The control of the stoichiometry of Li$_{1+x}$Zn$_{2-y}$Mo$_3$O$_8$ was achieved by the solid-state-reaction. We found that the best sample that has the chemical composition Li$_{0.95(4)}$Zn$_{1.92(8)}$Mo$_3$O$_8$ was obtained from the starting nominal composition with Li : Zn : Mo : O = $(1+w)$ : $(2.8-w)$ : $3$ : $8.6$ with $w = -0.1$, indicating that the stoichiometry is greatly improved compared to those in the earlier reports. For larger $w$ detailed structural analysis indicates that the mixed sites of Li and Zn are preferentially occupied by Li atoms, as well as the fraction of the non-magnetic secondary phase Zn$_2$Mo$_3$O$_8$ decreases. Magnetic susceptibility of the improved stoichiometry powder samples shows a broad hump in the temperature range of 100 $< T <$ 200 K. This suggests that the development of antiferromagnetic correlations at the high temperatures is inherent to the ideal stoichiometric LiZn$_2$Mo$_3$O$_8$.
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