A polycrystalline diamond compact includes a polycrystalline diamond material having a plurality of grains of diamond bonded to one another by inter-granular bonds and an intermetallic gamma prime (γ′) or κ-carbide phase disposed within interstitial spaces between the inter-bonded diamond grains. The ordered intermetallic gamma prime (γ′) or κ-carbide phase includes a Group VIII metal, aluminum, and a stabilizer. An earth-boring tool includes a bit body and a polycrystalline diamond compact secured to the bit body. A method of forming polycrystalline diamond includes subjecting diamond particles in the presence of a metal material comprising a Group VIII metal and aluminum to a pressure of at least 4.5 GPa and a temperature of at least 1,000° C. to form inter-granular bonds between adjacent diamond particles, cooling the diamond particles and the metal material to a temperature below 500° C., and forming an intermetallic gamma prime (γ′) or κ-carbide phase adjacent the diamond particles.