The source of random static electrical fields, which is determined by both the piezoelectric coupling and the static elastic deformations induced by substitutional disorder of ions with different ionic radii has been considered for mixed crystals of the KH2PO4 family. It is shown that the random electrical fields act mainly on the lattice polarization along the c axis and up-down proton configurations. The short-range interactions of four acid protons surrounding a PO4 group are represented as the random local uniaxial anisotropy for the mixed crystals provided the ice rule condition is fulfilled. It is also shown that the distinction of symmetry between the up-down and lateral proton configuration, and the peculiarities of proton-lattice interaction can lead to the coexistence of long-range order (for up-down/lateral configuration) with the glass or paraelectric (for lateral/up-down configuration) state.

The long-time correlations of fluctuations of lattice displacements in the quantum paraelectrics and are studied within the framework of the mode-coupling theory of the dynamic transition from an ergodic to a non-ergodic state caused by defects. It is shown that the very hard local non-symmetry-breaking defects formed by the oxygen vacancies can induce the dynamic transition at . The low-temperature non-ergodic state is characterized by long-time correlations of local fluctuations of the polar displacements, which continuously arise for . Simultaneously, the local non-symmetry-breaking defects lead to the appearance of long-time correlations of long-wavelength fluctuations of acoustic displacements via the local random piezoelectric coupling for . The random local piezoelectric coupling is caused by the electrostrictive interaction, which is modified by the random electric fields of the frozen symmetry-breaking defects. The conditions that must be met for the dynamic transition to be induced by the oxygen vacancies are analysed. It is also shown that the unavoidable oxygen vacancies in the nominally pure and are quite sufficient in number to cause the non-ergodic state. The role of the dynamic transition in the formation of the glass state for lightly doped and is discussed.

Results of a theoretical and experimental study of cooperative behaviour in soft lattices with off-center ions characterized by elastic dipole moments are presented. The influence of random elastic fields on the impurity-induced ferroelectric phase transition is investigated.

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