Phase separation in lithium intercalated anatase: A theory

Abstract

Lithium intercalated anatase used in Li-ion batteries has some special features: coexistence of Li-rich and Lipoor 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.

Bose-Einstein condensation and/or modulation of "displacements" in the two-state Bose-Hubbard model

“…Being rather some kind of approximation, the HCB model is still widely exploited for a description of the Bose-Einstein condensate (BEC) in optical lattices (see [9]). Beside ultracold systems, the model is used in the theory of ionic conductors [10], the systems of particles intercalated or adsorbed on the crystal surfaces [11][12][13], as well as in describing the local electron pairing in the theory of high-temperature superconductors [14].…”

Phonon-like excitations in the two-state Bose-Hubbard model

“…The main attention was usually paid to phase transition between normal (NO) phase and phase with the Bose-Einstein (BE) condensate [so-called Mott-insulator (MI) -superfluid state (SF) transition] [3][4][5][6]. The model is also intensively used for theoretical description of other phenomena, such as quantum delocalization of hydrogen atoms adsorbed on the surface of transition metal [7,8], quantum diffusion of light particles on the surface or in the bulk [9,10], thermodynamics of the impurity ion intercalation into semiconductors [11,12].…”

Two-state Bose-Hubbard model in the hard-core boson limit

“…The Bose-Hubbard model is also intensively used for a theoretical description of a wide range of phenomena: quantum delocalization of hydrogen atoms adsorbed on the surface of transition metals [13,14], quantum diffusion of light particles on the surface or in the bulk [15,16], thermodynamics of the impurity ion intercalation into semiconductors [17,18].…”