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Probabilistic model of structural phase transition in perovskites by:1 (Source: Crossref)

    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 E(τ1)=((λβ)28+λβ2+1)E(ξ1) and D(τ1)=((λβ)496+(λβ)3123(λβ)28λβ2)(Eξ1)2+((λβ)28+λβ2+1)D(ξ1) are given for the mathematical expectation and variance of random variable τ1, which is the moment when the stochastic process X(t) deviation from the boundary [0, β] 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.


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