Negative and zero thermal expansion in K0.5Bi0.5TiO3

We show that a synergy of the covalency effect associated with the $A$-site and $B$-site cations in ${\mathrm{K}}_{0.5}{\mathrm{Bi}}_{0.5}\mathrm{Ti}{\mathrm{O}}_{3}$ (KBT) makes it unique among the Pb-free ferroelectrics by imparting a rare property of negative and zero thermal expansion (ZTE). We tuned this synergy in two different KBT alloys, ${\mathrm{K}}_{0.5}{\mathrm{Bi}}_{0.5}\mathrm{Ti}{\mathrm{O}}_{3}\ensuremath{-}{\mathrm{Na}}_{0.5}{\mathrm{Bi}}_{0.5}\mathrm{Ti}{\mathrm{O}}_{3}$ and ${\mathrm{K}}_{0.5}{\mathrm{Bi}}_{0.5}\mathrm{Ti}{\mathrm{O}}_{3}\ensuremath{-}\mathrm{Bi}({\mathrm{Mg}}_{0.5}{\mathrm{Ti}}_{0.5}){\mathrm{O}}_{3}$, and identified a common critical tetragonality below which the ZTE behavior disappears completely in both the systems.