An initiator nanoconstituent comprises a nanoparticle covalently bonded to a group having a free radical. The nanoparticle may be bonded to the group via an ether group or an amide group. The initiator nanoconstituent may be formed in situ, in a mixture comprising an elastomer material to be crosslinked. The initiator nanoconstituent is formed from an organic nanoconstituent compound that includes the nanoparticle and an organic group that does not include a free radical at the time the mixture is formed. At least one chemical bond of the organic nanoconstituent compound may be ruptured, in situ, to form the initiator nanoconstituent, which may then bond with polymer molecules of the elastomer material and form a crosslinked elastomer material. Downhole tools or components thereof may include such crosslinked elastomer material.