Electron probe microanalysis

1
Electron probe microanalysis

• Accuracy and Precision in EPMA
• Understanding Errors

Modified 11/15/10
2
Whats the point?
How much can I trust the compositions that the
probe computer spits out? Are two analyses
equivalent? Can I compare my numbers with those
published by other researchers using EPMA?
3
Goal and Issues

• Goal achievement of high accuracy and
  precision in quantitative analyses,
  recognizing sources of errors and minimizing them
• Issues involved with achieving this goal
• Standards
• Instrumental stability
• Sample and standard physical condition
• Beam impact on sample complications
• Spectral issues
• Counting statistics
• Matrix correction

4
Standards how good are they? well
characterized? homogeneous? Instrumental
conditions beam stability spectrometer
reproducibility thermal stability detector
pulse height stability/adjustment reflected
light optics (stage Z) Matrix correction any
issues (eg MACs for light elements)? wide range
in Z for binary (eg PbO) Sample and standard
conditions rough surface? polish? etched? tilt?
sensitive to beam? C coat thickness if
used Counting statistics enough counting time?
Spectral issues peak and background
overlaps? Sample size vs interaction volume
homogeneous? small particles? secondary
fluorescence?
5
These can be categorized into random and
systematic errors.
6
Random Errors

• Random errors include
• random nature of X-ray generation and emission
• instrumental (random) instability
• operator inconsistency (e.g. little attention to
  correct optical focus sometime ok, othertimes
  not ok)
• sample surface roughness
• interaction volume intersecting two phases
• secondary fluorescence from hidden (below
  surface) phases
• stray cosmic rays

7
Systematic errors

• Systematic errors include
• instrumental instability (temperature effect on
  crystal 2d, and on gas pressure stage Z drifts
  as it heats up)
• inappropriate matrix correction
• poor electrical ground of either standard or
  unknown
• beam change/damage to unknown (e.g. Na in glass)
• difference in peak shape/position (standard vs
  unknown)
• peak or background interference
• pulse height depression on standard
• fluorescence across observed phase boundaries
  (e.g. diffusion couple)

8
Precision and Accuracy in Error Analysis
Precision refers to the reproducibility of the
counts and thus the ability to be able to
compare compositions, whether within a sample, or
between samples, or between analytical sessions.
It is directly tied to counting statistics. It is
a relative description. Accuracy refers the
truth of the analysis, and is directly tied to
the standards used and the matrix correction
applied to the raw data, as well most of the
other variables listed previously that could
affect the X-ray intensities (background and peak
interferences, beam damage, etc). It is an
absolute description. EPMA quantitative error
analysis is a combination of both, precision
being very easy to define, accuracy more
difficult. Precision for major elements could
easily be lt1, but when combined with accuracy,
total EPMA error probably 1-2 in the best cases
(for major elements).
9
Precision and Accuracy
Low Precision
High Precision
Low Accuracy
High Accuracy
10
Instrumental Errors-1

• Beam current stability with Faraday cup
  measurements made for each analysis, long term
  drift should not be a problem as the counts for
  each analysis are normalized to a common
  reference current value (could be 1, or 20 nA).
  For long count times (minutes ) for trace element
  work, it is recommended that the peak and
  background counting be constantly cycled so that
  any longer period issues be spread out over the
  whole time period.
• Spectrometer reproducibility with modern
  microprobes, this should not be a serious
  problem, although problems do crop up with age.
  Where crystals are flipped, in a small fraction
  of cases there is an error generally it is not
  recommended to flip crystals within analyses.
  When spectrometer reproducibility is a problem,
  it is seen as backlash of the gears to minimize
  errors, the peaks should always be approached
  from the same direction. This is set up within
  the software.

11
Instrumental Errors-2

• Thermal stability Spectrometers could drift if
  there is a change in the room temperature, though
  this would presumably be noticeable to the
  operator (air conditioning fails in hot spell). I
  have not seen problems with PET nor LIF. P10 gas
  pressure is sensitive to the temperature change.
  We attempt to keep the room at 68-70C and the
  circulating water temperature in the machine is
  very close to this. Stage height (Z) drifts due
  to motor heating during long (overnight) runs.
• Detector pulse height adjustment/stability The
  bias (voltage) of the gold wire in the detector
  must be set to the proper value this is a
  function of the energy of the X-ray and gas
  pressure. The operator must verify that the bias,
  gain and baseline are set properly (the last
  particularly where the Ar-escape peak is
  partially resolved).

12
Instrumental Errors-3

• Dead time In WDS, counts are dead time
  corrected. If dead time is not accurately
  determined, there could be a systematic error
  here. Cameca probes operate somewhat differently
  from JEOL and others, in that Cameca introduces a
  hard constant time delay (e.g. 3 msecs)
  automatically into the counting circuitry and
  then uses that value to correct the counts.
• Probe labs should verify (at least once) that the
  manufacturers official or default dead time
  factors are correct. This is done by counting on
  a metal standard (e.g. Si or Ge) at varying
  Faraday currents, with the dead time correction
  turned off. These data can then be plugged into a
  spreadsheet that which Paul Carpenter (Washington
  University) has developed to calculate the most
  accurate dead time actually present on a
  particular probe. Also, in our Probe for EPMA
  software, there is an option for an alternate,
  more complex dead time correction equation, for
  high count rate (gt50K cps)

13
Instrumental Errors-4

• Specimen focus (stage height) Samples and
  standards must be positioned at the same stage
  height, so that they will all be at the same
  position vis a vis the Rowland Circle ( in X-ray
  focus for Bragg defraction). Sometimes it is
  difficult decide within 1-3 um which is the
  best height this small Z difference is not
  critical. It becomes critical when it reaches the
  5 or 10 um out of focus realm, which can occur
  during unattended overnight runs as the sample
  and stage heat up (heat from stage motors) this
  can be addressed by using the stage Z autofocus
  automation (but test it out first, as it must be
  calibrated).
• (On JEOL probes, there is a base plate
  adjustment for tweaking this Cameca probes does
  not have any easy adjustment.)

14
Sample/standard Error Physical issues - 1

• Surface irregularities the matrix correction
  relies upon the correct take off angle to
  calculate the path length for the absorption
  correction, and irregular surfaces will have
  variable path lengths and thus the measured X-ray
  intensities will not be consistent between
  analytical spots. Moreover, in using different
  spectrometers mounted in different directions,
  the path length will vary between spectrometers
  for one analytical spot.
• Etched samples generally, etching may introduce
  some irregularity, and should be avoided.
  However, I have seen slightly etched samples
  analyzed without apparent problem.
• Polishing samples should be polished with final
  stage using lt1 mm diamond or alumina or silica.

15
Sample/standard Error Surface Irregularities
These Monte Carlo simulations show the effect on
K and L line X-rays of Ni and Al, of
one-directional V-grooves of height (h) varying
from .1 to 1 mm. The smallest (.1 mm) grooves
have no noticeable effect, but the deeper grooves
clearly have major impacts on Al Ka and Ni La
(due to more or less absorption), with the
greatest impact on the lowest energy line.
Lifshin and Gauvin, 2001,Fig. 4, p. 171.
16
Sample/standard Error Physical issues - 2

• Specimen homogeneity a key assumption of
  quantitative EPMA is that the interaction volume
  is one phase (is homogeneous).
• If more than 1 phase is overlapped by the beam
  the matrix correction usually overcompensates and
  produces an erroneous composition gt100 wt. This
  is common for small eutectic (groundmass) phases.
• If trace elements are being considered, then
  also the adjacent surrounding volume (up to
  50-100 mm away) must not contain phases with
  higher concentrations of the elements of
  interest, which might be secondarily fluoresced.
• Diffusion couples have similar constraints, in
  that secondary fluorescence across the boundary
  can yield X-ray intensities up to a couple of
  percent (which could also give high totals).
  Users need to either empirically or theoretically
  verify this is NOT happening.

17
Sample/standard Error Physical issues - 3

• Incorrect geometry (non-orthogonal surface)
  this occurs too often with 1 diameter plugs that
  have been automatically polished. For whatever
  reason, the sample surface ends up at a slant to
  the wall, and when the set screw is tightened in
  the holder, the surface ends up at an angle to
  the horizontal. This introduces an error in the
  take off angle. Also, the area of interest may be
  too low and impossible to reach stage Z focus.

This Monte Carlo simulation shows that a 5 tilt
of the sample will alter the K ratio of Al Ka by
.01, which equals a 8 relative error before
matrix correction. An Al ZAF of 1.5 would thus
increase the error to 12.
Lifshin and Gauvin, 2001, Fig 3., p. 170.
18
Sample/standard Error Physical issues - 4

• Incorrect geometry - edge effects materials
  mounted in epoxy and then polished with loose
  polishing compound commonly have differential
  erosion at the epoxy-material interface,
  producing a moat or channel in the epoxy,
  resulting in a rounding of the material at the
  edge. Efforts to do quantitative EPMA of the edge
  (rim) will be in error as the absorption path
  length will be non-uniform and different from the
  nominal length. Special polishing technique will
  minimize or eliminate this problem.

Epoxy
Specimen
Common erosion problem, rounding of specimen edge
Epoxy
Specimen
Desired geometry no rounding of specimen edge
19
Sample/standard Error Physical issues - 5

• Oxide coating/film this can be a significant
  problem for metals that oxidize (e.g., Al, Mn,
  Mg, Ti, etc.), particularly for standards. These
  can reach fractions of a mm in depth, and
  significantly alter the X-ray intensity of the
  line being acquired for the standard, resulting
  in an overestimate of the element in the unknown.

This plot shows the effect of a thin oxide skin
(TiO2) on reducing the characteristic X-rays from
a pure metal standard (Ti), and is most severe
for lower E0. (Modeled with GMRFilm software).
20
Sample/standard Error Physical issues - 6

• Smear coat soft materials may smear and cross
  contaminate other materials that are being
  polished either in the same holder, or in a
  subsequent sample, producing a thin smear coat.
  I have seen one reference in the literature to Pb
  or Sn smearing. It is not normally considered a
  major problem, at least for major element
  analysis.
• Polishing artifacts Diamond and alumina
  polishing particles can get caught in pores in
  the material been polished. I have seen mm
  fragments of brass from a brass sample holder
  become lodged in feldspar and biotite.
• Charging this will reduce the effective E0.
  Conductive samples in epoxy must be grounded with
  conductive tape (preferred rather than paint).
  Semi-conductors conduct ok. Non-conductive
  samples need to be coated (C, Al, Ag, Be...).
• Porosity There could be (at least one) error in
  non-conductive porous material, with charging as
  the electrons travel between pores (vacuum) and
  material.

21
Sample/standard Error Physical issues - 7

• Carbon coat the conductive coating on the
  samples should be of the same thickness as on the
  standards being used. This can be evaluated
  experimentally or with the GMRFilm modeling
  program. Kerrick et al. (1973) measured the
  effect and showed it affected the light elements
  most strongly, and was worst at lower E0 a
  difference of 200 Å between sample and standard
  translated to a 4 difference in F Ka intensity.
  There is some antidotal evidence that old (many
  years-decade?) carbon coats may go bad
  (oxidize? delaminate?) and lose conductivity.

Kerrick et al, 1973, American Mineralogist, 58,
920-925.
22
Sample/standard Error Procedural issues - 1

• Peak interferences If measured peaks are
  overlapped by peaks of other elements, obvious
  errors will result. Such interferences can exist
  both in standards and unknowns. Such errors in
  unknowns can yield high totals. Unavoidable peak
  interferences must be addressed by using
  interference standards, to subtract the correct
  fraction of counts attributed to the interfering
  element.
• Background position interferences Incorrect
  placement of background counting positions can
  lead to errors, as the background estimate at the
  peak position usually is inflated, yielding less
  than true counts for the element. Wavescans
  should be done on typical phases, and/or Virtual
  WDS used to evaluate the situation.

23
Sample/standard Error Procedural issues - 2

• Peak shift/shape differences We have discussed
  the issues of peak shifts for S Ka. Al Ka is
  another element with a well documented issue of
  differences between the metal, oxide, and
  alumino-silicate phases. Also F and other light
  elements, and L lines of Co and Ni also have such
  issues. Peak shifts can yield small to
  significant errors.
• PHA settings Bias, gain, and baselines should
  be checked. Gross errors in them could produce
  significant errors in the analytical results.
  Pulse height depression occurs mainly where there
  is a large discrepancy in count rate between
  standard and unknown, e.g. 50000 cps on std B vs
  500 cps on Mo-Si-B phase) count rates up to
  10-15000 cps should be OK. Dropping the current
  on the B standard from 30 to 1 nA worked.

24
Counting Statistics - 1
We desire to count X-ray intensities of peak and
backgrounds, for both standards and unknowns,
with high precision and accuracy. X-ray
production is a random process (Poisson
statistics), where each repeated measurement
represents a sample of the same specimen volume.
The expected distribution can be described by
Poisson statistics, which for large number of
counts is closely approximated by the normal
(Gaussian) distribution. For Poisson
distributions, 1 sigma square root of the
counts, and 68.3 of the sampled counts should
fall within 1 sigma, 95.4 within 2 sigma, and
99.7 within 3 sigma.
Lifshin and Gauvin, 2001, Fig. 6, p. 172
25
Counting Statistics-2
The precision of the composition ultimately is a
combination of the counting statistics of both
standard and unknown, and Ziebold (1967)
developed an equation for it. Recall that the
K-ratio is where P and B refer to peak and
background. The corresponding precision in the K
ratio is given by where n and n are the
number of repetitions of counts on the unknown
and standard respectively. (The rearranged sK/K
-- with square roots taken-- term was sometimes
referred to as the sigma upon K value.)
26
Counting Statistics-3
From MAC shortcourse volume
Another format for considering cumulative
precision of the unknown is the above graph. A
maximum error at the 99 confidence interval can
calculated, based upon the total counts acquired
upon both the standard and the unknown e.g. to
have 1 max counting error you must have at least
120,000 counts on the unknown and on the
standard you could get 2 with 30,000 counts on
each.
27
Probe for EPMA Statistics -1
PfE provides several statistics in the normal
default log window printout for bkg subtracted
peak counts average, standard deviation, 1
sigma, std dev/1 sigma (SIGR), standard error,
and relative std dev. For Si the average is 4479
cps, and the average sample uncertainty (SDEV)
for each of the 3 measurements is 15 cps. The
counting error (1 sigma) is somewhat larger (21
cps), and the ratio of std dev to sigma is lt1,
indicating good homogeneity in Si.
For homogeneous samples, we can define a standard
error for the average here, 8 cps.
Finally, the printout shows the relative standard
deviation as a percentage (0.3, excellent).
NB These measurements only speak to precision,
both in counting variation and sample variation.
28
Probe for EPMA Statistics - 2
After the raw counts, the elemental weight
percents are printed, with some of the same
statistics, followed by the specific standard
(number) used. Following that are the std
K-ratio, and std peak (P-B) count rate. Below
that are the unknown K-ratio, the unknown peak
count rate, and the unknown background count.
Below that are the ZAF (ZCOR) for the element,
the raw K-ratio of the unknown, the
peak-background ratio of the unknown, and any
interference correction applied (INT, as
percentage of measured counts).
NB The number of digits after a decimal point in
a printout composition needs to be used with
common sense!
29
Probe for EPMA Statistics - 3
PfE software provides for additional optional
statistics. One set relates to detection limits,
i.e. what is the lowest level you can be
confident in reporting.We will deal with them
later, when we talk about trace elements in a few
weeks. The other set of statistics relates to the
homogeneity of the unknowns as well as
calculation of analytical error. We will now
discuss these statistics.
30
Analytical error - single line
This calculation is for analytical sensitivity of
each line ( one measurement), considering both
peak and background count rates (Love and Scott,
1974). It is a similar type of statistic as the 1
sigma counting precision figure, but it is
presented as a percentage.
Love and Scott, 1974
31
Additional analytical statistics
Probe for EPMA provides a more advanced set of
calculations for analytical statistics. The
calculations are based on the number of data
points acquired in the sample and the measured
standard deviation for each element. This is
important because although x-ray counts
theoretically have a standard deviation equal to
square root of the mean, the actual standard
deviation is usually larger due to variability of
instrument drift, x-ray focusing errors, and
x-ray production. A common question is whether a
phase being analyzed by EPMA is homogeneous, or
is the same or distinct from another separate
sample. An simple calculation is to look at the
average composition and see if all analyses are
within some range of sigmas (2 for 95, 3 for 99
normal probability).
32
Homogeneity confidence intervals
A more exacting criterion is calculating a
precise range (in wt) and level (in ) of
homogeneity. These calculations utilize the
standard deviation of measured values and the
degree of statistical confidence in the
determination of the average. The degree of
confidence means that we wish to avoid a risk a
of rejecting a good result a large per cent of
the time (95 or 99) of the time. Students t
distribution gives various confidence levels
for evaluation of data, i.e. whether a particular
value could be said to be within the expected
range of a population -- or more likely, whether
two compositions could be confidently said to be
the same. The degree of confidence is given as 1-
a, usually .95 or .99. This means we can define a
range of homogeneity, in wt, where on the
average only 5 or 1 of repeated random points
would be outside this range.
33
Students t distribution
The general problem, where the sample size is
small and the population variance is unknown, was
first treated in 1905 by W.S. Gossett, who
published his analysis under the pseudonym
Student. His employer, the Guinness Breweries
of Ireland, had a policy of keeping all their
research as proprietary secrets. The importance
of his work argued for its being published, but
it was felt that anonymity would protect the
company. (S.L. Meyer, Data Analysis for
Scientists and Engineers, 1975, p. 274.)
Goldstein et al, p. 497
34
Test for homogeneity
35
Recall the original analysis
Olivine analysis Example of homogeneity tests
What this means for Si, at highest level (95),
we can say that there is chance that only 5 of
number of random points will be .14 wt greater
or lesser than 18.89 wt (or as a percent, 0.7).
PfE also provides a handy table to show if the
sample is homogeneous at the 1 precision level,
and if so, at what confidence level.
36
Counting Statistics
Analytical sensitivity is the ability to
distinguish, for an element, between two
measurements that are nearly equal.
So here, at the 95 confidence level, two samples
would have to have a difference in Si of gt .20
wt to be considered reliably different in Si.
37
Numbers of significant figures-1
There have been cases where people have taken
reported compositions (i.e. wt elements or
oxides) from probe printouts and then faithfully
reproduced them exactly as they got them. Once
someone took figures that were reported to 3
decimal points and argued that a difference in
the 3rd decimal place had some geochemical
significance. The number of significant figures
reported in a printout is a mere programming
format issue, and has nothing to do with
scientific precision! (However, a feature of PfE
is an option to output only the actual
significant number of digits. This is not
normally enabled.) Having said that, it is
tradition to report to 2 decimal places.
However, that should not be taken to represent
precision, without a statistical test, such as
given before.
38
Numbers of significant figures - 2
In the example of the olivine analysis above,
where Si was printed out as 18.886 wt, it would
be reported as 18.89 -- but looking at the
limited number of analyses and the homogeneity
tests, I would feel uncomfortable telling someone
that another analysis somewhere between 18.6 and
19.2 were not the same material. Nor would I be
uncomfortable with someone reporting the Si as
18.9 wt (though I stick to tradition.)
Considering silicate mineral or glass
compositions, Si is traditionally reported with 4
significant figures. If we were to be rigorous
regarding significant figures, we would follow
the rule that we would be bound by the least
number of figures in a calculation where we
multiply our measurement (K-ratio, which will
have thousands of counts divided by thousands of
counts) by the ZAF. As you can appreciate there
are many calculations that comprise each part of
the ZAF, and it would be stretching it to argue
that the ZAF itself can have more than 3
significant figures. Ergo, we should not strictly
report Si with more than 3 significant figures.
39
Numbers of significant figures - 3
When we enable the PfE Analytical Option Display
only statistically significant number of
numerical digits for the olivine analysis, heres
the result
Wrong
For comparison, heres the original printout
40
Errors in Matrix Correction
The K-ratio is multiplied by a matrix correction
factor. There are various models alpha, ZAF,
f(rz) and versions. Assuming that you are using
the appropriate correction type, there may be
some issues regarding specific parameters, e.g.
mass absorption coefficients, or the f(rz)
profile. There is a possibility of error for
certain situations, particularly for light
elements as well as compounds that have
drastically different Z elements where pure
element standards are used. The figure above
shows that a small (2) error in the mass
absorption
Lifshin and Gauvin, 2001, p. 176.
coefficient for Al in NiAl will yield an error of
1.5 in the matrix correction. This is a strong
incentive to either use standards similar to the
unknown, and/or use secondary standards to verify
the correctness of the EPMA analysis.
41
Summary How to know if the EPMA results are
good?

• There are only 2 tests to prove your results are
  good actually, it is more correct to say that
  if your results can pass the test(s), then you
  know they are not necessarily bad analyses
• 100 wt totals (NOT 100 atomic totals). The
  fact that the total is near 100 wt. Typically, a
  range from 98.5 - 100.5 wt for silicates,
  glasses and other compounds is considered good.
  It extends on the low side a little to
  accommodate a small amount of trace elements that
  are realistically present in most natural (earth)
  materials. These analyses typically do oxygen by
  stoichometry which can introduce some
  undercounting where the FeO ratio has been set
  to a default of 11, and some the iron is ferric
  (FeO 23). So for spinels (e.g. Fe3O4), a
  perfectly good total could be 93 wt.
• Stoichometry, if such a test is valid (e.g. the
  material is a line compound, or a mineral of a
  set stoichometry.

42
Checking our olivine analysis

• The total is excellent, 99.98 wt
• The stoichometry is pretty good (not excellent)
  on the 4 oxygens, there should be 1.00 Si atoms
  and we have .985. The total cations MgFeCaNi
  should be 2.00, and we have 2.03.
• The analysis is OK and could be published. If
  this were seen at the time of analysis, it might
  be useful to recheck the Si and Mg peak positions
  , and reacquire standard counts for Si and Mg. If
  this were only seen after the fact, you could
  re-examine the

standard counts and see if there are any obvious
outliers that were included and could be
legitimately discarded.