DISCUSSION AND CONCLUSIONSmore efficient random number generation methods (12) could lead to a further reduction in the required computer time of 50% or so.
APPENDIXThe flow chart of the Monte Carlo program, Figure 4, outlines the basic steps involved in the calculation of the primary, secondary, and tertiary intensities of a ternary alloy. The pertinent equations and derivations may be found in the appendix of Reference 1.The Monte Carlo program previously developed for discrete energy photon excitation (1) has been adapted to account for the continuous energy photon excitation required when treating a conventional X-ray tube. The results of the Monte Carlo calculations agree quite well with values calculated numerically ( 4 , 5) that have been experimentally verified. We have obtained an estimate through private communication (11 ) that the computer time now required for the analytical method for the case when it can be used is probably a factor of from four to 40 times less than that for the present Monte Carlo model. However, it should be reiterated that it is not suggested that the Monte Carlo model compete directly with the analytical method. Rather it should be used in those situations where the analytical method either cannot be applied or for those applications where the analytical method requires more calculation time. This should include applications for thin samples, for cases in which diverging incidence or exit beams exist, or for layered samples. In general, it is applicable when the geometry of the system is complex.The Monte Carlo program requires only about 45 seconds on an IBM 370/165 computer to calculate sufficient histories (7000) to yield a standard deviation of 1.5% or less for ternary samples. This indicates that the model will be very useful to the analyst. We have already begun investigations of the use of the model directly in the inverse calculation of elemental amounts from experimental X-ray intensities on radioisotope-source, energy-dispersive systems.We estimate that optimization of the program by choosing
LITERATURE CITED