  The X-ray diffraction, Raman and infrared spectroscopies and magnetic
measurements were used to explore the correlated changes of the structure,
lattice dynamics and magnetic properties of the LuFeO3 nanoparticles, which
appear in dependence on their sintering temperature. We revealed a gradual
substitution of the hexagonal phase by the orthorhombic phase in the
nanoparticles, which sintering temperature increases from 700 C to 1100 C. The
origin and stability of the hexagonal phase in the LuFeO3 nanoparticles is of
the special interest, because the nanoparticle in the phase can be a
room-temperature multiferroic with a weak ferromagnetic and pronounced
structural and ferroelectric long-range ordering, while the antiferromagnetic
and nonpolar orthorhombic phase is more stable in the bulk LuFeO3. To define
the ranges of the hexagonal phase stability, we determine the bulk and
interface energy densities of different phases from the comparison of the Gibbs
model with experimental results. Using the Gibbs model parameters, we predict
the influence of size effects and temperature on the structural and polar
properties of the LuFeO3 nanoparticles. Analysis of the obtained results shows
that the combination of the X-ray diffraction, Raman and infrared spectroscopy,
magnetic measurements and theoretical modelling of structural and polar
properties allows to establish the interplay between the phase composition,
lattice dynamics and multiferroic properties of the LuFeO3 nanoparticles
prepared in different conditions.
