Anal. Chem. 1995, 67, 1866-1871
LcStandardlessyy Quantitative Electron Probe Microanalysis with Energy-Dispersive X-ray Spectrometry: Is It Worth the Risk? Dale E. Newbury,*lt Carol R. Swyt,* and Robert L. Myklebustt National Institute of Standards and Technology, Gaithersburg, Maryland 20899, and National lnstitutes of Health, Bethesda, Maryland 20892
“Standardless”procedures for quantitative electron probe X-ray microanalysis attempt to eliminate the need for standardization through calculation of standard (pure element) intensities. Either “first principles”calculations, which account for all aspects of X-ray generation, propagation, and detection, or %tkd standards” calculations, which use mathematical fits to measured intensities from a limited set of pure standards, can form the basis for standardless analysis. The first principles standardless analysis procedure embedded in the National Institutes of HealWNational Institute of Standards and Technoloa comprehensive X-ray calculation engine and database, Desktop Spectrum Analyzer, has been tested against spectra measured on NIST standard reference materials, research materials, and binary compounds. The resulting distribution of errors is broad, ranging from -90%to +150%relative. First principles standardless analysis can thus lead to unacceptably large errors. Rigorous quantitative electron probe X-ray microanalysis is based upon determining the intensity ratio between a characteristic X-ray peak in the unknown and the same peak in a standard measured under identical operating conditions of beam energy, known dose, detector efficiency, and specimen orientation and position.’ This ratio of intensities, known as the “k-value” or “kratio”, forms the starting point for quantitation. To a first approximation,the k-ratio is proportional to the ratio of concentrations between the unknown and the standard. The ratio of measured intensities differs from the ratio of concentrations because of matrix (interelement) effects: electron backscattering, electron stopping power, X-ray absorption, and secondary fluorescence, all of which depend upon the sample composition. Several methods exist to calculate the complex electron/ X-ray physics that form the basis of these matrix corrections, including various formulationsof the “Z4F ” [atomicnumber (2)-absorption (A) -fluorescence (n]and methods, as well as the ZieboldOgilvie pence-Albee) empirical method.’ These theoretical/ empirical procedures permit analysis of unknown multielement compositions based on the use of a suite of standards that can be as simple as pure elements. For those elements which are not solid under the conditions of ambient temperature and low pressure (10-100 pPa) typical of an electron beam instrument, NIST. NIH. (1) Goldstein, J. I.; et al. Scanning Electron Microscopy and X-ray Microanalysis; Plenum Press: New York, 1992; p 395. +
1866 Analytical Chemistry, Vol. 67, No. 7 7 , June 7, 1995
or which are subject to degradation under electron bombardment, stoichiometric binary compounds such as GaP or HgTe can be used. The more than 40 year history of the development of these quantitative microanalysis procedures has included extensive testing through the measurement of homogeneous multielement samples whose compositions were characterized by independent analytical techniques.2 From these studies, error distribution histograms have been developed, such as that illustrated in Figure 1,which shows the systematic errors that remain when random counting errors have been reduced to a negligible leveL3 Such error distributions have been determined for various categories of variables that influence the analytical procedure (such as the class of the material, e.g., for metal alloys, minerals, etc.; the specimen shape, e.g., for particles; the choice of standards, e.g., for pure elements, compounds, minerals, glasses, etc.) and for specific matrix correction procedures (e.g., the choice of the absorption correction, etc) .4 Close examination of the errors as a function of the magnitude of the matrix corrections can reveal the source of the most significant errors. For example, in Figure 1, partitioning the errors on the basis of the magnitude of the absorption correction V,) reveals uniformly smaller errors for analyses with absorption corrections less than 30%V, > 0.7). The importance of such error histograms is that they permit the analyst to make an estimate of the range of possible systematic errors associated with a particular correction procedure. When a quantitative result is reported, this estimate of systematic error should be supplied in addition to the precision of the measurement based upon random counting errors. For example, considering the error distribution in Figure 1,which was determined for flat, polished, metallic specimens analyzed with pure element standards and the NIST implementation of ZAF,the systematic errors can be described as having a width of f 5 %relative error for 95% of the cases s t ~ d i e d . ~ A great deal of effort has been expended by numerous authors to improve the performance of analytical procedures since the error distribution shown in Figure 1 was reported! These improved procedures have been successful in eliminatingvirtually all of the outliers seen in Figure 1, and in special cases, such as that of mineral analyses where standards close in composition to the unknown are available, the error distribution has been reduced (2) Heinrich, K. F. J. In Electron Probe Quantitution; Heinrich, K. F. J., Newbury, D. E., Eds.; Plenum Press: New York, 1991; p 9. (3) Heinrich, IC F. J.; Yakowitz, H., cited in Goldstein, J. I.; Yakowitz, H.; Newbury, D. E.; Lifshin, E.; Colby, J. W.; Coleman, J. R. Practical Scanning Electron Microscopy; Plenum Press: New York, 1975; p 338. (4) Scott, V. D.; Love, G. In Electron Probe Quantitation; Heinrich, K. F. J., Newbury, D. E., Eds.; Plenum Press: New York, 1991; p 19.
This article not subject to U.S. Copyright. Published 1995 by the American Chemical Society
50
-
N B S DATA 2 6 4 ANALYSES
40 45
*
35
(BERGER- SELTZER J) @INCONSISTENT DATA (SkV)
-
:
30-
8 25-
E
IS IO -
20
5-
0
9
>-I4
PERCENT RELATIVE ERROR Figure 1. Error histogram observed with pure element standards and a ZAF matrix correction procedure.’* H-Y refers to the HeinrichYakowitz parametrization of the absorption matrix correction, denoted fP.’*
to less than f 2 %relative for 95%of the analyses.’ Careful attention to the details of microanalytical practice (e.g., specimen preparation, electron beam operating conditions, and spectrometer calibration, resolution, and performance), coupled with knowledge of proper analytical strategy (e.g., the choice of the matrix correction procedure, selection of the optimum beam energy for the analysis of particular elements depending on their excitation energies, etc.), can lead to a consistent level of analytical performance, so that the analyst can predict with confidence the range of systematic error to be associated with reported concentration values, accompanied by a statement of the measurement precision. Further refinements of the error estimate are possible. For example, inspection of the magnitude of the matrix correction factors can be used to estimate the error limits. In figure 1,the subset of all analyses for which the absorption correction is less than ~ W (solid O black) shows a substantially narrower error range. The accumulated experience encapsulated in Figure 1forms the basis for the credibility of quantitative electron probe X-ray microanalysis. STANDARDLESS ANALYSIS The k-valuelstandards approach to quantitative electron probe X-ray microanalysis was developed out of necessity in response to the limitations imposed upon analytical procedures when only wavelength-dispersive X-ray spectrometry (WDS) was available.5 WDS is capable of measuring only a narrow (10 ev) energy window in the spectrum, requiring serial measurement of each element present with mechanical repositioning of the crystal and detector for each X-ray peak. The efficiency of a WDS spectrometer is dficult to measure, and moreover, when used with a gasfilled proportional counter operating at atmospheric pressure, as (5) Heinrich, K F. J. Electron Beam X-ray Microanalysis; Van Nostrand Reinhold New York, 1981; p 99.
maintained by a bubbler, the efficiency can vary with barometric pressure. By using an intensity ratio procedure in which the same X-ray line is measured in the unknown and the standard over a short period of time, the spectrometer efficiency factor cancels in the ratio, as long as standardization is performed with suflicient frequency through a series of measurements. As an additional benefit of the k-ratio, certain physical parameters such as the fluorescence yield, which is the fraction of ionizations that result in photon emission, cancel in the ratio. The matrix correction factors used to multiply the k-ratio to produce concentration values are themselves calculated as ratios based upon the estimated composition of the unknoivn and the known composition of the standard, rather than as absolute values. The development of the energy-dispersiveX-ray spectrometer (EDS) has provided the analyst with the means to view the entire X-ray spectrum.6 Although the measurement of X-rays with the EDS remains serial in time, the photoelectric detection process effectively provides parallel detection of all X-ray energies excited by the incident beam, which permits a direct comparison of X-ray peak intensities between different elements from a single spectrometer. Moreover, the efficiency of the EDS as a function of energy can be estimated, and EDS performance is reasonably stable over time, providing the integrity of the detector crystal is maintained by the vacuum isolation window. Thus, it has become attractive to develop quantitative analytical procedures that calculate interelement corrections rather than corrections based upon the measurement of k-ratios for the same elements. Such procedures eliminate the need for standardization and are typically referred to as “standardless” analysis. Standardless analysis procedures are routinely incorporated in virtually all commercial presentations of software for quantitative electron probe X-ray microanalysis. (6) Fitzgerald, R.: Keil, K; Heinrich, K F. J. Science 1968, 159, 528.
Analytical Chemistry, Vol. 67, No. 1 1, June 1 , 1995
1867
Standardless analysis procedures can be developed along at least two different lines: first principles and fitted standards. In the first principles approach, physical descriptions of the X-ray generation, propagation, and detection processes are used to calculate the intensities of pure element standards. To eliminate the need to accurately characterize the solid angle of the X-ray detector, the first principles approach may be augmented with the measurement of a single pure element standard for the purpose of scaling the calculated standards to avoid the requirement for normalization of the analytical total. In the fitted standards approach, experimental measurements of a suite of pure element standards are used in combination with physical models of X-ray generation, propagation, and detection as the basis to develop general expressions of X-ray intensity as a function of atomic number, electron excitation conditions, and detector performance. FIRST PRINCIPLES STANDARDLESS ANALYSIS
First principles standardless analysis is the most ambitious form because it attempts to calculate every aspect of X-ray generation, propagation, and detection that intluences the measured X-ray intensity. There exists an extensive literature of the physics of electron and X-ray interactions that forms the basis for implementing a first principles approach to standardless analysis. The following development is based upon careful consideration of the available formulations for various parameters. X-ray Generation. The generation of characteristic X-rays by high-energy electrons scattering within a solid target can be described by
I, =
"*RciJEc Ai
Qi
EO (-dE/ds)
where'J I, is the characteristic X-ray intensity per incident electron, w is the fluorescence yield ( X-rays/ionization), NOis Avogadro's number, e is the density, R is the backscatter loss factor, Ci is the concentration of species i, Ai is the atomic weight of species i, E, is the critical ionization energy for the shell of interest, EOis the incident beam energy, Qi is the ionization cross section of species i, and dE/ds is the rate of energy loss due to inelastic scattering. The expression of Pouchou and Pichoir, based upon the Bethe expression with modifications for low-electron energy, is used for the stopping powers7 Because of the phenomenon of electron backscattering due to elastic scattering, a significant fraction of beam electrons escape the specimen and carry off ionizing power. This "backscatter loss" is expressed in terms of a multiplicative backscatter loss factor, R, which has been derived empirically from experimental measurements of backscattering and theoretically from Monte Carlo electron trajectory simulation. For the present work, the expression due to Myklebust and Newbury, which incorporates the Fabre K-shell cross section, is u ~ e d : ~ , ~ ~
~~
(7) Pouchou, J.-L.; Pichoir, F. In Electron Probe Quantitation; Heinrich, K F. J., Newbury, D. E., Eds.; Plenum Press: New York, 1991; p 31. (8) Myklebust, R. L.; Newbury, D. E. In Electron Probe Quantitation; Heinrich, K F. J., Newbury, D. E., Eds.; Plenum Press: New York, 1991; p 177. (9) Fabre dela Ripelle, M. J Phys. (Paris) 1949, 10, 319.
1868 Analytical Chemistry, Vol. 67,No. 7 7 , June 7, 7995
where w = E d E . (Note that EK is the critical excitation energy for the K-shell). J is the mean ionization potential according to 2eller:'O
J (eV) = 10.04 + 8.25 exp(-2/11.22)
(34
dvldw is the backscattered electron energy distribution according to Czyzewski and SzymanskF w0.6
&l= ~ dw 1 . 6 p s (1 - w1.6)1+p{(1 - s)
+ [s/(l - w1.6)pl>2 (3b) +
where 17 is the backscatter coefficient, p = (0.8 217) ln(l/$, s = 0.105[3 - 1 (V2.25 cos @ I D , and 8 is the specimen tilt angle. Because the R factor has been shown to be relatively insensitive to the choice of cross sections, the same cross section expression is used for the L and M-shells. Specimen Absorption and Fluorescence. The X-ray intensity is generated over a range of depth in the target. While propagating through the specimen to reach the detector, the X-ray flux is subject to photoelectric absorption, which decreases the emitted intensity relative to the generated intensity. For this work, the expression for the absorption factor,& according to Heinrich and Yakowitz is used12
+
where b/e) is the X-ray mass absorption coefficient and li, is the X-ray take-off angle. Detector Absorption and Transmission. The efficiency with which X-rays are measured with the EDS detector depends on losses due to absorption (below 5 kev) and transmission (above 15 kev):
where @/g)i is the mass absorption coefficient and ti is the thickness for each material through which the photons pass, e.g., the spectrometer window, ice on the detector, gold surface electrode, partially active silicon, and the active silicon. The first term in brackets represents the loss of X-rays due to absorption while passing into the active portion of the detector, while the second term in brackets represents the loss of X-rays due to transmission through the detector. (10) Zeller, C., cited in Ruste, J.; Gantois, M. /. Phys. D., Appl. Phys. 1975, 8, 872. (11) Czyzewski, Z.; Szymanski, H. Proceedings of the lGth International Conference on Electron Microscopy, Vol. 1; Offizon Paul Hartung: Hamburg, 1982; p 261. (12) Heinrich, K F. J.; Yakowitz, H. Anal. Chem. 1975, 47, 2408.
Choice of Parameters in First Principles Standardless Analysis. A first principles standardless analysis procedure based on eqs 1-5 is incorporated in NIST-NIH Desktop Spectrum Analyzer (DTSA), a comprehensive X-ray spectrometry calculation engine and X-ray database.I3 For each standard needed in the analysis of an unknown, the intensity emitted from a pure element target is calculated by means of eqs 1-5. The k-ratio is then calculated with each intensity extracted from the spectrum of the unknown and the corresponding theoretical standard intensity. After k-values for all constituents have been calculated, the ZAF matrix correction procedure is performed in the normal manner. Following the matrix correction, the concentrations are reported as normalized values. Because of uncertainties in the ionization cross section($ and other physical parameters, the calculated absolute standard intensity may differ significantly from that observed experimentally, and the normalization step becomes critical if the concentrations are to be presented on a sensible basis. DTSA provides the analyst with the opportunity to choose the ionization cross section separately for the K-, L, and M-shellsfrom a wide variety of published cross sections. For the present work, several cross sections were tested, and for the development of a comprehensive error histogram, the cross section of Fabre was used for the K-shell and the Bethe cross section was used for the L and M - ~ h e l l s . ~Constants J~ for the L and M-shells proposed by Fiori were used.I3 Note that while a pure element standard is not subject to secondary fluorescence induced by characteristic radiation, the continuum-inducedfluorescence which does occur is not considered in the DTSA formulation of the standard intensity. EXPERIMENTAL SECTION
To test the performance of the first principles standardless analysis procedure in DTSA, an extensive series of metallographically polished materials was measured, including NIST standard reference materials, research materials, and candidate standards under development. The compositions of these materials are listed in Table 1. In addition, the following stoichiometric compounds were also measured: PbSe, InP, GaTe, PbTe, Gap, GaAs, FeS (troilite), ZnS, CuS, CdTe, HgTe, KCl, I B r , KI, GeTe, SrTe, SrS, SrS04, TIBr, BizSe3, LaAlO3, and single crystal YBa2Cu307-x Compositions were chosen so that the analytical peaks did not interfere significantly in most cases. For those situations in which interferences did occur, the peak overlaps were well within the capabilities of spectral deconvolution, so that the extraction of peak intensities was not a significant issue. The top hat digital spectral filter and the nonlinear sequential simplex peak fitting procedures incorporated in DTSA were used for background removal and spectral deconvolution. Detector parameters were chosen on the basis of manufacturer’s specifications for the detector windows and optimization based on background modeling with DTSA. X-ray spectra were measured with an incident beam energy of 20 keV. The beam current was selected to restrict the deadtime to be less than 40% for all materials. Spectrum accumulation times were sufficient (500-2000 s) to provide integrated peak counts with a relative standard deviation of 0.3% (>100000 counts) or less for all major constituents. Only (13) Fiori, C. E.; Swyt, C. R.; Myklebust, R L. (National Institute of Standards
and Technology, Gaithersburg, MD 20899). Desktop Spectrum Analyzer. US. Patent 529913, 1993. (14) Bethe. H. Ann. Phys. 1930,5, 325.
Table 1. Compositions of Test Materials. material
constituents
Si, 0.0935; Pb, 0.743 Al, 0.0265; Si, 0.140; Zn, 0.0402; Ba, 0.0896; Ta, 0.0409; Pb, 0.418 Mg, 0.0302; Si, 0.187; Zr, 0.0740; Ba, 0.269; Zn, NIST glass K240 0.0402 Al, 0.0265; Si, 0.140; Ta, 0.0819; Pb, 0.395; Ba, NIST glass K249 0.0896 NIST glass K252 Si, 0.187; Ba, 0.313; Mn, 0.0316; Co, 0.0393; Cu, 0.0399; Zn, 0.0803 Al, 0.0794; Si, 0.187; Ca, 0.107; Fe, 0.105; Ba, 0.134 NIST glass K309 Mn, 0.0885: Si, 0.254; Ca, 0.111; Fe, 0.112 NIST glass K411 M i , 0.116; Al, 0.0491; Si, 0.212; Ca, 0.109; Fe, 0.0774 NIST glass K412 Ge, 0.287; Pb, 0.545 NIST glass K453 Si, 0.135; Pb, 0.661 NIST glass K456 Si, 0.115; Ge, 0.170; Ba, 0.219; Pb, 0.227 NIST glass K873 NIST glass K961 Na, 0.0297; Mg, 0.0302; Al, 0.0582; Si, 0.299; K, 0.0249: Ti. 0.0120: Fe. 0.0350 NIST glass K1013 Mg, 0.0524; Al, 0.0582; P, 0.334 NIST glass K1070 Mg, 0.0754; Si, 0.187; Ca, 0.0893; Zn, 0.100; Ba, 0.112; Pb, 0.0928 NIST glass K1132 Al, 0.0793; Si, 0.214; Ca, 0.107; Ni, 0.0118; Mo, 0.0167; Ba, 0.134 NIST glass K2754 Si, 0.187; Ba, 0.313; Y, 0.118 Cu, 0.0799 NIST SRM Au-4OCu Au, 0.604; Cu, 0.396 NIST SRM Au-~OCUAu, 0.201; CU,0.798 NIST glass K227 NIST glass K230
0
All values in mass fraction; balance is oxygen.
analytical peaks with X-ray energies above 1 keV were used for this study. When present, oxygen was calculated on the basis of assumed stoichiometry. However, oxygen values were not included in the error distribution reported below because of the constrained dependence of the oxygen component on the analyzed cation species. Only constituents present at concentrations greater than 1 wt % were used for error distribution studies. In fact, most of the materials contained only major constituents with concentrations greater than 10 wt % so that the measured analytical peaks were well above background, thus minimizing possible errors arising from background subtraction. The percent relative error (RE%)was calculated as
RE%= [ (calculated concn - true concn)/ trueconcnl x 100% Note that in calculating this relative error, the composition of each material measured is assumed to be known without error. Considering the magnitude of the relative errors that are observed, this assumption seems to be reasonable. The elemental constituents present in the various materials required selection of analytical peaks that frequently involved a mixture of K-, L, and M-shell X-rays, thus providing a significant challenge to first principles standardless analysis. Many of these materials contained elements that offered a choice of analytical peaks arising from two different shells, such as K-L or L-M. Every possible choice of analytical lines was tested. For example, analysis for PbSe was performed with Se-K and Pb-L, Se-K and Pb-M, Se-L and Pb-L, and Se-L and Pb-M. RESULTS AND DISCUSSION
Choice of Cross Sections. Table 2 contains an example of a single analysis of a steel where all of the constituents, Cr, Fe, Ni, and Si, are analyzed by means of K-shell X-rays. Results from conventional ZAF analysis with standards are compared to standardless analysis with various choices for the K-shell cross Analytical Chemistv, Vol. 67, No. 11, June 1, 1995
1869
Table 2. Analysis of a Steela
Si ZAF/standards 0.0083 standardless K-shell cross section Casnati 0.0101 (+22%) Fabre 0.0084 (+l%) Kolbenstvedt 0.0134 (+61%) Mott-Massey 0.0168 (+102%) Worthington-Tomlin 0.0122 (+47%) a
Ni
Cr
Fe
0.196
0.703
0.0880
0.193 (-1.5%) 0.188 (-4.1%) 0.198 (+l%) 0.206 (+5.1%) 0.195 (-0.5%)
0.722 (+2.7%) 0.718 (+2.1%) 0.714 (+1.6%) 0.707 (+0.6%) 0.713 (+1.4%)
0.0744 (-15%) 0.0856 (-2.7%) 0.0743 (-16%) 0.0699 (-21%) 0.0806 (-8.4%)
All values in mass fraction.
formula value
L, Bethe (Fiori)
L, Bethe (Powell) L, Brown
30 25
20
-
s
-
- - t
>
,
>
. ._
>
,
n
*
1
-
15 -
. .-
10 -
-
5
-
.
_-
IIIIIIIIIII
0
50
100
150
Relative Error, %
Y
Ba
cu
Ob
0.133 0.138 (+3.8%) 0.210 (+58%) 0.181 (+36%) 0.237 (+78%)
0.412 0.411 (-0.2%) 0.448 (+8.7%) 0.626 (+52%) 0.531 (+29%)
0.286 0.281 (-1.8%) 0.186 (-35%) 0.0574 (-80%) 0.0850 (-70%)
0.168 0.156 0.156 0.136 0.147
a All values in mass fraction. K-shell cross section, Fabre. Sample courtesy of D. Kaiser, Materials Science and Engineering Laboratory, NIST. Oxygen calculated by assumed stoichiometry, Cu = 2.
section. This particular steel is not a standard, and so errors for the ZAF/standards analysis are not reported. The issue here is the agreement, or lack thereof, of the standardless results obtained from the same spectrum. The standardless analyses are in reasonable agreement for Cr, Fe, and Ni regardless of the choice of ionization cross section. Results similar to these are often quoted in support of the apparent utility of standardless analysis. Since the analysis of Cr, Fe, and Ni involves X-rays from the same shell with similar critical excitation energies, the X-rays are excited with similar efficiency (ionization cross section multiplied by the fluorescence yield). The X-rays of Cr, Fe, and Ni are of sdliciently high energy that they undergo relatively small and similar absorption losses in the specimen and detector. Taking the ZAF/ standards analysis as a reference, the errors for the various standardless analyses with different K-shell ionization expressions are within f2W0relative. The errors for Si, however, span a factor of 2 for the cross sections tested. Si has a significantly lower X-ray energy than the transition elements and is therefore excited with a much higher efficiency. Because it is generated to a greater fraction of the electron range, the Si X-ray intensity is subject to much greater absorption losses in the specimen and standard, and because of its low energy, it is also more highly attenuated during passage into the EDS. Table 3 contains an analysis of a Y13a2Cu307single crystal. In this case, the constituents must be analyzed with a mix of K- (Cu) and Lshell (Y, Ba) X-ray lines to satisfy the requirement that all analyzed lines be greater than 1 keV in energy. Conventional analysis with standards and ZAF produces small errors relative to the ideal stoichiometriccomposition values, whereas standardless analysis with the Fabre cross section for the K-shell and various formulations for the Lshell results in very large errors. 1870 Analytical Chemistry, Vol. 67, No. 11, June 1, 1995
. .-
L l
>
0 1 1 1 1 1I1 1 l I I -150 -100 -50
Table 3. Analysis of a YBa2Cu307 Single Crystala
ZAF/ stan dards
I I I I I I I I I I I I I I I I I I I I I I I I I I I I I
35
Figure 2. Error histogram for DTSA standardless analysis: 20 keV; K-, L-, and/or M-shell energy > 1 keV.
€0 =
In fact, the errors observed in the standardless analyses are so large that it would not be possible to deduce the 1-2-3 formula of the stoichiometric compound from “quantitative”electron probe X-ray microanalysis. Error Distribution for First Principles Standardless Analysis. Based on the above tests of standardless analysis as well as separate studies of spectral simulation, the Fabre cross section was selected for K-shell calculations, and the Bethe cross section with constants suggested by Fiori was selected for L and M-shell calculations. With these choices, Figure 2 shows the distribution of errors observed for the analysis of 238 individual constituents from the suite of 41 standard reference materials, research materials, candidate standards, and stoichiometric compounds. The distribution is seen to be extremely broad and somewhat asymmetric about zero error, with a tail extending to large positive errors. If these same samples were analyzed by conventional k-value measurement with pure element standards combined with ZAF or $(p)matrix corrections, all of the errors could be expected to fit into just two bins (-10% to +lo% relative error) of the error histogram in Figure 2! With the further refinements that are possible through optimization of the matrix correction procedure and the use of multielement standards more similar in composition to the unknowns, all of the errors would be expected to fit into the width of a single bin of Figure 2. The broad range of errors observed in first principles standardless analysis is a consequence of our imperfect knowledge of electron beam/X-ray interactions with matter and point to the need for more accurate databases. Equations 1-5 require the provision of extensive physical data in order to be implemented. While a subset of this physical data is also required for the calculation of the matrix correction factors for conventionalzAF/ standards analysis, it is important to note that, in the conventional approach to quantitative X-ray microanalysis, the use of an intensity ratio involving the same analytical X-ray line in the unknown and the standard reduces the dependence on the exact accuracy with which the physical parameters are known. Indeed, some important parameters, such as the fluorescenceyield, cancel out in the k-ratio. Standardless analysis essentially relies upon predicting the X-ray intensities from different elements relative to each other, so that the absolute accuracy with which parameters are known for one element relative to another becomes critical.
The error histogram reported in Figure 2 presumably represents the worst case scenario for standardless analysis, since the first principles standardless procedure attempts to calculate everything about X-ray generation, propagation, and detection needed for quantitative analysis. Another possible formulation of standardless analysis is the fitted standards approach, based upon actual measurements of pure element standard intensities under known conditions of beam energy and electron dose. These measured intensities are corrected for efficiency of the spectrometer used, and the corrected data are then subjected to mathematical fitting to parametrize the intensity dependence on atomic number. The resulting algorithms can then be used to calculate any required standard intensity, including correction for the local detector efficiency. Generally in this procedure, the pure element standards data are measured only at a single energy, e.g., 20 keV, and an X-ray production expression such as eq 1is used to scale the intensity to another beam energy when required. Since the calculated standard intensities are actually connected to real measurements, the accuracy of fitted standards standardless analysis is expected to be better than that of first principles standardless analysis. Tests of the fitted standards procedure will be carried out in future work. Implications of SemiquantitativeEPMA Analysis. Sometimes the phrase “semiquantitativeanalysis” is used to describe standardless analysis. The implication of the term semiquantitative analysis as used in the electron probe X-ray microanalysis community seems to be that while the result of a semiquantitative analysis is a numerical concentration value, this value is somehow not subject to the same level of scrutiny as a fully quantitative analysis. There is potentially a very negative consequence of semiquantitative analysis. The analyst must be aware that any numerical value reported will be assumed to be absolutely true by subsequent users of the result unless a description of the overall uncertainty associated with the measurement accompanies the result. This statement of uncertainty must include not only the precision of the measurement, which is based upcn the counting statistics, but also a statement of the possible systematic error, which can be predicted from an error distribution such as that shown in Figure 1or 2. The important point is that the analyst must know which error distribution is appropriate. The credibility of electron probe X-ray microanalysis is based to a great extent on the error distribution shown in Figure 1,which was established more than 20 years ago. That level of analytical accuracy should be achievable by any analyst who is analyzing flat polished specimens with pure element or simple compound standards and calculated matrix corrections (e.g., ZAF or $@z) calculations). Users of electron probe microanalysis results have come to expect the level of performance implied by Figure 1. It harms the credibility of the electron probe X-ray microanalysis field when standardless analysis is performed and the implications of its much broader distribution of systematic errors are not made abundantly clear to the user of the analytical results. Standardless analysis results such as those given in Table 3 show such large errors as to be useless for determining even basic information or characteristics of the specimen, such as a compound formula. Unless an error distribution such as that shown in Figure 2 is attached
to a numerical result from a standardless analysis,perhaps a better strategy to utilize the results would be to broadly assign a name rather than a number to the concentration level, e.g., using arbitrary dehitions such as “major” (> 10 wt %) , “minor” (1-10 wt %),or “trace” (< 1wt %). Avoiding Unnecessary Risk. This situation presented by the use of standardless analysis is particularly unfortunate because it is so unnecessary. Standardless analysis is usually performed because it is quick only the spectrum of the unknown is needed, and the speed of computation is just a few seconds. However, the stability of modern energy-dispersive X-ray spectrometry systems is so high and the reproducibility of experimental conditions on the electron column instrument is so good that, with a careful quality assurance procedure in place to monitor the analytical conditions, it is possible to reproduce peak intensities over long periods of time while introducing negligible errors, less than f0.5%. This long-term stability means that standard spectra or intensities derived from those standard spectra can be measured, archived, and then called upon as needed for analysis of unknowns. The time penalty incurred in such an operation is actually quite modest when the greatly improved accuracy of the result is considered. The analyst must decide which error distribution, Figure 1 or Figure 2, brings greater credibility to the report of analysis and, by extension, to the analyst‘s reputation. Standardless analysis not accompanied by a meaningful statement of uncertainty is simply not worth the risk. CONCLUSIONS First principles standardless analysis is subject to large errors due to uncertainties in the physical parameters needed in the theoretical formulation. Analysis of a suite of 41 standard reference materials, research materials, candidate standards, and stoichiometric compounds results in a distribution of relative errors that ranges from -90% to +15w0. Errors of this magnitude can reduce the value of standardless quantitative results to the point of being worthless when basic questions are asked, such as the formula of a compound. The conventional approach to quantitative electron probe microanalysis, which involves the concurrent measurement of standards or the use of archival standard spectra coupled with careful attention to the establishment of consistent measurement conditions, results in a much higher value analytical product. ACKNOWLEDGMENT The authors wish to acknowledge the contributions to this work of the late Charles E. (“Chuck”) Fiori, the principal architect of Desktop Spectrum Analyzer. Chuck began the development of DTSA to provide a research software tool which would enable the type of detailed analytical study reported herein. We know that he would have been an enthusiastic participant in such uses. Received for review November 15, 1994. Accepted March 9, 1995.@ AC9411132 ~
~
~~
@Abstractpublished in Adunnce ACS Abstracts, May 1, 1995
Analytical Chetnistty, Vol. 67, No. 1 1 , June 1, 1995
1871
