MATRIX-INDEPENDENT XRF METHODS FOR CERTIFICATION OF STANDARD REFERENCE MATERIALS

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1 Copyright (c)jcpds-international Centre for Diffraction Data 2002, Advances in X-ray Analysis, Volume MATRIX-INDEPENDENT XRF METHODS FOR CERTIFICATION OF STANDARD REFERENCE MATERIALS ABSTRACT John R. Sieber National Institute of Standards and Technology 100 Bureau Dr., Mail Stop 8391, Gaithersburg, MD , USA The Spectrochemical Methods Group of the Analytical Chemistry Division at the National Institute of Standards and Technology develops and applies matrix-independent methods for its certification of Standard Reference Materials (SRM). Such methods are required to achieve accuracy, i.e., to minimize potential sources of analytical uncertainty. This paper delineates a matrix-independent method for X-ray fluorescence spectrometry that uses destructive sample preparation instead of matrix corrections. The method is based on borate fusion of samples and synthesis of calibration standards that closely mimic the complete composition of the fused samples. The method is described in detail and illustrated using recent work on cements and zeolites. A typical uncertainty budget is itemized and sources of uncertainty are discussed. Expanded relative uncertainties are 1 % or lower. The technique is applicable to major, minor and sometimes trace constituents. Excellent agreement is demonstrated with both a classical gravimetric method and instrumental neutron activation analysis. INTRODUCTION The NIST Analytical Chemistry Division (ACD) has as its primary mission the improvement of chemical metrology in support of the United States economy [1,2,3]. This mission is accomplished, in part, by the development of new analytical methods for application to industrial, environmental and healthcare problems and by the development of Standard Reference Materials (SRM) with which users can establish traceability to NIST calibration and measurement certificates. The broad scope of the Division s mission results in analyses of a wide variety of materials. Accuracy, the principle goal of NIST measurement and standards efforts, is achieved when all sources of analytical uncertainty are understood and minimized. For this reason, the ACD emphasizes the application of matrix-independent methods in its work [4]. Although matrix-dependent methods are important and broadly applied in chemical analysis, the reliance of these methods on standards similar in matrix composition to the unknowns limits their utility to certifying new standards with similar matrix composition. In fact, matrixdependent methods create much of the demand for the breadth and quality of reference materials, especially for calibration of instrumentation. In X-ray fluorescence spectrometry (XRF), a matrix-independent method may involve fundamental parameters calculations, matrix correction algorithms, or a number of calibration techniques. This paper explores one useful approach for the development of reference materials. It describes a matrix-independent XRF method through which the calibration of the spectrometer is directly related to primary reference materials and through which a variety of materials of different matrix are directly related to said calibration without the use of mathematical correction procedures or matrix-matched reference materials (hereafter called artifact standards). This

2 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 ICDD Website -

3 Copyright (c)jcpds-international Centre for Diffraction Data 2002, Advances in X-ray Analysis, Volume approach sets aside matrix corrections in favor of destructive and somewhat labor-intensive sample preparation. Recent work on cements and zeolites using the method of borate fusion demonstrates the usefulness of this procedure for matrix independence in XRF. Sources of random error are minimized by taking advantage of the excellent repeatability of the borate fusion technique, analytical balances, and X-ray spectrometers. Sources of bias are minimized by the preparation of bracketing calibration standards from ultrahigh purity compounds and NIST Single Element Standard Solutions SRMs. A typical error budget is itemized and explained. Expanded relative uncertainties are 1 % or lower. Excellent agreement is obtained with classical methods and other instrumental techniques. MATRIX-INDEPENDENCE The primary goal of matrix-independence is to address the effects of differences in matrix among materials and to eliminate those differences as a source of bias. As stated in the introduction, there are a number of possible approaches to matrix-independence for XRF. It is well known that matrix differences lead to X-ray spectral responses that differ due to the absorption of characteristic X-rays, the amount of scattering of primary X-rays, and spectral line overlaps. Even among materials of a similar matrix composition, there may be differences due to surface finish or particle size distribution resulting from grinding and polishing. In the worst case, there may be no reference materials similar to the unknown and the analyst will have no choice but to use destructive sample preparation. In addition to the elimination of sources of bias is the objective to reduce the specificity of the procedure so it can be applied simultaneously to a variety of materials and to as many constituents of those materials as possible. The internal standard technique illustrates this point since it can be used to eliminate matrix differences as a source of bias. However, the application is limited to a narrow range of materials into which the internal standard is completely miscible and that do not contain a significant quantity of any element having an absorption edge between the internal standard element and the analyte. Consequently, the use of internal standards is limited to specific materials and constituents, i.e., it is not matrix-independent. Because XRF is nondestructive and artifact standards are widely available for many materials, the majority of XRF analysts choose to collect a set of artifact standards similar to their unknowns to create calibrations. Analyses are fast because little or no labor is required once calibrations are established. One reason people request new SRMs from NIST is that new materials require new artifact standards for new calibrations. A second reason they come to NIST is to obtain artifact standards for verification of method accuracy as part of their quality system. The artifact standards can be used to create calibration curves, with or without corrections for interelement effects and matrix absorption. The process can be combined with fundamental parameters software that calculates the corrections from first principles with the advantage that it requires fewer artifact standards. NIST procedures for value assignment of reference materials allow the use of this approach to calibrate XRF. It is acceptable for a NIST analyst to calibrate a spectrometer using artifact

4 Copyright (c)jcpds-international Centre for Diffraction Data 2002, Advances in X-ray Analysis, Volume standards. However, the process must be fully documented with an exhaustive error analysis and the uncertainty must be quite small to make the result useful for value assignment. To ensure that an SRM is useful for decision-making in product quality control, the stated uncertainty of the certified value should be an order of magnitude smaller than the product specification range for the manufacturing process. Therefore, the NIST method of analysis must be inherently better than any quality control requirement. NIST strives to obtain levels of uncertainty that are more stringent, often better by a factor of 10, than related, industrial quality control applications. A way to reduce biases when using artifact standards is to get standards that are closer in composition to the unknown and have stated uncertainties that are similar in magnitude to the total uncertainty needed for the new SRM. This puts the analyst in a conundrum because he needs high quality artifact standards of nearly the same composition as the requested SRM in order to create a new SRM. Destructive sample preparation provides another approach. If the analyst can relate the calibration of the spectrometer directly to primary reference materials, the reliance on artifact standards is eliminated. Primary reference materials, pure elements and pure compounds are carefully characterized so that the stated uncertainty in an assigned value is significantly smaller than for most artifact standards. Pure compounds are available with assay values exceeding % purity. G. Staats published the results of a careful study of the certainty of such an assay [5] and sources of uncertainty introduced by handling pure compounds and concluded that it was possible to limit the uncertainty to the order of 0.03 % to 0.1 %. For certified reference materials and other artifact standards, estimates of uncertainty in composition values are nearly always one order of magnitude greater. To take advantage of this superior quality, the analyst must prepare samples without introducing significant sources of bias. They must synthesize calibration standards that closely match the prepared samples. The match must be close enough to control matrix effects, which usually means that all elements must be accounted for and the mass fractions in the synthetic standards must be within a few percent relative of the unknown. The ideal case for SRM value assignment would use a matrix-independent method that provides a comparison of the unknown material to one or more primary reference materials. One mode for value-assignment and certification is measurement using a single, primary method of analysis [4]. While this mode of value-assignment does not state that primary reference materials must be used, it does list a number of requirements for a primary method: 1. a. A primary direct method measures the value of an unknown without reference to a standard; or b. A primary ratio method measures the value of a ratio of an unknown to a standard of the same quantity; its operation must be completely described by a measurement equation. 2. Certification at NIST requires that all potentially significant sources of error have been evaluated explicitly for the application of the method and the matrix under investigation. 3. Confirmation of measurements must be accomplished by determination of certified constituents in certified reference materials of similar matrix, or by a second NIST technique, or by results from selected outside laboratories. In the face of these requirements, an X-ray spectroscopist must decide how to achieve matrixindependence. For most industrial materials, there are two obvious paths to be explored: 1) destructive sample preparation with synthetic calibration standards and 2) fundamental parameters calculations with a set of reference materials with similar matrix composition to the

5 Copyright (c)jcpds-international Centre for Diffraction Data 2002, Advances in X-ray Analysis, Volume unknown. It will be shown below that option 1 using the technique of borate fusion has fewer sources of uncertainty than option 2. BRACKETING STANDARDS The borate fusion process represents a solution to most of the difficulties of other forms of destructive sample preparation. Borate fusion has been discussed extensively in numerous articles and books in the scientific literature [6-14]. Many methods have been documented and the list of difficulties is relatively short. If a material can be oxidized and fused, it can be converted to a homogeneous solid solution. It is well known that oxidized materials dissolve in the flux at temperatures well below the melting point of the compound minimizing losses of volatile elements. Borate fusion has been used in the past to create synthetic calibration standards from primary reference materials. However, these synthetic standards covered wide ranges of mass fraction and were used in combination with matrix correction algorithms. Calibration standards can be prepared to bracket unknowns that have been fused in the same manner. To obtain control over inter-element effects, the bracketing standards are designed to mimic the entire unknown specimen in its fused form for all analytes. That is, the mass fractions of all major and minor constituents of the synthetic standards and fused specimens differ by no more than a few percent relative. A small level of variety is designed into the synthetic standards so they can be used to create straight-line calibrations without the use of influence coefficients. Correlations of high and low mass fractions are avoided. All of the preparation work is done gravimetrically using an analytical balance. The author developed a set of procedures that take advantage of the combination of XRF and borate fusion to create an analysis method that provides complete control over sources of uncertainty. The process relies on careful attention to good weighing practices. All mass values are corrected for buoyancy. Dilution factors are calculated from the mass of the sample and the total mass of borate glass created by fusion. The Pt crucible and casting dish are weighed before and after fusion to account for all borate glass. No corrections are required for loss on ignition. The process consists of the following steps. 1. Perform a preliminary analysis of the unknown using a fundamental parameters-based method to identify all analytes and their approximate mass fractions in the material. 2. Create a procedure for borate fusion of the unknown using a low dilution factor and a low temperature to prevent loss by volatilization. Characterize the repeatability of the procedure. 3. For the unknowns, prepare duplicate fused specimens from each of at least six containers. At NIST, the number and identities of containers is chosen by a qualified statistician. 4. Analyze the unknown in its fused form using the fundamental parameters-based method. The results of this analysis are the target values for design of synthetic calibration standards. 5. To decide which elements to include in the synthetic standards, combine the list of analytes with any additional elements that exhibit significant matrix effects on the analytes. 6. Design at least four synthetic calibration standards, made from primary reference materials, which bracket all constituents of the fused unknown to within ±2.5 % relative for major constituents, ±5 % for minor constituents, and within the linear calibration range for trace constituents, usually up to approximately 300 mg/kg in fused form.

6 Copyright (c)jcpds-international Centre for Diffraction Data 2002, Advances in X-ray Analysis, Volume Prepare small quantities of the primary reference compounds according to established heat treatment practices to ensure that the compounds have the correct stoichiometry and moisture content [15-17]. 8. Dilute individual reference compounds or metals by borate fusion when the mass to be weighed for the synthetic standards is less than 50 mg because the uncertainty due to weighing becomes significant below 50 mg on a 5-place analytical balance. 9. Create an XRF measurement program for all analytes, plus the tube Compton scatter peak and a line from the halide used in the non-wetting agent. Acquire count rate data for all measured lines and backgrounds with counting statistical errors below 0.1 % preferably, below 0.25 % if possible, or with the lowest uncertainty possible. 10. Prepare one synthetic standard and measure it alongside one fused unknown specimen to verify that the range of count rates of the synthetic standards will bracket the unknowns. If not, redesign the remaining synthetic standards before preparing them. 11. Choose a control sample, preferably a certified reference material of similar matrix to the unknown, and prepare it in duplicate by borate fusion. Fuse a quantity of the control sample that results in a borate bead containing as many analytes in the bracketed calibration range as possible. For example, if the unknowns were prepared using 0.5 g and the control contains lower levels of major and minor constituents, it may be appropriate to fuse 0.75 g to get the fused control beads to more closely match the unknown sample beads. 12. Measure all synthetic calibration standards and unknown specimens in random order. 13. Create calibrations using a straight-line model for all analytes incorporating line overlap corrections, if needed, and using the tube Compton scatter measurement to correct for bead mass thickness effects, if needed and where possible. 14. Calculate compositions for all analytes in all unknown specimens and perform an analysis of uncertainty according to NIST policy [18]. 15. Use the results for the control sample(s) to test for biases in the analytical results [19]. This may require more than just duplicate specimens of the control. This approach requires the laboratory to maintain a collection of ultrahigh purity compounds, metals, and primary solution standards. In the author s laboratory, oxide and carbonate compounds and metals are used as ingredients for synthetic standards. Metals and NIST single element solution standards are employed to verify the assay of each batch of commercial, ultrahigh purity compound. EXPERIMENTAL All specimens were prepared using the method of borate fusion. A Philips/SOLED Perl X 3 automated bead preparation machine was used to fuse and cast samples as 30 mm diameter beads. For portland cements and their associated synthetic standards, fusion was carried out at a temperature of 975 ºC for 6 minutes to fuse 2.50 g of cement with 5.00 g of flux (pre-fused 66 % lithium tetraborate, 34 % lithium metaborate by mass, % purity). For zeolite materials and their associated synthetic standards, fusion was carried out at a temperature of 1100 ºC for 6 minutes to fuse either 0.75 g of material with 6.25 g of flux or 0.50 g with 6.50 g of flux. Lithium iodide solution (0.25 g/g) was used as a non-wetting agent. Beads were cast in one of two platinum dishes, which were shown to produce identical beads having flat, smooth surfaces requiring no surface preparation before measurement.

7 Copyright (c)jcpds-international Centre for Diffraction Data 2002, Advances in X-ray Analysis, Volume Portland cement was sampled and analyzed as received, which is the conventional approach in the cement industry [20]. The three Zeolite materials, Linde Type A (LTA), faujasite (FAU), and ZSM-5 (MFI) were sampled on a hydrated basis. Specimens were placed in small, plastic weighing scoops, hydrated for at least 48 h and weighed in a glove box maintained at 54 % RH ± 1 % RH [21] using a slurry of Mg(NO 3 ) 2. The maximum depth of material in each scoop was 5 mm. Therefore, the scoops held only 0.75 g of LTA, 0.75 g of FAU or 0.50 g of MFI. A Philips model PW2404 WDXRF spectrometer was used to measure the K-L 2,3 characteristic X-rays of all elements. Measurements were performed in vacuum with the generator operated at 3.6 kilowatts. A single sample holder with a 29 mm inner diameter was used with a centering ring of Delrin plastic to carry samples into the spectrometer and hold them in the measurement position. The mask between the sample and the collimator was set to view a 27 mm circular area of the sample. The L 3 -M 4,5 line of iodine was measured to correct the overlap of the I L 2 -M 4 line on the Ti K-L 2,3 line. The Rh KL Compton scatter line from the X-ray tube was measured as an internal reference to compensate for the effects of differences in bead mass thickness on elements with higher energy, characteristic X-rays. RESULTS AND DISCUSSION In a number of recent projects involving portland cement, the bracket standard approach was used to calibrate the spectrometer for 14 elements. Table 1 displays the compositions of four synthetic standards used for certification analysis of SRM 1880a. It is possible to demonstrate the improvement afforded by calibration using these bracketing standards by looking at the data for Fe 2 O 3. Figure 1 shows two calibration curves with curve 1a prepared using the original portland cement SRM series 1880, 1881, and curve 1b prepared using the four synthetic standards. Curve 1a uses certified mass fractions for all concentrations with alpha coefficients estimated from first principles to correct matrix absorption effects as in Equation 1. Curve 1b is a simple straight line with the net Fe count rate divided by the gross Rh KL Compton scatter count rate to correct for variations in bead mass thickness as in Equation 2. The plots include confidence intervals created using the Working-Hotelling-Schiff algorithm [22]. From the confidence intervals, one can estimate the uncertainty associated with prediction of a value of 1.00 % for the mass fraction of Fe 2 O 3 in a specimen. For curve 1a, the estimated uncertainty is % mass fraction, which is clearly unacceptable for value assignment of a certified reference material. For curve 1b, the effort required to prepare synthetic standards is rewarded with an uncertainty of % mass fraction. C j C = + + i D ( L i i, l Cl ) Ei R 1 i α i, j l j 100 C i Di l ( i, l l E = L C ) + i Ri Rs (1) (2) where C = mass fraction (%), D = y-axis intercept, L = line overlap correction factor, E = the inverse of the sensitivity, R = net count rate, α ij = matrix influence coefficient.

8 Copyright (c)jcpds-international Centre for Diffraction Data 2002, Advances in X-ray Analysis, Volume There are several reasons for the improvement in performance gained from bracketing standards. First, chemical composition values for the SRMs have associated uncertainty values that are significantly greater than the uncertainties in the assay values for the high purity compounds used to prepare the synthetic standards. Second, in curve 1a, there are no points in the immediate vicinity of 1 % mass fraction, causing the calculated confidence intervals to broaden. Third, Equation 1 describing the calibration with matrix corrections is subject to a larger number of sources of uncertainty than a simple straight-line model. It is obvious that a number of parameters in Equation 1 are not needed in Equation 2. Each of these parameters (α ij and C j ) has an associated uncertainty that propagates into the final result. Therefore, synthetic bracketing standards provide a clear advantage by eliminating sources of uncertainty a Net Count Rate , Fe2O3 (%mass) b Figure 1. a. Calibration Using 1880-series Portland Cement SRMs b. Calibration Using Synthetic Standards from Table 1. Ratio (Fe/Rh) , Fe2O3, %mass It is useful to illustrate the reduction in matrix corrections obtained with bracketing standards compared to calibration using artifact standards. In Table 2, α Fej C j /100 values (column 4) are the matrix corrections needed for the effect of each compound on the measured amount of Fe 2 O 3 when artifact standards are used along with Eq 1. The total correction, calculated from the term in Eq 1. containing α ij, is greater than 120 % of the amount of Fe 2 O 3. Column 5 of Table 2 shows the matrix effect,, which remains when using bracketing standards. The value of was

9 Copyright (c)jcpds-international Centre for Diffraction Data 2002, Advances in X-ray Analysis, Volume calculated from the product of the α ij and one-half the range of the mass fraction of each compound in the synthetic standards in Table 1. In this example, the matrix effects are reduced to less than This value could be reduced further with closer bracketing of the CaO mass fraction. However, the design of the synthetic standards ensures that the analyte is subject to a slightly greater absorption due to a given interfering element in some standards while it is subject to a slightly lesser absorption in the other standards. Therefore, the variety designed into the synthetic standards contributes to the error of the fit of a straight-line model to the measured count rates and chemical composition values. So long as the unknowns are completely bracketed by the synthetic standards, no additional corrections or components of uncertainty are needed because the uncertainty is adequately estimated by the rms error in the straight line fit. Table 1. Compositions of Synthetic Bracket Standards for SRM 1880a Portland Cement. All values in mass fraction (%) ID 80a1 80a2 80a3 80a4 Compound CaO SiO Al 2 O Fe 2 O SO MgO K 2 O TiO Na 2 O SrO P 2 O Mn 2 O ZnO Cr 2 O An example of the power of the borate fusion/synthetic standard approach is found in recent analyses of zeolite compounds. XRF, instrumental neutron activation analysis (INAA) and a gravimetric method using Na 2 CO 3 fusions were used to analyze three zeolite compounds for the elements Si, Al, Na, and Fe. The details of the gravimetric and INAA methods are beyond the scope of this paper; however, the author can provide information on request. Comparisons of the results are shown in Table 3 for Si, Table 4 for Al, Table 5 for Na, and Table 6 for Fe. Several things are clear from the information in these tables. For Si, the XRF approach rivals gravimetry for accuracy and expanded uncertainty. For Al, Na, and Fe, the XRF approach is superior to INAA for expanded uncertainty. This is due to the fact that in this particular determination INAA suffers from low count rates that limit the inherent precision of the method. Examination of the data for Al and Na in FAU and LTA zeolites reveals that the XRF and INAA results do not agree within the 95 % confidence intervals. The results agree when the expanded uncertainty estimates are expressed at the 99 % confidence level. This is an indication that an unidentified

10 Copyright (c)jcpds-international Centre for Diffraction Data 2002, Advances in X-ray Analysis, Volume source of uncertainty or bias exists in one or both methods. Therefore, additional investigation is required before a certified value can be assigned. This problem would not have been discovered if the XRF work was done using artifact standards for calibration. Table 2. Matrix Effects in Fused Specimens of Portland Cement. Compound Average α Fej α Fej C j /100 mass fraction (%) CaO SiO Al 2 O Fe 2 O SO MgO K 2 O TiO Na 2 O SrO P 2 O Mn 2 O ZnO Cr 2 O Total Correction = where: Average = average composition of four synthetic standards in Table 1, α Fej = theoretical coefficients calculated using average composition, and = matrix effect due to range of composition of bracketing standards. The uncertainty budget for XRF analysis of FAU zeolite (faujasite) in Table 7 is instructive for the magnitudes of the various components of uncertainty. A Type A uncertainty component is estimated using statistical methods. A Type B uncertainty component is estimated using other means such as manufacturer s specifications, prior experience, and uncertainties assigned to reference data [18]. Even with the advantages of bracketing standards, the most significant source of uncertainty is the fit of the calibration model, Eq. 2, to the measured count rates and calculated mass fractions for the synthetic standards. In this case, five synthetic standards were created which explains why there are three degrees of freedom in the calibration fit. CONCLUSION The combination of borate fusion, synthetic bracketing standards and X-ray fluorescence spectrometry constitutes a matrix-independent analysis method. Synthetic bracketing standards, while labor-intensive, offer significant reduction of the uncertainty due to calibration by eliminating matrix differences among samples and calibration standards. The calibration approach is simplified considerably and no artifact standards are needed. Borate fusion allows flexibility in the choice of control samples for validation of the method because the dilution

11 Copyright (c)jcpds-international Centre for Diffraction Data 2002, Advances in X-ray Analysis, Volume factor can be adjusted so that fused beads prepared from the control sample match beads prepared from unknowns. One disadvantage of borate fusion is dilution of the matrix and reduced capability for determination of trace constituents. Of course, this depends on the nature of the specimens and the dilution required to create stable, homogeneous borate beads. In the zeolite example, XRF rivals a classical method for accuracy and expanded uncertainty. Performance also compares favorably to instrumental neutron activation analysis. When applied for certification analyses for SRM development, this approach results in expanded uncertainty estimates (95 % confidence level) in the range of 0.2 % to 1 % relative to the quantitative results. Table 3. Silicon in Zeolites XRF/Borate Fusion vs. Gravimetry Table 4. Aluminum in Zeolites XRF/Borate Fusion vs. INAA SRM Mass Fraction U Zeolite SRM Mass Fraction U Zeolite (proposed) (%) (%) (proposed) (%) (%) 2850 XRF Faujasite 2850 XRF Faujasite Grav INAA XRF Linde A 2851 XRF Linde A Grav INAA XRF ZSM XRF ZSM-5 Grav INAA Table 5. Sodium in Zeolites XRF/Borate Fusion vs. INAA Table 6. Iron in Zeolites XRF/Borate Fusion vs. INAA SRM Mass Fraction U Zeolite SRM Mass Fraction U Zeolite (proposed) (%) (%) (proposed) (%) (%) 2850 XRF Faujasite 2850 XRF Faujasite INAA INAA XRF Linde A 2851 XRF Linde A INAA INAA XRF <0.004 ZSM XRF ZSM-5 INAA INAA where: U = expanded uncertainty at the 95 % confidence level; Grav. = Gravimetry by Na 2 CO 3 fusion; INAA = Instrumental Neutron Activation Analysis These materials are under investigation and values may change prior to certification. ACKNOWLEDGEMENTS The author wishes to acknowledge the assistance of A. F. Marlow, who prepared most of the samples, and S. D. Leigh, who assisted with statistical evaluations. T. W. Vetter performed gravimetric determinations of Si in zeolites at NIST. R. Zeisler performed instrumental neutron activation analysis at NIST.

12 Copyright (c)jcpds-international Centre for Diffraction Data 2002, Advances in X-ray Analysis, Volume Table 7. Uncertainty Budget for Faujasite Zeolite (FAU) from XRF Determinations. All values are % mass fraction with the relative uncertainty in parentheses below each value. Element Na Al Si Fe Recommended value Source of Uncertainty Type df Replication A (% relative) (0.26) (0.27) (0.30) (3.5) Calibration line fit A * (% relative) (0.07) (0.51) (0.67) (4.4) Calibration of balance B inf. (% relative) (0.01) (0.01) (0.01) (0.01) Weighing sample B inf. (% relative) (0.03) (0.03) (0.03) (0.03) Weighing glass B inf. (% relative) (0.01) (0.01) (0.01) (0.01) Compound assay B inf. (% relative) (0.10) (0.10) (0.10) (0.10) Combined, u c (% relative) (0.13) (0.32) (0.41) (1.9) Expanded, U = 2u c (% relative) (0.26) (0.64) (0.81) (3.8) Terms: df denotes degrees of freedom; * for Fe, df = 7; inf. signifies infinite; u c denotes combined uncertainty; U denotes expanded uncertainty estimated at the 95 % confidence level. DISCLAIMER Certain commercial products are identified in this paper to adequately specify the experimental procedure. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the products are necessarily the best available for the stated purpose. REFERENCES 1. National Institute of Standards and Technology, Public Internet Site, March 6, 2001.

13 Copyright (c)jcpds-international Centre for Diffraction Data 2002, Advances in X-ray Analysis, Volume National Institute of Standards and Technology, Chemical Science and Technology Laboratory, Public Internet Site, March 6, National Institute of Standards and Technology, Chemical Science and Technology Laboratory, Analytical Chemistry Division, Public Internet Site, March 6, May, W., Parris, R., Beck, C., Fassett, J. Greenberg, R., Guenther, F., Kramer, G., Wise, S., Gills, T., Colbert, J., Gettings, R., and MacDonald, B., Definitions of Terms and Modes Used at NIST for Value-Assignment of Reference Materials for Chemical Measurements, NIST Spec. Pub , U. S. Government Printing Office, Washington, DC, 2000, 16pp. 5. Staats, G., Fresenius J. Anal. Chem. 336, 132 (1990). 6. Claisse, F., Norelco Reporter, Vol. III, No. 1, 3 (1957). 7. LeHouillier, R., Turmel, S., Claisse, F., Anal. Chem. 46, 734 (1974). 8. LeHouillier, R., Turmel, S., Claisse, F., Advances in X-Ray Analysis, Vol. 20, 459 (1977). 9. Haukka, M. T., Thomas, I. L., X-Ray Spectrom. 6(4), 204 (1977). 10. Couture, R. A., Advances in X-Ray Analysis, Vol. 32, 233 (1988). 11. Eastell, J., Willis, J. P., X-Ray Spectrom. 19(1), 3 (1990). 12. Alvarez, M., X-Ray Spectrom. 19(4), 203 (1990). 13. Eastell, J., Willis, J. P., X-Ray Spectrom. 22(2), 71 (1993). 14. Giles, H. L., Hurley, P. W., Webster, H. W. M., X-Ray Spectrom. 22(3), 132 (1995). 15. Staats, G., Fresenius Z. Anal. Chem. 330, 469 (1988). 16. Staats, G, and S. Strieder, X-Ray Spectrom. 22(3), 132 (1993). 17. Giles, H. L., Hurley, P. W., Ingham, M. N., X-Ray Spectrom. 24(3), 115 (1995). 18. Taylor, B. N. and C. E. Kuyatt, Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, NIST Tech. Note 1297, U. S. Printing Office, Washington, DC, 1994, 24 pp., Becker, D., R. Christensen, L. Currie, B. Diamondstone, K. Eberhardt, T. Gills, H. Hertz, G. Klouda, J. Moody, R. Parris, R. Schaffer, E. Steel, J. Taylor, R. Watters, and R. Zeisler, Use of NIST Standard Reference Materials for Decisions on Performance of Analytical Chemical Methods and Laboratories, NIST Spec. Pub. 829, U. S. Government Printing Office, Washington DC, 1992, 30 pp. 20. ASTM C , Standard Test Methods for Chemical Analysis of Hydraulic Cement, Annual Book of ASTM Standards, Vol , West Conshohocken, PA. 21. ASTM E (1996), Standard Practice for Maintaining Constant Relative Humidity by Means of Aqueous Solutions, Annual Book of ASTM Standards, Vol , West Conshohocken, PA. 22. J. D. Spurrier, Encyclopedia of Statistical Sciences, Vol. 9, S. Kotz and C. B. Read, eds., pp , Wiley, New York, 1988.