Effect of Ca2+ Ion Substitution by the Trivalent Ions (Sc3+, In3+, La3+, Bi3+) on the Ferroelectric Instability in Orthorhombic CaTiO3

Abstract

Vibration frequencies of instable ferroelectric modes, as well as dependencies of crystal energy on ion's displacement amplitudes of these modes in doped compounds Ca1–x A x Ti1–x/4□ x /4O3 (space group Pbmn) with А–Sc3+, In3+, La3+, Bi3+ (□–vacancy) have been calculated in the framework of generalized nonparametric Gordon–Kim model. To compensate excessive positive charge the vacancies were considered to be at Ti4+ sites. Calculations were carried out in the «average» crystal approximation for the impurity concentration x = 0.25. For this purpose 40 atoms’ supercell sets with the different ordering of the heterovalent ions Ca2+ and impurity А3+ have been considered. Every type of impurity has been found to induce ferroelectric instability in doped compounds.