a hard aggregate
A hard aggregate is a cluster of small particles that have become chemically welded together so firmly that ordinary milling cannot break them apart. Picture a handful of snow left out and refrozen into a solid ice ball: the flakes are still there, but they have fused, and no gentle shaking will separate them again. In a powder, hard aggregates behave like single large, misshapen particles even though they are secretly made of many small ones bonded neck to neck.
The key distinction is how strongly the particles are held. In a hard aggregate the primary particles are joined by strong chemical bonds or solid necks that grew where particles touched and partly sintered together, so pulling them apart would mean breaking real bonds. This is different from a soft agglomerate, whose particles merely cling by weak surface forces and come apart easily. Hard aggregates are usually born in the calcination step: if the precursor is fired too hot or too long, the fresh particles begin to sinter to one another before you ever intended them to, freezing in these hard clumps. Once formed, they survive milling and dispersing and travel right through the process into the pressed body.
Hard aggregates are the sinterer's enemy because they wreck the uniformity that fine powder was meant to provide. When you press a body, the aggregates pack differently from the free particles, leaving large gaps between them, and during firing the inside of each aggregate densifies quickly while the big gaps around it lag behind, leaving large residual pores that never close and become the flaws that limit strength. This is why powder makers work so hard to avoid them, calcining as gently as possible and choosing chemical routes that resist hard-aggregate formation. The honest reality is that a hard aggregate cannot be fixed downstream; unlike a soft agglomerate you can mill away, a hard aggregate must be prevented at the powder stage, because by firing time it is already too late.
Over-calcined zirconia often carries hard aggregates: dense clumps of sintered-together crystallites that survive milling. In the fired part each aggregate is ringed by a large pore the sintering could not close, and those pores set the fracture strength.
Chemically welded clumps survive milling and leave large residual pores that milling cannot cure.
A hard aggregate cannot be milled away and cannot be fixed at firing. It must be prevented at the powder stage by gentle calcination, because once its particles are chemically bonded, the large pores it will leave in the fired ceramic are effectively locked in.