ASTM E1361-90(1999)
(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
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).
1.2 This document is not intended to be a comprehensive treatment of the many different techniques employed to compensate for interelement effects. Consult References 2 through 4 for descriptions of other commonly used techniques such as standard addition, internal standardization, etc.
General Information
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Standards Content (Sample)
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Designation: E 1361 – 90 (Reapproved 1999)
Standard Guide for
Correction of Interelement Effects in X-Ray Spectrometric
Analysis
This standard is issued under the fixed designation E 1361; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope from a loosely bound electron which has undergone collision
with an incident X-ray photon and has been caused to vibrate.
1.1 This guide is an introduction to mathematical proce-
The vibration is at the same frequency as the incident photon
dures for correction of interelement (matrix) effects in quanti-
and the photon loses no energy. (See 3.2.7.)
tative X-ray spectrometric analysis.
3.2.5 dead-time—time interval during which the X-ray
1.1.1 The procedures described correct only for the inter-
detection system, after having responded to an incident photon,
element effect(s) arising from a homogeneous chemical com-
cannot respond properly to a successive incident photon.
position of the specimen. Effects related to either particle size,
3.2.6 fluorescence yield—a ratio of the number of photons
or mineralogical or metallurgical phases in a specimen are not
of all X-ray lines in a particular series divided by the number
treated.
of shell vacancies originally produced.
1.1.2 These procedures apply to both wavelength and
3.2.7 incoherent (Compton) scatter—the emission of energy
energy-dispersive X-ray spectrometry where the specimen is
from a loosely bound electron which has undergone collision
considered to be infinitely thick, flat, and homogeneous with
2 with an incident photon and the electron has recoiled under the
respect to the depth of penetration of the exciting X rays (1).
impact, carrying away some of the energy of the photon.
1.2 This document is not intended to be a comprehensive
3.2.8 influence coeffıcient—designated by a, a matrix cor-
treatment of the many different techniques employed to com-
rection factor for converting apparent concentrations to actual
pensate for interelement effects. Consult References 2 through
concentrations in a specimen. Other terms commonly used are
4 for descriptions of other commonly used techniques such as
alpha coefficient and interelement effect coefficient.
standard addition, internal standardization, etc.
3.2.9 mass absorption coeffıcient—designated by μ, an
2. Referenced Documents
atomic property of each element which expresses the X-ray
absorption per unit mass per unit area, cm /g.
2.1 ASTM Standards:
3.2.10 primary absorption—absorption of incident X rays
E 135 Terminology Relating to Analytical Chemistry for
by the specimen. The extent of primary absorption depends on
Metals, Ores, and Related Materials
the composition of the specimen and the X-ray source spectral
3. Terminology
distribution.
3.2.11 primary spectral distribution—the output X-ray
3.1 For definitions of terms used in this guide, refer to
spectral distribution usually from an X-ray tube. The X-ray
Terminology E 135.
continuum is usually expressed in units of absolute intensity
3.2 Definitions of Terms Specific to This Standard:
per unit wavelength per electron per unit solid angle.
3.2.1 absorption edge—the maximum wavelength (mini-
3.2.12 relative intensity—the ratio of an analyte X-ray line
mum X-ray photon energy) that can expel an electron from a
intensity measured from the specimen to that of the pure
given level in an atom of a given element.
analyte element. It is sometimes expressed relative to the
3.2.2 analyte—an element in the specimen whose concen-
analyte element in a multi-component standard reference
tration is to be determined.
material.
3.2.3 characteristic radiation—X radiation produced by an
3.2.13 secondary absorption—the absorption of the charac-
element in the specimen as a result of electron transitions
teristic X radiation produced in the specimen by all the
between different atomic shells.
elements in the specimen.
3.2.4 coherent (Rayleigh) scatter—the emission of energy
3.2.14 secondary fluorescence (enhancement)—the genera-
tion of X rays from the analyte caused by characteristic X rays
This guide is under the jurisdiction of ASTM Committee E-1 on Analytical
from other elements in the sample whose energies are greater
Chemistry for Metals, Ores, and Related Materials and is the direct responsibility of
than the absorption edge of the analyte.
Subcommittee E01.20 on Fundamental Practices.
Current edition approved June 29, 1990. Published August 1990.
3.2.15 weight fraction—a concentration unit expressed as a
The boldface numbers in parentheses refer to the list of references at the end of
ratio of the mass of analyte to the total mass.
this standard.
3 3.2.16 X-ray source—an excitation source which produces
Annual Book of ASTM Standards, Vol 03.05.
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NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
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E 1361
X rays such as an X-ray tube, radioactive isotope, or secondary specimen (Note 1). Linear relationships often exist in thin
target emitter. specimens, or in cases where the matrix effect is constant. Low
alloy steels, for example, exhibit constant matrix effects in that
4. Significance and Use
the concentrations of the minor constituents vary, but the major
4.1 Accuracy in quantitative X-ray spectrometric analysis constituent, that is, iron, remains relatively constant. In gen-
depends upon adequate accounting for interelement effects. eral, Curve B is obtained when the absorption by the matrix
This guide is intended to serve as an introduction to users of elements in the specimen of either the primary X rays or
X-ray fluorescence correction methods. For this reason, only analyte characteristic X rays, or both, is greater than the
selected mathematical models for correcting interelement ef- absorption by the analyte alone. This secondary absorption
fects are presented. The reader is referred to several texts for a effect is often referred to simply as absorption. The magnitude
more comprehensive treatment of the subject (2-6). of the displacement of Curve B from Curve A in Fig. 1, for
example, is typical of the strong absorption of nickel K X rays
a
5. Description of Matrix Effects
in Fe-Ni alloys. Curve C represents the general case where the
5.1 Matrix effects in X-ray spectrometry are caused by matrix elements in the specimen absorb the primary X rays or
absorption and enhancement of X rays in the specimen. characteristic X rays, or both, to a lesser degree than the
Primary absorption occurs as the X rays from the source are analyte alone. This type of secondary absorption is often
absorbed by the specimen. The extent of primary absorption referred to as negative absorption. The magnitude of the
depends on the composition of the specimen, the output energy displacement of Curve C from Curve A in Fig. 1, for example,
distribution of the exciting source, such as an X-ray tube, and is typical of alloys in which the atomic number of the matrix
element (for example, aluminum) is much lower than the
the geometry of the spectrometer. Secondary absorption occurs
as the characteristic X radiation produced in the specimen is analyte (for example, nickel). Curve D in Fig. 1 illustrates an
enhancement effect as defined previously, and represents in this
absorbed by the elements in the specimen. When matrix
elements emit characteristic X-ray lines which lie on the case the enhancement of iron K X rays by nickel K X rays in
a a
short-wavelength (high energy) side of the analyte absorption Fe-Ni binaries.
edge, the analyte can be excited to emit characteristic line
NOTE 1—The relative intensity rather than absolute intensity of the
radiation in addition to that excited directly by the X-ray
analyte will be used in this document for purposes of convenience. It is not
source. This is called secondary fluorescence or enhancement.
meant to imply that measurement of the pure element is required, unless
5.2 These effects can be represented as shown in Fig. 1
under special circumstances as described in 9.1.
using binary alloys as examples. When matrix effects are either
6. General Comments Concerning Interelement
negligible or constant, Curve A in Fig. 1 would be obtained.
Correction Procedures
That is, a plot of analyte relative intensity (corrected for
6.1 Historically, the development of mathematical methods
background, dead-time, etc.) versus analyte concentration
for correction of matrix effects has evolved into two ap-
would yield a straight line over a wide concentration range and
proaches which are currently employed in quantitative X-ray
would be independent of the other elements present in the
analysis. When the field of X-ray spectrometric analysis was
new, researchers proposed mathematical expressions which
required prior knowledge of corrective factors called influence
coefficients or alphas prior to analysis of the specimens. These
factors were usually determined experimentally by regression
analysis using reference materials, and for this reason are
typically referred to as empirical or semi-empirical procedures
(see 7.1.3, 7.2, and 7.8). During the late 1960s, another
approach was introduced which involved the calculation of
interelement corrections directly from first principle expres-
sions such as those given in Section 8. First principle expres-
sions are derived from basic physical principles, and contain
physical constants and parameters, for example, which include
absorption coefficients, fluorescence yields, primary spectral
distributions, and spectrometer geometry. Fundamental param-
eter methods is a term commonly used to describe interelement
correction procedures based on first principle equations (see
Curve A—Linear calibration curve.
Curve B—Absorption of analyte by matrix. For example, R versus C in
Section 8).
Ni Ni
Ni-Fe binary alloys where nickel is the analyte element and iron is the matrix
6.2 In recent years, several workers have proposed funda-
element.
mental parameter methods to correct measured X ray intensi-
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
ties directly for matrix effects or, alternatively, proposed
Ni
matrix element.
mathematical expressions in which influence coefficients are
Curve D—Enhancement of analyte by matrix. For example, R versus C in
Fe Fe
calculated from first principles (see Sections 7 and 8). Such
Fe-Ni alloys where iron is the analyte element and nickel is the matrix ele-
ment.
influence coefficient expressions are referred to as fundamental
FIG. 1 Interelement Effects in X-Ray Fluorescence Analysis influence coefficient methods.
NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
E 1361
7. Influence Coefficient Correction Procedures bracket each of the analyte elements over the concentration
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 For the purposes of this guide, it is instructive to begin
same type. The weakness of the multiple-regression technique
with one of the simplest, yet fundamental, correction models
as applied in X-ray analysis is that the accuracy of the influence
within certain limits. Referring to Fig. 1, either Curve B or C
coefficients obtained is not known unless verified, for example,
(that is, absorption only) can be represented mathematically by
from first principle calculations. As the number of components
a hyperbolic expression such as the Lachance-Traill equation
in a specimen increases, this becomes more of a problem.
(LT) (7). For a binary specimen containing elements i and j, the
Results of analysis should be checked for accuracy by incor-
LT equation is:
porating reference materials in the analysis scheme and treating
LT
C 5 R ~11a C ! (1)
them as unknown specimens. Comparison of the known values
i i ij j
with those found by analysis should give acceptable agree-
where:
ment, if the influence coefficients are sufficiently accurate. This
C 5 weight fraction of analyte i,
i
test is valid only when reference materials analyzed as un-
C 5 weight fraction of matrix element j,
j
knowns are not included in the set of reference materials from
R 5 the analyte intensity in the specimen expressed as
i
which the influence coefficients were obtained.
a ratio to the pure analyte element, and
LT
7.1.4 Determination of Influence Coeffıcients from First
a 5 the influence coefficient, a constant.
ij
Principles—Influence coefficients can be calculated from fun-
The subscript i denotes the analyte and the subscript j
LT
damental parameter expressions (see X1.1.3 of Appendix X1).
denotes the matrix element. The subscript ina denotes the
ij
This is usually done by arbitrarily considering the composition
influence of matrix element j on the analyte i in the binary
of a complex specimen to be made up of the analyte and one
specimen. The LT superscript denotes that the influence coef-
matrix element at a time (for example, a series of binary
ficient is that coefficient in the LT equation. The magnitude of
elements, or compounds such as oxides). In this way, a series
the displacement of Curves B and C from Curve A is
LT
of influence coefficients are calculated assuming hypothetical
represented by a which takes on positive values for B type
ij
compositions for the binary series of elements or compounds
curves and negative values for C type curves.
which comprise the specimen(s). The hypothetical composi-
7.1.2 The general form of the LT equation when extended to
tions can be selected at certain well-defined limits. Details of
multicomponent specimens is:
this procedure are given in 9.3.
LT
C 5 R ~1 1 ( a C ! (2)
i i ij j
7.1.5 Use of Relative Intensities in Correction Methods—As
stated in Note 1, relative intensities are used for purposes of
For a ternary system, for example, containing elements i, j
and k, three equations can be written wherein each of the convenience in most correction methods. This does not mean
that the pure element is required in the analysis unless it is the
elements are considered analytes in turn:
only reference material available. In that case, only fundamen-
LT LT
C 5 R ~11a C 1a C ! (3)
i i ij j ik k
ta
...
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