I think you should take first 1 mole of each precursor of material like for La you should take lanthanum nitrate( MW-433 and 0.1 mol=43.3). Like this proportion you tried each one and select any method of preparation. After preparation assure your material by taking XRD. But be careful for precursor choice, always take metal with organic precursor, so that it will be easy to remove from your material.
You can prepare the starting materials in the above mentioned proportions, but take care that aluminum oxide was not a high temperature modification, but the kow temperature one obtained from aluminum nitrate upon thermal decomposition at no more than 400 oC
At first you should determine how much higroscopic is you La-oxide! Expose the La-oxide to moisture for so long that the weight is not changing anymore. Then dry the La-oxide at app. 200 C to get rid of water. Weigh it again and from the difference you will learn how much excess (x) of La2O3 you have to add in order to have stoichiometric final composition of LaTi2Al9O19. Then you can mix together the proposed composition: 1/2(La2O3 +X) + 2TiO2 + 9/2Al2O3 in which X is the excess of La2O3!
As Ti is at its classical Ti4+ oxidation state (and no problem with La3+ and Al3+), first the synthesis atmosphere would be air (always check that in case you need perhaps Ti3+, you should use reducing atmosphere). Then, for the synthesis, two classical ways:
- Solid state synthesis (Shake and Bake) but as mentionned by Danilo, be careful with La2O3. A little mistake in Danilo´s answer. 200°C is not sufficient to "dry" La2O3 because not only this is a question of humidity but worst a question of CO2 (another acid gas very difficult to avoid with basic oxides). My recommendation to avoid any deviation from stoichiometry is to put the powder in alumina crucible (or platinum) at 1000°C for 1h (depends on quantity) and cool fastly and weigh, even a bit hot ,(200°C it´s ok) and rapidly to avoid CO2 contamination.
- Pechini or "solgel" like synthesis, better for good chemical homogeneity and 1-step synthesis at lower temperature (finer grains).