Theoretics-directed effect of copper or aluminum content on the ductility characteristics of Al-based(Al_3Ti,AlTi,AlCu,AlTiCu_2)intermetallic compounds

First-principle simulations have been applied to investigate the effect of copper(Cu) or aluminum(Al) content on the ductility of Al_3Ti,AlTi,AlCu,and AlTiCu_2 alloys.The mechanical stable and elastic properties of Al-based intermetallic compounds are researched by density functional theory with the generalized gradient approximation(DFT-GGA).The calculated lattice constants are in conformity with the previous experimental and theoretical data.The deduced elastic constants show that the investigated Al_3Ti,AlTi,AlCu,and AlTiCu_2 structures are mechanically stable.Shear modulus,Young's modulus,Poisson's ratio,and the ratio B/G have also been figured out by using reckoned elastic constants.A further analysis of Young's modulus and Poisson's ratio reveals that the third added element copper content has significant effects on the Al-Ti-based ICs ductile character.     

First-Principle Calculations of Elastic Properties of Wurtzite-Type Aluminum Nitride Under Pressure

The elastic properties of the wurtzite-type aluminum nitride （w-AlN） are investigated by ab initio plane-wave pseudopotential density functional theory method. The pressure dependences of the normalized primitive cell volume V/Vo, the elastic constants cij, the aggregate elastic modulus （B, G, E）, the Poisson＇s ratio （v）, and the Debye temperature θD are successfully obtained. From the elastic constants of the w-AlN under pressure, we find that the w-AlN should be unstable at higher pressure than 61.33 GPa.     

用超声背向散射谱定征柱状固体的弹性常数

根据流体中圆柱固体对超声波的背向散射谱与固体弹性参数的密切关系,本提出了材料弹性参数测量的一种新方法－超声背向散射谱法;测量了铜合金杆和铝合金杆的超声背向散射谱,并反演得到了它们的杨氏模量和泊松比。和传统的静力学方法相比,超声背向散射法测得的数据较精确,且对被测材料不会造成任何损伤。     

Estimation of dynamic elastic constants from the amplitude and velocity of Rayleigh waves

In this paper a method is proposed to characterize the elasticity of isotropic linear materials from the generation and detection of an acoustic surface wave. For the calculation of the elastic constants, it is sufficient that only one of the faces of the sample be accessible. The methodology is based on both the measurement of the Rayleigh wave velocity and on the determination of the normal to longitudinal amplitude ratio calculated from the normal and longitudinal components of the displacement of a point. The detection of two consecutive surface wave pulses using a single experimental setup permits the determination of the elastic constants. The method is applied to calculate Young's modulus and Poisson's ratio of an aluminum sample as well as their systematic uncertainties. The results obtained give a relative uncertainty for Young's modulus on the order of the sixth part of that calculated for Poisson's ratio.     

Physical Properties of C-Si Alloys in C2/m Structure

Using the first principles calculations based on density functional theory, the crystal structure, elastic anisotropy, and electronic properties of carbon, silicon and their alloys(C_(12)Si_4, C_8Si_8, and C_4Si_(12)) in a monoclinic structure(C2/m) are investigated. The calculated results such as lattice parameters, elastic constants, bulk modulus,and shear modulus of C_(16) and Si_(16) in C2/m structure are in good accord with previous work. The elastic constants show that C_(16), Si_(16), and their alloys in C2/m structure are mechanically stable. The calculated results of universal anisotropy index, compression and shear anisotropy percent factors indicate that C-Si alloys present elastic anisotropy,and C_8Si_8 shows a greater anisotropy. The Poisson's ratio and the B/G value show that C_8Si_8 is ductile material and other four C-Si alloys are brittle materials. In addition, Debye temperature and average sound velocity are predicted utilizing elastic modulus and density of C-Si alloys. The band structure and the partial density of states imply that C_(16) and Si_(16) are indirect band gap semiconductors, while C_(12)Si_4, C_8Si_8, and C_4Si_(12) are semi-metallic alloys.     

Nematic order in small systems: measuring the elastic and wall-anchoring constants in vibrofluidized granular rods

We investigate nematic order in vibrated granular rods confined to a small quasi-2D container less than 10 rod lengths in diameter. As rod density ρ increases, patterning shifts from bipolar to uniform alignment. We find that a continuum liquid crystal free energy functional captures key patterning features down to almost the particle size. By fitting theory to experiments, we estimate the relative values of bend and splay elastic constants and wall anchoring. We find that splay is softer than bend for all ρ and rod lengths tested, while the ratio of the average elastic constant to wall anchoring increases with ρ.     

Bending elasticity of surfactant films: the role of the hydrophobic tails

We study the tail contributions to the elastic constants of an amphiphilic layer. For dense systems the terms arising from the attractive van der Waals interactions prevail, whereas the translational entropy of the liquid layer is essential at lower density. Both the membrane rigidity kappa and the Gaussian bending elastic constant kappa; strongly vary with the density of the hydrocarbon chains; for dense systems, they are of the order 100kT with a ratio kappa;/kappa = -2 / 3. At lower density, partial cancellation of interaction and entropic contributions leads to elastic constants of the order of kT, with a ratio close to the value -2 observed for microemulsions.     

L12型铝合金的结构、弹性和电子性质的第一性原理研究

运用第一性原理方法研究了L12型铝合金相Al3Sc和Al3Zr的晶体结构、电子结构和弹性.结合能和形成能的计算表明,两种合金具有较强的合金化能力,且Al3Zr较Al3Sc具有更强的结构稳定性.电子结构分析表明,费米能级以下较多的价电子数决定了Al3Zr具有较强的结构稳定性.计算并分析比较了两种合金相的单晶弹性常数(C11,C12和C44)以及多晶弹性模量(体弹性模量B、剪切模量G、杨氏模量Y、泊松比ν和各向异性因子A).通过对比实验和其他理论计算结果,进一步分析和解释了两种合金相的力学性质.     

点缺陷浓度对非化学计量比L12型结构的A13Sc弹性性能的影响

采用密度泛函理论与Wagner-Schottky热力学模型计算了金属间化合物L1₂-A1₃Sc中点缺陷浓度与温度、成分间的关系. 结果表明: 在考察的温度区间(T=300-1200 K), 理想化学计量比L1₂-A1₃Sc中的点缺陷主要为Al空位和Sc空位, 且缺陷浓度较低(在1200 K时仅约为10^-6). 当L1₂-A1₃Sc偏离化学计量比成分时, 富Al成分端的点缺陷主要为Al反位与Sc空位, 且两种缺陷的浓度相当; 富Sc成分端的点缺陷则主要为Sc反位. 利用超胞模型进一步计算了含点缺陷L1₂-A1₃Sc晶体的弹性常数, 并计算预测了点缺陷形式和浓度对其弹性性能的影响. 结果表明: 在理想化学计量比成分附近, 点缺陷的引入均会降低非化学计量比L1₂-Al₃Sc晶体的杨氏、剪切和体积弹性模量, 增加非化学计量比L1₂-Al₃Sc弹性性能的各向异性, 但是对其脆-韧性的影响不大.     

Orientation dependence of elastic properties in orthorhombic Ca_3Mn_2O_7

Elastic properties are important in fundamental understanding of multiferroic materials. However, up to now, there is no work about anisotropy of elastic properties in orthorhombic Ca_3Mn_2O_7. In this study, using coordinate transformation method, we investigated basic elastic parameters(elastic constants c'_(ij)) and engineering elastic parameters(Young's modulus E, Poisson's ratio v, and the rigidity modulus G') of orthorhombic Ca_3Mn_2O_7 along arbitrary orientations. The detailed anisotropic characteristics of these parameters were presented. The results reveal the orientation related elastic properties in mm2 point group orthorhombic Ca_3Mn_2O_7.     

On the use of hollow tube geometries for resonant ultrasound spectroscopy

Resonant ultrasound spectroscopy (RUS) can nondestructively obtain the elastic constants of compact specimens, however many materials have hollow cross-sections and frequency analysis of such geometries is required before inclusion in the RUS methodology. Resonant mode shapes of tubes with length equal to diameter and varying ratios of tube inner to outer diameter (Λ) as well as Poisson's ratio (ν) were identified by eigenvalue analysis using a commercial finite element code. Longitudinal and shear RUS experiments were conducted on tubes with Λ varying between 0 and 0.95 and compared to the numerical results. Simulations predict that the fundamental mode transitions from pure torsion to symmetric or antisymmetric ring bending at Λ = 0.3. The frequency of the first torsion mode is invariant to Λ and unequivocal identification of this mode is obscured by overlap of bending harmonics as Λ approaches 0.95. In the context of rapid calculation of isotropic elastic constants, shear moduli were calculated from the first torsional mode and Poisson's ratio was inferred from the Demarest maps of the mode structure's dependence upon Poisson's ratio. An average shear modulus of 27.5 + 1.5 ∕ -0.6 GPa, about 5% larger than literature values for 6061 aluminum, and ν of 0.33 were inferred. Errors are attributed to tube aspect ratios slightly greater than 1 and weak material anisotropy. Existing analytical solutions for ring bending modes derived from shell approximations and for infinitely long tubes under plane strain assumptions do not adequately describe the fundamental modes for short tubes. The shear modulus can be calculated for all Λ using the existing analytical solution.     

Elastic constants of a plate from impact-echo resonance and Rayleigh wave velocity

A new method is proposed for calculating the dynamic elastic constants of an isotropic plate from measurements of the impact-echo resonance and Rayleigh wave velocity. Poisson's ratio is shown to be a single-valued function of the ratio between thickness frequency and Rayleigh wave velocity. This dependence is derived theoretically from the condition of resonance at the minimum frequency of the first-order symmetric Lamb mode. A finite element model is developed to determine how this frequency varies with Poisson's ratio. The results obtained by modal analysis and the power-spectral density technique are in good agreement with those calculated as the solution of the S1 Lamb mode equation. The method is verified by impact-echo tests on concrete and methacrylate plates. A laser interferometer is used to detect the vibration. Thickness frequencies are accurately identified by applying the multicross-spectral density to the signals detected at several points close to the impact point. In a separate experiment, Rayleigh waves are generated by the mediator technique. The wave velocities are determined from the arrival times of the surface wave at several points. Finally, the main sources of uncertainty are evaluated.     

Elastic properties and electronic structures of lanthanide hexaborides

The structural, elastic, and electronic properties of a series of lanthanide hexaborides(Ln B6) have been investigated by performing ab initio calculations based on the density functional theory using the Vienna ab initio simulation package.The calculated lattice and elastic constants of Ln B6 are in good agreement with the available experimental data and other theoretical results. The polycrystalline Young's modulus, shear modulus, the ratio of bulk to shear modulus B/G, Poisson's ratios, Zener anisotropy factors, as well as the Debye temperature are calculated, and all of the properties display some regularity with increasing atomic number of lanthanide atoms, whereas anomalies are observed for Eu B6 and Yb B6. In addition, detailed electronic structure calculations are carried out to shed light on the peculiar elastic properties of Ln B6.The total density of states demonstrates the existence of a pseudogap and indicates lower structure stability of Eu B6 and Yb B6 compared with others.     

Resonant frequency method for the measurement and uncertainty analysis of acoustic and elastic properties

A resonant frequency method is proposed to determine the bar speed and the Poisson's ratio of a rod several meters long of the kind often used for manufacturing power sonic transducers and mechanical horns in mass production. This method is shown to be robust in a field test and with high resolution for estimation of the bar speed. The uncertainty (standard deviation/average) for the bar speed and the Poisson's ratio can be reduced by appropriately selecting the mode number pairs and increasing the mode number. In this study, the uncertainties of the bar speed and Poisson's ratio are less than 0.043% and 2.9%, respectively. The resonant frequency method is verified by comparing the dilatational wave speeds calculated by elastic theory with those from experiments, the difference between them being less than 0.17%.     

Structural and elastic properties of Zr<Subscript>2</Subscript>AlX and Ti<Subscript>2</Subscript>AlX (X = C and N) under pressure effect

Using first-principles density functional calculations, the effect of high pressures, up to 20 GPa, on the structural and elastic properties of Zr₂AlX and Ti₂AlX, with X = C and N, were studied by means of the pseudo-potential plane-waves method. Calculations were performed within the local density approximation to the exchange-correlation approximation energy. The lattice constants and the internal parameters are in agreement with the available results. The elastic constants and their pressure dependence are calculated using the static finite strain technique. We derived the bulk and shear moduli, Young's moduli and Poisson's ratio for ideal polycrystalline Zr₂AlX and Ti₂AlX aggregates. We estimated the Debye temperature of Zr₂AlX and Ti₂AlX from the average sound velocity. This is the first quantitative theoretical prediction of the elastic properties of Zr₂AlC, Zr₂AlN and Ti₂AlN compounds, and it still awaits experimental confirmation.     

Electronic structures and mechanical properties of uranium monocarbide from first-principles and calculations

The electronic structure, elastic constants, Poisson's ratio, and phonon dispersion curves of UC have been systematically investigated from the first-principles calculations by the projector-augmented-wave (PAW) method. In order to describe precisely the strong on-site Coulomb repulsion among the localized U 5f electrons, we adopt the local density approximation (LDA)+U and generalized gradient approximation (GGA)+U formalisms for the exchange correlation term. We systematically study how the electronic properties and elastic constants of UC are affected by the different choice of U as well as the exchange-correlation potential. We show that by choosing an appropriate Hubbard U parameter within the GGA+U approach, most of our calculated results are in good agreement with the experimental data. Therefore, the results obtained by the GGA+U with effective Hubbard parameter U chosen around 3 eV for UC are considered to be reasonable.     

First-principles study of the structural, elastic, electronic, optical, and vibrational properties of intermetallic Pd2Ga

The structural, elastic, electronic, optical, and vibrational properties of the orthorhombic Pd₂Ga compound are investigated using the norm-conserving pseudopotentials within the local density approximation in the frame of density functional theory. The calculated lattice parameters have been compared with the experimental values and found to be in good agreement with these results. The second-order elastic constants and the other relevant quantities, such as the Young's modulus, shear modulus, Poisson's ratio, anisotropy factor, sound velocity, and Debye temperature, have been calculated. It is shown that this compound is mechanically stable after analysing the calculated elastic constants. Furthermore, the real and imaginary parts of the dielectric function and the optical constants, such as the optical dielectric constant and the effective number of electrons per unit cell, are calculated and presented. The phonon dispersion curves are derived using the direct method. The present results demonstrate that this compound is dynamically stable.     

Ab initio calculations of the elastic, electronic, optical, and vibrational properties of PdGa compound under pressure

The structural, elastic, electronic, optical, and vibrational properties of cubic PdGa compound are investigated using the norm-conserving pseudopotentials within the local density approximation (LDA) in the framework of the density functional theory. The calculated lattice constant has been compared with the experimental value and has been found to be in good agreement with experimental data. The obtained electronic band structures show that PdGa compound has no band gap. The second-order elastic constants have been calculated, and the other related quantities such as the Young’s modulus, shear modulus, Poisson’s ratio, anisotropy factor, sound velocities, and Debye temperature have also been estimated. Our calculated results of elastic constants show that this compound is mechanically stable. Furthermore, the real and imaginary parts of the dielectric function and the optical constants such as the electron energy-loss function, the optical dielectric constant and the effective number of electrons per unit cell are calculated and presented in the study. The phonon dispersion curves are also derived using the direct method.     

Structural and elastic properties under pressure effect of the cubic antiperovskite compounds ANCa3 (A = P, As, Sb, and Bi)

Using first-principles density functional calculations, the effect of high pressures, up to 40 GPa, on the structural and elastic properties of ANCa₃, with A = P, As, Sb, and Bi, were studied by means of the pseudo-potential plane-waves method. Calculations were performed within the local density approximation and the generalized gradient approximation for exchange-correlation effects. The lattice constants are in good agreement with the available results. The elastic constants and their pressure dependence are calculated using the static finite strain technique. We derived the bulk and shear moduli, Young's modulus, Poisson's ratio and Lamé's constants for ideal polycrystalline ANCa₃ aggregates. By analysing the ratio between the bulk and shear moduli, we conclude that ANCa₃ compounds are brittle in nature. We estimated the Debye temperature of ANCa₃ from the average sound velocity. This is the first quantitative theoretical prediction of the elastic properties of PNCa₃, AsNCa₃, SbNCa₃, and BiNCa₃ compounds, and it still awaits experimental confirmation.     

石墨烯/羟基磷灰石复合材料力学性能的数值研究

为了研究石墨烯/羟基磷灰石复合材料力学性能（弹性模量和泊松比）,开发了石墨烯/羟基磷灰石复合材料的随机分布模型自动生成算法及相应的计算程序;建立石墨烯/羟基磷灰石复合材料的有限元模型,计算添加不同质量分数的石墨烯对复合材料力学性能的影响,通过与实验数据对比验证算法的有效性.结果表明：添加0.25%~1.25%（质量分数）的石墨烯可使复合材料的弹性模量增加12%~50%,表明添加少量石墨烯即能有效地改善羟基磷灰石的力学性能.