# ASTM E1361-02 (Reapproved 2014)e1

Designation: E1361 − 02 (Reapproved 2014)´1Standard Guide forCorrection of Interelement Effects in X-Ray SpectrometricAnalysis1This standard is issued under the fixed designation E1361; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.ε1NOTE—Editorial corrections were made throughout in April 2015.1. Scope1.1 This guide is an introduction to mathematical proce-dures for correction of interelement (matrix) effects in quanti-tative X-ray spectrometric analysis.1.1.1 The procedures described correct only for the interele-ment effect(s) arising from a homogeneous chemical compo-sition of the specimen. Effects related to either particle size, ormineralogical or metallurgical phases in a specimen are nottreated.1.1.2 These procedures apply to both wavelength andenergy-dispersive X-ray spectrometry where the specimen isconsidered to be infinitely thick, flat, and homogeneous withrespect to the depth of penetration of the exciting X-rays (1).21.2 This document is not intended to be a comprehensivetreatment of the many different techniques employed to com-pensate for interelement effects. Consult Refs (2-5) for descrip-tions of other commonly used techniques such as standardaddition, internal standardization, etc.2. Referenced Documents2.1 ASTM Standards:3E135 Terminology Relating to Analytical Chemistry forMetals, Ores, and Related Materials3. Terminology3.1 For definitions of terms used in this guide, refer toTerminology E135.3.2 Definitions of Terms Specific to This Standard:3.2.1 absorption edge—the maximum wavelength (mini-mum X-ray photon energy) that can expel an electron from agiven level in an atom of a given element.3.2.2 analyte—an element in the specimen to be determinedby measurement.3.2.3 characteristic radiation—X radiation produced by anelement in the specimen as a result of electron transitionsbetween different atomic shells.3.2.4 coherent (Rayleigh) scatter—the emission of energyfrom a loosely bound electron that has undergone collisionwith an incident X-ray photon and has been caused to vibrate.The vibration is at the same frequency as the incident photonand the photon loses no energy. (See 3.2.7.)3.2.5 dead-time—time interval during which the X-ray de-tection system, after having responded to an incident photon,cannot respond properly to a successive incident photon.3.2.6 fluorescence yield—a ratio of the number of photonsof all X-ray lines in a particular series divided by the numberof shell vacancies originally produced.3.2.7 incoherent (Compton) scatter—the emission of energyfrom a loosely bound electron that has undergone collisionwith an incident photon and the electron has recoiled under theimpact, carrying away some of the energy of the photon.3.2.8 influence coeffıcient—designated by α (β, γ, δ andother Greek letters are also used in certain mathematicalmodels), a correction factor for converting apparent massfractions to actual mass fractions in a specimen. Other termscommonly used are alpha coefficient and interelement effectcoefficient.3.2.9 mass absorption coeffıcient—designated by µ, anatomic property of each element which expresses the X-rayabsorption per unit mass per unit area, cm2/g.3.2.10 primary absorption—absorption of incident X-raysby the specimen. The extent of primary absorption depends onthe composition of the specimen and the X-ray source primaryspectral distribution.3.2.11 primary spectral distribution—the output X-rayspectral distribution usually from an X-ray tube. The X-ray1This guide is under the jurisdiction of ASTM Committee E01 on AnalyticalChemistry for Metals, Ores, and Related Materials and is the direct responsibility ofSubcommittee E01.20 on Fundamental Practices.Current edition approved Nov. 15, 2014. Published April 2015. Originallyapproved in 1990. Last previous edition approved in 2007 as E1361 – 02 (2007).DOI: 10.1520/E1361-02R14E01.2The boldface numbers in parentheses refer to the list of references at the end ofthis standard.3For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1continuum is usually expressed in units of absolute intensityper unit wavelength per electron per unit solid angle.3.2.12 relative intensity—the ratio of an analyte X-ray lineintensity measured from the specimen to that of the pureanalyte element. It is sometimes expressed relative to theanalyte element in a multi-component reference material.3.2.13 secondary absorption—the absorption of the charac-teristic X radiation produced in the specimen by all elements inthe specimen.3.2.14 secondary fluorescence (enhancement)—the genera-tion of X-rays from the analyte caused by characteristic X-raysfrom other elements in the sample whose energies are greaterthan the absorption edge of the analyte.3.2.15 X-ray source—an excitation source which producesX-rays such as an X-ray tube, radioactive isotope, or secondarytarget emitter.4. Significance and Use4.1 Accuracy in quantitative X-ray spectrometric analysisdepends upon adequate accounting for interelement effectseither through sample preparation or through mathematicalcorrection procedures, or both. This guide is intended to serveas an introduction to users of X-ray fluorescence correctionmethods. For this reason, only selected mathematical modelsfor correcting interelement effects are presented. The reader isreferred to several texts for a more comprehensive treatment ofthe subject (2-7).5. Description of Interelement Effects5.1 Matrix effects in X-ray spectrometry are caused byabsorption and enhancement of X-rays in the specimen. Pri-mary absorption occurs as the specimen absorbs the X -raysfrom the source. The extent of primary absorption depends onthe composition of the specimen, the output energy distributionof the exciting source, such as an X-ray tube, and the geometryof the spectrometer. Secondary absorption occurs as the char-acteristic X radiation produced in the specimen is absorbed bythe elements in the specimen. When matrix elements emitcharacteristic X-ray lines that lie on the short-wavelength (highenergy) side of the analyte absorption edge, the analyte can beexcited to emit characteristic radiation in addition to thatexcited directly by the X-ray source. This is called secondaryfluorescence or enhancement.5.2 These effects can be represented as shown in Fig. 1using binary alloys as examples. When matrix effects are eithernegligible or constant, Curve A in Fig. 1 would be obtained.That is, a plot of analyte relative intensity (corrected forbackground, dead-time, etc.) versus analyte mass fractionwould yield a straight line over a wide mass fraction range andwould be independent of the other elements present in thespecimen (Note 1). Linear relationships often exist in thinspecimens, or in cases where the matrix composition isconstant. Low alloy steels, for example, exhibit constantinterelement effects in that the mass fractions of the minorconstituents vary, but the major constituent, iron, remainsrelatively constant. In general, Curve B is obtained when theabsorption by the matrix elements in the specimen of either theprimary X-rays or analyte characteristic X-rays, or both, isgreater than the absorption by the analyte alone. This second-ary absorption effect is often referred to simply as absorption.The magnitude of the displacement of Curve B from Curve Ain Fig. 1, for example, is typical of the strong absorption ofnickel K-L2,3(Kα) X-rays in Fe-Ni alloys. Curve C representsthe general case where the matrix elements in the specimenabsorb the primary X-rays or characteristic X-rays, or both, toa lesser degree than the analyte alone. This type of secondaryabsorption is often referred to as negative absorption. Themagnitude of the displacement of Curve C from Curve A inFig. 1, for example, is typical of alloys in which the atomicnumber of the matrix element (for example, aluminum) ismuch lower than the analyte (for example, nickel). Curve D inFig. 1 illustrates an enhancement effect as defined previously,and represents in this case the enhancement of iron K-L2,3(Kα)X-rays by nickel K-L2,3(Kα) X-rays in Fe-Ni binaries.NOTE 1—The relative intensity rather than absolute intensity of theanalyte will be used in this document for purposes of convenience. It is notmeant to imply that measurement of the pure element is required, unlessunder special circumstances as described in 9.1.6. General Comments Concerning InterelementCorrection Procedures6.1 Historically, the development of mathematical methodsfor correction of interelement effects has evolved into twoapproaches, which are currently employed in quantitativeX-ray analysis. When the field of X-ray spectrometric analysiswas new, researchers proposed mathematical expressions,which required prior knowledge of corrective factors calledinfluence coefficients or alphas prior to analysis of the speci-mens. These factors were usually determined experimentallyby regression analysis using reference materials, and for thisCurve A—Linear calibration curve.Curve B—Absorption of analyte by matrix. For example, RNiversus CNiinNi-Fe binary alloys where nickel is the analyte element and iron is the matrixelement.Curve C—Negative absorption of analyte by matrix. For example, RNiversusCNiin Ni-Al alloys where nickel is the analyte element and aluminum is thematrix element.Curve D—Enhancement of analyte by matrix. For example, RFeversus CFeinFe-Ni alloys where iron is the analyte element and nickel is the matrix ele-ment.FIG. 1 Interelement Effects in X-Ray Fluorescence AnalysisE1361 − 02 (2014)´12reason are typically referred to as empirical or semi-empiricalprocedures (see 7.1.3, 7.2, and 7.8). During the late 1960s,another approach was introduced which involved the calcula-tion of interelement corrections directly from first principlesexpressions such as those given in Section 8. First principlesexpressions are derived from basic physical principles andcontain physical constants and parameters, for example, whichinclude absorption coefficients, fluorescence yields, primaryspectral distributions, and spectrometer geometry. Fundamen-tal parameters method is a term commonly used to describeinterelement correction procedures based on first principleequations (see Section 8).6.2 In recent years, several researchers have proposedfundamental parameters methods to correct measured X-rayintensities directly for interelement effects or, alternatively,proposed mathematical expressions in which influence coeffi-cients are calculated from first principles (see Sections 7 and8). Such influence coefficient expressions are referred to asfundamental influence coefficient methods.7. Influence Coefficient Correction Procedures7.1 The Lachance-Traill Equation:7.1.1 For the purposes of this guide, it is instructive to beginwith one of the simplest, yet fundamental, correction modelswithin certain limits. Referring to Fig. 1, either Curve B or C(that is, absorption only) can be represented mathematically bya hyperbolic expression such as the Lachance-Traill equation(LT) (8). For a binary specimen containing elements i and j, theLT equation is:Ci5 Ri~11αijLTCj! (1)where:Ci= mass fraction of analyte i,Cj= mass fraction of matrix element j,Ri= the analyte intensity in the specimen expressed as aratio to the pure analyte element, andαijLT= the influence coefficient, a constant.The subscript i denotes the analyte and the subscript jdenotes the matrix element. The subscript in αijLTdenotes theinfluence of matrix element j on the analyte i in the binaryspecimen. The LT superscript denotes that the influence coef-ficient is that coefficient in the LT equation. The magnitude ofthe displacement of Curves B and C from Curve A isrepresented by αijLTwhich takes on positive values for B typecurves and negative values for C type curves.7.1.2 The general form of the LT equation when extended tomulticomponent specimens is:Ci5 Ri~11(αijLTCj! (2)For a ternary system, for example, containing elements i, jand k, three equations can be written wherein each of theelements are considered analytes in turn:Ci5 Ri~11αijLTCj1αikLTCk! (3)Cj5 Rj~11αjiLTCi1αjkLTCk! (4)Ck5 Rk~11αkiLTCi1αkjLTCj! (5)Therefore, six alpha coefficients are required to solve for themass fractions Ci, Cj, and Ck(see Appendix X1). Once theinfluence coefficients are determined, Eq 3-5 can be solved forthe unknown mass fractions with a computer using iterativetechniques (see Appendix X2).7.1.3 Determination of Influence (Alpha) Coeffıcients fromRegression Analysis—Alpha coefficients can be obtained ex-perimentally using regression analysis of reference materials inwhich the elements to be measured are known and cover abroad mass fraction range. An example of this method is givenin X1.1.1 of Appendix X1. Eq 1 can be rewritten for a binaryspecimen in the form:~Ci/Ri! 2 1 5 αijRCj(6)where: αijR= influence coefficient obtained by regressionanalysis. A plot of (Ci/Ri) − 1 versus Cjgives a straight linewith slope αijR(see Fig. X1.1 of Appendix X1). Note that thesuperscript LT is replaced by R because alphas obtained byregression analysis of multi-component reference materials donot generally have the same values as αijLT(as determined fromfirst principles calculations). This does not present a problemgenerally in the results of analysis if the reference materialsbracket each of the analyte elements over the mass fractionranges that exist in the specimen(s). Best results are obtainedonly when the specimens and reference materials are of thesame type. The weakness of the multiple-regression techniqueas applied in X-ray analysis is that the accuracy of the influencecoefficients obtained is not known unless verified, for example,from first principles calculations. As the number of compo-nents in a specimen increases, this becomes more of a problem.Results of analysis should be checked for accuracy by incor-porating reference materials in the analysis scheme and treatingthem as unknown specimens. Comparison of the known valueswith those found by analysis should give acceptableagreement, if the influence coefficients are sufficiently accu-rate. This test is valid only when reference materials analyzedas unknowns are not included in the set of reference materialsfrom which the influence coefficients were obtained.7.1.4 Determination of Influence Coeffıcients from FirstPrinciples—Influence coefficients can be calculated from fun-damental parameters expressions (see X1.1.3 of Appendix X1).This is usually done by arbitrarily considering the composi