There is about 1-2 cm of free space between the floor slab stones and the two-part vault hood all around. How must this be backfilled?

The radius of the bottom is always about 2 cm smaller than the outer dimensions of the dome, so that the bottom can be changed (if necessary) and the bricks have a chance to expand. The fireclay has a higher expansion than the dome parts and should not press against the dome. Normally, this gap remains open and becomes clogged with ash etc. over time. Purely visually, it can be grouted with mortar in the front area or optionally filled with sand.