Dipole-dipole forces and a proton intersite separation in hydrogen-bonded ferroelectrics

A method to compute effectively the influence of the proton-lattice interaction through specific dipole-dipole forces on the mechanism of phase transitions in hydrogen-bonded ferroelectrics (KDP, DKDP) is exposed in details. We specifically direct our study to a tetragonal unit cell with four kinds of potassium atoms, each being a centre of the dipole moment d, and four different hydrogen bonds, each being represented by a dipole moment mu, which surround a given phosphate group. Basically, the protons are bound to the lattice structure by a square-well potential field, perfectly symmetrical with respect to the middle point for each hydrogen bond, while only two protons appear close to a given phosphate group the other two being farther away, according to the principle of minimum energy. However, an effective dipole-dipole interaction, although rather small in magnitude when compared with the basic potential field, nevertheless seems necessary and yet capable of explaining the actual mechanism when the lattice structure is transformed from a state with broken symmetry (ordered phase) to a perfectly symmetrical state (disordered phase). Numerical results reveal a weak potential-hill model on the other side of the bond, if a H3 proton is "at home", with an equally weak potential-valley model on the same side of the bond, if this proton is "away. Since in both cases the H3 proton lies at a potential bottom, such an energy state compels this proton to stay at one or another equilibrium position. There is an entirely opposite destiny for the H2 proton. The proton intersite separation is given by twice the elementary length b(0), where b(0) is a distance separating the middle point of a given hydrogen bond from the bottom, or the top, of a given potential-valley, or the potential-hill model, respectively. Our theoretical result, 2b(0) approximate to 0.40 Angstrom, (1 Angstrom = 10(-10) m) might be considered as satisfactory in comparison with observations, 0.36(0.44) Angstrom for protons (deuterons).