1、Designation: E 1361 02 (Reapproved 2007)Standard Guide forCorrection of Interelement Effects in X-Ray SpectrometricAnalysis1This standard is issued under the fixed designation E 1361; 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 (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This guide is an introduction to mathematical proce-dures for correction of interelement (matrix) effect
3、s in quanti-tative X-ray spectrometric analysis.1.1.1 The procedures described correct only for the inter-element effect(s) arising from a homogeneous chemical com-position of the specimen. Effects related to either particle size,or mineralogical or metallurgical phases in a specimen are nottreated.
4、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 o
5、f 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:3E 135 Terminology Relating to Analytical Chemist
6、ry forMetals, Ores, and Related Materials3. Terminology3.1 For definitions of terms used in this guide, refer toTerminology E 135.3.2 Definitions of Terms Specific to This Standard:3.2.1 absorption edgethe maximum wavelength (mini-mum X-ray photon energy) that can expel an electron from agiven level
7、 in an atom of a given element.3.2.2 analytean element in the specimen whose concen-tration is to be determined.3.2.3 characteristic radiationX radiation produced by anelement in the specimen as a result of electron transitionsbetween different atomic shells.3.2.4 coherent (Rayleigh) scatterthe emis
8、sion 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-timetime interval during which the X-raydetection s
9、ystem, 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 originally produced.3.2.7 incoherent (Compton) scatter
10、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 coeffcientdesignated by a (b, g, d andother Greek letters are also used in certain mat
11、hematicalmodels), 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 property of each element which expresses the
12、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 primary spectral distributionthe output X-rays
13、pectral distribution usually from an X-ray tube. The X-raycontinuum 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 elem
14、ent. It is sometimes expressed relative to theanalyte element in a multi-component reference material.1This 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 Practi
15、ces.Current edition approved Jan. 15, 2007. Published January 2007. Originallyapproved in 1990. Last previous edition approved in 2002 as E 1361 02.2The boldface numbers in parentheses refer to the list of references at the end ofthis standard.3For referenced ASTM standards, visit the ASTM website,
16、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.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.
17、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 by characteristic X raysfrom other elements in the sample whose energies are
18、 greaterthan the absorption edge of the analyte.3.2.15 mass fractiona concentration unit expressed as aratio of the mass of analyte to the total mass.3.2.16 X-ray sourcean excitation source which producesX rays such as an X-ray tube, radioactive isotope, or secondarytarget emitter.4. Significance an
19、d 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 correctionm
20、ethods. 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 byabsor
21、ption and enhancement of X rays in the specimen.Primary 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 th
22、e 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 b
23、eexcited 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
24、 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 relation
25、ships 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 o
26、btained 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 o
27、f Curve B from Curve Ain Fig. 1, for example, is typical of the strong absorption ofnickel nickel K-L2,3(Ka) X rays in Fe-Ni alloys. Curve Crepresents the general case where the matrix elements in thespecimen absorb the primary X rays or characteristic X rays, orboth, to a lesser degree than the ana
28、lyte alone. This type ofsecondary absorption is often referred to as negative absorp-tion. The magnitude of the displacement of Curve C fromCurveAin Fig. 1, for example, is typical of alloys in which theatomic number of the matrix element (for example, aluminum)is much lower than the analyte (for ex
29、ample, nickel). Curve Din Fig. 1 illustrates an enhancement effect as defined previ-ously, and represents in this case the enhancement of ironK-L2,3(Ka) X rays by nickel K-L2,3(Ka) X rays in Fe-Nibinaries.NOTE 1The relative intensity rather than absolute intensity of theanalyte will be used in this
30、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 correctio
31、n 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
32、 or alphas prior to analysis of the speci-mens. These factors were usually determined experimentallyby regression analysis using reference materials, and for thisreason are typically referred to as empirical or semi-empiricalprocedures (see 7.1.3, 7.2, and 7.8). During the late 1960s,another approac
33、h 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 andCurve ALinear calibration curve.Curve BAbsorption of analyte by matrix. F
34、or example, RNiversus CNiinNi-Fe binary alloys where nickel is the analyte element and iron is the matrixelement.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 analy
35、te 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 AnalysisE 1361 02 (2007)2contain physical constants and parameters, for example, whichinclude absorption coefficients, fluoresc
36、ence 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 workers have proposed funda-mental parameters met
37、hods to correct measured X-ray inten-sities directly for interelement effects or, alternatively, pro-posed mathematical expressions in which influence coefficientsare calculated from first principles (see Sections 7 and 8). Suchinfluence coefficient expressions are referred to as fundamentalinfluenc
38、e 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, ab
39、sorption 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 Ri1 1aijLTCj! (1)where:Ci= mass fraction of analyte i,Cj= mass fraction of matrix element j,Ri= the analyt
40、e intensity in the specimen expressed asa ratio to the pure analyte element, andaijLT= the influence coefficient, a constant.The subscript i denotes the analyte and the subscript jdenotes the matrix element. The subscript in aijLTdenotes theinfluence of matrix element j on the analyte i in the binar
41、yspecimen. 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 aijLTwhich takes on positive values for B typecurves and negative values for C type curves.7.1.2 The general
42、form of the LT equation when extended tomulticomponent specimens is:Ci5 Ri1 1 ( aijLTCj! (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 Ri1 1aijLTCj1aikLTCk! (3)Cj5 Rj1 1ajiLTCi1ajkLT
43、Ck! (4)Ck5 Rk1 1akiLTCi1akjLTCj! (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
44、 X2).7.1.3 Determination of Influence (Alpha) Coeffcients 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 giveni
45、n X1.1.1 of Appendix X1. Eq 1 can be rewritten for a binaryspecimen in the form:Ci/Ri! 2 1 5aijRCj(6)where: aijR= influence coefficient obtained by regressionanalysis. A plot of (Ci/Ri) 1 versus Cjgives a straight linewith slope aijR(see Fig. X1.1 of Appendix X1). Note that thesuperscript LT is repl
46、aced by R because alphas obtained byregression analysis of multi-component reference materials donot generally have the same values as aijLT(as determined fromfirst principles calculations). This does not present a problemgenerally in the results of analysis if the reference materialsbracket each of
47、 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 influencecoefficie
48、nts 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 treating
49、them as unknown specimens. Comparison of the known valueswith those found by analysis should give acceptable agree-ment, if the influence coefficients are sufficiently accurate. Thistest is valid only when reference materials analyzed as un-knowns are not included in the set of reference materials fromwhich 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 ofAppendix X1).This is usually done by arbitr
