1、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,
2、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.1NOTEEditorial corrections were made throughout in April 2015.1. Scope1.1 This guide is an introduction to mathematica
3、l 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, ormineral
4、ogical 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 Th
5、is 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
6、 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 edgethe maximum wavelength (mini-mum X-ray p
7、hoton energy) that can expel an electron from agiven level in an atom of a given element.3.2.2 analytean element in the specimen to be determinedby measurement.3.2.3 characteristic radiationX radiation produced by anelement in the specimen as a result of electron transitionsbetween different atomic
8、shells.3.2.4 coherent (Rayleigh) scatterthe 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-tim
9、etime 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 yielda ratio of the number of photonsof all X-ray lines in a particular series divided by the numberof shell vacancies orig
10、inally produced.3.2.7 incoherent (Compton) scatterthe 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 coeffcientdesignated by (, , andothe
11、r 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 coeffcientdesignated by , anatomic p
12、roperty of each element which expresses the X-rayabsorption per unit mass per unit area, cm2/g.3.2.10 primary absorptionabsorption 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 pr
13、imary spectral distributionthe 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 Pract
14、ices.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 st
15、andards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken,
16、 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 intensitythe ratio of an analyte X-ray lineintensity measured from the specimen to that of the pureanalyte element. It is sometimes express
17、ed relative to theanalyte element in a multi-component reference material.3.2.13 secondary absorptionthe 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
18、by characteristic X-raysfrom other elements in the sample whose energies are greaterthan the absorption edge of the analyte.3.2.15 X-ray sourcean excitation source which producesX-rays such as an X-ray tube, radioactive isotope, or secondarytarget emitter.4. Significance and Use4.1 Accuracy in quant
19、itative 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, o
20、nly 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
21、-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. Secondar
22、y 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 charact
23、eristic 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 obta
24、ined.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 thi
25、nspecimens, 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 theabsorpti
26、on 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
27、 Fig. 1, for example, is typical of the strong absorption ofnickel K-L2,3(K) 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 seconda
28、ryabsorption 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
29、 illustrates an enhancement effect as defined previously,and represents in this case the enhancement of iron K-L2,3(K)X-rays by nickel K-L2,3(K) X-rays in Fe-Ni binaries.NOTE 1The relative intensity rather than absolute intensity of theanalyte will be used in this document for purposes of convenienc
30、e. 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 evolv
31、ed 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
32、 speci-mens. These factors were usually determined experimentallyby regression analysis using reference materials, and for thisCurve ALinear calibration curve.Curve BAbsorption of analyte by matrix. For example, RNiversus CNiinNi-Fe binary alloys where nickel is the analyte element and iron is the m
33、atrixelement.Curve CNegative absorption of analyte by matrix. For example, RNiversusCNiin Ni-Al alloys where nickel is the analyte element and aluminum is thematrix element.Curve DEnhancement of analyte by matrix. For example, RFeversus CFeinFe-Ni alloys where iron is the analyte element and nickel
34、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
35、 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 distri
36、butions, 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-rayint
37、ensities 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
38、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 m
39、athematically bya hyperbolic expression such as the Lachance-Traill equation(LT) (8). For a binary specimen containing elements i and j, theLT equation is:Ci5 Ri11ijLTCj! (1)where:Ci= mass fraction of analyte i,Cj= mass fraction of matrix element j,Ri= the analyte intensity in the specimen expressed
40、 as aratio to the pure analyte element, andijLT= the influence coefficient, a constant.The subscript i denotes the analyte and the subscript jdenotes the matrix element. The subscript in ijLTdenotes theinfluence of matrix element j on the analyte i in the binaryspecimen. The LT superscript denotes t
41、hat 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 ijLTwhich 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 to
42、multicomponent specimens is:Ci5 Ri11(ijLTCj! (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 Ri11ijLTCj1ikLTCk! (3)Cj5 Rj11jiLTCi1jkLTCk! (4)Ck5 Rk11kiLTCi1kjLTCj! (5)Therefore, six al
43、pha 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) Coeffci
44、ents fromRegression AnalysisAlpha 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
45、binaryspecimen in the form:Ci/Ri! 2 1 5 ijRCj(6)where: ijR= influence coefficient obtained by regressionanalysis. A plot of (Ci/Ri) 1 versus Cjgives a straight linewith slope ijR(see Fig. X1.1 of Appendix X1). Note that thesuperscript LT is replaced by R because alphas obtained byregression analysis
46、 of multi-component reference materials donot generally have the same values as ijLT(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
47、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,f
48、rom 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 value
49、swith 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 Coeffcients from FirstPrinciplesInfluence 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
