Electron Probe Microanalysis EPMAMain PointRaw data needs correctionAbsorption and FluorescenceSlide 6K ratiosCastaing’s First Approximation...close but not exactSlide 10Z A FStopping Power CorrectionBackscatter CorrectionZ correctionBeers LawMass Absorption CoefficientsSlide 17AbsorptionSlide 19Slide 20f(rz) [phi-rho-z] CurvesTracer MethodFluorescence CorrectionSlide 24Next Generation (>1980): Phi-Rho-Z modelsNext Generation (>mid 1980s): Phi-Rho-Z modelsHow do EPMA theoriticians ‘prove’ their matrix correction is “correct”?How do EPMA theoriticans ‘prove’ their matrix correction is “correct”?PowerPoint PresentationFluorescence ProblemsFluorescence across boundariesAn SF real storySecondary Fluorescence CorrectionMatrix Correction ProgramsZAF optionsAlpha correctionZiebold and Ogilvie - binary a-factorsZiebold and Ogilvie - ternary a-factorsBence-Albee -multicomponent systemsEvaluating matrix correctionsBefore we forget....Slide 42Slide 43Slide 44Slide 45Impact of unaccounted for oxygenPhysical Parameters Needed“State of EPMA parameters”Slide 49“So what do we do?”Electron Probe MicroanalysisEPMA UW-Madison Geoscience 777Quantitative AnalysisandMatrix CorrectionsRevised 5/1/2014Main PointUW- Madison Geology 777•For a hypothetical compound that is 50 wt% of Element A and 50 wt% Element B, the x-ray intensities of Element A and Element B will never (except in rare isolated cases) be some simple ratio equal to the composition!•Therefore some corrections need to be applied•This is the “matrix correction” (the matrix is the matrix of elements in the material)•It can be some empirical correction, or a highly sophisticated physically model (or something in between)Raw data needs correctionThis plot of Fe Ka X-ray intensity data demonstrates why we must correct for matrix effects. Here 3 Fe alloys show distinct variations. Consider the 3 alloys at 40% Fe. X-ray intensity of the Fe-Ni alloy is ~5% higher than for the Fe-Mn, and the Fe-Cr is ~5% lower than the Fe-Mn. Thus, we cannot use the raw X-ray intensity to determine the compositions of the Fe-Ni and Fe-Cr alloys. (Note the hyperbolic functionality of the upper and lower curves)UW- Madison Geology 777Absorption and Fluorescence• Note that the Fe-Mn alloys plot along a 1:1 line, and so is a good reference.• The Fe-Ni alloys plot above the 1:1 line (have apparently higher Fe than they really do), because the Ni atoms present produce X-rays of 7.278 keV, which is greater than the Fe K edge of 7.111 keV.Thus, additional Fe Ka are produced by this secondary fluorescence.• The Fe-Cr alloys plot below the 1:1 line (have apparently lower Fe than they really do), because the Fe atoms present produce X-rays of 6.404 keV, which is greater than the Cr K edge of 5.989 keV. Thus, Cr Ka is increased, with Fe Ka are “used up” in this secondary fluorescence process.UW- Madison Geology 777Theoretical approach to corrections UW- Madison Geology 777*Merlet and Llovet….One can write an equation showing the relationship between x-ray intensity IA and elemental concentration CA, using fundamental physical parameters*:Rearranging the equation and solving for CA is not that easy! So the material scientists, chemists and geologists who took up the electron probe as a crucial tool came up with some alternatives…Heinrich* summarizes the 4 actual types of models used for matrix corrections in EPMA:1.Empirical: simplest, based on known binary experimental data;2.ZAF: 1st generalized algebraic procedure; assumes a linear relation between concentration and x-ray intensity;3.Phi-rho-Z: based upon depth profile (tracer) experiments;4.Monte Carlo: based upon statistical probabilities of electron-sample interactions, particularly for unusual specimen geometries.Actual approaches to corrections UW- Madison Geology 777*Heinrich, 1991, Strategies of electron probe data reduction, in Electron Probe Quantitation, Ed. Heinrich and Newbury, Plenum, New York, 9-18.K ratiosRecall Castaing’s approach to quantitative analysis, where specimen intensities are ratioed to standard intensities: where K is the “K ratio” for element i, I is the X-ray intensity of the phase and subscript i is the element.With the counts acquired on BOTH unknowns and standards on the same instrument, under the same operating conditions, we assume that many physical parameters of the machine that would be needed in a rigorous physical model cancel each other out (same in numerator and denominator).Ki=IiunkIistdUW- Madison Geology 777This is for ONE element. There will be 9 K ratios if there are 9 elements in the unknown sample.Castaing’s First ApproximationCastaing’ s “first approximation” follows this approach. The composition C of element i of the unknown is the K ratio times the composition of the standard. In the simple case where the standard is the pure element, then, the fraction K is roughly equal to the fraction of the element in the unknown.In the ‘simplest’ case where pure element standards can be used, Cistd = 1 and drops out.Ciunk»IiunkIistdCistd=KiCistdUW- Madison Geology 777...close but not exactHowever, it was immediately obvious to Castaing that the raw data had to be corrected in order to achieve the full potential of this new approach to quantitative microanalysis.The next two slides give a graphic demonstration of the need for development of a correction procedure.Ciunk»IiunkIistdCistd=KiCistdUW- Madison Geology 777In his 1951 Ph.D. thesis, Castaing laid out two of the approaches that could be used to apply matrix corrections to the data, using his brilliant construct of the K-ratio:• an empirical ‘alpha factor’ correction for binary compounds, where each pair of elements has a pair of constant -factors representing the effect that each element has upon the other for measured X-ray intensity, and• a more rigorous physical model taking into account absorption and fluorescence in the specimen. This later approach also now includes atomic number effects* and became known as the ZAF correction.• This ZAF has been surplanted in many/most EPMA labs by the “phi-rho-Z” matrix correction (it can be a little confusing, discussed later, as the phrase is used in another context)Two approaches to corrections UW- Madison Geology 777* Atomic number effect only recognized in 1961-3 (Scott and Ranzetta; Kirianenko; Archard and Mulvey), in samples with widely different atomic numbersZ A
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