Local-structure evidence for a phase transition in a lead-free single crystal of (Na1/2Bi1/2)TiO3−0.06BaTiO3 by absorption fine-structure spectroscopy with synchrotron x-ray radiation

$(\mathrm{N}{\mathrm{a}}_1/2\mathrm{B}{\mathrm{i}}_1/2)\mathrm{Ti}{\mathrm{O}}₃\text{\ensuremath{-}}x\mathrm{BaTi}{\mathrm{O}}₃(\mathrm{NBT}\text{\ensuremath{-}}x\mathrm{BT})$ single crystal, as one of the most promising candidates to replace lead-based ferroelectrics, is a typical and unique lead-free system with morphotropic phase boundary (MPB) by far. In this paper, the phase transition process of NBT-0.06BT crystal in a wide temperature range of $20\ensuremath{\sim}550{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$ was analyzed at atomic scale by theoretical fitting to the measured synchrotron radiation x-ray absorption fine structure spectra quantitatively. Detailed analysis revealed a gradually transition of local structure at the point of phase transition from rhombohedral to tetragonal phase in NBT-0.06BT crystal on the bond lengths of Bi-O and Bi-Ti. The continuous evolution of local structure with no obvious barrier to overcome is one of the intrinsic characteristics of MPB at atomic scale and is responsible for the high piezoelectric properties. These results could promote the understanding of the origin of the high piezoelectric performance around the MPB and meanwhile guide new lead-free material designs.