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.
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