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Analysis of correlations between various physical properties of solids provides a formulation of simple criteria applicable to the search for new superhard materials. The prospects for the synthesis of new substances with the key elastic moduli, whose values approach or even exceed those of diamond are also discussed. We introduce the concept of ideal hardness and strength, which relates the elastic properties of materials to the corresponding mechanical characteristics, the concepts that are less unambiguously determined and that depend on the conditions of measurements. The control of material nanostructure makes it possible to approach the ideal hardness. The formulation of trends interrelating physical properties is expected to allow an essential guidance in the synthesis of new classes of superhard materials.volume V m , bulk modulus K and cohesive energy E c (see the data from Young (1991)). In particular, the relationshipwas proposed by Aleksandrov et al. (1987). For elemental solids, the ratio KV m =E c c varies approximatel y from 0.5 to 16 (®gure 2), although for the overwhelming majority of elements it lies within the much narrower interval of 1±4. If the normalized energy and volume for a certain group of substances are related by the universal scaling function, EˆE 0 f …V=V 0 †, where E 0 and V 0 are the Harder than diamond: dreams and reality 233

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