ALPHA-FACTOR
Early EPMA workers did not have the luxury of high speed computers, and the complex rigorous physics-based matrix corrections could not be easily performed in an applications-oriented probe lab. Alpha factors or coefficients for matrix correction in binary compounds (e.g., Fe on Ni Ka, Ni on Fe Ka) were initially conceived of by Castaing in his 1951 Ph.D. dissertation. Ziebold and Ogilvie (1964) revisited alpha factors in the popular scientific literature as the development of commercial electron microprobes took off. Shortly thereafter, efforts to consider phases of more than 2 elements spurred the development of beta-factors. This was applied to geological EPMA by Bence and Albee (1968) who developed oxide alpha factors; this paper is one of the most frequently cited references in geology (over 1800 citations between 1982-2001). Several decades later, it was recognized that the alpha-factor approach could be fine-tuned for improved quantitative results using additional fit coefficients (linear and polynomial) (Rivers, pers. comm., 1990, and Armstrong, 1991).
These factors are derived by fitting concentrations vs. alpha-factors, from calculated or measured k-ratios in a system of binary standards covering a range of composition. See also beta-factors. The expression for the calculation of a single alpha-factor is shown below:
where : C is the elemental weight fraction of the element
K is the calculated or measured k-ratio at that concentration
The calculation of the matrix correction for an unknown sample is shown below:
where : 
is the unknown beta-factor
is the standard beta-factor