ALCA
Aluminum oxide, calcined · Refractory — stays solid to around 2070°C (3760°F) · Won't shrink or give off gas in the kiln · A batt and shelf wash material, and a placing powder · A source of alumina on its own in a glaze, without silica or flux
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Calcined alumina is aluminum oxide that's already been fired, so there's nothing left in it to burn off or shrink. It goes into kiln shelf and batt washes, into the placing powders that keep work from sticking, and into glazes as a way of adding alumina on its own.
Calcined alumina has been heated hot enough to drive off its water and settle into its stable form. It won't shrink, it won't give off gas, and it stays solid to around 2070°C (3760°F), far above any temperature a pottery kiln reaches. Those properties are what make it useful between ware and shelf: it goes into batt and shelf washes, and it is used as a placing powder under work that is inclined to stick. Kiln shelves and kiln furniture are made with it as well. In a glaze it adds alumina on its own, without the silica that comes with it in a clay or the flux that comes with it in a feldspar. Most of the alumina in a glaze comes from clay and feldspar, so calcined alumina is usually a deliberate addition rather than a staple, and it dissolves into a melt more slowly than either of them.