Self-ordered second-component clusters in solid solutions on the basis of ferroelectric perovskites: Nb clusters in KTaO[sub 3]

Semi-empirical Hartree-Fock calculations using the intermediate neglect of differential overlap (INDO) method, for self-ordered cubic symmetry clusters of seven Nb ions in ${\mathrm{KTaO}}_{\mathrm{3}}$ are performed with the aim of verifying the cluster model [1] of second component-induced phase transitions in ferroelectric perovskite matrices. It is shown that such a seven-particle cluster in ${\mathrm{KTaO}}_{\mathrm{3}}\mathrm{:Nb}$ has two types of quasidegenerate states of different nature. Namely, the state with the equilibrium full-symmetric dilatation and off-center displacements in [111]-directions of the central Nb-ion in the cluster, and the state with the equilibrium full-symmetric compression without any off-center effect. The consequences of such cluster structures on the multi-well potential are discussed. In particular, an avalanche-like behaviour of the temperature dependence of the ferroelectric order parameter is obtained. The results of semi-empirical INDO calculations of a seven-impurities cluster of Nb-ions in ${\mathrm{KTaO}}_{\mathrm{3}}$ confirm the key assumptions of the cluster model of induced phase transitions.