Neutron pair distribution function analysis and first principles calculations have been employed to study short-range correlations in heavily disordered dielectric material Sr$_x$Ba$_{1-x}$Nb$_2$O$_6$ ($x=0.35, 0.5$ and 0.61). The combination of methods has been fruitful in pinpointing main local-structure features, their temperature behaviour and interrelation. A rather complex system of tilts is found to be both temperature and Sr-content sensitive with the biggest tilt magnitudes reached at low temperatures and high $x$. Relative Nb-O$_6$ displacements, directly responsible for materials ferroelectric properties, are shown to be distinct in two octahedra sub-systems with different freezing temperatures and disparate levels of deviation from macroscopic polarization direction. Intrinsic disorder caused by Sr, Ba and vacancy distribution is found to introduce local strain to the structure and directly influence octahedra tilting. These findings establish a new atomistic picture of the local structure -- property relationship in Sr$_x$Ba$_{1-x}$Nb$_2$O$_6$.
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