Hello probe experts,
Perhaps this is a simple question, but my intuition is stumped by competing effects. We are mapping phosphorus zoning in olivine, and we know there are apatite inclusions. The question is whether a Ca map provides a faithful detector of subsurface apatite grains, such that P anomalies can be confidently taken as dissolved in the olivine itself. In other words, are Ca and P K-alpha X-ray production and escape from subsurface in Fe80 olivine more or less equally efficient, or is there a depth range where you could get P signal without Ca?
I imagine P X-ray (lower energy than Ca X-rays) production extends deeper into the sample, but I expect Ca X-rays to be able to escape more efficiently from depth. So, which effect wins?
Thanks,
-- Paul Asimow
Hi Paul,
Excellent question!
There are 3 methods I can offer to approach this question in order of increasing complexity (and accuracy).
First we can get a rough idea by just using CalcZAF to tell us how efficiently these emitted x-rays transmit in these materials. For the olivine case we will assume two compositions, first pure end-member Fe2SiO4 and second, pure end-member Mg2SiO4. These done by simply clicking the Run | Calculate Electron and X-ray Ranges menu in CalcZAF and entering the appropriate densities and compositions:
(https://smf.probesoftware.com/oldpics/i62.tinypic.com/az9dfo.jpg)
More explanation on these electron and x-ray range calculations is available here:
http://smf.probesoftware.com/index.php?topic=86.0
We summarize these results showing the 99% electron ranges for the two compounds at 15 keV and 20 keV:
Composition: Mg2SiO4 Fe2SiO4
Density: 3.27 4.39
Electron Range (15 keV): 2.02 um 1.68 um
Electron Range (20 keV): 3.27 um 2.73 um
Note that the x-ray excitation ranges are slightly less than the 99% electron ranges but not by much since these are relatively low energy emission lines.
So, now let's assume that the buried apatite phase is just at the 99% electron range so there would be a very small amount of primary electron excitation in the apatite, from which any x-ray emissions must then transmit through the olivine to be observed. Let's start by calculating the x-ray transmissions at each electron range distance using the same dialog in CalcZAF by entering the 99% electron distance here:
(https://smf.probesoftware.com/oldpics/i62.tinypic.com/awt7jp.jpg)
We now obtain these results for the various compositions and electron energies:
Composition: Mg2SiO4 Fe2SiO4
99% Elec. Dist. (15 keV): 2.02 um 1.68 um
P Ka Transmission: 36 % 34 %
Ca Ka Transmission: 82 % 81 %
99% Elec. Dist. (20 keV): 3.27 um 2.73 um
P Ka Transmission: 19 % 17 %
Ca Ka Transmission: 73 % 71 %
So, we can see that in all cases the Ca Ka x-ray has a greater penetration in all olivine compositions at both 15 and 20 keV, so just on the basis of absorption, one is able to say that if no Ca is observed, the P signal is *not* from apatite, assuming equal detection sensitivity for both P Ka and Ca Ka.
But what about secondary fluorescence? Even if the primary electrons do *not* penetrate to the buried apatite, since x-ray fluorescence is isotropic could the generated Fe ka x-rays in the olivine phase "travel down" to the apatite phase and excite the P and/or Ca Ka emission lines? Yes indeed...
We can calculate this effect as a function of depth by "turning the problem on its side" and modeling this situation as a secondary fluorescent boundary case using Standard.exe and the Penfluor/Fanal SF calculation dialog as seen here with Fe2SiO4 (the only fluorescent x-rays from Mg2SiO4 that could excite the P or Ca k edge are continuum fluorescence because Si ka, Mg ka and O ka cannot excite the P or Ca k-edges in apatite):
(https://smf.probesoftware.com/oldpics/i59.tinypic.com/5fp7w9.jpg)
which shows the effect for P ka where we can see roughly 35 PPM P ka intensity at a distance of 10 um due to secondary fluorescence.
But what about Ca ka? Here is where it gets interesting. The secondary fluorescence effect is about 10 times larger for Ca ka than P ka as seen here:
(https://smf.probesoftware.com/oldpics/i59.tinypic.com/2m7ypev.jpg)
This is because Fe ka fluorescence more efficiently excites the Ca K edge than the P k edge. Of course these effects at 20 keV will be a little larger but we'll leave that as an exercise for the reader.
Edit by John: I hasten to add that because we "turned the problem on its side" and our actual geometry is "buried" as opposed to "adjacent" these secondary fluorescence intensities should at least be corrected for absorption through the olivine as described in the method above using CalcZAF for improved accuracy.
More details on how to perform these SF calculations can be found here, but the bottom line for this olivine-apatite system is, again, if you can't detect Ca, any observed P ka emissions are *not* from apatite:
http://smf.probesoftware.com/index.php?topic=58.0
Finally, the most rigorous (and tedious) calculation for this problem is of course running the full blown Penepma 2012 Monte-Carlo software for the specific compositions and geometry. For this situation I would suggest running a bi-layer geometry model (treat the buried apatite grain as a substrate with the olivine composition as a thin film on top) as described here:
http://smf.probesoftware.com/index.php?topic=57.0
The full Penepma calculation has the advantage of including all known physics rigorously so that the electron energy loss, fluorescence and x-ray absorption are all calculated, albeit only for a single composition, at a single electron energy for a specific geometry.