Transcript Electron probe microanalysis - UW

Electron probe microanalysis
Accuracy and Precision
in EPMA:
Understanding Errors
Modified 11/15/10
What’s 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?
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
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?
These can be categorized into
“random” and
“systematic” errors.
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
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)
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 <1%, but when
combined with accuracy, total EPMA error probably 1-2% in the
best cases (for major elements).
Precision and Accuracy
Low Precision
Low
Accuracy
High
Accuracy
High Precision
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.
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 68-70°C 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).
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 manufacturer’s
“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
(>50K cps)
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.)
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 <1 mm
diamond or alumina or silica.
Sample/standard Error:
Surface Irregularities
These Monte Carlo
simulations show the
effect on K and L line Xrays of Ni and Al, of
one-directional Vgrooves 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.
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 >100
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.
Sample/standard Error:
Physical issues - 3
• Incorrect geometry (nonorthogonal 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.
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
Sample/standard Error:
Physical issues - 5
1.00
0.95
0.90
Ti Ka K-ratio
• 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.
10 keV
20 keV
0.85
0.80
0.75
0.70
0.05
0.10
0.15
Oxide thickness (microns)
0.20
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).
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). Semiconductors 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.
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.
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.
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.
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
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.
unk
unk
I

I
Recall that the K-ratio is
K  Pst d Bst d
IP  IB
where P and B refer to peak and background.
The corresponding precision in the K ratio is given by
 unk

unk
st d
st d
IP  IB
IP  IB

s K2  K 2 

2
2
 unk unk

st d
st d
n
I

I
n

I

I
 P B  
  P
B 
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.)
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.
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 <1,
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.
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 Kratio, 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!
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.
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
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).
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. “Student’s 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.
Student’s 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
Test for homogeneity
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.
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 > .20 wt% to be
considered reliably different in Si.
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.
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.
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, here’s the original printout:
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.
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 Fe:O ratio
has been set to a default of 1:1, and some the iron is ferric (Fe:O 2:3). 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.
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
Mg+Fe+Ca+Ni 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.