Ab initio investigation of the mechanical properties of copper

Employing the ab initio total energy method based on the density functional theory with the generalized gradient approximation, we have systematically investigated the theoretical mechanical properties of copper (Cu). The theoretical tensile strengths are calculated to be 25.3 GPa, 5.9 GPa, and 37.6 GPa for the fcc Cu single crystal in the [001], [110], and [111] directions, respectively. Among the three directions, the [110] direction is the weakest one due to the occurrence of structure transition at the lower strain and the weakest interaction of atoms between the (110) planes, while the [111] direction is the strongest direction because of the strongest interaction of atoms between the (111) planes. In terms of the elastic constants of Cu single crystal, we also estimate some mechanical quantities of polycrystalline Cu, including bulk modulus B, shear modulus G, Young’s modulus E p , and Poisson’s ratio ν.     

Ab initio investigation on mechanical properties of copper

Employing the ab initio total energy method based on the density functional theory with the generalized gradient approximation, we have investigated the theoretical mechanical properties of copper (Cu) systematically. The theoretical tensile strengths are calculated to be 25.3 GPa, 5.9 GPa, and 37.6 GPa for the fcc Cu single crystal in the [001], [110], and [111] directions, respectively. Among the three directions, the [110] direction is the weakest one due to the occurrence of structure transition at the lower strain and the weakest interaction of atoms between the (110) planes, while the [111] direction is the strongest direction because of the strongest interaction of atoms between the (111) planes. In terms of the elastic constants of Cu single crystal, we also estimate some mechanical quantities of polycrystalline Cu, including bulk modulus B, shear modulus G, Young's modulus E_p, and Poisson's ratio ν.     

Atomistic multiscale simulations on the anisotropic tensile behaviour of copper-alloyed alpha-iron at different states of thermal ageing

The mechanical behaviour of steels is strongly related to their underlying atomistic structures which evolve during thermal treatment. Cu-alloyed α-Fe undergoes a change in material behaviour during the ageing process, especially at temperatures of above 300°C, where precipitates form on a large time-scale within the α-Fe matrix, yielding first a precipitation strengthening of the material. As the precipitates grow further in time, the material strength decreases again. This complex process is modelled with a multiscale approach, combining Kinetic Monte Carlo (KMC) with Molecular Dynamics (MD) simulations in a sequential way and exploiting the advantages of both methods while simultaneously circumventing their particular disadvantages. The formation of precipitates is modelled on a single-crystal lattice with a diffusion based KMC approach. Transferring selected precipitation states at different ageing times to MD simulations allows the performance of nano tensile tests and the analysis of failure initiation. The anisotropic tensile behaviour is investigated in the [100], [110] and [111] directions, showing monotonically decreasing tensile strengths and deformation strains. Hence precipitation strengthening is mainly due to dislocation–precipitate interactions which are non-existent at small tensile loadings in this scenario. At the point of ductile failure, dislocations are generated at the interfaces between precipitates and the Fe matrix. Straining in the [100] direction, they lie on {110} and {112} glide planes, as expected. With the method presented here, the changes of the anisotropic tensile moduli are related to different states of thermal ageing, i.e., to nucleation, growth and Ostwald ripening of Cu precipitates.     

Effects of magnetic field on shape evolution of Fe–Co particles in a Cu matrix

The effects of magnetic field on the shape evolution of ferromagnetic fcc Fe–Co particles in Cu–0.83 at.% Fe–1.37 at.% Co alloy single crystals were examined using magnetic anisotropy measurements. The Cu–Fe–Co single crystals were aged at 993 K for 2 h to 24 h under a magnetic field of 10 T parallel to either the [001] or [011] direction. The magnetic anisotropy was examined by measuring magnetic torque around the (100) plane. It was found that the fcc Fe–Co particles are elongated in the direction parallel to the magnetic field. Furthermore, the elongation along [001] is more remarkable than that along [011]. The results are explained quantitatively by considering the minimization of the sum of the interface energy, elastic strain energy and magnetostatic energy of spheroidal particles.     

Lattice stability and the effect of Co and Re on the ideal strength of Ni:First-principles study of uniaxial tensile deformation

Using first-principles density functional calculations, lattice stability of γ-Ni under [001], [110], and [111] uniaxial tensions and the effect of alloying elements Co and Re on the uniaxial tensile behavior of γ-Ni were studied in this paper.With elastic constants and phonon spectra calculations, we examined the mechanical stability and phonon stability of Ni during the uniaxial tensions along the three characteristic directions. The results show that the mechanical stability and phonon stability of a lattice occurs before the maximum stress–strain point under the [001] and [111] tension, respectively.The effects of Co and Re on the ideal tensile strength of γ-Ni show a significant directivity: Co and Re have little effect on the stresses in [001] and [111] directions, but increases the ideal strength of the system in the weakest uniaxial tensile direction. Moreover, the strengthening effect of Re is significantly better than that of Co. By further analyzing electronic structure, it is found that the effect of alloying elements on the uniaxial tensile behavior of γ-Ni comes from their interactions with host atoms.     

单轴应变条件下Fe从α到ε结构相变机制的第一性原理计算

采用基于密度泛函理论的平面波赝势方法,研究了沿［001］方向单轴应变条件下Fe从体心立方结构(bcc,α相)到六角密排结构(hcp,ε相)相变的临界压力、相变路径、相变势垒以及相变过程中原子磁性的变化.结果发现:单轴应变条件下Fe从α到ε结构的相变路径与以前理论计算模拟给出的静水压力条件下的相变路径明显不同;原子磁矩沿着相变路径突然降低,同时伴随着能量和体积的突然变化,是典型的一阶磁性相转变,表明原子磁性的丧失导致了bcc结构不稳定而向hcp结构转变.对单轴应变下吉布斯自由能的计算表明,相变势垒随着单轴应 关键词： 相变 单轴应变 第一性原理 铁     

Stability of Ferromagnetism in Fe, Co, and Ni Metals under High Pressure with GGA and GGA+U

The stability of the ferromagnetic state in Fe, Co, and Ni metals under high pressure is investigated using generalized gradient approximation (GGA) and GGA+U within the density functional theory (DFT). It is found that the ferromagnetic state under pressure is very different for Fe, Co, and Ni metals, and is closely associated with the crystal structure. In the case of Fe, a ferromagnetic bcc ground state is obtained at ambient pressure and a nonmagnetic hcp ground state is found at pressure around 12 and 115 GPa for GGA and GGA+U, respectively. For Co, the phase transition from a ferromagnetic hcp to a nonmagnetic fcc is found around 107 GPa for GGA. In contrast to Fe and Co, a ferromagnetic fcc state in Ni is maintained even at 200 GPa. The calculated results suggest that the suppression of ferromagnetism in Fe, Co, and Ni is due to pressure-induced decrease of the density of state at the Fermi level.     

面心立方单晶镍纳米线稳定性及磁性的第一性原理计算

本文采用第一性原理方法,研究了轴向为低指数晶向的面心立方(fcc)单晶镍纳米线的稳定性和磁性.计算表明,[110] 是fcc镍纳米线最容易出现的取向,[111] 取向次之,而 [001] 取向则很难出现,这一结果与实验事实符合.镍纳米线按照原子位置和磁性强弱的不同,可以分成简单的芯-壳结构,在纳米线芯部,原子的磁矩大小与块体基本一致.在纳米线表面,镍原子的磁矩比芯部原子有所增加.表面原子磁矩与轴向的取向相关,[110] 为轴向的纳米线表面原子磁矩最低,而[001] 为轴向的纳米线表面原子磁矩最高. 关键词： 镍 纳米线 第一性原理 原子磁矩     

Structural and Mössbauer studies of aerosol FeCu nanoparticles in a wide composition range

Structure and magnetic state of aerosol FeCu nanoparticles of 10–30 nm size with Cu content of 0.6–92.1 at.% have been examined by X-ray diffraction and Mössbauer spectroscopy. The FeCu particles have been shown to consist of an iron core surrounded by a copper and Fe oxide shell. With increasing Cu content the iron core having a bcc structure is reduced down to its complete disappearance followed by vanishing ferromagnetism of the particles. Within the copper content from 4.9 to 74.3 at.% the bcc and fcc phases coexist, with the fcc phase having a lattice constant close to that of pure copper and the bcc lattice constant being slightly higher than that for pure Fe due to embedding Cu atoms into the Fe lattice. At Fe-rich FeCu samples a presence of two-spin (ferromagnetic and paramagnetic) components of the fcc Fe is also observed. In the case of a thin copper shell there is only the ferromagnetic fcc Fe, whereas with further thickening of the shell both spin states of the fcc Fe appear existing up to a 20% Cu content. For FeCu samples with a higher Cu content they disappear due to oxidation of the copper grains. The Cu-rich samples with Cu content higher 80 at.% have a fcc structure, with the lattice constant being slightly higher than that of copper and they are paramagnetic. A slight increase of the lattice constant is due to the penetration of small iron aggregations into the Cu grains. In contact with air, the FeCu particles become covered with Fe₃O₄ and Cu₂O. Their long-term exposure to ambient conditions leads to further oxidation process of Cu₂O to CuO.     

On the energetics of transversal and longitudinal fluctuations of atomic magnetic moments

By constrained spin-density functional calculations we estimate the relative role of the longitudinal and transversal fluctuations of the magnetic moments in the series of 3d metals (bcc Fe, hcp and fcc Co, and fcc Ni) for weak excitations from the ferromagnetic ground state. It is shown that the importance of longitudinal fluctuations strongly varies from relatively small in bcc Fe to large in fcc Ni. This means that a consistent adiabatic treatment of the low-energy spin fluctuations should include independent longitudinal fluctuations.     

Growth of Fe films on Rh(001): a photoemission study

The growth mode and electronic structures of Fe thin films, epitaxially grown on Rh(001), were studied by various photoemission measurements for the film thickness of 0–12 monolayers. By comparing the valence band structures obtained from the angle-resolved photoemission spectra and the theoretical band calculations for the bulk Fe, we concluded that the valence band structure of the Fe film resembles that of fcc(001) in the low coverage region and that of bcc(110) in the high coverage region. This transformation of the electronic structure is considered to be related to the thickness dependence of the interlayer spacing of the films.     

不同取向下单晶铁纳米线拉伸行为的模拟研究

本文利用分子动力学模拟的方法研究了不同取向、尺寸和温度因素对单晶体心立方铁纳米线的拉伸变形行为的影响.铁纳米线轴向初始取向分别为<001>、<110>、<111>、<102>、<112>,模拟了不同温度(10～700 K)和不同尺寸范围(1.5～5 nm)下的变形机制.研究结果表明取向、尺寸和温度会显著影响单晶体心立方铁纳米线的拉伸变形行为.分子动力学模拟结果表明，直径为2 nm的<001>铁纳米线在300 K的拉伸载荷下，主要通过孪晶的模式发生变形，最后拉伸取向转变为<110>.而在700 K下，<001>铁纳米线的拉伸变形模式由滑移主导.不同初始取向在不同温度和尺寸下其变形机制截然不同，这导致了铁纳米线不同的力学性能.本文系统性地研究了在不同取向下的铁纳米线变形机制随尺寸和温度变化发生的转变.     

Study of disordering processes in a copper-palladium alloy

Disordering processes in aCu-40 at.% Pd alloy are studied by the method of successive quenching. For analyzing the transformations, measurements of electrical resistance and microhardness are supplemented by x-ray diffraction. For certain quench temperatures the ordered and disordered phases are present at the same time. On increasing the quench temperature the amount of ordered phase is reduced; the crystal lattice constants of the main and precipitated phases nevertheless remain constant within the limits of experimental error. During the transformation the microhardness diminishes and the electrical resistance increases, constant values being reached at a quench temperature of 760C, at which the alloy is completely disordered. The transition from the ordered to the disordered state occurs without the formation of any intermediate metastable phases. An x-ray diffraction analysis of the alloy reveals the orientational relationship between the matrix and precipitated phases. Experiments indicate the following mutual directions [001] bcc [110]fcc and [110] bcc [111]fcc.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 7, pp. 51–56, July, 1973.     

Magnetic reversal of the ferroelectric polarization in a multiferroic spinel oxide

Ferroelectric transition has been detected in a ferrimagnetic spinel oxide of CoCr2O4 upon the transition to the conical spin order below 25 K. The direction [110] of the spontaneous polarization is normal to both the magnetization easy axis [001] and to the propagation axis [110] of the transverse spiral component, in accord with the prediction based on the spin-current model. The reversal of the spontaneous magnetization by a small magnetic field (approximately 0.1 T) induces the reversal of the spontaneous polarization, indicating the clamping of the ferromagnetic and ferroelectric domain walls.     

First-principles studies of the magnetic hyperfine field in Fe multilayers

A detailed theoretical study of the magnetic moments and magnetic hyperfine fields in several Fe multilayers (Fe fcc(001)/5X fcc(001), X=Cu and Ag, and Fe bcc(001)/5X fcc(001), X=Ag and Au) as well as in bulk Fe is presented. The calculations have been performed using the spin-polarized, relativistic linear muffin-tin orbital (SPR-LMTO) method of band structure calculation. Therefore, not only the contribution to the hyperfine fields due to the conventional Fermi contact interaction but also due to the spin dipolar and orbital contributions induced by the crystal field and by spin-orbit coupling are accounted for. To decompose the hyperfine field of non-s-electrons into these contributions it has been assumed that they are proportional to the corresponding so-called magnetic dipole moment and the orbital magnetic moment, respectively. In contrast to previous results for pure metals and alloys not only the orbital but also the spin dipolar hyperfine field was found to be non-negligible. The anisotropy of the hyperfine field determined by calculations for in-plane and perpendicular orientation of the magnetisation was found to be very pronounced and closely connected with the corresponding anisotropy of the magnetic dipole moment and the orbital moment.     

Electronic structures and magnetism of Fe nanowires on Cu（001） and Ag（O01）： A first-principles study

The electronic structures and magnetism of Fe nanowires along the [110] direction on Cu（001） and Ag（001） [Fe（nw）/Cu（001） and Fe（nw）/Ag（001）] are investigated by using the all-electron full-potential linearized augmented plane wave method in the generalized gradient approximation. It is found that the magnetic moment of Fe atom for the Fe（nw）/Cu（001） is 2.99#B, which is slightly smaller than that （3.02μB） for the Fe（nw）/Ag（001） but much larger than that （2.22μB） for the bcc iron. The great enhancement of magnetic moment in the Fe nanowires can be explained by the Fe d-band narrowing and enhancement of the spin-splitting due to a reduction in coordination number, From the calculated spin-polarized layer-projected density of states, it is found that the Fe 3d-states are strongly hybridized with the adjacent Cu 3d-states in the Fe（nw）/Cu（001）, and there exists a strong hybridization between the Fe sp-and the adjacent Ag 4d-states in the Fe（nw）/Ag（001）.     

Ni,Pd和Pt的表面应力

半经验的修正嵌入原子方法用于Ni，Pd和Pt的低指数面的表面应力计算，得到了与第一原理计算相符合的结果．给出了（110）表面［110］方向的应力是［001］方向应力的两倍左右；阐明了应力各向异性是所有fc金属（110）面的一般特性．预言了Pd和Pt（100）的表面应力的大小． 关键词：     

THEORETICAL STRENGTH AND PHASE STABILITY OF Cu AND Ni UNDER [100] UNIAXIAL LOADING

Based on Born's criteria we studied phase stability and theoretical strength of fcc crystals of copper and nickel under [100] uniaxial loading. The calculation was carried out using a simple and completely analytical embedded atom method(EAM) potential proposed by the present authors. For Cu, the calculated value of its theoretical strength (0.33×10¹¹ dyn·cm^-2) agrees well with the experimental value (0.30×10¹¹ dyn·cm^-2), while the calculated strain (9.76%) is somewhat larger than the experimental one (2.8%). For Ni, its theoretical strength and strain predicted using the EAM potential are found smaller than those predicted using a pair potential. It is worthy to note that unlike previous calculations, in which pair potentials were used and three unstressed fcc, bcc, and fct structures included (for Ni only fcc state is found stable, while for Cu both fcc and bcc states are predicted stable), in present calculations using EAM potential the [100] primary loading path passes through only two zeroes (a stable unstressed fcc structure and an unstable stress-free bcc structure) either for Cu or for Ni.     

Development of magnetic anisotropies in ultrathin epitaxial films of Fe(001) and Ni(001)

Ultrathin films, bcc Fe(001) on Ag(001), fcc Fe(001) on Cu(001) and Fe/Ni(001) bilayers on Ag, were grown by molecular beam epitaxy. A wide range of surface science tools were employed to establish the quality of epitaxial growth. Ferromagnetic resonance and Brillouin light scattering were used to extract the magnetic properties. Emphasis was placed on the study of magnetic anisotropies. Large uniaxial anisotropies with easy axis perpendicular to the film surface were observed in all ultrathin structures studied. These anisotropies were particularly strong in fcc Fe and bcc Fe films. In sufficiently thin samples the saturation magnetization was oriented perpendicularly to the film surface in the absence of an applied field. It has been demonstrated that in bcc Fe films the uniaxial perpendicular anisotropy originates at the film interfaces. In situ measurements indentified the strength of the uniaxial perpendicular anisotropy constant at the Fe/vacuum, Fe/Ag and Fe/Au interfaces asK _us = 0.96, 0.63, and 0.3 ergs/cm² respectively. The surface anisotropies deduced for [bulk Fe/noble metal] interfaces are in good agreement with the values obtained from ultrathin films. Hence the perpendicular surface ansiotropies originate in the broken symmetry at abrupt interfaces. An observed decrease in the cubic anisotropy in bcc Fe ultrathin films has been explained by the presence of a weak 4th order in-plane surface anisotropy,K _1S=0.012 ergs/cm². Fe/Ni bilayers were also investigated. Ni grew in the pure bcc structure for the first 3–6 ML and then transformed to a new structure which exhibited unique magnetic properties. Transformed ultrathin bilayers possessed large inplane 4th order anisotropies far surpassing those observed in bulk Fe and Ni. The large 4th order anisotropies originate in crystallographic defects formed during the Ni lattice transformation.     

Response of fcc metals and L12 and D022 type trialuminides to uniaxial loading along [100] and [001]: ab initio DFT calculations

Ab initio density-functional calculations have been used to investigate the response of the face-centred cubic (fcc) metals Al and Cu, and of the L1₂- and D0₂₂-type trialuminides Al₃(Sc,Ti,V) to uniaxial loading along the [100] and [001] directions. The results obtained under uniaxial strains are compared to the response to biaxial (epitaxial) strains. The ideal tensile and compressive strengths and their limitation by shear instabilities along these deformation paths have been calculated. Although the response of both pure fcc metals could be expected to be very similar, our results show a fundamental difference: whereas for Cu a special invariant state with C ₂₂?=?C ₂₃, leading to a bifurcation from the tetragonal to an orthorhombic deformation path, is reached at a strain of 10%, for Al this state is reached only at a strain of 33% close to the critical strain defining the ideal tensile strength. The reaction of the L1₂-type trialuminides is comparable to the response of Al; no bifurcation to an orthorhombic deformation path is predicted. The response of the D0₂₂-type trialuminides is different from that of the L1₂-type phases because of the difference in the stacking of the atomic planes along the [001] direction. For D0₂₂-type trialuminides, the uniaxial compression along this direction or epitaxial tension in the (001) plane leads to the formation of a stress-free D0₃ structure, in complete analogy to the fcc???bcc transformations observed for the pure metals. Under uniaxial [100] loading the guiding symmetry along the deformation path is orthorhombic and leads to the formation of special structures under both tension and compression parts, which are related to the D0₃ structure in the same way as the parent D0₂₂-lattice is related to the L1₂ structure.