Highlights • Asymmetrical crack propagation is found at Cu/SiC interface. • Crack defection is observed at strong Cu/SiC interface but not the weak one. • R–T model is applicable for the crack propagation at Cu/SiC interface. • Dislocation at the crack tip can blunt the crack and prevent its propagation. The propagation of the interfacial cracks at Cu/SiC interface under tensile (mode I) loadings and combination of tensile and shear (mixed mode) loadings are studied by molecular dynamics (MD) simulations. For the mode I, the asymmetrical interfacial crack propagation is observed at the interface, and the stress concentration is found both at the crack tip and somewhere of interface due to the lattice mismatch. Six loading methods with different loading angles are considered in this work, the behaviors of the crack propagation are found to be dependent on the loading angles. In addition, the Rice and Thomson (R–T) model is also used to predict the behaviors of interfacial crack growth theoretically. With pure tensile loading, the energies necessary for dislocation nucleation at the two crack tips are found to be different, which leads to asymmetrical crack propagation. For the mixed modes, the behaviors of the crack propagation are predicted by comparing the dislocation nucleation energy and the decohesion energy. The predictions of the R–T model are consistent with the MD results qualitatively. This research is intended to provide a fundamental explanation of the asymmetrical crack propagation at interface from atomscale.

Highlights • The elastic constants and moduli of Fe–W–C ternary compounds are estimated by first principles calculations. • The anisotropy of Fe–W–C ternary compounds has been systematically discussed. • The chemical bonding in these carbides are evaluated by calculating the density of states and Mulliken analysis. • These carbides are thermodynamically stable. The mechanical and electronic properties of Fe–W–C (Fe2W2C, Fe3W3C, Fe6W6C and Fe21W2C6) ternary compounds were investigated by first-principles calculations. The cohesive energy and formation enthalpy of these compounds show that they are thermodynamically stable. The elastic constants were calculated by using stress–strain method and the Voigt–Reuss–Hill approximation was applied to estimate the mechanical moduli. The calculated bulk modulus values of Fe2W2C, Fe3W3C, Fe6W6C and Fe21W2C6 are 324.9 GPa, 326.0 GPa, 326.1 GPa and 336.1 GPa, respectively, which are larger than Fe3C and Cr7C3. The surface constructions of Young’s moduli were plotted to indicate the mechanical anisotropy. Using a theoretical method based on the works of Tian, the hardness of the crystal is estimated. Moreover, the chemical bonding in these carbides were evaluated by calculating the density of states and Mulliken analysis. The results indicate that all the bonding behaviors in Fe–W–C ternary compounds are the combinations of metallic and covalent bonds.

Highlights • Electronic transport properties in single molecular coulomb blockade devices. • Negative differential resistance (NDR) can be observed. • The NDR behavior involves Jahn–Teller effect and symmetry-breaking. Using valence bond theory in combination with a master equation technique, we have investigated the electron transport properties of benzene-based coulomb blockade devices. The results show that the benzene molecule undergoes a Jahn–Teller distortion when ionized, which lifts the state degeneracy. The lifted degenerate states couple differently to the left and right electrodes, leading to negative differential resistance. This type of negative differential resistance involves the Jahn–Teller effect and symmetry-breaking, which provides a way to design coulomb blockade devices with negative differential resistance behavior.

Highlights • Finite-T estimations of elastic and thermodynamics properties of ZrB12 are given. • The tensile stiffness of ZrB12 is superior to its shear stiffness. • CP has experienced stronger pressure dependences than CV. • From 300 to 2000 K, the calculated CTE rise from 1.98 × 10−5 to 6.01 × 10−5 K−1. • Bulk modulus and Debye temperature of ZrB12 are high up to 231.32 GPa and 1190 K. The calculations based on density functional theory have been performed for the cubic zirconium dodecaboride (ZrB12). Structural and elastic properties were obtained using Perdew–Burke–Enzerh (PBE) exchange- correlation functional. The lattice parameters and elastic constants at different pressures (0–30 GPa) have been calculated and total energies were used to determine the equation of state and free energy within the quasi-harmonic approximation. The agreement between the theoretical and experimental properties was found to be satisfactory. The thermodynamic properties including the normalized volume V/V0, bulk modulus B, thermal expansion α, heat capacity CP and CV, Grüneisen constant γ and Debye temperature have been estimated at pressures from 0 to 50 GPa and temperatures from 0 to 2000 K, respectively. We anticipate that the calculated elastic and thermodynamic results can give an important reference especially to those not easy to be experimentally obtained.

The influence of temperature and pressure on the mechanical and thermodynamic properties of single crystal Bismuth Telluride material was investigated by the first-principle calculation and quasi-harmonic Debye model. The computation results indicated that the lattice constant in the c axis increases nonlinearly and the elastic constants Cij and bulk module B0 increase linearly with increasing the pressure. The Young modulus of the Bi2Te3 crystal in the x and y axes are 28.6% larger than that in the z axis. The Poisson’s ratios along the three axes range from 0.2752 to 0.3853. When the temperature is less than 150 K, the lattice specific heat capacity of Bi2Te3 depends on the temperature. The thermal expansion coefficients of Bi2Te3 vary remarkably with the temperature and pressure. The chemical balance bonding of Bi2Te3 is predicated to be Bi 2 + 0.15 Te - 0.14 Te 2 - 0.08 based on the density functional theory, revealing the evident natural bonding interaction between Bi–Te and Te–Te. Those calculations are in good agreement with previous experimental data. Graphical abstract Download : Download full-size image Highlights • We obtain six anisotropic values of Young modulus and the Poisson ratios. • The high pressure properties of elastic constants and Bulk module are acquired. • The lattice constant c performs nonlinear deformation with the pressure to Bi2Te3. • The chemical structural formula of Bismuth Telluride should be Bi 2 + 0.15 Te - 0.14 Te 2 - 0.08 . • Quasi-harmonic Debye model assesses thermodynamic properties of Bi2Te3 availably.

Highlights • Silicene is a two-dimensional allotrope of silicon, analogous to graphene. • We use full atomistic molecular dynamics (MD) to characterize silicene. • We implement uniaxial tensile tests to determine stiffness and failure states. • We use an energy minimization approach to calculate the monolayer bending rigidity. • Understanding of mechanical performance is necessary for future application. The potential of atomistically two-dimensional (2D) materials has created a new paradigm of materials science. Among the various 2D crystalline structures is silicene – a monolayer allotrope of silicon – similar to the structure of graphene. While this material has been previous investigated for potential in electrical applications, successful implementation in such nanodevices requires full understanding of its mechanical behavior. Here, using full atomistic first-principles-based ReaxFF molecular dynamics (MD) we quantify the elastic stiffness (50.44 N/m for zigzag direction, 62.31 N/m for armchair direction) and limit states (ultimate strength on the order of 5.85 N/m, ultimate strain on the order of 18%) of monolayer silicene. A weak directional dependence is observed. Moreover, we quantify the effective bending stiffness of silicene (38.63 eV per unit width), indicating that its corrugated-like structure increases the bending rigidity compared to the similar system of graphene.

Highlights • The atomistic details have been encapsulated into the finite element formulation. • Typical fracture modes have been investigated using the proposed approach. • Graphene behavior depends on both load and graphene geometry. A previously developed specialty molecular mechanics based finite element for graphene is extended to enable prediction of mechanical failure and crack propagation in graphene sheets. The failure mechanisms at the atomistic level are based on bond breaking and elimination of atomic interactions. The developed molecular finite element method is employed to simulate modes I, II and III types of fracture in finite size graphene. Numerical results investigate the effect of chirality, and quantify crack propagation.

Highlights • We have investigated trigonal Ge2Sb2Te5 using DFT-D2 method. • DFT-D2 improves the structure but not the electronic structure. • The band gap of ∼0.5 eV has been obtained from DFT-D2+HSE06 hybrid functions. • The elastic constants were further compared with the experimental Young’s modulus. The Te–Te weak van der Waals-type bonding plays an important role in Ge2Sb2Te5, a widely investigated phase-change material and a potential topological insulator. In this work, we have studied the electronic and mechanical properties of stable Ge2Sb2Te5 using ab initio calculations with the van der Waals corrections. The results show that the van der Waals corrections combined with hybrid functions improve the descriptions of the electronic structure of stable Ge2Sb2Te5. The band gap of ∼0.5 eV in very good agreement with the experimental value for stable Ge2Sb2Te5 has been successfully reproduced. Furthermore, we have predicted the elastic constants and mechanical properties of stable trigonal Ge2Sb2Te5.

Highlights • We study the electronic structure and optical properties of (Zr–Al)-codoped ZnO. • (Zr–Al)-codoped ZnO may enhance the visible-light photocatalytic ability. • Oxygen vacancy can improve the photocatalytic activity of (Zr–Al) codoped ZnO. • Zinc vacancy has weak effect on the absorption spectrum of (Zr–Al) codoped ZnO. The Heyd–Scuseria–Ernzerhof (HSE) hybrid density functional was used to investigate the electronic structure and optical properties of (Zr–Al)-codoped ZnO. The calculated results show that the formation energy of (Zr–Al)-codoped ZnO is low, indicating that it is the energetically favorable structure and the first absorption peak of optical absorption spectra for (Zr–Al)-codoped ZnO has a red-shift compared with pure ZnO, which may lead to the improvement on the visible-light photocatalytic ability. The zinc and oxygen vacancies introduced by (Zr–Al)-codoped ZnO have also been investigated. Through analysis the main absorption peaks of the imaginary part of the dielectric function on polarization vectors perpendicular or parallel to the Z axis, we think that oxygen vacancy introduced by (Zr–Al) codoping can also improve the visible-light photocatalytic ability and zinc vacancy has weak effect to enhance the optical photocatalytic ability compared with (Zr–Al)-codoped ZnO. Graphical abstract Download : Download full-size image

Highlights • Elastic, electronic, magnetic and thermodynamic properties of Ni2ZrX (X = Sn, Sb) are investigated. • The first-principle calculations and quasi-harmonic Debye model are used in this paper. • Optimized lattice constants, Bulk and Shear moduli, ductility and Poisson’s ratio are obtained. • The effect of T and P on Cv is opposite and the effect of T and P on α is small. • Ni2ZrX alloy has little magnetism due to different atomic position in the generalized Heusler alloy. The elastic stabilities, electronic, magnetic and thermodynamic properties of Ni2ZrX (X = Sn and Sb) alloy under pressure are extensively investigated by using the first-principle calculations and quasi-harmonic Debye model. Through a series of researches, for instance Gibbs free energy as a function of pressure, P–V equation of states and elastic stabilities, the optimized lattice constants, Bulk, Shear and Young’s moduli, Anisotropy, ductility, Density of State (DOS) and Poisson’s ratio of Ni2ZrX alloy are obtained. The effects of temperature (T) and pressure (P) on heat capacity are opposite, and the effect of T is larger than P, which are consistent with a compression rate of volume. The results of thermal expansion coefficient (α) show the effect of T and P on α is small. The magnetic studies indicate that Ni2ZrX has little magnetism due to different atomic position in the generalized Heusler alloy structure. The DOS of Sn p and Sb p electrons form double-peak. Graphical abstract The figure presents: (a) the total DOS of Ni2ZrSn and Ni2ZrSb and the partial DOS of (b) 5s and 4d component of Zr atoms (c) 3d component of Ni atoms (d) 5s and 5p component of Sn and Sb atoms, respectively. Download : Download full-size image