Bond Length and Charge Transfer Dominance

Philips [37] and Liu and Cohen [39] have proposed another relationship for the 

All the expressions indicate that shorter and denser chemical bonds as well as smaller ionicity should favor hardness. In order to obtain a compound with large bulk modulus, one must find such a covalent compound that has both shorter bond length and smaller ionicity, and high compactness in atomic arrangement inside. Thus, the atomic CN-imperfection-induced bond contraction should contribute directly to the hardness at the surface or sites surrounding defects. Therefore, a nanometer-sized diamond is expected to be 100 % (0.88 — 1) harder than the 

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