First-principles study of structural stability and elastic property of pre-perovskite PbTiO_3

The structural stability and the elastic properties of a novel structure of lead titanate, which is named pre- perovskite PbTiO3 （PP-PTO） and is constructed with TiO6 octahedral columns arranged in a one-dimensional manner, are investigated by using first-principles calculations. PP-PTO is energetically unstable compared with conventional perovskite phases, however it is mechanically stable. The equilibrium transition pressures for changing from pre- perovskite to cubic and tetragonal phases are -0.5 GPa and -1.4 GPa, respectively, with first-order characteristics. Further, the differences in elastic properties between pre-perovskite and conventional perovskite phases are discussed for the covalent bonding network, which shows a highly anisotropic character in PP-PTO. This study provides a crucial insight into the structural stabilities of PP-PTO and conventional perovskite.

Analytical solution for the effective elastic properties of rocks with the tilted penny-shaped cracks in the transversely isotropic background

Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.

Toward Improved Accuracy in Quasi-Static Elastography Using Deep Learning

Elastography is a non-invasive medical imaging technique to map the spatial variation of elastic properties of soft tissues.The quality of reconstruction results in elastography is highly sensitive to the noise induced by imaging measurements and processing.To address this issue,we propose a deep learning(DL)model based on conditional Generative Adversarial Networks(cGANs)to improve the quality of nonhomogeneous shear modulus reconstruction.To train this model,we generated a synthetic displacement field with finite element simulation under known nonhomogeneous shear modulus distribution.Both the simulated and experimental displacement fields are used to validate the proposed method.The reconstructed results demonstrate that the DL model with synthetic training data is able to improve the quality of the reconstruction compared with the well-established optimization method.Moreover,we emphasize that our DL model is only trained on synthetic data.This might provide a way to alleviate the challenge of obtaining clinical or experimental data in elastography.Overall,this work addresses several fatal issues in applying the DL technique into elastography,and the proposed method has shown great potential in improving the accuracy of the disease diagnosis in clinical medicine.

First-principles calculations of structural,elastic and electronic properties of AB_(2)type intermetallics in Mg–Zn–Ca–Cu alloy

Electronic structure and elastic properties of MgCu_(2),Mg_(2)Ca and MgZn_(2)phases were investigated by means of first-principles calculations from CASTEP program based on density functional theory(DFT).The calculated lattice parameters were in good agreement with the experimental and literature values.The calculated heats of formation and cohesive energies shown that MgCu_(2)has the strongest alloying ability and structural stability.The elastic constants of MgCu_(2),Mg_(2)Ca and MgZn_(2)phases were calculated,the bulk moduli,shear moduli,Young's moduli and Poisson's ratio were derived.The calculated results shown that MgCu_(2),Mg_(2)Ca and MgZn_(2)are all ductile phases.Among the three phases,MgCu_(2)has the strongest stiffness and the plasticity of MgZn_(2)phase is the best.The density of states(DOS),Mulliken electron occupation number and charge density difference of MgCu_(2),Mg_(2)Ca and MgZn_(2)phases were discussed to analyze the mechanism of structural stability and mechanical properties.

First-principles calculations of structural,elastic and electronic properties of(TaNb)0.67(HfZrTi)0.33 high-entropy alloy under high pressure

To clarify the effect of pressure on a(TaNb)0.67(HfZrTi)0.33 alloy composed of a solid solution with a single body-centered-cubic crystal structure,we used first-principles calculations to theoretically investigate the structural,elastic,and electronic properties of this alloy at different pressures.The results show that the calculated equilibrium lattice parameters are consistent with the experimental results,and that the normalized structural parameters of lattice constants and volume decrease whereas the total enthalpy differenceΔE and elastic constants increase with increasing pressure.The(TaNb)0.67(HfZrTi)0.33 alloy exhibits mechanical stability at high pressures lower than 400 GPa.At high pressure,the bulk modulus B shows larger values than the shear modulus G,and the alloy exhibits an obvious anisotropic feature at pressures ranging from 30 to 70 GPa.Our analysis of the electronic structures reveals that the atomic orbitals are occupied by the electrons change due to the compression of the crystal lattices under the effect of high pressure,which results in a decrease in the total density of states and a wider electron energy level.This factor is favorable for zero resistance.

First-principles investigation of the electronic,elastic and thermodynamic properties of VC under high pressure

An investigation of the electronic, elastic and thermodynamic properties of VC under high pressure has been conducted using first-principles calculations based on density functional theory （DFT） with the plane-wave basis set, as implemented in the CASTEP code. At elevated pressures, VC is predicted to undergo a structural transition from a relatively open NaCl-type structure to a more dense CsCl,type one. The predicted transition pressure is 520 GPa. The elastic constant, Debye temperature and heat capacity each as a function of pressure and/or temperature of VC are presented for the first time.

INFLUENCE OF COLD-WORKING AND HEAT TREATING ON ELASTIC PROPERTIES OF Nb AND Nb-BASE ALLOYS

The elastic limit of single-phase alloy Nb-2Mo-2Zr-1Ti is higher as recovered state in comparison with as cold-rolled or recrystallized one.For Nb-40Ti-5.5AI alloy of age-hardening type,the elastic limit is lower as cold-rolled state,but increases considerably after proper aging.However,its elastic modulus changes no more,so the stored-energy (σ_e^2/E)may raise significantly.The temperature dependence on elastic modulus for pure Nb as intensely cold-worked or recrystallized state is anomalous.This anomaly may disap- pear after recovered treatment of intensely cold-worked state at 600℃ for 4 h.and may change no more after that of recrystallized state.The anomalous behaviour of elasticity was also discussed on the non-magnetic Nb.

Anisotropy of elasticity and minimum thermal conductivity of monocrystal M_4AlC_3(M=Ti,Zr,Hf)

The elastic constants, elastic anisotropy index, and anisotropic fractional ratios of Ti4AlC3, Zr4AlC3, and Hf4AlC3 are studied by using a plane wave method based on density functional theory. All compounds are characterized by the elastic anisotropy index. The bond length, population, and hardness of the three compounds are calculated. The degrees of hardness are then compared. The minimum thermal conductivity at high temperature limitation in the propagation direction of [000l] （0001） is calculated by the acoustic wave velocity, which indicates that the thermal conductivity is also anisotropic. Finally, the electronic structures of the compounds are analyzed numerically. We show that the bonding of the M4AlC3 lattice exhibits mixed properties of covalent bonding, ionic bonding, and metallic bonding. Moreover, no energy gap is observed at the Fermi level, indicating that various compounds exhibit metallic conductivity at the ground state.

A NEW APPROXIMATE SOLUTION TO THE MULTIPLE SCATTERING THEORY FOR THE ELASTIC PROPERTIES OF HETEROGENEOUS MATERIALS

The multiple scattering theory has been a powerful tool in determining the effective properties of heterogeneous materials. In this paper , a simple relationship between the scattering theory and the micromechanics theory based on the Eshelby principle has been suggested. According to the relationship, a new and simple approximate solution to the exact multiple scattering theory has been given in terms of Eshelby' s S-tensor. The solution easily shows those known results for isotropic composites with spherical inclusions and for tracnsversely isotropic composites, and first gives non-setf-consistent (average t-matrix) and symmetric self-consistent (effective medium or coherent potential) approximate results for isotropic composites with spheroidal inclusions.

Anisotropic elastic properties and ideal uniaxial compressive strength of TiB_2 from first principles calculations

The structural, anisotropic elastic properties and the ideal compressive and tensile strengths of titanium diboride （TiB2） were investigated using first-principles calculations based on density functional theory. The stress-strain relationships of TiB2 under 〈10i0〉, 〈12i0〉, and 〈0001〉 compressive loads were calculated. Our results showed that the ideal uniaxial compressive strengths are ｜σ〈02i0〉）｜ = 142.96 GPa, ｜σ〈0001〉 ] = 188.75 GPa, and ｜σ〈10i0〉｜ = 245.33 GPa, at strains -0.16, -0.32, and -0.24, respectively. The variational trend is just the opposite to that of the ideal tensile strength with σ〈10i0〉 = 44.13 GPa, σ〈0001〉 = 47.03 GPa, and σ〈i2i0〉 = 56.09 GPa, at strains 0.14, 0.28, and 0.22, respectively. Furthermore, it was found that TiB2 is much stronger under compression than in tension. The ratios of the ideal compressive to tensile strengths are 5.56, 2.55, and 4.01 for crystallographic directions （10i0）, 〈12i0〉, and 〈0001〉, respectively. The present results are in excellent agreement with the most recent experimental data and should be helpful to the understanding of the compressive property of TiB2.

Electronic,thermodynamic and elastic properties of pyrite RuO_2

This paper calculates the elastic, thermodynamic and electronic properties of pyrite （Pa^-3） RuO2 by the plane-wave pseudopotential density functional theory （DFT） method. The lattice parameters, normalized elastic constants, Cauchy pressure, brittle-ductile relations, heat capacity and Debye temperature are successfully obtained. The Murnaghan equation of state shows that pyrite RuO2 is a potential superhard material. Internal coordinate parameter increases with pressure, which disagrees with experimental data. An analysis based on electronic structure and the pseudogap reveals that the bonding nature in RuO2 is a combination of covalent, ionic and metallic bonding. A study of the elastic properties indicates that the pyrite phase is isotropic under usual conditions. The relationship between brittleness and ductility shows that pyrite RuO2 behaves in a ductile matter at zero pressure and the degree of ductility increases with pressure.

Theoretical investigation on the electronic structure,elastic properties, and intrinsic hardness of Si2N20

According to the density functional theory we systematically study the electronic structure, the mechanical prop- erties and the intrinsic hardness of Si2N2O polymorphs using the first-principles method. The elastic constants of four Si2N2O structures are obtained using the stress-strain method. The mechanical moduli （bulk modulus, Young’s mod-ulus, and shear modulus） are evaluated using the Voigt-Reuss-Hill approach. It is found that the tetragonal Si2N2O exhibits a larger mechanical modulus than the other phases. Some empirical methods are used to calculate the Vickers hardnesses of the Si2N2O structures. We further estimate the Vickers hardnesses of the four Si2N2O crystal structures, suggesting all Si2N2O phases are not the superhard compounds. The results imply that the tetragonal Si2N2O is the hardest phase. The hardness of tetragonal Si2N2O is 31.52 GPa which is close to values of β-Si3N4 and γ-Si3N4.

AB INITIO CALCULATION OF THE ELASTIC AND OPTICAL PROPERTIES OF Al3Sc COMPOUND

The ab initio method has been performed to explore the elastic and optical properties of Al3Sc compound, based on a plane wave pseudopotential method. It can be seen that the calculated equilibrium lattice parameter and elastic constants are in reasonable agreement with the previous experimental data. The elastic constants satisfy the requirement for mechanical stability in the cubic structure of the Al3Sc compound. The optical property calculations show that a strong absorptive peak exists from O-15eV and a relative small absorptive peak exists around 30eV. The form is caused by the optical transitions between high s, p, and d bands, and the latter results from the optical transitions from high s, p, and d bands to the low 2p band.

Numerical Simulation for Analysis and Optimization of the Elastic Properties of a C-spring Tube

In this paper we use the finite element analysis software ANSYS10.0 to establish a finite element model for pressure gauge C -spring tube, and the main factors affected the relation between the pressure and distortion displacement are analyzed. The results show that with the increasing of the spring tube wall thickness T and the minor axis length B, the elastic rigidity of spring tube increases, which is reduced with spring tube diameter D. Moreover, the major axis length H increases. Meanwhile, a pressure gauge spring tube has been optimized according to the simulation results bused on a model with special features, and the design results achieve the intended purpose. The analysis results provide a reliable method for the research and design of similar elastic elements.

ELASTIC BEHAVIOR ANALYSIS OF 3D ANGLE-INTERLOCK WOVEN CERAMIC COMPOSITES

A micromechanical model for elastic behavior analysis of angle-interlock woven ceramic composites is proposed in this paper. This model takes into account the actual fabric structure by considering the fiber undulation and continuity in space, the cavities between adjacent yarns and the actual cross-section geometry of the yarn. Based on the laminate theory, the elastic properties of 3D angle-interlock woven ceramic composites are predicted. Different numbers of interlaced wefts have almost the same elastic moduli. The thickness of ceramic matrix has little effect on elastic moduli. When the undulation ratio increases longitudinal modulus decreases and the other Young＇s moduli increase. Good agreement between theoretical predictions and experimental results demonstrates the feasibility of the proposed model in analyzing the elastic properties of 3D angle-interlock woven ceramic composites. The results of this paper verify the fact that the method of analyzing polyester matrix composites is suitable for woven ceramic composites.

Phase stability,elastic properties and electronic structures of Mg-Y intermetallics from first-principles calculations

The phase stability,elastic properties and electronic structures of three typical Mg-Y intermetallics including Mg_(24)Y_(5),Mg_(2)Y and MgY are systematically investigated using first-principles calculations based on density functional theory.The optimized structural parameters including lattice constants and atomic coordinates are in good agreement with experimental values.The calculated cohesive energies and formation enthalpies show that either phase stability or alloying ability of the three intermetallics is gradually enhanced with increasing Y content.The single-crystal elastic constants C_(ij) of Mg-Y intermetallics are also calculated,and the bulk modulus B,shear modulus G,Young's modulus E,Poisson ratio v and anisotropy factor A of polycrystalline materials are derived.It is suggested that the resistances to volume and shear deformation as well as the stiffness of the three intermetallics are raised with increasing Y content.Besides,these intermetallics all exhibit ductile characteristics,and they are isotropic in compression but anisotropic to a certain degree in shear and stiffness.Comparatively,Mg_(24)Y_(5) presents a relatively higher ductility,while MgY has a relatively stronger anisotropy in shear and stiffness.Further analysis of electronic structures indicates that the phase stability of Mg-Y intermetallics is closely related with their bonding electrons numbers below Fermi level.Namely,the more bonding electrons number below Fermi level corresponds to the higher structural stability of Mg-Y intermetallics.

Phase stability,electronic,elastic and thermodynamic properties of Al-RE intermetallics in Mg-Al-RE alloy:A first principles study

Electronic structure and elastic properties of Al_(2)Y,Al_(3)Y,Al_(2)Gd and Al_(3)Gd phases were investigated by means of first-principles calculations from CASTEP program based on density functional theory(DFT).The ground state energy and elastic constants of each phase were calculated,the formation enthalpy(ΔH),bulk modulus(B),shear modulus(G),Young's modulus(E),Poisson's ratio(ν)and anisotropic coefficient(A)were derived.The formation enthalpy shows that Al_(2)RE is more stable than Al_(3)RE,and Al-Y intermetallics have stronger phase stability than Al-Gd intermetallics.The calculated mechanical properties indicate that all these four intermetallics are strong and hard brittle phases,it may lead to the similar performance when deforming due to their similar elastic constants.The total and partial electron density of states(DOS),Mulliken population and metallicity were calculated to analyze the electron structure and bonding characteristics of the phases.Finally,phonon calculation was conducted,and the thermodynamic properties were obtained and further discussed.

Phase transition, elastic and electronic properties of topological insulator Sb_2Te_3 under pressure: First principle study

The phase transition, elastic and electronic properties of three phases（phase Ⅰ,Ⅱ, and Ⅲ） of Sb_2Te_3 are investigated by using the generalized gradient approximation（GGA） with the PBESOL exchange–correlation functional in the framework of density-functional theory. Some basic physical parameters, such as lattice constants, bulk modulus, shear modulus,Young＇s modulus, Poisson＇s ratio, acoustic velocity, and Debye temperature Θ are calculated. The obtained lattice parameters under various pressures are consistent with experimental data. Phase transition pressures are 9.4 GPa（Ⅰ→Ⅱ） and 14.1 GPa（Ⅱ→Ⅲ）, which are in agreement with the experimental results. According to calculated elastic constants, we also discuss the ductile or brittle characters and elastic anisotropies of three phases. Phases Ⅰ and Ⅲ are brittle, while phaseⅡ is ductile. Of the three phases, phaseⅡ has the most serious degree of elastic anisotropy and phase Ⅲ has the slightest one.Finally, we investigate the partial densities of states（PDOSs） of three phases and find that the three phases possess some covalent features.

Theoretical study of elastic, mechanical and thermodynamic properties of MgRh intermetallic compound

In the last years,Magnesium alloys are known to be of great technological importance and high scientific interest.In this work,density functional theory plane-wave pseudo potential method,with local density approximation(LDA)and generalized gradient approximation(GGA)are used to perform first-principles quantum mechanics calculations in order to investigate the structural,elastic and mechanical properties of the intermetallic compound MgRh with a CsCl-type structure.Comparison of the calculated equilibrium lattice constant and experimental data shows good agreement.The elastic constants were determined from a linear fit of the calculated stress-strain function according to Hooke's law.From the elastic constants,the bulk modulus B,shear modulus G,Young's modulus E,Poisson's ratioσ,anisotropy factor A and the ratio B/G for MgRh compound are obtained.The sound velocities and Debye temperature are also predicted from elastic constants.Finally,the linear response method has been used to calculate the thermodynamic properties.The temperature dependence of the enthalpy H,free energy F,entropy S,and heat capacity at constant volume C_(v)of MgRh crystal in a quasi-harmonic approximation have been obtained from phonon density of states and discussed for the first report.This is the first quantitative theoretical prediction of these properties.

Determination of Elastic and Creep Properties of Thin-film Systems from indentation Experiments

Based on the detailed computer simulation of the indentation testing on the thin-film systems, the present paper explores the detailed procedure of determining elastic properties (elastic modulusE^(f) and Poisson ratio v(f)) and creep parameters (CCREEP^(f) and nCREEP^(f)) for a simple Norton law (ε=CCREEP^(f)σ^n CREE^(f), where e is creep strain rate, and a is the stress) material for a thin film coated on a creep substrate, whose elastic properties(E^(s) and v^(s)) and creep properties (CCREEP^(s) and nCREEP^(s)) of the substrate are known, from indentation elastic and creep testing,respectively. The influences of the thickness of the thin-film and the size of the indenter on the indentation behavior have been discussed. It is shown that the boundary between the thin film and the substrate has great influence on the indentation creep behavior. The relative sizes of indentation systems are chosen so that the behavior of the indentation on the film is influenced by the substrate. The two elastic parameters E^(f) and v^(f) of the film are coupled on the influence of the elastic behavior of indentation. With the two different size indenters, the two elastic parameters E^(f) and v^(f) of the film can be uniquely determined by the indentation experimental slopes of depth to applied net section stress results. The procedure of determining of the two Norton law parameters CCREEP^(f) and nCREEP^(f) includes the following steps by the steady indentation rate d. The first step to calculate the creep indentation rate on certain loads of the two different sizes of indenters on a set of assumed values of CCREEP^(f) and nCREEP^(f)Then to build relationship between the creep indentation rate and the assumed CCREEP^(f) and nCREEP^(f) With the experimental creep indentation rate to intersect two sets of which have the same values of d. The last step is to build the CCREEP^(f) and nCREEP^(f)curves from the intersection points for the two indenters. These two curves CCREEP^(f) and nCREEP^(f)