Microscopic models of hardness

Abstract

Microscopic models of hardness

Elastic stability and electronic structure of tantalum boride investigated via first-principles density functional calculations

“…There are two factors to determine the hardness of a covalent material which are the strength of bonding and the number of bonds per unit area [39]. According to Gao's theory [40,41], the theoretical calculation hardness of crystal can be expressed as follows:…”

Mechanical and structural properties of titanium dioxide deposited by innovative magnetron sputtering process

“…The hardness of the thin films is usually many times smaller than that of the bulk. However, it was found that for thin films with dense structure the hardness is higher, and for nanomaterials it is possible to achieve the hardness even greater as compared to the bulk [10]. This is because the hardness of the material increases when the grain size decreases with the maximum in the nanometer range (Hall-Petch effect) [10].…”

“…However, it was found that for thin films with dense structure the hardness is higher, and for nanomaterials it is possible to achieve the hardness even greater as compared to the bulk [10]. This is because the hardness of the material increases when the grain size decreases with the maximum in the nanometer range (Hall-Petch effect) [10]. Results of the research presented in the subject literature show that oxide materials, which are composed from crystallites of single nanometers in size, exhibit completely different properties than the bulk material of the same chemical composition.…”

Investigation of microstructure, micro-mechanical and optical properties of HfTiO 4 thin films prepared by magnetron co-sputtering

“…Studies in the field of hard films [e.g. 22] show, that increased hardness may be easier obtained by manufacturing of multicomponent materials. However, in the subject literature, up to now there is a lack of reports regarding research of mechanical properties of thin film optical coatings manufactured in the form of mixtures, e.g.…”