Effect of Ca~(2+) Ion Substitution by the Trivalent Ions (Sc~(3+), In~(3+), La~(3+), Bi~(3+)) on the Ferroelectric Instability in Orthorhombic CaTiO_3

摘要

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_xTi_(1-x/4)□_(x/4)O_3 (space group Pbmn) with A-Sc~(3+), In~(3+), La~(3+), Bi~(3+)(O-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 Ti~(4+) 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 Ca~(2+) and impurity A~(3+) have been considered. Every type of impurity has been found to induce ferroelectric instability in doped compounds.