Effect of High-Temperature Structure and Diffusion on Grain-Boundary Diffusion Creep in fcc Metals

Molecular dynamics simulations of high-energy twist and tilt bicrystals of fcc palladium reveal a universal, liquid-like, isotropic high-temperature diffusion mechanism, characterized by a rather low self-diffusion activation energy that is independent of the boundary type or misorientation. Medium-energy grain boundaries exhibit the same behavior at the highest temperatures; however, at lower temperatures the diffusion mechanism becomes anisotropic, with a higher, misorientation-dependent activation energy. Our simulations demonstrate that the lower activation energy at elevated temperatures is caused by a structural transition, from a solid boundary structure at low temperatures to a liquid-like structure at high temperatures. We demonstrate that the existence of such a transition has important consequences for diffusion creep in nanocrystalline fcc metals. In particular, our simulations reveal that in the absence of grain growth, nanocrystalline microstructures containing only high-energy grain boundaries exhibit steady-state diffusion creep with a creep rate that agrees quantitatively with that given by the Coble-creep formula. Remarkably, the activation energy for the high-temperature creep rate is the same as that characterizing the universal high-temperature diffusion in high-energy energy bicrystalline grain boundaries.     

fcc金属层错能的EAM法计算

采用嵌入原子法(EAM)计算了Cu，Ag，Au，Ni，Al，Rh，Ir，Pd，Pt和Pb等10种面心立方(fcc)金属的层错能，除Rh和Ir两种金属外，其他金属的计算结果和实验结果基本一致. 关键词： 面心立方金属 层错能 EAM     

Nucleation of deformation twins in nanocrystalline fcc alloys

An earlier dislocation model for predicting the grain size effect on deformation twinning in nanocrystalline (nc) face-centred-cubic (fcc) metals has been found valid for pure metals but problematic for alloys. The problem arises from the assumption that the stacking-fault energy (γ_SF) is twice the coherent twin-boundary energy (γ_fcc), which is approximately correct for pure fcc metals, but not for alloys. Here we developed a modified dislocation model to explain the deformation twinning nucleation in fcc alloy systems, where γ_SF ≠ 2γ_twin. This model can explain the differences in the formations of deformation twins in pure metals and alloys, which is significant in low stacking-fault energy alloys. We also describe the procedure to calculate the optimum grain size for twinning in alloy systems and present a method to estimate γ_twin.     

Calculation of the surface energy of fcc metals with modified embedded-atom method

The surface energies for 38 surfaces of fcc metals Cu, Ag, Au, Ni, Pd, Pt, A1, Pb, Rh and Ir have been calculated by using the modified embedded-atom method. The results show that, for Cu, Ag, Ni, A1, Pb and Ir, the average values of the surface energies are very close to the polycrystalline experimental data. For all fcc metals, as predicted, the close-packed (111) surface has the lowest surface energy. The surface energies for the other surfaces increase linearly with increasing angle between the surfaces (hkl) and (111). This can be used to estimate the relative values of the surface energy.     

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.     

fcc金属表面能的各向异性分析及表面偏析的预测

本文将元素变量(φ^*和n_WS)和MAEAM相结合,从原子尺度上对10种fcc金属Cu,Ag,Au,Ni,Pd,Pt,Rh,Al,Ir和Pb的38个不同晶面的表面能进行模拟计算及各向异性分析. 结果表明,fcc金属的密排面(111)的表面能最小,则该晶粒取向优先生长,与实验结果和第一原理的LMTO-ASA计算结果一致;各个晶面的表面能均随着其他晶面与(111)晶面的夹角cosθ_(hkl)的增长而呈线性 关键词： FCC金属 MAEAM 表面能 表面偏析     

FCC金属空位的MAEAM理论研究

应用涉及更远邻原子的改进分析型嵌入原子方法（MAEAM）计算了面心立方（fcc）金属（Ag,Al,Au,Cu,Ir,Ni,Pd,Pt,Rh）的空位性能。在MAEAM计算中,考虑了远邻原子相互作用和单空位迁移能,对两体势进行了坚挺处理,并采用新的截尾函数和加强光滑连接条件对两体势作了截尾处理。同时为了更好的符合面心立方晶体的结合能、弹性常数和平衡条件,调整了多体势的模型常数。未弛豫空位性能计算中考虑了两体势的截尾距离和电子密度分布函数的截尾距离之间近邻原子的作用以及双空位迁移途径周围的原子非对称分布。结果与其它方法计算结果基本一致,但更加接近实验值。对双空位迁移能的计算结果有利地说明了fcc金属双空位5种迁移途径的扩散机制。     

FCC金属结构稳定性和声子谱的MAEAM研究

应用改进分析型嵌入原子方法(MAEAM)计算fcc金属的结构稳定性和声子谱.考虑更远邻原子之间的相互作用,提出新的两体势函数,并采用新的截尾处理函数和加强光滑连接条件.通过拟合单空位迁移能、结合能、三个独立弹性常数及晶体平衡条件,确定了模型参数.在体积不变条件下,计算金属不同结构的能量,说明Ag、Al、Au、Cu、Ir、Ni、Pd、Pt和Rh的fcc结构比较稳定.它们的能量-体积曲线与Rose方程结果基本-致,进-步说明了体积变化时的结构稳定性.同时发现[100]、[110]和[111]三个方向声子谱的计算结果符合实验值和其它计算结果.     

New deformation twinning mechanism generates zero macroscopic strain in nanocrystalline metals

Macroscopic strain was hitherto considered a necessary corollary of deformation twinning in coarse-grained metals. Recently, twinning has been found to be a preeminent deformation mechanism in nanocrystalline face-centered-cubic (fcc) metals with medium-to-high stacking fault energies. Here we report a surprising discovery that the vast majority of deformation twins in nanocrystalline Al, Ni, and Cu, contrary to popular belief, yield zero net macroscopic strain. We propose a new twinning mechanism, random activation of partials, to explain this unusual phenomenon. The random activation of partials mechanism appears to be the most plausible mechanism and may be unique to nanocrystalline fcc metals with implications for their deformation behavior and mechanical properties.     

Electronic structure of hydrogen and muonium in Al,Mg and Cu

The electronic structure of hydrogen and muonium in simple metals is investigated. The spherical solid model potential is used for the discrete lattice and the Blatt correction for lattice dilation. The proton and muon are kept at the octahedral sites in the fcc and hcp lattices and self-consistent non-linear screening calculations are carried out. The scattering phase shifts, electronic charge density, effective impurity potential, self-energy, charge transfer, residual resistivity and Knight shift are calculated. The spherical solid potential changes the scattering character of impurity. The phase shifts are found slowly converging. The scattering is more prominent in Al than in Mg and Cu. The virtual bound states of proton and muon are favoured in all the three metals. The calculated value of residual resistivity for CuH is in good agreement with the experimental value. The results for Knight shift forμ ⁺ in Cu and Mg are in reasonable agreement with the experimental values while those forμ ⁺ in Al are lower than the experimental value. The analytical expressions for effective impurity potential and electronic charge density are suggested.     

Point-defect properties in HCP rare earth metals with analytic modified embedded atom potentials

The analytic embedded atom method (EAM) type many-body potentials of hcp rare earth metals (Dy, Er, Gd, Ho, Nd, Pr, and Tb) have been constructed. The hcp lattice is shown to be energetically most stable when compared with the fcc and bcc structure, and the hcp lattice with ideal c/a. The mechanical stability of the corresponding hcp lattice with respect to large change of density and c/a ratio is examined. The phonon spectra, stacking fault and surface energy are calculated. The activation energy for vacancy diffusion in these metals has been calculated and the most possible diffusion paths are predicted. Finally, the self-interstitial atom (SIA) formation energy and volume have been evaluated for eight possible sites. This calculation suggests that the crowdion and basal split are the most stable configurations. The SIA formation energy increases linearly with the increase of the melting temperature.Received: 26 March 2003, Published online: 9 September 2003PACS: 34.20.Cf Interatomic potentials and forces - 66.30.Fq Self-diffusion in metals, semimetals, and alloys - 61.72.Ji Point defects (vacancies, interstitials, color centers, etc.) and defect clusters - 61.72.Bb Theories and models of crystal defects     

Multilayer relaxation of fcc metals (001) surface: A modified embedded atom method study

The (001) surface multilayer relaxation results calculated by the modified embedded atom method (MEAM) show that Ni, Al, Rh and Ir (001) surface are ‘anomalous’ outward relaxation, while Cu, Ag, Au, Pd, Pt and Pb (001) surface are inward relaxation. For the inward relaxation metals, the relaxation between the first two layers increase for the 3d, 4d and 5d metals at the same column in the periodic table, successively. The expansion (contraction) between the first two layers at fcc (001) surfaces is accompanied by the decrease (increase) in the electronic density at the lattice of the first two layers. The surface energies results show that the surface energies decrease for all fcc (001) surfaces due to relaxation, whereas the changes not more than 5%.     

Interaction of Point Defects with Grain Boundaries in fcc Metals

Structures of several symmetrical tilt grain boundaries (GBs) with different tilt axes in Cu and Al and their interaction with vacancies and interstitials are studied using atomistic computer simulations with embedded-atom potentials. The lowest defect formation energy in a GB is found to correlate with the GB energy in both Cu and Al. Importantly, vacancies and self-interstitials in GBs have comparable formation energies, suggesting that both defects are equally important for GB diffusion and other properties. Vacancies in GBs can be either localized at certain sites or be delocalized over several sites. Some GB sites do not support a stable vacancy at all. Self-interstitial atoms can occupy relatively open interatomic positions, form split dumbbell configurations, or give rise to highly delocalized displacement zones. These structural forms of point defects have been observed across the whole set of twelve GBs in Cu and six GBs in Al studied in this paper as well as in our previous work [Interface Science 11, 131–148 (2003)]. It is suggested that these structural forms are general to all GBs in fcc metals. They can be explained by the existence of internal stresses and alternating tension and compression regions in the GB core.     

Size effects in the hardness of fcc metals on micro- and nanoscales

The size effects in the hardness of three fcc metals, namely, Ni, Cu, and Al, are studied by micro- and nanoindentation, and the boundaries of regions with size effects of various types and the characters of these effects are determined.     

Can vacancies lubricate dislocation motion in aluminum?

The interaction of vacancy with dislocations in Al is studied using the semidiscrete variational Peierls-Nabarro model with ab initio determined gamma surface. For the first time, we confirm theoretically the so-called vacancy lubrication effect on dislocation motion in Al, a discovery that can settle a long-standing controversy in dislocation theory for fcc metals. We provide insights into the lubrication effect by exploring the connection between dislocation mobility and its core width. We predict an increased dislocation splitting in the presence of vacancy. We find that on average there is a weak repulsion between vacancies and dislocations which is independent of dislocation character.     

Calculation of the activation energy for surface self-diffusion of transition-metal atoms

The cohesion-based approach developed earlier for describing the adsorptive properties of d-metal atoms on d substrates was used to calculate the self-diffusion on the (111) and (100) planes of fcc metals, and the (110) plane of bcc metals. The results of the calculation are compared with the data obtained by other researchers and with available measurements. Fiz. Tverd. Tela (St. Petersburg) 41, 11–13 (January 1999)     

A novel potential: the interlayer potential for the fcc (111) plane family

We propose a novel interlayer potential, which is different from usual interatomic potentials. The interlayer potential represents the interaction between atomic layers in a layered material. Based on the Chen-M?bius inversion method in combination with ab initio calculations, the interlayer interactions are obtained for the face centered cubic (fcc) (111) planes. In order to check the validity of our interlayer potential, we calculate the intrinsic stacking fault energy (γ(sf)) and the surface energy (γ(s)) of five metals: Al, Ni, Cu, Ag and Au. The predicted γ(sf) and γ(s) values are compared with the theoretical results obtained from direct calculations and also with the available experimental data. Using the interlayer potentials, we also investigate the phonon dispersion and phonon density of state in the fcc (111) plane family of the considered metals.     

Universal relationships for the phonon spectra in BCC,FCC, and HCP crystals with a short-range interatomic interaction

The frequencies of the phonon branches that correspond to the vibrations of the close-packed atomic planes in bcc, fcc, and hcp crystals with short-range interatomic interaction are shown to be described by a universal relationship, which only contains two parameters for each branch, for any polarization λ. These phonon branches correspond to the (ξ, ξ, 0) direction in bcc crystals, the (ξ, ξ, ξ) direction in fcc crystals, and the (0, 0, ξ) direction in hcp crystals. This universal relationship can only be violated by long-range interactions, namely, the interactions outside the sixth coordination shell in a bcc crystal, the fifth coordination shell in an fcc crystal, and the eleventh or tenth coordination shell in an hcp crystal. The effect of these long-range interactions for each phonon branch can be quantitatively characterized by certain parameters Δ _nλ, which are simply expressed in terms of the frequencies of three phonons of the branch. The values of these parameters are presented for all bcc, fcc, and hcp metals whose phonon spectra are measured. In most cases, the proposed relationships for the frequencies are found to be fulfilled accurate to several percent. In the cases where the Δ _nλ parameters are not small, they can give substantial information on the type and scale of long-range interaction effects in various metals.     

Diffusion of Al in ion-implanted α-Zr and α-Hf

The diffusion of Al in the group IVa metals Zr and Hf has been studied for the first time in the temperature ranges 600°–800°C (Zr) and 750°–900°C (Hf) using ion-beam techniques. Diffusion couples were created by ion-implantation. The time-dependent diffusion profiles were monitored by the use of the Nuclear Resonance Broadening (NRB) technique. The linear Arrhenius plots extracted from the measured diffusivities indicate that the diffusivity of implanted Al in Zr and Hf can be described by the activation energyQ=2.9±0.2eV and 3.7±0.3eV and the pre-exponential factorD ₀=17±42cm²/s and 170±600cm²/s, respectively.     

Predicted diffusion rates on fcc (001) metal surfaces for adsorbate/substrate combinations of Ni, Cu, Rh, Pd, Ag, Pt, Au

We investigate the diffusion of a single metal atom on the surface of a fcc (001) metal. Two points concerning the application of kinetic models to diffusion were considered. First, we test the assumption of kinetic models that diffusion occurs via a sequence of uncorrelated jumps. Second, when kinetic models are applicable we predict reasonable values of the kinetic rate constants.

Direct molecular dynamics (MD) simulations were performed for Ag on Ag(001) and Rh on Rh(001) systems. Diffusion was found to obey an Arrhenius-type dependence on temperature in both systems. The barriers and prefactors extracted from the MD results agree with estimates made from transition state theory (TST) and the experimental values for the Rh system. We conclude that kinetic models are applicable to diffusion on fcc (001) surfaces.

Transition state theory was then used to estimate diffusion parameters for all other adsorbate/ substrate combinations of the metals Ni, Cu, Rh, Pd, Ag, Pt, and Au. These results indicate that the characteristics of diffusion are primarily a property of the adsorbate. We also predict Ag atoms to have an anomalously low diffusion barrier on all of the substrates in this study. We use the accurate many-body density functional based MD/MC-CEM potential energy surface which allows us to consistently treat these multi-component systems.