The present paper proposes a novel model for estimating the free-volume size of the porous materials based on the analysis of the experimental ortho-positronium (o-Ps) lifetimes collecting within more than four decades. The model is derived by combining the semi-classical (SE) physics model, which works in the region of large pores (pore size R > 1 nm), with the conventional Tao-Eldrup (TE) model, which is applicable only for the small-pore region (R < 1 nm). Thus, the resulting model, called the hybrid (HYB) model, is able to smoothly connect the o-Ps lifetimes in the two regions of the pore. Moreover, by introducing the o-Ps diffusion probability parameter (D), the HYB model has reproduced quite well the experimental o-Ps lifetimes in the whole region of pore sizes. It is even in a better agreement with the experimental data than the most up-to-date rectangular TE (RTE) and Tokyo models. In particular, by adjusting the value of D, * Corresponding Author the HYB model can also describe very well the two defined sets of experimental o-Ps lifetime in the pores with spherical and channel geometries. The merit of the present model, in comparison with the previously proposed ones, is that it is applicable for the pore size in the universal range of 0.2 − 400 nm for most of porous materials with different geometries.
A gamma backscattering technique is applied to calculate the saturation curve and the effective mass attenuation coefficient of material. A NaI(Tl) detector collimated by collimator of large diameter is modeled by Monte Carlo technique using both MCNP5 and GEANT4 codes. The result shows a good agreement in response function of the scattering spectra for the two codes. Based on such spectra, the saturation curve of heat-resistant steel is determined. The results represent a strong confirmation that it is appropriate to use the detector collimator of large diameter to obtain the scattering spectra and this work is also the basis of experimental setup for determining the thickness of material.
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