The properties and structures of the mono- and the di- vacancy in Cu crystal

The structures and energies of formation and migration of the mono- and di-vacancy in Cu crystal have been described and calculated with modified analytical embedded atom method (MAEAM). The lattice relaxation is considered with molecular dynamics (MD) method at T=0 K. The results show the FN di-vacancy is the most stable and likely occurs in practice from the energy minimization. Compared with the mono-vacancy, the formation energy of the FN di-vacancy is higher than that of a mono-vacancy, but lower than that of two isolated mono-vacancy. The preferred migration mechanism of the FN di-vacancy is multi-jump of either vacancy (rotating the di-vacancy). The calculated migration energy of the FN di-vacancy is lower than that of a mono-vacancy, so the FN di-vacancy is easier to migrate. All of the calculated results are in good agreement with the experimental values.     

Formation mechanism of the di-vacancy in FCC metal Pt

The formation mechanism of the di-vacancy in FCC metal Pt has been studied from the migration of the two vacancies by using the modified analytical embedded atom method (MAEAM). The lattice relaxation resulted from the existence of the vacancies is performed with the molecular dynamics (MD) method. For migration of an isolated vacancy in Pt, the favorable path is the first-nearest-neighbor (1NN) migration. From the minimum formation energy or the maximum binding energy of the di-vacancy, we know that the 1NN configuration of the di-vacancy is the most stable. Up to the fifth-nearest-neighbor (5NN) configuration of the di-vacancy, the migration of the two vacancies is always to approach each other in the shortest paths of 5NN→2NN→1NN, 4NN→1NN, 3NN→1NN and 2NN→1NN.     

Structural properties and diffusion processes of the Cu3Au (0 0 1) surface

The surface relaxation and surface energy of both the mixed AuCu and pure Cu terminated Cu₃Au (0 0 1) surfaces are simulated and calculated by using the modified analytical embedded-atom method. We find that the mixed AuCu termination is energetically preferred over the pure Cu termination thereby the mono-vacancy diffusion is also investigated in the topmost few layers of the mixed AuCu terminated Cu₃Au (0 0 1) surface. In the mixed AuCu terminated surface the relaxed Au atoms are raised above Cu atoms for 0.13 Å in the topmost layer. All the surface atoms displace outwards, this effect occurs in the first three layers and changes the first two inter-layer spacing. For mono-vacancy migration in the first layer, the migration energies of Au and Cu mono-vacancy via two-type in-plane displace: the nearest neighbor jump (NNJ) and the second nearest neighbor jump (2NNJ), are calculated and the results show that the NNJ requires a much lower energy than 2NNJ. For the evolution of the energy requirements for successive nearest neighbor jumps (SNNJ) along three different paths: circularity, zigzag and beeline, we find that the circularity path is preferred over the other two paths due to its minimum energy barriers and final energies. In the second layer, the NN jumps in intra- and inter-layer of the Cu mono-vacancy are investigated. The calculated energy barriers and final energies show that the vacancy prefer jump up to a proximate Cu site. This replacement between the Cu vacancy in the second layer and Cu atom in the first layer is remunerative for the Au atoms enrichment in the topmost layer.     

Radiation-stimulated diffusion in Al–Si alloys

A di-vacancy low-temperature diffusion is proposed to explain diffusion-controlled processes in Al–Si alloys responsible for neutron-induced silicon precipitation. Ab initio calculations of potential barriers for Si atom hopping in aluminium lattice showed that in the case of di-vacancy diffusion, they are small compared with that of mono-vacancy diffusion. The low temperature diffusivity of mono-vacancies is too small to account for the measured Si diffusivities in aluminium. The dependencies of radiation-stimulated diffusion on the neutron flux and on the temperature are obtained and can be used for the experimental verification of the developed model.     

Self-diffusion of BCC transition metals calculated with MAEAM

The energy during the process of self-diffusion in BCC transition metals Fe, W, Mo, Cr, Ta, Nb and V has been calculated by using modified analytic embedded-atom method (MAEAM). For each kind of three diffusion mechanisms nearest-neighbor (NN), next-nearest-neighbor (NNN) and third-nearest-neighbor (TNN), the energy curve is symmetric and the maximum value of the energy appears at the middle point of the diffusion path. Determined mono-vacancy formation energy , migration energy and activation energy Q_1v for self-diffusion agree well with available experimental data of NN diffusion and are better than those obtained by the analytic embedded-atom method (AEAM) and Finnis–Sinclair models. Compared the energies corresponding to three diffusion mechanisms, the NN diffusion needs the lowest activation energy (and thus the lowest migration energy). So that, the NN mono-vacancy diffusion is favorable in BCC transition metals.     

Atomic simulation of the vacancies in BCC metals with MAEAM

The formation energy of the mono-vacancy and both the formation energy and binding energy of the di-and tri-vacancy in BCC alkali metals and transition metals have been calculated by using the modified analytical embedded-atom method (MAEAM). The formation energy of each type of configuration of the vacancies in the alkali metals is much lower than that in the transition metals. From minimum of the formation energy or maximum of the binding energy, the favorable configuration of the di-vacancy and tri-vacancy respectively is the first-nearest-neighbor (FN) or second-nearest-neighbor (SN) di-vacancy and the [112] tri-vacancy constructed by two first-and one second-nearest-neighbor vacancies. It is indicated that there is a concentration tendency for vacancies in BCC metals.     

Atomistic simulation of the vacancy diffusion in (0 0 1) surface of MoTa alloy

The formation and diffusion of a single Mo or Ta vacancy in the (0 0 1) surface of the B₂-type MoTa alloy have been investigated by using modified analytical embedded-atom method (MAEAM). The results show that the effect of the surface on the vacancy is only down to the sixth layer. It is easier for the vacancy to form in the first layer. Comparing the migration energy of the vacancy migrating in the intra-layer, to the upper layer and to the nether layer via 2NN jump, we find that the vacancy in the first or second layer is preferred to migrate in intra-layer, and that in the third or fourth layer is favorable to migrate to the upper layer. Although 1NN jump will result in an anti-site so that a disorder in the order alloy, it may also occur due to the much lower migration energy especially for the vacancy in the second and third layer to migrate to the first and second layer, respectively.     

Interactions between vacancies and prismatic Σ3 grain boundary in α-Al_2O_3:First principles study

Interactions between vacancies and Σ3 prismatic screw-rotation grain boundary in α-Al_2O_3 are investigated by the first principles projector-augmented wave method.It turns out that the vacancy formation energy decreases with reducing the distance between vacancy and grain boundary(GB) plane and reaches the minimum on the GB plane(at the atomic layer next to the GB) for an O(Al) vacancy.The O vacancy located on the GB plane can attract other vacancies nearby to form an O–O di-vacancy while the Al vacancy cannot.Moreover,the O–O di-vacancy can further attract other O vacancies to form a zigzag O vacancy chain on the GB plane,which may have an influence on the diffusion behavior of small atoms such as H and He along the GB plane of α-Al_2O_3.     

Atomistic simulation of the point defects in B2-type MoTa alloy

The formation and migration mechanisms of three different point defects (mono-vacancy, anti-site defect and interstitial atom) in B₂-type MoTa alloy have been investigated by combining molecular dynamics (MD) simulation with modified analytic embedded-atom method (MAEAM). From minimization of the formation energy, we find that the anti-site defects Mo_Ta and Ta_Mo are easier to form than Mo and Ta mono-vacancies, while Mo and Ta interstitial atoms are difficult to form in the alloy. In six migration mechanisms of Mo and Ta mono-vacancies, one nearest-neighbor jump (1NNJ) is the most favorable due to its lowest activation and migration energies, but it will cause a disorder in the alloy. One next-nearest-neighbor jump (1NNNJ) and one third-nearest-neighbor jump (1TNNJ) can maintain the ordered property of the alloy but require higher activation and migration energies, so the 1NNNJ and 1TNNJ should be replaced by straight [1 0 0] six nearest-neighbor cyclic jumps (S[1 0 0]6NNCJ) or bent [1 0 0] six nearest-neighbor cyclic jumps (B[1 0 0]6NNCJ) and [1 1 0] six nearest-neighbor cyclic jumps ([1 1 0]6NNCJ), respectively. Although the migrations of Mo and Ta interstitial atoms need much lower energy than Mo and Ta mono-vacancies, they are not main migration mechanisms due to difficult to form in the alloy.     

Density functional theory investigation of S2 in KCl: evidence for the existence of a di-vacancy site

Electron paramagnetic resonance experiments have shown that, depending on the doping procedure, two different S₂⁻ centers may coexist in KCl. These centers have the ²B_2g and the ²B_3g ground state, respectively. As no experimental ligand hyperfine data are available, it could not be determined whether the S₂⁻ molecular ion replaces a single halide ion (mono-vacancy site) or two nearest neighbor halide ions (di-vacancy site). Also, other defect models could a priory be considered. In this work, cluster in vacuo density functional theory calculations of the g and ³³S hyperfine tensors show that the S₂⁻ ion at a mono-vacancy site has the ²B_2g ground state, whereas S₂⁻ in a di-vacancy exhibits a ²B_3g ground state. For the latter center, the possibility of charge compensation by a cation vacancy is also considered. The calculations indicate that a possible vacancy is not in the direct vicinity (nearest or next-nearest neighbor) of the S₂⁻ ion.     

Properties of mono-vacancy in L12-type Ni3Al ordered alloy

The relaxed structures and the formation and migration energies of the mono-vacancy in L1₂-type Ni₃Al ordered alloy have been investigated by combining the modified analytical embedded-atom method (MAEAM) with molecular dynamics (MD) simulation. The movements of the atoms in the vicinity of the mono-vacancy are toward the vacancy, except for the second-nearest-neighbor Al atoms and the fifth-nearest-neighbor Ni atoms around an Al vacancy and the third-nearest-neighbor Al atoms and the fourth-nearest-neighbor Ni atoms around a Ni vacancy that move outward from the vacancy. Furthermore, each of the atoms in the vicinity of either an Al or a Ni vacancy moves approximately along a line connected between the atom and the vacancy. From energy minimization, it is easy for a Ni vacancy to form and to migrate in one nearest-neighbor jump.     

Ab initio study of palladium and silicon carbide

Ab initio methods have been used to investigate the properties of Pd as impurity in bulk SiC at five charged states within the framework of density functional theory using the local spin density approximation. It was found that Pd interstitials and substitutionals have similar energy to their intrinsic counterparts. In addition, Pd substitutes for a vacancy, di-vacancy, and tri-vacancy with similar energies. Pd diffuses through SiC via an interstitial mechanism employing the tetrahedral sites and Pd can substitute for Si and C at positive charged states. Removing electrons (p-type doping) from SiC lowers the formation and migration energies of Pd defects in SiC for most configurations.     

Ellipsometric configurations using a phase retarder and a rotating polarizer and analyzer at any speed ratio

In this paper,we propose an ellipsometer using a phase retarder and rotating polarizer and analyzer at a speed ratio 1:N.Different ellipsometric configurations are presented by assuming N = 1,2,and 3.Moreover,two values of the offset angle of the retarder are considered for each ellipsometric configuration.The Mueller formalism is employed to extract the Stokes parameters,from which the intensity received by the detector is obtained.The optical properties of c-Si are calculated using all configurations.A comparison between different configurations is carried out considering the effect of the noise on the results and the uncertainties in the ellipsometric parameters as functions of the uncertainties of the Fourier coefficients.It is found that the alignment of the phase retarder has a crucial impact on the results and the ellipsometric configuration with speed ratio 1:1 is preferred over the other configurations.     

Different angle-resolved polarization configurations of Raman spectroscopy: A case on the basal and edge plane of two-dimensional materials

Angle-resolved polarized Raman(ARPR) spectroscopy can be utilized to assign the Raman modes based on crystal symmetry and Raman selection rules and also to characterize the crystallographic orientation of anisotropic materials.However, polarized Raman measurements can be implemented by several different configurations and thus lead to different results. In this work, we systematically analyze three typical polarization configurations: 1) to change the polarization of the incident laser, 2) to rotate the sample, and 3) to set a half-wave plate in the common optical path of incident laser and scattered Raman signal to simultaneously vary their polarization directions. We provide a general approach of polarization analysis on the Raman intensity under the three polarization configurations and demonstrate that the latter two cases are equivalent to each other. Because the basal plane of highly ordered pyrolytic graphite(HOPG) exhibits isotropic feature and its edge plane is highly anisotropic, HOPG can be treated as a modelling system to study ARPR spectroscopy of twodimensional materials on their basal and edge planes. Therefore, we verify the ARPR behaviors of HOPG on its basal and edge planes at three different polarization configurations. The orientation direction of HOPG edge plane can be accurately determined by the angle-resolved polarization-dependent G mode intensity without rotating sample, which shows potential application for orientation determination of other anisotropic and vertically standing two-dimensional materials and other materials.     

Initial stages of contact-induced plasticity in sapphire. II. Mechanisms of plasticity initiation

Part II of the present study focuses on the yield point phenomenon, a discontinuous transition from the apparently elastic to the elastic–plastic regime for basal [C, (0001)], rhombohedral [R, (1 012)] and prism [A, (12 10) and M, (101 0)] planes of sapphire (Al₂O₃) under spherical contacts. The yield point mechanisms are predicted by supplementing the analysis presented in Part I with a criterion for the yield point transition. The proposed criterion accounts for the low-symmetry structure of sapphire. The resulting theoretical predictions are compared with experimental results. This comparison focuses on the effects of surface orientation and loading rates on the yield point load and on the peculiarities of yield point mechanisms, as reflected in the acoustic emission (AE) signals associated with the yield point. For the C plane, the availability of pyramidal and prism slip is expected to be a limiting factor for the yield point transition. Depending on the loading rate, either basal slip or basal twinning dominates the yield point mechanism for the M plane. For the A plane, the yield point is determined by basal slip. For the R plane, a yield point mechanism involving rhombohedral twinning combined with basal or pyramidal slip is possible. Consistent with the experimental results, the highest and the lowest yield point loads are predicted for C and R planes, respectively.     

Dibaryon Signals in NN Scattering Data and Further Measurement at COSY,LEPS and CSR

The NΔ and ΔΔ dibaryon resonances are studied by calculating the NN scattering phase shifts with explicitly coupling these dibaryon channels in a multi-channel coupling calculation with two quark models.These quark models,the chiral quark model and quark delocalization color screening model,describe the NN S-,D-wave phase shifts below the π production threshold quantitatively well.Both quark models predict the ~1D_2 resonance discovered in NN partial wave phase shift analysis and the J=1 or 3 isoscalar resonance recently reported by CELSIUS-WASA Collaboration are NΔ~5S_2 and ΔΔ~7S_3 resonance,respectively.Further measurements at COSY,LEPS and Lanzhou Cooling Storage Ring(CSR) to check the ΔΔ resonance are discussed.     

Influence of the Jahn-Teller distortion on magnetic ordering in TbMn_1-xFe_xO₃

The Jahn-Teller distortion plays an important role in determining the exchange interaction in rare-earth manganites.In this work we study the influence of the Jahn-Teller distortion on the magnetic structures of TbMn1-xFexO3(x = 0,0.02,0.05,0.10,and 0.20) single crystals in the basal MnO2 plane.The decrease in the quadruple splitting with the increasing Fe doping indicates the reduction of the Jahn-Teller distortion,which makes the nearest neighboring(NN) FM interaction dominant over the next nearest neighbor(NNN) AFM interaction.This alteration is favorable for the development of A-type AFM ordering instead of the spiral magnetic ordering,which collapses when x ≥ 0.05.The analysis of dielectric data indicates that the ferroelectricity is arising from the peculiar spiral magnetic ordering.     

Athermal migration of vacancies in iron and copper induced by electron irradiation

Abstract

Irradiation with high-energy particles induces athermal migration of point defects, which affects defect reactions at low temperatures where thermal migration is negligible. We conducted molecular dynamics simulations of vacancy migration in iron and copper driven by recoil energies under electron irradiation in a high-voltage electron microscope. Minimum kinetic energy required for migration was about 0.8 and 1.0 eV in iron and copper at 20 K, which was slightly higher than the activation energy for vacancy migration. Around the minimum energy, the migration succeeded only when a first nearest neighbour (1NN) atom received the kinetic energy towards the vacancy. The migration was induced by higher kinetic energies even with larger deflection angles. Above several electron-volts and a few 10s of electron-volts, vacancies migrated directly to 2NN and 3NN sites, respectively. Vacancy migration had complicated directional dependence at higher kinetic energies through multiple collisions and replacement of atoms. The probability of vacancy migration increased with the kinetic energy and remained around 0.3–0.5 jumps per recoil event for 20–100 eV. At higher temperatures, thermal energies slightly increased the probability for kinetic energies less than 1.5 eV. The cross section of vacancy migration was 3040 and 2940 barns for 1NN atoms in iron and copper under irradiation with 1.25 MV electrons at 20 K: the previous result was overestimated by about five times.     

Atomistic simulation of the point defects in TaW ordered alloy

Combining molecular dynamics (MD) simulation with modified analytic embedded-atom method (MAEAM), the formation, migration and activation energies of the point defects for six-kind migration mechanisms in B₂-type TaW alloy have been investigated. The results showed that the anti-site defects Ta_W and W_Ta were easier to form than Ta and W vacancies owing to their lower formation energies. Comparing the migration and activation energies needed for six-kind migration mechanisms of a Ta (or W) vacancy, we found that one nearest-neighbour jump (1NNJ) was the most favourable because of its lowest migration and activation energies, but it would lead to a disorder in the alloy. One next-nearest-neighbour jump (1NNNJ) and one third-nearest-neighbour jump (1TNNJ) could maintain the ordered property of the alloy but required higher migration and activation energies. So the 1NNNJ and 1TNNJ should be replaced by straight [100] six nearest-neighbor cyclic jumps (S[100]6NNCJ) (especially) or bent [100] six nearest-neighbour cyclic jumps (B[100]6NNCJ) and [110] six nearest-neighbor cyclic jumps ([110]6NNCJ), respectively.     

Kinetics versus thermodynamics in materials modeling: The case of the di-vacancy in iron

Monte Carlo models are widely used for the study of microstructural and microchemical evolution of materials under irradiation. However, they often link explicitly the relevant activation energies to the energy difference between local equilibrium states. We provide a simple example (di-vacancy migration in iron) in which a rigorous activation energy calculation, by means of both empirical interatomic potentials and density functional theory methods, clearly shows that such a link is not granted, revealing a migration mechanism that a thermodynamics-linked activation energy model cannot predict. Such a mechanism is, however, fully consistent with thermodynamics. This example emphasizes the importance of basing Monte Carlo methods on models where the activation energies are rigorously calculated, rather than deduced from widespread heuristic equations.