Point Defect Pairs Research Articles

An object kinetic Monte Carlo method to model precipitation and segregation in alloys under irradiation

A method based on object kinetic Monte Carlo that can account for segregation and precipitation in metallic alloys in the presence of both vacancies and self-interstitials is presented. Here the model has been applied specifically to FeCr alloys, but could be used for other alloys with proper parametrization. The model is based on the division of the simulation box into cells where only the local concentration of the alloy is considered and not the explicit location of each alloy atom, in a mean field type of approach. This concentration, together with those of neighboring cells, is used to bias defect migration taking into account the proper thermodynamics of the alloy at hand and the stiffness coefficient to include neighboring effects. The novelty of this implementation is, among other things, the explicit description of mixed pairs of point defects with the alloy element: vacancy-Cr (VCr) and self-interstitial-Cr (ICr) whenever necessary. This explicit description allows the temperature dependence of defect evolution to be correctly reproduced. In this paper we present the model in detail for the particular case of processes that take place in the presence of vacancies, to show the robustness and applicability of this method.

Annihilation of point defect pairs in freely suspended liquid-crystal films

We study the annihilation of topological defect pairs in the quasi-twodimensional (2D) geometry of freely suspended smectic films. This elementary process is at the basis of all models describing the statistics of complex defect patterns. We prepare pairs with opposite topological charges and retrieve the interaction mechanisms from their trajectories. The square-root dependence of the defect separation on the time until annihilation and the asymmetry in propagation velocities of the opponents predicted by theory are confirmed. The importance of defect orientations is demonstrated. Trajectories are in general curved, depending on the mutual orientations (phase mismatch) of the defects and on the orientation of the pair respective to the far, undisturbed director. The experiments provide the basis for an adaption of the theoretical models to the real complexity of the annihilation.

Theory of The Oxidation of Metals and Semiconductors: The Phenomenon of Isoparametric Generation of Nonstoichiometric Point Defects in Anodic Oxide Films

A unified theory of the oxidation of materials is formulated, according to which the differences between these processes are related to the degree of deviation from equilibrium of the processes of the generation and recombination of point defects at the boundary of the oxide film, which are responsible for mass transfer. Anodic oxidation occurs under nonequilibrium conditions and is controlled by the rate of generation of two types of basic point defects. The generation of both defects is characterized by the identity of parameters, and occurs as a result of a jump of the same particle (oxygen ion or metal) at the boundary of the oxide film, and this explains the phenomenon of simultaneous mobility of anions and cations. The mechanisms of isoparametric generation of a pair of point defects are proposed: the initiating jump mechanism and the displacement mechanism. Their implementation in oxides with excess or deficiency of oxygen is shown. Criteria are proposed for determining the mechanism of generation of defects during the oxidation of various substances. The conditions of thermal oxidation are close to equilibrium, and point defects have time to recombine at the oxide boundary; therefore, defects with a higher recombination activation energy predominate.

Continuum Modelling of Silicon Diffusion and Activation in in0.53Ga0.47As

A continuum based-model of Silicon diffusion in ion-implanted InGaAs is presented. Several 5×1014 10keV Si+ implants into InGaAs were Rapid Thermal Annealed (RTA) at 750°C ranging from 10-40s. Box-like profiles characteristic of concentration-dependent diffusion were observed, similar to furnace anneals reported previously. Diffusivity extractions were carried out using FLOOPS (Florida Object Oriented Process Simulator), using point defect pairs, and Fermi level effects. Overall consideration of model fits and possible options for further development are suggested.

An atomistic picture of the diffusion of two vacancies forming a di‐vacancy in Si

A method is proposed to calculate the formation of a point defect pair in Si based on an atomistic picture. As an illustration, the capturing of a vacancy (V) by another V forming a di‐vacancy is described semi‐quantitatively. It is shown that in Si, the number of most likely diffusion paths of two vacancies V to form a di‐vacancy is limited. The energetically most favorable diffusion paths are the twelve zigzag Si chains surrounding the V along the ⟨110⟩ directions. Systematically calculating all of the irreducible configurations of two vacancies, each with its weight (=total number of each possible configuration), enables determining all possible V diffusion paths with their relative weights. This obtained picture is different from diffusion in the continuum model, which does not take into account the anisotropy of covalent bonds in the diamond lattice. The proposed approach is a first step towards the calculation of the effective “capture cross‐section” for the formation of point defect pairs that can be used in continuum models.

Quasi chemical and defect correlation models for intermetallic compounds with B2-structure: new applications

A generalized, quantitative, and predictive statistical-thermodynamic model is proposed employing a quasi-chemical argument for description of thermodynamic behavior and ordering phenomena in B2 ordered binary intermetallic materials. A modified procedure is given for the application of the Bethe-Guggenheim QC method which takes into account the presence of all possible defects in the structure, both vacancies and anti-structure atoms. Interactions between nearest-neighbor atoms result in correlations between their arrangements in the crystal lattice. The QC method which can be regarded as the simplest form of the cluster variation method takes these correlations into consideration by describing the formation of point defect pairs and assuming random distribution of these point defect pairs. The results are compared with those obtained by the defect correlation model, a simple Ising-type model which is, however, able to describe defect clusters formed by two, three or even more atoms or vacancies in non-frustrated crystal lattices like the B2 structure. Both modeling approaches were applied for description of thermodynamic activities and vacancy concentrations over composition range and temperature in non-stoichiometric B2 ordered intermetallic compounds with triple-defect mechanism (PdIn, NiGa, and CoGa), as well as with substitutional (anti-structure) defect mechanism (FeCo, NiZn, AgMg). The (hypothetical) critical temperatures of the order–disorder transformations were derived from the model calculations. Comparison with a wealth of experimental data provided in the literature confirms the viability of these simple models.

On the Stacking Fault Energy of Fe-18 Pct Mn-0.6 Pct C-1.5 Pct Al Twinning-Induced Plasticity Steel

The stacking fault energy (SFE) of Fe-18 pct Mn-0.6 pct C-1.5 pct Al twinning-induced plasticity (TWIP) steel was measured using weak-beam dark-field imaging of dissociated dislocations observed in transmission electron microscopy. The SFE was found to be 30 mJ/m2. A relatively wide scatter was observed in the experimentally measured partial dislocation separation of screw dislocations. It is argued that the anomalously wide partial dislocation separation is due to the interaction of point-defect pairs involving interstitial C atoms with the strain field of the partial dislocations. Internal friction (IF) experiments were carried out to detect the presence of point-defect pairs that might affect the dislocation separation, and a clear Finkelshtein–Rosin (FR) peak related to point-defect pairs involving interstitial C atoms was observed in the IF spectrum.

On Understanding Stacking Fault Formation in Ice

Despite dedicated efforts aimed at revealing possible molecular structures of the ice defects associated with stacking faults in ice (I), these molecular arrangements have remained a puzzle. Here we demonstrate how the reorganization of water molecules on different faces of ice (I) can facilitate formation of stacking faults within a crystal. We show that a pair of point defects can manifest a particular combination of coupled five- and eight-membered rings (5-8 rings). These structural motifs can facilitate a shift in layers within an ice (I) crystal, thereby inducing stacking faults. Furthermore, the presence of molecular solutes such as methane at the ice interface appears to trigger the formation of coupled 5-8 rings. The observation of such coupled 5-8 ring defects provides insights into the possible molecular mechanisms of stacking fault formation in ice (I) and has implications for ice crystal growth phenomenology and the consequent physical and chemical properties of ice.

Charged inclusion in nematic liquid crystals

We present a general theory of liquid crystals under inhomogeneous electric field in a Ginzburg-Landau scheme. The molecular orientation can be deformed by electric field when the dielectric tensor is orientation dependent. We then investigate the influence of a charged particle on the orientation order in a nematic state. The director is aligned either along or perpendicular to the local electric field around the charge, depending on the sign of the dielectric anisotropy. The deformation becomes stronger with increasing the ratio Ze/R, where Ze is the charge and R is the radius of the particle. Numerical analysis shows the presence of defects around the particle for large Ze/R. They are nanometer-scale defects for microscopic ions. If the dielectric anisotropy is positive, a Saturn ring defect appears. If it is negative, a pair of point defects appear apart from the particle surface, each being connected to the surface by a disclination line segment.

Point-defect properties of and sputtering events in the {001} surfaces of Ni3Al I. Surface and point-defect properties

Constant-area and fully relaxed molecular dynamics methods are employed to study the properties of the surface and point defects at and near {001} surfaces of bulk and thin-film Ni, Al and Ni3Al respectively. The surface tension is larger than the surface energy for all {001} surfaces considered in the sequence: Al (1005 mJ m−2)< Ni3Al (mixed Ni–Al plane outermost, 1725 mJ m−2)< Ni3Al (all-Ni-atoms plane outermost, 1969 mJ m−2)< Ni (1993 mJ m−2). For a surface of bulk Ni3Al crystal with a Ni–Al mixed plane outermost, Al atoms stand out by 0.0679 Å compared with the surface Ni atoms and, for the all-Ni-atoms surface, Al atoms in the second layer stand out by 0.0205 Å compared with Ni atoms in the same layer. Vacancy formation energies are about half the bulk values in the first layer and reach a maximum in the second layer where the atomic energy is close to the bulk value but the change in embedding energy of neighbouring atoms before and after vacancy formation is greater than that in the bulk. Both the vacancy formation energy and the surface tension suggest that the fourth layer is in a bulk state for all the surfaces. The formation energy of adatoms, antisite defects and point-defect pairs at and near {001} surfaces of Ni3Al are also given.

Defect configurations and dynamical behavior in a gay-berne nematic emulsion

To model a nematic emulsion consisting of a surfactant-coated water droplet dispersed in a nematic host, we performed a molecular dynamics simulation of a droplet immersed in a system of 2048 Gay-Berne ellipsoids in a nematic phase. Strong radial anchoring at the surface of the droplet induced a Saturn ring defect configuration, consistent with theoretical predictions for very small droplets. A surface ring configuration was observed for lower radial anchoring strengths, and a pair of point defects was found near the poles of the droplet for tangential anchoring. We also simulated the falling ball experiment and measured the drag force anisotropy, in the presence of strong radial anchoring as well as zero anchoring strength.

Nucleation of Topological Dipoles¶in Nematic Liquid Crystals

A topological dipole is a pair of point defects with opposite topological charges. In this paper we show by example how the nucleation of such a dipole within a smooth field can drive a metastable state into a stable one. Building on our previous work, we construct a mathematical model for the dynamics of both monopoles and dipoles in a capillary filled with a nematic liquid crystal. Though our analysis is fit for liquid crystals, a similar mechanism is also likely to apply to the field theory for other ordered media.

Mechanism of dislocation climb in binary and mixed III-V semiconductors

Abstract A model for dislocation climb is proposed, and its underlying basis is that dislocations can act as sources and sinks for point defects. By invoking this property, the pair of point defects required for climb can be produced simultaneously at the dislocation core even when only one type of point defect is absorbed at the core. In real materials where supersaturation of one type of point defect is present, an asymmetry exists in the climb behaviour of α and β dislocations. Also, the presence of phase separation and atomic ordering in mixed III-V materials imposes a drag on dislocation climb. The supporting arguments have been developed.

Determination of Diffusion Parameters for Arsenic

AbstractThis paper deals with an analysis of the oxynitridation and direct nitridation experiments of Fahey et al.(1984[1]). The inconsistencies in the evaluation of the fiactional component of diffusion for aisenic are discussed. Using a recently developed diffusion model an explanation for the diffusion data for arsenic is given. The standard equation for analyzing diffusion under nonequilibrium conditions is shown to lead to erroneous results. A consistent treatment must account for the concentrations of arsenic, point defects and arsenic point defect pairs. Pair formation kinetics must be included. Values are presented for the diffusion constants DIAs, DVAS, and the reaction constants kIAs, kVAs depending on the fractional interstitial component of diffusion .

ANELASTIC INTERACTION BETWEEN MOVING KINK AND MOBILE PAIRS OF POINT DEFECTS

The micro-diffusion equation for Zener pairs and asymmetric pairs of point defects in fcc metals under the action of periodic distributional moving sources of inner stress have been solved by using finite Fourier transformation and Laplace transformation. Finite sum formulae for rigidity and damping coefficient of a kink have been obtained.Numerical results are given. A simple analytic result is obtained for anelastic interaction between edge dislocation and asymmetric pairs of point defects, which is found to be in agreement with other results based on a different approach.The enhanced internal friction due to the interaction between dislocation and point defects is discussed.

Relaxation modes of point defect pairs in ionic crystals: Approximate solutions for the three-shell model

Precise studies of the lattice parameters as a function of composition in LixTiS2 TiS2 provide conclusive evidence that a single-phase product exists for all x values. The data indicate that the TiS2 lattice expands on intercalation with Li because of charge transfer from the Li+ to TiS2- and not because of a propping of the layer by the Li+. Trends in the lattice parameters and the thermoelectric power suggests that there is a change in the composition-dependent electron transfer near x=13. For x<13 a rigid band model describes the electron donation. These results are consistent with recent band structure calculations.

Relaxation modes of point defect pairs in ionic crystals: Approximate solutions for the threeshell model

A perturbation technique is used to obtain first-order expressions for the relaxation frequencies for the relaxation modes of the three-shell model of pairs of coupled defects moving on the same fcc lattice (e.g. divalent cation-cation vacancy in the rocksalt structure) or on interpenetrating fcc lattices (vacancy pairs in the rocksalt structure, or interstitial anion—excess valency cation in the fluorite structure). For the dielectrically-active T lu modes, expressions are given for the relaxation intensities in the zero-order approximation. These results are then used to discuss experimental data for NaCl and KCl containing divalent cations and for alkaline earth fluorides containing trivalent rare earth ions.

Stress-induced interaction of pairs of point defects in bcc solutions

The theory of the stress-induced interaction1 has been used to calculate the interaction energies of interstitials, vacancies as well as interstitials and vacancies, and host atom displacements around a vacancy and interstitial in four metals with the bcc lattice: aFe, V, Nb, and Ta. The cases of interstitial location both in octahedral and tetrahedral interstices are discussed. The elastic constants, cohesion energy (for vacancies), Born-Karman constant of the host lattice and coefficients of the concentration expansion of the solid solution lattice due to the interstitials are the numerical parameters of the theory. The computer calculation was carried out in the general form suitable for any interstitial in these four metals and specifically for the interstitial solutions H, O, N in V, Nb, Ta and C, and N in aFe. In the only case when the quantitative comparison of the calculated characteristics with the experimental one is possible (interaction of the vacancies with C in aFe), there is good agreement between calculated and observed values.

Elastic Interaction of Small Defects and Defect Clusters in Hexagonal Crystals

AbstractAn analysis is given of the elastic interaction between small defects and/or defect clusters in hexagonal crystals. Simple explicit expressions for the interaction energy are obtained directly from the Green's function given by Kröner. Some typical calculated results are presented for various combinations of axially symmetric defects, e.g., a pair of point defects, a pair of dislocation loops, and a point defect and a dislocation loop. Applications to a study of Frenkel defects recombination processes in irradiated hexagonal crystals are discussed.

Asymptotic Interaction Energy between Pairs of Point Defects in Cubic Metals

We have calculated the asymptotic interaction energies between pairs of interstitial Cu atoms in Cu and between pairs of vacancies in Al, Na, and K. These calculations were performed using the asymptotic equations of the method of lattice statics. The exact method of lattice statics is based on the Fourier transformation of the direct-space equilibrium equations for a supercell of the lattice containing one defect surrounded by a large number of host atoms. The asymptotic interaction energies were compared with the corresponding results obtained from the exact method of lattice statics. This comparison indicates that elasticity theory cannot be used to obtain strain-field interaction energies for defects nearer than at least 26 or 27 neighbors from each other, and is probably not truly valid until much larger interdefect separations are considered. This result places a heavy restriction on the use of elasticity theory in practical defectinteraction calculations.