers through 256 since the ICP-MS can analyze for u*U180 in scan mode.

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CHEATHAM et al

Note that the concentration for a given element is dlstnbuted equally amongst the isotopes of that element when the element 1s not monoisotopic. There is no need to determine the concentration contributed by each isotope based on its lsotoplc abundance. The subtle differences in final concentrations calculated between isotopes for a given element 1s not due to isotopic abundance but to oxide contribution or polyatomic molecule contribution. Beware. If a value for a standard is missing leaving a blank m the middle of the Excel “LINEST” function, an error will be generated. If this occurs, you must correct the problem by hand. Enter the ASCIIINT datasheet, and remove the “s” from m front of the standard name. Or enter the output sheet, unhide rows 2-12 and delete the missing standard value hne from the appropriate standard. Names requested by the MACRO must be continuous. NO blanks, otherwise the program will fail. To run. Before beginning, make sure that the standard concentration sheet, the ASCIIINT data file, and the DCS macro are all m the same folder. Problems will occur if this is not done. Open and close the larger file level to update the desktop If needed. Open only the ICP-DATAREDUCTION(V~.~) macro m Excel Go to the menu bar and pull down the Macro box, select run. A dialog box appears, scroll down the hst of names until the item appears that is preceded by a small case “r”. Select that file by clicking on it and choosmg the “OK” box. The macro will begin to run. Answer the two Alerts and three request boxes. Once this 1s done, the macro will take about 15-45 mm to run through the data (longer for more standards), generally about 25 min. The procedure will create one output file, with regression graphs and solution concentrations. Once all reductions are complete, the macro closes itself. Alteratton of ICP-DATA_REDlJCTION(v3.1) ICP-MS mstruments

macro to reduce data from other

The data file to be reduced with a modified version of the macro must be m a spreadsheet format. There should be no more than 44 “samples” in the data set. The names of the “samples” should be in row 1 columns 2-45. There should be no rows where all the data m the row are zeroes. These rows must be removed from the spreadsheet The data for each “sample” should begin m row 9; it should be in ascending mass order as the row number increases Column 1 beginning at row 9 will contain the mass number and should be in ascending order as the row number increases. The spreadsheet can contain values for all masses from 1 to 255. To modify the macro to accept data m a spreadsheet format rather than in VG Fisons ASCIIINT format two changes are needed. Open the macro from within Excel on the Macintosh. Remove the ‘<=” sign from cells BlO and Bll, i.e. change cell BlO from “=RUN(Make_sheet)” and change cell Bll from “=RUN(Form_completer)” to to “RUN(Make-sheet)“, “RUN(Form-completer)“. Document Preparation The word processor used to prepare the text for this paper IS Microsoft Word 5 0. The tables were prepared with Microsoft Excel 4 0 The figures were prepared usmg Deneba Softwares Canvas 3 04. The data for Figs l-3 were first prepared with Prescience’s Theonst. Figures 1 and 2 were created using simple equations Figure 3 utilized actual data. Copyright The program, the data files, the manual, and the hard copy text, m their totality published as a paper m Spectrochlmrca Acta Electronrca, are copynghted by the authors Readers of Spectrochrmrca Acta Efectronrca are permltted by the Publisher, Pergamon Press, to make a copy of the material on the disk for then own pnvate, non-commercial use, and to run the program accordmg to the instructions provided by the Authors. No charge for any copies may be requested, neither may the program or any modified version of it be sold or used for commercial purposes. Those who wish to use the program and data files m a commercial environment should contact the corresponding Author at the address given m the hard copy paper Programs of which the source code IS made avadable by the authors may be freely modified by the readers However, If a modified version IS brought mto the pubhc domain, the orlgmal Authors and the Journal reference should be clearly stated m all subsequent use and dlssemmatlon Disclaimer Neither the Authors nor the Publisher warrant that the program IS free from defects, that It operates as deslgned, or that the documentation IS accurate Neither the Authors nor the Publisher are hable for any damage of whatever kmd sustamed through copymg the disk(s) and/or using the program and the data files. By copying and/or using the program the reader of Spectrochlmlca Acta Electronrca, actmg as a user of an electromc pubhcatlon therem, agrees to the above terms and conditions.