  Lithium intercalated anatase used in Li-ion batteries has some special
features: coexistence of Li-rich and Li-poor phases as well as two possible
positions for Li ions in the oxygen tetrahedron. A theoretical description of
the compound considering those peculiarities is presented. As shown by the
performed symmetry analysis, the intercalation induced lattice deformation can
be accompanied by the ordering of antiferroelectric type (internal
piezoeffect). In the following step, a qualitative illustration of the phase
separation in the lithiated anatase is given within the Landau expansion at the
proper choice of coefficients. A microscopic model for description of the
compound is also proposed which combines features of the Mitsui and
Blume-Emery-Griffits models and utilizes the symmetry analysis results. Various
ground state and temperature-dependent phase diagrams of the model are studied
to find a set of model parameters corresponding to the lithiated anatase. A
phase separation into the empty and half-filled phases in a wide temperature
range has been found closely resembling the phase coexistence in the
intercalated crystal. In the framework of the model, the two-position Li
subsystem could have the ordering of ferro- or antiferroelectric types which,
however, has not been yet observed by the experiment.
