Theoretical equations for a particle size-determination method by applying an attenuated-total-reflection (ATR) technique were obtained. Based on these equations, the ATR-spectral intensities were calculated as functions of the sample amount and on the particle size for various choices of the experimental parameters. A mono layer region was more adequate for size measurements than a multiple-layers region. A prism and the incidence angle should be adequately selected according to the aims of the measurements. Experimental results of the sample amount dependences of the spectral intensities were almost consistent with calculations. The experimental results of size dependences showed the same tendency as those by calculations for SiO2 and SiC; especially for SiC, they were in just accord with those by calculations in the case of a KBr prism. Each component of a mixed plural-kind-particles sample almost agreed in its spectral intensity with that of a corresponding single-kind-particles sample. The particle size-determination method, based on the ATR technique, was theoretically supported, and its characteristics were reveled.

A method using an incidence-angle dependence of the spectral intensity was proposed to determine a particle size in a particle-size measurement by applying an infrared attenuated-total-reflection (ATR) technique. A formula, which is proportional to the infrared ATR-spectral intensity, was constructed as a function of the particle size, amount of particles, and incidence angle, f. Its f dependences were calculated for SiO2 particles of less than a mono layer on a Ge prism, and differed at every particle size. Some simulations of determining both particle size and particle amount were carried out for the samples of particles with sizes of 1 to 3 kinds by using algebraic-simultaneous equations with the software of Mathematica 5.2, and resulted in showing its usefulness.