Harmonization of Uncertainties of X-Ray Fluorescence Data for PM 2.5 Air Filter Analysis

Transcription

1 Journal of the Air & Waste Management Association ISSN: (Print) (Online) Journal homepage: Harmonization of Uncertainties of X-Ray Fluorescence Data for PM 2.5 Air Filter Analysis William Gutknecht, James Flanagan, Andrea McWilliams, R.K.M. Jayanty, Robert Kellogg, Joann Rice, Paul Duda & Richard H. Sarver To cite this article: William Gutknecht, James Flanagan, Andrea McWilliams, R.K.M. Jayanty, Robert Kellogg, Joann Rice, Paul Duda & Richard H. Sarver (2010) Harmonization of Uncertainties of X-Ray Fluorescence Data for PM 2.5 Air Filter Analysis, Journal of the Air & Waste Management Association, 60:2, , DOI: / To link to this article: Published online: 24 Jan Submit your article to this journal Article views: 398 View related articles Citing articles: 10 View citing articles Full Terms & Conditions of access and use can be found at

2 TECHNICAL PAPER ISSN: J. Air & Waste Manage. Assoc. 60: DOI: / Copyright 2010 Air & Waste Management Association Harmonization of Uncertainties of X-Ray Fluorescence Data for PM 2.5 Air Filter Analysis William Gutknecht, James Flanagan, Andrea McWilliams, and R.K.M. Jayanty RTI International, Research Triangle Park, NC Robert Kellogg Alion Science and Technology Corporation, Durham, NC Joann Rice U.S. Environmental Protection Agency, Office of Air Quality Planning and Standards, Research Triangle Park, NC Paul Duda and Richard H. Sarver Chester Labnet, Tigard, OR ABSTRACT The U.S. Environmental Protection Agency (EPA) s PM 2.5 Chemical Speciation Network (CSN) and the Interagency Monitoring of Protected Visual Environments (IMPROVE) network use X-ray fluorescence (XRF) analysis to quantify trace elements in samples of fine particles less than 2.5 microns in aerodynamic diameter (PM 2.5 ). Methods for calculating uncertainty values for XRF results vary considerably among laboratories and instrument makes and models. To support certain types of modeling and data analysis, uncertainty estimates are required that are consistent within and between monitoring programs, and that are independent of the laboratories that performed the analyses and the analytical instrumentation used. The goal of this work was to develop a consensus model for uncertainties associated with XRF analysis of PM 2.5 filter samples. The following important components of uncertainty are included in the model described herein: variability in peak area, calibration, field sampling, and attenuation of X-ray intensity for light elements. This paper includes a detailed analysis of how attenuation uncertainties for light elements are derived. For the remaining IMPLICATIONS This paper describes a uniform approach to estimating analytical uncertainties for XRF analysis of PM 2.5 filter samples. This method can be adapted for use with most XRF instruments without the need for complex reprogramming of on-board software. Researchers and regulators should consider use of the algorithms described herein when setting up new PM speciation monitoring programs, as should data analysts who need to calculate consistent uncertainties for existing data. The algorithms described in this paper are being used to calculate the uncertainties for the PM 2.5 CSN energy dispersive XRF data currently posted in EPA s Air Quality System database. uncertainty components included in the model, an approach and recommendations are presented to ensure that laboratories performing this type of analysis can use similar equations and parameterizations. By applying this uniform approach, it is illustrated how the uncertainties reported by the CSN and IMPROVE network laboratories can be brought into very good agreement. The proposed method is best applied at the time of data generation, but retrospective estimation of uncertainties in existing datasets is also possible. This paper serves to document the equations used for calculating the uncertainties in speciated PM 2.5 data currently being posted on EPA s Air Quality System database for the PM 2.5 CSN program. INTRODUCTION The U.S. Environmental Protection Agency (EPA) s PM 2.5 Chemical Speciation Network (CSN), also sometimes known as the Speciation Trends Network (STN), 1 and the Interagency Monitoring of Protected Visual Environments (IMPROVE) 2 network currently use X-ray fluorescence (XRF) analysis to quantify trace elements in fine particles less than 2.5 microns in aerodynamic diameter (PM 2.5 ). The many filter samples generated by the CSN program have necessitated the use of multiple laboratories and several XRF instruments within each laboratory to analyze the filter samples. Uncertainty values reported with the trace element concentration data are used as weighting factors for source attribution models. Because this is a key use, the reported XRF measurement uncertainty values need to be consistent from instrument to instrument within each network and should also be consistent from network to network if their results are to be used in the same model or data analysis. However, examination of early XRF results from the CSN program revealed internal inconsistencies in the reported uncertainties that were of concern to data users. 3 Comparison of uncertainties reported by 184 Journal of the Air & Waste Management Association Volume 60 February 2010

3 Table 1. Sources of uncertainty currently included by different laboratories. Uncertainty Component CSN Laboratory 1 (ThermoNoran XRF) CSN Laboratory 2 (Kevex XRF) Laboratory 3 (EPA; Custom XRF) Laboratory 4 (IMPROVE; Custom XRF) Peak fit (based on regression) Calibration uncertainty (based on calibration standards and/or reported NIST SRM uncertainties) Attenuation with calibration standard (Z 11 Na to 14 Si) Attenuation with calibration standard (Z 14) Attenuation with field sample (Z 11 Na to 14 Si) Attenuation with field sample (Z 14) Interferences (i.e., near 0% to near 100% peak overlap) X-ray tube, detector, and associated electronics Sampler flow rate (sample volume) Sample deposit area Calculated from Poisson Calculated from Poisson Calculated from Poisson Calculated from statistics statistics statistics Lorentzian statistics Not applied 5% for all elements Element specific ( %) 5% for all elements Not applied Self-absorption and particle size based on SRM2783 a Mass-based using XRF analysis results (0 3%) Not applied Not applied Self-absorption up to Z 20 b Mass-based using XRF analysis Not applied results (1%) Not applied Self-absorption and particle size Particle-based (3 6%) Particle-based (8 22%) Not applied Self-absorption up to Z 20 Mass-based using XRF analysis Particle-based (2%) (Ca) results (1%) Applied Applied Applied Applied Not applied Not applied 1% Not applied Included in 5% total field sampling uncertainty Included in 5% total field sampling uncertainty Not applied 2 5% Included in 5% total field sampling uncertainty Not applied Average 2% Included in 5% total field sampling uncertainty Notes: a CSN Laboratory 2 uses NIST 2783 as a calibration standard to determine attenuation for Z and estimates self-absorption values on the basis of NIST-supplied deposit density; b CSN Laboratory 2 does not apply absorption corrections for Z 20. the CSN and IMPROVE programs also showed significant differences. Although all of the CSN XRF laboratories were generally compliant with the EPA Compendium method for XRF analysis (IO ), it was found that the methods used to calculate uncertainty varied considerably among laboratories. The main components of uncertainty recognized by the laboratories and by IO 3.3 were similar but differed in how they were parameterized, as will be described below. Differences in instrumentation (e.g., excitation conditions, which vary from one laboratory to another) also had an impact on detection levels and reported uncertainties. These interlaboratory differences have resulted in the discrepancies in the CSN uncertainty data reported by Kim and Hopke. 3 In response to the concerns about these discrepancies, the authors investigated how uncertainty values were being generated by the different XRF laboratories used in the CSN and IMPROVE networks and by the EPA Office of Research and Development (ORD) laboratory in Research Triangle Park, NC. A consensus uncertainty model was developed and used to harmonize the uncertainty calculations between XRF laboratories analyzing filters for the CSN program. All uncertainty values that had already been loaded into EPA s Air Quality System (AQS) for the CSN dataset were recalculated using the consensus uncertainty model and the revised uncertainties reloaded into AQS, replacing the original values. All subsequent CSN XRF data posted to AQS will use the harmonized uncertainty equations. This paper describes the basic theory of calculating uncertainty in XRF measurements for CSN, identifies the main components of uncertainty, and provides the consensus equations that are now being used in the program. The resulting improvements in agreement among the uncertainties generated by several different instruments are illustrated using data from the CSN program. SOURCES OF MEASUREMENT UNCERTAINTY IN XRF ANALYSIS OF PM 2.5 Measurement uncertainty in XRF arises from several different sources. The primary sources of measurement uncertainty that will be addressed here are the following: Peak area, counting, and deconvolution uncertainty. Interferences between elements (line overlap). Calibration uncertainty and detector variability. Field and sampling error, which include variations in deposit area and air sampling volume, sample loss due to shipping and handling, and contamination. Attenuation of X-ray intensity for light elements. The components of XRF uncertainty historically used by four laboratories the two that generate data for the CSN program, an EPA laboratory, and the IMPROVE laboratory are shown in Table 1. Components of uncertainty are typically assumed to be random error terms, and bias is generally neglected, except where variations in bias could contribute to pseudorandom variability (as when filters are randomly assigned to different instruments) or sensitivity variations over time. Following the International Organization for Standardization (ISO) s Guide to the Expression of Uncertainty in Measurements 5 (hereafter, the ISO Guide), specifically eq 10 in ISO Guide Section 5.1.2, total uncertainty due to random errors (excluding constant bias) will be calculated as the square root of the combined variances, as shown in eq 1: Volume 60 February 2010 Journal of the Air & Waste Management Association 185

4 U total 2 i (1) i where i denotes the uncertainty for each component i contributing to the total uncertainty. Correlations between different error terms (i.e., covariance) as addressed in eq 13 of the ISO Guide are thought to be minor, with the exception of overlap and interference corrections between the XRF emission lines of different elements. Covariance relationships are discussed within the context of the individual components of uncertainty in the sections below, so that eq 1 can be used for calculating the total uncertainty. If it is found that such covariance relationships are severe enough to propagate to the calculated uncertainties for certain elements, the laboratories should take steps to minimize them, including possibly changing analytical conditions. According to the ISO Guide, the components of uncertainty are typically determined in two fundamentally different ways: (1) Statistical determination (e.g., by repeated measurement, standard errors returned by regression routines, and Poisson counting statistics). (2) Estimation based on scientific judgment (estimation may be done when it is impractical to gather sufficient data of the right type to determine them statistically). The various components of uncertainty discussed in this paper were calculated using one or the other of these two methods. One of the sources of uncertainty attenuation was particularly problematic for several of the light elements and is the focus of much of what is discussed in this paper. Harmonization of the other uncertainty components was primarily a matter of ensuring that each component was included in the uncertainty model and that consistent parameter values were used for estimating the components. Peak Area and Deconvolution Uncertainty Most XRF emission peaks have some degree of overlap with other peaks, be it partial or nearly complete, from elements with spectral lines possessing similar energy. In the case of partial overlap, several least-squares deconvolution approaches are available, 6 such as fitting with measured library reference spectra or analytical functions and spectrum stripping to separate the overlapping intensity contributions for each element. 6 9 Counting uncertainties in these net intensities arise from the random nature of X-ray production. These uncertainties are computed using the mathematics of multiple regression and are similar to simpler counting statistics for radioactive sources that, rigorously speaking, are only applicable to completely isolated peaks. Severe peak overlap (100%) is referred to as interference and is actually easier to correct. Here, deconvolution algorithms produce extremely large errors and are impractical, if not impossible, to use; therefore, a subtractive coefficient 10 approach is used instead. Depending on the analytical strategy used by each laboratory, only a few such interferences occur (for example, between the Br L and Al K emission peaks, and between the S K and Mo L emission peaks). The end result of the deconvolution and/or interference correction is to produce elemental intensities for comparison with quantification standards. A simple example of uncertainty calculation for a peak with interference is as follows: N P B RI (2) where N represents the net counts for an element (count), P represents peak counts (count), B represents background counts (count), I is the intensity of the analyte line for an interfering element (count), and R is the interference coefficient for the interfering element (dimensionless). 10 Propagating errors, one obtains N P B RI 2 IR (3) The interference coefficients, R, are available from various sources. 10 In the more common (and complex) case where partial overlap occurs, multiple regression fitting yields the total peak count, N*, and its uncertainty, N*, which may contain contributions from interfering species. Analogous to eqs 2 and 3 above, the net elemental count and the uncertainty are as follows: N N* RI (4) N N* 2 RI (5) The counts N and N are converted to concentration via the instrument s sensitivity factor. The relative uncertainty in concentration can vary from 100% at the 1 detection limit to less than 5% at high concentrations, where the lower figure is dominated by other sources of uncertainty addressed in this paper. Peak area uncertainty (and subsequently, element concentration uncertainty) is considered an instrument parameter. The uncertainty values for the various elements are typically calculated by the commercial instrument manufacturer s proprietary software and cannot be altered by the instrument operator; also, laboratories that develop their own software to perform this same function do not alter that software to change how uncertainty values are calculated from sample to sample. The calculated uncertainties are usually included with the concentration values delivered by the instrument operating system. Calibration Uncertainty Calibration uncertainty arises from several sources, one of which is the uncertainty of the standard calibration films. The CSN and IMPROVE laboratories use calibration films produced by MicroMatter (Arlington, WA). The uncertainties for sample standards from MicroMatter are typically given by the manufacturer as 5% for all elements. For most elements, the films concentrations do not change significantly over time. The manufacturer s uncertainty specification should be interpreted as a constant 186 Journal of the Air & Waste Management Association Volume 60 February 2010

5 bias and not a random variation from measurement to measurement. However, because the participating analytical laboratories must of necessity use different films for calibrations, randomly assigning filters to the different laboratories could inject a pseudorandom signal that is related to any bias errors in the standards used by the laboratories. The IMPROVE network currently uses only one analytical laboratory (Crocker Nuclear Laboratory, University of California Davis) for all of its XRF analyses, so this phenomenon should not contribute to the random error in the IMPROVE data. The CSN has used as many as three independent XRF laboratories, and currently uses two, so bias between the calibration materials used by the participating laboratories could potentially contribute to the random error of measurement in the CSN dataset. This contribution will be included in the error attributable to calibration in the overall expression for uncertainty described herein. Monitoring programs that commingle data generated by multiple XRF laboratories should include intercomparison of calibration standards as part of their quality assurance oversight and, if necessary, augment their uncertainty estimates if significant uncorrectable biases are found between laboratories. Calibration uncertainty also arises from (1) uncertainty in the standard response function (e.g., standard curve) based on measurement of multiple standards wherein there is a difference between the expected and actual values for these standards, and (2) statistical variation between replicate determinations. It is possible to reduce the calibration uncertainty slightly by using multiple standards to give a weighted deviation for each suite of elements measured by a given instrument. Another potential reduction in the calibration uncertainty can be accomplished by measuring replicate standards at each nominal concentration and performing statistical analysis of the response curve. This approach has been used by Kellogg 11 with a resulting concentration uncertainty of 3 4%. However, this approach is expensive and time-consuming. It should be noted that the standard materials available from sources such as MicroMatter and the National Institutes of Standards and Technology (NIST) are typically much higher in concentration (mass per area) than is usually encountered on particulate matter (PM) filters sampled in programs such as CSN and IMPROVE. This means that the calibration factors are unavoidably extrapolated to lower concentration, which can introduce another unknown, but hopefully small, component of error. Other small contributors to analytical uncertainty are X-ray source and detector instability and drift and variation in electronic signal processing, but these can be minimized by making adjustments as required to keep routine quality control samples within acceptance limits. The uncertainties associated with these sources are generally insignificant compared with other sources described here. If one considers each of these sources of uncertainty, a conservative estimate of the uncertainty value is best represented by the uncertainty of the calibration standards. For approximately 15% of the 48 elements measured in the CSN program, only a single standard is available. The two-point calibration curve is defined by this single standard and the zero intercept. Accordingly, a consensus among staff from several laboratories is that 5% is a conservative and reasonable estimate for calibration uncertainty. Field Sampling Uncertainty Field sampling variability arises from several sources, including variation in air sampler flow rates and sample volume, deposit size (which affects the deposit density on the filter), and shipping/handling effects, including sample loss and contamination. In the 2001 PM 2.5 Chemical Speciation Quality Assurance Report for CSN, 12 the flow rates for 10 MetOne spiral ambient speciation samplers (SASS; and 10 Andersen reference ambient air samplers (RAAS) were audited. The standard deviations for the airflows for the SASS and RAAS samplers were 1.7 and 3.9%, respectively. Some portion of these reported errors is undoubtedly attributable to the audit standards and the audit process itself, so that an uncertainty of approximately 1.5% attributable to flow rate seems reasonable for samplers having mass flow controllers. The URG MASS aerosol sampling system (MASS; which is also used in the CSN, is expected to have a similar flow uncertainty because it also incorporates a mass flow controller. Another source of uncertainty in the field sampling category is variability in the sample deposit area on the filter. For the 4.62-cm diameter filter used by the CSN samplers, the actual deposit diameter is approximately 3.9 cm. If the uncertainty in the deposit diameter is assumed to be 0.05 cm because of differences between support rings and filter stretching during disassembly and handling, then the deposit area will have a relative area uncertainty of approximately 2.5%. Finally, shipping and handling in the field contribute to uncertainty because of contamination and loss of material from the filters. Empirically, the shipping and handling variability seems to depend on the elemental species and the filter loading (high or low). The substantial effects of shipping and handling were shown by comparing the variability of CSN field replicates from colocated samplers against the variability of laboratory replicates. 13 These data suggest an average uncertainty of approximately 4% (concentration-proportional) arising from these sources. Assuming an estimated relative standard deviation of 1.5% for the air sampler flow rate (i.e., the sample volume), 2.5% for the deposit area variability, and 4% attributable to field shipping and handling, the total uncertainty related to field sampling is estimated to be approximately 5% when the individual components are summed according to eq 1 (i.e., [ ] 1/2 ). Attenuation Uncertainty The final contributor to uncertainty to be considered is attenuation, which has been approached differently by various laboratories. X-ray attenuation occurs when (1) incoming (excitation) X-ray photons are absorbed by components of the sample other than the elements of interest and do not yield the desired fluorescence, and (2) outgoing (fluorescent) photons from elements of interest are absorbed by other components of the sample and are therefore not available for detection. The net effect is that Volume 60 February 2010 Journal of the Air & Waste Management Association 187

6 the instrument detects a smaller signal from an element than would be expected, as illustrated in eq 6. C reported,i C measured,i A i (6) where C reported,i is the attenuation-corrected concentration for element i, C measured,i is the instrumental measurement after application of calibration for element i, and A i is the attenuation factor for element i (a value of 1 indicates no attenuation correction; smaller values indicate a greater attenuation effect). The attenuation effect is most significant for the lighter elements (e.g., Na, Mg, Al, Si, P, S, Cl, K, and Ca), which are excited by and emit lower energy, or soft, X-rays. The true correct elemental attenuation factor for any particular sample is unknown and subject to variation according to particle size and composition of the deposit. The attenuation factors are also influenced by instrumental parameters, as described below, but these fixed effects tend not to contribute to the attenuation uncertainty. For the lightest elements (Na, Mg, Al, and Si), the uncertainty in the attenuation factor may be the principal source of uncertainty, except at low concentrations, where the peak area determination uncertainty predominates. X-ray attenuation losses depend on the energy of the excitation X-ray(s), the energies of the fluorescent X-rays, the mass and composition of the deposit, and the size and size distribution of the particles (larger particles attenuate XRF signals more than smaller particles). Attenuation has been addressed by several researchers using different approaches. For example, Rhodes and Hunter 14 used the Berry-Furuta-Rhodes model to derive formulas for determining X-ray intensity as a function of particle size. One of these formulas is for a thin, homogeneous sample, multiplied by a grain-size-dependent factor. Markowicz 15 developed a correction for particle size effect that requires the use of two sources of exciting gamma or X-ray radiation of different energies. Dzubay and Nelson 16 addressed this issue on the basis of analytical data for air filters, as well as first principles of X-ray absorption. Their approach was used here to analyze attenuation correction uncertainty for the harmonization of the CSN data. Original Work by Dzubay and Nelson. Dzubay and Nelson 16 calculated attenuation factors separately for fine and coarse particles on the basis of reports in the literature in the 1970s of a bimodal distribution of particle volume as a function of diameter (see Figure 1). These early researchers defined coarse as the particles between 2.5 and 20 m in diameter. More recently, the range for coarse particles has been defined as 2.5 to 10 m in diameter, on the basis of health effects. Dzubay and Nelson noted that fine particles were attributed to aerosol growth by gas-to-particle conversion and coagulation, such that the particles would be expected to be similar in composition. In contrast, coarse particles were attributed to breakdown of larger particles by mechanical processes (grinding, abrasion), such that their composition would be diverse. A summary of their methods for fine and coarse particles is provided in the next sections. dc/d Log(D) Aerodynamic Diameter Figure 1. Idealized particle size distributions for fine and coarse particles. 22,23 Fine Particles. If the X-ray absorption is negligible within individual particles and the particle diameter is small compared with the thickness of the layer, then the sample can be considered homogeneous. Dzubay and Nelson assumed this was the case for fine particles, and therefore the attenuation factor, A, for an element within a homogeneous layer having mass per unit area, m, on the surface of the filter is 1 exp m A m (7) where A is the attenuation factor (dimensionless), m is the areal density of the deposit (g/cm 2 ), and is the total mass absorption coefficient (cm 2 /g). For each element, the term is a function of the relative geometry of the X-ray excitation source and the X-ray detector, the mass absorption coefficients for each element in the incoming (excitation) X-rays and the exiting (fluorescing) X-rays, 17 and the fraction by weight of each element in the deposit. (The composition of the deposit is iteratively deduced from the XRF analysis along with the attenuation factors.) Only elements actually present in the deposit are included in the calculations. Dzubay and Nelson calculated attenuations for the light elements using the concentrations given in Table 2. After accounting for the seven elements listed in the table, and the other elements with atomic number (Z) greater than 13, the remaining 81.4% unaccounted elemental mass (Z 13) was assigned as cellulose (C 6 H 10 O 5 ). C 6 H 10 O 5 was considered a reasonable estimate of the composition of the organic material present in the sample that is not detected by XRF. Dzubay and Nelson estimated attenuation factors at particle filter loadings of 0.1 and 0.5 mg/cm 2 and uncertainties at a filter loading of 0.5 mg/cm 2 ; these values are shown in Table 3. Heavier particle loadings result in greater attenuation (and hence lower attenuation factors). On the basis of filters collected in the urban CSN, a heavily loaded CSN filter would be approximately 0.1 mg/cm 2 total fine particulate mass, not counting the mass of the Teflon filter; a more typical PM 2.5 filter loading would be in the range of 0.01 to 0.05 mg/cm 2. Thus, the 188 Journal of the Air & Waste Management Association Volume 60 February 2010

7 Table 2. Percent composition by weight of fine aerosol collected by a dichotomous sampler in a St. Louis residential neighborhood in August 1973 and analyzed by XRF. Element Z Fine Aerosol (%) Si S Ca Ti Fe Br Pb Other Z Other Z Notes: Adapted with permission from Dzubay and Nelson 16 Copyright 1975 Plenum, Advances in X-Ray Analysis. estimated maximum attenuation for the CSN would produce an attenuation factor in the range of approximately 0.90 for Mg and Al to 0.98 for K and Ca, as shown in Table 3. The uncertainty values were determined as the range of attenuation factors associated with a change in the composition of the 81.4% unknown mass noted in Table 2. Dzubay and Nelson assumed the unknown mass to be either C 6 H 10 O 5 or only oxygen (O) and then calculated the attenuation for each element for each of these two compositions. The change in attenuation (which reflects the total uncertainty) associated with this large change in composition for the organic/carbonaceous phase was small for all but the lightest elements (i.e., Na, Mg, Si, S). Coarse Particles. Dzubay and Nelson also determined attenuation in the presence of coarse particles. 16 They assumed the particles were collected as a monolayer and that the particles were equivalent spheres. Each attenuation factor, A(sphere), was considered a complex function of several parameters, including: Mass absorption coefficients Geometric particle diameter Particle density Relative geometry of the X-ray excitation source and the X-ray detector To compute the net attenuation for an element within the sample, A(sphere) must be averaged over the particle size distribution on the filter. Acoarse 0 Asphere dv dd TDdD 0 dv dd TDdD (8) where dv/dd is the lognormal particle volume distribution as a function of the aerodynamic diameter, D; D is the aerodynamic particle diameter (m) and is equivalent to d g S 1/2, where d g is the geometric particle diameter (m) and S is the density of the particle (g/cm 3 ); and T(D)isthe relative particle collection efficiency (dimensionless). The particles are assumed to have a lognormal distribution shown in eq 9 (the form used by Dzubay and Nelson 16 ). dv dd 1 D ln exp D D p 12 ln212 2 lnw (9) where D is the aerodynamic diameter (m), D p is the aerodynamic diameter corresponding to the peak of the distribution (m), and W is the full width of the particle size distribution peak at half maximum (m). Values of X-ray attenuation were calculated for various elements in the presence of coarse particles. The assumptions were that W 5 m, D p 10 m, and that the particles ranged from all botanical (95.7% C 6 H 10 O 5,2% Ca, 1.5% K, 0.6% Mg, 0.2% P, and 0.03% Fe) to almandine (Fe 3 Al 2 Si 3 O 12 ). As with the fine particles, the attenuation was calculated for each element for each of these two compositions. The range of the attenuation factors for each element for these two conditions was, in this case, divided by 2 to determine the uncertainty values. Dividing by 2 was considered appropriate because the range defined from all botanical to all almandine is a broader range of composition than would normally be expected in typical samples. The reported attenuation factors (see Table 4) correspond to a composition midway between the botanical and almandine compositions. Because botanical matter was considered to be an unlikely source of Al and Si, Dzubay and Nelson used the attenuation in quartz as the upper limit for these two particular elements. Extension of Dzubay and Nelson s Work by Kellogg. Kellogg 11 has extended the work of Dzubay and Nelson to calculate attenuations for the light elements, taking into consideration particle size, mass, and composition. He assumes that Na through Si (Z 11 14) are concentrated in the tail of the coarse mode in a size range of approximately m. He ignores submicron combustion-generated particles for these elements. If an airshed contains a fume (or Table 3. Attenuation for K X-rays of various elements in fine particulates. a Element Z Attenuation at Particle Loading b of 0.1 mg/cm 2 Attenuation at Particle Loading of 0.5 mg/cm 2 Mg Al Si P S Cl K Ca Notes: a Adapted with permission from Dzubay and Nelson. 16 Copyright 1975 Plenum, Advances in X-Ray Analysis. b The confidence level was not specified by Dzubay and Nelson. Volume 60 February 2010 Journal of the Air & Waste Management Association 189

8 exceedingly small particles) of these elements, then Kellogg s attenuation factors will cause concentrations to be too high, although this is not considered a significant risk. (If such a fume is known to be the dominant source, Kellogg s software easily allows a change in the model for Na through Si from the coarse particle model to the homogeneous layer model. If such a source of fine particles is identified after the data have been reported, data users can choose to apply their own attenuation correction factors to the data, or to downweight the data in their models.) Attenuation Due to Particle Size. Kellogg 11 calculates the attenuations for Na, Mg, Al, and Si as due only to particle size. The calculations are performed using the mathematics used by Dzubay and Nelson, 16 but the set of most likely mineral forms that could include these elements has been expanded. In total, 46 different minerals were considered in the same manner as noted in Dzubay and Nelson. 16 Kellogg uses the particle attenuation model and applies it to particles of these minerals. The attenuation for each of the four elements is calculated for each particle type that includes that element over the range of particle volumes described by the lognormal size distribution found in real-world sampling. The average of the maximum and minimum attenuation factors for each element is taken as the attenuation for that element in the sample; the uncertainty is calculated as one-half of the full range of attenuation factors over the mineral set. Kellogg considers the mineral set comprehensive, so the uncertainty is expected to accurately represent the range of attenuations and is therefore assumed to be 2.5 standard deviations (2.5). Values for attenuation provided by Kellogg for the Kevex Model 771 instrument using two different fluorescers are shown in Table 5. For the purposes of reporting the uncertainty to a database such as AQS, uncertainties have been converted to a 1 basis, as presented in Table 5. Table 4. Attenuation for K X-rays of various elements in coarse particles (PM ) for composition halfway between botanical and almandine (quartz and almandine for Al and Si). Element Z Attenuation (4.5-KeV excitation) Attenuation (18-KeV excitation) Al Si P S Cl K Ca Ti V Cr Mn Fe Ni Cu Zn Table 5. Attenuation factors 1 uncertainties for low-atomic-number fine particles based on averaging attenuations for different potential mineral forms containing the element. Element Z Al Fluorescer, Kevex XRF (PM 2.5 ) Attenuation for Heavier Elements Based on Homogeneous Layer Model. Kellogg 11 uses the homogeneous layer-based attenuation model for Z 14. The attenuation is compositionand areal-density dependent, so it is calculated for each sample. Attenuation is calculated for each element and each primary or secondary excitation source on the basis of the mass on the filter and the raw concentrations of each element measured assuming the unknown mass is initially C 6 H 10 O 5. Kellogg goes through an iterative process to determine the attenuation; that is, the concentration is adjusted for the calculated attenuation and the new concentration values are then used to calculate new attenuation factors. This process is continued until the change is negligible. The nonanalyzable elements are allowed to vary from O to C 6 H 10 O 5 to benzene (C 6 H 6 ); the attenuation calculated with C 6 H 10 O 5 is taken as the true attenuation for the sample. The span of attenuations associated with O and C 6 H 6 provides the measure of uncertainty. Kellogg assumes the uncertainty calculated is 3 because of the extreme assumptions about the composition of the nonanalyzable mass of the sample. The average attenuation and attenuation uncertainties are quite low, less than 1%. These uncertainty values are much less than the 5% calibration uncertainty and the 5% field sampling uncertainty and are therefore not significant relative to the total uncertainty. Harmonization Approach for Attenuation Uncertainty CSN Laboratories. Harmonizing the uncertainty calculations for attenuation between the range of XRF analyzers used in the CSN program requires a clear understanding of the uncertainty methods currently in use. First, as shown in Table 1, CSN Laboratory 1 did not provide corrections for attenuation or include attenuation uncertainty in its overall uncertainty calculations. In contrast, CSN Laboratory 2 does calculate mass (homogeneous layer) absorption (referred to as self absorption ) uncertainties for the thin-film standards and mass absorption plus particle size correction uncertainties for field filter samples. The formula used by this laboratory to calculate absorption correction uncertainty, which is based on statistical modeling, differs from that used by Dzubay/Nelson and Kellogg, as shown in eq 10. c 2 2 i 2 s 1/2 A a N c A 2 Ti Fluorescer, Kevex XRF (PM 2.5 ) Na (5.8%) Mg (5.2%) Al (4.3%) Si (2.6%) 2 1/2 A p (10) 190 Journal of the Air & Waste Management Association Volume 60 February 2010

9 Table 6. Uncertainty values calculated by CSN Laboratory 2 for thin-film standards and NIST SRM Element Z Thin-Film Standard a (%) SRM 2783 b (%) Na MDL c Mg Al Si P MDL S Cl K Ca No values determined Notes: a Self-absorption only; b Self-absorption and particle size; c Method detection limit limited by counting statistics and noise at the low end. where a is the absorption correction uncertainty, c is the Poisson counting uncertainty, i is the spectral overlap uncertainty (count), s is the calibration uncertainty (count), N c is the corrected net counts (count), A is the homogeneous absorption correction factor (0 A 1), and A p is the size correction factor (0 A p 1). The uncertainty values calculated by CSN Laboratory 2 for thin-film standards and NIST Standard Reference Material (SRM) 2783 are shown in Table 6. The uncertainty values reported by this laboratory for elements Na through Ca were significantly higher than those reported by other laboratories. Furthermore, Table 6 shows an unexpectedly abrupt downward change in the reported uncertainty after Ca (i.e., Sc and above). These discrepancies were traced to the method used to compute the attenuation factor uncertainty (eq 10) and were significant motivations for undertaking this investigation. IMPROVE XRF Laboratory. Attenuation for the light elements is included in the calculation of concentration in the IMPROVE program. 18 IMPROVE s Standard Operating Procedure (SOP) 301, X-Ray Fluorescence Analysis, describes corrections to the data for the shadowing effect of particles on filters. 19 These corrections were derived in the 1970s through experimentation with various substrates and deposits to derive values for expected filter and loading types. Correction values are reported by the IM- PROVE SOP 19 for select elements with Z 14 and are 0.98, 0.97, and 0.97 for S, K, and Ca, respectively. The IMPROVE uncertainty calculations are provided in IMPROVE s SOP 351, Data Processing and Validation, 20 which provides the following estimate of precision for concentration (see Section , eq of the SOP): c 2 c 2 f s 2 f a 2 f v 2 (11) where (c) is the precision of concentration (ng/m 3 ), c is the concentration (ng/m 3 ), and f s is the statistical fractional precision (dimensionless). 20 f 2 s 1 N 1 2 N b (12) N Gutknecht et al. where N represents the counts in peak, N b represents the counts in the background under the peak, f a is the component of analytical precision that is a constant fraction (dimensionless), and f v is the fractional volume precision (dimensionless). The discussion on page A-48 of SOP 351 states: The precision is calculated separately for each variable at the time of spectral analysis using f a 0.04 and f v The quadratic sum of these two is At small concentrations the statistical term is dominant, while at large concentrations the precision approaches 5%. IMPROVE data were obtained from the IMPROVE Web site ( and plots of reported uncertainty versus concentration were examined. Table 7 shows the uncertainties estimated from these plots for a range of real-world ambient concentrations. This table shows slopes of approximately 5% for Al, Si, Cl, S, K, and Ca, which agree with the equation in IMPROVE SOP 351 in which the total concentrationproportional factor is only a function of f a and f v, because f s becomes negligible at higher concentrations (larger N and c values). HARMONIZATION PROCEDURE Light Elements Particle Size Model Along with earlier researchers, Dzubay and Nelson 16 laid the fundamentals for calculating the effects of the physical structure and composition on attenuation of X-rays in X-ray spectrometry. Eldred 21 and Kellogg 11 advanced the work of these early researchers by considering the fact that the high end of the fine particle distribution will contain coarse particles because there is considerable overlap between the high end of the PM 2.5 distribution and the low end of the PM 10 (particles 10 m in aerodynamic diameter) distribution. Kellogg has taken this concept a step farther by assuming that the particles containing the elements Na, Mg, Al, and Si are predominately found as crustal particles at the high end of the fine particle distribution. It is understood that the most common crustal minerals are the silicates (e.g., quartz, silica [SiO 2 ]), aluminosilicates (e.g., K-feldspar [orthoclase], KAlSi 3 O 8 ), and oxides (e.g., hematite [Fe 2 O 3 ]). In the Earth s crust, O and Si predominate, and Al, Fe, Ca, Na, K, and Mg follow in descending concentration. By averaging over a broad set of likely minerals that includes the element of interest, Kellogg s model should provide a reasonable estimate of attenuation uncertainty. If Kellogg s premise is accepted, then it makes good sense to consider the composition of these large particles as a mixture of all Table 7. IMPROVE uncertainty values estimated from real-world data. Element Estimated Uncertainty (%) Na 23 (very scattered data) Mg 29 (very scattered data) Al 5.8 Si 5.3 Cl 5.8 S 4.9 K 5.0 Ca 5.0 Volume 60 February 2010 Journal of the Air & Waste Management Association 191

10 Table 8. Variation in composition used as basis for determining uncertainty of attenuation. XRF Laboratory Homogeneous Layer Model Particle Size Model Dzubay and Nelson 16 Nonmeasured mass varied from C 6 H 10 O 5 to C 6 H 6 to O (O only) Varied particle composition from botanical soil b to almandine (quartz to almandine for Al and Si) Eldred/IMPROVE 21 No uncertainty calculated. Assumed average PM 2.5 composition on the basis of 15,000 samples a No uncertainty calculated but did calculate attenuation for all oxides and soil c Kellogg 11 For Z 14, nonmeasured mass varied from C 6 H 10 O 5 to C 6 H 6 to O (O only) For Z 11 14, calculated range of attenuations on the basis of all reasonable minerals that would contain the element of interest CSN Laboratory 2 On the basis of statistical model On the basis of statistical model Notes: a 4.8% H, 25.3% C, 15.1% N, 38.0% O, 9.4% S, 1.45% Al, 3.19% Si, 0.78% K, 0.86% Ca, 0.85% Fe, 0.08% Ti, 0.06% Zn, 0.05% V to Sr; b 95.7% C 6 H 10 O 5, 2% Ca, 1.5% K, 0.6% Mg, 0.2% P, and 0.03% Fe; c 50% O, 24% Si, 11% Al, 3% K, 5% Ca, 6% Fe, 0.6% Ti, 0.1% Mn. likely minerals, as Kellogg did. Of the light elements, P and Cl are generally present at very low levels in PM 2.5 ; the exception is high chloride in coastal samples. S (as sulfate) will most likely be found as a condensate particle and therefore will not likely occur in the upper end of the fine particle distribution. Thus, the Kellogg particle size attenuation model was only used for the Na, Mg, Al, and Si uncertainty calculations. Heavier Elements Homogeneous Layer Model The attenuation corrections for elements with Z 14, although small and generally inconsequential for realworld samples, are determined using the homogeneous layer model. These corrections are low because the X-rays for those elements are of relatively high energy and are not readily captured by other sample elements. The decision to be made is that of the composition of the deposited layer not measured by XRF. Earlier in this paper, it was reported that approximately 81% of the fine particulate was not measured by XRF. On the basis of IMPROVE data, Eldred 21 estimated the composition of this material as 4.8% H, 25.3% C, 15.1% N, and 38% O. CSN PM 2.5 filters analyzed during 2005 by RTI International showed estimated composition to be 3% H on the basis of ammonium and organic carbon (OC) as C 6 H 10 O 5, 23% C, 10% N, and approximately 36% O on the basis of sulfate, nitrate, and OC as C 6 H 10 O 5 for a total of 72% of sampled material not measurable by XRF. These results agree reasonably well with Eldred s results using IMPROVE data. Dzubay and Nelson 16 and Kellogg 11 determined their uncertainties by assuming variation in the composition of non-xrf measured materials that ranged from O only to C 6 H 10 O 5 to C 6 H 6. values of Kellogg 11 as calculated with his chosen set of minerals and the particle-based model. As an improvement, the ranges of attenuation factors were calculated for the elements Na, Mg, Al, and Si that would be measured on the instruments used at the two CSN XRF laboratories for a set of preselected mineral particles. These values are presented in Table 9. With the mineral set being comprehensive, it is reasonable to assume a confidence level in the calculated uncertainties between 2 and 3, as was done by Kellogg. 11 As noted, the changes in attenuation uncertainty with changes in the instrument operating parameters are minimal. Also, the small differences in attenuation uncertainties will not be significant when these uncertainties are combined with the fitting uncertainty, the calibration uncertainty, and the field sampling uncertainty, as described below. Homogeneous Layer Model for Z 14. As with Na, Mg, Al, and Si, the attenuation factors determined for Z 14 are instrument dependent (excitation energies and source/ detector geometry). They are also sample-composition dependent and must be calculated separately for each sample. The uncertainties, if significantly different between laboratory instruments, would be applied to the concentrations measured by the associated instrument. However, as noted earlier, attenuations for Z 14 for typical ambient aerosol samples are very close to 1, and so the uncertainties are generally negligible compared with uncertainties from calibration, field sampling, and sample deposit size. Uncertainties may be significant if the filter loading is exceptionally high (i.e., above 0.1 mg/cm 2 ), but PM 2.5 loadings are typically mg/cm 2. Final Harmonized Uncertainties The variations in composition that served as a basis for these uncertainty calculations are summarized in Table 8, which includes results from the particle size model and the homogenous layer model. Particle Size Model for Na, Mg, Al, and Si. The attenuation factors are instrument dependent (excitation energies and source/detector geometry) and must be calculated separately by each laboratory. As to the uncertainty, it was determined that the best choice, given the high values for peak/curve fitting uncertainty, would be to accept the Table 9. PM 2.5 attenuation uncertainties for Na, Mg, Al, and Si with XRF spectrometers from Laboratories 1 and 2. Element CSN Laboratory 1 ThermoNoran QuanX XRFs CSN Laboratory 2 Kevex XRFs Na (6.5%) (16.3%) (6.9%) (17.2%) Mg (4.6%) (11.5%) (4.8%) (12.1%) Al (4.5%) (11.2%) (5.2%) (13.0%) Si (4.3%) (10.7%) (4.7%) (11.9%) 192 Journal of the Air & Waste Management Association Volume 60 February 2010

11 Uncertainty, µg/filter CSN Lab 1, Inst 1 CSN Lab 1, Inst 2 CSN Lab 2, Inst 1 CSN Lab 2, Inst 2 IMPROVE Uncertainty, µg/filter CSN Lab 1, Inst 1 CSN Lab 1, Inst 2 CSN Lab 2, Inst 1 CSN Lab 2, Inst 2 IMPROVE Concentration, µg/filter Figure 2. Total uncertainty estimates for PM 2.5 Si before harmonization. Total Uncertainty. The attenuation uncertainties calculated as shown above have been combined with the uncertainties of (1) curve fitting, (2) calibration (5%), and (3) field sampling (5%) using eq 1 to arrive at total uncertainties for each sample. Attenuation for the thin-film standards was considered to be insignificant. As noted above, the total uncertainties reported by CSN Laboratory 2 for certain light elements were unexpectedly high, as shown in Table 6. Once the origin of the discrepant uncertainty data had been identified, the laboratory re-examined its equations for estimating uncertainties in the attenuation factors and decided that it was too conservative and that revisions were needed. An adjustment to the model was made and the uncertainty values recalculated. These new uncertainty values were much more consistent with those calculated by the other laboratories. RESULTS AND DISCUSSION Figures 2 and 3 illustrate the effects of recalculating the total uncertainties for Si data from the two CSN laboratories. These figures also show uncertainty data from the IMPROVE network for comparison. Figure 2 shows the uncertainties as originally reported by the respective CSN laboratories, and Figure 3 shows total uncertainty for the two CSN laboratories data with the changes described above to harmonize the calculations. The IMPROVE concentration and uncertainty values shown are taken from Uncertainty, µg/filter CSN Lab 1, Inst 1 CSN Lab 1, Inst 2 CSN Lab 2, Inst 1 CSN Lab 2, Inst 2 IMPROVE Concentration, µg/filter Figure 3. Total uncertainty estimates for PM 2.5 Si after harmonization (IMPROVE data not harmonized) Concentration, µg/filter Figure 4. Total uncertainty estimates for PM 2.5 Si after harmonization (IMPROVE data harmonized). the VIEWS Web site; data were taken from randomly chosen sites to illustrate the dependency between concentration and reported uncertainty. The IMPROVE uncertainty estimates include the determination of the analyte X-ray emission peak areas and 4% for calibration uncertainty, but they do not include an attenuation uncertainty. Harmonization of the IMPROVE uncertainty estimates with CSN, principally through inclusion of attenuation uncertainties, would make the IMPROVE and CSN total uncertainty values agree even better, as shown in Figure 4. The figures show a considerable improvement in the comparability of the total uncertainties as a result of this approach to harmonization. As noted, the values for a vary between researchers, and these values could potentially be refined further by using improved estimates of the composition and structure of the PM 2.5 samples. However, the effects of further revisions to the overall uncertainty calculation would be small and of little value for most purposes, provided the uncertainties are calculated on a consistent basis. CONCLUSIONS Using similar methods for calculating concentrations and the associated uncertainties is critical in achieving comparable data for XRF analysis of fine particulate samples for modeling and other data use needs. In the absence of well-characterized errors for field sampling (e.g., flow rate, deposit area, sample handling) and calibration, it is reasonable to assume nominal uncertainties equal to an aggregate 5% of concentration for both of these components. The uncertainties for X-ray attenuation losses, although based on an extreme range of deposit compositions, are reasonable and conservative estimates; only exhaustive, actual measurement of particle composition and size distribution would allow calculation of more accurate values. The success of this approach to harmonizing uncertainties across laboratories has been illustrated using data generated by three different laboratories (two CSN laboratories and the IMPROVE laboratory). The interlaboratory comparability issues discussed in this paper are potentially even more important for the chemical speciation of coarse particles (between 2.5 and 10 m in aerodynamic diameter) than for PM 2.5 because size-related effects such as X-ray attenuation are more Volume 60 February 2010 Journal of the Air & Waste Management Association 193