Thermoelastic and mechanical properties in diamond, c-BN, c-SiC, $$\hbox {TiO}_{2}$$, $$\hbox {TiO}_{1.85}$$TiO1.85 and w-ZnO

Thermoelastic and mechanical properties have been obtained in materials with high (diamond, c-SiC, c-BN), medium (\(\hbox {TiO}_{2}\), \(\hbox {TiO}_{1.85}\)) and low (w-ZnO) hardness by means of ab initio calculations. Our methodology combines the ab initio results of SIESTA code with discrete element method (DEM) to describe the fracture in brittle materials. This methodology has shown to be efficient in predicting \(\hbox {TiO}_{2}\) hardness at the normal and high-pressure phases, and to describe low hardness materials such as cassiterite (\(\hbox {SnO}_{2}\)). On the other hand, micro-hardness Vickers models such as Sim\(\mathring{\mathrm{u}}\)nek et al. were applied to predict the hardness using structural and electronic parameters of single crystals, showing the importance of the information provided by self-consistent calculations. Our results show that it is possible to extend this methodology to the evaluation of the micro-hardness of a wide range of materials, and consequently, the methodology could be extended more reliably in a systematic searching of hardness in the design of solid solutions.