Assessment of the mechanical properties of monolayer graphene using the energy and strain-fluctuation methods.

Molecular statics and dynamics simulations were performed to investigate the mechanical properties of a monolayer graphene sheet using an efficient energy method and strain-fluctuation method. Using the energy method, we observed that the mechanical properties of an infinite graphene sheet are isotropic, whereas for a finite sheet, they are anisotropic. This work is the first to report the temperature-dependent elastic constants of graphene between 100 and 1000 K using the strain-fluctuation method. We found that the out-of-plane thermal excursions in a graphene membrane lead to strong anharmonic behavior, which allows large deviations from isotropic elasticity. The computed Young's modulus and Poisson's ratio of a sheet with an infinite spatial extent are 0.939 TPa and 0.223, respectively. We also found that graphene sheets with both finite and infinite spatial extent satisfy the Born elastic stability conditions. We extracted the variation in bending modulus with the system size at zero kelvin (0.83 eV) using a formula derived from the Foppl-von Karman approach. When the temperature increases, the Young's modulus of the sample decreases, which effectively reduces the longitudinal and shear wave velocities.

Delineating the role of ripples on the thermal expansion of 2D honeycomb materials: graphene, 2D h-BN and monolayer (ML)-MoS2.

We delineated the role of thermally excited ripples on the thermal expansion properties of 2D honeycomb materials (free-standing graphene, 2D h-BN, and ML-MoS2), by explicitly carrying out three-dimensional (3D) and two-dimensional (2D) molecular dynamics simulations. In 3D simulations, the in-plane lattice parameter (a-lattice) of graphene and 2D h-BN shows thermal contraction over a wide range of temperatures and exhibits a strong system size dependence. The 2D simulations of the very same system show a reverse trend, where the a-lattice expands in the whole computed temperature range. In contrast to graphene and 2D h-BN, the a-lattice of ML-MoS2 shows thermal expansion in both 2D and 3D simulations and their system size dependence is marginal. By analyzing the phonon dispersion at 300 K, we found that the discrepancy between 2D and 3D simulations of graphene and 2D h-BN is due to the absence of out-of-plane bending modes (ZA) in 2D simulations, which is responsible for the thermal contraction of the a-lattice at low temperature. Meanwhile, all the phonon modes are present in the 2D phonon dispersion of ML-MoS2, which indicates that the origin of the ZA mode is not purely due to the out-of-plane movement of atoms and also its effect on thermal expansion is not significant as found in graphene and 2D h-BN.

Directional anisotropy, finite size effect and elastic properties of hexagonal boron nitride.

Classical molecular dynamics simulations have been performed to analyze the elastic and mechanical properties of two-dimensional (2D) hexagonal boron nitride (h-BN) using a Tersoff-type interatomic empirical potential. We present a systematic study of h-BN for various system sizes. Young's modulus and Poisson's ratio are found to be anisotropic for finite sheets whereas they are isotropic for the infinite sheet. Both of them increase with system size in accordance with a power law. It is concluded from the computed values of elastic constants that h-BN sheets, finite or infinite, satisfy Born's criterion for mechanical stability. Due to the the strong in-plane sp2 bonds and the small mass of boron and nitrogen atoms, h-BN possesses high longitudinal and shear velocities. The variation of bending rigidity with system size is calculated using the Foppl-von Karman approach by coupling the in-plane bending and out-of-plane stretching modes of the 2D h-BN.

Effect of strong phonon-phonon coupling on the temperature dependent structural stability and frequency shift of 2D hexagonal boron nitride.

The temperature dependent structural stability, frequency shift and linewidth of 2D hexagonal boron nitride (h-BN) are studied using a combination of lattice dynamics (LD) and molecular dynamics (MD) simulations. The in-plane lattice parameter shows a negative thermal expansion in the whole computed temperature range (0-2000 K). When the in-plane lattice parameter falls below the equilibrium value, the quasi-harmonic bending (ZA) mode frequency becomes imaginary along the Γ-M direction in the Brillouin zone, leading to a structural instability of the 2D sheet. The ZA mode is seen to be stabilized in the dispersion obtained from MD simulations, due to the automatic incorporation of higher order phonon scattering processes in MD, which are absent in a quasi-harmonic dispersion. The mode resolved phonon spectra computed with a quasi-harmonic method predict a blueshift of the longitudinal and transverse (LO/TO) optic mode frequencies with an increase in temperature. On the other hand, both canonical (NVT) and isobaric-isothermal (NPT) ensembles predict a redshift with an increase in temperature, which is more prominent in the NVT ensemble. The strong phonon-phonon coupling dominates over the thermal contraction effect and leads to a redshift in LO/TO mode frequency in the NPT ensemble simulations. The out-of-plane (ZO) optic mode quasi-harmonic frequencies are redshifted due to a membrane effect. The phonon-phonon coupling effects in the NVT and NPT ensemble simulations lead to a further reduction in the ZO mode frequencies. The linewidth of the LO/TO and ZO mode frequencies increases in a monotonic fashion. The temperature dependence of acoustic modes is also analyzed. The quasi-harmonic calculations predict a redshift of ZA mode, and at the same time the TA (transverse acoustic) and LA (longitudinal acoustic) mode frequencies are blueshifted. The strong phonon-phonon coupling in MD simulations causes a redshift of the LA and TA mode frequencies, while the ZA mode frequencies are blueshifted with an increase in temperature.

Phase stability and lattice dynamics of ammonium azide under hydrostatic compression.

We have investigated the effect of hydrostatic pressure and temperature on phase stability of hydro-nitrogen solids using dispersion corrected density functional theory calculations. From our total energy calculations, ammonium azide (AA) is found to be the thermodynamic ground state of N4H4 compounds in preference to trans-tetrazene (TTZ), hydro-nitrogen solid-1 (HNS-1) and HNS-2 phases. We have carried out a detailed study on structure and lattice dynamics of the equilibrium phase (AA). AA undergoes a phase transition to TTZ at around ∼39-43 GPa followed by TTZ to HNS-1 at around 80-90 GPa under the studied temperature range 0-650 K. The accelerated and decelerated compression of a and c lattice constants suggest that the ambient phase of AA transforms to a tetragonal phase and then to a low symmetry structure with less anisotropy upon further compression. We have noticed that the angle made by type-II azides with the c-axis shows a rapid decrease and reaches a minimum value at 12 GPa, and thereafter increases up to 50 GPa. Softening of the shear elastic moduli is suggestive of a mechanical instability of AA under high pressure. In addition, we have also performed density functional perturbation theory calculations to obtain the vibrational spectrum of AA at ambient as well as at high pressures. Furthermore, we have made a complete assignment of all the vibrational modes which is in good agreement with the experimental observations at ambient pressure. Moreover, the calculated pressure dependent IR spectra show that the N-H stretching frequencies undergo red and blue-shifts corresponding to strengthening and weakening of hydrogen bonding, respectively, below and above 4 GPa. The intensity of the N-H asymmetric stretching mode B2u is found to diminish gradually and the weak coupling between NH4 and N3 ions makes B1u and B3u modes to degenerate with progression of pressure up to 4 GPa which causes weakening of hydrogen bonding and these effects may lead to a structural phase transition in AA around 4 GPa. Furthermore, we have also calculated the phonon dispersion curves at 0 and 6 GPa and no soft phonon mode is observed under high pressure.

Temperature dependent structural properties and bending rigidity of pristine and defective hexagonal boron nitride.

Structural and thermodynamical properties of monolayer pristine and defective boron nitride sheets (h-BN) have been investigated in a wide temperature range by carrying out atomistic simulations using a tuned Tersoff-type inter-atomic empirical potential. The temperature dependence of lattice parameter, radial distribution function, specific heat at constant volume, linear thermal expansion coefficient and the height correlation function of the thermally excited ripples on pristine as well as defective h-BN sheet have been investigated. Specific heat shows considerable increase beyond the Dulong-Petit limit at high temperatures, which is interpreted as a signature of strong anharmonicity present in h-BN. Analysis of the height fluctuations, ⟨h2⟩, shows that the bending rigidity and variance of height fluctuations are strongly temperature dependent and this is explained using the continuum theory of membranes. A detailed study of the height-height correlation function shows deviation from the prediction of harmonic theory of membranes as a consequence of the strong anharmonicity in h-BN. It is also seen that the variance of the height fluctuations increases with defect concentration.

Efficacy of surface error corrections to density functional theory calculations of vacancy formation energy in transition metals.

We calculate properties like equilibrium lattice parameter, bulk modulus and monovacancy formation energy for nickel (Ni), iron (Fe) and chromium (Cr) using Kohn-Sham density functional theory (DFT). We compare the relative performance of local density approximation (LDA) and generalized gradient approximation (GGA) for predicting such physical properties for these metals. We also make a relative study between two different flavors of GGA exchange correlation functional, namely PW91 and PBE. These calculations show that there is a discrepancy between DFT calculations and experimental data. In order to understand this discrepancy in the calculation of vacancy formation energy, we introduce a correction for the surface intrinsic error corresponding to an exchange correlation functional using the scheme implemented by Mattsson et al (2006 Phys. Rev. B 73 195123) and compare the effectiveness of the correction scheme for Al and the 3d transition metals.

Long-wavelength transverse modes in charged colloidal crystals.

The dynamics of closely index matched colloidal crystals of charged silica spheres dispersed in deionized ethylene glycol-water mixture is investigated using dynamic light scattering. At variance with the reports of phonon dispersion measurements on thin colloidal crystals, our observations on millimeter-sized crystals show unambiguous evidence for overdamped transverse modes turning propagative in the range of small wave numbers in agreement with the theory of hydrodynamic interactions in charged colloidal crystals.

Glass transition and dynamical heterogeneities in charged colloidal suspensions under pressure.

Constant-pressure Monte Carlo simulations have been performed to study the static and dynamical properties of a liquidlike ordered suspension of like-charged colloidal particles subjected to a sudden compression. We report for the first time a liquidlike ordered monodisperse suspension undergoing a glass transition at a very low volume fraction ( straight phi = 0.003) and existence of dynamical heterogeneities near the glass transition. Mobile particles have been identified using the non-Gaussian parameter for the self-part of the Van Hove correlation function, and they are found to form clusters. The pressure dependence of mean cluster size and the cluster-size distribution of the mobile particles are discussed.