Ground state parameters,electronic properties and elastic constants of CaMg3:DFT study

The present study aims to investigate the equation of state(EOS)parameters of CaMg3 in aReCh(D09),AIFR(DO3),CU3A11(LI2)and CuTi3(L60)structures,using full potential linear muffin-tin orbitals(FP-LMTO)approach based on the density functional theory(DFT).The local density approximation(LDA)and the generalized gradient approximation(GGA)were both applied for the exchange-correlation potential term.The calculated equation of slate parameters at equilibrium,in general,agreed well with the available data of the literature.The calculations showed that under compression CaMg3 transforms from DO3 to DO9 at about 29.96GPa,and 25.1 GPa using LDA and GGA,respectively.The elastic constants C,y,aggregate moduli,Vickers hardness,sound velocity,and Debye temperature of CaMg3 in D03 structure were also reported,discussed and analyzed.Using LDA(GGA),the calculated values of Hv andθD were found at around 5.80GPa(5.93GPa)and 393.44 K(389.91 K),respectively.Electronic band structure,total density of states(TDOS)as well as the partial density of states(PDOS)have been also obtained.The electronic band structure confirms the metallic behavior of CaMg3 in DO3 phase,the valence bands are dominated by the maximum contribution of‘d’like states of Ca in the energy ranging from 2 to 3 eV for GGA,and from 4.5 to 5 eV for LDA,respectively.

First-principles study of the elastic constants and optical properties of uranium metal

We perform first-principles calculations of the lattice constants, elastic constants, and optical properties for alpha- and gamma-uranium based on the ultra-soft pseudopotential method. Lattice constants and equilibrium atomic volume are consistent pretty well with the experimental results. Some difference exists between our calculated elastic constants and the experimental data. Based on the satisfactory ground state electronic structure calculations, the optical co ductivity, dielectric function, refractive index, and extinction coefficients are also obtained. These calculated optical properties are compared with our results and other published experimental data.

Elastic constants characterization on graphite at 500℃ by the virtual fields method

In this paper the elastic constants of graphite at elevated temperature were experimentally investigated by using the virtual fields method （VFM）. A new method was presented for the characterization of mechanical properties at elevated temperature. The three-point bending tests were performed on graphite materials by an universal testing machine equipped with heating fumace. Based on the heterogeneous deformation fields measured by the digital image correlation （DIC） technique, the elastic constants were then extracted by using VFM. The measurement results of the elastic constants at 500℃ were obtained. The ef- fect on the experimental results was also analyzed. The successful results verify the feasibility of using the proposed method to measure the properties of graphite at high temperature, and the proposed method is believed to have a good potential for further applications.

Macroscopic Elastic Constants of Pure Metal Based on the Interactions between Microscopic Particles

The research activities of the calculation of the elastic constants of metal are mainly focused on the elastic constants of crystal at the micro level. To the calculation of the macroscopic elastic constants of metal, although molecular dynamics method and quasicontinuum method can be used, but there are shortcomings in them, such as a large amount of computation and that the spatial scale of the study model is limited. Therefore, with a pure metal thin plate composed of a single layer of microscopic particles as research object, a new mechanical model is established after the interactions between microscopic particles of the thin plate are applied on the continuum mechanics model of the thin plate. According to this model, the calculation formulas for the microscopic elastic constants, which are the elastic constants of any triangle region in the model, are obtained. After the concept of the ideal micro structure is presented, the calculation formulas for the macroscopic elastic constants, the elastic modulus and the Poisson’s ratio of pure metal are obtained, where the Poisson＇s ratio is the constant that is equal to 1？3. As an example, the elastic constants and the elastic modulus of pure copper are solved, where c11 is 175.811 GPa, c12 is 58.604 GPa, c33 is 58.604 GPa and E is 156.277 GPa, the rationality and the correctness of the model are verified. The model presented fully embodies the discreteness of the microstructure of solid, is a development to the continuum model, and is more suitable to reality, more simplified and more new to the study of the macroscopic elastic constants of pure metal.

Accurate calculations of the high-pressure elastic constants based on the first-principles

The energy term corresponding to the first order of the strain in Taylor series expansion of the energy with respect to strain is always ignored when high-pressure elastic constants are calculated. Whether the modus operandi would affect the results of the high-pressure elastic constants is still unsolved. To clarify this query, we calculate the high-pressure elastic constants of tantalum and rhenium when the energy term mentioned above is considered and neglected, respectively.Results show that the neglect of the energy term corresponding to the first order of the strain indeed would influence the veracity of the high-pressure elastic constants, and this influence becomes larger with pressure increasing. Therefore, the energy term corresponding to the first-order of the strain should be considered when the high-pressure elastic constants are calculated.

Elastic constants and thermodynamic properties of Mg_2Si_xSn_(1-x) from first-principles calculations

This paper stuides the elastic constants and some thermodynamic properties of Mg2SixSn1-x （x = 0, 0.25, 0.5, 0.75, 1） compounds by first-principles total energy calculations using the pseudo-potential plane-waves approach based on density functional theory, within the generalized gradient approximation for the exchange and correlation potential. The elastic constants of Mg2SixSn1-x were calculated. It shows that, at 273 K, the elastic constants of Mg2Si and Mg2Sn are well consistent with previous experimental data. The isotropy decreases with increasing Sn content. The dependences of the elastic constants, the bulk modulus, the shear modulus and the Debye temperatures of Mg2Si and Mg2Si0.5Sn0.5 on pressure were discussed. Through the quasi-harmonic Debye model, in which phononic effects were considered, the specific heat capacities of Mg2SixSn1-x at constant volume and constant pressure were calculated. The calculated specific heat capacities are well consistent with the previous experimental data.

A Comparative Study of Elastic Constants of NiTi and NiAl Alloys from First-Principle Calculations

To investigate the origin of the strong dependence of martensitic transformation temperature on composition, the elastic properties of high temperature B2 phases of both NiTi and NiAI were calculated by a first-principle method, the exact-muffin orbital method within coherent potential approximation. In the composition range of 50-56 at. pct Ni of NiTi and 60-70 at. pct Ni of NiAI in which martensitic transformation occurs, non-basalplane shear modulus c44 increases with increasing Ni content, while basal-plane shear modulus c＇ decreases. In the above composition ranges however the transformation temperature of NiAI increases with increasing Ni content while that of NiTi decreases from experimental observation. The softening of c＇ is experimentally observed only in NiAI, and the decrease of c＇ with increasing Ni content is responsible for the increase of transformation temperature. The result of the present work demonstrates that, besides c＇, c44 also influences the martensitic transformation of NiTi and plays quite important a role.

Singular variation property of elastic constants of piezoelectric ceramics shunted to negative capacitance

Piezoelectric shunt damping has been widely used in vibration suppression, sound absorption, noise elimination, etc. In such applications, the variant elastic constants of piezoelectric materials are the essential parameters that determine the performances of the systems, when piezoelectric materials are shunted to normal electrical elements, i.e., resistance, inductance and capacitance, as well as their combinations. In recent years, many researches have demonstrated that the wideband sound absorption or vibration suppression can be realized with piezoelectric materials shunted to negative capacitance. However, most systems using the negative-capacitance shunt circuits show their instabilities in the optimal condition, which are essentially caused by the singular variation properties of elastic constants of piezoelectric materials when shunted to negative capacitance. This paper aims at investigating the effects of negative-capacitance shunt circuits on elastic constants of a piezoelectric ceramic plate through theoretical analyses and experiments, which gives an rational explanation for why negative capacitance shunt circuit is prone to make structure instable. First, the relationships between the elastic constants c11, c33, c55 of the piezoelectric ceramic and the shunt negative capacitance are derived with the piezoelectric constitutive law theoretically. Then, an experimental setup is established to verify the theoretical results through observing the change of elastic constant c55 of the shunted piezoelectric plate with the variation of negative capacitance. The experimental results are in good agreement with the theoretical analyses, which reveals that the instability of the shunt damping system is essentially caused by the singular variation property of the elastic constants of piezoelectric material shunted to negative capacitance.

Stress in Thin Films; Diffraction Elastic Constants and Grain Interaction

Untextured bulk polycrystals usually possess macroscopically isotropic elastic properties whereas for most thin films transverse isotropy is expected, owing to the limited dimensionality. The usually applied models for the calculation of elastic constants of polycrystals from single crystal elastic constants (so-called grain interaction models) erroneously predict macroscopic isotropy for an (untextured) thin film. This paper presents a summary of recent work where it has been demonstrated for the first time by X-ray diffraction analysis of stresses in thin films that elastic grain interaction can lead to macroscopically elastically anisotropic behaviour (shown by non-linear sin2ψ plots). A new grain interaction model, predicting the macroscopically anisotropic behaviour of thin films, is proposed.

Elastic constants of Al and TiN calculated by ab initio method

The elastic constants of Al single crystal were calculated by ab initio method for calibration. Three deformation directions were selected in order to obtain the different constants of c 11 , c 12 and c 44 . The cohesion energy curves of the three deformation directions were calculated. The results of the second order partial differential at the equilibrium point of the cohesion energy curve provide the elastic constants of the Al single crystal. The changes of crystal symmetry and lattice can lead to the deviations of the calculated cohesion energy curves and the accurate elastic constants can not be obtained, but when the correction is taken into calculation, the calculated results are very close to the literature data. It is very difficult to obtain the elastic constants of thin films by experiment and the data from the handbook are scattered in a large scale. However, the elastic constants calculated by this method can be served as a standard. Though the errors of TiN elastic constants calculated by this method are a little higher than that for Al, the results are acceptable. [

INTERNAL FRICTION AND ELASTIC CONSTANTS OF Pd-B-H ALLOYS

Internal friction measurements on binary and ternary α-phase alloys of Pd with hydrogen and boron have been performed with a torsion pendulum and by observing the cttenuation of ultrasonic pulses. A pronounced damping maximum of binary Pd-B alloys at 220K and measuring frequencies of about 4Hz could not be established at a frequency of 15MH. Ternary Pd-B-H alloys show an additional damping maximum besides the hydrogen Zener effect, which is interpreted in terms of a changed jump frequency of hydrogen in the neighborhood of boron atoms.

Comparative first-principles study of elastic constants of covalent and ionic materials with LDA,GGA,and meta-GGA functionals and the prediction of mechanical hardness

Accurate prediction of single-crystal elastic constants is critical for materials design and for understanding phase transition and elastic interactions in materials.In this work,the accuracy of elastic constants calculated with three density functional approximations has been compared,including the local density approximation(LDA),the generalized gradient approximation(GGA),and the recently developed strongly constrained and appropriately normed(SCAN)meta-GGA.The results show that SCAN and PBE describe elastic constants better than LDA.The strong correlation between the mechanical hardness and the stiffness of the softest eigenmode(SSE)has been given for above three density functionals.The correlation is capable of predicting accurately the hardness of covalent,ionic,and mixed covalent-ionic crystals,and providing us a convenient indicator for the discovery of hard or superhard materials.

Elastic constants and softening of acoustic mode in K_2SnCl_6 crystal studied by Brillouin scattering

In this paper we present the Brillouin Scattering measurements of the longitudinal and transverse sound velocities for the hexahalome-atllate K2SnCl6 at room temperature . The elastic constants , refractive index , volume compressibility are determined from the Brillouin line shifts. Furthermore, the sound velocity in the [111] direction is investigated as a function of temperature 252K<T<270K . An acoustic adrupt change of the c11+2c12 mode is observed as the temperature approaches 256K from above, which has been analysed by means of the Pippard relations. The conclusion is that K2SnCl6 undergoes first order phase transition near T=256K. This acoustic anomaly can be interpreted by the nonlinear coupling of the elastic strain field to the fluctuation of the soft-mode coordinate.

Investigation of Electronic, Elastic and Dynamic Properties of AgNbO3 and AgTaO3 under Pressure: Ab Initio Calculation

Based on the density functional theory within the local density approximation (LDA), we studied the electronic, elastic, and dynamic properties of AgNbO3 and AgTaO3 compounds under pressure. The elastic constants, optic and static dielectric constants, born effective charges, and dynamic properties of AgNbO3 and AgTaO3 in cubic phase were studied as pressure dependences with the ab initio method. For these compounds, we have also calculated the bulk modulus, Young’s modulus, shear modulus, Vickers hardness, Poisson’s ratio, anisotropy factor, sound velocities, and Debye temperature from the obtained elastic constants. In addition, the brittleness and ductility properties of these compounds were estimated from Poisson’s ratio and Pugh’s rule (G/B). Our calculated values also show that AgNbO3 (0.37) and AgTaO3 (0.39) behave as ductile materials and steer away from brittleness by increasing pressure. The calculated values of Vicker hardness for both compounds indicate that they are soft materials. The results show that band gaps, elastic constants, elastic modules, and dynamic properties for both compounds are sensitive to pressure changes. We have also made some comparisons with related experimental and theoretical data that is available in the literature.

Prediction on temperature dependent elastic constants of “soft” metal Al by AIMD and QHA

First-principles methods based on density functional theory(DFT)are nowadays routinely applied to calculate the elastic constants of materials at temperature of 0 K.Nevertheless,the first-principles calculations of elastic constants at finite temperature are not straightforward.In the present work,the feasibility of the ab initio molecular dynamic(AIMD)method in calculations of the temperature dependent elastic constants of relatively"soft"metals,taking face centered cubic(FCC)aluminum(Al)as example,is explored.The AIMD calculations are performed with carefully selected strain tensors and strain magnitude.In parallel with the AIMD calculations,first-principles calculations with the quasiharmonic approximation(QHA)are performed as well.We show that all three independent elastic constant components(C11,C12 and C44)of Al from both the AIMD and QHA calculations decrease with increasing temperature T,in good agreement with those from experimental measurements.Our work allows us to quantify the individual contributions of the volume expansion,lattice vibration(excluding those contributed to the volume expansion),and electronic temperature effects to the temperature induced variation of the elastic constants.For Al with stable FCC crystal structure,the volume expansion effect contributes the major part(about 75%~80%)in the temperature induced variation of the elastic constants.The contribution of the lattice vibration is minor(about 20%~25%)while the electronic temperature effect is negligible.Although the elastic constants soften with increasing temperature,FCC Al satisfies the Born elastic stability criteria with temperature up to the experimental melting point.

Determination of elastic,piezoelectric,and dielectric constants of an R:BaTiO_3 single crystal by Brillouin scattering

From the sound velocity measured using the Brillouin scattering technique, the elastic, piezoelectric, and dielectric constants of a high-quality monodomain tetragonal Rh：BaTiO3 single crystal are determined at room temperature. The elastic constants are in fairly good agreement with those of the BaTiO3 single crystal, measured previously by Brillouin scattering and the low-frequency equivalent circuit methods. However, their electromeehanical properties are significantly different. Based on the sound propagation equations and these results, the directional dependence of the compressional modulus and the shear modulus of Rh：BaTiO3 in the （010） plane is investigated. Some properties of sound propagation and electromechanical coupling in the crystal are discussed.

Dynamic Testing of Elastic Modulus,Shear Modulus,and Poisson’s Ratio of Bamboo Scrimber

The bamboo scrimber is an anisotropic material.The elastic constant values of the bamboo scrimber specimens measured by the dynamic and static methods are consistent,and the dynamic test method has the advantages of rapidity,simplicity,good repeatability,and high precision.Bamboo scrimber has strong potential as a building material,and its elastic constant is an important index to measure its mechanical properties.To quickly,simply,non-destructively,and accurately detect the elastic constant of the bamboo scrimber,they were dynamically tested by the free plate transient excitation method and cantilever plate torsional vibration method.The static four-point bending method was used to verify the accuracy and reliability of the dynamic elastic modulus,shear modulus,and Poisson’s ratio of the bamboo scrimber.The mechanism analysis and evaluation of the quality grade,homogeneity,and size effect of the bamboo scrimber whole board were carried out.The main results show that the dynamic elastic modulus,shear modulus,and Poisson’s ratio of the bamboo scrimber are 12 GPa,1500 MPa,and 0.31,respectively,which meet the requirements of GB/T 40247-2021 for structural bamboo scrimber.

Study of the Physical and Mechanical Properties of Titanium in Volume by the MEAM Method

In this work we present the results of our study on the physical and mechanical properties of titanium in volume. The work consisted in determining its physical and mechanical properties under different crystallographic structures (HCP, FCC, BCC and SC) using the Modified Embedded Atom Method (MEAM) and the MEAM potential of titanium. We used the LAMMPS calculation code, based on classical molecular dynamics, to determine the most stable structure of titanium, which is the hexagonal compact structure (HCP) with crystal parameters a = 2.952 Å and c = 4.821 Å and a cohesion energy of -4.87 eV. This structure is seconded by the cubic centred structure (BCC) with a lattice parameter a = 3.274 Å and a cohesive energy of -4.84 eV. It was shown that titanium can crystallise into a third structure which is the face-centred cubic (FCC) structure with a lattice parameter a = 4.143 Å and a cohesive energy of -4.82 eV. The results obtained in this study were compared with the theoretical results and showed considerable agreement.

Density Functional Calculations of the Mechanical, Electronic and Dynamical Properties of Antiperovskite Ca3BO (B = Pb, Ge, Sn)

An analysis of mechanical, electronic and dynamical properties of antiperovskite Ca3BO (B = Pb, Ge, Sn) in cubic phase space group Pm-3m (221) has been studied using first principle density functional theory (DFT). Ground state energy computation was done using the Projector Augmented Wave (PAW) Pseudo Potentials and the Plane Wave (PW) basis set. The Generalized Gradient Approximation (GGA) was used for the exchange correlation. The open source code QUANTUM ESPRESSO (QE) was used in this study in which plane wave basis sets are applied for the expansion of the electronic structure wave function. Thermo_pw as a post-processing code was used for the computation of mechanical properties including bulk modulus and elastic constants with their derivatives. The lattice parameters are here calculated to be 4.87 Å, 4.86 Å and 4.84 Å for Ca3BO (B = Pb, Ge, Sn) respectively which compares well with other works. This also shows that the three crystals are similar in size and in most of their properties. In addition to this, projected density of states and band structure are also computed both showing that these materials are of semi-metallic nature and are stable in cubic phase. Phonon modes at gamma are also reported.