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I was preparing $\ce{Mn3O4}$ but it was when characterized by XRD, a $\ce{Mn2O3}$ phase existed. Now how can I convert $\ce{Mn2O3}$ to $\ce{Mn3O4}$?

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You may need a good lab oven.

Manganese(II,III) oxide on Wikipedia

Preparation

$\ce{Mn3O4}$ formed when any manganese oxide is heated in air above 1000 °C. Considerable research has centred on producing nanocrystalline $\ce{Mn3O4}$ and various syntheses that involve oxidation of $\ce{Mn^{II}}$ or reduction of $\ce{Mn^{VI}}.$

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As @Poutnik has answered, heating manganese oxides at elevated temperature results in forming of $\ce{Mn3O4}$, research paper suggest that the reaction gets affected not only temperature but the partial pressure of oxygen and further heating at 1400 °C results in formation of $\ce{MnO}$. Here is an excerpt from a research paper [1] (emphasis mine):

TG and DTA curves of $\ce{γ-MnO2}$ have been obtained in nitrogen, air and oxygen. The reactions $\ce{MnO2 → Mn2O3}$ and $\ce{Mn2O3→ Mn3O4}$ were observed in the ranges 450° to 600° and 750° to 1100° respectively, and the decomposition temperatures are affected by the partial pressure of oxygen. The endotherm at ~1200° is unaffected by the atmosphere and is not accompanied by weight loss. It is, therefore, due to a polymorphic transformation of $\ce{Mn3O4}$ rather than formation of $\ce{MnO}$.

Another process is carbothermic reduction [2], i.e. reduction of manganese oxides with the help of carbon or carbon monoxide. It requires high carbon monoxide/carbon dioxide pressure and precise change of pressure w.r.t. to temperature. The following reactions depicts how the standard energy of formation varies with temperature:

$$ \begin{align} \ce{3 Mn2O3 + C &->[$T = \pu{1100 °C}$] 2 Mn3O4 + CO} &\quad ∆G^\circ &= -0.25 - 0.17T\\ \ce{3 Mn2O3 + CO &->[$T = \pu{1100 °C}$] 2 Mn3O4 + CO2} &\quad ∆G^\circ &= -170.71 - 0.004T\\ \end{align} $$

References

  1. Tinsley, D. M.; Sharp, J. H. Thermal Analysis of Manganese Dioxide in Controlled Atmospheres. Journal of Thermal Analysis 1971, 3 (1), 43–48. https://doi.org/10/bvwj2v.
  2. https://www.alliedacademies.org/articles/practical-reduction-of-manganese-oxide.pdf
  3. Puerta, M. C.; Valerga, P. Thermal Decomposition of a Natural Manganese Dioxide: A Laboratory Experiment for Undergraduate Students. J. Chem. Educ. 1990, 67 (4), 344. https://doi.org/10/fqg3kp.
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