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IMPROVED INTER-ELEMENT CORRECTION FACTORS FOR THE DETERMINATION OF ADDITIVE AND TRACE ELEMENTS IN LUBRICANTS

Mario Van Driessche’ Texaco Technology Ghent, Technologiepark - Zwijnaarde 2, B-9052 Ghent - Zwijnaarde, Belgium

and John R. Sieber

Texaco Fuels and Lubricants Technology Department, P. 0. Box 509, Beacon, NY 12508

Wavelength dispersive x-ray fluorescence spectrometry is the technique used within the Texaco laboratories for the determination of additive and trace elements in fresh oils and additive packages. The main strengths of the technique are reproducibility, accuracy and ease of operation. The test method is an extension of the ASTM D 4927 (1) test method and covers the determination of thirteen elements: Na, Mg, Si, P, S, Cl, K, Ca, Fe, Cu , Zn, MO and Ba.

The first part of this paper describes the calibration of the method starting from pure, high concentration single element standards which are blended to single element calibration standards. Since all elements are then calibrated independently from the theoretical calculated inter-element correction factors, better known as Alphas, it is possible to empirically determine all Alphas. The second step of this paper covers the empirical determination of all Alphas. The empirically obtained Alphas were plotted against atomic number and compared with the calculated Alphas. By observing the Alphas for a series of elements in relation to their atomic number, they could be smoothed. This results in a final set of empirically obtained Alphas which were proven to correct fairly well for the inter-element effects.

CALIBRATION OF TEIE METHOD.

Introduction. The ASTM test method describes the calibration starting from pure element standards which are blended to multi-element standards. Interelement effects are compensated by theoretical Alphas. This approach has some disadvantages: l Difficulties acquiring reliable, certified, high concentration standards for each element. Often traces of

other elements are present and, if not taken into account, can lead to errors in multi-element blends. l Difficulties preparing stable multi-element blends. They often precipitate or have a short shelf life. l Dependence on theoretical Alphas for calculation of the slope and the X-axis intercept. l Accuracy of the measurements strongly depends on the theoretical Alphas.

In order to overcome the problems mentioned above, an experiment was set up which consists of two steps. The first step covers the introduction of a new calibration approach. This approach exists of a calibration of each element with five singleelement calibration standards. The main advantages of this approach are: . No dependence on the presence of trace elements in the standards, since a lot of blanks are available. l No dependence on Alphas for the calculation of the slope and the X-axis intercept. l Line overlap correction factors and all Alphas for self absorption are obtained in the most accurate way. l Standards are easy to prepare and stable.

Since all elements are now calibrated independently from the theoretical Alphas, it is possible to empirically determine all Alphas. This is the second stop as described in the next section.

’ Address all correspondence to this author.

Copyright (C) JCPDS-International Centre for Diffraction Data 1999ISSN 1097-0002, Advances in X-ray Analysis, Volume 41

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This document was presented at the Denver X-ray Conference (DXC) on Applications of X-ray Analysis. Sponsored by the International Centre for Diffraction Data (ICDD). This document is provided by ICDD in cooperation with the authors and presenters of the DXC for the express purpose of educating the scientific community. All copyrights for the document are retained by ICDD. Usage is restricted for the purposes of education and scientific research. DXC Website – www.dxcicdd.com

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ISSN 1097-0002, Advances in X-ray Analysis, Volume 41

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Instrumental parameters.

General instrumental uarameters. l Instrument: Philips PW 1480 l Spinner: on l Excitation source: Scandium side window tube 0 Sample cups: 37.5 mm inner diameter l X-ray path: Helium l Film for liquid cup: polypropylene, 6 pm thick l Delay time before first measurement: 10 set 0 Sample mass: 12 + 0.1 gram l Channel mask: 24 mm

Instrumental parameters for the selected lines.

All elements were measured with their optimum kV/mA settings as listed in table 1.1, except for Ca, K and MO. A scandium X-ray source results in a very strong excitation for calcium. To obtain a long working range, 50 kV/30 mA settings were chosen in combination with the Ge crystal. These settings guarantee a working range from 5 ppm up to 7 %. The same reasoning was applied to potassium. Molybdenum was measured with 60 kV/50 mA settings rather than the optimum settings of 75 kV/40 mA to be in agreement with Fe, Zn and Cu and to change the kV/mA settings as little as possible.

A fine collimator was used for all elements, except Na, Mg, Si and P. For the first three elements, the reason is their low intrinsic sensitivity. For phosphorous, there is another reason. The calibration is based on triphenylphosphate but phosphorous is present in most samples as zinc-dithiophosphate. There is a difference in angle between those two components of 0.025” when using the fine collimator. By using the coarse collimator, the peak is broader, so small chemical shifts do not introduce any bias.

Drift correction. Long term drift correction is performed by a bead monitor containing all elements to be measured. The principle of the drift correction by monitor is based on the ratio between the intensities obtained on the monitor now and the intensities obtained on the monitor at the time of calibration of the method. The raw intensities measured from a sample are multiplied by this ratio before conversion to elemental concentrations. This compensates for drifts of all origin, even the replacement of the tube, so long as the counting statistical errors of all measurements are kept below 0.25 percent.


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It is important to mention there is a difference in angle of 0.09” between sulfur present in the fused bead and sulfur present in oils resulting in a difference in intensity of about 12% relative. In order to avoid imprecision caused by measuring on the wing of the peak, it is necessary to change the angle for the analytical channel of sulfur before every measurement of the fused bead.

Concentrated standards used for calibration standard wewratioa We used a set of organometallic standards of different origin and of different chemical composition. Most were certified by ICP against Conostan 5,000 ppm solutions except for sulfur and chlorine. The sulfur standard solution is a mixture of a homologous series of di-(dodecyl)sulfide compounds which is certified by comparison to a LECO@ Hydrocarbon Calibration Sample For Suljhr (9.47%) to have a value of 37.0%. For chlorine, S-chloro-octane of 99.5% purity is used and the chlorine concentration is obtained by calculation. Blends are prepared with liquid paraffin, containing no analyte elements at a concentration higher than 1 ppm~

Chemical composition of the calibration standards. Three blank samples (pure liquid par-tin) and five single-element calibration standards of every analyte element are measured. The concentrations of the calibration standards %(wtAvt) are as follows: l 0.050 - 0.125 - 0.250- 0.375 -0.500 % for Ca, Zn and P. l 0.050 - 0.100 - 0.200 -0.300 - 0.400 % for Na, Mg, Si, Cl, K, Fe, Cu, MO and Ba. l 0.200 - 0.400 - 0.800 - 1.20 - 1.60 % for S The calibration standards are homogenized on a magnetic stirrer. The elements Ca and Na contain 1 gram of 2-ethylhexanoic acid to form a stable solution.

Calculation of Alphas and repression analvsis. Regression analysis is performed by the Philips X40 software. We chose the De Jongh model since the theoretical Alphas obtained from the Alphas Qn Line software are used. The formula to correct for inter- element effects is listed below:

Ci=Di+E**R,*(l+Cj,aljCj) where Ci = concentration of element i Di = X-axis intercept of element i

a, = Alpha of element j on element i

Ei = inverse slope of element i Cj = concentration of element j

Ri = measured net count rate of element i e = eliminated component (oil, defined as CHZ)

The Alphas in table 1.2 were calculated for the instrumental parameters and line selections described in Section 1.2. and for following average concentrations: l 0.005% for Na, Si, Cl, K, Fe, Cu, MO, Ba 0 0.200% for Ca 0 0.010% for Mg 0 0.400% for S l O.lOO%forPandZn

One of the features of the latest release of the Uniquant 4.0 version (the software that allows semiquantitative analysis of 72 elements in all matrices) is the possibility of an off-line calculation of Alphas. Mr. Will De Jo& of Omega Data Systems (ODS) calculated a set of Alphas for this paper. The Alphas are calculated with the UniQuanto measurement settings of 80 kV/35 mA for MO and 40 kV/70 mA for all other elements. Qnly the Alphas for Na, Mg, Si, P, S, Cl and Ba are calculated with the same parameters as the quantitative method, the elements Ca, K, Cu, Fe, Zn and MO are calculated with slightly different parameters. The Alphas obtained by ODS are listed in table 1.3.


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Table 1.2. Theoretical Alnhas obtained from the Alnhas On Line software.

I8 1 14,29 1 15,35 1 15,78 1 17,20 1 l&65 1 19,81 1 20,18 1 23,54 1 2,81 1 17,65 1 l&99 1 19,53 1 21,36 1 23,21 1 24,73 1 25,20 1 29,67

K 1 -0,02 1 0,28 1 1,22 1 1,96 1 2,90 1 4,05 1 10,Ol 1 30,04 1 33,21 1 36,48 1 39,22 1 4OJO 1 48,75 1 0,06 1 0,39 1 1,46 1 2,29 1 3,34 1 4,62 1 8,23 1 14,20 1 39,88 1 42,95 1 46,35 1 47,44 1 58,18

1 5,68 1 5,98 1 6,27 1 6,81 1 7,04 1 3,42 1 23,38 1 85,56 1 87,42 1 109,s 1 8,51 1 8,91 1 9,65 1 9,96 1 4,63 1 2,85 1 33,98 1 34,96 1 142,2

4,56 4,82 5,39 5,32 6,93 7,70 8,lO 3,84 7,48 8,40 8,88 9,36 9,83 10,71 11,84 5,64 3,26 28,75 39,31 157,4 2,00 2,58 3,86 4,85 6,53 19,25 31,05 31,85 32,75 34,50 34,19 33,41 125,s 5,50 6,70 8,77 9,48 lo,20 lo,92 12,31 12,93 24,88 83,32 90,91 93,49 118,6

Table 1.3. Theoretical Alohas obtained from Omega Data Svstems UniOuant@ version 4.0.

I 1 NaKa [ Mg~a I SXa 1 P Ka 1 S KA I CIKa 1 KKs 1 CaKa [ I&LB 1 FeKa 1 CuKa I %Ka I MoKa

I/ Na I -0,55 1

0,79 1 1,03 1 2,37 1 3,18 1 4,21 1 20,92 1 21,35 1 23,34 1 25,lS 1 26,51 1 26,82 1 11,37

EMPIRICAL DETERMINATION OF TEE ALPHAS.

Description of the experiment. For this experiment, the regression analysis was recalculated without use of the theoretically obtained Alphas. The Alpha of the element on itself was calculated by the X40 software from the calibration curve. Potential small traces of elements other than the analyte element were calculated as spectral line-overlaps.

The experiment consists of the preparation of test solutions which contain two elements dissolved in liquid paraffin. One element is present at a relatively low concentration, the other element at a relatively high concentration. For every series of elements, twelve test solutions and two reference solutions are prepared. The two reference solutions contain element A in a concentration of approximately 0.100%. The twelve test solutions contain element A in a concentration of approximately 0.100% and element B in a concentration of approximately 0.400%. For sodium, element A is present in a concentration of 0.20% due to low sensitivity. For sulfur, element B is present in a concentration of 0.80% to be more in accordance with real samples. All solutions are prepared by using an analytical balance with an accuracy of 0.0001 g and all weights are recorded. Solutions are adjusted to a weight of approximately 20 g with liquid paraffin, homogenized by a magnetic stirrer and measured according to the instrumental parameters described in previous section.


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The reference solutions contain only the element in low concentration and are used in order to recalculate the concentration of the concentrated standard solutions. The obtained averaged concentration is then further used for the calculation of the concentration of every test solution. This approach allows us to work independently from potential small deviations in the calibration curves. To illustrate the approach, table 2.1 shows the results obtained for two series of elements.

Table 2.1. Results obtained for two series of elements in binary solutions. Only corrections for self absorption were applied.

Ekments Cakulatd Measured Elements Calculated Measured 0.1 - 0.4% concentration concentration 0.1 - 0.4% concentration concentration

(Element A-B) ofdement A of element A (Elqent A-B) of elenq& A ofelement A Zn-Na 0.1003 0.0959 Fe-Na 0.0982 0.0933 Zll-Mg 0.0997 0.0920 Fe-Mg 0.0993 0.0921 Zn-Si 0.1004 0.0947 F&i 0.0983 0.0924

The measured concentration of element A is lower than the calculated concentration since no correction is made for the absorption of characteristic radiation by element B. Self-absorption is corrected. We assume that the difference in concentration between the measured and calculated concentration is due to absorption of radiation from element A by element B. To compensate for this absorption, the Alpha of element B on the element A is calculated from the simplified inter-element correction equation:

CA=DA+EA*RA*(l+afi *CA+asa*Cg) in which CA = concentration of element A = 0.1% a AA = Alpha of element A on element A DA = X-axis intercept of element A a BA = Alpha of element B on element A EA = inverse slope of element A Cg = concentration of element B = 0.4% RA = measured net count rate of element A

Discussion of the test results.

All Alpha’s were determined twice. If there was no good agreement between both measurements, a third and fourth experiment was performed. Depending on the test results, averages were made, or some of the individual test results were rejected.

The Alphas of all elements on sodium, magnesium and silicon show no consistent results. This is mainly due to the fact that the spectrometer is not very sensitive to those elements, so every individual measurement has a relatively high uncertainty. Besides this, blends prepared with silicon have ihe

disadvantage of not being stable (precipitation). For these reasons, the empirically obtained Alphas were


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superseded by the theoretically calculated ones. The Alphas of sodium, magnesium and silicon on the other elements were recalculated.

For all the other elements (P, S, Cl, K, Ca, Fe, Cu, Zn, MO and Ba), there was a fairly good relationship between both experiments, and averages were made.

Table 2.2 lists the average set of empirically determined Alphas. The empirically determined Alphas for the series of Na, Mg and Si are superseded by the theoretically calculated ones and the correction factors of Na, Mg and Si on the other elements were recalculated. The table is completed by the correction factors of the elements on themselves as calculated from the calibration curve. These values are shown in italic font.

Check on empirically obtained Alphas with in-house certified reference materials.

Table 2.3. Results obtained on in-house certified reference materials. Element 1 Found Certified Element 1 Found Certified

Reference 1 diluted 4x Reference 4 diluted 35x 2.147 f 0.021 Ca 15.53 15.5 f 0.3

0.21 f 0.01 S 2.152 2.169 f 0.039

II p 1.86 1.91 f 0.06 zn 1.089 1.058 f 0.013 Ir-~~ Zn 2.12 2.05 kO.08 cu 0.1122 0.1085 f 0.0007

Ca S P Zn

Reference 3 Reference 6 0.250 0.25 f 0.01 Ca 0.0056 0.0056 f 0.0006 0.567 0.59 f 0.009 P 0.0239 0.0246 f 0.0003 0.1149 0.11s f 0.009 S 0.494 0.495 f 0.0014 0.1346 0.134 f 0.003 zn 0.0289 0.0289 f 0.0007


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Based on table 2.3, some observations are: l the results of phosphorous are slightly too low l the results of zinc and copper are slightly too high l the results of calcium are very good l the results of sulfur are fairly good, sometimes slightly too low

The ratio Zn/P is biased since zinc results are too high and phosphorous results are too low. Phosphorous is too low, mainly in presence of calcium. The Alpha of calcium on phosphorous was determined again and a value of 6.50 was found. Two years ago, the Alpha was determined and a value of 10.00 was found. A value of 8.00 was used for recalculation of the samples. Also the Alpha of sulfur on phosphorous was slightly adjusted from 0.20 to 1 .OO in accordance with the theoretical obtained value. Zinc is too high, only in presence of calcium. The Alpha of calcium on zinc was lowered from 50.95 to 47.00 in accordance with the theoretical value of 47.44. The Alpha was previously determined two years ago and a value of 47.00 was found. The Alpha of calcium on copper was slightly adjusted from 48.28 to 46.00. The Alpha of copper on sulfur was interpolated because the strong negative value (-7) was induced by precipitation of sulfur in presence of copper.

Comparison of theoreticallv obtained versus emriricallv obtained Alphas.

For every series of elements, the empirically obtained Alphas together with the theoretically obtained Alphas were plotted versus wavelength in Figures 1 through 13. Some correction factors were changed (smoothed) to fit a smooth relationship with respect to atomic number.

Figures 1 through 13. Plots of the Alphas by element.

Intlueuce of Sodium on the other elements

Wavelength/Line

Influence of Magnesium on the other elements

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Copyright (C) JCPDS International Centre for Diffraction Data 1999ISSN 1097-0002, Advances in X-ray Analysis, Volume 41

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Influence of Potassium on the other elements

WwelengtWLine

Iutluence of Calcium on the other elements

Influence of Iron on the other elements

Influence of Copper on the other elements

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Intluence of Molybdenum on the other elements

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Innuence of Barium on the other elements

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Influence of Zinc on the other elements

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Wavelength/Line

The set of Alphas after smoothing are listed in table 2.4 and the recalculated results of the certified reference materials are listed in table 2.5. These results indicate two problems: zinc is still too high in the presence of considerable amounts of calcium, and phosphorous is sometimes a bit too low. The Alpha of calcium on zinc was determined several times and gave reproducible results. Because zinc is mainly too high in presence of calcium, sulfur and phosphorous, a valuable explanation could be the so called “thud element effect”. Therefore an experiment was set up in order to see the influence of sulfur and phosphorous in the presence of calcium on the zinc determination. Blends were prepared with known concentration of zinc and addition of respectively calcium, calcium and phosphorous, calcium and sulfur. The results are listed in table 2.6. This table clearly shows that the third element effect exists. Since we have no possibility to calculate the third element for every compound and since sulfur is nearly always present in oils and additives when calcium and zinc are present, the problem is solved by a slight adjustment of the Alpha of calcium on zinc.


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Table 2.4. Set of emniricallv determined Alphas after modification and smoothing.

P 1 -0125 1 -0109 1 0,43 1 4,

S 1 -0.25 1 -0.05 1 0.56 1 1.00

1 5,32 1 6,39 1 7,70 ( 9,95 1 11,00 1 14,33 1 14,00 1 8,38 1 14,35 1 lo,55 1 32,43 1 33,98 1 34, - 3,84 7,48 8,40 9,00 10,OO lo,95 12,50 11,00 14,55 8,33 28,49 32,24 37,88 2,00 2,48 3,86 6,23 8,25 20,OO 33,40 34,80 40,OO 42,18 39,65 37,23 31,18 5,50 6,70 8,77 8,95 11,68 8,15 1,60 14,95 31,OO SO,23 83,78 82,25 28,63

Table 2 5. Recalculation of the results obtained on in-house certified reference materials. Element 1 Found Certified Element 1 Found Certiiied

Reference 1 diluted 4x Reference 4 diluted 35x S 2.138 2.147 * 0.021 Ca 15.48 15.5 zt 0.3 P 0.0966 0.0985 zt 0.0011 Reference 5 diluted 5x

Reference 2 diluted 7x Ca 2.096 1 2.086 f 0.013 Ca cu P

Zn

Ca

3.10 3.10 f 0.15 0.223 0.21 f 0.01 1.88 1.91 f 0.06 2.10 2.05 *to.08

Reference 3 Reference 6 0.251 0.25 f 0.01 Ca 0.0056 1 0.0056 f 0.0006

II s 0.569 1 0.59~0.009 11 P 0.0240 1 0.0246 f 0.0003 P 0.1170 0.118 f 0.009 S 0.493 0.495 f 0.0014

Zn 0.1336 0.134 f 0.003 zn 0.0289 0.0289 f 0.0007

Table 2.6. Results obtained on blends with known concentrations of zinc.

It is difficult to find an explanation for the too low phosphorous results. Concentrated in-house standards, requiring high dilution, give perfect values, but complex oil mixtures with a lot of components often give biased results. The explanation can be found in two reasons. The penetration depth for phosphorous changes when a higher concentration of heavy elements is present in these oils compared to the calibration standards which contain only the element phosphorous. Also, there may be present an unmeasured element which could absorb a part of the radiation emitted by phosphorous. Oxygen is the only unmeasured


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element which is not present in the standards, but which is always present in the samples in varying concentrations. In order to check the effect of oxygen, we prepared a set of test solutions spiked with an increasing amount of oxygen was added as 2-ethylhexanoic acid and the suppression of the signal was measured as a function of oxygen concentration. The results show that oxygen causes a decrease of the signal of phosphorous by approximately two percent for every 1 % wt/wt of oxygen added. Therefore, a variable oxygen concentration will be one of the main reasons why slightly biased results for phosphorous are often found.

Table 2.8. Final recalculation of the in-house certified reference materials. Element I Found Certified Element I Found Certified

Reference 1 diluted 4x Reference 4 diluted 35x S 2.138 2.147 f 0.021 Ca 15.48 15.5 f 0.3 P 0.0966 0.0985 f 0.0011 Reference 5 diluted 5x

2.06 2.05 ho.08 cu 0.1121 1 0.1085 : k 0.0007 Reference 3 Reference 6 0.252 0.25 f 0.01 Ca 0.0056 0.0056 f O.OO( 16 0.573 0.59 f 0.009 P 0.0240 0.0246 f 0.0003 0.1174 0.118 f 0.009 S 0.496 0.495 f 0.0014 0.1328 0.134 f 0.003 zn 0.0289 0.0289 f 0.0007

zn

Ca S P

Zn

CONCLUSION. I

The aim of this study was to empirically determine the Alphas used for the determination of thirteen additive and trace elements in oils and to compare the obtained Alphas with theoretically calculated ones. Based on the thirteen plots of the Alphas by element (see previous pages), following conclusions can be drawn: . Most empirically obtained Alphas agree very well with the theoretical Alphas. a The empirical Alphas correcting for magnesium and sodium absorbency of all other elements are about

twice the magnitude of theoretically calculated ones.


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l The empirical Alphas for molybdenum show a bias of about a factor 4 compared to those obtained from the Alphas On Line software.

What is the correct set of Alphas for molybdenum? We prepared a test solution with, besides molybdenum, three other important additive elements. The concentration of all elements was calculated from the known concentrations of the standard solutions and the recorded weights. The sample was measured and the result was calculated with both the theoretical and empirical Alphas. The results are listed in table 3.1 which clearly shows that the empirically obtained set of Alphas give the best performance. One can be assured it is not possible to analyze molybdenum in oils using the most sensitive Ka-line and using theoretically obtained Alphas In view of the increasing use of molybdenum in lubricants, this conclusion is significant.

Table 3.1. Results obtained on a blend with known concentration of Molybdenum.

Element With empirical Alphas With thexx~has Calculated value Zn 0.0991 0.0976 0.0977 P 0.0900 0.0913 0.0884 Ca 0.2950 0.2970 0.2950 MO 0.1021 0.1305 0.1011

The reason for the biased molybdenum Alphas as calculated by the Alphas On Line software seems quite obvious: the software does not take into account finite thickness of the sample and spectrometer geometry. That is the reason why only biased Alphas are calculated for elements with relative high atomic number (starting from the fifth row in the periodic table of the elements) in light matrices. The correction factors as obtained by the UniQuanto 4.0 version, although not calculated with the correct kV settings, seem to agree fairly well. This software does take into account finite thickness and spectrometer geometry.

l Alphas are not a solution to all problems. There are also the phenomena of the third element effect, absorption of characteristic radiation by oxygen and changed penetration depth when not working in the same total elemental concentration as the calibration samples. These phenomena can only be corrected by a more fundamental approach.

References

l (1) ASTM method D 4927 - 1997 Annual Book of ASTM Standards, Section 5 l (2) X44 Software for XRF - Third edition, February 1988 - Philips Electronics l (3) UniQuant@ 4.0 manual - W.K. De Jongh, 1997


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