We have performed calculations of the size effect in the temperature dependence of the
BaTiO3
nanograin ceramic specific heat and dielectric permittivity. We took into account the
distribution of grain sizes that exists in any real nanomaterial. This distribution led to a
distribution of the temperatures of the size driven transition from the ferroelectric to the
paraelectric phase because of the relation between the temperature and the size. We
calculated the transition temperature distribution function on the basis of the size
distribution function. This function allows us to calculate the temperature dependence of
any physical quantity for a nanomaterial. As examples, we calculated the specific heat and
dielectric permittivity for nanograin ferroelectric ceramics. The results demonstrate the
strong influence of the size distribution on the observed properties and especially on the
values of the critical size and temperature extracted from experiment. We carried out a
comparison of the theory with the measured specific heat and dielectric permittivity for
BaTiO3
nanomaterial. The theory developed described the experimental data fairly well. The
possibility of extracting size distribution function parameters as well as real values of
critical parameters from experimental data is discussed.
In this work, for the very first time a calculation of the ferroelectric size effect of cone-shaped nanoparticles (nanocones) was performed. To solve the appropriate EulerLagrange equations, a direct variational method was used. An approximate analytical expression for the phase transition temperature dependence on the nanocone volume was derived. We have shown that the transition temperature might be higher by up to a factor of 2.5 compared to bulk materials.
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