Temperature-dependent elastic moduli of lead telluride-based thermoelectric materials

In the open literature, reports of mechanical properties are limited for semiconducting thermoelectric materials, including the temperature dependence of elastic moduli. In this study, for both cast ingots and hot-pressed billets of Ag-, Sb-, Sn- and S-doped PbTe thermoelectric materials, resonant ultrasound spectroscopy (RUS) was utilized to determine the temperature dependence of elastic moduli, including Young's modulus, shear modulus and Poisson's ratio. This study is the first to determine the temperature-dependent elastic moduli for these PbTe-based thermoelectrics, and among the few determinations of elasticity of any thermoelectric material for temperatures above 300 K. The Young's modulus and Poisson's ratio, measured from room temperature to 773 K during heating and cooling, agreed well. Also, the observed Young's modulus, E, versus temperature, T, relationship, E(T) = E ₀(1–bT), is consistent with predictions for materials in the range well above the Debye temperature. A nanoindentation study of Young's modulus on the specimen faces showed that both the cast and hot-pressed specimens were approximately elastically isotropic.     

Determination of solid materials rigidity modulus by a new nondestructive optical method

We propose a new optical method for the determination of the rigidity modulus G of solid materials. The rigidity modulus is determined by measuring the twisted angle θ as a response of the material sample, depending on the applied force. The measuring of this twisted angle can be carried out by using an adapted polarimetric sensor. The effective measurement of rigidity modulus G for aluminum, Plexiglas and steel was experimentally obtained 1.4464×10¹⁰,0.99417×10⁹ and 1.0395×10¹¹ N m, respectively. The study has demonstrated the effective usefulness of our method for evaluating the rigidity modulus. A good agreement between the theoretical and experimental results was achieved.     

Structure, internal friction, and Young’s modulus of fractal carbon deposits

We have observed that carbon deposits obtained by atomizing graphite in an electric arc in an atmosphere of argon and helium exhibit porosity and possess fractal structure. The results of measurements of the internal friction Q ⁻¹ and the effective Young’s modulus E as a function of temperature are presented. Data on the resistivity, density, and microhardness of the carbon deposits are presented. A possible mechanism for formation of fractal structures in carbon deposits is discussed. Fiz. Tverd. Tela (St. Petersburg) 40, 584–586 (March 1998)     

一种计算金属剪切模量的本构模型：以Al为例

用两步法构建了一个与温度和压力相关的适用于金属材料的剪切模量本构模型,其中的第一步任务是求得沿0 K等温线上剪切模量随压力的变化规律,即求得G₁=G₁（P,0 K）的函数式.第二步是从0 K等温线上某一给定P的G值出发,求出沿等压线上剪切模量随温度T变化的规律,从而最终求得剪切模量本构模型G=G（P,T）的具体表达式.在这两个阶段的研究中都利用了超声波测量和第一性原理计算方法的研究结果.用铝为模型材料,对本模型的合理性进行了检验.结果表明,G的模型预测数据与试验测量及理论计算数据相比较,无论G的演化是沿冲击压缩轨迹、等熵压缩轨迹、等温压缩轨迹还是等压线轨迹,都能达到令人满意的程度,故可认为本模型具有良好的普适性和合理性. 关键词： 铝 本构模型 剪切模量 冲击波压缩     

Effect of interfacial debonding and matrix cracking on mechanical properties of multidirectional composites

In composites, debonding at the fiber–matrix interface and matrix cracking due to loading or residual stresses can effect the mechanical properties. Here three different architectures — 3-directional orthogonal, 3-directional 8-harness satin weave and 4-directional in-plane multidirectional composites — are investigated and their effective properties are determined for different volume fractions using unit cell modeling with appropriate periodic boundary conditions. A cohesive zone model (CZM) has been used to simulate the interfacial debonding, and an octahedral shear stress failure criterion is used for the matrix cracking. The debonding and matrix cracking have significant effect on the mechanical properties of the composite. As strain increases, debonding increases, which produces a significant reduction in all the moduli of the composite. In the presence of residual stresses, debonding and resulting deterioration in properties occurs at much lower strains. Debonding accompanied with matrix cracking leads to further deterioration in the properties. The interfacial strength has a significant effect on debonding initiation and mechanical properties in the absence of residual stresses, whereas, in the presence of residual stresses, there is no effect on mechanical properties. A comparison of predicted results with experimental results shows that, while the tensile moduli E ₁₁, E ₃₃and shear modulus G ₁₂ match well, the predicted shear modulus G ₁₃ is much lower.     

Structural and anisotropic elastic properties of hexagonal MP (M = Ti,Zr, Hf) monophosphides determined by first-principles calculations

First-principles calculations were performed to investigate the structural properties, phase stabilities, elastic properties and thermal conductivities of MP (M = Ti, Zr, Hf) monophosphides. These monophosphides are thermodynamically and mechanically stable. Values for the bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratio ν were calculated by Voigt–Reuss–Hill approximation. The mechanical anisotropy was discussed via several anisotropy indices and three-dimensional (3D) surface constructions. The order of elastic anisotropy is ZrP > HfP > TiP. The minimum thermal conductivities of these monophosphides were investigated using Clarke’s model and Cahill’s model. The results revealed that these monophosphides are suitable for use as thermal insulating materials and that their minimum thermal conductivities are anisotropic.     

Thickness dependence of elastic modulus of polycarbonate interphase

The oligomer of bis-phenol A (oligo-PC) with M _w = 1300 and bis-phenol A polycar-bonate (PC) with M _w = 20 000 were deposited onto E-glass surface using SiCl₄ as the grafting and cross-linking agent. Thickness of the deposited layers was varied from 30 to 10⁶ nm and the layers were investigated as prepared and after thermal annealing at 245°C for 10 min in the air. Vibrational piezoelectric resonator technique and the speed of Rayleigh wave measurement were used to determine elastic moduli of the ultra thin layers deposited on flat E-glass substrate as a function of their thickness. In all cases, increase of the Young modulus of the interphase, E _i, with decreasing layer thickness, t _i, was observed. At a given thickness, the E _i of PC layer was significantly lower than that for the oligo-PC layer. Thermal annealing of the deposited PC layer resulted in a significant increase of its E _i compared to the as received layer. No significant change was observed for oligo-PC interphases. Increase of the shear strength of the interface, τ _a, with reducing interphase thickness, t _i, was observed. The observed increase of E _i with the decreasing t _i was ascribed to the reduction of the molecular mobility of chains near solid surface compared to their mobility in the bulk. Most probably, the observed increase of E _i after thermal annealing of PC was caused by rearrangement of both segment density distribution in individual PC coils near the solid surface and cooperative rearrangements of multiple PC chains. Since the oligomers attached to the surface attained presumably more regular extended conformations with lower conformation entropy compared to the PC random coils, the effect of thermal annealing was negligible. In agreement with theoretical predictions, increase of E _i at the same extent of interfacial interactions resulted in the observed increase of the τ _a measured using the single embedded fiber test.     

A direct numerical simulation method for complex modulus of particle dispersions

We report an extension of the smoothed profile method (SPM) (Y. Nakayama, K. Kim, and R. Yamamoto, Eur. Phys. J. E 26, 361 (2008)), a direct numerical simulation method for calculating the complex modulus of the dispersion of particles, in which we introduce a temporally oscillatory external force into the system. The validity of the method was examined by evaluating the storage G’(w \omega) and loss G”(w \omega) moduli of a system composed of identical spherical particles dispersed in an incompressible Newtonian host fluid at volume fractions of F \Phi = 0 , 0.41, 0.46, and 0.51. The moduli were evaluated at several frequencies of shear flow; the shear flow used here has a zigzag profile, as is consistent with the usual periodic boundary conditions. The simulation results were compared with several experiments for colloidal dispersions of spherical particles.     

Elastic moduli of hard c‐Zr3N4 from laser ultrasonic measurements

The bulk and shear moduli of dense polycrystalline oxygen‐bearing c‐Zr₃N₄ were determined to be B₀ = 217(20) GPa and G₀ = 163(9) GPa, respectively, using laser ultrasonic technique combined with a numerical analysis of the sample porosity. While the obtained B₀ is in excellent agreement with the earlier high‐pressure compression measurements, the G₀ value is 70% higher than the previous estimate. Since both G₀ and hardness of the dense c‐Zr₃N₄ exceed those of γ‐Si₃N₄, c‐Zr₃N₄ vies for the rank of the third hardest material after diamond and cubic BN. Our results also support the suggestion that shear modulus is a robust predictor of hardness. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computer simulation of the relation between mechanical behavior and structural evolution of oxide ceramics under dynamic loading

Computer simulation is used to investigate the deformation and damage processes taking place in brittle porous oxide ceramics under intense dynamic loading. The pore structure is shown to substantially affect the size of the fragments and the strength of the materials. In porous ceramics subjected to shock loading, deformation is localized in mesoscopic bands having characteristic orientations along, across, and at ∼45° to the direction of propagation of the shock wave front. The localized-deformation bands may be transformed into macroscopic cracks. A method is proposed for a theoretical estimation of the effective elastic moduli of ceramics with pore structure without resorting to well-known hypotheses for the relation between elastic moduli and porosity of the materials.     

Atomic dynamics of lead embedded into nanoporous glass

The thermal atomic vibration spectrum of lead nanostructured in porous glass with an average pore size of 7 nm and the thermal vibration spectrum of conventional bulk lead (taken for comparison) are measured using inelastic neutron scattering. The density of states in the phonon spectrum of lead nanoparticles is found to exceed the density of states in the spectrum of bulk lead at both low (E < 2.5 meV) and high (E > 9.5 meV) energies. These data are used to propose a model for the structure of a porous glass-lead nano-composite.     

Regulation of the elastic modulus of polyurethane microarrays and its influence on gecko-inspired dry adhesion

We studied the influence of the elastic modulus on the gecko-inspired dry adhesion by regulating the elastic modulus of bulk polyurethane combined with changing the size of microarrays. Segmented polyurethane (PU) was utilized to fabricate micro arrays by the porous polydimethyl siloxane (PDMS) membrane molding method. The properties of the micro arrays, such as the elastic modulus and adhesion, were investigated by Triboindenter. The study demonstrates that bulk surfaces show the highest elastic modulus, with similar values at around 175 MPa and decreasing the arrays radius causes a significant decrease in E, down to 0.62 MPa. The corresponding adhesion experiments show that decrease of the elastic modulus can enhance the adhesion which is consistent with the recent theoretical models.     

Viscoelasticity and morphology of an organic hybrid of chlorinated polyethylene and N,N′-dicyclohexyl-2-benzothiazolyl sulfenamide

The viscoelasticity and morphology of an organic hybrid of chlorinated polyethylene (CPE) and N,N′-dicyclohexyl-2-benzothiazolyl sulfenamide (DBS) were studied by means of tensile and shear complex modulus and differential scanning calorimetry (DSC) analysis. Tensile and shear loss modulus (E″ and G″), which are shown as indexes of vibration damping performance, showed one peak corresponding to the glass transition. The peak maximum values (E″_max and G″_max)increased in proportion to DBS content ( _DBS) and the slope of E″_max against _DBS became steep above a certain DBS content, i.e. the critical DBS content ( _c). A high damping material was obtained by the addition of DBS, especially when DBS content was higher than _c. These increases in loss moduli below and above _c are caused by the interaction between CPE and DBS molecules and the friction between DBS molecules, respectively. It was found that CPE/DBS is a compatible blend at all DBS contents from the analysis of the glass transition temperature with DSC. Furthermore, the influence of chlorine content in CPE on those characteristics was investigated. Higher chlorine content led to lower _c, a decrease in E″ below _c and an increase in E″ above _c. These results are due to the increase in the number of dichloromethylene units (CCl₂), which reduces the α-hydrogen atom in CPE.     

Symplectic Structures of Moduli Space¶of Higgs Bundles over a Curve and Hilbert Scheme¶of Points on the Canonical Bundle

The moduli space of triples of the form (E,θ,s) are considered, where (E,θ) is a Higgs bundle on a fixed Riemann surface X, and s is a nonzero holomorphic section of E. Such a moduli space admits a natural map to the moduli space of Higgs bundles simply by forgetting s. If (Y,L) is the spectral data for the Higgs bundle (E,θ), then s defines a section of the line bundle L over Y. The divisor of this section gives a point of a Hilbert scheme, parametrizing 0-dimensional subschemes of the total space of the canonical bundle K _X , since Y is a curve on K _X . The main result says that the pullback of the symplectic form on the moduli space of Higgs bundles to the moduli space of triples coincides with the pullback of the natural symplectic form on the Hilbert scheme using the map that sends any triple (E,θ,s) to the divisor of the corresponding section of the line bundle on the spectral curve. Received: 15 January 2000 / Accepted: 25 March 2001     

Elastic moduli of η‐Ta2N3, a tough self‐healing material,via laser ultrasonics

The elastic moduli of the dense polycrystalline oxygen‐bearing η‐Ta₂N₃, a novel hard and tough high‐pressure (HP) material, were measured using the laser ultrasonic technique. The bulk modulus was determined to be B₀ = 281(15) GPa which is only ～11% below that from HP compression measurements. Our value of the shear modulus G₀ = 123(2) GPa is below those ones predicted theoretically for model structures. The discrepancies in G₀ could be due to a substitution of an‐ ions and the formation of cation vacancies in η‐Ta₂N₃. Self‐healing behaviour of η‐Ta₂N₃ by mechanical polishing was observed and confirmed by two independent experimental methods. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Phase stability,anisotropic elastic properties and electronic structures of C15-type Laves phases ZrM2 (M = Cr,Mo and W) from first-principles calculations

Abstract

Systematic investigations of phase stability and mechanical properties of C15-type ZrM₂ (M = Cr, Mo and W) Laves phases were performed using first-principles calculations. The formation enthalpies of ZrM₂ are in good agreement with the theoretical and experimental values. The elastic properties, including elastic constants and moduli, Poisson’s ratio and B/G, were discussed. The elastic anisotropy was also investigated via the anisotropy indexes (A^U, A^Z, A_shear and A_comp), the anisotropy of shear modulus and the 3D construction of bulk and Young’s moduli. The elastic anisotropy of ZrM₂ is in order of ZrCr₂ < ZrMo₂ < ZrW₂. The variations in the shear modulus and hardness show similar trends with increasing values from ZrCr₂ to ZrW₂. The electronic structures for these C15-type Laves phases were analysed to obtain deeper understanding of chemical bonds and phase stabilities. Finally, the sound velocities and Debye temperatures were also investigated.     

α-Al_2O_3介孔材料导热特性的模拟

本文针对α-Al2O3有序介孔材料的导热特性开展分子动力学模拟分析.提出了一种保证电中性的孔道结构构造方法;采用逆非平衡分子动力学方法(muller-plathe法),选取Matsui势为作用势,模拟计算了Al2O3介孔晶体材料在不同环境温度下沿孔道轴向方向的热导率;并借助全面实验分析法,设计了模拟条件,以考察孔径和孔隙率对热导率的影响.模拟结果显示:介孔Al2O3热导率先随温度的升高呈上升趋势,并在200—400 K之间取得极值;而后在400—1400 K范围内,热导率随温度的升高几乎呈线性下降.孔隙率一定时,随孔径增大,介孔Al2O3材料比表面积降低,界面散射的抑制作用减弱,使材料热导率略有上升;孔径一定时,随孔隙率上升,孔道壁面声子数减少,材料热导率下降明显;相对于孔径因素,材料孔隙率对声子导热影响更大.     

First-principles calculations on elasticity of under pressure

First-principles calculations of the crystal structure and the elastic properties of OsN₂ have been carried out with the plane-wave pseudopotential density functional theory method. The calculated values are in very good agreement with experimental data as well as with some of the existing model calculations. The dependence of the elastic constants c_ij, the aggregate elastic moduli (B,G,E), Poisson’s ratio, and the elastic anisotropy on pressure has been investigated. Moreover, the variation of the Debye temperature and the compressional and shear elastic wave velocities with pressure P up to 60 GPa at 0 K have been investigated for the first time.     

Elasticity and thermodynamic properties of RuB2 under pressure

First-principles calculations of the crystal structure and the elastic properties of RuB₂ have been carried out with the plane-wave pseudopotential density functional theory method. The calculated values are in very good agreement with experimental data as well as with some of the existing model calculations. The elastic constants c_ij, the aggregate elastic moduli (B, G, E), Poisson's ratio, and the elastic anisotropy with pressure have been investigated. Through the quasi-harmonic Debye model considering the phonon effects, the isothermal bulk modulus, the thermal expansions, Grüneisen parameters, and Debye temperatures depending on the temperature and pressure are obtained in the whole pressure range from 0 to 60 GPa and temperature range from 0 to 1100 K as well as compared to available data.     

Study of elastic properties of CeO2 by statistical moment method

The purpose of the present paper is to investigate the temperature and pressure dependences of the elastic properties of cerium dioxide using the statistical moment method (SMM). The equation of states of bulk CeO₂ is derived from the Helmholtz free energy, and the pressure dependences of the elastic moduli like the bulk modulus, B_T, shear modulus, G, Young’s modulus, E, and elastic constants (C11, C12, and C44) are presented taking into account the anharmonicity effects of the thermal lattice vibrations. In the present study, the influence of temperature and pressure on the elastic moduli and elastic constants of CeO₂ has also been studied, using three different interatomic potentials. We compare the results of the present calculations with those of the previous theoretical calculations as well as with the available experiments.