Minimizing Errors in Electron Microprobe AnalysisEric Lifshin1* and Raynald Gauvin21New York State Corporate Center for Advanced Thin Film Technology, State University of New York at Albany, Albany, NY2Department of Mechanical Engineering, University de Sherbrooke, Quebec, Canada, J1K 2R1Abstract: Errors in quantitative electron microprobe analysis arise from many sources including those asso-ciated with sampling, specimen preparation, instrument operation, data collection, and analysis. The relativemagnitudes of some of these factors are assessed for a sample of NiAl used to demonstrate important concernsin the analysis of even a relatively simple system measured under standard operating conditions. The resultspresented are intended to serve more as a guideline for developing an analytical strategy than as a detailed errorpropagation model that includes all possible sources of variability and inaccuracy. The use of a variety of toolsto assess errors is demonstrated. It is also shown that, as sample characteristics depart from those under whichmany of the quantitative methods were developed, errors can increase significantly.Key words: precision, accuracy, quantitative analysis, energy-dispersive X-ray spectrometry, crystal diffractionspectrometry, Monte Carlo calculations, X-ray counting statisticsINTRODUCTIONQuantitative electron microprobe analysis is an analyticalprocedure in which the intensity of electron excited X-raysis measured for specific elements in a specimen, and thatintensity data is then used to determine chemical compo-sition. Castaing first described the basic principles of mi-croprobe analysis 50 years ago in his PhD thesis (Castaing,1951), and although his quantitative model has been im-proved upon since then, the basic concepts remain the sametoday. Detailed descriptions of how to collect and analyzedata by a variety of approaches can be found in a numberof texts (Goldstein et al., 1992; Reed, 1997). Selected com-pounds and alloys have been used to study the accuracy ofdifferent models for quantitative electron microprobeanalysis. Comparisons between these models and the resultsobtained by established classical analytical procedures showthat, in some cases, accuracy of 2% relative or better ispossible (Pouchou and Pichoir, 1991; Poole, 1968).The precision of the measurements has been given farless scrutiny, however, and estimates are often based solelyon X-ray counting statistics. Even those estimates rarelyused propagation of error calculations to link the uncer-tainty of all of the X-ray measurements, including peaks andbackgrounds with the uncertainty in the final composition.There are also a number of other factors that can effect thevariability of quantitative analysis, and they are summarizedin the process map given in Figure 1. The first step is sampleselection. Sample selection is usually based on a desire toanswer a specific question. For example:• What have I made (as in the case of the discovery of anew material)?• What changes have occurred in an established manufac-Received February 14, 2000; accepted September 25, 2000.*Corresponding author, at University at Albany, State University of New York,CESTM, 251 Fuller Road, Albany, NY 12203.Microsc. Microanal. 7, 168–177, 2001DOI: 10.1007/s100050010084Microscopy ANDMicroanalysis© MICROSCOPY SOCIETY OF AMERICA 2001turing process leading to a change in the properties of afinished product (quality control)?• Why has something failed?When you are trying to explain the behavior of a criti-cal component of a system, it is important to select a samplethat tests some hypothesis. As an example, suppose youbelieve that a particle found in a pit in a fracture surface wassuspected of be responsible for the initiation of that frac-ture. An analysis would be made of the particle to deter-mine if it is some foreign material accidentally introducedinto the casting operation that formed the finished compo-nent or the result of some departure from standard pro-cessing conditions. Also, knowing what to look for and whyyou are looking for it, at the beginning of an analysis, cansave a lot of time, particularly since sometimes differencesare found between samples, or between samples and mate-rial specifications, that may have no bearing on the problemto be solved.Another important consideration is that of sample ho-mogeneity. Electron microprobe analysis typically samples avolume of material of a few cubic microns. Since one cubicmicron represents only 1 part in 1012of a cubic centimeter,a single reading will not tell you whether the composition ofa large region meets some average composition specifica-tion. Multiple measurements of a single point are necessaryto establish the composition mean and variance of thatpoint, and multiple point measurements are required toestablish point-to-point differences (the degree of homoge-neity). When an analyst is handed a sample with little in-formation other than a request for the amounts of specificelements present, it is obvious that the final results will onlybe of value if a rigorous sample selection process was used.What follows next is a description of how to look at thevariability of the remaining steps in the process map givenin Figure 1. The authors are not aware of any publishedstudies that reflect an exhaustive set of measurements of thetype to be shown that lead to true confidence intervals inconnection with any published microanalysis results. Asyou will see, there are just too many steps in the overallanalytical process, and to determine all of the sources ofvariability would generally be too expensive and time con-suming to ever become routine. Nevertheless, the approachgiven can help establish some guidelines so that the analystcan select experimental conditions that will minimize er-rors, although not always quantify them. In many of theexamples given, data or calculations are for a standard ofNiAl specially prepared to be very close to a one-to-oneatomic ratio, as determined independently by wet chemicalanalysis, and determined to be homogeneous by micro-probe analysis. This standard was selected because nickel-based superalloys are technologically very important, andalso this system has significant atomic number and absorp-tion corrections when doing quantitative analysis.SAMPLE PREPARATIONQuantitative analysis has been traditionally performed onpolished samples to eliminate the influence of topographiceffects. These effects arise from the fact that
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