DOI: 10.11648/j.am.20261502.15 ISSN: 2327-252X

How to Estimate Bulk Modulus and Phonon Frequency of a Crystal from Numerical Values of Vickers Hardness Expressed in GPa

Antonín Šimůnek
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Several empirical formulas based on the bulk and shear moduli of crystals have been proposed to calculate hardness, but the mathematical expressions usually do not correspond to the units in GPa measured experimentally. The aim of this work is to reveal the relationship between measured and calculated units and to find quantities that could be derived from the numerical values of Vickers hardness measured experimentally in GPa. For this purpose, bond strength model of hardness is applied because it establishes a quantitative relationship between macroscopic hardness and the bonding characteristics in a crystal. It is shown that experimental GPa values of Vickers hardness is proportional to the magnitude of interatomic force densities calculated in [N/m 3 ]. Hardness corresponds to the average of all interatomic forces, but in crystals where all interatomic forces are equal, hardness is directly proportional to this force. This work shows how to derive the magnitude of interatomic forces from experimental Vickers hardness values in the crystals with tetrahedrally coordinated structures, NaCl-like, CsCl-like or NiAs-like structures, and how to apply these forces to estimate the bulk moduli and phonon frequencies of these materials. For zinc-blende type structures quantitative results are compared with experimental data for typical A III -B V crystals.

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