  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 fixed volume
(rather than 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 fixed volume V. Our
approach combines the Landau-Ginzburg-Devonshire phenomenology, classical
electrostatics and elasticity theory. Our results show that the size effects of
the phase diagrams and polarization of semi-ellipsoidal BiFeO3 nanoparticles
nontrivially depends on V. These findings provide a path to optimize the polar
properties of nanoparticles by controlling their phase diagrams at a fixed
volume.
