Concentration phase diagram of Ba(x)Sr(1-x)TiO3 solid solutions

TL;DR

This paper introduces a new thermodynamic approach to derive phase diagrams for Ba(x)Sr(1-x)TiO3 solid solutions, accounting for elastic strain effects, and demonstrates its validity through experimental data analysis.

Contribution

A novel method for deriving thermodynamic potentials of solid solutions incorporating elastic strain effects, applied to Ba(x)Sr(1-x)TiO3.

Findings

Identified a tricritical point in the phase diagram.

Discovered multiple multiphase points with up to 6 phases.

Validated the method with experimental coefficients.

Abstract

Method of derivation of phenomenological thermodynamic potential of solid solutions is proposed in which the interaction of the order parameters of constituents is introduced through the account of elastic strain due to misfit of the lattice parameters of the end-members. The validity of the method is demonstrated for Ba(x)Sr(1-x)TiO3 system being a typical example of ferroelectric solid solution. Its phase diagram is determined using experimental data for the coefficients in the phenomenological potentials of SrTiO3 and BaTiO3. In the phase diagram of the Ba(x)Sr(1-x)TiO3 system for small Ba concentration, there are a tricritical point and two multiphase points one of which is associated with up to 6 possible phases.