The process where dissolved minerals (such as quartz) precipitate within the pore spaces of sediment creating a gluey material leading to the binding of the sediment is called

I think this process is called Cementation. Cementation is a type of precipitation, a heterogeneous process in which ions are reduced to zero valence at a solid metallic interface. It involves hardening and welding of clastic sediments (the ones formed from preexisting rock fragments) by the precipitation of  mineral matter in the pore spaces. It is the last stage in the formation of sedimentary rocks.