“…Thus, there are many microstructurally-based mechanisms that lead to hardness changes as a function of composition, including solid solution hardening [1][2][3], inclusions and nanoinclusions [6,7], and spinodal decomposition [14,15]. In addition to the often-observed correlation between hardness and composition [1][2][3][4][5][6][7][8], a number of material properties are functions of hardness, H. The mechanical properties linked to hardness include compressive strength [16,17], fracture toughness [18], and Young's modulus [19]. For example, an upper limit for the compressive fracture strength, σ c , can be estimated from the relationship σ c (upper bound) ≈H/3 [16,17].…”