The method produces powder particles that are uniformly coated with functional groups. It includes homogenizing, in an agitator mill, a suspension of glass, quartz, glass ceramic, and/or ceramic particles in a suspending agent together with a coating agent, so that the particles in the suspension react with the coating agent in the agitator mill to form the uniformly coated powder particles with functional groups. Preferably a weight ratio of the suspending agent to the particles is from 0.5:1 to 5:1. The suspending agent is preferably an aqueous solvent and the coating agent is preferably a silane. The uniformly coated powder particles have a particle size (d50) of less than 2 μm, have a specific surface of 5 to 40 m2/g, and are free of agglomerates.