  We have investigated experimentally and theoretically the series
(Na$_{1-x}$Li$_{x}$)$_{2}$IrO$_{3}$. Contrary to what has been believed so far,
only for $x\leq0.25$ the system forms uniform solid solutions. For larger Li
content, as evidenced by powder X-ray diffraction, scanning electron microscopy
and density functional theory calculations, the system shows a miscibility gap
and a phase separation into an ordered Na$_{3}$LiIr$_2$O$_{6}$ phase with
alternating Na$_3$ and LiIr$_2$O$_6$ planes, and a Li-rich phase close to pure
Li$_{2}$IrO$_{3}$. For $x\leq 0.25$ we observe (1) an increase of $c/a$ with Li
doping up to $x=0.25$, despite the fact that $c/a$ in pure Li$_{2}$IrO$_{3}$ is
smaller than in Na$_{2}$IrO$_{3}$, and (2) a gradual reduction of the
antiferromagnetic ordering temperature $T_{N}$ and ordered moment. The
previously proposed magnetic quantum phase transition at $x\approx 0.7$ may
occur in a multiphase region and its nature needs to be re-evaluated.
