Fixed volume effect on polar properties and phase diagrams of ferroelectric semi-ellipsoidal nanoparticles

For advanced applications in modern industry, it is very important to reduce the volume of ferroelectric nanoparticles without serious deterioration of their polar properties. In many practically important cases, the fixed volume (rather than the fixed size) corresponds to realistic technological conditions of nanoparticles fabrication. The letter is focused on the theoretical study of the behavior of ferroelectric polarization, paramagnetoelectric coefficient and phase diagrams of semi-ellipsoidal nanoparticles with a fixed volume V. Our approach combines the Landau-Ginzburg-Devonshire phenomenology, the classical electrostatics, and the elasticity theory. Our results show that the size effects on the phase diagrams and polarization of semi-ellipsoidal BiFeO₃ nanoparticles nontrivially depend on V. These findings provide a path to optimize the polar properties of nanoparticles by controlling their phase diagrams at a fixed volume.