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.     

Temperature derivatives of the bulk modulus of ZrB2 calculated by using the pressure derivative of the bulk modulus

The temperature dependence of the bulk modulus of ZrB₂ above room temperature was calculated by using the equations by Garai and Laugier (J. Appl. Phys. 101 (2007) p.023514) and Lawson and Ledbetter (Philos Mag. 91 (2011) p.1425). The present calculations involve the accurate data for pressure derivative of the bulk modulus for the Anderson–Grüneisen parameter in addition to the other experimental parameters involved. It is interesting to note that the cited equations derived by different thermodynamic approaches give almost equivalent values for the temperature dependencies of the bulk modulus of ZrB₂. The present results for the temperature derivatives of the bulk modulus of ZrB₂ vary from ?0.016?GPa/K at 300–400?K to ?0.022?GPa/K at 1500–1600?K, being in good agreements with the corresponding experimental values.     

高压下纳米锗的状态方程与相变

采用同步辐射能量色散X射线衍射技术和金刚石对顶砧高压装置，对晶粒尺寸分别为13，49，100nm的Ge进行了原位高压X射线衍射实验，最高压力为35GPa. 所得的体弹性模量分别为112，92，88GPa. 可以看出 随着晶粒尺寸的减小，其体弹性模量逐渐升高. 同时由立方金刚石结构转变为四方白锡结构的相变压力亦随之提高，其值分别为16.4，12.4，11.5GPa. 建立了一个描述晶粒尺寸与体弹性模量关系的模型，并用理论公式计算了相变压力随晶粒尺寸的变化. 尽管在数值上存在一定的误差，但理论计算结果成功预示了随着晶粒尺寸的减小，体弹性模量和相变压力增加的趋势，与实验结果相一致.     

An isothermal equation of state for solids

An isothermal equation of state (EOS) for solids, recently suggested by the authors in the realistic form, V/V₀=f(P), with relative volume as the dependent and the pressure as the independent variable, was shown to have an advantage for some close-packed materials in that it allows B′_∞=(∂B_s/∂P)_s(P→∞) to be fitted, and this is where the usual standard equations fail. In the present study, our EOS is applied to a number of inorganic as well as organic solids, including alloys, glasses, rubbers and plastics; varying widely in their bonding and structural characteristics, as well as in their bulk modulus values. A very good agreement is observed between the data and fits. The results obtained are compared with those from two well-known equations, expressible in the realistic form, proposed by Murnaghan and Luban. Further, the results are also compared with those from the widely used two- and three-parameter EOSs, expressible in the unrealistic form only, P=f(V/V₀), proposed by Birch—and also with those from the EOS model of Keane in which B′_∞ is explicitly expressed as an equation of state parameter. The results obtained from our model compare well to these EOSs. Our EOS, in general, yields the smallest mean-squared deviations between data and fits. The values of B′_∞calculated from our EOS are compared with those from Keane's model. Further, we have studied the variation of B′_∞with temperature using the experimental isotherms of Mo and W at 10 different temperatures ranging from 100 to 1000 K, and observed that the values of B′_∞ yielded by our model and that of Keane vary, as expected, within a narrow range. Furthermore, our EOS is applied to study the stability of the fit parameters with variation in the pressure ranges with reference to the isothermal compression data on Mo and W—and also to study the variation of isothermal bulk modulus with pressure, with reference to the ultrasonic data on NaCl and noted a very good agreement with experiment. In addition, our model is applied, with B₀ and B′₀ constrained to the theoretical values, to the five theoretical isotherms of MgO at 300, 500, 1000, 1500 and 2000 K obtained on the basis of a first principles approach—a good agreement is observed with the predictions, and the values of B′_∞ inferred at different temperatures tend to converge to a constant value.     

Pressure derivatives of isothermal bulk modulus of rare gas solids

In the present study we have derived the expression for the bulk modulus using the Hildebrand approximation and the lattice potential energy for rare gas solids (RGS). The derived relation is further used to derive the expression for first and second order pressure derivatives of the bulk modulus for RGS. The derived relations are also used to compute the values of these constants in the case of Ne, Ar, Kr and Xe which are compared with the available values.     

Equation of state and temperature variation of the bulk modulus of the alkaline earth fluorides

The isotherms for the alkaline earth fluorides (CaF₂, SrF₂ and BaF₂) have been computed using the expression for the total free energy of a crystal in the quasiharmonic approximation. The theoretical points for SrF₂ and BaF₂ have been compared with the points derived from Bridgman’s experimental relation. The temperature variation of the isothermal bulk modulus of the alkaline earth fluorides has been worked out on the basis of Axe’s shell model. The theoretica points are compared with the points obtained from the temperature variation of the elastic constants data. It is found that the vibrational contribution to the temperature variation of the elastic constants in these crystals is significant.     

Kinetic details of crystallization in supercooled liquid Pb during the isothermal relaxation

The kinetic details of crystallization in supercooled liquid Pb during the isothermal relaxation process have been investigated by molecular dynamics simulations, and the microstructure evolution analyzed by the cluster-type index method (CTIM) and the tracing method. It has been found that, the dynamic features are consistently correlated with the microstructure evolution and the crystallization characteristics in the mean square displacement (MSD) and the non-Gaussian parameter (NGP): the β relaxation regime corresponds to the minor structural rearrangement because of the “cage effect”, and the atoms attempt to escape from the “cages”; the α relaxation regime is related to a more diffusive movement of atoms, and the appearance of the second plateau in MSD and the non-zero plateau in NGP corresponds to the completion of crystallization. In addition, three distinct stages of nucleation, growth of nuclei and coarsening of crystallites in the crystallization process have been clearly revealed.     

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。     

First principles study on the charge density and the bulk modulus of the transition metals and their carbides and nitrides

A first principles study of the electronic properties and bulk modulus （B0） of the fcc and bcc transition metals, transition metal carbides and nitrides is presented. The calculations were performed by plane-wave pseudopotential method in the framework of the density functional theory with local density approximation. The density of states and the valence charge densities of these solids are plotted. The results show that B0 does not vary monotonically when the number of the valence d electrons increases. B0 reaches a maximum and then decreases for each of the four sorts of solids. It is related to the occupation of the bonding and anti-bonding states in the solid. The value of the valence charge density at the midpoint between the two nearest metal atoms tends to be proportional to B0.     

Effect of voids and pressure on melting of nano-particulate and bulk aluminum

Molecular dynamics simulations are performed using isobaric–isoenthalpic (NPH) ensembles to study the effect of internal defects in the form of voids on the melting of bulk and nano-particulate aluminum in the size range of 2–9 nm. The main objectives are to determine the critical interfacial area required to overcome the free energy barrier for the thermodynamic phase transition, and to explore the underlying mechanisms for defect-nucleated melting. The inter-atomic interactions are captured using the Glue potential, which has been validated against the melting temperature and elastic constants for bulk aluminum. A combination of structural and thermodynamic parameters, such as the potential energy, Lindemann index, translational-order parameter, and radial-distribution functions, are employed to characterize the melting process. The study considers a variety of void shapes and sizes, and results are compared with perfect crystals. For nano aluminum particles smaller than 9 nm, the melting temperature is size dependent. The presence of voids does not impact the melting properties due to the dominancy of nucleation at the surface, unless the void size exceeds a critical value beyond which lattice collapse occurs. The critical void size depends on the particle dimension. The effect of pressure on the particulate melting is found to be insignificant in the range of 1–300 atm. The melting behavior of bulk aluminum is also examined as a benchmark. The critical interfacial area required for the solid–liquid phase transition is obtained as a function of the number of atoms considered in the simulation. Imperfections such as voids reduce the melting point. The ratio between the structural and thermodynamic melting points is 1.32. This value is comparable to the ratio of 1.23 for metals like copper.     

Intuitive understandings of negative bulk modulus of metamaterials composed of Helmholtz resonators

We present theoretical and experimental results to obtain an intuitive understanding of bulk modulus of metamaterials composed of Helmholtz resonators (HR). Using transmission line theory, we introduce an intuitive method to determine the frequency domain in which the negative bulk modulus appears. The results obtained by simulations and experiments are consistent with theoretical results found using transmission line theory. The results suggest that wider negative (BNG) areas of bulk modulus can be obtained using two HRs than one HR of the same total cavity volume.     

Temperature-controlled tunable acoustic metamaterial with active band gap and negative bulk modulus

The local resonant band gap and the negative bulk modulus of the acoustic metamaterial with Helmholtz resonators are strongly affected by the temperature of water. In this paper, the acoustic transmission line method (ATLM) is introduced to investigate the influences of the temperature of water on the local resonant band gap and the negative bulk modulus of the acoustic metamaterial. Results show that the relative variations of the local resonant band gap and the negative effective bulk modulus suffering from the change of the temperature of water are approximately equivalent and are up to about 11%. The reason is that the local resonant frequency is proportional to the sound speed of fluid which is strongly effects by the temperature of water. By achieving the unambiguous relationships between these unusual properties of the acoustic metamaterial and the temperature of water, we find that the temperature-controlled acoustic metamaterial with the active band gap and the active negative bulk modulus can be realized in theory. This idea opens a new avenue for the design of the tunable acoustic metamaterial that can modulate the acoustic wave propagation.     

液体体变弹性模量测量实验及研究

介绍了一种测量液体体变弹性模量的方法．同时研究了不同液体的密度、温度对液体体变弹性模量的影响．     

Total energy, equation of state and bulk modulus of AlP, AlAs and AlSb semiconductors

Recently proposed model potential which combines both linear and quadratic types of interactions is employed for the investigation of some properties like the total energy, equation of state and bulk modulus of AlP, AlAs and AlSb semiconductor compounds using higher-order perturbation theory. The model potential parameter is determined using zero pressure condition. The ratio of the covalent bonding termE _cov to the secondorder termE ₂ is 6.77% to 11.85% which shows that contribution from higher order terms are important for zinc-blende-type crystals. The calculated numerical results of the total energy, energy band gap at Jones-zone face and bulk modulus of these compounds are in good agreement with the experimental data and found much better than other such theoretical findings. We have also studied pressure-volume relations of these compounds. The present study is carried out using six different screening functions along with latest screening function proposed by Sarkaret al. It is found from the present study that effect of exchange and correlation is clearly distinguishable.     

New isothermal equation of state of solids applied to high pressures

In the present paper, a new two-parameter inverted equation of state (EOS) is developed which is found to be working very well in the high-pressure region. To check its success and validity, this EOS has been applied in a number of solids. The computed volume compression is found to be in very good agreement with the experimental data in the whole range of pressure in all the solids. The minimum and the maximum pressure range used in the present study is 0–320 kbar and 0–3000 kbar, respectively.     

Study of temperature dependence of density, bulk modulus, shear modulus and thermal pressure for mantle minerals

The temperature dependence of different parameters i.e. density ρ(T), bulk modulus K_T(T), shear modulus G_T(T) and thermal pressure ΔP_th for mantle minerals i.e. X₂SiO₄ (X=Mg, Fe, Co, Mn) have been studied in high temperature range on the basis of semi-phenomenological isobaric equation of state. The calculated values of these parameters are showing good agreements with experimental value in case of each mantle minerals.     

The effect of temperature on elastic constants and bulk modulus

A model pseudopotential depending on an effective core radius is proposed to study the elastic constants C ₁₁, C ₁₂, C ₄₄ and bulk modulus B of Cu, Ag, Au, Ni, Pt and Rh at various temperatures (300–1500 K). The contribution of d-like electron is taken into account by introducing repulsive short-range Born-Mayer term. An excellent agreement between theoretical investigation and experimental findings has confirmed our formalism.     

Prediction of a superhard material of ReN4 with a high shear modulus

Using first-principles calculations, this paper systematically investigates the structural, elastic, and electronic properties of ReN 4 . The calculated positive eigenvalues of the elastic constant matrix show that the orthorhombic P bca structure of ReN 4 is elastically stable. The calculated band structure indicates that ReN 4 is metallic. Compared with the synthesized superhard material WB 4 , it finds that ReN 4 exhibits larger bulk and shear moduli as well as a smaller Poisson’s ratio. In addition, the elastic constant c 44 of ReN 4 is larger than all the known 5d transition metal nitrides and borides. This combination of properties makes it an ideal candidate for a superhard material.     

Al、Cu、Ta高压熔化曲线的理论计算

由位错熔化理论和不同的静高压实验数据优化的体模量(B0)、剪切模量(G0)及它们对压力的一阶偏导数(B′0、G′0)值计算了Al、Cu、Ta的高压熔化曲线.理论计算的Al、Cu高压熔化曲线与静、动高压实验值较为吻合,Ta的理论高压熔化曲线与动高压实验结果一致,但与静高压实验结果相差较大.