  Enhanced room-temperature electromechanical coupling in the lead-free
ferroelectric system $(1-x)$BaZr$_{0.2}$Ti$_{0.8}$O$_{3}$ -
$x$Ba$_{0.7}$Ca$_{0.3}$TiO$_{3}$ (abbreviated as BZCT) at $x=0.5$ is attributed
to the existence of a morphotropic phase region (MPR) containing an
intermediate orthorhombic ($O$) phase between terminal rhombohedral ($R$) BZT
and tetragonal ($T$) BCT phases. However, there is ambiguity regarding the
morphotropic phase transition in BZCT at room temperature - while some
experiments suggest a single $O$ phase within the MPR, others indicate
coexistence of three polar phases ($T+R+O$). Therefore, to understand the
thermodynamic stability of polar phases and its relation to electromechanical
switching during morphotropic phase transition in BZCT, we develop a Landau
potential based on the theory of polar anisotropy. Since intrinsic
electrostrictive anisotropy changes as a function of electromechanical
processing, we establish a correlation between the parameters of our potential
and the coefficients of electrostriction. We also conducted phase-field
simulations based on this potential to demonstrate changes in domain
configuration from single-phase $O$ to three-phase $T+R+O$ at the equimolar
composition with the increase in electrostrictive anisotropy. Diffusionless
phase diagrams and the corresponding piezoelectric coefficients obtained from
our model compare well with the experimental findings. Increase in
electrostrictive anisotropy increases the degeneracy of the free energy at
ambient temperature and pressure leading to decreasing polar anisotropy,
although there is an accompanying increase in the electromechanical anisotropy
manifested by an increase in the difference between effective longitudinal and
transverse piezo-coefficients, $d_{33}$ and $d_{31}$.
