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Electron Probe Microanalysis
EPMA
Quantitative Analysis
and
Matrix Corrections
Revised 1/10/2016
Raimond Castaing (1921-1999)
• Advisor Andre Guinier studied
defects (Cu-Al inclusions) in Al
metals (for airplanes)
• Defects too small to define by
optical microscope
• Guinier famous X-ray
crystallographer
• He suggested Castaing try to find
inclusion compositions--measure Xrays generated by electron beam,
using war-surplus TEM
• Castaing succeeded, PhD 1951
“Application of Electron Probes to
Local Chemical and
Crystallographic Analysis”
Raimond Castaing (1921-1999)
His thesis laid out the basics of
EPMA which have remained
constant for the past 64 years
Key concept:
unk
i
i
std
i
where K is the “K ratio” for
element i, I is the X-ray intensity
of the phase and subscript i is
one element.
I
K =
I
Using K-factor simplifies analysis
unk
i
std
i
I
Ki =
I
• counts acquired on BOTH unknowns and
standards on the same instrument, under the
same operating conditions,
• All physical parameters of the machine that
would be needed in a rigorous physical
model cancel each other out
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Castaing’s First Approximation
unk
i
C
unk
i
std
i
I
»
I
std
i
C
std
i
= KiC
Castaing’s “first approximation” follows this approach. The
composition C of element i of the unknown is the K-ratio
times the composition of the standard.
In the ‘simplest’ case where pure element standards can be
used, Cistd = 1 and drops out.
…So how close are these K-ratios to the true composition?
Examples: some minerals
Fo90 Olivine
Hafnon HfSiO4
Zircon ZrSiO4
Notice the “differences” (between K-ratio
and true compositions….So we need a
MATRIX CORRECTION
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Raw data needs correction
This plot of Fe Ka Xray intensity data
demonstrates why we
must correct for matrix
effects. Here 3 Fe alloys
show distinct variations.
Consider the 3 alloys at
40% Fe. X-ray intensity
of the Fe-Ni alloy is
~5% higher than for the
Fe-Mn, and the Fe-Cr is
~5% lower than the FeMn. Thus, we cannot
use the raw X-ray
intensity to determine
the compositions of the
Fe-Ni and Fe-Cr alloys.
(Note the hyperbolic functionality of the upper and lower curves)
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Absorption and Fluorescence
• Note that the Fe-Mn alloys
plot along a 1:1 line, and so is a
good reference.
• The Fe-Ni alloys plot above
the 1:1 line (have apparently
higher Fe than they really do),
because the Ni atoms present
produce X-rays of 7.278 keV,
which is greater than the Fe K
edge of 7.111 keV.Thus,
additional Fe Ka are produced
by this secondary fluorescence.
• The Fe-Cr alloys plot below the 1:1 line (have apparently lower Fe than they
really do), because the Fe atoms present produce X-rays of 6.404 keV, which
is greater than the Cr K edge of 5.989 keV. Thus, Cr Ka is increased, with Fe
Ka are “used up” in this secondary fluorescence process.
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Theoretical approach to corrections
One can write an equation showing the relationship between x-ray intensity IA
and elemental concentration CA, using fundamental physical parameters*:
Rearranging the equation and solving for CA is not that easy! So the material
scientists, chemists and geologists who took up the electron probe as a crucial tool
came up with some alternatives…
*Merlet and Llovet….
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Actual approaches to corrections
Heinrich* summarizes the 4 actual types of models used for matrix
corrections in EPMA:
1.
Empirical: simplest, based on known binary experimental data;
2.
ZAF: 1st generalized algebraic procedure; assumes a linear
relation between concentration and x-ray intensity;
3.
Phi-rho-Z: based upon depth profile (tracer) experiments;
4.
Monte Carlo: based upon statistical probabilities of electronsample interactions, particularly for unusual specimen geometries.
*Heinrich, 1991, Strategies of electron probe data reduction, in Electron Probe
Quantitation, Ed. Heinrich and Newbury, Plenum, New York, 9-18.
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Two approaches to corrections
In his 1951 Ph.D. thesis, Castaing laid out two of the approaches that
could be used to apply matrix corrections to the data, using his
brilliant construct of the K-ratio:
• an empirical ‘alpha factor’ correction for binary compounds, where
each pair of elements has a pair of constant a-factors representing the
effect that each element has upon the other for measured X-ray
intensity, and
• a more rigorous physical model taking into account absorption and
fluorescence in the specimen. This later approach also now includes
atomic number effects* and became known as the ZAF correction.
• This ZAF has been surplanted in many/most EPMA labs by the
“phi-rho-Z” matrix correction (it can be a little confusing,
discussed later, as the phrase is used in another context)
* Atomic number effect only recognized in 1961-3 (Scott and Ranzetta;
Kirianenko; Archard and Mulvey), in samples with widely different atomic
numbers
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unk
i
C
Z unkA Funk
Ii ZAFi
std
= std
std Ci
Ii ZAFi
In addition to absorption (A) and fluorescence (F), there are two other matrix
corrections based upon the atomic number (Z) of the material: one dealing
with electron backscattering, the other with electron penetration (or stopping).
These deal with corrections to the generation of X-rays. C is composition as
wt% element (or elemental wt fraction).
We will now go through all these corrections in some detail, starting with the
Z correction, which has two parts: the stopping power correction, and the
backscatter correction.
Note that all these corrections require close attention to exactly what feature’s
value is being input: the target (matrix), or the X-ray in question.
Heinrich (1990) notes that this multiplicative scheme is not actually correct,
as that assumes an ideal linear calibration curve, not justifiable on the physics
involved… However, it still is used much (“gives close enough answers many
times”.)
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Stopping Power Correction
Incident electrons lose energy in
inelastic interactions with the inner
shell electrons of the target. The
“stopping power” (energy lost by HV
electrons per unit mass penetrated) is
not constant but drops with increasing
Z. A higher number of X-rays will be
produced in higher Z targets. Thus, if
the mean Z of the unknown is higher
than that of the standard, a downward
correction in the composition must be
applied. The stopping power
correction factor is “S”, and can be
approximated by:
Reed, 1996, Fig. 8.6, p. 135
Stopping power of pure elements for 20 keV electrons
Z æ 1.166 ´ Emean ö
S = lnç
÷
ø
A è
J
where J=11.5+ Z and Emean= (E0+Ec)/2
(J is the mean ionization energy; J, Z and A are of
the target, Emean is of the X-ray)
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Backscatter Correction
As we discussed earlier, the
fraction of high energy incident
elections that are backscattered (h)
increases with atomic number.
There then will be relatively less
incident electrons penetrating into
higher Z specimens, resulting in a
smaller number of X-rays. Thus, if
the mean Z of the unknown is
higher than that of the standard, a
upward correction in the
composition must be applied. The
backscatter correction factor is
“R”.
Reed, 1996, Fig. 2.11, p. 17
R can be approximated by
1
R=
1+ [0.008 ´ (1 - W) ´ Z]
where W = Ec/E0 (the inverse of overvoltage),
and Z is of the target, and W is of the X-ray
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Z correction
The total atomic number correction is formed
by multiplication of the R and S of the
unknown and standard thusly:
Z = Rstd/Runk * Sunk/Sstd
Overall the backscatter and the stopping power corrections
tend to cancel each other out. But if there is a (small)
correction, it is usually in the direction of the backscatter
correction.
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Beers Law
The intensity I of X-rays that pass
through a substance are subject to
attenuation of their initial intensity
I0 by the material over the distance
they travel within the material.
The attenuation follows an
exponential decay with a
characteristic linear attenuation
length 1/m, where m is the (linear)
absorption coefficient. Beers Law
can also be expressed in terms of
mass, using density terms:
I = I0 exp -(m/r)(r Z)
where (m/r) is the mass absorption coefficient (cm2/g), r is
the material density (g/cm3), and Z is the distance (cm)
Als-Nielsen and McMorrow, 2001, Fig 1.10, p. 19
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Mass Absorption Coefficients
Mass absorption coefficients
(MACs) have been tabulated* for
many X-rays through many
substances (though some are
extrapolations). They exist as a
matrix of numbers: absorption of a
particular X-ray line (emitter, e.g.
Ga ka) by a absorber or target (e.g.
As) will have one value (51.5).
Note that the absorption of As Ka
by Ga is a totally different
phenomenon with a distinct MAC
(221.4) .
Emitter = X-ray
(here, Ka)
Absorber =
matrix material
*See following discussion
Goldstein et al, 1992, p. 750.
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Mass Absorption Coefficients
Emitter = X-ray
(here, Ka)
Terminology:
“the mass absorption of Ga Ka
by As”
Question for you: Is the mass
absorption of As Ka by Ga the
same as the mass absorption of
Ga Ka by As?
Why or why not?
Absorber =
matrix material
Goldstein et al, 1992, p. 750.
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Absorption
X-rays produced within the material will
be propagated in all directions, and will
suffer attenuation in the process. Note
that the path length of travel of the X-ray
to the spectrometer is z cosecy, where y
(psi) is the takeoff angle (cosec = 1/sin).
Castaing’s approach was to integrate the
Beer’s Law equation over the depth at
the given y, producing the absorption
correction factor f(c) where c is defined
as m cosec y where m is the MAC.
f ( c) =
emergent intensity
generated intensity
The absorption (A) correction is then
defined as
A= f(c)std / f(c)sample
c = “Chi”
Reed, 1993,, p. 219
“Photoelectric absorption” is an
“all or nothing” process. When it
occurs the photon energy kicks out
an electron with lower binding
energy, and said electron is ejected
with the kinetic energy of the
photon minus its binding energy.
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Absorption
To be able to correct for this absorption
of the measured X-rays, we need to know
how the production of X-rays varies
with depth (Z) in the material.
The distribution of X-rays generated as a
function of depth is known as the f(rz)
[phi-rho-z] function, where a “mass
depth” parameter is used instead of
simple z (bottom right).
The f(rz) function is defined as the
intensity generated in a thin layer at some
depth z, relative to that generated in an
isolated layer of the same thickness. This
can then be integrated over the total
depth where the incident electrons
exceed the binding energy for that
particular characteristic x-ray.
Reed, 1993, p. 219
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Absorption
One commonly used simplified form
(Philibert 1963) was
f ( c) =
[
(1+ h)
] {
[
]}
1 + ( s ) ´ 1+ h ´ 1+ ( s )
c
c
where c = m cosec y , s is a measure
of electron absorption and depends on
effective electron energy, where
4.5 ´ 10 5
s = 1.65
E0 - Ec1.65
A
h = 1.2 ´ 2
Z
The Philibert approximation breaks
down, however, at the near surface,
creating errors when dealing with low
energy light elements, and we need to
go to more complicated and accurate
forms of the f(rz) function.
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f(rz) [phi-rho-z] Curves
To be able to correct
properly for absorption -particularly for light
elements, the exact shape
of the f(rz) [phi-rho-z]
curve must be known.
Each X-ray has its own
curve. There are 3 main
parameters that affect the
shape of the curve:
•E0 (accelerating voltage)
• Ec (critical excitation energy of a particular
element line
• mean Z of the material
Reed, 1993, p. 220
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Tracer Method
The f(rz) [phi-rho-z] curves are
usually determined by the “tracer
method”, where successive layers
are deposited by vacuum
evaporation. The tracer layer B is
deposited atop substrate A, with
successive layers of A deposited
on top.
Characteristic X-rays from the
tracer element are measured
(“emitted”) and then a generation
curve is calculated by correcting
each step for absorption and
fluorescence effects
Artistic
license?
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Fluorescence Correction
The X-rays produced within a
specimen have the potential for
producing a second generation of
X-rays: this is secondary
fluorescence, generally shortened
to fluorescence. This occurs when
the characteristic X-ray has an
energy greater than the absorption
edge energy of another element
present in the specimen.
As we saw earlier, Ni Ka (7.48
keV) is able to fluoresce Fe Ka
(Ec 7.11 keV). This effect is
maximized when there is a small
amount of the fluoresced element
present, e.g. Fe in a Ni-Fe alloy.
Reed gives an example where the Fe
intensity is 142% of what it “should be”.
Also, the continuum above an absorption
edge also causes fluorescence, although
this is generally weak.
Reed, 1996, Fig. 8.10, p. 139
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Fluorescence Correction
The form of the correction F is
F=
1
If
1+å
Ip
where If/Ip is the ratio of emitted X-rays from fluorescence, compared to the
X-ray intensity from inner shell ionization. In a compound, this term is
summed overall all the elements that could fluorescence the element of
interest.
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Next Generation (>1980):
Phi-Rho-Z models
We saw above how Castaing, as early as the 1950s, developed models of
x-ray generation and absorption within the target material, and called
these curves “phi-rho-Z” curves. Finding proper mathematical models,
however, was hard and so simplistic approximations were used.
Over time, and particularly with improvements in technology, people
desired to use EPMA to measure the “light elements” (B, C, N, O, F)
where absorption by the matrix is severe. Increased research as well as
development of computing power, led to a new variant, where the “Z”
correction is subsumed within the Phi-Rho-Z paradigm. Additionally,
more experiments occurred to determine more correct mass absorption
coefficients for the light elements.
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Next Generation (>mid 1980s):
Phi-Rho-Z models
Names you will see in regards to these models:
“PAP” – Jean-Louis Pouchou and Francoise Pichoir
(and ‘simplified’ version = XPP)
“PROZA” – Guillaume Bastin
“X-PHI” – Claude Merlet
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How do EPMA theoriticians ‘prove’ their
matrix correction is “correct”?
Example:
Here, use 826
“high
quality” x-ray
K-ratio data
(element
pairs) to
show that a
given matrix
correction
provides the
correct
answer (= the
actual binary
composition)
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How do EPMA theoriticans ‘prove’ their matrix
correction is “correct”?
Here, in a 1991 book, Pouchou and Pichoir show compare their
“PAP” matrix correction to a ZAF version. Note that both contain not
an insignificant number of data >5% error, and a heck of a lot >2%
error. And these are binary compounds.
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Fluorescence Problems
Secondary fluorescence is an
important issue that must be
appreciated. Generated X-rays are
not scattered nearly as much as
incident electrons, and thus the
generated X-rays can travel
relatively long distances (50 um in
Fig 3.49) within the specimen and
produce a second generation of Xrays. If the specimen (and
standards) are relatively large
(=homogeneous), this is not a
problem. However, if minor or
trace elements are being analyzed
in small grains (Phase 1 in Fig
16.10) and the host phase (2) has
high abundance, an error may be
made in the EPMA analysis.
Goldstein et al. p. 142; Reed 1993, p. 258
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Fluorescence across boundaries
Secondary fluorescence is a potential
source of analytical error across linear
boundaries, either horizontal (e.g. thin
films) or vertical (e.g., diffusion
couples).
In the example here of a vertical
interface between untreated Cu and Co,
there is NO diffusion. However, the
resulting EPMA profiles clearly imply
there is diffusion. There is NO diffusion
– there is only secondary fluorescence
across the boundary. Cu Ka X-rays can
excite Co, to the extent that there is
apparently 1 wt% Co about 15 um away
from the boundary within the Cu. But Co
Ka cannot excite Cu, so only the
continuum X-rays can create secondary
fluorescence, which is less – but
certainly distinguishable, an apparent 0.5
wt% Cu at 10 um from the boundary in
the Co.
Reed 1993, p. 259-260
Z
Ka
K edge
27
Co
6.93 keV
7.71 keV
29
Cu
8.05 keV
8.98 keV
“false Co”
Cu
“false Cu”
Co
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An SF real story
Another lab reported 10 wt% Nb (below)
in what should have been Nb-free phase
(by EDS at 30 kV). The issue was small
grain size and nearby Nb (right image)
When I ran WDS (18 kV) I found essentially
zero Nb -- what is the problem?
The original researchers used Nb Ka because,
with EDS, it is impossible to resolve Nb La
(it sits between Al Ka, Hf Ma and Pd La).
Fournelle, Kim and Perepezko (2005)
Above: EDS spectrum on Pd2HfAl 5 um
away from Nb. Pd Ka is very efficient at
traveling across the border and exiting the Nb
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Secondary Fluorescence Correction
A recent article (below left) reports an innovative approach
to correcting the secondary fluorescence (SF) in diffusion
couples and from adjacent phases. This utilizes a complex
Monte Carlo program called PENELOPE (Penetration and
Energy Loss of Positrons and Electrons) that permits
complicated geometric models of electron and X-ray behavior
in materials. SF can be simulated in a model that represents the
actual specimen (e.g. Fig 1 below), and then subtracted from
the observed data (right figure).
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Matrix Correction Programs
The raw X-ray intensities are first corrected for:
• background contribution
• beam drift (i.e. counts are normalized)
• deadtime
• interferences* (if appropriate)
and then the K-ratios are input into an automated matrix correction program.
To run, the correction calculations must assume an initial composition for
the unknown -- because the magnitude of each factor is proportional to the
abundance of the element times its correction in a pure end member. The
assumed composition is a normalized (to 100%) value of the K-ratio. Based
upon the first iteration with this assumed composition, the result gives a more
truer composition, which then is the input for the second iteration. The
process is iterated until convergence, usually 3-5 times.
* Probe for EPMA does the interference correction within the matrix correction, a far better approach compared to the
normal (antiquainted) procedure of correcting the data after the matrix correction is completed.
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ZAF options
One currently widely used matrix correction program is CITZAF, developed
by John Armstrong (then CIT, now at Carnegie Institution in DC) and
implemented in our Probe for Windows software. There are several options,
which we elucidate here, but that generally we do not modify them from the
default values. Probably the only parameter you would ever modify would
be mass absorption coefficients (there are different ones for the light
elements).
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Alpha correction
In the early decades of probing when computer power was
negligible, the alpha correction technique was widely used, as
it required less number crunching and relied mainly on
empirical data and less on complex physical models and
physics. Today, however, there may be a rekindled interest in
this approach, as it may “work better” in many cases.
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Ziebold and Ogilvie binary a-factors
In 1963-4, Ziebold and Ogilvie* developed a corrections for some binary
metal alloys, with an equation in the form
= C2
= K2
(1 - K1 )
(1 - C1 )
= a1 2
K1
C1
where a12 is the a-factor for element 1 in the binary with element 2, K is
the K-ratio, and composition (fractional) is C. This equation can be
rearranged in the form
C1
= a1 2 + (1 - a1 2)C1
K1
If experimental data exist for binary alloys, then a plot of C1/K1 versus C1
is a straight line with a slope of (1- a 12), leading to determination of a 12.
Such a hyperbolic relationship between C1 and K1 was shown to be correct
for several alloy and oxide systems, but it was difficult to find appropriate
intermediate compositions for many binary systems.
*Quantitative Analysis with the Electron Microanalyzer, Analytical Chemistry, Vol 35, May 1963, p. 621-627;
An Empirical Method for Electron Microanalysis, Analytical Chemistry, Vol 36, Feb. 1964, p. 322-327.
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Ziebold and Ogilvie ternary a-factors
Ziebold and Ogilvie showed that a corrections could be developed for
some ternary metal alloys, with an equation in the form
(1 - K1 )
(1- C1 )
= a123
K1
C1
where a123 is the a-factor for element 1 in the ternary with elements 2 and
3, and is defined as
a C +a C
a123 =
12 2
13 3
C2 + C3
This equation can be rearranged
C1
= a123 + (1 - a123)C1
K1
Similar relationships can be written for elements 2 and 3, and used to
calculate a-factors for the 3 binary systems of the ternary.These a-factors
were limited to a particular E0 and takeoff angle.
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Bence-Albee multicomponent systems
Bence and Albee* in 1968 showed that this approach could be extended to
silicates and other minerals, i.e. a system of n components, where for the
Cn
nth component a b-factor could be found
= bn
kn
where
k1a n1 + k2 an2 + k3an3 + ××× + k nan n
bn =
k1 + k2 + k3 + × ×× + kn
where an1 is the a-factor for the n1 binary.
These factors were determined for a limited set of conditions, i.e. 15 and
20 keV, and take off angles of 52.5° and 38.5°.
The 1968 Bence and Albee paper is one of the most highly cited papers in
the geological literature (over ~20,000 citations).
* Empirical correction factors for the electron microanalysis of silicates and oxides, J. Geology, Vol. 76, p.
382-403; also see Albee and Ray, Correction Factors for Electron Probe Microanalysis of Silicates, Oxides,
Carbonates, Phosphates, and Sulfates, Analytical Chemistry, Vol 42, Oct 1970, p. 1408-1414.
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Evaluating matrix corrections
In 1988, John Armstrong* reviewed the Bence-Albee (a-factor) correction
scheme for EPMA of oxide and silicate minerals. He evaluated the old
factors, and revised some, using a -factors calculated from newer ZAF and
f(rz) algorithms, and showed “that with some modifications the a -factor
corrections can be as accurate as any other correction procedure currently
available and much easier and quicker to process.”
*Bence-Albee after 20 years: review of the accuracy of a-factor correction procedures for oxide and silicate
minerals, in Microbeam Analysis-1988, p. 469-76.
Armstrong also reviewed† ZAF and f(rz) corrections and suggested that
some of these correction algorithms “produce poorer results in the analysis
of silicate and oxide minerals than some of the earlier corrections”. He
specifically was referring to various corrections that were optimized for
metal alloys
† Quantitative analysis of silicate and oxide materials: comparison of Monte Carlo, ZAF and f(rz)
procedures, in Microbeam Analysis-1988, p. 239+
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Before we forget....
Unanalyzed elements
The matrix corrections assume that all elements present (and interacting
with the X-rays) will be included. There are situations, however, where
either an element cannot be measured, or not easily, and thus the analyst
must make explicit in the quantitative setup the presence of unanalyzed
element/s -- and how they are to be input into the correction.
Typically oxygen (in
silicates) is calculated
“by stoichometry”.
Elements can also be
defined in set
amounts, or relative
proportions, or “by
difference” – although
this later method is
somewhat dangerous
as it assumes that
there are no other
elements present.
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Unanalyzed oxygen, carbon, etc
Oxygen is a major part of many materials (e.g. silicate minerals and
glasses). Carbon is a major part of carbonates. Oxygen and carbon are
typically not “acquired” (measured directly) in many EPMA
procedures, BUT THEY MUST BE SOMEHOW INCLUDED IN
THE MATRIX CORRECTION.
If oxygen (and say C in carbonates) is not included, there will be
errors in the matrix corrections of some elements, as the presence
these elements affects the electron (and x-ray behavior), e.g., the
backscattered % of incident HV electrons will be different, and there
may be absorption of those x-rays by the oxygen (and C) present.
In the next slides, we see the effect on a measurement of a carbonate
sample: first, with just the cations; then with just Oxygen added;
finally with both Oxygen and Carbon.
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First: how you do it
For a carbonate
1.
Declare C and O as elements in
the analysis (but not measured)
2.
Tell it to calculate with
stoichiometric oxygen
3.
Create a rule so that there is 1
atom of C to every 3 atoms of O
4.
Check: display results on basis
of 3 atoms of oxygen (perfect
result would be 5.000 total
atoms, and grand total of 100
wt%
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Good, Bad, Ugly …. Carbonate by EPMA
First, if only cations used for ZAF …
If both O and C included in the ZAF
Next, oxygen only included …
Notice the differences in the final
values of the elements (wt%)
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Unanalyzed oxygen
One complication for oxygen is variable valence states of elements
such as Fe. Robust software will allow you to enter case by case
different valence states.
In some cases, if oxygen is not included, there can be errors in the
matrix corrections of some elements, as the presence of O, OH, and
H2O can affect the actually measured elements, as there may be
significant absorption of those x-rays by the oxygen present*.
* Tingle, T.N., Neuhoff, P., Ostgergren, P., Jones, R.E. and Donovan, J.J. (1996)
The effect of “missing” unanalyzed oxygen on quantitative electron probe
microanalysis of hydrous silicate and oxide minerals. GSA Abstracts, 28, 212.
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Impact of unaccounted for oxygen
Consider: Apophyllite -- KCa4Si8O20(F,OH)•8 H2O
Which has LOTS of oxygen which typically is “unanalyzed” and
therefore not involved in the matrix correction
Solution: Iterate a
fixed amount of H2O
(16 atoms of H =
1.76 wt% H plus
stoichometric O) per
formula to achieve
good results.
As shown in the
bottom analysis
where the H2O is
missing, there is up
to 3% relative error
for cations.
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Physical Parameters Needed
The ZAF corrections require accurate and precise knowledge
about many physical parameters, such as
• Electron stopping power
• Mean ionization potentials
• Backscatter coefficients
• X-ray Ionization cross sections
• Mass absorption coefficients
• Surface ionization potentials
• Fluorescent yields
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“State of EPMA parameters”
As David Joy points out in his 2001 article “Constants for
Microanalysis”, there are problems in our knowledge of many
parameters:
• there are experimental stopping power profiles for 12 elements and
12 compounds, which raise questions about the traditional Bethe
equation
• only half of the elements whose K lines are used for EPMA have
measured K shell ionization cross-sections ; only 6 elements have
measured L shell cross-sections; there are zero M shell cross-sections
• K shell fluorescent yields are the best documented parameters; there
are gaps in the data for L shell yields; there are only 5 measured M
shell yields
• despite the fact that backscatter coefficients have been measured for
100 years, the data has many gaps and is of poor precision (i.e. 30%)
UW- Madison Geology 777
At the Eugene EPMA workshop in September 2003, John
Armstrong reviewed the state of EPMA matrix corrections
• Big problem with software/manufacturers, not documenting which
corrections used. Some have picked "improved" parameters which do not fit
with the other parameters, e.g. in some, where no formal fluorescence
correction, the absorption correction was tweaked to take fluor into account,
and then when later fluorescence corrections developed, to use this in addition
to absorption correction, has an overcorrection for fluorescence.
• Problem with researchers not stating in their publications which correction
they used; NIST is trying to develop some protocols which people can
reference (brief notation with pointer to NIST for full description).
• There are a few errors/typos in the long accepted X-ray tables (i.e., Bearden)
– 3 are major errors.
• Actually measured mass absorption factors are rare! Measurements exist for
Na Ka by Al; Si Ka by Al and Ni; Mg Ka by O, Al, Ti and Ni; and Al Ka by
O, Na .....
• There is over 30% variation in published values of some macs for
geologically relevant elements; they can’t all be correct!
UW- Madison Geology 777
“So what do we do?”
We have discussed various ways to correct the raw data, the goal being
to come up with the most accurate and precise analytical procedures to
give us the most trustworthy data.
We have just mentioned that everything is not as rosy as one would
hope.
So, can we trust the numbers we get out of the probe? In many/most
cases, given care, yes. But we cannot blindly look at the electron
probe and computer as a black box!
Stay tuned for an upcoming installment, where we discuss standards,
accuracy and precision in EPMA.