  We performed neutron powder diffraction measurements on
(Bi$_{0.5}$Na$_{0.5+x}$)TiO$_3$ and (Bi$_{0.5+y}$Na$_{0.5}$)TiO$_3$ to study
structural evolution induced by the non-stoichiometry. Despite the
non-stoichiometry, the local structure ($r$$\leq$ 3.5 {\AA}) from the pair
distribution function analysis is barely affected by the sodium deficit of up
to -5 mol%. With increasing pair distance, however, the atomic pair
correlations weaken due to the disorder caused by the sodium deficiency.
Although the sodium and the bismuth share the same crystallographic site, their
non-stoichiometry have rather opposite effects as revealed from a distinctive
distortion of the Bragg peaks. In addition, Rietveld refinement demonstrates
that the octahedral tilting is continually suppressed by the sodium deficit of
up to -5 mol%. This is contrary to the effect of the bismuth deficiency, which
enhances the octahedral tilting.
