In this study, LaSr0.5Co0.5O3 perovskite (LSCO), with 1, 2 and 4 wt% of LSCO nanoparticle inserted into the OPC (Ordinary Portland Cement) matrix via the sol-gel route. The sample nanocrystallite characteristics, surface topography, flexural strength, the influence of crystallite’s size, chemical interaction, and the correlation between carrier diffusion; surface roughness were studied using some related techniques and Master and Fokker-Planck approaches. The obtained results from LSCO/cement discrete cell structure show that the sample cement mortar containing 2 wt% LSCO nanocrystallites has a more stable mechanical structure and higher flexural strength due to the its permanent electric dipole, more occupation of the trap sites into the cement, and diffusion of particles (crystallites) through the cell boundary and inside the cells. For this purpose, microscopic parameters such as the trap and escaping rate in the LSCO+ cement discrete cells have been introduced and discussed with considering Master nonlinear Fokker–Planck and chemical reaction equations based on non-fluctuations of the LSCO particle position explored in the cells (which strongly correlated with random sequence). The results indicate an inhomogeneous nano structures characteristic, which is beyond the equilibrium stationary state with Gaussian fluctuations for the particle position.
