Interaction Of Point Defects Research Articles

Structure and interaction of point defects in transition-metal nitrides

Transition-metal nitrides (TMNs) are used in a variety of applications because of their renowned hardness and stability. Departure from the nominal 1:1 stoichiometry is often observed for TMNs and, therefore, defects have a prevalent role on TMN physical properties. Here, we report the results of first-principles calculations on nitrogen and metal point defects in the prototype system of TiN and in HfN and ZrN. We find features which are common to all systems, while we unravel also key differences. In certain cases---for example, N interstitials in TiN---the interaction between defects is attractive and it favors the formation of defect complexes. Other defects, like N interstitials in HfN and ZrN, do not pair up. We also present results on the effect of point defects on the electronic properties of TiN. Finally, we discuss pertinent experimental data and the implications of our findings on the thermal stability of TMN films.

Interaction of point defects in ferroelectrics ‐parameter identification and simulation

AbstractFerroelectric materials are used in a wide field of applications, where they are exposed to a high number of mechanical and electrical load cycles. This involves degradation of the material and a decrease of the electromechanical coupling capability, which is usually called electric fatigue. The causes are assumed to be ionic and electronic charge carriers, which interact with each other, with microstructural elements in the bulk and with interfaces. Accumulation of defects can lead to degradation, mechanical damage and dissociation reactions, for more details see e.g. [3].In order to get a better understanding of the defect accumulation processes, a model based on material forces is used in [6] to simulate the interaction of defects in periodic and in infinite cells. Applying thermodynamically reasonable kinetic laws, defect migration is simulated in a deterministic way in order to understand the general tendency of defect formations. The transversally isotropic material is modelled with linear electromechanical coupling. Here, the defect parameters used in the continuum model are obtained by fitting the results of molecular dynamics (MD) simulations to the continuous spatial fields. Transferring data from the atomic to the continuum level is a field of active research and no unique solution can be presented. On the atomic level, Coulomb–interaction causes a displacement field incompatible to an elastic solution. To address this difficulty, the volume change of a domain around the defect is used to determine defect parameters. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Magnetic origin of nano-clustering and point defect interaction in Fe–Cr alloys: an ab-initio study

To understand the behaviour of point defects generated in irradiated FeCr ferritic/martensitic steels and to identify the kinetic pathways of micro-structural evolution of binary model Fe–Cr alloys, we use a combination of density functional theory (DFT) with statistical approaches involving cluster expansion and Monte Carlo simulations. This makes it possible to generate in a systematic way the low-energy configurations required for the subsequent DFT study of intrinsic defects (vacancies, interstitials) and impurity-defect interactions over the entire range of Fe–Cr alloy compositions. In the limit of low Cr concentration, DFT calculations predict that an intermetallic compound Fe15Cr has the lowest negative heat of formation. At higher Cr concentrations, simulations performed using a 4 × 4 × 4 super-cell show that magnetism is responsible for the nano-segregation of the ferromagnetic Fe15Cr and anti-ferromagnetic (α′-Cr) phases giving rise to the formation of clusters characterised by a very low positive heat of formation. We perform a systematic investigation of formation energies of point defects and their energies of interaction with Cr atoms. Further investigation of interaction of interstitial and vacancy defects with impurities (V, Nb, Ta, Mo, W, Al, Si, P, S) also shows a complex picture of interplay between magnetism and short-range ordering that affects the interaction between defects and impurities in the presence of chromium in Fe-rich alloys.

Interaction of Point Defects with Twin Boundaries in Copper

The interaction between small vacancy clusters and twin boundaries incopper is studied by using many-body potential developed by Acklandet al. for fcc metals. The interaction energies of single-,di- and tri-vacancy clusters with (111) and (112) twin boundaries arecomputed using well established simulation techniques. For (111) twinsthe vacancy clusters are highly repelled when they are on the adjacentplanes, and are attracted when they are away from the boundary. In thecase of (112) twins, vacancy clusters are more attracted to theboundary when they are near the boundary as compared to away from it.Vacancy clusters on both the sides of the boundary are alsoinvestigated, and it is observed that the clusters energetically preferto lie on the off-mirror sites as compared to the mirror positionacross the twin.

Formation energy and interaction of point defects in two-dimensional colloidal crystals

The manipulation of individual colloidal particles using optical tweezers has allowed vacancies to be created in two-dimensional (2d) colloidal crystals, with unprecedented possibility of real-time monitoring the dynamics of such defects (Nature {\bf 413}, 147 (2001)). In this Letter, we employ molecular dynamics (MD) simulations to calculate the formation energy of single defects and the binding energy between pairs of defects in a 2d colloidal crystal. In the light of our results, experimental observations of vacancies could be explained and then compared to simulation results for the interstitial defects. We see a remarkable similarity between our results for a 2d colloidal crystal and the 2d Wigner crystal (Phys. Rev. Lett. {\bf 86}, 492 (2001)). The results show that the formation energy to create a single interstitial is $12% - 28%$ lower than that of the vacancy. Because the pair binding energies of the defects are strongly attractive for short distances, the ground state should correspond to bound pairs with the interstitial bound pairs being the most probable.

Contribution of point defects to the temperature anomaly of the yield stress in single crystals of the Ni3Ge alloy

The temperature dependence of the yield stress τ* Ni 3 Ge single crystals is studied. The temperature dependence τ*(T) in the high-temperature region (above 420 K) is found to be conditioned by thermally activated accumulation of the density of non-screw components of superdislocations. Interaction of point defects with edge dislocations and its effect on the temperature anomaly of the yield stress in Ni 3 Ge single crystals are analyzed. The calculated results are found to agree with experimental data.

Oxygen non-stoichiometry and defect thermodynamics in La 2Ni 0.9Fe 0.1O 4+δ

The oxygen hyperstoichiometry of K 2NiF 4-type La 2Ni 0.9Fe 0.1O 4+ δ , studied by thermogravimetric analysis and coulometric titration in the oxygen partial pressure range 6×10 −5–0.7 atm at 923–1223 K, is considerably higher than that of undoped lanthanum nickelate. The p(O 2)- T- δ diagram of iron-doped lanthanum nickelate can be adequately described by introducing point-defect interaction energy in the concentration-dependent part of defect chemical potentials and accounting for the site-exclusion effects. The critical factors affecting the equilibrium oxygen incorporation process include coulombic repulsion of interstitial anions, trapping of the p-type electronic charge carriers by iron, and interaction between Fe 3+ and holes localized on nickel cations. Due to low chemical expansion of La 2Ni 0.9Fe 0.1O 4+ δ lattice, the thermodynamic functions governing oxygen intercalation, site-blocking factors and hole mobility are all independent of the defect concentrations. The predominant 3+ state of iron cations under oxidizing conditions was confirmed by the Mössbauer spectroscopy. The stability of La 2NiO 4-based phase in reducing atmospheres is essentially unaffected by doping.

Thermally activated glide of edge superdislocations in a single-crystalline Ni3Ge alloy with point defects

Temperature dependence of the yield stress for Ni3Ge single crystals is investigated. Positive temperature dependence of the critical yield stress in the high-temperature region (above 420 K) is attributed to a thermally activated accumulation of a high nonscrew-superdislocation density. The mechanism of interaction of point defects with superdislocations and its contribution to the temperature anomaly is examined. Correlation is found between the calculated contribution from point defects and the observed increase in the critical yield stress with the test temperature.

Molecular dynamics simulations of point defect interactions in Fe–Cr alloys

Predicting the performance of Fe–Cr ferritic martensitic steels in fusion energy environments requires an understanding of point defect properties, including the influence of solutes, impurities and other defects on their migration behavior. This paper presents molecular dynamics simulations of the effect of Cr on the diffusion of single, di- and tri-interstitials in Fe–10%Cr alloys. Two Finnis–Sinclair-type potentials were used to model the Fe–Cr alloys, which alternately describe Cr as under- or over-sized in body-centered cubic Fe. In general, the diffusivity of the single interstitials and di- and tri-interstitial clusters was reduced in the Fe–10%Cr alloys, irrespective of interatomic potential, although the underlying mechanism was different. When Cr is undersized, interstitial diffusion is retarded through a trapping mechanism associated with bound Cr-interstitial (mixed dumbbell) complexes, whereas oversized Cr atoms retard interstitial diffusion by enhancing the rotation frequency away from one-dimensionally mobile 〈1 1 1〉 interstitial dumbbell configurations.

Stress adaptation in ceramic thin films

Two mechanisms by which an inorganic thin film may reversibly adapt to externally imposed strain have been considered: (1) the chemical strain effect and (2) self-organization of polycrystalline macro-domains. The chemical strain effect is due to the transformation of the elastic energy of an externally applied stress into chemical energy of interacting point defects. This effect may be observed in solids with a large concentration of interacting point defects if the interaction is accompanied by a large change in specific volume. Self-organization of polycrystalline macro-domains may take place when single-domain ferroelastic grains minimize intergrain strain via approximate mutual alignment of their crystallographic axes. Each such macro-domain region has a preferred size and direction of alignment. In the presence of externally applied stress, these regions may reorganize, thereby partially converting the elastic energy of the external stress into the elastic energy of intergrain stress. Although very different in nature, both mechanisms result in reversible strain-relaxation. The conditions under which each of these effects may be present are understood well enough to provide clear guidance for preparation of materials and for their incorporation into practical devices.

Atomic kinetic Monte Carlo model based on ab initio data: Simulation of microstructural evolution under irradiation of dilute Fe–CuNiMnSi alloys

The embrittlement of pressure vessel steels under radiation has been long ago correlated with the presence of Cu solutes. Other solutes such as Ni, Mn and Si are now suspected to contribute also to the embrittlement. The interactions of these solutes with radiation induced point defects thus need to be characterized properly in order to understand the elementary mechanisms behind the formation of the clusters formed upon radiation. Ab initio calculations based on the density functional theory have been performed to determine the interactions of point defects with solute atoms in dilute FeX alloys (X = Cu, Mn, Ni or Si) in order to build a database used to parameterise an atomic kinetic Monte Carlo model. Some results of irradiation damage in dilute Fe–CuNiMnSi alloys obtained with this model are presented.

3D Simulation of Point Defect Migration in Ferroelectrics

AbstractElectric fatigue in functional materials involves a set of phenomena which lead to the degradation of materials with an increasing number of electrical cycles. Ionic and electronic charge carriers, later 0 as point defects, interact with each other and with microstructural elements in the bulk and with interfaces, which can lead to degradation, or finally to mechanical damage and dissociation reactions, see e.g. [1].With this in mind, efforts are made to calculate the fields caused by point defects to simulate their interaction as well as to verify the used material parameters. Here, a material with linear electro mechanical coupling is used. The applied methods are integral transforms (Radon Transform) and a combination of Difference Methods and a Fast Fourier Transform to obtain solutions in an infinite domain and under periodic boundary conditions, respectively. The point defect interaction is studied within the framework of material or configurational forces. These forces are used in combination with reasonable kinetic laws to simulate defect migration, cf. [2]. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

On the Atomistic Dynamic Modelling of Simultaneous Diffusion of Dopant and Point Defect (B, V, I) in Silicon Material

Understanding the atomic movements of simultanous diffusion of dopant (B) and point defects (V, I) in silicon is of great importance for both experimental and theoretical diffusion studies. This paper presents the atomistic dynamic diffusion modelling of boron (B), self-interstitial (I) and vacancy (V) process in silicon based on simultaneous diffusion of boron dopant and point defects based on a previous developed theory. The simulation is based on the random walk theory with three main diffusion mechanisms: namely vacancy, interstitial and interstitialcy mechanism. The migration frequencies of dopant and point defects have been programmed based on the experimental diffusion data of boron, vacancy and Si self-interstitial. This simulation procedure can be seen very clearly about the atomic movements, the interactions between dopant and point defects via three diffusion mechanisms. The diffusion depth of B, V, I in very short time can be estimated from the simulation picture on the screen. The simulation results reflect the simultaneous diffusion as well as the interaction of boron and point defects via the three diffusion mechanisms. The point defects (V, I) were generated during the dopant diffusion and they diffused further into the depth as shown in the results of the simulation as well as in the previous published experimental findings.

Defect formation inLaGa(Mg,Ni)O3−δ: A statistical thermodynamic analysis validated by mixed conductivity and magnetic susceptibility measurements

A statistical thermodynamic approach to analyze defect thermodynamics in strongly nonideal solid solutions was proposed and validated by a case study focused on the oxygen intercalation processes in mixed-conducting $\mathrm{La}{\mathrm{Ga}}_{0.65}{\mathrm{Mg}}_{0.15}{\mathrm{Ni}}_{0.20}{\mathrm{O}}_{3\ensuremath{-}\ensuremath{\delta}}$ perovskite. The oxygen nonstoichiometry of Ni-doped lanthanum gallate, measured by coulometric titration and thermogravimetric analysis at $923\char21{}1223\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ in the oxygen partial pressure range $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}0.9\phantom{\rule{0.3em}{0ex}}\mathrm{atm}$, indicates the coexistence of ${\mathrm{Ni}}^{2+}$, ${\mathrm{Ni}}^{3+}$, and ${\mathrm{Ni}}^{4+}$ oxidation states. The formation of tetravalent nickel was also confirmed by the magnetic susceptibility data at $77\char21{}600\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, and by the analysis of $p$-type electronic conductivity and Seebeck coefficient as function of the oxygen pressure at $1023\char21{}1223\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The oxygen thermodynamics and the partial ionic and hole conductivities are strongly affected by the point-defect interactions, primarily the Coulombic repulsion between oxygen vacancies and/or electron holes and the vacancy association with ${\mathrm{Mg}}^{2+}$ cations. These factors can be analyzed by introducing the defect interaction energy in the concentration-dependent part of defect chemical potentials expressed by the discrete Fermi-Dirac distribution, and taking into account the probabilities of local configurations calculated via binomial distributions.

Helium–self-interstitial atom interaction in α-iron

The effect of He impurities on the properties and behavior of self-interstitial atom (SIA) clusters in α-Fe has been simulated by atomistic molecular dynamics (MD) and molecular statics (MS) simulation techniques using semi-empirical interatomic potentials and compared to ab initio electronic structure calculations. The MD simulations reveal many interactions between He and SIA clusters, including a spontaneous SIA–substitutional He recombination and replacement mechanism that ejects He into interstitial positions and a strong interaction between He, in either interstitial or substitutional positions, with SIA and SIA clusters and also with other He atoms. The MS calculations reveal relatively small interaction trapping radii of about 1 nm between interstitial He and SIA cluster complexes, but strong binding energies from 1.3 to 4.4 eV, depending on cluster size and interaction geometry. The comparisons between the ab initio and semi-empirical interactions are in generally good agreement and indicate that the He–point defect interactions in bcc Fe are well represented by considering the displacement (strain) field interactions amongst the defects.

Solute interaction with point defects in α Fe during thermal ageing: A combined ab initio and atomic kinetic Monte Carlo approach

Solute Cu plays a major role in the embrittlement of reactor pressure vessel (RPV) steels under radiation. In RPV steels and dilute FeCu alloys, characterization techniques such as the tomographic atom probe (TAP), or the small angle neutron scattering (SANS) have revealed the formation of solute rich clusters (with Cu, Ni, Mn and Si) under neutron flux. It is thus very important to characterize the interactions of these solutes with radiation-induced point defects in order to understand the elementary mechanisms behind the formation of these clusters. Ab initio calculations based on the density functional theory have been made in order to build a database used to parameterise an atomic kinetic Monte Carlo model. The interactions of point defects and solute atoms in dilute FeX alloys (X = Cu, Mn, Ni or Si) have been evaluated for different configurations of small solute clusters and solute–vacancy complexes. First results obtained with the kinetic Monte Carlo model will be presented and compared to some experimental observations.

Mechanical properties and defect chemistry

A brief overview of changes in mechanical properties of solids driven by the chemistry of point defects is given. Two major types of effects are considered: direct effects caused by non-interacting point defects and collective effects induced by interacting point defects. The first group includes (1) changes in the linear dimensions of a solid in response to a change in defect concentration and (2) stress induced due to an inhomogeneous distribution of point defects, a so-called chemical stress. The second group includes (1) defect order–disorder transitions accompanied by self-strain and (2) deviations from linear elastic behavior due to the dissociation/association of point defects. All of the above become important if the concentration of point defects is very high (above 10 21 cm − 3 ). These effects may lead to significant anomalies in mechanical properties: spontaneous stress and strain and changes in elastic constants. These effects may significantly affect the application of materials with a large concentration of point defects.

Mathematical Modeling of Solid-State Diffusion during Mechanical Alloying

It is known experimentally that solid-state interdiffusion is substantially enhanced during plastic deformation. This is especially noticeable in Mechanical Alloying (MA) which is used for producing a wide range of metastable materials (supersaturated solid solutions, amorphous phases, nanostructures) with unique properties. However, a physical mechanism of enhanced diffusion during MA is not clearly understood yet, and a comprehensive model of this complex phenomenon has not been developed so far. Moreover, the role of the diffusion process in MA is hotly debated in literature. In this work a new, self-consistent mathematical model of solid-state interdiffusion in a binary substitutional system A-B during periodic plastic deformation is developed. The model includes basic physical factors that affect diffusion, such as generation of non-equilibrium point defects by gliding screw dislocations during deformation and their relaxation in periods between impacts. The cross-link terms are considered, and interaction of point defects with edge dislocations and incoherent phase boundary A/B is taken into account. Computer simulation is performed using realistic data (e.g., quasi-equilibrium self-diffusion coefficients known in literature) and the process parameters typical of MA in a vibratory mill. A repeated “deformation-rest” cycle is considered. The results of modeling reveal the physical mechanism of the enhancement of solid-state diffusion by periodic plastic deformation during MA and demonstrate that within the frame of this approach supersaturated solid solutions can form within a reasonably short processing time.

Elasticity of Solids with a Large Concentration of Point Defects

AbstractThe elastic behavior of solids with a large concentration of interacting point defects has been analyzed. The analysis predicts that, in such solids, mechanical stress may be partially relieved by a shift in the association/dissociation equilibrium of the point defects. Association/dissociation of the point defects in response to an external stress will proceed until the decrease in elastic energy is balanced by the increased chemical energy of the defect distribution. The resulting change in the linear dimensions may be called “chemical strain”, in analogy to the previously studied “chemical stress”. A solid in which chemical strain may develop in response to external stress should exhibit two distinct Young's moduli: relaxed, on a time scale which allows the defects to reach equilibrium; and unrelaxed, on a time scale which is too short for the defect equilibrium to be established. Our analysis suggests that materials exhibiting the chemical‐strain effect are capable of reversible adaptation to external mechanical constraints. Measurements on a self‐supported film of Ce0.8Gd0.2O1.9 strongly support the theoretical predictions.

Point Defects Interaction with Extended Defects and Impurities and Its Influence on the Si-SiO<sub>2</sub> System Properties

The type and density of the point defects that are generated in the Si surface layer during thermal oxidation depend on the oxidation condition: temperature, cooling rate, oxidation time, impurity content. The interaction between point defects with extended defects and impurities affect the Si-SiO2 interface properties. The influence of point defects may be diminished and the interface properties improved by an appropriate choice of oxidation conditions.