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1
Probe for EPMA / Re: Improving sensitivity using duplicate elements and aggregate mode
« Last post by Probeman on September 18, 2020, 08:18:21 am »
No worries.

I also agree that getting a large number of high purity synthetic mineral standards will require “concerted effort” by the microanalysis community. But if we don’t make an effort to start creating global standards, we are simply giving up. Imagine if in the 18th century we had decided to not bother with creating global meter and kilogram standards?

But it’s not so hard to get specific standards in many cases. Let’s start with some relatively simple materials that already are produced on industrial scales, e.g., the MgO, Al2O3, and MgAl2O4 materials we’ve already mentioned, plus other materials mentioned such as a synthetic Mg2SiO4 and SiO2. Then there’s synthetic TiO2. Crystalgrower mentioned quite a few others that are already commercially available.

We just have to start with a few such industrially produced materials that already available and go on from there.
2
Hi John
Thanks for the paper, I will have a read of it.

I do agree with everything you said re: secondary standards. With regards to having a repository of synthetic high purity matrix matched minerals though, I feel like the situation isn't going to get better anytime soon though. Would take a real concerted effort from the whole analytical community, probably across techniques as well as I can see the application of these kind of materials in other techniques as well such as SIMS and LA-ICP-MS.

I assume these are these kind of things discussed at FIGMAS. One day hopefully in my lifetime I will be allowed to fly again...and one day this century hopefully the university will give us back our travel budget so I can attend an M&M in person.

Cheers
3
Probe for EPMA / Re: Improving sensitivity using duplicate elements and aggregate mode
« Last post by Probeman on September 17, 2020, 11:02:19 am »
To give you some background on the relatively high beam conditions for what might seem like relatively high Cl concentrations, that glass shown was just one of many analysed, others having down to single digit Cl concentrations.  It has been shown many times now that measuring Ti in quartz can get really nice DL via EPMA with aggregation on large xtals and blank subtraction, so I was just wondering how low we could go with Cl as well.

Hi Ben,
Absolutely. When one requires ultimate sensitivity increasing geometric efficiency is the way to go.  Right now larger Bragg crystals and running the same element on multiple spectrometers using aggregate mode is the only options we have.   Of course running at higher beam energies can also increase sensitivity (while reducing spatial resolution), assuming the emission line you are observing is sufficiently energetic to be emitted at those depths.

As an example of improving the Ti sensitivity using multiple spectrometers and aggregate mode I attach below a recent publication from one of our students here in Oregon (yes, the fire smoke is really bad, but starting to improve a little yesterday) on Ti in quartz.

We have a group interested in low level halogens in minerals (F,Cl,Br,I), and although I can’t help them too much for low level Br and I via EPMA, I could have a go at Cl given I have four large and one regular PET xtal to sum.  As with everything the main problem has been finding secondary standards with certified Cl concentrations to test against….which of course don’t really exist.  There are a bunch of the common glass standards (NIST, USGS basalt glasses, MPI-DING etc) which have Cl numbers on them, but can vary quite a bit  both inter technique (ie SIMS, Noble Gas, LA-ICP-MS, EPMA) and intra technique.  There have been some attempts at creating halogen glass standards and I have kindly been given a few of them from researchers, but haven’t had a chance to analyse them yet. Also they are commonly in high concentration as to use as primary standards, so not great for checking your low level accuracy.

Yeah finding a good Cl primary standard that is also not beam sensitive is tough. We have utilized a synthetic apatite grown at the University of Nice, but it is definitely not robust under the beam.

As for secondary standards, I will say it again (while everyone rolls their eyes), but I think that trying to find such trace level standards is a waste of our collective time.  Even if we had such a "doped" material how well do we know its accuracy or homogeneity?  It's always an open question.   Instead, I think what we should be looking for (and/or synthesizing) are matrix matched synthetic materials that contain a zero concentration of the element(s) in question. That is, below the detection limit of the EPMA, and for most elements this is around 1 PPM or lower. 

If the standard concentration is below the instrumental detection limit, we know that it's a zero concentration which is accurate to within our measurement precision.

To take the example of your Cl sensitivity measurements that I posted above, where you have a three sigma detection limit of 3 PPM (t-test) for the 5 aggregated spectrometers, that means (if you had a known zero concentration of Cl in (ideally) a similar matrix matched standard, you would now be able to claim a trace level *accuracy* of 3 PPM for all your measurements.

We literally cannot do better than that on the EPMA!   :D

For more information on the blank correction see here:

https://probesoftware.com/smf/index.php?topic=29.0

Also Donovan et al., 2011:

https://epmalab.uoregon.edu/pdfs/3631Donovan.pdf

So yes, we need a robust accurate primary standard with a high concentration of the element (matrix matched is nice, but not required as the matrix corrections can deal with that), and we also need an accurate zero concentration standard (in this case a matrix matched standard is important, because the shape of the continuum is determined by the major and minor element concentrations), to test our trace level accuracy. Everything else is (iterative) interpolation between these two endpoints.

One problem I had is that for some glasses I was underestimating the concentration, others were OK. One of the glasses that has very low level Cl returned negative concentrations.  If I plotted Cr concentration against the LO/HI background ratio there was a positive correlation, and it turns out there is a Cr Ka(II) peak right where I had set my low background (see plots below)….whoops.  Given a lot of these were basalt glasses as well, some had high Cr. Its not a huge interference and was subtracting anywhere from 5-25 ppm from the peak measurement, so not much but enough to give negative concentrations in one of the glasses and affect some of the other low level ones.

Yeah, subtle off-peak interferences that are not discovered in a "normal" sensitivity wavescan are troublesome. And of course, as you know, this is why for ultimate accuracy when using off-peak measurements, the multi-point background (MPB) is the way to go.  As I have said before, it's like combining your quant acquisition with a high precision wavescan!

For those who haven't tried the MPB method here is a topic on the technique:

https://probesoftware.com/smf/index.php?topic=131.0

The full peer reviewed paper on multi-point background (and the related "shared" background) method is here:

https://search.proquest.com/openview/208992e799d48f657d3508a6ef11ca1c
4
Hi John

Yes thanks for sorting that out John, I was definitely confused as to what was going on until you pointed out I needed to disable the same channel in the primary standard as well…

To give you some background on the relatively high beam conditions for what might seem like relatively high Cl concentrations, that glass shown was just one of many analysed, others having down to single digit Cl concentrations.  It has been shown many times now that measuring Ti in quartz can get really nice DL via EPMA with aggregation on large xtals and blank subtraction, so I was just wondering how low we could go with Cl as well.

We have a group interested in low level halogens in minerals (F,Cl,Br,I), and although I can’t help them too much for low level Br and I via EPMA, I could have a go at Cl given I have four large and one regular PET xtal to sum.  As with everything the main problem has been finding secondary standards with certified Cl concentrations to test against….which of course don’t really exist.  There are a bunch of the common glass standards (NIST, USGS basalt glasses, MPI-DING etc) which have Cl numbers on them, but can vary quite a bit  both inter technique (ie SIMS, Noble Gas, LA-ICP-MS, EPMA) and intra technique.  There have been some attempts at creating halogen glass standards and I have kindly been given a few of them from researchers, but haven’t had a chance to analyse them yet. Also they are commonly in high concentration as to use as primary standards, so not great for checking your low level accuracy.

So it was a suck it and see. I ran spots at relatively moderate conditions (15kV, 40nA, 20um defocussed, 360 on peak, 180 off peak using alternating On/Off peak mode), and at more extreme conditions (20kV, 80nA, 20um defocussed, 360 on peak, 180 off peak using alternating On/Off peak mode).  Individual spot errors halved with the higher conditions, and the TDI correction range was identical between both ranging from <1 to 2%.  This is probably due to my highly defocussed beam, I am sure there would be a difference if I used a more focussed beam.

One problem I had is that for some glasses I was underestimating the concentration, others were OK. One of the glasses that has very low level Cl returned negative concentrations.  If I plotted Cr concentration against the LO/HI background ratio there was a positive correlation, and it turns out there is a Cr Ka(II) peak right where I had set my low background (see plots below)….whoops.  Given a lot of these were basalt glasses as well, some had high Cr. Its not a huge interference and was subtracting anywhere from 5-25 ppm from the peak measurement, so not much but enough to give negative concentrations in one of the glasses and affect some of the other low level ones.

I did do wavelength scans in the initial setup, but obviously:
1)   at nowhere near long enough dwell times to pick up the small interference, and;
2)   I didn’t do wavelength scans on all the glasses…only on BCR2G which has low Cr so wouldn’t have seen it anyway.




I also played around with blank subtraction, with the obvious problem what do I have that I know has either zero Cl in it, or that I know definitely what the Cl values is.  The answer was nothing, so I just tried a couple of candidates, namely Astimex almandine garnet and San Carlos olivine.  Below is a compilation table of the 20kV test results



Turns out that San Carlos olivine ?probably? has some very small amount of Cl in it, despite being quite variable.  The Astimex garnet was pretty much right on zero, and as  a result there isn’t much difference between the uncorrected data and the blank (garnet) corrected data.  If I trust the SIMS value for the ML3B-G glass and use that as a blank corrector, I get Cl concentrations identical to when I use the Astimex garnet.

Anyway, I now have some other standards to try, I am also going to go back to 15kV and use higher beam current. Currently all these runs have been done using natural tugtupite as a primary standard.  Its internal variance is quite good (0.22% RSD on raw CPS/nA), however who knows how accurate the “certified” value is...  As mentioned I do now have a halogen glass which I am going to use as a primary standard and see how it compares.  Given the current state of the available standards I think accuracy is always going to be the biggest issue over precision.

Cheers
5
Probe for EPMA / Improving sensitivity using duplicate elements and aggregate mode
« Last post by John Donovan on September 16, 2020, 01:22:39 pm »
I recently posted here:

https://probesoftware.com/smf/index.php?topic=155.msg9457#msg9457

about the need to acquire (and treat) ones standard samples, similar to their unknown samples, when using duplicate elements in aggregate mode. Basically, if you disable quantification for an element channel in your unknown sample, you should also disable quantification for the corresponding element channel in your standard sample.  Because in aggregate mode the software basically adds up all the photons for the on and off-peak measurements for all channels that are the same element, emission line (though not necessarily the same Bragg crystal!), and also the same beam energy of course.

But I noticed that Ben Wade's sample provides a nice example of improving sensitivity by using duplicate elements in aggregate mode so I started a new topic to discuss this.  Let's start with my initial observation with his glass sample, that the variance in the totals (where all elements except Cl are specified as fixed concentrations, so all the variance comes from the Cl measurements), before the aggregate mode is turned on (see Analytical | Analysis Options menu) as shown here is around :

ELEM:       Cl      Cl      Cl      Cl      Cl   SUM 
XRAY:     (ka)    (ka)    (ka)    (ka)    (ka)
   229  .03827  .03803  .03709  .03733  .03756 100.367
   230  .03833  .03919  .03795  .03770  .03694 100.369
   231  .03773  .03516  .03829  .03928  .03818 100.368
   232  .03869  .03898  .03822  .03723  .03735 100.369
   233  .03840  .03895  .03783  .03689  .03848 100.369
   234  .03791  .03882  .03796  .03869  .03805 100.370
   235  .03952  .03721  .03832  .03809  .03766 100.369
   236  .03761  .03892  .03753  .03841  .03867 100.370
   237  .03797  .03810  .03787  .03667  .03878 100.368
   238  .03903  .03849  .03795  .03692  .03833 100.369

AVER:   .03834  .03819  .03790  .03772  .03800 100.369
SDEV:   .00060  .00122  .00037  .00087  .00060  .00103
SERR:   .00019  .00039  .00012  .00028  .00019
%RSD:  1.56001 3.19181  .97764 2.30551 1.59035
STDS:      545     545     545     545     545

Note that the variance on the total is 0.00103 or around 10 PPM and the variances on the Cl channels range from 0.00037 to 0.00122 (or roughly 4 to 12 PPM).  Now with the aggregate mode on, we get this result:

ELEM:       Cl      Cl      Cl      Cl      Cl   SUM 
XRAY:     (ka)    (ka)    (ka)    (ka)    (ka)
   229  .03760  .00000  .00000  .00000  .00000 100.217
   230  .03781  .00000  .00000  .00000  .00000 100.217
   231  .03806  .00000  .00000  .00000  .00000 100.217
   232  .03799  .00000  .00000  .00000  .00000 100.217
   233  .03809  .00000  .00000  .00000  .00000 100.217
   234  .03816  .00000  .00000  .00000  .00000 100.217
   235  .03828  .00000  .00000  .00000  .00000 100.217
   236  .03811  .00000  .00000  .00000  .00000 100.217
   237  .03799  .00000  .00000  .00000  .00000 100.217
   238  .03818  .00000  .00000  .00000  .00000 100.217

AVER:   .03803  .00000  .00000  .00000  .00000 100.217
SDEV:   .00020  .00000  .00000  .00000  .00000  .00015
SERR:   .00006  .00000  .00000  .00000  .00000
%RSD:   .51712   .0000   .0000   .0000   .0000
STDS:      545       0       0       0       0

Now the variance on the total decreased to 0.00015 or about 1.5 PPM!  While the variance on the aggregated Cl channels is now 0.00020 or 2 PPM!

So, yes this is exactly what one would expect by aggregating our duplicate channels. Now we can ask how does this affect our detection limits?  Well, starting again with the unaggregated Cl channels we get single point detection limits as seen here:

Detection limit at 99 % Confidence in Elemental Weight Percent (Single Line):

ELEM:       Cl      Cl      Cl      Cl      Cl
   229  .00100  .00204  .00086  .00114  .00094
   230  .00101  .00206  .00086  .00113  .00094
   231  .00100  .00206  .00086  .00111  .00093
   232  .00101  .00206  .00086  .00113  .00093
   233  .00100  .00206  .00086  .00113  .00093
   234  .00101  .00203  .00086  .00113  .00093
   235  .00100  .00206  .00087  .00113  .00094
   236  .00101  .00204  .00086  .00113  .00093
   237  .00101  .00205  .00086  .00114  .00093
   238  .00100  .00208  .00086  .00113  .00093

AVER:   .00100  .00205  .00086  .00113  .00093
SDEV:   .00000  .00001  .00000  .00001  .00000
SERR:   .00000  .00000  .00000  .00000  .00000

And t-test values shown here:

Detection Limit (t-test) in Elemental Weight Percent (Average of Sample):

ELEM:       Cl      Cl      Cl      Cl      Cl
  60ci  .00023  .00052  .00015  .00026  .00019
  80ci  .00036  .00081  .00023  .00041  .00030
  90ci  .00048  .00107  .00031  .00055  .00040
  95ci  .00059  .00133  .00038  .00068  .00049
  99ci  .00084  .00191  .00055  .00097  .00071

So single point detection limits from 8 to 20 PPM and t-test detection limits (at 99% confidence) from 5 to 19 PPM for the average of all points. This indicates that the sample is quite homogeneous in Cl.

Now with the aggregated Cl channels, we get this for single line detection limits:

Detection limit at 99 % Confidence in Elemental Weight Percent (Single Line):

ELEM:       Cl      Cl      Cl      Cl      Cl
   229  .00048  .00000  .00000  .00000  .00000
   230  .00048  .00000  .00000  .00000  .00000
   231  .00047  .00000  .00000  .00000  .00000
   232  .00047  .00000  .00000  .00000  .00000
   233  .00047  .00000  .00000  .00000  .00000
   234  .00047  .00000  .00000  .00000  .00000
   235  .00048  .00000  .00000  .00000  .00000
   236  .00048  .00000  .00000  .00000  .00000
   237  .00047  .00000  .00000  .00000  .00000
   238  .00048  .00000  .00000  .00000  .00000

AVER:   .00047  .00000  .00000  .00000  .00000
SDEV:   .00000  .00000  .00000  .00000  .00000
SERR:   .00000  .00000  .00000  .00000  .00000

Now our single line detection limit is down around 5 PPM (compared to 8 to 20 PPM with the unaggregated data). And here is the aggregated t-test results:

Detection Limit (t-test) in Elemental Weight Percent (Average of Sample):

ELEM:       Cl      Cl      Cl      Cl      Cl
  60ci  .00009     ---     ---     ---     ---
  80ci  .00014     ---     ---     ---     ---
  90ci  .00018     ---     ---     ---     ---
  95ci  .00023     ---     ---     ---     ---
  99ci  .00032     ---     ---     ---     ---

Which is now down to around 3 PPM for a 99% confidence t-test (compared to 5 to 19 PPM for the unaggregated channels).  So we can see that by utilizing duplicate elements and the aggregate mode in Probe for EPMA we can significantly improve our trace element sensitivities.

By the way, Ben's conditions were 20 keV and 80 nA with an on-peak counting time of 360 seconds and 180 seconds on each off-peak.  He also utilized the TDI correction during the on-peak acquisition which showed an increase in the Cl intensities over that time of between 1 and 2%. Which makes sense since Cl is a negative ion and would tend to migrate to the surface from the effects of subsurface charging.  Thus increasing the emitted intensity over time due to the shallower emission depth.

Pretty darn interesting dataset actually.  I hope Ben will feel free to chime in with his own observations...
6
Probe for EPMA / Re: Using Duplicate Elements in Probe for EPMA
« Last post by John Donovan on September 15, 2020, 06:06:21 pm »
I'm popping this topic forward because Ben Wade noticed that when he disabled some duplicate elements in a sample he found an anomaly in the aggregate averages of the aggregated channel. So, make sure you are "buckled in" because this gets "down into the weeds" as they say!

It's really my fault because I could not figure out how to handle this issue automatically, but it's simply the case, that when you are analyzing duplicate elements on multiple spectrometers (usually to improve your sensitivity for trace elements), one must acquire their standard intensities in the same manner as their unknown intensities.  You know, the k-ratio is the unknown intensity divided by the standard intensity, Iu/Is.  So this is also true when acquiring duplicate elements on multiple spectrometers.

So here, Ben (used with permission), analyzed chlorine using all 5 spectrometers:

ELEM:       Cl      Cl      Cl      Cl      Cl   SUM
XRAY:     (ka)    (ka)    (ka)    (ka)    (ka)
   229  .03827  .03803  .03709  .03733  .03756 100.367
   230  .03833  .03919  .03795  .03770  .03694 100.369
   231  .03773  .03516  .03829  .03928  .03818 100.368
   232  .03869  .03898  .03822  .03723  .03735 100.369
   233  .03840  .03895  .03783  .03689  .03848 100.369
   234  .03791  .03882  .03796  .03869  .03805 100.370
   235  .03952  .03721  .03832  .03809  .03766 100.369
   236  .03761  .03892  .03753  .03841  .03867 100.370
   237  .03797  .03810  .03787  .03667  .03878 100.368
   238  .03903  .03849  .03795  .03692  .03833 100.369

AVER:   .03834  .03819  .03790  .03772  .03800 100.369
SDEV:   .00060  .00122  .00037  .00087  .00060  .00103
SERR:   .00019  .00039  .00012  .00028  .00019
%RSD:  1.56001 3.19181  .97764 2.30551 1.59035
STDS:      545     545     545     545     545


All channels show roughly 380 PPM of Cl. Now here he aggregates all these duplicate elements:

ELEM:       Cl      Cl      Cl      Cl      Cl   SUM
XRAY:     (ka)    (ka)    (ka)    (ka)    (ka)

   229  .03760  .00000  .00000  .00000  .00000 100.217
   230  .03781  .00000  .00000  .00000  .00000 100.217
   231  .03806  .00000  .00000  .00000  .00000 100.217
   232  .03799  .00000  .00000  .00000  .00000 100.217
   233  .03809  .00000  .00000  .00000  .00000 100.217
   234  .03816  .00000  .00000  .00000  .00000 100.217
   235  .03828  .00000  .00000  .00000  .00000 100.217
   236  .03811  .00000  .00000  .00000  .00000 100.217
   237  .03799  .00000  .00000  .00000  .00000 100.217
   238  .03818  .00000  .00000  .00000  .00000 100.217

AVER:   .03803  .00000  .00000  .00000  .00000 100.217
SDEV:   .00020  .00000  .00000  .00000  .00000  .00015
SERR:   .00006  .00000  .00000  .00000  .00000
%RSD:   .51712   .0000   .0000   .0000   .0000
STDS:      545       0       0       0       0


Everything looks as expected. Now he disables the 5th Cl channel:

ELEM:       Cl      Cl      Cl      Cl    Cl-D   SUM
XRAY:     (ka)    (ka)    (ka)    (ka)    (ka)

   229  .02709  .00000  .00000  .00000     --- 100.208
   230  .02748  .00000  .00000  .00000     --- 100.209
   231  .02738  .00000  .00000  .00000     --- 100.209
   232  .02755  .00000  .00000  .00000     --- 100.209
   233  .02732  .00000  .00000  .00000     --- 100.209
   234  .02751  .00000  .00000  .00000     --- 100.209
   235  .02775  .00000  .00000  .00000     --- 100.209
   236  .02729  .00000  .00000  .00000     --- 100.209
   237  .02714  .00000  .00000  .00000     --- 100.208
   238  .02745  .00000  .00000  .00000     --- 100.209

AVER:   .02740  .00000  .00000  .00000     --- 100.209
SDEV:   .00020  .00000  .00000  .00000     ---  .00015
SERR:   .00006  .00000  .00000  .00000     ---
%RSD:   .71560   .0000   .0000   .0000     ---
STDS:      545       0       0       0     ---


And now the average Cl is significantly lower. How is this possible?  The answer is that because one of the unknown elements was disabled for quant, but the same element channel in the standard was *not* disabled for quant, the k-ratio was improperly constructed.

The solution is to also disable the 5th element channel in the standard sample. Once we've done that, we get the following correct results:

ELEM:       Cl      Cl      Cl      Cl    Cl-D   SUM
XRAY:     (ka)    (ka)    (ka)    (ka)    (ka)
   229  .03761  .00000  .00000  .00000     --- 100.217
   230  .03815  .00000  .00000  .00000     --- 100.217
   231  .03801  .00000  .00000  .00000     --- 100.217
   232  .03824  .00000  .00000  .00000     --- 100.217
   233  .03793  .00000  .00000  .00000     --- 100.217
   234  .03820  .00000  .00000  .00000     --- 100.217
   235  .03852  .00000  .00000  .00000     --- 100.217
   236  .03789  .00000  .00000  .00000     --- 100.217
   237  .03768  .00000  .00000  .00000     --- 100.217
   238  .03811  .00000  .00000  .00000     --- 100.217

AVER:   .03803  .00000  .00000  .00000     --- 100.217
SDEV:   .00027  .00000  .00000  .00000     ---  .00021
SERR:   .00009  .00000  .00000  .00000     ---
%RSD:   .71557   .0000   .0000   .0000     ---
STDS:      545       0       0       0     ---

My bad was that I did not have a warning about this possible situation, where once is acquiring duplicate elements, using "aggregate" mode to combine the intensities, but then disabling one of the duplicate elements channels.  This now fixed in the latest version of PFE as seen here:



Again, my apologies, and thank-you to Ben Wade for noticing this oversight and reporting it to me.  Update, as usual, from the PFE Help menu and you will now have this warning when it is appropriate.
7
Discussion of General EPMA Issues / Re: Looking for ICXOM 11 volume
« Last post by JohnF on September 15, 2020, 09:38:42 am »
Here are several papers by Pouchou and Pichoir on the PAP phi-rho-Z  (other than the one in the "Green Book")
8
Discussion of General EPMA Issues / Re: Looking for ICXOM 11 volume
« Last post by Probeman on September 14, 2020, 08:58:45 pm »
By any chance, does anyone have a copy of this paper from the 11th ICXOM? (Or access to that hard-to-find volume)

Journal Title: 11th International Congress on X-ray Optics and Microanalysis : ICXOM 11, London, 4-8 Aug. '86, Canada = 11ème Congrès international d'optique des rayons X et de microanalyse
Article Author: Pouchou L, Pichoir F
Article Title: Basic Expression of "PAP" Computation for Quantitative EPMA
Date:   1987(1986)
Pages: 249+

Thanks.

John

Please post the pdf as an attachment here when you get a chance.
9
Discussion of General EPMA Issues / Re: Looking for ICXOM 11 volume
« Last post by jrminter on September 14, 2020, 10:46:57 am »
I checked and I do not have it. This is one of those conference proceeding books. Have you tried interlibary loan? When I was still at Kodak, our research librarians helped me borrow some hard to find volumes.
10
Discussion of General EPMA Issues / Looking for ICXOM 11 volume
« Last post by JohnF on September 14, 2020, 08:59:05 am »
By any chance, does anyone have a copy of this paper from the 11th ICXOM? (Or access to that hard-to-find volume)

Journal Title: 11th International Congress on X-ray Optics and Microanalysis : ICXOM 11, London, 4-8 Aug. '86, Canada = 11ème Congrès international d'optique des rayons X et de microanalyse
Article Author: Pouchou L, Pichoir F
Article Title: Basic Expression of "PAP" Computation for Quantitative EPMA
Date:   1987(1986)
Pages: 249+

Thanks.

John
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