V. P. Sakhnenko

Rendering barium titanate semiconductive by doping with rareearth elements

Abstract Distribution of doping cations between A and B sites of perovskite ABO3 structure obeys certain conditions derived in terms of energy. These can be applied to predict semiconducting BaTiO3-based compositions, to account for yet unexplained anomalies in concentrational dependencies of electrical resistivity and Curie temperature, and to understand the relatively unimportant effect of doping in the case of solid solutions such as Ba1−x Sr x TiO3 and Ba1−x Ca x TiO3.

Non-linear normal modes for systems with discrete symmetry

Abstract Normal modes in linear mechanical systems with a discrete symmetry group in their equilibrium state can be classified by irreducible representations (irreps) of this group. In non-linear dynamical systems, excitation of a given mode spreads to a number of other modes associated with different irreps, and this collection of modes was called a “bush” of modes in previous papers. There are some special cases where, because of symmetry restrictions , a bush is “irreducible” — it contains modes associated with a single irrep only. We looked for all irreducible bushes of vibrational modes for N -particle mechanical systems with the symmetry of any of the 230 space groups and, for the case of analytical potentials, found that there exist only 19 classes of such bushes. As a result, all modal subspaces to which symmetry determined similar non-linear normal modes (introduced by Rosenberg) belong, were found, as well as all analytical mechanical systems whose dynamics, with a certain mode being initially excited, strictly reduces to only one resonance subspace corresponding to a single irrep. We found that the dimensionality of such resonance subspaces does not exceed four.

Correlation between the lattice parameters of crystals with perovskite structure

AbstractThe correlation

Phase transitions in PbMg1/3 Nb2/3 O3-PbTiO3 system

(\bar a_2 + \bar a_3 ) = (\bar a_1 + \bar a_4 )

Ferroelectric and ferroelastic phase states of crystals caused by atomic ordering

has been established for the mean parameters of the reduced perovskite unit cells,

Atomic ordering and ferroelectricity

\bar a_1 ,\bar a_2 ,\bar a_3