A method of quantitative phase analysis without standards

It is shown that to determine the quantitative phase composition of n samples each of which contains n phases it is sufficient to obtain a set of n² intensities values of analytical lines, I_ij, where 1 ≤ i ≤ n is the phase number in a sample of number 1 ≤ j ≤ n. It is supposed that in every sample the complete phase composition is determined. To calculate concentrations in one sample a system of consisting of n linears equations was obtained:

where s is the number of the sample, the mass absorption coefficient of the phase to be determined, x_is the weight fraction of the ith phase in the analysed sample. This system is modified if there are additional data on the samples, e.g. values of mass absorption coefficients. The use of this method excludes measurement of analytical line intensity in the pure phase or mixture of pure phases. Experimental verification of the method with two- and three-phase artificial mixtures gave satisfactory results. The necessary conditions for the application of this method are essential differences in the quantitative phase composition of the samples analysed.