Self-interstitial Configurations Research Articles

MD simulation of vacancy and interstitial diffusion in FeCr alloy

The diffusion mobility of iron and chromium atoms in Fe-9%Cr and Fe-20%Cr alloys for temperature up to 1000 K has been studied by molecular dynamics simulation. Both vacancy and interstitial migration of atoms has been considered. Corresponding diffusion coefficients of iron and chromium atoms, as well as the diffusion coefficients of a vacancy and self-interstitial configuration, have been evaluated. The values obtained for the vacancy diffusion satisfactory agree with experimental results taken from the literature.

Distribution of niobium atoms in self-interstitial configurations in binary alloys Zr–(0.5–3)%Nb after passing the atomic displacements cascade

The Zr–Nb alloys are widely used structural materials of modern nuclear power plants, where they undergo a significant neutron irradiation. In the present work, the cascades of atomic displacements in the Zr–n%Nb binary alloy (n = 0.5%, 1%, 1.5%, 2%, 2.5%, 3%) at temperatures 0 and 600 K are studied by means of the molecular dynamics simulation. The parameters of primary radiation damage are obtained. The results show that niobium atoms are actively involved in the formation of self-interstitial configurations: the fraction of niobium atoms in these structures is significantly higher than in the matrix, it ranges from 34% to 45% for considered alloys. Mostly, the niobium atoms form single interstitials: their fraction is no less than 82% depending on the niobium fraction in the matrix.

A tungsten-rhenium interatomic potential for point defect studies

A tungsten-rhenium (W-Re) classical interatomic potential is developed within the embedded atom method interaction framework. A force-matching method is employed to fit the potential to ab initio forces, energies, and stresses. Simulated annealing is combined with the conjugate gradient technique to search for an optimum potential from over 1000 initial trial sets. The potential is designed for studying point defects in W-Re systems. It gives good predictions of the formation energies of Re defects in W and the binding energies of W self-interstitial clusters with Re. The potential is further evaluated for describing the formation energy of structures in the σ and χ intermetallic phases. The predicted convex-hulls of formation energy are in excellent agreement with ab initio data. In pure Re, the potential can reproduce the formation energies of vacancies and self-interstitial defects sufficiently accurately and gives the correct ground state self-interstitial configuration. Furthermore, by including liquid structures in the fit, the potential yields a Re melting temperature (3130 K) that is close to the experimental value (3459 K).

Primary radiation damage of Zr-0.5%Nb binary alloy: atomistic simulation by molecular dynamics method

Ab initio calculations predict high positive binding energy (∼1 eV) between niobium atoms and self-interstitial configurations in hcp zirconium. It allows the expectation of increased niobium fraction in self-interstitials formed under neutron irradiation in atomic displacement cascades. In this paper, we report the results of molecular dynamics simulation of atomic displacement cascades in Zr-0.5%Nb binary alloy and pure Zr at the temperature of 300 K. Two sets of n-body interatomic potentials have been used for the Zr-Nb system. We consider a cascade energy range of 2–20 keV. Calculations show close estimations of the average number of produced Frenkel pairs in the alloy and pure Zr. A high fraction of Nb is observed in the self-interstitial configurations. Nb is mainly detected in single self-interstitial configurations, where its fraction reaches tens of percent, i.e. more than its tenfold concentration in the matrix. The basic mechanism of this phenomenon is the trapping of mobile self-interstitial configurations by niobium. The diffusion of pure zirconium and mixed zirconium-niobium self-interstitial configurations in the zirconium matrix at 300 K has been simulated. We observe a strong dependence of the estimated diffusion coefficients and fractions of Nb in self-interstitials produced in displacement cascades on the potential.

Effective Atomic Displacements in Fe-9at.%Cr Alloy

A computer simulation of atomic displacement cascades in Fe-9at.%Cr binary alloy has been performed by molecular dynamics method for temperature of 300 K and cascade energies from 100 eV to 20 keV. The average number of Frenkel pairs produced in cascade has been calculated. The data on point defect clusterization have been obtained. Obtained evaluations of effective fraction of surviving defects are well approximated by the sum of power and linear functions of cascade energy. Increased chromium fraction in the self-interstitial (SIA) configurations has been observed and has been explained by combination of two factors: positive binding energy of Cr atom with SIAs and mobility of SIA configuration. The diffusion coefficient of single SIA configuration in the matrix of pure bcc Fe has been evaluated for the temperature range of 300 – 1000 K. We have prepared 100 group neutron cross-sections of effective displacement generation in Fe-9at.%Cr binary alloy. It has been shown that effective dpa generation rate can be 2-3 times lower than corresponding rates of conventional dpa generation rate.

Self-interstitials structure in the hcp metals: A further perspective from first-principles calculations

We study the structure of several standard and non-standard self-interstitial configurations in a series of hcp metals, by using Density Functional Theory as embodied in the computer codes SIESTA and WIEN2k. The considered metals include Be, Mg, Ti, Zr, Co, Zn, and Cd, thus spanning the whole range of experimental c/a ratios, different kinds of bonding, and even magnetism (Co). The results show the importance of low symmetry configurations, closely related to the non-basal crowdion, in order to rationalize the experimental data on self-interstitial structure and migration.

Effect of Strain Field on Threshold Displacement Energy of Tungsten Studied by Molecular Dynamics Simulation**Supported by the National Natural Science Foundation of China under Grant Nos 11375242, 91026002, 91426301 and 11405231, the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No XDA03010301. WS and RJK acknowledge the support of the Office of Fusion Energy Sciences, U.S.

The influence of strain field on defect formation energy and threshold displacement energy (Ed) in body-centered cubic tungsten (W) is studied with molecular dynamics simulation. Two different W potentials (Fikar and Juslin) are compared and the results indicate that the connection distance and selected function linking the short-range and long-range portions of the potentials affect the threshold displacement energy and its direction-specific values. The minimum Ed direction calculated with the Fikar potential is 〈100〉 and with the Juslin potential is 〈111〉. Nevertheless, the most stable self-interstitial configuration is found to be a 〈111〉-crowdion for both the potentials. This stable configuration does not change with the applied strain. Varying the strain from compression to tension increases the vacancy formation energy while decreases the self-interstitial formation energy. The formation energy of a self-interstitial changes more significantly than a vacancy such that Ed decreases with the applied hydrostatic strain from compression to tension.

Stability of concentration-related self-interstitial atoms in fusion material tungsten**Project supported by the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant Nos. A0920502051411-5 and 2682014ZT30), the Program of International Science and Technology Cooperation, China (Grant No. 2013DFA51050), the National Magnetic Confinement Fusion Science Program, China (Grant Nos. 2011GB112001 and 2013GB110001), the National High Technology Research

Based on the density functional theory, we calculated the structures of the two main possible self-interstitial atoms (SIAs) as well as the migration energy of tungsten (W) atoms. It was found that the difference of the 〈110〉 and 〈111〉 formation energies is 0.05–0.3 eV. Further analysis indicated that the stability of SIAs is closely related to the concentration of the defect. When the concentration of the point defect is high, 〈110〉 SIAs are more likely to exist, 〈111〉 SIAs are the opposite. In addition, the vacancy migration probability and self-recovery zones for these SIAs were researched by making a detailed comparison. The calculation provided a new viewpoint about the stability of point defects for self-interstitial configurations and would benefit the understanding of the control mechanism of defect behavior for this novel fusion material.

Energetics and configurations of He–He pair in vacancy of transition metals

We report an atomistic study of energetics and configurations of He–He pair in vacancy of bcc transition metals (V, Nb, Ta, Cr, Mo, W, and Fe) using first-principles methods. The results show He-vacancy attractions in the group VB metals are 2–3 times weaker than those in Cr, Mo, W and Fe. The 〈111〉 dumbbell configuration for He–He pair in vacancy is the most stable except for V. Calculated formation energies of He–He pair in vacancy of group VB metals (3.2–3.95eV) are systematically lower than those of group VIB and VIIIB metals (4.25–5.67eV), while He–He distance for V metal is greater than other metals. He–metal repulsion is stronger than He–He due to longer He–metal distance in metal vacancy. Calculated densities of states provide a reasonable explanation for most stable configuration; thus the stability of He–He pairs depends strongly on the electronic structure of the host and insignificantly on its atomic size. Moreover, the group-specific trends of He–He and self-interstitial configurations are discussed.

Self-interstitial configurations in hcp Zr: a first principles analysis

The alignment of vacancy loops and voids along basal planes observed in irradiated Zr and Zr alloys requires anisotropic point-defect transport with a dominant contribution along the basal plane. For neutron irradiation, this can be explained by one-dimensional mobility of self-interstitial atom (SIA) clusters, but experiments with electron irradiation indicate unambiguously that even single SIA should exhibit anisotropic diffusion. No experimental information is available on SIA properties in Zr and the previous ab initio calculations did not provide any evidence of anisotropic diffusion mechanisms. An extensive investigation of SIAs in Zr has been performed from first principles using two different codes. It was demonstrated that the simulation cell size, type of pseudopotential, exchange-correlation functional and the c/a ratio are crucially important for determining the properties of interstitials in hcp Zr. The most stable SIA configurations lie in the basal plane, which should lead to SIA diffusion mainly along basal planes.

Formation of dislocation loops during He clustering in bcc Fe

The clustering of helium in bcc (body centered cubic) iron and the growth of a helium bubble are simulated at the atomistic level for the helium-rich vacancy-poor condition. It is shown that a dislocation loop is formed as a sequential collection of 〈111〉 crowdions, the latter being the most stable self-interstitial atom configuration in the presence of a He cluster.

Hydrogen interaction with point defects in tungsten

First-principles calculations were used in determining the binding and trapping properties of hydrogen to point defects in tungsten. Hydrogen zero-point vibrations were taken into account. It was concluded that the monovacancy can hold up to five hydrogen atoms at room temperature. The hydrogen was found to distort the self-interstitial atom configuration geometry. The interaction of hydrogen with the transmutation reaction impurities Re and Os were studied. It was found that the substitutional Re and Os have a negligible effect on the hydrogen trapping whereas the interstitial Os may increase the hydrogen inventory in tungsten.

Prediction of the formation of stable periodic self-interstitial cluster chains [(I4)m,m=1–4] in Si under biaxial strain

Using density functional theory calculations, we examined the structure and stability of extendable self-interstitial cluster configurations (In,n=12,16) with four-atom periodicity in crystalline silicon under biaxial strain (−4%≤ε≤4%) on Si(100). In the absence of strain, the ground state configurations of I12 and I16 share a common structure (I12-like) with C2h symmetry and a four-atom repeating unit; however, we identified an extended configuration based on I4 (D2d symmetry) cluster aggregates [(I4)m(m=3,4)] along ⟨110⟩ that is more favorable under certain magnitudes of strain. While both the I12-like and (I4)m configurations exhibit relative stabilities that are a function of both strain and orientation, the larger (I4)m orientation effect is the primary reason that these structures are preferred in both highly tensile and highly compressive environments. This suggests that I4 derivatives may participate in the growth transition of Si self-interstitial clusters in the compact-to-extended size regime (10≤n≤20) under strain.

Self-interstitial configuration in molybdenum studied by modified analytical embedded atom method

The stability of various atomic configurations containing a self-interstitial atom (SIA) in a model representing Mo has been investigated using the modified analytical embedded atom method (MAEAM). The lattice relaxations are treated with the molecular dynamics (MD) simulation at absolute zero of temperature. Six relatively stable self-interstitial configurations and formation energies have been described and calculated. The results indicate that the [111] dumbbell interstitial S111 has the lowest formation energy, and in ascending order, the sequence of the configurations is predicted to be S111, C, S110, T, S001 and O. From relaxed displacement field up to the fifth-NN atoms of six configurations, we know that the relaxed displacements depend not only on separation distances of the NN atoms from the defect centre but also strongly on the direction of the connected line between the NN atoms and the defect centre. The equilibrium distances between two nearest atoms in the core of the S111, C, S110, T, S001 and O configurations are 0.72a, 0.72a, 0.71a, 0.72a, 0.70a and 0.70a, respectively.

Correlation between self-diffusion in Si and the migration mechanisms of vacancies and self-interstitials: An atomistic study

The migration of point defects in silicon and the corresponding atomic mobility are investigated by comprehensive classical molecular-dynamics simulations using the Stillinger-Weber potential and the Tersoff potential. In contrast to most of the previous studies both the point defect diffusivity and the self-diffusion coefficient per defect are calculated separately so that the diffusion-correlation factor can be determined. Simulations with both the Stillinger-Weber and the Tersoff potential show that vacancy migration is characterized by the transformation of the tetrahedral vacancy to the split vacancy and vice versa and the diffusion-correlation factor ${f}_{V}$ is about 0.5. This value was also derived by the statistical diffusion theory under the assumption of the same migration mechanism. The mechanisms of self-interstitial migration are more complex. The detailed study, including a visual analysis and investigations with the nudged elastic band method, reveals a variety of transformations between different self-interstitial configurations. Molecular-dynamics simulations using the Stillinger-Weber potential show that the self-interstitial migration is dominated by a dumbbell mechanism, whereas in the case of the Tersoff potential the interstitialcy mechanism prevails. The corresponding values of the correlation factor ${f}_{I}$ are different, namely, 0.59 and 0.69 for the dumbbell and the interstitialcy mechanisms, respectively. The latter value is nearly equal to that obtained by the statistical theory which assumes the interstitialcy mechanism. Recent analysis of experimental results demonstrated that in the framework of state-of-the-art diffusion and reaction models the best interpretation of point defect data can be given by assuming ${f}_{I}\ensuremath{\approx}0.6$. The comparison with the present atomistic study leads to the conclusion that the self-interstitial migration in Si should be governed by a dumbbell mechanism.

Multiscale modeling of crowdion and vacancy defects in body-centered-cubic transition metals

We investigate the structure and mobility of single self-interstitial atom and vacancy defects in body-centered-cubic transition metals forming groups 5B (vanadium, niobium, and tantalum) and 6B (chromium, molybdenum, and tungsten) of the Periodic Table. Density-functional calculations show that in all these metals the axially symmetric ⟨111⟩ self-interstitial atom configuration has the lowest formation energy. In chromium, the difference between the energies of the ⟨111⟩ and the ⟨110⟩ self-interstitial configurations is very small, making the two structures almost degenerate. Local densities of states for the atoms forming the core of crowdion configurations exhibit systematic widening of the ``local'' $d$ band and an upward shift of the antibonding peak. Using the information provided by electronic structure calculations, we derive a family of Finnis-Sinclair-type interatomic potentials for vanadium, niobium, tantalum, molybdenum, and tungsten. Using these potentials, we investigate the thermally activated migration of self-interstitial atom defects in tungsten. We rationalize the results of simulations using analytical solutions of the multistring Frenkel-Kontorova model describing nonlinear elastic interactions between a defect and phonon excitations. We find that the discreteness of the crystal lattice plays a dominant part in the picture of mobility of defects. We are also able to explain the origin of the non-Arrhenius diffusion of crowdions and to show that at elevated temperatures the diffusion coefficient varies linearly as a function of absolute temperature.

First-principles calculation of intrinsic defect formation volumes in silicon

We present an extensive first-principles study of the pressure dependence of the formation enthalpies of all the know vacancy and self-interstitial configurations in silicon, in each charge state from -2 through +2. The neutral vacancy is found to have a formation volume that varies markedly with pressure, leading to a remarkably large negative value (-0.68 atomic volumes) for the zero-pressure formation volume of a Frenkel pair (V + I). The interaction of volume and charge was examined, leading to pressure--Fermi level stability diagrams of the defects. Finally, we quantify the anisotropic nature of the lattice relaxation around the neutral defects.

Small self-interstitial clusters in GaAs

Recent studies have shown evidence for the aggregation of self-interstitials inion-implanted Si, resulting in nanoscopic damage structures. Similarly,self-interstitial atoms are expected to play an important role for defect clusteringin ion-implanted GaAs. Accurate first-principles total-energy calculations arereported for different As and Ga self-interstitial configurations. These results areused to study by first-principles total-energy calculations the structural andelectronic properties of small complexes involving self-interstitials and/orantisites.

Self-Interstitial Configuration in B.C.C. Metals. An Analysis Based on Many-Body Potentials for Fe and Mo

A computer simulation study of the static distortion and stability of self-interstitials in Fe and Mo is presented. Many-body potentials of the type Embedded Atom and Embedded Defect, both developed by us, are employed. We confirm a result found earlier, that relatively short-range potentials predict the (measured) 〈110〉 dumbbell configuration to be of minimum energy, while longer range ones favour 〈111〉 extended structures. This finding is rationalized by considering the resulting different energy distributions within the defect cores. Also, for most potentials studied more than one mechanically stable interstitial is found. Based on the analysis of the saddle point configurations obtained with either interatomic potential, interstitial migration via both short and long jumps are expected in Fe, whereas only short jumps would be relevant in Mo.

Atomistic simulation of ideal shear strength, point defects, and screw dislocations in bcc transition metals: Mo as a prototype.

Using multi-ion interatomic potentials derived from first-principles generalized pseudopotential theory, we have studied ideal shear strength, point defects, and screw dislocations in the prototype bcc transition metal molybdenum (Mo). Many-body angular forces, which are important to the structural and mechanical properties of such central transition metals with partially filled d bands, are accounted for in the present theory through explicit three- and four-ion potentials. For the ideal shear strength of Mo, our computed results agree well with those predicted by full electronic-structure calculations. For point defects in Mo, our calculated vacancy-formation and activation energies are in excellent agreement with experimental results. The energetics of six self-interstitial configurations have also been investigated. The 〈110〉 split dumbbell interstitial is found to have the lowest formation energy, in agreement with the configuration found by x-ray diffuse scattering measurements. In ascending order, the sequence of energetically stable interstitials is predicted to be 〈110〉 split dumbbell, crowdion, 〈111〉 split dumbbell, tetrahedral site, 〈001〉 split dumbbell, and octahedral site. In addition, the migration paths for the 〈110〉 dumbbell self-interstitial have been studied. The migration energies are found to be 3--15 times higher than previous theoretical estimates obtained using simple radial-force Finnis-Sinclair potentials. Finally, the atomic structure and energetics of 〈111〉 screw dislocations in Mo have been investigated. We have found that the so-called ``easy'' core configuration has a lower formation energy than the ``hard'' one, consistent with previous theoretical studies. The former has a distinctive threefold symmetry with a spread out of the dislocation core along the 〈112〉 directions, an effect which is driven by the strong angular forces present in these metals. \textcopyright{} 1996 The American Physical Society.