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On the theory of thermodynamic properties of geometrically confined disordered ferroelectrics. (English) Zbl 1295.82030
The author proposes an approach to calculate the equilibrium thermodynamic characteristics (like ferroelectric phase transition temperature, spontaneous polarization, dielectric susceptibility, specific heat, etc.) of geometrically confined disordered ferroelectrics in the case when they are monodomains with emphasis on corresponding thin films and multilayers. The typical example is incipient ferroelectrics with dipole impurities. The physical properties of the impurity ferroelectrics depend on the characteristics of the random fields defined by their distribution function (in the disordered ferroelectric thin film they depend on the film thickness). To calculate the thermodynamic characteristics, the author uses a random field method modified for the case of thin films. The essence of the modification consists in altering the interaction between impurity dipoles in an incipient ferroelectric by geometrical confinement. This, in turn, generates the thickness dependence of the distribution function of random electric fields, which is responsible for observable properties of the disordered ferroelectric. To recapitulate the main steps of derivation of the random field distribution function, the Hamiltonian of a system of impurity dipoles chaotically distributed over the sites of a host lattice is considered first. All information on the host dielectric (its shape, the symmetry of its crystal lattice, etc.) is contained in the potential of interaction between impurity dipoles, and the potential is altered due to the effects of geometrical confinement. The author considers the simplest model with only two permissible orientations of an impurity dipole in the host lattice (corresponding to the disordered Ising model). The only nonzero order parameter is the ferroelectric one, characterizing the number of coherently oriented impurity dipoles in the sample. A Gaussian distribution function is used to obtain the equilibrium thermodynamic properties of disordered ferroelectrics. The next step is connected with a substitution of the thickness-dependent first moment and the width of a distribution function in the model equations to obtain the thickness dependence of the thermodynamic characteristics of a thin film. As a result, the author states a self-consistent equation for a long-range order parameter leading to the expression for the free energy of the disordered ferroelectric. This free energy function allows one to calculate physically observable quantities, in particular, the phase transition temperature of the disordered ferroelectric, which in this case depends on the impurity dipole concentration and the film thickness.
MSC:
82D45 Statistical mechanical studies of ferroelectrics
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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