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.     

The formation and migration of the vacancies in HCP metal Mg

The formation and migration energies of the mono- and di-vacancy in Mg crystal have been calculated using the modified analytical embedded atom method. The results show that, for mono-vacancy, the migration in the basal plane is slightly preferred to the migration out of the basal plane. For di-vacancy, the 1NN and 2NN configurations are not only easier to form but also more stable than the other configurations. The preferred migration mechanisms of the 1NN and 2NN di-vacancy are either invariable 1NN or 2NN configurations during migration in the basal plane or exchange 1NN for 2NN or 2NN for 1NN for migration out of the basal plane. These two-jump migration mechanisms of the di-vacancy, especially the former, are still preferred over the migration of the mono-vacancy. It is concluded that the greater the number of resting vicinity vacancies, the easier the migrating vacancy moves.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Theoretical study of the effects of vacancy and oxygen impurity on Ti_2GaC

This paper presents the mono-vacancy formation and migration energies of each element Ti, Ga, and C in the MAX phase Ti2GaC, which are obtained by first principles calculations. We also calculate the formation energies of oxygen substituting for Ti, Ga, and C and two formation energies of oxygen interstitial in different sites. The results show that the formation energy of oxygen substituting for Ti is the highest, and the formation energies of the O substitution for Ga atoms decrease as the oxygen concentration increases. The two different formation energies of one oxygen interstitial show that the stable site for the oxygen interstitial is at the center of the triangle composed by three Ga atoms. The effects of vacancy,oxygen substitution, and the interstitial on the electronic properties of Ti2GaC are also discussed in light of the density of states and the electron charge density.     

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。     

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.     

Atomic simulation of the dynamic properties for a double period structure with 90° partial dislocation in Si

The dynamic properties of a double period (DP) structure with a 90° partial dislocation were investigated by atomic simulation methods in Si. By the use of molecular dynamics (MD) method, the motion sequences of kinks and reconstruction defect (RD) of DP structure were obtained. Based on the conjugate gradients (CG) results and tight-binding (TB) potential, the formation energies E_f of kinks were computed. In addition, the migration barriers W_m of kinks were also calculated via nudged elastic band (NEB) method with TB potential. The results show that E_f is smaller than W_m, which means that the migration barrier of kink dominates the motion of DP structure. According to the activation energies of short dislocation segments (2.17 eV) and long dislocation segments (1.61 eV), we predict that the experimental results may be between these two values.     

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.     

Ab initio study of formation, migration and binding properties of helium-vacancy clusters in aluminum

Ab initio calculations based on density functional theory have been performed to study the dissolution and migration of helium, and the stability of small helium-vacancy clusters He_nV_m (n, m=0-4) in aluminum. The results indicate that the octahedral configuration is more stable than the tetrahedral. Interstitial helium atoms are predicted to have attractive interactions and jump between two octahedral sites via an intermediate tetrahedral site with low migration energy. The binding energies of an interstitial He atom and an isolated vacancy to a He_nV_m cluster are also obtained from the calculated formation energies of the clusters. We find that the di- and tri-vacancy clusters are not stable, but He atoms can increase the stability of vacancy clusters.     

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.     

A comparative study of the energy migration and energy transfer in highly doped Nd:YAG single crystal

The donor-donor (D-D) energy migration interaction parameter C_DD in high-concentration Nd³⁺-doped YAG laser crystal is estimated, for the first time, by using the Yokota-Tanimoto (Y-T) model and the spectral overlap model (SOM) of Kushida. Firstly, the experimental luminescence decay curves of ⁴F_3/2 state of Nd³⁺ ions in YAG laser crystal at room temperature for 2.0 and 3.0 at% Nd³⁺ concentrations reported by Mao are fitted successfully by using the Y-T model and the parameter C_DD is obtained to be 1.50×10⁻³⁹ cm⁶/s. Secondly, the parameter C_DD is also directly calculated by using the SOM of Kushida: C_DD is calculated to be 2.73×10⁻³⁹ cm⁶/s. By comparing the energy migration interaction parameter C_DD and the donor-acceptor (D-A) energy transfer interaction parameter C_DA (1.794×10⁻⁴⁰ cm⁶/s), it is concluded that energy migration rate between Nd³⁺ ions in YAG laser crystal was about 11 times larger than energy transfer rate, and that energy migration would play a very important role in high-concentration Nd³⁺ -doped YAG laser crystal.     

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.     

Atomistic simulation of point defects at low-index surfaces of noble metals

The formation energies and the migration energies of an isolated vacancy and adatom formed on low-index surfaces are calculated with MAEAM for three noble metals Cu, Ag and Au. The results indicate that the formation energies of an isolated vacancy or adatom increase with increasing atom density in the sequence (1 1 0) → (1 0 0) → (1 1 1), and it is more difficult to form an adatom than to form a vacancy at the same surface. For the mobility of an isolated vacancy, the migration energy grows in the sequence (1 0 0) → (1 1 0) → (1 1 1) for each noble metal. However, a much less migration energy is obtained for the migration of an adatom on (1 1 1) surface.