Hardness of Covalent Crystals

Abstract

Based on the idea that the hardness of covalent crystal is intrinsic and equivalent to the sum of the resistance to the indenter of each bond per unit area, a semiempirical method for the evaluation of hardness of multicomponent crystals is presented. Applied to beta-BC2N crystal, the predicted value of hardness is in good agreement with the experimental value. It is found that bond density or electronic density, bond length, and degree of covalent bonding are three determinative factors for the hardness of a polar covalent crystal. Our method offers the advantage of applicability to a broad class of materials and initializes a link between macroscopic property and electronic structure from first principles calculation.

Intrinsic hardness of crystalline solids

“…The mutual agreement between the two different empirical schemes and the overall agreement with experimental hardness are striking. This observation indicates that although (shear) elasticity was not explicitly included, after fitting to experimental data, the model of Gao [18] apparently includes this effect implicitly. On the other hand, the strong correlation shows that hardness can also be estimated from the shear modulus.…”

“…Nevertheless, the Phillips-van Vachten energy scheme is being employed in recent formulations relating the hardness to the strength of a chemical bond. A notable success is the method suggested by Gao et al [18], which will be discussed in the next section.…”

“…The barrier, or resistance force, to the plastic glide is related to the number of covalent bond (N a ), the solid and the corresponding energy gap E g . This simple assumption is reasonable as it relates the intrinsic hardness (H a ) to the bond strength (E g ) and the coordination number [18],…”

Elastic properties, hardness, and anisotropy in baddeleyite IVTMO2 (M=Ti, Zr, Hf)

“…There are several models for estimating hardness. For example, Gao et al [42] proposed a formula for covalent compounds that suits diamond-like superhard materials quite well. Chen et al [43,44] In Table 3, the values of Vickers hardness calculated with the LDA are slightly larger than those calculated with the GGA for m-TiO 2 and m-ZrO 2 , and the values from Tian's model are larger and closer to experimental data than those from Chen's.…”

Electronic structures and mechanical properties of boron and boron-rich crystals (Part I)

“…This suggests that the hardness is not at all determined by the elastic constant solely. Qualification of the hardness by DFT is barely to begin recently [16][17][18][19][20]. Accordingly, the mechanical properties descried in this paper are limited to a level of elastic properties and phonon properties.…”