Preparation of Barium Hexaaluminate using co-precipitation reaction mechanism
@Maurice, I always thought that barium nitrate and aluminium nitrate will react with ammonium carbonate and barium carbonate and aluminium hydroxide will precipitate down.

$$
\begin{align}
\ce{2 Al(NO3)3 (aq) + 3 (NH4)2CO3 (aq) &amp;-&gt; Al2(CO3)3 (s) + 6 NH4NO3 (aq)}\tag{R1}\\
\ce{Ba(NO3)2 (aq) + (NH4)2CO3 (aq) &amp;-&gt; BaCO3 (s) + 2 NH4NO3 (aq)}\tag{R2}
\end{align}
$$

(As aluminium carbonate is not stable and readily decomposes to form aluminium hydroxide.)

After that, if we keep the ratio of barium and aluminium $1:12$ and raise the temperature above $\pu{1200 °C}$ by calcinating the dried precipitate, barium hexaaluminate forms.

Also, can you clarify what $\ce{BaAl6(OH)20}$ is, because according to my understanding the general formula of barium hexaluminate is $\ce{BaO.6(Al2O3)}.$

Reference


Li, J. Q.; Wang, R. K.; Chen, C. Y. Preparation of Barium Aluminate with $\ce{BaCO3}$ and $\ce{Al(OH)3}$. AMR 2015, 1096, 156–160. DOI: 10.4028/www.scientific.net/AMR.1096.156.