New method for calibration of dead times (and picoammeter)

[Probeman]

Correct. I have not moved any slits etc. all counts for 60 sec on peak 10 sec off. Pha parameters set so that i could get good results at high and low counts. No obvious charging that I could detect.

All done according to the pdf I was surprised at the count rates also, si metal counts were ~2500 cps/nA on tap sp1, orthoclase was ~600 cps/nA. All measurements at 15kV.

Hi Dan,
OK, thanks.

Remember, you only need to check the PHA settings at the *highest* (expected) count rate in INTEGRAL mode.  Also when you calculate your "predicted" count rates, you should use the count rates observed at the lowest beam currents (in cps/nA) for the primary standard and just multiple by the beam currents.  After all, it's the high count rates on the primary standard (Si metal in this case) that is stressing the dead time correction model in the k-ratios.

I know this goes against everything we were taught back in the day, but if the PHA peak is fully above the baseline level at the highest (expected) count rate, then at lower count rates the PHA peak will merely shift to the right and still be counted in INTEGRAL mode as described here:

https://probesoftware.com/smf/index.php?topic=1466.msg11450#msg11450

Also be sure your beam is defocused to 5 or 10 um or so.  I assume that none your your crystals are TAPL crystals?  That would explain the lower count rates.  But really it's not the count rates that bother me, and your k-ratios look fairly constant, though I don't understand why they are going non-linear at these relatively low count rates. 

But what really bothers me is that your spectrometers are giving such different k-ratios.  That is, we don't really care what the absolute values of the k-ratios are, after all we are measuring Si Ka in Orthoclase relative to Si metal, and of course there is a significant emission (energy) peak shift between the two materials, especially for Si Ka.

But regardless of what that k-ratio value is observed to be (at the lowest count rates where the dead time correction is insignificant), we still should be seeing that *same* k-ratio on all our spectrometers.  Your plot shows k-ratios from ~0.17 to ~ 0.25 for Si ka in these two materials and that is a significant difference as you have noted on your plot.  Though if you utilized a mix of TAP and PET crystals that could explain some of the differences.  Can you plot the PET and TAP constant k-ratios in separate plots (maybe that is what you did to begin with)?   

Yes, it could also be sample (or stage) tilt. Scott Boroughs raised that question to me here:

https://probesoftware.com/smf/index.php?topic=1466.msg11329#msg11329

as he saw similar (though smaller) variations in his simultaneous constant k-ratios, which he felt might also be due to sample (or stage) tilt in that it appeared systematic with respect the spectrometer orientations around the instrument. And I responded in the next post that this is something, which if appropriately characterized, we could compensate for in the absorption correction by changing the "effective" takeoff angle for each spectrometer. 

As you can see in my response, Probe Software had modified the underlying physics code in CalcZAF to handle different spectrometer take off angles for each spectrometer and utilizing that in the absorption correction.  I haven't heard back from Scott if a change in the effective takeoff angle due to sample (or stage) tilt would compensate for this.

More disturbing is the possibility that the variation in these simultaneous constant k-ratios could be the result of differences due to asymmetrical Bragg diffraction. In this case, each crystal could demonstrate a different effective takeoff angle.  The problem is knowing which spectrometer has the correct effective takeoff angle!  And for that determination we would need to worry about differences in the emission peak position, differences in the carbon coating, native oxide thickness, etc, etc. All the usual suspects we deal with in any quantitative analysis...

PS you might want to try Ti Ka on TiO2 and Ti metal as the emission peak shifts will be significantly less for these materials, though you'll still have the native oxide layer issue with Ti metal.  But again, the absolute value of the k-ratios do not matter, only that they remain constant as a function of count rates!

[Dan R]

Thanks for the input! I'm about to have a PM so I will do this again once that's over and assuming the spectros pass the testing.

[Probeman]

Thanks for the input! I'm about to have a PM so I will do this again once that's over and assuming the spectros pass the testing.

Cool. 

Just a thought: you might want to present this data to your engineer and ask them why the spectrometers are yielding such different k-ratios...

Of course if these two plots are actually showing the difference due to PET vs. TAP, that larger difference (0.2x vs. 0.1x) in the k-ratios is probably explainable simply by the Si Ka emission line shift from metal to oxide with these different spectral resolution Bragg crystals:



But because the PET crystal k-ratios should be similar to themselves and the TAP k-ratios should be similar to themselves, and they are actually pretty different even just compared to themselves, there still appears to be a problem with the different spectrometers. To avoid this PET/TAP spectral resolution peak shift issue it would be better to re-run the constant k-ratios using orthoclase and SiO2 as the primary standard instead of Si metal when you get a chance (or Ti Ka using SrTiO3 and TiO2, though of course that would be for PET and LiF crystals).

[sem-geologist]

We have saying in Poland "the deeper in the forest - the more trees" (BTW, I am not a pole). Anyway, the more I look into Cameca counting electronics the more confused I am getting. I have access to the new generation (2014) and old generation (SX100, 1998) counting boards. The working principles looks very similar, and I thought that gain amplification is reversing the polarity of the signal, but after latest inspection I think I was in error (thus those comparator input plots in previous posts by me are wrong!). I also previously overlooked very important diode between gain amplification and counting part - that means that counting part sees only positive pulse parts, and ignores the negative "after-pulse" - thus my previous plots of "what the comparator would see" are partially wrong, and there is rather no possibility in decreasing the additional dead time (Which is actually a very good finding from math model construction POV). My speculation that at high count rate the dead time also could in some cases be shortened is wrong. Thus the increase in the additional dead time should scale progressively with increasing count rate.

The worst part in investigating these boards are that those are very timing sensitive with main VME CPU Motorola board, if it is mounted with extension board the firmware will not boot it (WDS board) and thus it can't be probed with oscilloscope in its natural working conditions (other boards (especially older generation) could be troubleshooted like that). I think I am giving up the ultimate idea to understand the system in very details and will rather focus my efforts to finish the arbitrary wave generator to measure the dead time of such counting system as a whole, and move on with FPGA design of new pulse counting system based on real-time deconvolution (Having working pulse generator, which can mimic the detector output will allow me to experiment without taking time of EPMA).

At least with recognizing those diodes between amplification and sensing parts I got a final and definitive answer to the question Why is the PHA minimum 500mV...?. It also definitely answers some of my hypothesis of possibility about integral mode for pulses below 560mV - it is not possible at current hardware. And finally it is clear why the count rate stops increasing when hitting some high count rate - pulses with the top below 560mV will be blocked after gain amplification and won't even reach the pulse sensing and counting part. I think dependency of baseline shift from count rate can be defined mathematically from count rate - and thus fraction of shifted out pulses (below baseline) should be then possible to calculate. The increasing of Gain can efficiently increase amplitude of pulses. It is not only Ar esc pulses, but normal pulses too if they happen to be produced at moment after few positively interfering coincident pulses (and thus after pulse is deeper than from single event - deep enought to hide the whole normal pulse from primitive detection system). This is demonstrated in this oscilloscope annotated snapshot:

and This is where I was some time ago wrong. Previously, I was sure that pulse nr 3 in that picture would be counted in integral mode if dead time would be set to 1µs - but it would not reach the pulse sensing electronics due to diode threshold of 560mV. In case of increasing gain (in this case enormously, probably at max available 4095), maybe this 3rd pulse could be pulled-out over the diode threshold for detection. However, had this 3rd pulse be Ar esc, or randomly of slightly lower amplitude, it would have absolutely no chance to pass the diode between amplification and sensing parts even with maximum gain amplification. The gain amplification expands the amplitude symmetrically around 0V. I just will repeat - decreasing/increasing the gain actually does not shift the PHA left or right (the notation which is unfortunately used often in these forums), but just expands the amplitude around 0V (everything what is positive gets more (or less) positive,  everything what is negative gets more (or less) negative, and zero stays zero).

It still is not satisfactory to explain the squiggle (I think it is more general problem with general approach of i_raw/(1-tau*i_raw)), but I  think this could explain why log equation fits better than canonical equation.

[Probeman]

...that means that counting part sees only positive pulse parts, and ignores the negative "after-pulse" - thus my previous plots of "what the comparator would see" are partially wrong, and there is rather no possibility in decreasing the additional dead time (Which is actually a very good finding from math model construction POV). My speculation that at high count rate the dead time also could in some cases be shortened is wrong. Thus the increase in the additional dead time should scale progressively with increasing count rate.

I think that this makes sense. At count rates below ~50 kcps we have a fairly linear response and the traditional expression seems to be working well.  Above ~50 kcps and up to about 300 to 400 kcps, the observed non-linear of the pulse processing system becomes very evident and the logarithmic expression seems to work well to handle this non-linearity. But above 300 to 400 kcps I suspect that the system becomes even more non-linear response and this could indeed be due to an "extending" of the dead time constant (increased dead time constants) beyond what we calibrated at count rates below 300 to 400 kcps.

I just will repeat - decreasing/increasing the gain actually does not shift the PHA left or right (the notation which is unfortunately used often in these forums), but just expands the amplitude around 0V (everything what is positive gets more (or less) positive,  everything what is negative gets more (or less) negative, and zero stays zero).

It still is not satisfactory to explain the squiggle (I think it is more general problem with general approach of i_raw/(1-tau*i_raw)), but I  think this could explain why log equation fits better than canonical equation.

Understood. But since we cannot see what is getting shifted negative in our PHA distribution plots, I think it makes sense to keep describing the gain shifting as a shift to the right.

As for these subtle "squiggles" I think it is important for other readers of this topic to keep in mind that these artifacts are quite small (~1% or less) and would be quite unobservable without the sensitivity of the constant k-ratio method.

SG: have you had a chance to run some constant k-ratio measurement of your own?  I think it would be most excellent if you could share what you find on your system with us. Maybe start with k-ratio measurements of SrTiO3 and TiO2 for Ti Ka (LIF and PET) and SiO2 and say a robust silicate for Si Ka (PET and TAP).

[John Donovan]

I thought I would follow up with some high speed mapping we did recently on some olivines provided to me by Peng Jiang, now at the University of Hawaii.

In an effort to demonstrate the utility of the new non-linear (logarithmic) dead time correction we mapped an olivine grain for Si, Fe, Mg, Ca and Mn using a 200 nA beam, while the standards were acquired, as usual at 30 nA. All 5 (3 major and 2 minor) elements were acquired simultaneously using a 500 msec pixel dwell time and using the MAN background correction to avoid having to also acquire off-peak background maps.

Here are the quantitative results using the traditional (linear) dead time first:



Note that the totals map shows olivine totals around 97 wt%.  Next we turn on the logarithmic dead time correction and re-run the pixel quantification and we now obtain this map:



Note the the totals map has improved to over 99 wt%, next we take a look at the detection limits map that was calculated at the same time:



Note that the *single* pixel detection limits are around 400 PPM for Ca and 800 PPM for Mn. Of course we expect to get some improved sensitivity when using the MAN corrected because there is essentially no variance associated with the MAN background intensities (Donovan et al., 2016), but for 400 msec integration time that is not too bad.

And remember when averaging pixels we can further improve these detection limits by a factor of Sqrt(2) for each doubling of the pixels averaged...

It is also interesting to note the subtle variation in the detection limit maps, which I think reflects a small amount of drift in the standard/background intensities acquired before and after the x-ray map acquisition as seen here:

Selected Samples...
Un    7  Jiang olivine random points at 15.00 keV

Assigned average standard intensities for sample Un    7  Jiang olivine random points

Drift array background intensities (cps/1nA) for standards:
ELMXRY:    mg ka   ca ka   mn ka   si ka   fe ka
MOTCRY:  1   TAP 2  LPET 3  LLIF 4   TAP 5   LIF
INTEGR:        0       0       0       0       0
STDASS:       12     306      25      14     395
STDVIR:        0       0       0       0       0
             .64    1.17    1.21    1.30     .43
             .65    1.16    1.19    1.33     .44
             .64    1.16    1.22    1.27     .43
 
Drift array standard intensities (cps/1nA) (background corrected):
ELMXRY:    mg ka   ca ka   mn ka   si ka   fe ka
MOTCRY:  1   TAP 2  LPET 3  LLIF 4   TAP 5   LIF
STDASS:       12     306      25      14     395
STDVIR:        0       0       0       0       0
          628.90  202.25  516.71  778.58  139.57
          621.29  201.76  517.08  776.49  139.44
          629.98  203.40  518.29  788.12  140.13

The point being of course being that with the new logarithmic dead time expression in Probe for EPMA, we can now perform high accuracy and high sensitivity quantitative point analyses and high speed (high beam current/low dwell time) X-ray mapping at the same time for major, minor and trace elements.

As mentioned in prior posts, those of you that already have Probe for EPMA should first use the Help | Update Probe for EPMA menu to get the latest version of Probe for EPMA and then also refer to the Help | How To Use Constant K-ratios To Calibrate Your Instrument menu pdf document to perform high sensitivity dead time calibrations to allow you to take advantage of this new dead time expression. This will allow for quantitative analyses up to several hundred nA of beam current even with large area Bragg crystals.

I hope to provide some additional examples of high speed quantitative mapping using the logarithmic dead time expression, but if you have any examples of your own that you'd like to share, please feel free to post them here.

[John Donovan]

In case anyone is curious about the PHA tuning adjustments for the above high speed maps I'll remind everyone that when utilizing a large range of count rates we should keep in mind the pulse height depression which occurs at high count rates.

This pulse height depression effect causes the PHA peak to shift towards lower voltages at higher count rates, thus increasing the possibility of some counts being cut off by the baseline level at these higher count rates. The solution is to always tune ones PHA settings at the highest expected count rate (highest beam current on a material with the highest expected concentration- usually one's primary standard).

In the above high speed mapping example we utilized SiO2 as the primary standard for Si Ka, therefore we should tune our PHA settings on that material at the highest expected beam current. However, since we intend to acquire our olivine unknowns at 200 nA and our primary standards at only 30 nA, and since the concentration of Si in SiO2 is about 50% and the concentration of Si in olivines is about 20% (in round numbers), we could compare these concentrations and beam currents by considering that our olivines have 2.5 times less Si than our primary standard, but will be measured at 6.6 times the beam current, so we should probably tune our Si Ka PHA on the olivine unknown at 200 nA for the highest expected count rate (of course the exact count rate depends on the absorption correction differences between these materials also, but we're just speaking in round numbers here).

But to make things more interesting I decided to tune the PHA settings on the primary standards at 200 nA. Here is Si Ka on SiO2 at 200 nA:



Note that the gain was adjusted to place the PHA peak fully above the baseline level even at this quite high count rate (~160 kcps). And remember, although the PHA peak appears to be slightly cut off at the right side of the plot, that is merely an artifacts of the PHA display system. All counts to the right of the plot axis are fully counted because we are in INTEGRAL mode.

Next here is the Si Ka PHA scan again on SiO2 at the same PHA settings but using a beam current of 30 nA:



We can see that the PHA peak has shifted even further to the right, but again we don't care as all pulse to the right of the plot will all be counted in INTEGRAL mode.

Remember, on Cameca instruments we will be adjusting the gain to place the PHA peak above the baseline at the highest expected count rate, while on JEOL instruments, we will be adjusting the bias the place the PHA peak above the baseline level at the highest expected count rate.