  We have performed the calculations of the size effect in the temperature
dependence of BaTiO3 nanograin ceramics specific heat and dielectric
permittivity. We took into account the distribution of the grain sizes, that
exists in any real nanomaterial. This distribution lead to the distribution of
the temperatures of the size driven transition from ferroelectric to
paraelectric phase because of relation between the temperature and the sizes.
We calculated the transition temperature distribution function on the basis of
the sizes distribution function. This function allowed to calculate the
temperature dependence of any physical quantity in a nanomaterial. As an
examples we calculated specific heat and dielectric permittivity in nanograin
ferroelectric ceramics. The results demonstrate the strong influence of the
size distribution on the observed properties and especially on extracted from
experiment values of critical size and temperature. We carried out the
comparison of the theory with the measured specific heat and dielectric
permittivity in BaTiO3 nanomaterial. The developed theory described the
experimental data pretty good. The possibility of the extraction of size
distribution function parameters as well as real values of critical parameters
from experimental data is discussed.
