UofO- Geology 619
Electron Beam MicroAnalysisTheory and Application
Electron Probe MicroAnalysis (EPMA)
WDS (Wavelength Dispersive
Spectrometry):
(Parameters)
Modified from Fournelle, 2006
Generic EMPA/SEM WDS
Electron gun
Column/ Electron
optics
Optical microscope
EDS detector
Scanning coils
SE,BSE detectors
Vacuum
pumps
WDS
spectrometers
Faraday current
measurement
Key points
• X-rays are dispersed by crystal with only one wavelength
(nl) reflected (=diffracted), with only one wavelength (nl)
passed to the detector
• Detector is a gas-filled (sealed or flow-through) tube where
gas is ionized by X-rays, yielding a massive multiplication
factor (‘proportional counter’)
• X-ray focusing assumes geometry known as the Rowland
Circle
• Key features of WDS are high spectral resolution and low
detection limits
WDS Spectrometers
An electron microprobe
generally has 3-5
spectrometers, with 1-4
crystals in each. Here, SP4
(spectro #4, LF) with its
cover off.
Crystals
(2 pairs)
Proportional
Counting Tube
(note tubing for gas)
PreAmp
Key points
• X-rays are dispersed by a crystal with only one
wavelength (nl) reflected (=diffracted), with that one
wavelength (nl) passed to the detector.This is a
monochrometer. Recall that n can be >1, so other
elements can cause interference if their wavelengths
are at an integral fraction of the desired wavelength.
• The detector is a gas-filled (sealed or flow-through)
tube where gas is ionized by X-rays, yielding a
massive multiplication factor (‘proportional counter’)
• X-ray focusing assumes geometry known as the
Rowland Circle
• Key features of WDS are high spectral resolution
and low detection limits
Spectrometers- Orientation
The typical electron microprobe
has vertically mounted
spectrometers (a), i.e. the Rowland
circle is vertical. This orientation
permits up to 5 spectrometers to be
mounted around the column, as well
as having room for an EDS detector.
In this orientation, X-ray intensities
are susceptible to small differences
in the Z position of the sample (= Xray defocusing, not good). We use
polished planar samples, and focus
the sample Z with reflected light.
There are some applications (e.g., industry) where the probe is utilized in
production, and samples are rough surfaces. For this specialized situation, the
spectrometer can be inclined (b), which then permits X-ray diffraction from a
range of heights, all now on the inclined Rowland circle. However, only 2
inclined spectrometers will then fit around the column.
Reed, 1993, Fig. 6.9, p. 70.
Inclined Spectrometer
Focussing Geometry
The point source of X-rays in the
electron microprobe is not optimally
diffracted by a flat crystal, where
only a small region is “in focus” for
the one wavelength of interest.
X-ray intensities are improved by
adding curvature to the crystals:
• Johann geometry: the crystal is
bent/curved to a radius 2r (=diameter
of Rowland circle);
• Johansson geometry: the crystal is
curved to 2r, and the surface is
ground to r. This is a difficult
process, so most crystals have
Johann geometry.
Reed, 1993, p. 67.
Rowland Circle
For most efficient detection
of X-rays, 3 points must lie
upon the focusing circle
known as the Rowland
Circle. These points are
• the beam impact point on
the sample (A),
• the active central region of
the crystal (B), and
• the detector -- gas-flow
proportional counter (C).
C
B
A
Rowland Circle
The loci of 3 points must
always lie on the Rowland
Circle. Starting at the top
position (blue), there is a
shallow angle of the X-ray
beam with the analyzing
crystal. To be able to
defract a longer
wavelength X-ray on the
same spectrometer, the
crystal travels a distance
further out, and effectively
the (green) Rowland Circle
“rolls”, pinned by the
beam-specimen interaction
point.
Bragg defocussing
X-ray path
Only a small % of X-rays
reach the spectrometer. They
first must pass thru small
holes (~10-15 mm dia; red
arrows) in the top of the
chamber (above, looking
straight up), then thru the
column windows (below,
SP4).Thus, in our EMP, there
are different vacuum regimes
in the chamber vs the
spectrometer.
BSE detectors
alternate
Wavelength Dispersion
Of the small % of X-rays that reach the crystal, only those
that satisfy Braggs Law will be diffracted out of the crystal.
nl = 2d sinq
BA’ = A’C = d sinq
for
constructive reinforcement of a
wave, the distance BA’ must be
one half the wavelength. Thus,
2d sinq = l and by similar
geometric construction = nl
Note that exact fractions of l
will satisfy the conditions for
defraction. Thus, there is a
possibility of “higher order”
(n=2,3,...11,?) interference in
WDS (but there also is the
means electronically to
discriminate against the
interference).
Lots of Analyzing Crystals
Over the course
of the first 30
years of EPMA,
~50 crystals and
pseudocrystals
have been used.
Temperature Dependence
We attempt to keep a constant temperature in the probe lab, around
68°F (20°C). This is also the temperature of the chilled water that
circulates both through the electronic cabinet as well as the column
(and outer jacket of diffusion pump).
Two aspects of the instrument are sensitive to temperature changes –
the spectrometer crystals, and the detector P10 gas.
• Spectrometer crystals have a linear expansion coefficient, and
expansion will change the 2d. The effect upon PET is 4x worse than
upon LIF, and increases rapidly with increasing sin q.
• P10 gas pressure must be constant, as this is critical to having
reproducibility in counting rates between the standards and the
unknowns, both over short time spans as well as longer (e.g. 24 hour)
durations. (Loss of air conditioning on very hot summer days precludes
probing.)
Spectral Resolution
WDS provides roughly an order of
magnitude higher spectral
resolution (sharper peaks)
compared with EDS. Plotted here
are resolutions of the 3 commonly
used crystals, with the x-axis being
the characteristic energy of
detectable elements.
Note that for elements that are
detectable by two spectrometers
(e.g., Y La by TAP and PET, V
Ka by PET and LIF), one of the
two crystals will have superior
resolution. When there is an
interfering peak and you want to
try to minimize it, this knowledge
comes in very handy.
Reed, 1995, Fig 13.11, in Williams,
Goldstein and Newbury (Fiori volume)
Spectrometer Efficiency
The intensity of a WDS spectrometer
is a function of the solid angle
subtended by the crystal, reflection
efficiency, and detector efficiency.
Reed (right) compared empirically
the efficiency of various crystals vs
EDS. However,the curves represent
generation efficiency (recall
overvoltage) and detection
effeciency.
Reed suggests that the WDS spectrometer has ~10% the collection
efficiency relative to the EDS detector.
How to explain the curvature of each crystal’s intensity function? At high Z,
the overvoltage is presumably minimized (assuming Reed is using 15 or 20
keV). Low Z equates larger wavelength, and thus higher sinq, and thus the
crystal is further away from the sample, with a smaller solid angle.
Reed, 1996, Fig 4.19, p. 63
Crystals and PC/LSMs
Consider the order of 2d in Braggs Law: sin q varies from .2-.8, and l
varies over a wide range from hundreds to fractions of an A. Thus, we
need diffractors that cover a similiar range of 2d, from around 1 Å to
hundreds of Å. In our SX50/100, we utilize TAP, PET and LIF crystals
for the shorter wavelengths. For longer wavelengths, there are 2 options:
• Pseudocrystals (PCs), produced by repeated dipping of a substrate in
water upon which a monolayer (~soap film) floats,progressively adding
layer upon layer, or
• Layered synthetic microstructures (LSMs; also LDEs, layered
diffracting elements), produced by sputtering of alternating light and
heavy elements, such as W and Si, or Ni and C.
• Both these are periodic structures that diffract X-rays. The LSMs yield
much higher count rates; however, peaks are much broader, which have
good/bad consequences, discussed later.
• In reality, people interchange the words PC, LSM, LDE, etc. Cameca
uses PC and JEOL uses LDE, for same things.
Crystals and PCs
on the UofO SX50/100
Crys tal
LIF
PET
TAP
PC0
PC1
PC2
PC3
nam e
Lithium flu oride
Pentaerythri tol
Tha lliu m acid phth alate
form ula
C(CH2OH)4
TlHC8H4O4
W-Si
W-Si
Ni-C
Mo-B4C
orie ntation
2d (Å)
k
200
002
101 0
4.0 267
8.7 5
25.745
45.0
60
98
200
0.0 0005 8
0.0 0014 4
0.0 0218 0
0.0 1483 0
0.0 1000 0
0.0 1300 0
0.0 1000 0
App rox rang e(Å)
.8 - 3.0
2.2 - 7.1
6.5 - 20
11. - 36 .
15 - 48
25-8 0
50-1 60
There is a more accurate form of Braggs Law, that takes
into account refraction effects, which are more
pronounced in the layered synthetic diffractors (why?),
nl = 2d sinq(1-k/n2)
k is refraction factor, n is order of diffraction
Crystals and PCs: Which to use?
The EPMA user may have some control over which crystal to
use; some element lines can be detected by either of 2
crystals (e.g. Si Ka by PET or TAP, V Ka by PET or LIF),
whereas other elements can only be detected by one (e.g. S
Ka by PET). Each probe has its own (unique?) set of crystals
and the user has to work out the optimal configuration,
taking into account concerns such as
• time and money (resolution vs. count rate)
• interferences vs counting statistics (sharper peaks usually
have lower count rates)
• stability (thermal coefficient of expansion)
•sensitivity to de-focussing, peak shape/shift
Pseudocrystals/LSMs
Goldstein et al, p. 280
Crystal comparison
The class project
in 2002 was to
collect data that
will be put in a
chart to compare
the efficiency of
different crystals/
PCs for certain
elements.
TAP gives a higher
count rate, and
wider peak for Si
Ka vs. using PET
Å
Å
Si Ka on TAP
sin q = 27714
P/B= 4862/40=122
FWHM=0.038 Å
Si Ka on PET
sin q = 81504
P/B= 207/1.3=159
FWHM=0.006 Å
Full Width Half Max
Max
4862 cts
Peak (spectral)
resolution is
described by
FTWM
Full Width
Si Ka on TAP
sin q = 27714
P/B= 4862/40=122
FWHM=0.038 Å
Å
Half max
2431 cts
WDS detector
P10 gas (90% Ar - 10% CH4)
is commonly used as an
ionization medium. The X-ray
enters through the thin
window and 3 things can
occur: (1) the X-ray may pass
thru the gas unabsorbed (esp
for high keV X-rays); (2) it
may produce a trail of ion
pairs (Ar+ + e), with number
of pairs proportional to the
X-ray energy; and (3) if the
X-ray is >3206 eV it can
knock out an Ar K electron,
with L shell electron falling in
its place. There are also 3
possibilities that can result
from this new photon:
(3a) internal conversion of the excess energy
with emission of Auger electron (which can
produce Ar+ + e pairs); (3b) Ar Ka X-ray itself
can knock out electron of another Ar molecule,
producing Ar+ + e pair; or (3c) the Ar Ka X-ray
can escape out thru a window, reducing the
number of Ar+ + e pairs by that amount of
energy (2958 eV)
Detector amplification
Nominally, it takes 16 eV to
produce one Ar+- electron pair,
but the real (effective) value is
28 eV. For Mn Ka (2895 eV),
210 ion pairs are initially
created per X-ray. However,
there is a multiplier effect
(Townsend avalanching). For
our example of Mn Ka, all 210
electrons are accelerated
toward the center anode (which
has a positive voltage [bias]
of1200-2000v) and produces
many secondary ionizations.
This yields a very large
amplification factor (~105), and
has a large dynamic range (050,000 counts/sec).
Detector windows
Thin (polypropylene) windows are used for light X-rays (e.g. those
detected by TAP and PC crystals). Since the windows are thin, the gas
pressure must be low (~0.1 atm). And being thin windows, some of
the gas molecules can diffuse out through them -- so the gas is
replenished by having a constant flow. For thicker windows (mylar),
1 atm gas pressure is used (with higher counts resulting). Sealed
detectors with higher pressure gas (e.g. Xe) are also used by some.
WDS detector
The bias on the anode
in the gas proportional
counter tube needs to
be adjusted to be in the
proportional range. Too
high bias can produce a
Geiger counter effect.
Too low produces no
amplification.
WDS pulse processing
The small electron pulses
(charges) generated in the
tube are first amplified in the
pre-amp (top) located just
outside the vacuum on the
outside of the spectrometer,
then sent to the PHA board
where they are amplified
(center) and shaped
(bottom). Each figure is for
one (the same) pulse.
Goldstein et al Fig. 5.10
Ar-escape peak
Reed, 1993, p. 90
There is a probability that a small
number of Ar Ka X-rays produced
by the incident X-ray (here, Fe
Ka) will escape out of the
counting tube. If this happens,
then those affected Fe Ka X-rays
will have pulses deficient by 2958
eV. Fig 7.8 is an unusual plot of
this (for teaching purposes); what
is normally seen is the Pulse
Height distribution where the
pulses are plotted on an X-axis of
a maximum of 5 or 10 volts.
Actual PHA
plot for Si Ka:
there is no Arescape peak.
WHY?
Higher order reflections
Recall nl = 2d sinq. Higher order reflections are possible in
your specimens, and must be avoided to prevent errors in
your analyses.
Reed (1993) reports that LIF can show a strong second order
peak, up to 10% of the first order peak.
In 1999, the 777 class examined the higher order reflections
of Cr Ka lines. On PET, 2nd and 3rd order peaks were
present, and decreased ~an order of magnitude with
increasing n. On LIF, up to the 8th order peak was present.
Here, the intensity of the odd numbered orders was less than
the following even order, e.g. the 5th order Ka had 30%
fewer counts than the 6th order line.
Differential mode of pulse height analysis (PHA) may be
used to ignore counting higher order X-rays.
Integral vs Differential PHA
Analysis of ‘light elements’ such as C is
complicated because of the long
wavelength (44 Å) which means that higher
order reflections of many elements can
interfere. At top, where the PHA is set to
the “count everything” integral mode, the
3rd order reflection of Ni La1 falls very
close to C Ka and adds some to C peak
counts. Note also the 2 and 3 order Fe L
lines. By setting the detector electronics to
the discrimination mode (“differential”),
bottom, the higher order lines are strongly
(but not totally) suppressed.
Spectrometer scans
Goldstein et al, p.507-8
Spectrum =
Characteristic + continuum
Recall that the X-rays generated by
electron bombardment are both
characteristic of each element
present in the specimen, as well as
the broadband “continuum”. And
recall that the background level
increases with increasing mean
atomic number of the specimen. In
EPMA, several steps must occur.
First, the peak position must be
precisely found.
Bkg
under
peak
Then, trustworthy background positions must be found in order to model
the background level at the peak position. Above, the Mg ka peak position
is at the white (center) line and we need to determine where adjacent to it
would be the best places to measure the background level, in order to
calculate (model) the continuum level under the peak..
Probe for EPMA
Peak and Background displays
Our software provides handy
ways to store wavescans. The
standard procedure is to peak the
elements of interest and use
either default background
positions or ones previously
chosen.
Bkg
under
peak
The displayed wavescans have a
central line that is white. This is
the peak of interest (here, Mg
Ka).Background positions are
shown by yellow lines. If a
background position has been changed, the old position is shown in
magenta.The “background model” is a line, here red (normally yellow).
Curved background-1
There. are some cases where the background has a curvature, particularly at low
sin theta A linear model (below) results in too high calculated background.
Curved background-2
An exponential curved background, however, provides a better result.
Note the presence of several other background models in the right box.
Congested backgrounds
In some (many) cases, adjacent peaks can interfere with either high or low
background position, requiring same side backgrounds: here, average of 2
measurements on the high side. Highest peak is 3rd order Ca Ka.
Background Offsets
How far away from the
peak should the
background offsets be?
Reed demonstrates
mathematically
(adjacent figure) that a
small overlap on the
tails of the peak ends up
making no significant
difference.
However, he warns (and it is my experience) that being too close to the
peak is not good practice, and should only be done in extreme cases
where it is impossible to find a ‘free area’ in the adjacent background.
Reed, 1993, p. 150
Backgrounds and Absorption Edges
You need to be aware of
potential for error if you
position your low background
too far to the left (low sinq,
short wavelength), below the
absorption edge of the element
you are measuring. For the K
edges, this is at the Kb
position.
This is an EDS
view of the
absorp;tion edge.
To translate to
WDS (wavelength
or sin q), just
reverse the axes.
The background level to the low sinq (=higher energy) side of the edge will
be depressed because these continuum X-rays have energies great enough to
be “used up” causing secondary fluorescence of the element in question,
and thus produce a misleadingly low background. If a low background
position between the peak and absorption edge can’t be taken, then only
measurements on the high side should occur. “These considerations do not apply to
small peaks for which the associated absorption step is negligible.”–Reed, 1993, p. 151
Ar Absorption Edge
Analysts need to understand
the possible implications of the
Ar absorption edge (recall Ar
is in the detector P10 gas). A
certain fraction of X-rays with
energy lower than the argon K
edge (3.202 keV) will pass
through the gas without
interaction. However, for Xrays with energies > 3.202 keV,
approximately twice as many
will interact with the gas and
be detected.
From Paul Carpenter’s talk at April 2002 NIST-MAS EPMA workshop
• Lines of the same family that fall on either side will have ‘abnormal’
proportions–normally the La > Lb, but for Cd, it is reversed due to this.
• Trace element studies utilizing the U Ma line must utilize only
background offsets on the high sinq side of the peak (see figure above).
Holes in the Background-1
In 1987, Bruce Robinson
(Australia) reported on a
phenomenon uncovered during
examination of arsenopyrite for
trace amounts of gold. After
looking at unknowns, he checked a
reference arsenopyrite that should
have had no Au in it – but it showed
100 ppm. High resolution scan of
the background near the Au La peak
on the LIF crystal showed a distinct
drop (trough) by ~10% relative to
the adjacent background. With an
incorrect (artifically “low”)
background, zero Au had become
100 ppm Au.
Au La peak
position
From Remond et al, 2002, NIST Journal of Research
Holes in the Background-2
These holes or ‘negative peaks’ are
caused by reflections of the
continuum X-rays from planes in
the crystal other than the correct
plane (the 200 in LIF). These Xrays do not reach the counter.
The point is that when you are
looking for very low detection
levels, it pays to pay very close
attention to the shape of the
background and to try to understand
it well. And to have some well
characterized secondary standards
to evaluate your procedure with.
Au La peak
position
On Peak Interferences
Users must be vigilant for
interferences upon the peaks
being measured, both in the
unknowns and in the standards.
The figure to the right shows
an interference type seen
where peak B overlaps peak A.
For elements whose wavelengths can be diffracted by a choice of 2
crystals, one will be better for spectral resolution (the lower 2d, with
higher sin theta position).
Reed, 1993, p. 153
On Peak Interference-Slight
REE analysis is particularly tricky, since there are so many elements present and
there are so many L lines.Here the high side tail of Ce Lb1 interferes with Nd La.
Interference Correction
We must correct
for interferences,
by software
options, if we have
standards that have
the interfering
element (here Ce)
but none of the
interfered with
element (here Nd).
During count acquisition (“calibration” or “standardization”) on the Ce
standard (356), we also acquire interference counts at the Nd La peak
position. Then during analysis of unknowns, an appropriate correction is
made for the overlap.
Peak Centering-1
Quantitative analysis requires
knowledge of the peak
intensity, which is a function of
the composition of the
specimen.We could also use the
integrated area of the peak, but
that is time-consuming.
The peak position is first
determined upon either the
specimen or the standard, with
the general assumption that the
position is the same (with
important exceptions!).
Then that position (and user-determined background offsets) are
utilized in the automated movement of the spectrometers during
analysis.
Peak Centering-2
There are several methods possible to find the peak center. In times past,
manual searching was done (aided by an audio device whose pitch
increased as counts increased). Today we have automated peaking routines.
We have developed a routine of (1) using one of the top 3 methods (usually
the fast ROM) to get pretty close to the peak, and then (2) a “post-scan”
across the top of the peak that allows the operator the final decision of
picking the optimal peak position. (This option was added based upon
detailed peak scans done by 777 students in the Fall of 2002.)
Peak Centering-3
It is very important to start with the “best”
peak position, which means the center of
the peak (usually the highest counts –
though not necessarily). At the right are
two “post-scans” where the red vertical
line is the position selected by the ROM
automation—very good for the Si Ka
position, but about 7 units too high for Al
Ka. The “post-scan” option gives the
operator the freedom to over-ride the
computer’s best guess with an intelligent
decision. Best operating practice calls for
picking the center of the peak centroid,
because there may be slight offsets
developed over a probe session due to
mechanical drift and there is also the
question of real peak shifts; by starting in
the dead center, these variables should be
minimized.
X-ray Peaks Poisson Distribution
X-ray peaks follow a
Poisson distribution,
which describes the
counting of events that
occur at random but at a
definite average rate.
“It can be shown” that for
a Poisson distribution, the
standard deviation is the
square root of the counts.
The Poisson distribution is similar to, but different from the Gauss
distribution. The Gauss distribution is bell shaped and symmetrical about
its mean value, while the Poisson distribution has neither of these
properties in general.
John R. Taylor, An Introduction to Error Analysis, 2nd
Ed., 1997. p. 245-256
Peak Shifts-1
Al Ka Peaks
Shifts in peak shape of certain
elements can occur due to difference
in chemical bonding, between
different samples/standards. Some
well understand examples are Al Ka
and S ka, as well as P ka, and the
“light” element K lines.
Articles have been published that
show evidence of peak shifts of Si and
Al kb as well as Fe La/Lb in relation
to valence/bonding.
PbS
BaSO4
Peak Shifts-2
These shifts can be understood if you
understand that a characteristic peak is
actually a cumulative sum of several
discrete peaks which the spectrometer
may not resolve, though many times
one can discern humps within each
peak.
Figures from Remond et al, 2002, NIST Journal of Research
Peak
Shifts-3
Over the past year I
have been trying to
track down the
cause of some
errors in silicate
analyses (e.g., totals
of <99 vs 100 wt%).
Silica Ka is clearly
a very important
peak to “get right”.
There appears to be a ~5 unit shift , with garnet and enstatite higher than opx,
with the Fo90 olivine in between. This could explain a 1-2% deficiency.
There is some theoretical basis for this: the Ka1 and Ka2 peaks may have
different weights (John Armstrong, pers. comm. 9/25/03)
Peak Shifts-4
If unrecognized, shifts can affect the X-ray intensity measured at the defined
“peak center position”, producing errors.
This is predominately an effect on the “light elements” (B, C, N, O, F) where the
valence electrons are involved in X-ray production.
We will discuss this further in
the section on “Light element
analysis”, referring to (1)
integration under the peak, and
(2) Area Peak Factors.
Work in progress here: L lines
of elements like Co apparently
have peak shifts.
Excellent
article on this
subject is
Remond et al,
from the NIST
2202 Journal.
A pdf file is on
the Geol 777
web site.
Identifying Lines in Spectra
In “normal” WDS
quantitataive analysis,
the analyst is concerned
with a pre-determined
set of elements defined
by previous knowledge.
You focus only upon
these elements.
However, there are times when you must identify unknown elements. EDS is a
quick way to search for elements; however, there are limitations with EDS,
and you may then turn to WDS scans. The easiest is running through a small
list of elements (looking for a peak for each), but if this fails, you must do full
wave scans on all the spectrometers, and manually identify the peaks (using
the X-ray database in the software to assist). There is an optimal order for
doing this identification of peaks.
Guidelines for WDS peak ID-1
1. Always start with the shortest wavelengths, where you have the
highest chance of finding first order (n=1) peaks. These will be on the
crystal with the lowest 2d, the LIF crystal. Spectra on the other crystals
may have higher order reflections of elements present here.
2. Identify the highest intensity peak at the low wavelength end of LIF. It
should be a Ka or La peak. If you find such a peak, you immediately
assume that you will find a related “family of lines”, such as Kb or Lb1,
Lb2 , Lb3 , Lb4 etc –you immediately look for them on all the crystals.
The rough ratio of Ka to Kb is 10:1, and La to Lb1 is 2:1.You can also
use this relationship to exclude some lines; e.g. a peak at 1.176Å could
be either As Ka or Pb La. Inspection shows there is no As Kb, but there
are other Pb L lines. Thus, the peak is due to Pb.
Guidelines for WDS peak ID-2
3. If you find a strong K line, you will probably also find some L lines of
that element. And if you find a strong L line, you could also find some M
lines.They may be on a different crystal.
4. Once all first order elements found initially from of the LIF spectrum
have been identified and all’family member’ peaks on all spectra
checked off, then all possible higher order peaks need to be accounted
for.
5. Only now should you proceed to the next unidentified high intensity,
low wavelength peak, repeating steps 1-4. Then continue repeating until
all peaks are identified.