Predicting the solid state phase diagram for glass-forming alloys of copper and zirconium

The free energies of six crystal structures associated with Cu-Zr alloys-Cu (face centred cubic), Cu(2)Zr, Cu(10)Zr(7), CuZr, CuZr(2) and Zr (hexagonal close packed)-are calculated using the embedded atom potential of Mendelev et al (2009 Phil. Mag. 89 967). We find that the observed low temperature stability of the Cu(10)Zr(7) and CuZr(2) phases is not reproduced. Instead, the model predicts that the CuZr phase remains stable down to T = 0 K. This discrepancy is largely removed when the interaction potentials are cut off at a short distance, such as that used by Duan et al (2005 Phys. Rev. B 71 224208). We present evidence, however, that the cut-off distance necessary to achieve the change in phase stability results in pathological artefacts in the energetics of some crystal phases.     

孤立的Eu2+在立方晶场中基态能级的分裂

用量子力学微扰论方法计算了Eu^2 在立方晶场中基态能级分裂的一级修正，并给出了相应能级的零级近似波矢。     

Ab initio study of the structural,electronic, elastic and thermal conductivity properties of SrClF with pressure effects

Abstract

SrClF is an important optical crystal and can be used as pressure gauge in diamond anvil cell at high pressure. In this work, we performed a systematic study on the structural, electronic and elastic properties of SrClF under pressure, as well as its thermal conductivity, by first-principles calculation. Different exchange-correlation functionals were tested and PBESOL was finally chosen to study these properties of SrClF. Studies reveal that SrClF has a bulk modulus of about 56.2 GPa (by fitting equation of states) or 54.3 GPa (derived from elastic constants), which agree well with the experimental result. SrClF is mechanically and dynamically stable up to 50 GPa. Its elastic constants increase with the applied pressure, but its mechanical anisotropy deteriorates as the pressure increases. Investigation of its electronic properties reveals that SrClF is a direct band-gap insulator with a gap value of 5.73 eV at 0 GPa, which decreases with the increasing pressure and the reason is found by analysing the partial density of states. Based on the calculated phonon dispersion curves, thermal conductivity of SrClF is predicated. At ambient conditions, the predicted thermal conductivity is about 3.74 Wm^?1 K^?1, while that obtained using the simplified Slack model give a slightly larger value of 4.62 Wm^?1 K^?1.     

Automatic procedure for stable tetragonal or hexagonal structures: application to tetragonal Y and Cd

A simple effective procedure (MNP) for finding equilibrium tetragonal and hexagonal states under pressure is described and applied. The MNP procedure finds a path to minima of the Gibbs free energy G at T=0 K (G=E+pV, E=energy per atom, p=pressure, V=volume per atom) for tetragonal and hexagonal structures by using the approximate expansion of G in linear and quadratic strains at an arbitrary initial structure to find a change in the strains which moves toward a minimum of G. Iteration automatically proceeds to a minimum within preset convergence criteria on the calculation of the minimum. Comparison is made with experimental results for the ground states of seven metallic elements in hexagonal close-packed (hcp), face- and body-centered cubic structures, and with a previous procedure for finding minima based on tracing G along the epitaxial Bain path (EBP) to a minimum; the MNP is more easily generalized than the EBP procedure to lower symmetry and more atoms in the unit cell. Comparison is also made with a molecular-dynamics program for crystal equilibrium structures under pressure and with CRYSTAL, a program for crystal equilibrium structures at zero pressure. Application of MNP to the elements Y and Cd, which have hcp ground states at zero pressure, finds minima of E at face-centered cubic (fcc) structure for both Y and Cd. Evaluation of all the elastic constants shows that fcc Y is stable, hence a metastable phase, but fcc Cd is unstable.     

钙钛矿结构ZrBeO3稳定性的第一性原理研究

基于密度泛函理论构建了钙钛矿结构ZrBeO3晶体模型,计算了该晶体模型结合能,表明了该构型热力学稳定性;计算出该结构在不同压力下的弹性常数,并据此计算了ZrBeO3的体积模量、剪切模量、杨氏模量、泊松比、BH/GH(体模量/剪切模量)等参数,结果表明该材料具有机械稳定性,随着等静压力增加,材料由脆性向韧性转变;计算了零压下ZrBeO3的硬度,为34.5 GPa,表明该结构晶体应为超硬材料;计算了ZrBeO3的声子能谱,结果表明ZrBeO3在低温零压下热动力学不稳定,为此分析比较了不同压力下的声子能谱、不同原子轨道及化学键布居值,研究表明随着压力增加,Be原子sp杂化后形成的Be-O共价键成分增强、Zr-O键离子键成分增强,晶格动力学趋于稳定。     

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。     

高压下RhB的相变、弹性性质、电子结构及硬度的第一性原理计算

采用密度泛函理论中的赝势平面波方法系统地研究了高压下RhB的结构相变、弹性性质、电子结构和硬度.分析表明,RhB在25.3 GPa时从anti-NiAs结构相变到FeB结构,这两种结构的弹性常数、体弹模量、剪切模量、杨氏模量和弹性各向异性因子的外压力效应明显.电子态密度的计算结果显示,这两种结构是金属性的,且费米能级附近的峰随着压强的增大向两侧移动,赝能隙变宽,轨道杂化增强,共价性增强,非局域化更加明显.此外,硬度计算结果显示,anti-NiAs-RhB的金属性比较弱,有着较高的硬度,属于硬质材料.     

Atomistic properties of γ uranium

The properties of the body-centered cubic γ phase of uranium (U) are calculated using atomistic simulations. First, a modified embedded-atom method interatomic potential is developed for the high temperature body-centered cubic (γ) phase of U. This phase is stable only at high temperatures and is thus relatively inaccessible to first principles calculations and room temperature experiments. Using this potential, equilibrium volume and elastic constants are calculated at 0 K and found to be in close agreement with previous first principles calculations. Further, the melting point, heat capacity, enthalpy of fusion, thermal expansion and volume change upon melting are calculated and found to be in reasonable agreement with experiment. The low temperature mechanical instability of γ U is correctly predicted and investigated as a function of pressure. The mechanical instability is suppressed at pressures greater than 17.2 GPa. The vacancy formation energy is analyzed as a function of pressure and shows a linear trend, allowing for the calculation of the extrapolated zero pressure vacancy formation energy. Finally, the self-defect formation energy is analyzed as a function of temperature. This is the first atomistic calculation of γ U properties above 0 K with interatomic potentials.     

A first-principles study on the structural and elastic properties and the equation of state of wurtzite-type cadmium selenide under pressure

A first-principles investigation on the crystal structural and elastic properties and the equation of state of wurtzite-type cadmium selenide (w-CdSe) has been conducted using the plane-wave pseudo-potential density functional theory and the quasi-harmonic Debye model. The elastic constants, the aggregate elastic moduli, the elastic anisotropy, and Poisson's ratio under pressure have been investigated. Our calculated equilibrium lattice constants, the elastic constants, and the aggregate elastic moduli at zero pressure are in good agreement with the experimental data and other theoretical results. The variations in the compressional and shear elastic wave velocities with pressure at zero temperature up to pressure 2.7 GPa have been studied; the computed Debye temperature at zero pressure and zero temperature is in reasonable agreement with the result of Bonello et al., In addition, the equation of state of w-CdSe in the pressure range of 0–2.7 GPa and up to a temperature of 900 K has also been obtained.     

立方钙钛矿RbZnF3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方法研究了立方钙钛矿RbZnF3的电子结构和光学性质;利用静水有限应变技术计算研究了RbZnF3弹性常数Cij、体积弹性模量B和剪切模量G随压力的变化关系。基态下,RbZnF3晶格常数a和体积弹性模量B0计算值与实验值以及其他理论值一致。根据能带结构、总态密度以及分波态密度分析可知：基态下立方钙钛矿结构RbZnF3为间接带隙半导体材料,带隙为3.57eV,与其他计算结果比较,本文计算结果偏低,这是由于局域密度近似(LAD)或广义梯度近似(GGA)交换关联函数的局限性所致。基态下RbZnF3的Mulliken电荷分布和集居数说明：RbZnF3属于共价键和离子键所形成的混合键化合物;RbZnF3的电荷总数主要来源于Rb 4s和4p轨道,Zn 3d轨道,以及F 2s和2p轨道。电荷主要从Rb, Zn原子向F原子转移。同时,本文还计算研究了RbZnF3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。     

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.     

立方KCaF3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KCaF3的弹性、电子和光学性质。基态时,KCaF3平衡晶格常数、体积弹性模量和其他计实验和算值一致。根据Hooke定律和Christoffel方程,研究了KCaF3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KCaF3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KCaF3为直接带隙绝缘体材料,其禁带宽度为6.22eV;电荷主要从Ca和K原子向F原子转移;立方钙钛矿KCaF3属于纯粹的共价型化合物。同时,本文还计算研究了KCaF3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。     

Structural,electronic and mechanical properties of alkaline earth metal oxides MO (M=Be,Mg, Ca,Sr, Ba)

The structural, electronic and mechanical properties of alkaline earth metal oxides MO (M=Be, Mg, Ca, Sr, Ba) in the cubic (B1, B2 and B3) phases and in the wurtzite (B4) phase are investigated using density functional theory calculations as implemented in VASP code. The lattice constants, cohesive energy, bulk modulus, band structures and the density of states are computed. The calculated lattice parameters are in good agreement with the experimental and the other available theoretical results. Electronic structure reveals that all the five alkaline earth metal oxides exhibit semiconducting behavior at zero pressure. The estimated band gaps for the stable wurtzite phase of BeO is 7.2 eV and for the stable cubic NaCl phases of MgO, CaO, SrO and BaO are 4.436 eV, 4.166 eV, 4.013 eV, and 2.274 eV respectively. A pressure induced structural phase transition occurs from wurtzite (B4) to NaCl (B1) phase in BeO at 112.1 GPa and from NaCl (B1) to CsCl (B2) phase in MgO at 514.9 GPa, in CaO at 61.3 GPa, in SrO at 42 GPa and in BaO at 14.5 GPa. The elastic constants are computed at zero and elevated pressures for the B4 and B1 phases for BeO and for the B1 and B2 phases in the case of the other oxides in order to investigate their mechanical stability, anisotropy and hardness. The sound velocities and the Debye temperatures are calculated for all the oxides using the computed elastic constants.     

CaS电子结构和热力学性质的第一性原理计算

根据密度泛函理论,采用平面波赝势和广义梯度方法,计算了Ca S的晶体结构和电子结构.通过准谐徳拜模型预测了硫化钙的体积变化率、体弹模量、热膨胀系数分别与温度和压强的变化关系,以及热容和温度的变化关系.     

高温高压下立方氮化硼和六方氮化硼的结构、力学、热力学、电学以及光学性质的第一性原理研究

本文采用基于密度泛函理论的第一性原理平面波赝势和局域密度近似方法,优化了立方和六方氮化硼的几何结构,系统地研究了零温高压下立方和六方氮化硼的几何结构、力学、电学以及光学性质.结构与力学性质研究表明:立方氮化硼的结构更加稳定,两种结构的氮化硼均表现出一定的脆性,而六方氮化硼的热稳定性则相对较差;电学性质研究表明:立方氮化硼和六方氮化硼均为间接带隙半导体,且立方氮化硼比六方氮化硼局域性更强;光学性质结果显示:立方氮化硼和六方氮化硼对入射光的通过性都很好,在高能区立方氮化硼对入射光的表现更加敏感.此外,还研究了高温高压下立方氮化硼的热力学性质,并得到其热膨胀系数、热容、德拜温度和格林艾森系数随温度和压力的变化关系.本文的理论研究阐述了高压下立方氮化硼和六方氮化硼的相关性质,为今后的实验研究提供了比较可靠的理论依据.     

Ab-initio simulation of elastic constants for some ceramic materials

Athermal elasticity for some ceramic materials (α-Al₂O₃, SiC (α and β phases), TiO₂ (rutile and anatase), hexagonal AlN and TiB₂, cubic BN and CaF₂, and monoclinic ZrO₂) have been investigated via density functional theory. Energy-volume equation-of-state computations to obtain the zero pressure equilibrium volume and bulk modulus as well as computations of the full elastic constant tensor of these ceramics at the experimental zero pressure volume have been performed. The present results for the single crystal elasticity are in good agreement with experiments both for the aggregate properties (bulk and shear modulus) and the elastic anisotropy. In contrast, a considerable discrepancy for the zero pressure bulk modulus of some ceramics evaluated from the energy-volume fit to the computational zero pressure volume has been observed.     

各向异性立方晶体的弹性格林函数及其应用

本文计算了各向异性立方晶体的弹性格林函数的级数展开式,给出了直到二级近似的展开式的系数。将所得结果应用于弹性偶极子模型,给出了对称中心所产生的位移场及两对称中心间的弹性相互作用的表示式。应用于Cu,K等强各向异性立方晶体,虽然级数的收敛较慢,但所得关于对称中心的位移场,及二对称中心间的互作用能的数值结果,竟与基于点阵的不连续性作出的点阵静力学计算所得的结果基本一致。从而表明,本文给出的直到二级近似的弹性格林函数的解析表示提供了一个可以普遍应用的简便的方法。它可以较准确地描述立方晶体的某些力学行为。 关键词：     

First principles study of structural,phonon, optical,elastic and electronic properties of Y3Al5O12

Structural, phonon, optical, elastic and electronic properties of Y₃Al₅O₁₂ have been investigated by means of the first principles method with the Cambridge Serial Total Energy Package (CASTEP) code based on the density functional theory. The calculated lattice parameters, valence charge density, bond length and single crystal elastic properties at zero pressure are in good agreement with the available experimental data. The close agreement with the experimental values provides a good confirmation of the reliability of the calculations. Optical, elastic and phonon properties of Y₃Al₅O₁₂ under pressures are performed. The results that are obtained show the changes of optical and elastic properties under the influence of applied pressure, and proving the dynamical stability of YAG are destructed when applied pressure up to 7 GPa. Moreover, polycrystalline elastic moduli are deduced according to the Reuss assumption. Those elastic constants provide important parameters that describe reliability of both physical model and engineering application at the atomistic level. The result of the density of states explains the nature of the electronic band structure.     

Phase equilibrium in the formation of silicon carbide by topochemical conversion of silicon

Methods of linear algebra were used to find a basis of independent chemical reactions in the topochemical conversion of silicon into silicon carbide by the reaction with carbon monoxide. The pressure–flow phase diagram was calculated from this basis, describing the composition of the solid phase for a particular design of vacuum furnace. It was demonstrated that to grow pure silicon carbide, it is necessary to ensure the pressure of carbon monoxide less than a certain value and its flow more than a certain value, depending on the temperature of the process. The elastic fields around vacancies formed were considered for the first time in calculating the topochemical reaction. It was shown that the anisotropy of these fields in a cubic crystal increases the constant of the main reaction approximately fourfold.     

NbSi2奇异高压相及其热力学性质的第一性原理研究

采用基于粒子群优化算法的结构预测程序CALYPSO, 并结合第一性原理的VASP程序, 在175 GPa发现NbSi₂的奇异立方高压相. 在此结构中, Nb原子形成金刚石结构, 而Si原子则形成正四面体镶嵌在金刚石结构中. 声子谱计算结果表明该结构是动力学稳定的. 电子结构分析表明, 六角相和立方相NbSi₂均为金属, 对金属性贡献较大的是Nb原子, 而且Nb和Si原子之间存在明显的p-d杂化现象, 电荷更多地聚集在Si四面体中. 利用“应力应变”方法, 计算了NbSi₂的弹性常数, 分析了其体积模量、剪切模量、杨氏模量和德拜温度等热动力学性质随压力的变化并进行了详细的讨论. 根据剪切模量和体积模量的比值分析了NbSi₂两种相结构的脆性和延展性, 发现压力会导致六角相NbSi₂的延展性增加, 但对立方相结构的延展性影响较小; 采用经验算法计算了NbSi₂两种相结构硬度变化情况, 结合这一比值进行了详细的分析. 弹性各向异性计算结果表明, 随着压力增加, 六角结构的各向异性增强, 而立方结构的各向异性减小.