Computational Alchemy: The Search for New Superhard Materials
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promising structures — comparative crystallography,8"11 algorithms based upon the concepts of crystalline nets 9 and close packing,9"11 modern alloy theory methods,1213 and simulated annealing strategies1415 being some examples. An exciting example of the process of designing materials from first principles is the ongoing search16"31 for new superhard materials. Several hundred experimental efforts to synthesize and characterize these materials have begun based upon the assumption that hardness is determined primarily by the bulk modulus31"38 (a measure of its resistance to volume change upon reversible hydrostatic compression) and theoretical predictions that certain carbon nitrides have bulk moduli approaching38"4' and even exceeding45'46 that of diamond. Superhard materials can be defined as having a microhardness exceeding 40 GPa.31 In addition to high hardness, they usually possess other unique properties such as high thermal conductivity and compressional strength. This combination of properties makes these materials highly desirable for a number of industrial applications such as superabrasives, wearresistant coatings, heatsinks, radiation windows, and even surgical knives.17 This article describes the progress in the search for new superhard materials and introduces a better figure of merit for the prediction of hardness. This improved relationship indicates that finding materials with hardnesses rivaling or even exceeding that of diamond will be
exceedingly difficult. Considering this, a refocus is suggested on the search for new superhard materials to locate materials more useful than diamond, rather than harder than diamond.
Predicting Hardness "Hardness, like the storminess of the seas, is easily appreciated but not readily measured."
—H. O'Neill47
Hardness is not only difficult to measure, it is difficult to define. It is a quality that can only be defined by the exact specification of the testing manner. Hence as many kinds of hardness exist as there are ways of testing it.45"55 However in a general sense, hardness is "the resistance offered by a given material to external mechanical action looking to scratch, abrade, indent, or in any other way permanently affect its surface."33 The hardness of a material is ultimately defined at the atomic level. A rigid crystal should be more resistant to deformation than a compliant one. To relate the atomic structure to hardness, both the strength of the chemical bonds and the rigidity of the bonding network must be considered because it is possible to have flexible crystals with very strong bonds (consider for example the a-cristobalite polymorph of SiO 2 ). Goldschmidt attempted an atomic definition of hardness that considered the atomic valences and bond distances. Such physical properties as the "volumetric lattice energy,"56'S7 bond ionicity,58 melting point," and bandgap6"'61 can also help to predict hardness with varying degrees of success. An alternative approach considers the elastic properties of a material. These are a function of a crystal's elast
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