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 Ca_1–x A _x Ti_1–x/4□ _{x /4}O₃ (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.

Keywords:

• Ferroelectric
• polarization
• lattice dynamics

Acknowledgment

This work was supported by the Russian Foundation for Basic Research (project no. 09-02-00067)