Calculation of the spontaneous polarization for Pb1-xCaxTiO3 close to the tricritical point

Abstract

We calculate the spontaneous polarization as a function of temperature for a mixed crystal of Pb1-xCaxTiO3 close to the tricritical pointdx (x = 0.4). This calculation of the spontaneous polarization is performed using the effective field approximation for the dipolar (PbTiO3) and higher order ( quadrupolar and octopolar) interactions for the mixed system of Pb1-xCaxTiO3 at concentrations from x = 0 to x = 0.45. Our calculations show that as the T-c decreases with increasing the concentration x, first order ( discontinuous) transition which occurs at low concentrations (x < 0.3) becomes tricriticaldx (x = 0.41) and then the second order ( continuous) transition (x > 0.4) in Pb1-xCaxTiO3. Dipolar and also higher order ( quadrupolar and octopolar) interactions are needed to explain the mechanism of ferroelectric - paraelectric transition in Pb1-xCaxTiO3.