Defect Kinetics Research Articles

A comparative study of primary damage state in Ni and NiCr/NiFe with a model grain boundary structure

The interaction of displacement cascades with atomic interfaces, specifically grain boundaries (GBs) is of great importance in design and development of radical advanced Ni-based super alloys with self-healing capabilities for future fission reactors. In this work, pure Ni and NiCr (with 5, 10, 15 and 20 at.% Cr content) and NiFe (with 5, 10 and 15 at.% Fe content) alloys with symmetric tilt Σ5[1 0 0](0 1¯ 3)θ = 37° GBs are used as model structures to study the influence of Cr and Fe on the primary and long-term radiation response of Ni-based alloys with microstructures. Molecular dynamics is used in simulating the primary damage event and the continuous ion bombardments in NiCr/NiFe structures to qualitatively represent the severe irradiation condition expected in next-generation fission reactors. In general, we observe that the GBs in “pristine” and “damaged” (∼after being continuously bombarded) forms preferentially absorb radiation-produced interstitials both Ni and Cr/Fe, over vacancies which results in accumulation and clustering of immobile vacancies in the grain interiors. The presence of Cr and Fe does not significantly affect the sink properties of our model GB and therefore, does not change the clustering behavior of excess vacancies in the bulk grains on picosecond (ps) timescale. The only evident phenomenon is a notable variation in the energetics and probably kinetics of point defects that slightly changes the evolution pattern of displacement cascades in the damage regions on ps timescale. The GB roughening incident is also observed in both Ni and NiFe/NiCr alloys during irradiation. In alloys with GBs, we also analyzed changes in the short range order parameter of irradiated structures. Our results indicate that in the primary event of radiation damage, a single bombardment is not enough to induce any trend in ordering or disordering of Cr and Fe solutes; in a prolonged irradiation, on the other hand, MD results reveal a very weak tendency of solutes to diffuse toward each other, although we did not observe any obvious Cr or Fe clustering in any of the performed displacement cascade simulations. Eventually, on ps timescale, we conclude that the Cr and Fe solutes contribute in enhancement of radiation tolerance of binary alloys in similar ways as Ni atoms do; but further details about the diffusion mechanisms of solutes on a longer timescale is essentially required to have more accurate predictions from a radiation damage perspective.

Iron Interstitial Defects Stability: Under the Uniaxial Stress Effect

Understanding of defect kinetics under stress fields is important for multiscale modeling of nuclear materials degradation. By means of molecular dynamics (MD) simulation, the formation and migration energies were evaluated for self-interstitial atom (SIA) and SIA clusters (1~3 interstitials) in alpha Fe. Effects of 0~3% uniaxial tensile [100] strains were tested for SIAs of <110> and <111> dumbbell configurations. Regarding the stability, the <111> dumbbell configurations becomes more stabilized at larger strains and larger clusters. For the mobility, the diffusion of single SIA defects under tensile stresses were traced. Under the free-strain condition, the diffusivity of the SIA clusters has a gradual transition from three dimensional (3D) to one dimensional (1D) at saturated strain. The 1D transition was observed for large clusters and large strain while the 3D transition was for small clusters and lower strains and presented mainly for the <110> SIA alignment configuration. Under the tensile stress and for small clusters, diffusivity enhancement is bigger at a higher temperature. However, the temperature effect was small for larger clusters. These effects of strain fields can be explained by elastic interaction between defects and applied stress fields.

Impact of growth rate on graphene lattice-defect formation within a single crystalline domain

Chemical vapor deposition (CVD) is promising for the large scale production of graphene and other two-dimensional materials. Optimization of the CVD process for enhancing their quality is a focus of ongoing effort and significant progress has been made in decreasing the defectiveness associated with grain boundaries and nucleation spots. However, little is known about the quality and origin of structural defects in the outgrowing lattice which are present even in single-crystalline material and represent the limit of current optimization efforts. We here investigate the formation kinetics of such defects by controlling graphene’s growth rate over a wide range using nanoscale confinements. Statistical analysis of Raman spectroscopic results shows a clear trend between growth rate and defectiveness that is in quantitative agreement with a model where defects are healed preferentially at the growth front. Our results suggest that low growth rates are required to avoid the freezing of lattice defects and form high quality material. This conclusion is confirmed by a fourfold enhancement in graphene’s carrier mobility upon optimization of the growth rate.

Kinetics of cluster-related defects in silicon sensors irradiated with monoenergetic electrons

This work focuses on the kinetic mechanisms responsible for the annealing behavior of radiation cluster-related defects with impact on the electrical performance of silicon sensors. Such sensors were manufactured on high resistivity n-type standard float-zone (STFZ) and oxygen enriched float-zone (DOFZ) material and had been irradiated with mono-energetic electrons of 3.5 MeV energy and fluences of 3 × 1014 cm−2 and 6 × 1014 cm−2. After irradiation, the samples were subjected either to isochronal or isothermal heat treatments in the temperature range from 80 °C to 300 °C. The specific investigated defects are a group of three deep acceptors [H(116 K), H(140 K), and H(152 K)] with energy levels in the lower half of the band gap and a shallow donor E(30 K) with a level at 0.1 eV below the conduction band. The stability and kinetics of these defects at high temperatures are discussed on the basis of the extracted activation energies and frequency factors. The annealing of the H defects takes place similarly in both types of materials, suggesting a migration rather than a dissociation mechanism. On the contrary, the E(30 K) defect shows a very different annealing behavior, being stable in STFZ even at 300 °C, but annealing-out quickly in DOFZ material at temperatures higher than 200 °C , with a high frequency factor of the order of 1013 s−1. Such a behavior rules out a dissociation process, and the different annealing behavior is suggested to be related to a bistable behavior of the defect.

An analysis of two classes of phase field models for void growth and coarsening in irradiated crystalline solids

A formal asymptotic analysis of two classes of phase field models for void growth and coarsening in irradiated solids has been performed to assess their sharp-interface kinetics. It was found that the sharp interface limit of type B models, which include only point defect concentrations as order parameters governed by Cahn-Hilliard equations, captures diffusion-controlled kinetics. It was also found that a type B model reduces to a generalized one-sided classical Stefan problem in the case of a high driving thermodynamic force associated with the void growth stage, while it reduces to a generalized one-sided Mullins-Sekerka problem when the driving force is low in the case of void coarsening. The latter case corresponds to the famous rate theory description of void growth. Type C models, which include point defect concentrations and a non-conserved order parameter to distinguish between the void and solid phases and employ coupled Cahn-Hilliard and Allen-Cahn equations, are shown to represent mixed diffusion and interfacial kinetics. In particular, the Allen-Cahn equation of model C reduces to an interfacial constitutive law representing the attachment and emission kinetics of point defects at the void surface. In the limit of a high driving force associated with the void growth stage, a type C model reduces to a generalized one-sided Stefan problem with kinetic drag. In the limit of low driving forces characterizing the void coarsening stage, however, the model reduces to a generalized one-sided Mullins-Sekerka problem with kinetic drag. The analysis presented here paves the way for constructing quantitative phase field models for the irradiation-driven nucleation and growth of voids in crystalline solids by matching these models to a recently developed sharp interface theory.

First‐Principles Characterization of Equilibrium Vacancy Concentration in Metamagnetic Shape Memory Alloys: An Example of Ni2MnGa

Despite the fact that there is evidence for the important role that vacancies play in the martensitic transformation (MT) behavior of metamagnetic shape memory alloys (MMSMAs), little theoretical – and even experimental – work on the thermodynamics and kinetics of point defects in these systems has been carried out. Since the MT behavior of MMSMAs has a great influence on their magneto‐caloric response, investigating the vacancy evolution in MMSMAs has potentially a significant technological impact. Scarcity of studies may be due to the limited characterization capability available for studying vacancy properties as well as their impacts on the materials performance. The current work seeks to introduce the application of the grand‐canonical dilute‐solution model to the investigation of equilibrium (thermal) populations of point defects in Ni2MnGa, used as a prototypical MMSMA. The thermodynamic model is coupled to first‐principles calculations of the energetics of defect‐containing supercell structures. Such characterization capability allows for more realistic investigations of MMSMAs with the vacancy degree of freedom taken into account and subsequently opens up many interesting research topics. Here we demonstrate the capability of the first principles based characterization method by investigating the role of vacancy concentration in the kinetics of order–disorder (ODO) process and the MT temperature of Ni2MnGa.

Influence of the lattice constant on defects in cerium oxide.

The lattice constant has a crucial effect on the defect chemistry and defect kinetics in solid state materials. However, within density functional theory, some functionals perform badly in reproducing the experimental lattice constant. In this study, energies of defect formation, interaction and migration in the model system ceria were calculated for different lattice constants to investigate the impact on the energies. The GGA+U functional in the PBE and PBEsol parametrization as well as the hybrid functional HSE06 were applied and results are compared among these three commonly applied functionals. The results suggest a strong influence of the lattice constant on the energies especially regarding oxygen ion migration. This influence has an impact on the accurate prediction of defect properties from first principles but can also be utilized for specific tailoring of material properties by chemo-mechanical design. In addition, the issue of the correct lattice constant, which should be used in the defect calculations, is discussed in this paper.

Evolution of lateral V-defects on InGaN/GaN on Si(111) during PAMBE: the role of strain on defect kinetics

In this article, a unique correlation has been established between the defect kinetics of III-nitride adatoms and strain during plasma assisted molecular beam epitaxial (PAMBE) growth of InGaN/GaN heterostructures on silicon(111) for the first time.

Расчет влияния плотности ионного тока и температуры на кинетику накопления точечных дефектов при облучении кремния легкими ионами

AbstractNumerical calculations of the accumulation kinetics of point defects—vacancies and divacancies—under the irradiation of Si with ions having masses of M _1 ≤ 31 amu and energies of E ≤ 100 keV under various irradiation conditions are performed. The previously proposed diffusion-coagulation model is used without application of the “weak diffusion” approximation, which was performed during its analytical implementation. The main peculiarities of the dependences of the concentrations of vacancies and divacancies on the dose, ion-current density, and temperature under irradiation are analyzed. A physical interpretation of these results is given. The developed computing complex is rather flexible and makes it possible to analyze the influence of model input parameters by means of their variation and include additional processes into consideration if necessary.

The Interface Influence in TiN/SiN x Multilayer Nanocomposite Under Irradiation

The paper focuses on studying the kinetics of radiation-induced point defects formed in TiN/SiN x multilayer nanocomposites with account of their generation, diffusion recombination, and the influence of sinks functioning as interfaces. In order to describe the kinetics in nanocrystalline TiN and amorphous SiN x phases, a finite-difference method is used to solve the system of balance kinetic equations for absolute defect concentrations depending on the spatiotemporal variables. A model of the disclination-dislocation interface structure is used to study the absorption of radiation-induced point defects on the boundaries in created stress fields. It is shown that the interface effectively absorbs point defects in these phases of TiN/SiN x multilayer nanocomposite, thereby reducing their amount within the space between phases. This behavior of point defects partially explains a mechanism of the radiation resistance in this type of nanocomposites.

Mathematical modeling of failure process of AlMg2.5 alloy during highand very high cycle fatigue

Forecasting the limit of endurance in the high- and very high cycle loading range (102-1010) is an actual problem of aircraft engine construction and high-speed rail transport. It involves the development of models and their experimental verification, taking into account the stages of development of damage and the development of fatigue cracks in a damaged medium. The proposed model of the damage evolution, taking into account the kinetics of defects and effects of microplasticity, was used to study the process of fatigue failure of a structural alloy AlMg2.5. The model parameters were identified and verified using experimental data on static, dynamic and fatigue loading, as well as tests at various temperatures. The Weller curve is numerically constructed. It agrees well with experiment in the range of high cycle fatigue. The duality effect of the S-N diagram is described. A computational experiment on the effect of dynamic loading on fatigue strength showed a weak dependence of the fatigue limit on preliminary dynamic strain. It is confirmed by experimental data. Comparison of various mathematical packages and numerical methods for solving the constructed system of differential equations carried out. The optimality of the Adams method and its modifications for numerical integration of the problem under consideration is shown. Wolfram Mathematica is the preferred software package for numerical solution. The problem of convergence of the numerical solution has been investigated.

Structure, Stability, and Kinetics of Vacancy Defects in Monolayer PtSe2: A First-Principles Study.

The recent epitaxial growth of monolayer PtSe2 has raised hope for its novel applications in valleytronic, spintronic, and energy-harvesting devices. Compared with 2H-phase transition-metal dichalcogenides, the 1T-phase PtSe2 is much less studied and this is especially true for its defects behaviors and their influence on electronic properties. In this article, we systemically explore the structure, stability, and kinetics of both Pt and Se vacancies in monolayer PtSe2 using first-principles calculations. By examining the relative energies of these vacancies, we identify the most stable Se/Pt single and double vacancies. In particular, we reveal a new type of Se double vacancy structure with the lowest energy. Energetically, both Se and Pt single vacancies prefer to combine to form double vacancies. All Se and Pt vacancies have remarkable influence on the electronic properties. Moreover, Pt single and double vacancies can introduce strong spin polarization in PtSe2, which may be promising for spintronic applications. These findings not only enrich the fundamental understanding of 1T-phase PtSe2 but also provide useful guidance to design PtSe2 for its optoelectronic and spintronic applications.

Bimodal Structures of Solids Obtained under Megaplastic Strain

The evolution of the defect structure of aluminum alloys of different compositions under megaplastic strain at a high quasi-hydrostatic pressure has been studied. The theoretical analysis and numerical calculation of the evolution of the defect structure of solids (metals) under this impact have been performed within the three-defect model of nonequilibrium evolution thermodynamics. The calculation of defect kinetics shows that the presence of coarse grains submerged into a matrix of fine grains at specified parameters and coefficients leads to the additional generation of dislocations and, as a consequence, to the greater dislocation strengthening of a material.

Study of point defects diffusion in nickel using kinetic activation-relaxation technique

Point defects play a central role in materials properties. Yet, details regarding their diffusion and aggregation are still largely lacking beyond the monomer and dimer. Using the kinetic Activation Relaxation Technique (k-ART), a recently proposed off-lattice kinetic Monte Carlo method, the energy landscape, kinetics and diffusion mechanisms of point defect in fcc nickel are characterized, providing an exhaustive picture of the motion of one to five vacancies and self-interstitials in this system. Starting with a comparison of the prediction of four empirical potentials — the embedded atom method (EAM), the original modified embedded atom method (MEAM1NN), the second nearest neighbor modified embedded atom method (MEAM2NN) and the Reactive Force Field (ReaxFF) —, it is shown that while both EAM and ReaxFF capture the right physics, EAM provides the overall best agreement with ab initio and molecular dynamics simulations and available experiments both for vacancies and interstitial defect energetics and kinetics. Extensive k-ART simulations using this potential provide complete details of the energy landscape associated with these defects, demonstrated a complex set of mechanisms available to both vacancies and self-interstitials even in a simple environment such as crystalline Ni. We find, in particular, that the diffusion barriers of both vacancies and interstitials do not change monotonically with the cluster size and that some clusters of vacancies diffuse more easily than single ones. As self-interstitial clusters grow, moreover, we show that the fast diffusion takes place from excited states but ground states can act as pinning centers, contrary to what could be expected.

Thermal effects in ion irradiated Ti2AlC and Ti3SiC2

Abstract Structural materials in nuclear systems endure a harsh environment, like high temperature, high stress and intense radiation fluxes. MAX phases have been suggested for advanced nuclear reactor applications due to their excellent irradiation tolerance, especially in high temperature irradiation. To better understand the mechanisms of irradiation tolerance of MAX phases and the evolution of defects in high temperature irradiation, herein, we irradiated Ti 2 AlC and Ti 3 SiC 2 with 3 MeV Au ions at 25 °C, 360 °C and 700 °C to a dose of 1.5 × 10 16 cm −2 , and then thermal annealing at 360 °C and 700 °C were performed for samples irradiated at room temperature to study the defect kinetics. Raman spectrum, GIXRD and TEM were used to characterize microstructural evolution. Our results show that high temperature irradiation causes less damage than room temperature irradiation does in both materials. Fewer defects were produced in Ti 3 SiC 2 than that in Ti 2 AlC during high temperature irradiation. And Ti 2 AlC has a higher defect recovery efficiency than Ti 3 SiC 2 when annealed at high temperature.

In Situ TEM Multi-Beam Ion Irradiation as a Technique for Elucidating Synergistic Radiation Effects.

Materials designed for nuclear reactors undergo microstructural changes resulting from a combination of several environmental factors, including neutron irradiation damage, gas accumulation and elevated temperatures. Typical ion beam irradiation experiments designed for simulating a neutron irradiation environment involve irradiating the sample with a single ion beam and subsequent characterization of the resulting microstructure, often by transmission electron microscopy (TEM). This method does not allow for examination of microstructural effects due to simultaneous gas accumulation and displacement cascade damage, which occurs in a reactor. Sandia’s in situ ion irradiation TEM (I3TEM) offers the unique ability to observe microstructural changes due to irradiation damage caused by concurrent multi-beam ion irradiation in real time. This allows for time-dependent microstructure analysis. A plethora of additional in situ stages can be coupled with these experiments, e.g., for more accurately simulating defect kinetics at elevated reactor temperatures. This work outlines experiments showing synergistic effects in Au using in situ ion irradiation with various combinations of helium, deuterium and Au ions, as well as some initial work on materials utilized in tritium-producing burnable absorber rods (TPBARs): zirconium alloys and LiAlO2.

Inhomogeneous Oxygen Vacancy Distribution in Semiconductor Gas Sensors: Formation, Migration and Determination on Gas Sensing Characteristics

The density of oxygen vacancies in semiconductor gas sensors was often assumed to be identical throughout the grain in the numerical discussion of the gas-sensing mechanism of the devices. In contrast, the actual devices had grains with inhomogeneous distribution of oxygen vacancy under non-ideal conditions. This conflict between reality and discussion drove us to study the formation and migration of the oxygen defects in semiconductor grains. A model of the gradient-distributed oxygen vacancy was proposed based on the effects of cooling rate and re-annealing on semiconductive thin films. The model established the diffusion equations of oxygen vacancy according to the defect kinetics of diffusion and exclusion. We described that the steady-state and transient-state oxygen vacancy distributions, which were used to calculate the gas-sensing characteristics of the sensor resistance and response to reducing gases under two different conditions. The gradient-distributed oxygen vacancy model had the applications in simulating the sensor performances, such as the power law, the grain size effect and the effect of depletion layer width.

Cr-induced fast vacancy cluster formation and high Ni diffusion in concentrated Ni-Fe-Cr alloys

We have performed molecular dynamics (MD) simulations on pure Ni, Ni-Cr, Ni-Fe and Ni-Fe-Cr single phase concentrated solid solution systems to elucidate the kinetics of point defects and vacancy cluster formation. We find that diffusion-based vacancy clustering leads to the formation of stacking fault tetrahedra (SFT) in all of these systems. The presence of Cr leads to faster SFT formation and high Ni diffusion in Ni-Cr binary systems than in pure Ni and Ni-Fe binary systems. The same trend is observed for the ternary systems that have high Cr composition. This Cr-induced effect is due to the low Cr migration barrier that first induces vacancy diffusion and later leads to faster clustering and SFT formation. We find that the fast Ni diffusion is also Cr-induced, where the binding of two vacancies provides much lower migration barrier pathways for Ni diffusion. Due to this ‘Cr-effect’, the vacancy-vacancy pair distribution shows higher peaks in Ni-Cr and Ni-Fe-Cr systems than in pure Ni and Ni-Fe binary systems. The low migration barriers of Cr compared to Ni and Fe are confirmed by density functional theory calculations.

Thermodynamic equilibration of the carbon vacancy in 4H-SiC: A lifetime limiting defect

The carbon vacancy (VC) is a prominent defect in as-grown 4H-SiC epitaxial layers for high power bipolar devices. VC is electrically active with several deep levels in the bandgap, and it is an efficient “killer” of the minority carrier lifetime in n-type layers, limiting device performance. In this study, we provide new insight into the equilibration kinetics of the thermodynamic processes governing the VC concentration and how these processes can be tailored. A slow cooling rate after heat treatment at ∼2000 °C, typically employed to activate dopants in 4H-SiC, is shown to yield a strong reduction of the VC concentration relative to that for a fast rate. Further, post-growth heat treatment of epitaxial layers has been conducted over a wide temperature range (800–1600 °C) under C-rich surface conditions. It is found that the thermodynamic equilibration of VC at 1500 °C requires a duration less than 1 h resulting in a VC concentration of only ∼1011 cm−3, which is, indeed, beneficial for high voltage devices. In order to elucidate the physical processes controlling the equilibration of VC, a defect kinetics model is put forward. The model assumes Frenkel pair generation, injection of carbon interstitials (Ci's) from the C-rich surface (followed by recombination with VC's), and diffusion of VC's towards the surface as the major processes during the equilibration, and it exhibits good quantitative agreement with experiment.

Defects in Na-, K-, and Cd-Doped CuInSe$_2$ : Canonical Thermodynamics Based on Ab Initio Calculations

We extend a canonical-thermodynamic method for computing intrinsic point defect concentrations as a function of chemical stoichiometry and temperature to include extrinsic defect contributions, while applying this method to study defects in CuInSe $_2$ . This method relies on a large set of defect formation energies calculated from first principles, which require corrections for known errors arising from spurious interactions. Guided by recent experimental work exhibiting the complex interplay between Na, K, and Cd incorporation, we examine the behavior of dominant defects as the material composition varies under experimentally relevant conditions. In addition to identifying the regions of composition-parameter space relevant to the incorporation of impurities Na, K, and Cd, and stable against the formation of secondary compounds, we also study defect kinetics susceptible to the presence of these impurities. From this analysis, we propose a simple model for the enhanced diffusion of Cu-vacancies mediated by K, which could lead to the enhanced incorporation of Cd observed experimentally.