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The single-layer black phosphorus is characterized by its puckered configuration that possesses the hinge-like behavior, which leads to the highly anisotropic in-plane Poisson's ratios and the negative out-of-plane Poisson's ratio. We demonstrate that the hinge-like mechanism can be described by the angle–angle cross interaction, which, combined with the bond stretching and angle bending interactions, is able to provide a good description for the mechanical properties of single-layer black phosphorus. We also propose a nonlinear angle–angle cross interaction, which follows the form of Stillinger–Weber potential and can be advantageous for molecular dynamics simulations of single-layer black phosphorus under large deformation.

As a new two-dimensional (2D) material, phosphorene has drawn growing attention owing to its novel electronic properties, such as layer-dependent direct bandgaps and high carrier mobility. Herein we investigate the in-plane and cross-plane thermal conductivities of single- and multi-layer phosphorene, focusing on geometrical (sample size, orientation and layer number) and strain (compression and tension) effects. A strong anisotropy is found in the in-plane thermal conductivity with its value along the zigzag direction being much higher than that along the armchair direction. Interestingly, the in-plane thermal conductivity of multi-layer phosphorene is insensitive to the layer number, which is in strong contrast to that of graphene where the interlayer interactions strongly influence the thermal transport. Surprisingly, tensile strain leads to an anomalous increase in the in-plane thermal conductivity of phosphorene, in particular in the armchair direction. Both the in-plane and cross-plane thermal conductivities can be modulated by external strain; however, the strain modulation along the cross-plane direction is more effective and thus more tunable than that along the in-plane direction. Our findings here are of great importance for the thermal management in phosphorene-based nanoelectronic devices and for thermoelectric applications of phosphorene.

Armchair and zigzag are two popular principal directions in many quasi-two-dimensional nanostructures such as graphene, hexagonal boron nitride, and black phosphorus. To date, nearly all published works discuss the anisotropy for physical quantities based on the comparison between quantity values in these two principal directions in single-layer black phosphorus. However, in the present work, by analyzing the directional dependence for the Young's modulus with an analytic formula, we explore the third principal direction with a direction angle φ(tp) = 0.268π, besides the armchair and zigzag directions. This new principal direction is determined by the puckered configuration of black phosphorus. The largest Young's modulus value is neither in the armchair, nor in the zigzag direction. Instead it is the third principle direction along which the Young's modulus has the maximum value. This work reveals that armchair and zigzag directions are not enough for the discussion of anisotropic properties in the single-layer black phosphorus, and it is crucial to include this new principal direction for anisotropy discussions.

The interlayer breathing and shear modes in few-layer black phosphorus are investigated for their symmetry and lattice dynamical properties. The symmetry groups for the even-layer and odd-layer few-layer black phosphorus are utilized to determine the irreducible representation and the infrared and Raman activity for the interlayer modes. The valence force field model is applied to calculate the eigenvectorw and frequencies for the interlayer breathing and shear modes, which are explained using the atomic chain model. The anisotropic puckered configuration for black phosphorus leads to a highly anisotropic frequency for the two interlayer shear modes. More specifically, the frequency for the shear mode in the direction perpendicular to the pucker is less than half of the shear mode in the direction parallel with the pucker. We also report a set of interlayer modes having the same frequency for all few-layer black phosphorus with layer number N=3i with integer i, because of their collective vibrational displacements. The optical activity of the collective modes supports possible experimental identification for these modes., Comment: 10 figures, 7 tables

The phonon thermal conductivity in diamond nanowires (DNW) is studied by molecular dynamics simulation. It is found that the thermal conductivity in narrower DNW is lower and does not show obvious temperature dependence; a very small value (about 2.0 W/m/K) of thermal conductivity is observed in ultra-narrow DNW, which may be of potential applications in thermoelectric devices. These two phenomena are probably due to the dominant surface effect and phonon confinement effect in narrow DNW. Our simulation reveals a high anisotropy in the heat transport of DNW. Specifically, the thermal conductivity in DNW along [110] growth direction is about five times larger than that of [100] and [111] growth directions. The anisotropy is believed to root in the anisotropic group velocity for acoustic phonon modes in DNW along three different growth directions., Comment: accepted by PRB

The thermal expansion effect of silicon nanowires (SiNW) in [100], [110] and [111] directions with different sizes is theoretically investigated. At low temperatures, all SiNW studied exhibit thermal contraction effect due to the lowest energy of the bending vibration mode which has negative effect on the coefficient of thermal expansion (CTE). The CTE in [110] direction is distinctly larger than the other two growth directions because of the anisotropy of the bending mode in SiNW. Our study reveals that CTE decreases with an increase of the structure ratio $\gamma=length/diameter$, and is negative in whole temperature range with $\gamma=1.3$., Comment: accepted by Nanoscale

Two internal-friction (attenuation) peaks around 95 and 130 K in the polycrystal and single crystal of Bi-Sr-Ca-Cu-O are found to be related to the superconducting transition at 84 and 107 K, respectively. The jump of lattice parameter and shape-memory effect occurring at the peak temperatures reveal the characteristics of a martensitic transition. The velocity and attenuation versus temperature of ultrasonic longitudinal waves propagating along two directions in the a-b plane at 10\ifmmode^\circ\else\textdegree\fi{} to the a and b axes and of [010] shear waves with [100] polarization were measured for the ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$ single crystals. The anisotropic elasticity in the c plane is manifested. Only the longitudinal waves in a direction and the shear waves show an obvious softening minimum of velocity around 250 K, which is associated with an attenuation peak due to a phaselike transition, but other longitudinal waves reveal a monotonic stiffening from room temperature down to ${\mathit{T}}_{\mathit{c}}$. The origin of the overall trend of elastic stiffening that appears in the measurements so far for high-${\mathit{T}}_{\mathit{c}}$ oxides is discussed.

The single-layer black phosphorus is characteristic for its puckered structure, which has leaded to highly anisotropy in its optical, electronic, and mechanical properties. We report, using the non-equilibrium Green's function approach and the first-principles method, that the anisotropy in the thermal conduction is very weak in the single-layer black phosphorus -- the difference between two in-plane directions is less than 4%. Our phonon calculations disclose that the two in-plane acoustic phonon branches have lower group velocities in the direction perpendicular to the pucker, as the black phosphorus is softer in this direction, leading to a weakening effect for the thermal conductance in the perpendicular direction. However, the out-of-plane acoustic phonon branch behaviors abnormally; i.e., the group velocity of this phonon branch is higher in the perpendicular direction, although the single-layer black phosphorus is softer in this direction. The abnormal behavior of the out-of-plane phonon branch is closely related to the highly anisotropic Poisson's ratio in the single-layer black phosphorus. As a result of the counteraction between the in-plane phonon modes and the out-of-plane phonon mode, the thermal conductance in the perpendicular direction is weaker than the parallel direction, but the anisotropy is pretty small., Nanotechnology, published

The mechanical properties of single-layer black phosphrous under uniaxial deformation are investigated using first-principles calculations. Both Young's modulus and the ultimate strain are found to be highly anisotropic and nonlinear as a result of its quasi-two-dimensional puckered structure. Specifically, the in-plane Young's modulus is 44.0 GPa in the direction perpendicular to the pucker, and 92.7 GPa in the parallel direction. The ultimate strain is 0.48 and 0.20 in the perpendicular and parallel directions, respectively., Journal of Physics D: Applied Physics, accepted

This paper investigates the thermal conductivity of silicene nanosheets (SiNSs) via molecular dynamic simulation. It shows that the thermal conductivity of pristine SiNSs is about 25–30 W mK −1 and exhibits anisotropic behaviour. Moreover, it is found that isotopic doping is efficient in reducing the thermal conductivity of SiNSs. When SiNSs are randomly doped with 30 Si at the doping percentage of 50%, a maximum reduction of about 20% is obtained. This reduction can be increased when the dopants are arranged into a superlattice pattern. The thermal conductivity of these superlattice-structured SiNSs changes non-monotonically as the thickness of their lattice layers decreases. Detailed analysis of the phonon spectra demonstrates that the competing mechanism between the interface scattering and confinement effects of the phonon modes is responsible for this non-monotonical behaviour.

A new scheme is proposed to suppress the meandering spiral waves in the excitable media, which is described with two-dimensional variables. An external electronic signal with stochastic phase is imposed on a local area; few grids of the system are perturbed, for example, 4×4 and/or 5×5 grid nodes among all the 256×256 nodes, so that a new target wave may occur and competition between the newly generated target wave and the intrinsic meandering spiral waves develops dynamically. The numerical simulation results confirm that it is effective to suppress the meandering spiral wave in the Barkley model. Compared with a simple periodical driving in a local area, it shows some advantages such as shorter transient period to kill the spiral wave, and it is robust to spatiotempaoral noise. A new target wave could come into being and will kill the meandering spiral wave even in the anisotropic media,of which the diffusion coefficient is a function of space, when the intensity of the spatiotemporal noise is not too strong.

The velocity and attenuation versus temperature of ultrasonic longitudinal waves propagating along two directions in the a-b plane at 10° to the a and b axes were measured for a Bi 2 Sr 2 Ca 1 Cu 2 O 8 single crystal. The anisotropic elasticity in the a-b plane is manifested. One direction shows obvious softening around 250 K, the other reveals only monotonic stiffening from room temperature down to T c . Attenuation peaks at 95, 150, and 250 K are attributed to a phase-like transition of first order.