Electron Probe Microanalysis EPMA

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Electron Probe MicroanalysisEPMA
UW-Madison Geoscience 777

• Quantitative Analysis
• and
• Matrix Corrections

Revised 1/10/2016
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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 X-rays generated by
  electron beam, using war-surplus TEM
• Castaing succeeded, PhD 1951 Application of
  Electron Probes to Local Chemical and
  Crystallographic Analysis

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Raimond Castaing (1921-1999)
His thesis laid out the basics of EPMA which have
remained constant for the past 64 years Key
concept
where K is the K ratio for element i, I is the
X-ray intensity of the phase and subscript i is
one element.
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Using K-factor simplifies analysis

• 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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Castaings First Approximation
Castaings 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?
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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 X-ray 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 Fe-Mn. 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 11
  line, and so is a good reference.
• The Fe-Ni alloys plot above the 11 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 11 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
• Empirical simplest, based on known binary
  experimental data
• ZAF 1st generalized algebraic procedure assumes
  a linear relation between concentration and x-ray
  intensity
• Phi-rho-Z based upon depth profile (tracer)
  experiments
• Monte Carlo based upon statistical probabilities
  of electron-sample 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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Z A F
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 features
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
where J11.5 Z and Emean (E0Ec)/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
Reed, 1996, Fig. 2.11, p. 17
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.
R can be approximated by
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
Reed, 1993,, p. 219
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). Castaings approach was to
integrate the Beers 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. The absorption (A)
correction is then defined as A f(c)std /
f(c)sample
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.
c Chi
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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 where c m cosec y , s is a measure
of electron absorption and depends on effective
electron energy, where 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 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 (gt1980) 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 (gtmid 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 gt5 error, and a
heck of a lot gt2 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 X-rays. 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
false Co
false Cu
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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).
Above EDS spectrum on Pd2HfAl 5 um away from
Nb. Pd Ka is very efficient at traveling across
the border and exiting the Nb
Fournelle, Kim and Perepezko (2005)
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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
Geology 777
In 1963-4, Ziebold and Ogilvie developed a
corrections for some binary metal alloys, with an
equation in the form 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 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.
C2
K2
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 where a123 is the
a-factor for element 1 in the ternary with
elements 2 and 3, and is defined as This
equation can be rearranged 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 nth component a b-factor could be
found where 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
• Declare C and O as elements in the analysis (but
  not measured)
• Tell it to calculate with stoichiometric oxygen
• Create a rule so that there is 1 atom of C to
  every 3 atoms of O
• 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)
46
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.
47
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.
48
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

49
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)

50

• 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 cant all be correct!

51
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.