Correlation between the lattice parameters of crystals with perovskite structure

The correlation ((bar a_2 + bar a_3 ) = (bar a_1 + bar a_4 )) has been established for the mean parameters of the reduced perovskite unit cells, (bar a_1 ,bar a_2 ,bar a_3 ) and (bar a_4 ) of four arbitrary compounds with the perovskite structure having the compositions (1) ABX₃, (2) A′BX₃, (3) AB′X₃, and (4) A′B′X₃, where A, A′ and B, B′ are the pairs of metal atoms with equal valences and X is an oxygen or halogen atom. The above correlation is consistent with the model of harmonic quasi-elastic atomic interactions.