Probabilistic model of structural phase transition in perovskites

In this work, the crystal structures and phase transitions of compounds with perovskite structure were investigated. The classification of structural phase transitions in perovskites was carried out, the most common crystal structures and structural phase transitions were shown. A mathematical model was constructed, a theorem was given and proved for the probability of a possible transition. The formulas [Formula: see text] and [Formula: see text] are given for the mathematical expectation and variance of random variable [Formula: see text], which is the moment when the stochastic process [Formula: see text] deviation from the boundary [0, [Formula: see text]] interval for the first time. According to the mathematical model, one of the trajectories of random processes corresponding to the phase transitions that occur in perovskites is constructed.