  Machine learning has been establishing its potential in multiple areas of
condensed matter physics and materials science. Here we develop and use an
unsupervised machine learning workflow within a framework of
first-principles-based atomistic simulations to investigate phases, phase
transitions, and their structural origins in ferroelectric relaxors,
Ba(Ti$_{1-x}$,Zr$_x$)O$_3$. We first demonstrate the applicability of the
workflow to identify phases and phase transitions in the parent compound, a
prototypical ferroelectric BaTiO$_3$. We then apply the workflow on
Ba(Ti$_{1-x}$,Zr$_x$)O$_3$, with $x\leq0.25$ to reveal (i) that some of the
compounds bear a subtle memory of BaTiO$_3$, phases beyond the point of the
pinched phase transition, which could contribute to their enhanced
electromechanical response; (ii) the existence of peculiar phases with
delocalized precursors of nanodomains -- likely candidates for the
controversial polar nanoregions; and (iii) nanodomain phases for the largest
concentrations of $x$

Materials Science