Application of shell model in molecular dynamics simulation to MgO

The P－V－T equation of state of MgO has been simulated under high pressure and elevated temperature using the molecular dynamics (MD) method with the breathing shell model (BSM). It is found that the MD simulation with BSM is very successful in reproducing accurately the measured molar volumes of MgO over a wide range of temperature and pressure. In addition, the MD simulation reproduces accurately the measured volume compression data of MgO up to 100GPa at 300K. It is demonstrated that the MD simulated P－V－T equation of state of MgO could be applied as a useful internal pressure calibration standard at elevated temperatures and high pressures.     

Comparative investigations of the P-V-T relationship of NaCl at high pressure and temperature

Two different potential models of molecular dynamics (MD) simulations have been applied to investigate the pressure-volume-temperature (P-V-T) relationship and lattice parameter of NaCl under high pressure and temperature. The first one is the shell model (SM) potentials in which due to the short-range interaction pairs of ions are moved together as is the case in polarization of a crystal due to the motion of the positive and negative ions, and the second one is the two-body rigid-ion Born-Mayer-Huggins-Fumi-Tosi (BMHFT) potentials with full treatment of long-range Coulomb forces. The P-V relationship at 300 K, T-V relationship at zero pressure, and lattice parameter a, have been obtained and compared with the available experimental data and other theoretical results. Compared with SM potentials, the MD simulation with BMHFT potentials is very successful in reproducing accurately the measured volumes of NaCl. At an extended pressure and temperature ranges, P-V relationship under different isotherms at selected temperatures, T-V relationship under different pressures, and lattice parameter a have also been predicted. The properties of NaCl are summarized in the pressure range 0-30 GPa and the temperature up to 2000 K.     

Properties of MgO at high pressures: Shell-model molecular dynamics simulation

Shell-model molecular dynamics (MD) simulation has been performed to investigate the melting of the major Earth-forming mineral: periclase (MgO), at elevated temperatures and high pressures, based on the thermal instability analysis. The interatomic potential is taken to be the sum of pair-wise additive Coulomb, van der Waals attraction, and repulsive interactions. The MD simulation with selected Lewis–Catlow (LC) potential parameters is found to be very successful in describing the melting behavior for MgO, by taking account of the overheating of a crystalline solid at ambient pressure. The thermodynamic melting curve is estimated on the basis of the thermal instability MD simulations and compared with the available experimental data and other theoretical results in the pressure ranges 0–150 GPa. Our simulated melting curve of MgO is consistent with results obtained from Lindemann melting equation and two-phase simulated data at constant pressure by Belonoshko and Dubrovinsky, in the pressure below 20 GPa. The extrapolated melting temperatures in the lower mantle are in good agreement with the results obtained from Wang's empirical model up to 100 GPa. Compared with experimental measurements, our results are substantially higher than that determined by Zerr and Boehler, and the discrepancy between DAC and MD melting temperatures may be well explained with different melting mechanisms. Meanwhile, the radial distribution functions (RDFs) of Mg–Mg, O–Mg, and O–O ion pairs near the melting temperature have been investigated.     

Simulated equation of state of CaF2 with fluorite-type structure at high temperature and high pressure

The pressure-volume-temperature (P-V-T) equation of state (EOS), isothermal bulk modulus, and thermal expansivity of CaF₂ with cubic fluorite-type structure are investigated using the constant temperature and pressure shell model molecular dynamics (MD) method with effective pair potentials which consist of the Coulomb, dispersion, and repulsion interaction. It was shown that MD simulation is very successful in accurately reproducing the measured volumes of the CaF₂ over a wide range of pressures. The simulated P-V data matched X-ray diffraction experimental results up to 9.5 GPa at 300 K. In addition, volume thermal-expansion coefficient and isothermal bulk modulus were also calculated and compared with available experimental data and the latest theoretical results at ambient condition. At extended temperature and pressure ranges, The P-V EOS under different isotherms at selected temperatures, T-V EOS under different isobars at selected pressures, thermal expansivity, and isothermal bulk modulus were predicted up to 1500 K and 10 GPa. The detailed knowledge of thermodynamic behavior and EOS at extreme conditions are of fundamental importance to the understanding of the physical properties of CaF₂.     

Isothermal bulk modulus and its first pressure derivative of NaCl at high pressure and high temperature

The isothermal bulk modulus and its first pressure derivative of NaCl are investigated using the classical molecular dynamics method and the quasi-harmonic Debye model.To ensure faithful molecular dynamics simulations,two types of potentials,the shell-model(SM) potential and the two-body rigid-ion Born-Mayer-Huggins-Fumi-Tosi(BMHFT) potential,are fully tested.Compared with the SM potential based simulation,the molecular dynamics simulation with the BMHFT potential is very successful in reproducing accurately the measured bulk modulus of NaCl.Particular attention is paid to the prediction of the isothermal bulk modulus and its first pressure derivative using the reliable potential and to the comparison of the SM and the BMHFT potentials based molecular dynamics simulations with the quasi-harmonic Debye model.The properties of NaCl in the pressure range of 0-30 GPa at temperatures up to the melting temperature of 1050 K are investigated.     

Isothermal bulk modulus and its first pressure derivative of NaCl at high pressure and high temperature

The isothermal bulk modulus and its first pressure derivative of NaCl are investigated using the classical molecular dynamics method and the quasi-harmonic Debye model. To ensure faithful molecular dynamics simulations, two types of potentials, the shell-model (SM) potential and the two-body rigid-ion Born-Mayer-Huggins-Fumi-Tosi (BMHFT) potential, are fully tested. Compared with the SM potential based simulation, the molecular dynamics simulation with the BMHFT potential is very successful in reproducing accurately the measured bulk modulus of NaCl. Particular attention is paid to the prediction of the isothermal bulk modulus and its first pressure derivative using the reliable potential and to the comparison of the SM and the BMHFT potentials based molecular dynamics simulations with the quasi-harmonic Debye model. The properties of NaCl in the pressure range of 0-30 GPa at temperatures up to the melting temperature of 1050 K are investigated.     

Thermoelastic parameter αKT of sodium chloride at high pressure and high temperature

Two different potential models to the molecular dynamics (MD) simulations have been applied to investigate the thermoelastic parameter αK_T of sodium chloride (NaCl) under high pressure and high temperature. The first one is the shell model (SM) potential that due to the short-range interaction when pairs of ions are moved together as is the case in that polarization of a crystal due to the motion of the positive and negative ions, and the second one is the two-body rigid-ion Born–Mayer–Huggins–Fumi–Tosi (BMHFT) potential with full treatment of long-range Coulomb forces. Particular attention is paid to the comparison of the SM- and BMHFT-MD simulations with the Debye model for the first time, and this model combines with ab initio calculations within local density approximation (LDA) and generalized gradient approximation (GGA) using ultrasoft pseudopotentials and a plane-wave basis in the framework of density functional theory (DFT), and it takes into account the phononic effects within the quasi-harmonic approximation. Note that the MD calculated volumes using SM model is somewhat larger than both the DFT and experimental volumes despite not considering the temperature effect. Compared with SM potential, the MD simulated 300 K isotherm of NaCl with BMHFT potential is very successful in reproducing accurately the measured volumes and the GGA calculated volumes. Generally, it is found that there exist minor differences between the LDA and GGA computed the thermoelastic parameter αK_T of NaCl, with both average results giving good agreement with SM-MD simulations. At an extended pressure and temperature ranges, the variation of thermoelastic parameter αK_T which play a central role in the formulation of approximate equations of state has also been predicted. The properties of NaCl are summarized in the pressure range of 0–300 kbar and the temperature up to 2000 K.     

盐石结构MgO的状态方程的第一原理计算

利用平面波密度泛函理论研究了盐石结构MgO的状态方程,所得到的结果与实验值和其他作者的计算值符合很好.同时,还研究了热膨胀系数随温度和压强的变化关系.结果显示:在高压下,温度对盐石结构MgO热膨胀系数的影响很小.     

壳层模型分子动力学在CaO研究中的应用

利用壳层分子动力学方法结合有效的对势,研究了高压条件下CaO的熔化曲线。研究表明,分子动力学模拟结果精确地再现了广泛压强范围内CaO的状态方程。研究中考虑了分子动力学模拟熔化存在的过热现象,通过晶体的现代熔化理论,对CaO的分子动力学模拟熔化温度进行了修正,获得了高温高压下CaO正确的熔化温度。因此,常压下引入壳层模型的分子动力学为研究物质熔化提供了一个很好的方法,这种方法可进一步推广到其它物质的高压熔化研究中。     

Effects of pressure and temperature on the isothermal bulk modulus of CaO

Molecular dynamics (MD) simulations have been performed to investigate the effects of pressure and temperature on the isothermal bulk modulus of CaO using pair-wise interactions that include polarization effects through the shell model (SM). The dependence of isothermal bulk modulus B_T of CaO on the compression ratio V/V₀ and pressure P have been obtained from MD runs at T=300 K, and compared with the available experimental data and other theoretical results. A good agreement between theory and experiment is obtained. Meanwhile, B_T dependence on temperature T at zero pressure is investigated. At extended pressure and temperature ranges, SM-MD method has also been carried out for predicting the P-V-T equation of state and isothermal bulk modulus at different temperatures along the isotherms 0, 1000, 2000, 3000, and 4000 K, and at different pressures along the isobars 5, 15, 30, 40, and 50 GPa for CaO, respectively.     

Molecular dynamics of NaCl melting under pressure

We have performed one-phase molecular dynamics (MD) simulations to investigate the melting curve of NaCl over a wide range of pressures. To ensure faithful MD simulations, two types of potentials, the shell-model (SM) and the two-body rigid-ion Born-Mayer-Huggins-Fumi-Tosi (BMHFT) potentials, are fully tested. Compared with SM potential, the MD simulation with BMHFT potential is very successful in reproducing accurately the measured volumes of NaCl. The BMHFT potential can also produce a satisfactory melting curve, consistent with both experiments and two-phase simulations. Hence we recommend that the BMHFT should be the reliable potential for simulating high-pressure properties of NaCl.     

Nonlocal shear deformable shell model for thermal postbuckling of axially compressed double-walled carbon nanotubes

An investigation is reported of the thermal buckling and postbuckling of axially compressed double-walled carbon nanotubes (CNTs) subjected to a uniform temperature rise. The double-walled carbon nanotube is modeled as a nonlocal shear deformable cylindrical shell, which contains small-scale effects and van der Waals interaction forces. The governing equations are based on higher order shear deformation shell theory with a von Kármán–Donnell-type of kinematic nonlinearity and include thermal effects. Temperature-dependent material properties, which come from molecular dynamics (MD) simulations, and an initial point defect, which is simulated as a dimple on the tube wall, are both taken into account. The small-scale parameter, e ₀ a, is estimated by matching the buckling temperature of CNTs observed from the MD simulation results with the numerical results obtained from the nonlocal shear deformable shell model. The numerical illustrations concern the thermal postbuckling response of perfect and imperfect, single- and double-walled CNTs with different values of compressive load ratio. The results show that buckling temperature and postbuckling behavior of nanotubes are very sensitive to the small-scale parameter. The results reveal that temperature-dependent material properties have a significant effect on the thermal postbuckling behavior of both single- and double-walled CNTs.     

First-principles study of lattice dynamics and thermodynamics ofosmium under pressure

We have performed the first-principles linear response calculations of the lattice dynamics, thermal equation of state and thermodynamical properties of hcp Os metal by using the plane-wave pseudopotential method. The thermodynamical properties are deduced from the calculated Helmholtz free energy by taking into account the electronic contribution and lattice vibrational contribution. The phonon frequencies at Gamma point are consistent with experimental values and the dispersion curves at various pressures have been determined. The calculated volume, bulk modulus and their pressure derivatives as a function of temperature are in excellent agreement with the experimental results. The calculated specific heat indicates that the electronic contribution is important not only at very low temperatures but also at high temperatures due to the electronic thermal excitation. The calculated Debye temperature at a very low temperature is in good agreement with experimental values and drops to a constant until 100~K.     

Thermodynamic properties of ZnSe under pressure and with variation in temperature

The thermodynamic properties of Zn Se are obtained by using quasi-harmonic Debye model embedded in Gibbscode for pressure range 0–10 GPa and for temperature range 0–1000 K. Helmholtz free energy, internal energy, entropy,Debye temperature, and specific heat are calculated. The thermal expansion coefficient along with Gruneisen parameter are also calculated at room temperature for the pressure range. It is found that internal energy is pressure dependent at low temperature, whereas entropy and Helmholtz free energy are pressure sensitive at high temperature. At ambient conditions,the obtained results are found to be in close agreement to available theoretical and experimental data.     

Current-voltage characteristics of individual conducting polymer nanotubes and nanowires

We report the current-voltage (I-V) characteristics of individual polypyrrole nanotubes and poly(3,4-ethylenedioxythiophene) (PEDOT) nanowires in a temperature range from 300 K to 2 K. Considering the complex structures of such quasi-one-dimensional systems with an array of ordered conductive regions separated by disordered barriers, we use the extended fluctuation-induced tunneling (FIT) and thermal excitation model (Kaiser expression) to fit the temperature and electric-field dependent I–V curves. It is found that the I–V data measured at higher temper-atures or higher voltages can be well fitted by the Kaiser expression. However, the low-temperature data around the zero bias clearly deviate from those obtained from this model. The deviation (or zero-bias conductance suppression) could be possibly ascribed to the occurrence of the Coulomb-gap in the density of states near the Femi level and/or the enhancement of electron-electron interaction resulting from nanosize effects, which have been revealed in the previous studies on low-temperature electronic transport in conducting polymer films, pellets and nanostructures. In addition, similar I-V characteristics and deviation are also observed in an isolated K0.27MnO2 nanowire.     

Thermodynamic properties of MgO under high pressure from first-principles calculations

The equations of state (EOS) and other thermodynamic properties of the rocksalt (RS) structure MgO are investigated by ab initio plane-wave pseudopotential density functional theory method. The obtained results are consistent with the experimental data and those calculated by others. Through the quasi-harmonic Debye model, in which the phononic effects are considered, the dependences of relative volume V/V₀ on pressure P, cell volume V on temperature T, and Debye temperature Θ and specific heat C_V on pressure P are successfully obtained. The variation of the thermal expansion with temperature and pressure is investigated, which shows the temperature has hardly any effect on the thermal expansion at higher pressure.     

Theoretical study of a melting curve for tin

The melting curve of Sn has been calculated using the dislocation-mediated melting model with the `zone-linking method'. The results are in good agreement with the experimental data. According to our calculation, the melting temperature of γ -Sn at zero pressure is about 436~K obtained by the extrapolation of the method from the triple point of Sn. The results show that this calculation method is better than other theoretical methods for predicting the melting curve of polymorphic material Sn.     

The melting mechanism in binary Pd0.25Ni0.75 nanoparticles: molecular dynamics simulations

The melting mechanism for Pd_0.25Ni_0.75 alloy nanoparticles (NPs) was investigated using molecular dynamics (MD) simulations with quantum Sutton-Chen many-body potentials. NPs of six different sizes ranging from 682 to 22,242 atoms were studied to observe the effect of size on the melting point. The melting temperatures of the NPs were estimated by following the changes in both the thermodynamic and structural quantities such as the total energy, heat capacity and Lindemann index. We also used a thermodynamics model to better estimate the melting point and to check the accuracy of MD simulations. We observed that the melting points of the NPs decreased as their sizes decreased. Although the MD simulations for the bulk system yielded higher melting temperatures because of the lack of a seed for the liquid phase, the melting temperatures determined for both the bulk material and the NPs are in good agreement with those predicted from the thermodynamics model. The melting mechanism proceeds in two steps: firstly, a liquid-like shell is formed in the outer regions of the NP with increasing temperature. The thickness of the liquid-like shell increases with increasing temperature until the shell reaches a critical thickness. Then, the entire Pd–Ni NP including core-related solid-like regions melts at once.     

A novel method for studying the buckling of nanotubes considering geometrical imperfections

Buckling of nanotubes has been studied using many methods such as molecular dynamics (MD), molecular mechanics, and continuum-based shell theories. In MD, motion of the individual atoms is tracked under applied temperature and pressure, ensuring a reliable estimate of the material response. The response thus simulated varies for individual nanotubes and is only as accurate as the force field used to model the atomic interactions. On the other hand, there exists a rich literature on the understanding of continuum mechanics-based shell theories. Based on the observations on the behavior of nanotubes, there have been a number of shell theory-based approaches to study the buckling of nanotubes. Although some of these methods yield a reasonable estimate of the buckling stress, investigation and comparison of buckled mode shapes obtained from continuum analysis and MD are sparse. Previous studies show that the direct application of shell theories to study nanotube buckling often leads to erroneous results. The present study reveals that a major source of this error can be attributed to the departure of the shape of the nanotube from a perfect cylindrical shell. Analogous to the shell buckling in the macro-scale, in this work, the nanotube is modeled as a thin-shell with initial imperfection. Then, a nonlinear buckling analysis is carried out using the Riks method. It is observed that this proposed approach yields significantly improved estimate of the buckling stress and mode shapes. It is also shown that the present method can account for the variation of buckling stress as a function of the temperature considered. Hence, this can prove to be a robust method for a continuum analysis of nanosystems taking in the effect of variation of temperature as well.