Small-angle scattering from three-phase samples: application to coal undergoing an extraction process

The correlation functions of samples made up of three homogeneous phases, with a fixed geometrical configuration and different scattering densities, are linearly related among themselves. The same is true of the corresponding scattering intensities. The property holds approximately true if the phase boundaries of some of the previous samples are slightly modified. The analytical expressions of the coefficients involved in the relevant linear combinations are derived and applied to obtain the volume fractions and the scattering densities of the three phases of a coal from its small-angle scattering intensities collected during an extraction process.