Hardness is too complex to be described by first principles. Based on the dielectric chemical bond theory, a semiempirical approach for the evaluation of the hardness of ionic oxide crystals has been proposed. It was applied to predict the hardness of complex crystals such as the optical crystals yttrium aluminum garnet, the LaMgAl₁₁O₁₉ aluminates, and the high-Tc superconductor YBa₂Cu₃O₇. The calculated values were in agreement with the available experimental ones. The simplicity of the approach allows a broader class of researchers to access the method easily and to calculate the hardness of materials even using only a hand-calculator. Finally, the correlation between bond length and hardness in oxide crystals has been studied. The physical nature of the hardness of ionic crystals has been further discussed.
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Faming Gao (2004) studied this question.
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