Migration Of Point Defects Research Articles

The stress-driven diffusion of point defects to a slowly moving crack

The stress-driven diffusion of point defects to a slowly moving brittle crack is studied under the condition of pure drift. In the pure-drift approximation it is assumed that the point defect flow in the vicinity of a crack tip is dominated by the elastic interaction between the stress field of the crack and a point defect and that concentration gradient effects can be neglected. The first-order drift-diffusion equation for a slowly moving crack at uniform velocity is solved. This yields the flow lines of the point defects and the impurity segregation rate directly in terms of the crack growth rate. The flow line patterns reveal important insights with respect to the point defect migration kinetics near a steadily advancing crack.

The stress-driven migration of point defects to a slowly moving crack

The migration kinetics of point defects near a slowly moving brittle crack are studied under the condition of pure drift. In the pure-drift approximation it is assumed that the point-defect flow in the vicinity of a crack tip is dominated by the elastic interaction between the stress field of the crack and a point defect and that concentration gradient effects can be neglected. While such a pure-drift approach has been shown to be useful to calculate the short-time diffusion kinetics of impurity-induced subcritical crack growth, previous applications are based on the drift solutions for a stationary crack. In the present paper, the first-order drift diffusion equation for a slowly moving crack at uniform velocity is solved. This yields the flow lines of the point defects and the impurity segregation rate directly in terms of the crack growth rate. The flow line patterns reveal important insights with respect to the point-defect migration kinetics near a steadily advancing crack. Although the calculation is entirely elastic, it is shown that the present drift model maintains some relevance also in the presence of a plastic zone ahead of the crack tip.

Atomistic study of intrinsic defect migration in 3C-SiC

Atomic-scale computer simulations, both molecular dynamics (MD) and the nudged-elastic band methods, have been applied to investigate long-range migration of point defects in cubic SiC (3C-SiC) over the temperature range from $0.36{T}_{\mathrm{m}}\phantom{\rule{0.2em}{0ex}}$ to $0.95{T}_{\mathrm{m}}$ (melting temperature). The point defect diffusivities, activation energies, and defect correlation factors have been obtained. Stable C split interstitials can migrate via the first- or second-nearest-neighbor sites, but the relative probability for the latter mechanism is very low. Si interstitials migrate directly from one tetrahedral position to another neighboring equivalent position by a kick-in/kick-out process via a split-interstitial configuration. Both C and Si vacancies jump to one of their equivalent sites through a direct migration mechanism. The migration barriers obtained for C and Si interstitials are consistent with the activation energies observed experimentally for two distinct recovery stages in irradiated SiC. Also, energy barriers for C interstitial and vacancy diffusion are in reasonable agreement with ab initio data.

Development of an interatomic potential for phosphorus impurities inα-iron

We present the derivation of an interatomic potential for the iron–phosphorus system basedprimarily on ab initio data. Transferability in this system is extremely problematic, and thepotential is intended specifically to address the problem of radiation damage and pointdefects in iron containing low concentrations of phosphorus atoms. Some preliminarymolecular dynamics calculations show that P strongly affects point defect migration.

Atomic Computer Simulations of Defect Migration in 3C and 4H-SiC

Knowledge of the migration of intrinsic point defects is crucial to understand defect recovery, various annealing stages and microstructural evolution after irradiation or ion implantation. Molecular dynamics (MD) and the nudged-elastic band method have been applied to investigate long-range migration of point defects in SiC over the temperature range from 0.36 to 0.95 Tm , and the defect diffusion coefficient, activation energy and defect correlation factor have been determined. The results show that the activation energies for C and Si interstitials in 3C-SiC are about 0.74 and 1.53 eV, respectively, while it is about 0.77 eV for a C interstitial in 4H-SiC. The minima energy paths reveal that the activation energies for C and Si vacancies are about 4.1 and 2.35 eV, respectively. Finally, the results are discussed and compared with experimental observations and available ab initio data.

Dislocation-driven surface dynamics on solids.

Dislocations are line defects that bound plastically deformed regions in crystalline solids. Dislocations terminating on the surface of materials can strongly influence nanostructural and interfacial stability, mechanical properties, chemical reactions, transport phenomena, and other surface processes. While most theoretical and experimental studies have focused on dislocation motion in bulk solids under applied stress and step formation due to dislocations at surfaces during crystal growth, very little is known about the effects of dislocations on surface dynamics and morphological evolution. Here we investigate the near-equilibrium dynamics of surface-terminated dislocations using low-energy electron microscopy. We observe, in real time, the thermally driven nucleation and shape-preserving growth of spiral steps rotating at constant temperature-dependent angular velocities around cores of dislocations terminating on the (111) surface of TiN in the absence of applied external stress or net mass change. We attribute this phenomenon to point-defect migration from the bulk to the surface along dislocation lines. Our results demonstrate that dislocation-mediated surface roughening can occur even in the absence of deposition or evaporation, and provide fundamental insights into mechanisms controlling nanostructural stability.

Entropy of point defects calculated within periodic boundary conditions

A possibility to calculate both the entropies of formation and migration of point defects in semiconductors is presented. Knowledge of the entropic contributions is especially important for the correct description of high-temperature processes like growth or annealing. Using the self-consistent charge density-functional based tight-binding method (SCC-DFTB) we have calculated the predominant part of the entropy, resulting from lattice vibrations. Strong finite-size effects have been observed while investigating the formation entropies of isolated vacancies in diamond and silicon. We demonstrate how these problems can be overcome with the help of linear elasticity theory.

Effects of implantation temperature on damage accumulation in Al-implanted 4H–SiC

Damage accumulation in 4H–SiC under 1.1 MeV Al22+ irradiation is investigated as a function of dose at temperatures from 150 to 450 K. Based on Rutherford backscattering spectroscopy and nuclear reaction analysis channeling spectra, the damage accumulation on both the Si and C sublattices have been determined, and a disorder accumulation model has been fit to the data. The model fits indicate that defect-stimulated amorphization is the primary amorphization mechanism in SiC over the temperature range investigated. The temperature dependence of the cross section for defect-stimulated amorphization and the critical dose for amorphization indicate that two different dynamic recovery processes are present, which are attributed to short-range recombination and long-range migration of point defects below and above room temperature, respectively. As the irradiation temperature approaches the critical temperature for amorphization, cluster formation has an increasing effect on disorder accumulation, and ion flux plays an important role on the nature and evolution of disorder. Dislocation loops, which are mostly formed under high ion flux, act as sinks for point defects, thereby reducing the disorder accumulation rate.

Kinetics of short-range-ordering in αCu–10at.% Al conducted through differential isothermal calorimetry as influenced by solute–vacancy complexes

A modified first-order kinetic law which takes into account defect decay during an ordering process was employed to predict the short-range-order kinetics of a quenched αCu–10at.% Al alloy, in conjunction with experiments performed by differential isothermal calorimetry (DIC). The effective activation energy of point defect migration and its temperature dependence strongly suggests the contribution of bound vacancies to the ordering process. An estimate of 87.6 kJ mol −1 was made for the activation energy of solute–vacancy migration by applying an effective rate constant, a value which is quite reasonable, since it lies between the activation energy of migration of unbound vacancies and the activation energy for complex dissolution. The isothermal curves were utilized to determine the ordering energy: w=−3.66 kJ mol −1 .

Damage accumulation and dopant migration during shallow As and Sb implantation into Si

The damage evolution and concomitant dopant redistribution as a function of ion fluence during ultra shallow, heavy ion implants into Si have been investigated using medium energy ion scattering (MEIS) and secondary ion mass spectrometry (SIMS). These studies involved As and Sb ions implanted at room temperature, at energies of 2.5 and 2 keV to doses from 3 × 10 13 to 5 × 10 15 cm −2. MEIS is capable of detecting both the displaced atom and implant profiles with sub-nanometre depth resolution. These studies show that for doses up to 1 × 10 14 cm −2 (at which an amorphous layer is formed) the damage build up does not follow the energy deposition function. Instead it proceeds through the initial formation of a ∼4 nm wide amorphous layer immediately under the oxide, that grows inwards into the bulk with increasing dose. This behaviour is explained in terms of the migration of some of the interstitials produced along the length of the collision cascade to the oxide or amorphous/crystal Si interface, where their trapping nucleates the growth of a shallow amorphous layer and the subsequent planar growth inwards of the damage layer. Although for doses ⩾4 × 10 14 cm −2 the As depth profiles agreed well with TRIM calculations, for lower doses As was observed to have a shallower profile, ∼2 nm nearer to the surface. This behaviour is related the growth of the amorphous layer and ascribed to the movement of As into the near-surface amorphous layer (probably mediated by point defect migration) in which the larger dopant is accommodated more easily. SIMS studies have confirmed this dopant segregation effect. Shallow Sb implants also exhibit this novel dopant movement effect for low doses in combination with a damage evolution similar to As.

Fluorine-doping in titanium dioxide by ion implantation technique

We implanted 200 keV F + in single crystalline titanium dioxide (TiO 2) rutile at a nominal fluence of 1 × 10 16 to 1 × 10 17 ions cm −2 and then thermally annealed the implanted sample in air. The radiation damage and its recovery process during the annealing were analyzed by Rutherford backscattering spectrometry in channeling geometry and variable-energy positron annihilation spectroscopy. The lattice disorder was completely recovered at 1200 °C by the migration of point defects to the surface. According to secondary ion mass spectrometry analysis, the F depth profile was shifted to a shallower region along with the damage recovery and this resulted in the formation of an F-doped layer where the impurity concentration steadily increased toward the surface. The F doping proved to provide a modification to the conduction-band edge of TiO 2, as assessed by theoretical band calculations.

Influence of electron irradiation on the martensitic transformation of a binary TiNi shape memory alloy

TiNi shape memory alloy samples annealed at 673 K for 1 h were irradiated within R-phase by 1.7-MeV electrons with different doses. The two-step martensitic transformation temperatures were measured by differential scanning calorimeter. The results indicated that the temperature M s of the onset of R-phase-to-martensite transformation decreased with increasing electron dose. The electron irradiation had a slight effect on the other transformation temperatures. The second lifetime of positrons determined by positron annihilation technology were lowered with increment of the irradiated dose. Relaxation of the elastic stress fields around the Ti 3Ni 4 precipitates was the cause of the observed change of the transformation characteristics because of the migration and accumulation of irradiation-induced point defects.

A new empirical potential for simulating the formation of defects and their mobility in uranium dioxide

An empirical interaction potential has been developed primarily to simulate displacement cascades in a UO2 matrix. After a bibliographical survey revealed that the potentials discussed in the literature are not entirely suitable for describing point defects and their migration, we decided to adapt the most representative of the existing potentials. Our objective was specifically to reproduce transport phenomena, which are fundamental to a satisfactory description of atomic displacement cascades. The modified potential more correctly describes the experimental energies of formation and migration of point defects (interstitials, vacancies, etc.) as well as the oxygen diffusion coefficients in the superionic phase. Thermal expansion, heat capacity and enthalpy are also better modelled over a wide temperature range. The new potential is much more transferable than earlier potentials fitted mainly to the properties of perfect crystals. The initial simulated atomic displacement cascades showed that this potential is well suited to the description of structural effects created by decelerating recoil nuclei in a UO2 matrix.

Electron-irradiation-induced Changes of martensitic transformation characteristics in TiNi shape memory alloys

ABSTRACTTiNi shape memory alloy samples were irradiated within R-phase by 1.7 MeV electrons with different doses. The martensitic transformation temperatures were measured by Differential Scanning Calorimeter (DSC). The results indicated that the temperature Ms of the onset of R-phase-to-martensite transformation decreased with increasing the dose. The electron irradiation had a slight effect on the other transformation temperatures. The second lifetime of positrons determined by Positron Annihilation Technology were lowered with an increment of the irradiated dose. Relaxation of the elastic stress fields around the Ti3Ni4 precipitates was the cause of the observed change of the transformation characteristics because of the migration and accumulation of electron irradiation-induced point defects.

Non-thermodynamic approach to including bombardment-induced post-cascade redistribution of point defects in dynamic Monte Carlo code

The redistribution of the elements as a result of atomic relocations produced by the ions and the recoils due to the ballistic and transport processes is investigated by making use of a dynamic Monte Carlo code. Phenomena, such as radiation-enhanced diffusion (RED) and bombardment-induced segregation (BIS) triggered by the ion bombardment may also contribute to the migration of atoms within the target. In order to include both RED and BIS in the code, we suggest an approach which is considered as an extension of the binary collision approximation, i.e. it takes place “simultaneously” with the cascade and acts as a correction to the particle redistribution for low energies. Both RED and BIS models are based on the common approach to treat the transport processes as a result of a random migration of point defects (vacancies and interstitials) according to a probability given by a pre-defined Gaussian. The models are tested and the influence of the diffusion and segregation is illustrated in the cases of 12 keV 121Sb + implantation at low fluence in SiO 2/Si substrate and of self-sputtering of Ga + ions during profiling of SiO 2/Si interfaces.

Effects of Xe-ion irradiation at high temperature on single crystal rutile

Abstract Rutile (TiO 2 ) single crystals with (1 1 0) orientation were irradiated with 360 keV Xe 2+ ions at 923 K to fluences ranging from 7×10 14 to 1×10 16 Xe/cm 2 . Damage accumulation and evolution were analyzed using Rutherford backscattering spectroscopy combined with ion channeling analysis, and cross-sectional transmission electron microscopy. TiO 2 crystals were found to exhibit a layer-like damage structure after irradiation, with up to three characteristic layers: (1) a thin surface layer denuded of defects; (2) a second layer centered at the peak damage position, consisting of small voids about 1–3 nm in diameter; and (3) a third, deeper layer consisting of large defects such as dislocations and dislocation loops. The defect-denuded layer at the surface results from point defect diffusion and annealing. The voids in the second layer may be attributed to aggregation of vacancies. Point defect migration and precipitation is also responsible for the large defects observed in the deepest layer within the irradiated microstructure. Amorphization was not observed in the crystals irradiated at this high temperature.

Internal friction and effective shear modulus of single-crystal silicon in early stages of oxygen precipitation

Changes in the temperature spectra of the internal friction and the effective shear modulus in single-crystal silicon were studied in the range of 20–400°C in relation to the annealing duration at 400°C. Stable peaks growing in the course of annealing were observed in the absorption spectra. The peaks were attributed to the migration of point defects and their complexes. A suggestion concerning the probable nature of the detected effects was offered.

The Influence of Strain on Point Defect Dynamics

Stress migration of point and open-volume defects is an important problem in a wide variety of applications, ranging from semiconductor technology and basic metallurgical problems to ion implantation and surface modification. Often the driving force of the drift is the local stress field of other defects in the material, although other sources of residual stress as well as external loads play an important role. This paper concentrates on the behaviour of non-equilibrium vacancies in a non-uniformly strained material. Illustrative models of one-dimensional problems are developed and compared to available experimental results in different ion implanted materials.

Tight-Binding Theory of Native Point Defects in Silicon

▪ Abstract Vacancies and self-interstitial defects in silicon are here investigated by means of semi-empirical quantum molecular dynamics simulations performed within the tight-binding model. We extensively discuss the process of formation and migration of native point defects and investigate their interaction and clustering phenomena. The formation of larger stable structures is further studied by combining tight-binding and Monte Carlo simulations. Tight-binding simulation results provide a global picture for defect-induced microstructure evolution in bulk silicon. These results are consistent with state-of-the-art experimental data and elucidate many relevant atomic-scale mechanisms.

Migration of laser-induced point defects in IV–VI compounds

The laser-induced (hω<Eg) transformation of defects in IV–VI compounds is studied. The rate of defect production is found to increase with the free carrier concentration and the electric field strength in the laser wave. The directed migration of both the intrinsic and impurity defects under the combined action of laser radiation and an external electric field is analyzed in terms of a model where the defects are believed to arise mainly from the accumulation of inclusions whose sizes are significantly smaller than the laser wavelength in the crystal. It is proposed that the directed migration and other displacements of the induced defects over the crystal are due to the drag of the activated atoms by the free charge carriers in the laser field EL and the external electric field Eex. The diffusion coefficient and the effective charge of dragged laser-induced defects are estimated.