I have spent a fair bit of time on this project. The problem with measuring alpha factors is that, for example, in the MgO - Al2O3 binary, there is only one stoichiometric phase MgAl2O4 that defines the midpoint. So there is one measurement only on spinel for Mg and Al relative to MgO and Al2O3 standards. The precision of the measurement has to be very high and when you propagate errors and show the error bars on an alpha factor plot, you realize that there is no justification for using a formulation higher than linear (not constant, not polynomial). Similar problem in other binaries. In MgO - SiO2 there are forsterite and enstatite, but this is the exception. The authors came to this conclusion as well in their search for nonlinearity in the core CMAS system.
Clearly there is a basis for a polynomial formulation when using ZAF prz algorithms where you calculate factors at arbitrarily fine spaced increments of concentration, but that is not the point here.
Secondly. These measurements were made either on an ARL or the MAC probe and are subject to discussion regarding the instrumental stability in the case of the ARL (and takeoff angle not directly comparable to all other measurements made at 40 deg), and in the case of the MAC, non-normal beam incidence. When I was at Caltech I attempted to reconstruct the entire Bence Albee methodology from standards used for measurements and computer output of results. You have to understand that use of these standards predates BSE imaging. The fayalite standard used when I arrived had comments "avoid orange luminescent areas" which were quartz; the fayalite they were using historically was a synthetic material with coprecipitated quartz. The enstatite - Al graduated glasses are of unknown origin and pedigree but are clearly synthetic as well; I could only find two of the three glasses and basically no material left for futher use. Most MgO contains some amount of Ca and so is not pure, strictly speaking, and I doubt that was taken into consideration. There was not a standard mount that had all the standards for the study (so this means that multiple mounts having different carbon coats were used...). This is not to downplay the work that was done, but you have to keep these things in mind.
After the original and only measured alpha factors obtained at 52.5 deg on the ARL were published, they were superseded by the calculated values listed in the Albee Ray paper (and 40 degree factors appeared as well). From there on all factors were calculated by running ZAF in reverse. The desire to analyze S, Cl, etc. motivates a return to a-factors relative to pure element references, i.e., Ziebold Ogilvie, and again does not accomplish much relative to ZAF codes available today.
The real reason for development of BA alpha factors was to eliminate disagreement of ZAF results obtained on the Apollo 11 samples being analyzed by numerous labs, and also to have a small executable program that fit into microcomputers of the day. A BA correction on a Tracor TN2000 took about 1 minute whereas a ZAF correction took about 20 minutes (for an 8 element sample).
Going forward I think we have the same limitations unless one resorts to glasses which could in principle have any intermediate composition in a binary, but are probably goind to exhibit non-binary compositions (ie. a Fe-Si oxide glass could have ferric iron and iron loss to the Pt loop, etc.). The real utility of an alpha factor method is twofold: for graphical comparision of correction magnitude, and for processing X-ray maps (coupled with MAN background method).
I think the method I use is better and that is to compare the measured k-ratio for an element to that calculated by using CalcZAF. A value of kmeas / kcalc = 1 confirms the analytical measurement and all that it depends on (alignment, PHA and deadtime linearity, sample conductivity, etc.) and the correction algorithm (standard composition, algorithm, macs, etc.). Comparison of this measurement as a function of concentration for that element reveals any systematic errors and confirms the internal consistency of the standards used. This goes far beyond the evaluation within a binary join, and also reveals problems with the minor and trace element concentrations being used for microanalysis standards. This unbiased test is really the way to move forward.
Cheers,
Paul
Please keep your software updated for best results!