具有六方晶系结构的多晶体材料弹性常数——Y弹性常数

利用最近提出的新的物理参量——Ｙ弹性常数,将其应用于具有六方晶系结构的多晶体材料.推导了六方晶系结构的多晶体材料之Ｙ弹性常数,通过算例与具有六方晶系结构的多晶体材料之X射线弹性常数进行了比较.运用这个Ｙ弹性常数进一步推导出的多晶体材料整体之机械弹性常数的表达式与Kneer的研究结果中的表达式虽然形式不同,但针对具体材料所计算的结果却完全符合. 关键词： Y弹性常数 六方晶系 多晶体材料     

晶体弹性常数的数值计算方法

本文讨论了从实验测得的声速和声衰减值计算晶体弹性常数的方法与计算程序。晶体弹性常数可以利用克利斯托费尔(Christoffel)方程,通过下降法解非线性方程组的方法求得,我们根据这一思想用FORTRAN语言写出了计算程序,并对部分晶系晶体的弹性常数作了计算。利用本文的方法还可以计算晶体的粘滞常数。     

氢化铒高温高压下的弹性及热力学性质

利用第一性原理平面波赝势密度泛函理论, 并结合准谐德拜模型, 计算了立方萤石结构ErH2在不同温度和压强下的体积、热膨胀系数、体弹模量和等体热容等弹性性质及热力学性质。在温度高于1 100 K的条件下,计算出的等体热容趋近于Dulong-Petit极限。得到了绝对零度、零压强下ErH2的该结构的晶格常数为0.523 2 nm,与实验值0.523 0 nm非常接近。由不同的原胞体积得出了该体系的单点能与原胞体积的关系的数据;从计算出的高压下的弹性常数,根据立方晶系的力学稳定性条件,推断出立方萤石结构ErH2的相变压力约为20 GPa。     

Mg8Sn4-xMx结构稳定性与弹性常数的第一性原理计算

利用基于密度泛函理论的CASTEP软件构建Mg₈Sn_4-xM_x(M=Al、Cu;x=0、1或2)晶体结构模型，采用第一性原理计算其晶格常数、结构稳定性和弹性常数，并分析不同量的M原子固溶于Mg₂Sn后体系的电子特性、弹性性能和本征硬度.计算结果表明，M原子能自发固溶于Mg₂Sn相，且所得Mg₈Sn_4-xM_x(x=1或2)晶体结构均可稳定存在；当2个M原子固溶于Mg₂Sn时，使其晶体结构由立方晶系转变为四方晶系.态密度分析表明，M原子固溶后体系原子存在明显轨道杂化现象，表现出较强的共价键，增加M原子固溶量不会改变各原子对态密度的贡献规律，但会提高该原子对电子对态密度的贡献度.弹性性能和本征硬度分析表明：Mg₂Sn中固溶M原子后，体系力学性能仍稳定，增加M原子固溶量，体系硬度逐渐降低，韧塑性不断提高，即M原子固溶量增加能提升体系的...     

尺寸相关的弹性常数对应变硅纳米线电学性质的影响

从Keating模型出发,基于离散化思想建立了计算单晶硅纳米线弹性常数和杨氏模量的半连续原子晶格力学模型. 从微扰理论和形变势理论出发,采用有限差分方法建立了计算不同晶向应变硅纳米线价带结构的数值模型. 结合上述的两个计算模型,进而应用经典弹道传输模型研究了轴向应力和弹性常数对p型硅纳米线弹道晶体管电学特性的影响. 研究结果表明,硅纳米线的弹性常数和杨氏模量呈现尺寸效应,该结果与分子动力学的模拟结果具有很好的一致性. 同时发现尺寸相关的弹性常数对硅纳米线晶体管输运电流的影响强烈依赖于单轴应力对输运电流的影 关键词： 应变硅纳米线 弹性常数 弹道电流 价带结构模型     

铀的弹性、能带结构和光学常数的第一性原理计算

采用密度泛函理论,赝势平面波方法计算了金属铀a相的晶体结构,弹性常数,体模量,电子能带结构和光学常数(折射率n和消光系数k)等.其中,铀的晶格参数,弹性常数和体模量等与实验及其它第一性原理计算结果十分吻合.计算得到了铀的光学常数,与实验结果作了对比并进行了分析说明.     

YAG：N_d~（3＋）单晶的二阶和三阶弹性常数

我们采用超声“脉冲回波重合法”技术［１］，测定了立方晶体钇铝柘榴石（ＹＡＧ：）的二阶弹性常数，以及它们在静水压和单轴应力条件下，随压力变化，获得了三阶弹性常数．它们分别是：Ｃ１１＝３３４．７８ＧＰａ，Ｃ１２＝１０９．９５ＧＰａ，Ｃ４４＝１１５．２５ＧＰａ，和Ｃ１１１＝－３３７７．６６ＧＰａ，Ｃ１１２＝－８４１．１６Ｇｐａ，Ｃ１２３＝－３２．８６Ｇｐａ，Ｃ１４４＝－３７．６６Ｇｐａ，Ｃ１６６＝－５７９．３８Ｇｐａ，Ｃ４５６＝－１１４．６０Ｇｐａ．根据这些数据，我们还计算了ＹＡＧ：Ｎ＿ｄ￣（３＋）晶体的德拜温度以及Ｇｒｕｎｅｉｓｅｎ参数，以及ＹＡＧ：Ｎ＿ｄ￣（３＋）的状态方程．     

测量三阶弹性常数的非线性声学方法

三阶弹性常数反映了固体弹性在二级近似下的非线性性质，它在固体物理和材料特性的确认和评估中起着重要作用。着重介绍了测量三阶弹性常数的超声二次谐波激发方法。     

MgO和Cu的弹性常数随温度及压强变化关系的研究

从Anderson-Grüneisen参数定义式和热膨胀系数定义式出发,根据Tallon的普遍化理论,推导出了一个用于计算弹性常数的理论模型,用所得到的理论模型分别计算了MgO和Cu两种固体材料的弹性常数C_(11)、C_(12)和C_(44)随压强以及温度变化的理论数值,并将理论计算结果与Kumar模型计算结果以及相关实验数据进行了比较,对所得到的理论模型计算结果与Kumar模型计算结果之间的差异性进行了分析和探讨.研究结果表明:所推导的理论模型计算结果与实验数据更加符合,并且由于所用的推导方法不依赖于晶体的结构,因此该模型具有更好的合理性和普适性.     

立方KCaF_3电子、弹性和光学性质的第一性原理研究

基于密度泛函理论和赝势平面波近似法计算研究了立方钙钛矿KCaF_3的弹性、电子和光学性质.基态时,KCaF_3平衡晶格常数、体积弹性模量和实验及其他计算值一致.根据Hooke定律和Christoffel方程,研究了KCaF_3弹性常数Cij、体积弹性模量B、各向同性波速和弹性各向性异性因子随压力的变化关系.从电子能带理论出发,计算得到了KCaF_3电子能带、态密度和Milliken电荷布居数,并对其电子性质进行了详细分析.结果显示:立方钙钛矿KCaF_3为直接带隙绝缘体材料,其禁带宽度为6.22 e V;电荷主要从Ca和K原子向F原子转移;立方钙钛矿KCaF_3属于纯粹的共价型化合物.同时,本文还计算研究了KCaF_3的光学介电函数、吸收系数、复折射率、能量损失谱和反射系数等光学性质.     

Variational treatment of the elastic constants of disordered materials

Using the method of Hill a variational principle is derived to obtain upper and lower bounds for the effective elastic constants of disordered materials, such as polycrystals or multiphase materials. All bounds previously known are rederived and especially new bounds are given being closer than the ones of Hashin and Shtrikman. In detail the elastic constants of polycrystals built of cubic single crystals and of multiphase materials are considered. The analogous bounds for the dielectric constant of polycrystals are also given.     

First-principles study of structural, electronic and elastic properties of single crystal CuZr

Investigations into the structural, electronic and elastic properties of intermetallic CuZr compound had been conducted by the plane-wave pseudopotential method. The calculated lattice constant was consistent well with the experimental value. The absence of band gap and finite value of the density of states (DOS) at the Fermi level reveal the metallic behavior of CuZr crystal, and Zr 4d states give rise to the electrical conductivity. The calculated elastic constants for single crystal CuZr at zero pressure obey the cubic mechanical stability condition, which indicates that the cubic CuZr crystal is mechanical stable at zero pressure. By analyzing the ratio between the bulk and shear moduli, we conclude that CuZr crystal is ductile in nature. The present theoretical investigations might give prediction to polycrystalline CuZr system.     

Determination of the elastic constants by coherent neutron scattering in polycrystals

It is shown that elastic constants which usually can be determined in single crystals only may be measured in polycrystals by inelastic coherent neutron scattering. Measurements are reported for polycrystalline samples of aluminium, copper and stainless steel. The method is best suited for the determination of the elastic constants connected with transverse phonons.     

Einfluß der Kristallisation auf denE-Modul linearer Polykristalle

A linear polycrystal represents the one-dimensional model of a polycrystalline wire with bamboo-structure. It is formed by crystallization of a thread of a one-component melt within a capillary tube. In the paper is assumed, that the nuclei of crystallization are independently and randomly distributed along the thread, and that their crystallographic orientations are equidistributed in all directions. Furthermore it is assumed, that all nuclei are preformed and that they (and therefore their crystals) have a cubic crystalstructure. Four differently defined processes of crystallization, forming four different linear polycrystals, are considered. TheE- andG-moduls of these four linear polycrystals are calculated only from the knowledge about their conditions of crystallization and the elastic constants of cubic single crystal. We found: 1) The moduls of the linear polycrystals have the same value, independently whether their growth has been started at the same instant or successively. 2) If the growth-rate for all crystals has a distribution (anisotropic cubic growth) or has a constant value (isotropic growth), theE-moduls (and also theG-moduls) of their linear polycrystals vary only by about 1%.     

Structural,elastic, and electronic properties of new superhard isotropic cubic crystals of carbon nanotubes

The models of new isotropic cubic crystals of single-layered carbon nanotubes are proposed. The structural, elastic, and electronic properties and the energies of formation of these crystals were calculated using the density functional-based tight binding (DFTB) method. The crystals proposed were found to exhibit extreme compression moduli (550–650 GPa) and a minimum compressibility (0.0018–0.0015 GPa^?1); in this case, the type of conduction of the parent nanotubes was retained. For this reason, the above crystals are of interest for the development of new superhard materials with controllable electrophysical properties.     

Modeling of lattice constant and their relations with ionic radii and electronegativity of constituting ions of A2XY6 cubic crystals (A=K, Cs, Rb, Tl; X=tetravalent cation, Y=F, Cl, Br, I)

In the present paper a new empirical model is proposed to describe and predict the lattice constants for a series of cubic crystals, all of which have the A₂XY₆ composition (A=K, Cs, Rb, Tl; X=tetravalent cation, Y=F, Cl, Br, I). The model is based on a thorough analysis of structural properties of 85 representative crystals from this group. It was shown that the lattice constant is a linear function of the ionic radii and electronegativity of the constituting ions. A simple empirical equation was obtained as a result of the performed analysis. It gives very good agreement between the experimental and modeled values of the lattice parameters, with an average error of 1.05%. The developed approach can be efficiently used for a simple, fast, and reliable prediction of lattice constants and interionic distances in isostructural materials having a similar composition.     

理论研究VTiTaNbAl_x高熵合金的结构与弹性力学性质

实验已证明VTiTaNbAl_x高熵合金(HEAs)为单相固溶体,它采用了体心立方结构.在本文中,我们使用基于密度泛函理论的饼模轨道(EMTO)结合相干势近似(CPA)方法,计算并分析了此高熵合金体系的平衡体性质,弹性常数及多晶弹性模量.结果表明:此系列高熵合金符合单相高熵合金的理论判据,具有较好的内在塑性,等摩尔比的VTiTaNb高熵合金趋于弹性各向同性.随着Al含量的增加,此系列高熵合金的弹性各向异性趋于增大,但对多晶弹性模量几乎没有影响;同时讨论了基于弹性常数计算的德拜温度.     

理论研究VTiTaNbAlx高熵合金的结构与弹性力学性质

实验已证明VTiTaNbAlx高熵合金(HEAs)为单相固溶体,它采用了体心立方结构. 在这篇文章中,我们使用基于密度泛函理论的饼模轨道(EMTO)结合相干势近似(CPA)方法,计算并分析了此高熵合金体系的平衡体性质,弹性常数及多晶弹性模量. 结果表明：此系列高熵合金符合单相高熵合金的理论判据,具有较好的内在塑性,等摩尔比的VTiTaNb高熵合金趋于弹性各向同性. 随着Al含量的增加,此系列高熵合金的弹性各向异性趋于增大,但对多晶弹性模量几乎没有影响;同时讨论了基于弹性常数计算的德拜温度.     

Theoretical investigation of new type of ternary magnesium alloys AMgNi4 (A=Y,La, Ce,Pr and Nd)

New ternary magnesium alloys AMgNi₄ (A=Y, La, Ce, Pr and Nd) have been studied by First-Principles calculations within the generalized gradient approximation. The optimized structural parameters were in good agreement with the available experimental data. The calculated cohesive energies and formation enthalpies showed that these alloys had strong structural stability. Then the elastic constants C_ij of these AMgNi₄ alloys were calculated, and the bulk modulus B, shear modulus G, Young's modulus E, Poisson's ratio ν and anisotropy value A of polycrystalline materials were derived from the elastic constants, the related mechanical properties were further discussed. The electronic structures were also calculated to reveal the underlying mechanism for the structural stability and the elastic property.