Pressure Dependence Of Bulk Modulus Research Articles

Evaluation of mechanical properties of Bi12SiO20 sillenite using first principles and nanoindentation

ABSTRACT The mechanical and anisotropic elastic properties of Bi12SiO20 (BSO) were investigated using density functional theory (DFT) calculations and nanoindentation. The calculated and experimentally observed XRD patterns of the compound were reported and the crystal structure of the BSO was determined to be cubic with the lattice constant of a = 1.025 nm. The second-order elastic constants and related polycrystalline elastic moduli (e.g. shear modulus, Young’s modulus, Poisson’s ratio, linear compressibility and hardness) were calculated. The calculated elastic constants indicated that BSO is mechanically stable and exhibits anisotropic characteristics. Moreover, the directional dependencies of sound wave velocities were investigated in three dimensions. Pressure-dependent bulk modulus was plotted at temperatures between 0 and 800 K. Hardness and Young’s modulus were also determined by performing nanoindentation experiments on (222) and (631) planes of the BSO single crystal. The analyses of the experimental nanoindentation data resulted in hardness and Young’s modulus values of 7.2 and 97.0 GPa, respectively. The results of DFT and nanoindentation were discussed throughout the paper. The results of the present paper would provide valuable information on the mechanical behaviours of the BSO for the optoelectronic device applications.

Electronic and thermal properties of LuNi2B2C under pressure

The electronic and thermal properties of LuNi2B2C were studied by performing density-functional theory (DFT) and density functional perturbation theory (DFPT). No virtual frequencies appear on the phonon spectrum, indicating that LuNi2B2C is dynamically stable in the tetragonal structure up to 30 GPa. The density of states at Fermi energy EF is nonzero and falls on the sharp peak, which is why LuNi2B2C has a high superconducting temperature. Moreover, the temperature and pressure dependences of bulk modulus, heat capacity at constant pressure and thermal expansion coefficient in a wide temperature (0-900 K) and pressure (0-30 GPa) ranges are presented in this study.

Comments on the paper entitled “Pressure variation of melting temperatures of alkali halides”

The expressions for the pressure dependences of bulk modulus and the Grüneisen parameter used by Arafin and Singh [Int. J. Mod. Phys. B 30, 1750031 (2016)] in the Lindemann law for determining melting curves of 14 alkali halides have been found to yield no results which are consistent with the recent studies on equations of state. It is demonstrated here that Arafin–Singh’s expressions are physically not acceptable as they are shown here to give unrealistic values of bulk modulus and Grüneisen parameter for the materials at high pressures.

Trapped fluid in contact interface

We study the mechanical contact between a deformable body with a wavy surface and a rigid flat taking into account pressurized fluid trapped in the interface. A finite element model is formulated for a general problem of trapped fluid for frictionless and frictional contact. Using this model we investigate the evolution of the real contact area, maximal frictional traction and global coefficient of friction under increasing external pressure. Elastic and elasto-plastic material models, compressible and incompressible fluid models and different geometrical characteristics of the wavy surface are used. We show that in case of incompressible fluid, due to its pressurization, the real contact area and the global coefficient of friction decrease monotonically with the increasing external pressure. Eventually, the contact opens and the fluid occupies the entire interface resulting in vanishing of static friction. An asymptotic analytical result for the critical trap-opening pressure is found and shown to be independent of the surface slope if it is small. In case of compressible fluids with pressure-dependent bulk modulus we demonstrate a non-monotonous behaviour of the global coefficient of friction due to a competition between non-linear evolution of the contact area and of the fluid pressure. However, for realistic compressibility of solids and fluids, contact-opening cannot be reached at reasonable pressures. On the other hand, in case of elastic-perfectly plastic materials, we again observe fluid permeation into the contact interface. Finally, we study the distribution of frictional tractions during the depletion of the contact area under increasing external pressure. This process leads to emergence of singularity-like peaks in tangential tractions (bounded by the Coulomb’s limit) near the contact edges. We point out the similarity between the processes of trap opening and interfacial crack propagation, and estimate the complex stress intensity factor in the framework of linear elastic fracture mechanics.

Equations of state and pressure dependence of bulk modulus for aggregated diamond nanorods

In the present paper study of the high pressure behaviour of aggregated diamond nanorods (ADNRs) and diamond have been carried out. A comparative study of different equations of state is discussed to understand the high pressure behaviour of diamond and the aggregated diamond nanorods. In the present study the usual Tait’s equation of state has been modified to predict the high pressure behaviour of carbon material ADNRs and diamond. The results obtained in the present study are compared with available experimental evidences. Bulk moduli as a function of pressure are also computed for ADNRs and natural diamond in the light of recent investigations. Present study reveals that ADNRs are less compressible than diamond.

First-principles calculations of structural and thermodynamic properties of β-PbO**Project supported by the Research Project of Islamic Azad University, Urmia Branch.

We employed ab-initio calculations to investigate the structural and thermodynamic properties of Massicot or orthorhombic phase of PbO named β-PbO using the projector augmented-wave (PAW) method within the generalized gradient approximation (GGA). The temperature and pressure dependence of bulk modulus, heat capacity at constant pressure and constant volume, entropy, thermal expansion coefficient and Grüneisen parameter were discussed. Accuracy of two different models, the Debye and Debye–Grüneisen which are based on the quasi-harmonic approximation (QHA) for producing thermodynamic properties of material were compared. According to calculation results, these two models can be used to designate thermodynamic properties for β-PbO with sensible accuracy over a wide range of temperatures and pressures, and our work on the properties of this structure will be useful for more deeply understanding various properties of this structure.

Comparative study of Mo2Ga2C with superconducting MAX phase Mo2GaC: First-principles calculations

The structural, electronic, optical and thermodynamic properties of Mo2Ga2C are investigated using density functional theory (DFT) within the generalized gradient approximation (GGA). The optimized crystal structure is obtained and the lattice parameters are compared with available experimental data. The electronic density of states (DOS) is calculated and analyzed. The metallic behavior for the compound is confirmed and the value of DOS at Fermi level is 4.2 states per unit cell per eV. Technologically important optical parameters (e.g., dielectric function, refractive index, absorption coefficient, photo conductivity, reflectivity, and loss function) are calculated for the first time. The study of dielectric constant (ɛ1) indicates the Drude-like behavior. The absorption and conductivity spectra suggest that the compound is metallic. The reflectance spectrum shows that this compound has the potential to be used as a solar reflector. The thermodynamic properties such as the temperature and pressure dependent bulk modulus, Debye temperature, specific heats, and thermal expansion coefficient of Mo2Ga2C MAX phase are derived from the quasi-harmonic Debye model with phononic effect also for the first time. Analysis of Tc expression using available parameter values (DOS, Debye temperature, atomic mass, etc.) suggests that the compound is less likely to be superconductor.

Elastic, thermodynamic and optical behavior of V2AC (A = Al, Ga) MAX phases

This article reports the first-principles calculations of yet unexplored Mulliken bond population, Vickers hardness, thermodynamic and optical properties of MAX phases V2AC (A=Al, Ga). We have also revisited the structural and elastic properties of these phases in order to assess the reliability of our calculations. The temperature and pressure dependence of bulk modulus, Debye temperature, specific heats, and thermal expansion coefficient have been successfully estimated through the quasi-harmonic Debye model in the temperature range from 0 to 1000K and the pressure range from 0 to 50GPa. The optical properties such as the dielectric function, refractive index, photoconductivity, absorption coefficients, reflectivity and loss function are also evaluated for the first time. The reflectivity is found to be high which indicates that V2AC (A=Al, Ga) having the same characteristics could be good candidate materials to reduce solar heating up to ∼15eV.

The mechanical and thermodynamic properties of Heusler compounds Ni2XAl (X = Sc, Ti, V) under pressure and temperature: A first-principles study

The effect of pressure on structural and mechanical properties as well as the temperature dependence of thermodynamic properties, such as enthalpies of formation, elastic moduli, anisotropy, heat capacity and thermal expansion coefficient et al., of Ni2XAl (X=Sc, Ti, V) Heusler compounds are investigated implementing first-principles calculations. The influence of pressure on lattice parameters decreases as the increase of atomic number X (Sc, Ti, V). The Ni2XAl (X=Sc, Ti, V) show mechanically stable, ductility and anisotropy in 0–50GPa, and appropriate pressure can improve their mechanical properties because the bulk modulus B, shear modulus G, Young's modulus E, G/B and microhardness H almost linearly increase with pressure. The influence of pressure on B, G, E and H gradually decreases as the order of Ni2ScAl>Ni2TiAl>Ni2VAl, while it has an inverse effect on ductility and anisotropy. In addition, the resistance to volume deformation of NiAl alloys can be improved by second-phase strengthening with Ni2VAl and Ni2TiAl precipitates. Finally, the temperature and pressure dependences of bulk modulus, Debye temperature, heat capacity as well as thermal expansion coefficient of these compounds are elucidated using the quasi-harmonic Debye model. It is inverse for the effect of temperature and pressure on thermodynamic parameters.

Electronic, optical and thermal properties of TiCr2 and TiMn2 by ab initio simulations

A theoretical study of TiX2 (X = Cr, Mn) with C14 Laves phase compounds has been performed by using the first-principles pseudopotential plane-wave method within the generalized gradient approximation (GGA). The electronic properties (Fermi surface and charge density) have been calculated and analyzed. The optical characteristics (dielectric functions, absorption spectrum, conductivity, energy-loss spectrum and reflectivity) are calculated and discussed. The calculated large positive static dielectric constant indicates good dielectric properties. The reflectivity of TiX2 (X = Cr, Mn) is high in the IR–Visible–UV region up to [Formula: see text][Formula: see text]13 eV showing promise as a good solar heating barrier material. The temperature and pressure dependence of bulk modulus, Debye temperature, specific heats and thermal expansion coefficient are obtained for T = 1200 K and P = 50 GPa through quasi-harmonic Debye model with phononic effects. Fermi surface, optical and thermodynamic properties are very important for practical applications of the materials in optical and other devices.

Zirconium metal-based MAX phases Zr2AC (A = Al, Si, P and S): A first-principles study

We have investigated theoretical Vickers hardness, thermodynamic and optical properties of four zirconium metal-based MAX phases Zr 2 AC (A = Al , Si , P and S ) for the first time in addition to revisiting the structural, elastic and electronic properties. First-principles calculations are employed based on density functional theory (DFT) by means of the plane-wave pseudopotential method. The theoretical Vickers hardness has been estimated via the calculation of Mulliken bond populations and electronic density of states. The thermodynamic properties such as the temperature and pressure dependent bulk modulus, Debye temperature, specific heats and volume thermal expansion coefficient of all the compounds are derived from the quasi-harmonic Debye model. Further, the optical properties, e.g., dielectric functions, indices of refraction, absorption, energy loss function, reflectivity and optical conductivity of the nanolaminates have been calculated. The results are compared with available experiments and their various implications are discussed in detail. We have also shed light on the effect of different properties of Zr 2 AC as the A-group atom moves from Al to S across the periodic table.

Theoretical studies of the pressure-induced phase transition and elastic properties of BeS

First-principles calculations were performed to investigate the structural, electronic and elastic properties of BeS in both B3 and B8 structures. The structural phase transition from B3 to B8 occurs at 58.86GPa with a volume decrease of 10.74%. The results of the electronic band structure show that the energy gap is indirect for B3 and B8 phases. The pressure dependence of the direct and indirect band gaps for BeS has been investigated. Especially, the elastic constants of B8 BeS under high pressure have been studied for the first time. The mechanical stability of the two phases has been discussed based on the pressure dependence of the elastic constants. In addition, the pressure dependence of bulk modulus, shear modulus, Young’s modulus, elastic wave velocities and brittle–ductile behavior of BeS are all successfully obtained. Finally, the elastic anisotropy has been investigated by using two different methods.

Natural Storage Function for Passivity-Based Trajectory Control of Hydraulic Actuators

A passivity framework for hydraulic actuators is developed by considering the compressibility energy function for a fluid with a pressure-dependent bulk modulus. It is shown that the typical actuator's mechanical and pressure dynamics model can be obtained from the Euler-Lagrange equations for this energy function and that the actuator is passive with respect to a hydraulic supply rate which contains, in addition to the flow work (PQ), the compressibility energy also, which has often been ignored. A storage function for the pressure error is then proposed and the pressure error dynamics are shown to be a passive two-port subsystem. Trajectory tracking control laws are then derived using the storage function. A case study is presented to compare the new passivity-based approach and the traditional backstepping approach using a quadratic pressure error term. In this example, the proposed approach has one fewer parameter to tune, is less sensitive to velocity measurement error, and requires lower feedback gains than the traditional approach.

BAND STRUCTURE, HARDNESS, THERMODYNAMIC AND OPTICAL PROPERTIES OF SUPERCONDUCTING Nb2AsC, Nb2InC AND Mo2GaC

First-principles investigation of the geometry, electronic band structure, Vickers hardness, thermodynamic and optical properties of three superconducting MAX compounds Nb 2 AsC , Nb 2 InC and Mo 2 GaC have been carried out by the plane-wave pseudopotential method based on density functional theory (DFT) implemented in the CASTEP code. The theoretical Vickers hardness has been studied by means of Mulliken bond population analysis and electronic densities of states. The thermodynamic properties such as the temperature and pressure dependent bulk modulus, Debye temperature, specific heats and thermal expansion coefficient of the three 211 MAX phases are derived from the quasi-harmonic Debye model with phononic effect for the first time. Furthermore, all the optical properties are determined and analyzed for the first time for two different polarization directions. The theoretical findings are compared with relevant experiments (where available) and the various implications are discussed in details.

Theoretical investigation on Elastic, Thermodynamic and Optical Properties of Li<sub>3</sub>P Ionic Conductor

The elastic, thermodynamic and optical properties of Li3P have been studied for the first time using the plane-wave ultrasoft pseudopotential technique which is based on the first-principles density functional theory (DFT) with generalized gradient approximation (GGA). The optimized lattice parameters, independent elastic constants, Young’s modulus E, bulk modulus B, shear modulus G, Cauchy’s pressure, Pugh’s ductility index (G/B), and Poisson’s ratio ? have been calculated and discussed. The temperature and pressure dependence of bulk modulus, Debye temperature, specific heats, and volume thermal expansion coefficient are all obtained through the quasi-harmonic Debye model with phononic effects for T = 0-1000 K and P = 0-35 GPa. The large reflectivity in the ultraviolet energy region between 7 – 13.4 eV indicates the material to be a good candidate as coating to avoid solar heating.© 2013 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi: http://dx.doi.org/10.3329/jsr.v5i1.12413 J. Sci. Res. 5 (1), 33-42 (2013)

Rare earth rhodium borides RRh3B (R = Y, Zr, and Nb): mechanical, thermal and optical properties

We report here ab initio density functional theory (DFT) calculations of structural, elastic, Peierls stress, thermodynamic and optical properties of RRh3B (R = Y, Zr and Nb) using the plane wave pseudopotential method. The materials possess better ductile behavior in comparison with a selection of layered MAX phases but the anisotropy is strong, particularly in NbRh3B. The Peierls stress, approximately 3-4 times larger than in MAX phases, show that dislocation movement may follow but with much reduced occurrences compared to MAX phases. The temperature and pressure dependence of bulk modulus, specific heats, thermal expansion coefficient, and Debye temperature are calculated for the first time for two of the three compounds using the quasi-harmonic Debye model with phononic effects for elevated temperature and pressure. The obtained results are discussed in comparison to the behavior of other related compounds. Further the features of optical functions obtained for the first time are discussed. The study reveals that the reflectivity is high in the IR-UV regions up to ~17.5 eV (YRh3B, ZrRh3B) and 20 eV (NbRh3B), thus showing promise as good coating materials.

MAX phases Nb2AC (A = S, Sn): An ab initio study

An ab initio investigation of structural parameters, elastic, electronic, thermodynamic and optical properties of MAX phases Nb2AC (A=S, Sn) has been carried out by the plane wave pseudopotential method based on density functional theory (DFT). The effect on results of substitution of heavier Sn atoms for the lighter S atoms in the nanolaminate network has been made. The analysis of the electronic band structure shows that these compounds are electrical conductors, with contribution predominantly from the Nb 4d states. The temperature and pressure dependence of bulk modulus, Debye temperature, specific heats, thermal expansion coefficient of the nanolaminates are calculated for the first time using the quasi-harmonic Debye model with phononic effects. The estimated values of electron–phonon coupling constants (λ∼0.49, ∼0.59) imply that Nb2SC and Nb2SnC are moderately coupled superconductors. Further first time detailed analysis of all optical functions reveals that Nb2SC is a better dielectric material, and also both the phases, having similar reflectivity spectra, show promise as good coating materials in the energy regions 10–16.5eV.

Phase stability, elastic, electronic, thermal and optical properties of Ti3Al1−xSixC2 (0≤x≤1): First principle study

The structural parameters with stability upon Si incorporation and elastic, electronic, thermodynamic and optical properties of Ti3Al1−xSixC2 (0≤x≤1) are investigated systematically by the plane wave pseudopotential method based on the density functional theory (DFT). The increase of some elastic parameters with increasing Si-content renders the alloys to possess higher compressive and tensile strength. The Vickers hardness value obtained with the help of Mulliken population analysis increases as x is increased from 0 to 1. The solid solutions considered are all metallic with valence and conduction bands, which have a mainly Ti 3d character, crossing the Fermi level. The temperature and pressure dependences of bulk modulus, normalized volume, specific heats, thermal expansion coefficient, and Debye temperature are all obtained through the quasi-harmonic Debye model with phononic effects for T=0−1000 K and P=0−50 GPa. The obtained results are compared with other results available. Further an analysis of optical functions for two polarization vectors reveals that the reflectivity is high in the visible–ultraviolet region up to ∼10.5 eV region showing promise as a good coating material.

PRESSURE DEPENDENCE OF THE ELASTIC CONSTANTS WITH APPLICATION TO MINERALS

In the present paper, a new relationship for the pressure dependences of elastic constants is developed by using a new expression for the pressure dependence of bulk modulus and a method developed by Grover et al. The proposed relationship is applied to study elastic constants of MgO , NaCl , CaF2, and CaO . The results obtained for elastic constants are found in good accordance with the experimental and first-principle results.

On the “elastic” stiffness in a high-cycle accumulation model for sand: a comparison of drained and undrained cyclic triaxial tests

High-cycle accumulation (HCA) models may be used for the prediction of settlements or stress relaxation in soils due to a large number of cycles (N > 103) with a relatively small-strain amplitude (εampl < 10−3). This paper presents a discussion of the elastic stiffness, [Formula: see text], used in the basic constitutive equation of an HCA model, [Formula: see text], where [Formula: see text] is the trend of effective stress, [Formula: see text] is the trend of strain, [Formula: see text] is the rate of strain accumulation, and [Formula: see text] is the plastic strain rate. [Formula: see text] interrelates the “trends” of stress and strain evolution. For the experimental assessment of the bulk modulus, [Formula: see text], the rate of pore-water pressure accumulation, [Formula: see text], in undrained cyclic triaxial tests and the rate of volumetric strain accumulation, [Formula: see text], in drained cyclic tests have been compared. The pressure-dependent bulk modulus, K, was quantified from 15 pairs of drained and undrained tests with different consolidation pressures and stress amplitudes. It is demonstrated that both the curves [Formula: see text] in the drained tests and u(N) in the undrained tests are well predicted by the authors’ HCA model if the elastic stiffness is determined using the method described in the present paper. A simplified determination of K from the unloading and reloading curve in an oedometric compression test is discussed.