Universal Anisotropy Index Research Articles

Mechanical properties and hardness of new carbon-rich superhard C11N4 from first-principles investigations

The structural, mechanical properties and hardness of the new carbon-rich material C11N4 are studied by first-principles total energy calculations based on the density-functional theory. We use the empirical equations of state (EOS) to investigate the lattice properties and bulk modulus. It is found that the calculated lattice constants and bulk modulus are in good agreement with previous calculations. And the full set elastic constants are calculated using the stress-strain method. The Voigt-Reuss-Hill approximation is used to evaluate the mechanical moduli. The elastic constants show that the two phases of C11N4 are mechanically stable. The tetragonal-C11N4 (α-C11N4) exhibits larger mechanical moduli than the orthorhombic-C11N4 (β-C11N4). The mechanical anisotropy is calculated of several different anisotropic indexes and factors, such as universal anisotropic index (AU), the percent anisotropy (AG and AB) and shear anisotropic factors (A1, A2 and A3). Furthermore, the hardness of α-C11N4 and β-C11N4 are evaluated according to the intrinsic hardness calculation theory. α-C11N4 is predicted to be a superhard material with the Vickers hardness of 67.17GPa, which is slightly higher than that of the cubic boron nitride. And the β-C11N4 is also a superhard material with the calculated Vickers hardness of 45.63GPa. C11N4 can be considered as candidate superhard compounds.

Mechanical properties and chemical bonding characteristics of Cr7C3 type multicomponent carbides

The first principles calculations based on density functional theory are performed to investigate the mechanical properties and chemical bonding features of several Cr7C3 type multicomponent carbides (Fe16Cr12C12, Fe12Cr12W4C12, Fe12Cr12Mo4C12, Fe12Cr12W4C8B4, and Fe12Cr12Mo4C8B4). The full set elastic constants are calculated using stress-strain method. The Voigt–Reuss–Hill approximation is used to evaluate the mechanical moduli. The mechanical anisotropy is characterized by calculating several different anisotropic indexes and factors, such as universal anisotropic index (AU), shear anisotropic factors (A1, A2, and A3), and percent anisotropy (AB and AG). The surface constructions of bulk and Young’s moduli are illustrated to indicate the mechanical anisotropy. The obtained results indicate that the presence of B could deteriorate the mechanical moduli of (Fe,Cr)7C3 phase in Cr cast iron slightly. On the other hand, the chemical stability of (Fe,Cr)7C3 carbides is improved due to chemical bonding modifications through doping with B. These conclusions are in agreement with experimental results.

Electronic structure, mechanical properties and thermal conductivity of Ln2Zr2O7 (Ln = La, Pr, Nd, Sm, Eu and Gd) pyrochlore

The electronic structure, chemical bonding and mechanical properties of Ln2Zr2O7 (Ln=La, Pr, Nd, Sm, Eu and Gd) pyrochlore are investigated by local-density approximation of spin polarized scheme+U calculations (U is the Hubbard energy) and further verified by the experimental results. Ln2Zr2O7 compounds are wide band gap insulators, and this is consistent with the experiment results. The calculated spin polarized density of states of them indicates that they are in a ferromagnetic state and the magnetic moment is mainly attributed to the 4f shell of the Ln atoms. For the chemical bonds in the Ln2Zr2O7 crystals, the O–Zr bond is stronger than the O–Ln bond. The hardness, elastic constants, bulk modulus, shear modulus, Young’s modulus and Poisson’s ratio of Ln2Zr2O7 compounds are investigated and the theoretical values are in good agreement with the experiments. The mechanical anisotropic properties are discussed using Zener’s indexes and universal elastic anisotropic index (AU). The sound velocities along [100], [110] and [111] directions are calculated for each Ln2Zr2O7 crystal. The thermal conductivities of Ln2Zr2O7 compounds are evaluated and the obtained thermal conductivity of Ln2Zr2O7 is lower than that of yttria-stabilized zirconia, indicating that they could be good low thermally conductive materials at high temperature.

Universal Elastic Anisotropy Index

Practically all elastic single crystals are anisotropic, which calls for an appropriate universal measure to quantify the extent of anisotropy. A review of the existing anisotropy measures in the literature leads to a conclusion that they lack universality in the sense that they are non-unique and ignore contributions from the bulk part of the elastic stiffness (or compliance) tensor. Proceeding from extremal principles of elasticity, we introduce a new universal anisotropy index that overcomes the above limitations. Furthermore, we establish special relationships between the proposed anisotropy index and the existing anisotropy measures for special cases. A new elastic anisotropy diagram is constructed for over 100 different crystals (from cubic through triclinic), demonstrating that the proposed anisotropy measure is applicable to all types of elastic single crystals, and thus fills an important void in the existing literature.