UW-Madison G 777 - Uncertainty in Quantitative Electron Probe Microanalysis

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Volume 107, Number 6, November–December 2002Journal of Research of the National Institute of Standards and Technology[J. Res. Natl. Inst. Stand. Technol. 107, 483–485 (2002)]Uncertainty in Quantitative Electron ProbeMicroanalysisVolume 107 Number 6 November–December 2002Kurt F. J. HeinrichNational Institute of Standards andTechnology,Gaithersburg, MD 10899-0001Quantitative electron probe analysis is basedon models based on the physics or x-raygeneration, empirically adjusted to theanalyses of specimens of known compo-sition. Their accuracy can be estimated byapplying them to a set of specimens ofpresumably well-known composition.Key words: absorption coefficients; accu-racy; microanalysis; models; x-ray ab-sorption; x-ray spectrometry.Accepted: August 22, 2002Available online: http://www.nist.gov/jres1. Correction ProceduresThe doctoral thesis of Raymond Castaing [1] containsthe outlines of a procedure of quantitative electron probemicroanalysis (EPMA) analysis on which most subse-quent methods are modeled. His choices were influ-enced by the availability of instrumentation and data.The instrument he used had crystal spectrometers ofunnecessarily high wavelength resolution and inherentmechanical instability. His Geiger detectors had a veryhigh dead time (in the order of ms) so that no highintensities could be accurately measured. The beam sta-bility was not comparable to present standards, the vac-uum was usually poor, and there were no diffractingcrystals available for wavelengths below 0.1 nm. Theefficiency of his instrument was relatively low so that hewas forced to use acceleration voltages as high as 29 kVfor routine analysis. There was at this time no energy-dispersive equipment available, and, last but not least,there existed no computers that would have permittedextensive on-line calculations or storage of parameters.Since it was practically impossible to compare thegenerated intensities of x-ray emissions at differentwavelengths, Castaing chose to compare the measuredintensities of the same x-ray line from the specimen anda standard of known composition determined sequen-tially. [With modern energy spectrometers in which theefficiency change from one element to the next can beestimated accurately, quantitation by comparison of theintensity from several lines (“standardless analysis”) isnow feasible]. Usually, pure elements were used as stan-dards where possible.Castaing recognized the existence of absorption ef-fects in primary emission, of fluorescence due to char-acteristic lines, and of matrix effects (atomic numbereffects) in the primary emission. Hence he proposedthree “corrections” to the measured intensity: for ab-sorption, atomic number effect, and fluorescence (fromcharacteristic lines only). It was impossible to predictquantitatively the intensity of primary emission or thesignal losses due to the absorption of x-rays within thespecimen. Only the relative contribution of fluorescencedue to characteristic lines could be calculated from firstprinciples. Fluorescence by the continuum was ignored,as were at first the effects of electron backscatter, andmany parameters of importance in quantitative analysis,particularly the x-ray absorption coefficients that werenot well known.The most important effect to be accounted for wasthat of losses due to x-ray absorption, particularly sig-nificant because of the low take-off angle and the use ofhigh acceleration voltages. In his thesis Castaing tried to483Volume 107, Number 6, November–December 2002Journal of Research of the National Institute of Standards and Technologyobtain information concerning the depth distribution ofprimary x-ray generation, which must be known if theabsorption losses are to be calculated. Later he contin-ued this effort with the aid of special targets with thintracer layers buried at varied depth [2,3]. Complemen-tary information on this subject was obtained by Green[4] who measured the intensity of x-ray emission as afunction of the x-ray emergence angle. Based on theseobservations, Philibert first proposed a generalizedmodel for the calculation of the absorption losses ofprimary emission [5]. Further refinements of the“absorption correction” were later proposed by variousauthors [6]. The calculation required, however, a reason-ably accurate knowledge of the x-ray absorption coeffi-cients involved. This problem was tackled by experimen-tal determinations as well as by the generalized modelsfor the calculation of these coefficients [7].The accuracy of these models and of the analysesperformed with their aid is thus limited by the followingfactors:1. X-ray intensity measurement uncertainties due tocounting statistics, drift, dead-time corrections, andthose relating to line and band widths.2. Chemical shifts.3. Uncertainties in physical parameters used in the cor-rection procedure, such as mass absor ption coeffi-cients.4. Limitations in the amount and type of compositestandards used for the calibration of such procedures.5. Uncertainties in chemical analysis, inhomogeneity ofstandards and specimens, and in the assumed stoi-chiometry of the standards.6. Effects of standard preparation, surface conditions,poor conductivity, and specimen decompositionupon irradiation.Mechanisms of x-ray generation of less importance,such as fluorescence due to the continuum, and excita-tion by high-energy secondary electrons [8] are usuallyignored in the procedure. They may have been incorpo-rated inadvertently in one of the classical corrections ofthe ZAF procedure. In that case, adding a separate cal-culation for them may actually degrade the accuracy ofthe procedure.In view of the limited knowledge of the laws govern-ing the generation of primary x-rays in multi-elementtargets, any “correction method” is, or should be, basedon generalizing the results of analyses of specimens ofknown composition. The comparison of competing pro-cedures is also done on the basis of applying them tomeasurements on sets of standards of “known” compo-sition. Ideally one should evaluate a method with a set ofstandards that were not used for its creation, but this isvirtually impossible, given the scarcity of measurementson reliable standards. The evaluation of the residualerrors was usually done for the combined effects ofatomic number, absorption and fluorescence, but obvi-ously the tests for each of the corrections should be doneseparately for each effect. For instance, the inclusion ina test for


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