Concentration-dependent short-range order in the relaxor ferroelectric $(1-x{\left)\mathrm{Pb}\right(\mathrm{Sc},\mathrm{Ta})\mathrm{O}}_3\text{−}x{\mathrm{PbTiO}}_3$

Using the x-ray diffraction and x-ray absorption fine structure techniques, we have probed $\mathrm{Ti}$, $\mathrm{Ta}$, and $\mathrm{Sc}$ local environments in the solid solution system $(1-x{\left)\mathrm{Pb}\right(\mathrm{Sc},\mathrm{Ta})\mathrm{O}}_3\text{−}x{\mathrm{PbTiO}}_3$. This system is known to display a variety of ferroelectric behaviors ranging from variable order-disorder, to relaxor, to a mixed phase region, and then finally to normal ferroelectric, as the value of $x$ is increased. We find, in agreement with neutron diffraction studies, no detectable displacements of $\mathrm{Ta}$ or $\mathrm{Sc}$ atoms from their oxygen cage centers in any of these systems. Surprisingly, we find that the $\mathrm{Ti}$ atom is displaced along (111) from its inversion symmetry center for $x=0.05$. However, this average local $\mathrm{Ti}$ displacement gradually changes from (111) to (001) as $x$ increases, whereas the global crystal structure abruptly changes from rhombohedral to tetragonal at $x=0.45$. Our experimental results and theoretical modeling of others together suggest that this system consists of mixed regions, some characterized by a (111) $\mathrm{Ti}$ displacement and others characterized by a (001) $\mathrm{Ti}$ displacement. The displacement averaged over all regions becomes more weighted toward (001) as $x$ increases. Another significant result is that all our samples (with $x$ ranging from 0 to 0.5) have a high degree of local ordering of the $\mathrm{B}$ sites with alternate occupation of $\mathrm{Ta}$ and $\mathrm{Sc}$ atoms.