Hi Brian,
Yes, this Au in FeS2 example is nasty for background fitting, but pyrite is also (usually) a simple matrix where a pure "blank" standard may be obtained, so is therefore a perfect candidate for using the blank correction!
I'll start by describing it in my software, since this is a very simple process and good for the overview of the details explained later:
1. Acquire your unknown sample as usual (using off-peak or even MAN backgrounds as discussed here):
http://probesoftware.com/smf/index.php?topic=29.msg237#msg2372. Then yes, acquire another unknown using the *exact same* conditions (PHA settings, count time, beam current etc.) on a standard suitable for the blank correction. Note that this "blank" standard should be a material that is ideally exactly the same composition as your unknown, but with a known (zero) concentration of the element of interest. This known concentration is usually easiest if it is say a pure synthetic and therefore zero due to purity, but the blank "level" as it is called can also be non-zero,
so long as it is accurately known! Our Ti in SiO2 synthetic has 1.42 PPM Ti (which could usually be rounded to zero!). The Spectrosil silica described here:
http://probesoftware.com/smf/index.php?topic=130.msg606#msg606is even purer, but is not crystalline, so I'm not sure how that might effect its use as a blank std for quartz...
3. Finally perform a normal quant analysis on the blank standard and see how far off you are from the zero or non-zero concentration that you are expecting. This is your accuracy check.
So let's say, your FeS2 blank standard contains zero PPM of Au (could be checked by ICP-MS for example), but when you measure it on your EPMA (using off-peak or MAN modeling), you obtain -40 PPM (yes, negative 40 PPM, though the artifact could be positive as well, though it is usually negative due to secondary Bragg diffraction (Ti Ka in SiO2) or self absorption in the sample, which I believe is the case for Au Ma in FeS2).
For example, see the Ti in quartz example here:
http://probesoftware.com/smf/index.php?topic=29.msg387#msg387So, let's see what we have for our blank correction equation now remembering that we are only making an adjustment to the unknown intensity, I(A)_unk in your first equation:What we basically want to do is to calculate the intensity represented by the blank accuracy characterization, so that it can be added to the matrix iteration to improve accuracy (and be reflected in the matrix correction if it is not a small adjustment!). That is, because the blank correction is being performed with a full matrix correction (just like the interference correction), the "blank" value could be a minor or even major element! It all comes out in the iteration!
So, you'll want to ratio the blank concentration error, I(A)_blank_meas - I(A)_blank_level, to obtain the intensity error (to put it another way), as seen here:
I(A)_unk_corr = I(A)_unk - I(A)_std * (I(A)_blank_meas - I(A)_blank_level)/ C(A)_std * (ZAF_std/ZAF_unk)
where I(A)_blank_meas is the concentration we actually measure in the blank standard (negative 40 ppm in the pure Fes2 in the above example) and I(A)_blank_level is the concentration that we know is there from purity or ICP-MS or other considerations (ideally zero for a pure FeS2).
Now that we have the corrected I(A)_unk_corr value, that is simply plugged into the matrix correction using the general case (your first equation)...
However, since you aren't using Probe for EPMA (yet!), you won't be easily able to do that, so you could just do a one step subtraction since the matrix correction will not change significantly for a 40 PPM correction in the matrix.
Bottom line, you could skip the quant aspect completely and just subtract the measured from the expected from your unknown measurements, that is, add 40 PPM to all analyses using the same example above!
I think this is a perfect example for the blank correction, and particularly if you decide to use MAN backgrounds, to avoid the off-peak interferences, as described in this abstract:
http://probesoftware.com/smf/index.php?topic=29.msg706#msg706