the mixed-oxide route
The oldest and still the most common way to make a ceramic powder is almost embarrassingly simple: take the ingredient powders, mix them, and bake them until they react. This is the mixed-oxide route, sometimes affectionately called shake-and-bake. To make barium titanate (BaTiO3), for instance, you weigh out barium carbonate (BaCO3) and titanium dioxide (TiO2), grind them together, and fire the blend so the two solids react into the compound you actually want. It is the workhorse of industry because the starting oxides and carbonates are cheap, abundant, and easy to store.
The reaction happens entirely in the solid state, without melting, and that is exactly why it is slow and demanding. Atoms have to diffuse across the boundary where two different particles touch, growing a layer of product that then blocks the very path the atoms need. Because a diffusing atom might have to travel the whole width of a particle, the reaction speeds up dramatically when the powders are fine and intimately mixed, so the classic recipe is a repeating loop: mix, calcine (fire to react), then mill (grind) to break up the reacted mass and expose fresh unreacted material, and often mix-calcine-mill again until the reaction is complete and uniform. Each cycle homogenises the blend and shortens the diffusion distances the next firing must bridge.
The mixed-oxide route is prized for being cheap, scalable to tonnes, and forgiving, and it is how most tonnage ceramics, from spark plugs to capacitor dielectrics to ferrite magnets, are actually made. Its honest weaknesses are the flip side of its simplicity. Because mixing is only ever as good as your milling, some regions can end up richer in one ingredient than another, leaving unwanted second phases. The repeated high-temperature firings coarsen the powder and grow hard clumps, and every milling step risks grinding a little of the mill itself into the batch. When a job demands extreme purity, extreme fineness, or perfect chemical uniformity, engineers turn instead to the wet chemical routes.
Classic barium titanate: BaCO3 + TiO2 heated near 1100 to 1200 degrees C gives BaTiO3 + CO2. The carbonate conveniently releases carbon dioxide as it decomposes, driving the reaction forward, but any TiO2 that fails to react leaves a stray titanium-rich phase that hurts the capacitor.
Solid-state reaction plus a helpful gas by-product: cheap and scalable, but only as uniform as the mixing.
Grinding does not make the powders react; it only shortens the distances atoms must diffuse and refreshes the contact surfaces. The actual reaction is done by solid-state diffusion during firing, which is why a coarse, poorly mixed batch stays unreacted no matter how long you heat it.