  Thermodynamics of ferroelectric materials and their ferroelectric to
paraelectric (FE-PE) transitions including those in PbTiO3 is commonly
described by the phenomenological Landau theory and more recently by effective
Hamiltonian and various potentials, all with model parameters fitted to
experimental or theoretical data. Here we show that the zentropy theory, which
considers the total entropy of a system as a weighted sum of entropies of
configurations that the system may experience and the statistical entropy among
the configurations, can predict the FE-PE transition without fitting
parameters. For PbTiO3, the configurations are identified as the FE
configurations with 90- or 180-degree domain walls in addition to the ground
state of the FE configuration without domain wall. With the domain wall
energies predicted from first-principles calculations based on the density
functional theory in the literature as the only inputs, the FE-PE transition
for PbTiO3 is predicted showing remarkable agreement with experiments,
unveiling the microscopic fundamentals of the transition.
