ASTM E1361-02(2021)
(Guide)Standard Guide for Correction of Interelement Effects in X-Ray Spectrometric Analysis
Standard Guide for Correction of Interelement Effects in X-Ray Spectrometric Analysis
SIGNIFICANCE AND USE
4.1 Accuracy in quantitative X-ray spectrometric analysis depends upon adequate accounting for interelement effects either through sample preparation or through mathematical correction procedures, or both. This guide is intended to serve as an introduction to users of X-ray fluorescence correction methods. For this reason, only selected mathematical models for correcting interelement effects are presented. The reader is referred to several texts for a more comprehensive treatment of the subject (2-7).
SCOPE
1.1 This guide is an introduction to mathematical procedures for correction of interelement (matrix) effects in quantitative X-ray spectrometric analysis.
1.1.1 The procedures described correct only for the interelement effect(s) arising from a homogeneous chemical composition of the specimen. Effects related to either particle size, or mineralogical or metallurgical phases in a specimen are not treated.
1.1.2 These procedures apply to both wavelength and energy-dispersive X-ray spectrometry where the specimen is considered to be infinitely thick, flat, and homogeneous with respect to the depth of penetration of the exciting X-rays (1).2
1.2 This document is not intended to be a comprehensive treatment of the many different techniques employed to compensate for interelement effects. Consult Refs (2-5) for descriptions of other commonly used techniques such as standard addition, internal standardization, etc.
1.3 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
General Information
Relations
Standards Content (Sample)
This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: E1361 − 02 (Reapproved 2021)
Standard Guide for
Correction of Interelement Effects in X-Ray Spectrometric
Analysis
This standard is issued under the fixed designation E1361; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 3. Terminology
3.1 For definitions of terms used in this guide, refer to
1.1 This guide is an introduction to mathematical proce-
Terminology E135.
dures for correction of interelement (matrix) effects in quanti-
tative X-ray spectrometric analysis.
3.2 Definitions of Terms Specific to This Standard:
1.1.1 Theproceduresdescribedcorrectonlyfortheinterele-
3.2.1 absorption edge—the maximum wavelength (mini-
ment effect(s) arising from a homogeneous chemical compo-
mum X-ray photon energy) that can expel an electron from a
sition of the specimen. Effects related to either particle size, or
given level in an atom of a given element.
mineralogical or metallurgical phases in a specimen are not
3.2.2 analyte—an element in the specimen to be determined
treated.
by measurement.
1.1.2 These procedures apply to both wavelength and
3.2.3 characteristic radiation—X radiation produced by an
energy-dispersive X-ray spectrometry where the specimen is
element in the specimen as a result of electron transitions
considered to be infinitely thick, flat, and homogeneous with
between different atomic shells.
respect to the depth of penetration of the exciting X-rays (1).
3.2.4 coherent (Rayleigh) scatter—the emission of energy
1.2 This document is not intended to be a comprehensive
from a loosely bound electron that has undergone collision
treatment of the many different techniques employed to com-
with an incident X-ray photon and has been caused to vibrate.
pensateforinterelementeffects.ConsultRefs (2-5)fordescrip-
The vibration is at the same frequency as the incident photon
tions of other commonly used techniques such as standard
and the photon loses no energy. (See 3.2.7.)
addition, internal standardization, etc.
3.2.5 dead-time—time interval during which the X-ray de-
1.3 This international standard was developed in accor-
tection system, after having responded to an incident photon,
dance with internationally recognized principles on standard-
cannot respond properly to a successive incident photon.
ization established in the Decision on Principles for the
3.2.6 fluorescence yield—a ratio of the number of photons
Development of International Standards, Guides and Recom-
of all X-ray lines in a particular series divided by the number
mendations issued by the World Trade Organization Technical
of shell vacancies originally produced.
Barriers to Trade (TBT) Committee.
3.2.7 incoherent (Compton) scatter—theemissionofenergy
from a loosely bound electron that has undergone collision
2. Referenced Documents
withanincidentphotonandtheelectronhasrecoiledunderthe
2.1 ASTM Standards:
impact, carrying away some of the energy of the photon.
E135Terminology Relating to Analytical Chemistry for
3.2.8 influence coeffıcient—designated by α (β, γ, δ and
Metals, Ores, and Related Materials
other Greek letters are also used in certain mathematical
models), a correction factor for converting apparent mass
fractions to actual mass fractions in a specimen. Other terms
This guide is under the jurisdiction of ASTM Committee E01 on Analytical
commonly used are alpha coefficient and interelement effect
ChemistryforMetals,Ores,andRelatedMaterialsandisthedirectresponsibilityof
coefficient.
Subcommittee E01.20 on Fundamental Practices.
Current edition approved March 15, 2021. Published April 2021. Originally
3.2.9 mass absorption coeffıcient—designated by µ, an
ε1
approved in 1990. Last previous edition approved in 2014 as E1361–02(2014) .
atomic property of each element which expresses the X-ray
DOI: 10.1520/E1361-02R21.
absorption per unit mass per unit area, cm /g.
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
this standard.
3.2.10 primary absorption—absorption of incident X-rays
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
by the specimen.The extent of primary absorption depends on
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
the composition of the specimen and the X-ray source primary
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. spectral distribution.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E1361 − 02 (2021)
3.2.11 primary spectral distribution—the output X-ray
spectral distribution usually from an X-ray tube. The X-ray
continuum is usually expressed in units of absolute intensity
per unit wavelength per electron per unit solid angle.
3.2.12 relative intensity—the ratio of an analyte X-ray line
intensity measured from the specimen to that of the pure
analyte element. It is sometimes expressed relative to the
analyte element in a multi-component reference material.
3.2.13 secondary absorption—the absorption of the charac-
teristicXradiationproducedinthespecimenbyallelementsin
the specimen.
3.2.14 secondary fluorescence (enhancement)—the genera-
tionofX-raysfromtheanalytecausedbycharacteristicX-rays
from other elements in the sample whose energies are greater
than the absorption edge of the analyte.
Curve A—Linear calibration curve.
Curve B—Absorption of analyte by matrix. For example, R versus C in
3.2.15 X-ray source—an excitation source which produces
Ni Ni
Ni-Fe binary alloys where nickel is the analyte element and iron is the matrix
X-rayssuchasanX-raytube,radioactiveisotope,orsecondary
element.
target emitter.
Curve C—Negative absorption of analyte by matrix. For example, R versus
Ni
C in Ni-Al alloys where nickel is the analyte element and aluminum is the
Ni
matrix element.
4. Significance and Use
Curve D—Enhancement of analyte by matrix. For example, R versus C in
Fe Fe
Fe-Ni alloys where iron is the analyte element and nickel is the matrix ele-
4.1 Accuracy in quantitative X-ray spectrometric analysis
ment.
depends upon adequate accounting for interelement effects
either through sample preparation or through mathematical
FIG. 1 Interelement Effects in X-Ray Fluorescence Analysis
correction procedures, or both. This guide is intended to serve
as an introduction to users of X-ray fluorescence correction
methods. For this reason, only selected mathematical models
relatively constant. In general, Curve B is obtained when the
for correcting interelement effects are presented. The reader is
absorptionbythematrixelementsinthespecimenofeitherthe
referredtoseveraltextsforamorecomprehensivetreatmentof
primary X-rays or analyte characteristic X-rays, or both, is
the subject (2-7).
greater than the absorption by the analyte alone. This second-
ary absorption effect is often referred to simply as absorption.
5. Description of Interelement Effects
The magnitude of the displacement of Curve B from CurveA
5.1 Matrix effects in X-ray spectrometry are caused by
in Fig. 1, for example, is typical of the strong absorption of
absorption and enhancement of X-rays in the specimen. Pri-
nickel K-L (K ) X-rays in Fe-Ni alloys. Curve C represents
2,3 α
mary absorption occurs as the specimen absorbs the X -rays
the general case where the matrix elements in the specimen
from the source. The extent of primary absorption depends on
absorb the primary X-rays or characteristic X-rays, or both, to
thecompositionofthespecimen,theoutputenergydistribution
a lesser degree than the analyte alone. This type of secondary
oftheexcitingsource,suchasanX-raytube,andthegeometry
absorption is often referred to as negative absorption. The
of the spectrometer. Secondary absorption occurs as the char-
magnitude of the displacement of Curve C from Curve A in
acteristic X radiation produced in the specimen is absorbed by
Fig. 1, for example, is typical of alloys in which the atomic
the elements in the specimen. When matrix elements emit
number of the matrix element (for example, aluminum) is
characteristicX-raylinesthatlieontheshort-wavelength(high
much lower than the analyte (for example, nickel). Curve D in
energy) side of the analyte absorption edge, the analyte can be
Fig. 1 illustrates an enhancement effect as defined previously,
excited to emit characteristic radiation in addition to that
and represents in this case the enhancement of iron K-L (K )
2,3 α
excited directly by the X-ray source. This is called secondary
X-rays by nickel K-L (K ) X-rays in Fe-Ni binaries.
2,3 α
fluorescence or enhancement.
NOTE 1—The relative intensity rather than absolute intensity of the
5.2 These effects can be represented as shown in Fig. 1
analytewillbeusedinthisdocumentforpurposesofconvenience.Itisnot
usingbinaryalloysasexamples.Whenmatrixeffectsareeither
meant to imply that measurement of the pure element is required, unless
under special circumstances as described in 9.1.
negligible or constant, Curve A in Fig. 1 would be obtained.
That is, a plot of analyte relative intensity (corrected for
6. General Comments Concerning Interelement
background, dead-time, etc.) versus analyte mass fraction
Correction Procedures
wouldyieldastraightlineoverawidemassfractionrangeand
would be independent of the other elements present in the 6.1 Historically, the development of mathematical methods
specimen (Note 1). Linear relationships often exist in thin for correction of interelement effects has evolved into two
specimens, or in cases where the matrix composition is approaches, which are currently employed in quantitative
constant. Low alloy steels, for example, exhibit constant X-ray analysis.When the field of X-ray spectrometric analysis
interelement effects in that the mass fractions of the minor was new, researchers proposed mathematical expressions,
constituents vary, but the major constituent, iron, remains which required prior knowledge of corrective factors called
E1361 − 02 (2021)
LT LT
influence coefficients or alphas prior to analysis of the speci- C 5 R 11α C 1α C (5)
~ !
k k ki i kj j
mens. These factors were usually determined experimentally
Therefore, six alpha coefficients are required to solve for the
by regression analysis using reference materials, and for this
mass fractions C, C, and C (see Appendix X1). Once the
i j k
reason are typically referred to as empirical or semi-empirical
influence coefficients are determined, Eq 3-5 can be solved for
procedures (see 7.1.3, 7.2, and 7.8). During the late 1960s,
the unknown mass fractions with a computer using iterative
another approach was introduced which involved the calcula-
techniques (see Appendix X2).
tion of interelement corrections directly from first principles
7.1.3 Determination of Influence (Alpha) Coeffıcients from
expressions such as those given in Section 8. First principles
Regression Analysis—Alpha coefficients can be obtained ex-
expressions are derived from basic physical principles and
perimentallyusingregressionanalysisofreferencematerialsin
contain physical constants and parameters, for example, which
which the elements to be measured are known and cover a
include absorption coefficients, fluorescence yields, primary
broad mass fraction range.An example of this method is given
spectral distributions, and spectrometer geometry. Fundamen-
in X1.1.1 of Appendix X1. Eq 1 can be rewritten for a binary
tal parameters method is a term commonly used to describe
specimen in the form:
interelement correction procedures based on first principle
R
equations (see Section 8).
~C /R ! 2 1 5 α C (6)
i i ij j
R
6.2 In recent years, several researchers have proposed
where: α =influence coefficient obtained by regression
ij
fundamental parameters methods to correct measured X-ray
analysis. A plot of (C/R)−1 versus C gives a straight line
i i j
R
intensities directly for interelement effects or, alternatively,
with slope α (see Fig. X1.1 of Appendix X1). Note that the
ij
proposed mathematical expressions in which influence coeffi-
superscript LT is replaced by R because alphas obtained by
cients are calculated from first principles (see Sections 7 and
regression analysis of multi-component reference materials do
LT
8). Such influence coefficient expressions are referred to as
notgenerallyhavethesamevaluesas α (asdeterminedfrom
ij
fundamental influence coefficient methods.
first principles calculations). This does not present a problem
generally in the results of analysis if the reference materials
7. Influence Coefficient Correction Procedures
bracket each of the analyte elements over the mass fraction
ranges that exist in the specimen(s). Best results are obtained
7.1 The Lachance-Traill Equation:
only when the specimens and reference materials are of the
7.1.1 Forthepurposesofthisguide,itisinstructivetobegin
same type. The weakness of the multiple-regression technique
with one of the simplest, yet fundamental, correction models
asappliedinX-rayanalysisisthattheaccuracyoftheinfluence
within certain limits. Referring to Fig. 1, either Curve B or C
coefficientsobtainedisnotknownunlessverified,forexample,
(thatis,absorptiononly)canberepresentedmathematicallyby
from first principles calculations. As the number of compo-
a hyperbolic expression such as the Lachance-Traill equation
nentsinaspecimenincreases,thisbecomesmoreofaproblem.
(LT) (8).Forabinaryspecimencontainingelements iand j,the
Results of analysis should be checked for accuracy by incor-
LT equation is:
poratingreferencematerialsintheanalysisschemeandtreating
LT
C 5 R ~11α C ! (1)
i i ij j
themasunknownspecimens.Comparisonoftheknownvalues
with those found by analysis should give acceptable
where:
agreement, if the influence coefficients are sufficiently accu-
C = mass fraction of analyte i,
i
rate. This test is valid only when reference materials analyzed
C = mass fraction of matrix element j,
j
as unknowns are not included in the set of reference materials
R = the analyte intensity in the specimen expressed as a
i
from which the influence coefficients were obtained.
ratio to the pure analyte element, and
LT
α = the influence coefficient, a constant. 7.1.4 Determination of Influence Coeffıcients from First
ij
Principles—Influence coefficients can be calculated from fun-
The subscript i denotes the analyte and the subscript j
LT
damentalparametersexpressions(seeX1.1.3ofAppendixX1).
denotes the m
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.