Activation Energy For Vacancy Migration Research Articles

Diffusion of Vacancies Created by High‐Energy Heavy Ion Strike Into Diamond

A novel technique is proposed to measure how far vacancies diffuse from the initial damaged region with sub‐micrometer resolution. Vacancies created by a single heavy ion with high energy are considered. The most important feature of the single ion track is the quasi‐one‐dimensional vacancy distribution with high volume density, which exceeds 1019 vacancies cm−3. After annealing, the vacancies combine with nitrogen impurities to form nitrogen vacancy (NV) centers. With increasing annealing temperature and time, the distribution of NV centers becomes wider. Therefore, the vacancies created by a single heavy ion are suitable to investigate vacancy diffusion. The activation energy of vacancy migration in diamond is determined to be 2.12 eV, which is in reasonable agreement with reported values.

Athermal migration of vacancies in iron and copper induced by electron irradiation

Irradiation with high-energy particles induces athermal migration of point defects, which affects defect reactions at low temperatures where thermal migration is negligible. We conducted molecular dynamics simulations of vacancy migration in iron and copper driven by recoil energies under electron irradiation in a high-voltage electron microscope. Minimum kinetic energy required for migration was about 0.8 and 1.0 eV in iron and copper at 20 K, which was slightly higher than the activation energy for vacancy migration. Around the minimum energy, the migration succeeded only when a first nearest neighbour (1NN) atom received the kinetic energy towards the vacancy. The migration was induced by higher kinetic energies even with larger deflection angles. Above several electron-volts and a few 10s of electron-volts, vacancies migrated directly to 2NN and 3NN sites, respectively. Vacancy migration had complicated directional dependence at higher kinetic energies through multiple collisions and replacement of atoms. The probability of vacancy migration increased with the kinetic energy and remained around 0.3–0.5 jumps per recoil event for 20–100 eV. At higher temperatures, thermal energies slightly increased the probability for kinetic energies less than 1.5 eV. The cross section of vacancy migration was 3040 and 2940 barns for 1NN atoms in iron and copper under irradiation with 1.25 MV electrons at 20 K: the previous result was overestimated by about five times.

Structural stability and energetics of grain boundary triple junctions in face centered cubic materials

We present a systematic study to elucidate the role of triple junctions (TJs) and their constituent grain boundaries on the structural stability of nanocrystalline materials. Using atomistic simulations along with the nudge elastic band calculations, we explored the atomic structural and thermodynamic properties of TJs in three different fcc materials. We found that the magnitude of excess energy at a TJ was directly related to the atomic density of the metal. Further, the vacancy binding and migration energetics in the vicinity of the TJ were examined as they play a crucial role in the structural stability of NC materials. The resolved line tension which takes into account the stress buildup at the TJ was found to be a good measure in predicting the vacancy binding tendency near the TJ. The activation energy for vacancy migration along the TJ was directly correlated with the measured excess energy. Finally, we show that the resistance for vacancy diffusion increased for TJs with larger excess stored energy and the defect mobility at some TJs is slower than their constituent GBs. Hence, our results have general implications on the diffusional process in NC materials and provide new insight into stabilizing NC materials with tailored TJs.

Formation of vacancy-type defects in titanium nickelide

In this report we briefly review the current state-of-the-art and challenges in determining point defect properties from first-principles calculations as well as from experimental measurements in titanium nickelid. . Based on the vacancy formation energy and their activation energy for vacancy migration in TiNi, vacancy mediated diffusion mechanism was examined. The behavior of vacancy defects in the TiNi structural phase transition has been described.

A Simulation Study of Oxygen-Vacancy Behavior in Strontium Titanate: Beyond Nearest-Neighbor Interactions

We investigate the effect of acceptor-dopant cations on oxygen-vacancy migration in the perovskite oxide SrTiO3 by static lattice simulation techniques. We focus on two themes: dopant cations modifying the activation energies for vacancy migration, and dopant cations binding oxygen vacancies in binary associates. In both cases a variety of defect configurations exceeding the scope of first nearest neighbor (1NN) interaction is examined, i.e. 1NN, 2NN, 3NN, 4NN, and 5NN. The behavior of four divalent dopants (Ni2+, Fe2+, Co2+, and Mn2+) and one trivalent dopant (Al3+) is compared. The simulations predict that the binding energy of an oxygen vacancy to any of these dopants is negative at 1NN sites, but only converges to zero for 4NN sites. In addition the simulations show that the migration energy of a vacancy is affected by an acceptor-dopant cation over a length scale of several unit cells. A simple analytical model is used, together with the calculated site and activation energies, to predict how in gene...

Modifying the barriers for oxygen-vacancy migration in fluorite-structured CeO2electrolytes through strain: a computer simulation study

Static lattice simulation techniques were used to examine the effect of strain on oxygen-vacancy migration in the fluorite-structured oxygen-ion conducting electrolyte CeO2. Activation energies for vacancy migration, ΔEmig, were calculated as a function of isotropic and biaxial strain. In both cases, significant modification of the energetic barriers for oxygen-vacancy migration was found. Analysis of the data yields the activation volumes, ΔVmig, and activation enthalpies, ΔHmig. Simple comparisons based on the calculated data suggest that a biaxial, tensile strain of 4% may increase the in-plane conductivity at T = 500 K by close to four orders of magnitude. Enhancement of the oxygen-ion conductivity of an oxide heterostructure through space-charge effects is also discussed.

Dislocation Loop Formation and Growth under In Situ Laser and/or Electron Irradiation

Vacancies and interstitial atoms are primary lattice (point) defects that cause observable microstructural changes, such as the formation of dislocation loops and voids in crystalline solids. These defects' diffusion properties determine the phase stability and environmental resistibility of macroscopic materials under ambient conditions. Although in situ methods have been proposed for measuring the diffusion energy of point defects, direct measurement has been limited. In this study, we propose an alternative in situ method to measure the activation energy for vacancy migration under laser irradiation using a pulsed laser beam from a laser-equipped high-voltage electron microscope (laser-HVEM). We made in situ observations that revealed the formation and growth of vacancy dislocation loops in an austenitic stainless steel during laser irradiation. These loops continued to grow when thermal annealing was performed after laser irradiation at the same temperature. We anticipate that laser-HVEM will provide a new method for investigating lattice defects.

Predicting the optimal dopant concentration in gadolinium doped ceria: a kinetic lattice Monte Carlo approach

Gadolinium doped ceria (GDC) is a promising alternative electrolyte material for solid oxide fuel cells that offers the possibility of operation in the intermediate temperature range (773–1073 K). To determine the optimal dopant concentration in GDC, we have employed a systematic approach of applying a 3D kinetic lattice Monte Carlo (KLMC) model of vacancy diffusion in conjunction with previously calculated activation energies for vacancy migration in GDC as inputs. KLMC simulations were performed including the vacancy repelling effects in GDC. Increasing the dopant concentration increases the vacancy concentration, which increases the ionic conductivity. However, at higher concentrations, vacancy–vacancy repulsion impedes vacancy diffusion, and together with vacancy trapping by dopants decreases the ionic conductivity. The maximum ionic conductivity is predicted to occur at ≈20% to 25% mole fraction of Gd dopant. Placing Gd dopants in pairs, instead of randomly, was found to decrease the conductivity by ≈50%. Overall, the trends in ionic conductivity results obtained using the KLMC model developed in this work are in reasonable agreement with the available experimental data. This KLMC model can be applied to a variety of ceria-based electrolyte materials for predicting the optimum dopant concentration.

Kinetic lattice Monte Carlo model for oxygen vacancy diffusion in praseodymium doped ceria: Applications to materials design

Kinetic lattice Monte Carlo (KLMC) model is developed for investigating oxygen vacancy diffusion in praseodymium-doped ceria. The current approach uses a database of activation energies for oxygen vacancy migration, calculated using first-principles, for various migration pathways in praseodymium-doped ceria. Since the first-principles calculations revealed significant vacancy–vacancy repulsion, we investigate the importance of that effect by conducting simulations with and without a repulsive interaction. Initially, as dopant concentrations increase, vacancy concentration and thus conductivity increases. However, at higher concentrations, vacancies interfere and repel one another, and dopants trap vacancies, creating a “traffic jam” that decreases conductivity, which is consistent with the experimental findings. The modeled effective activation energy for vacancy migration slightly increased with increasing dopant concentration in qualitative agreement with the experiment. The current methodology comprising a blend of first-principle calculations and KLMC model provides a very powerful fundamental tool for predicting the optimal dopant concentration in ceria related materials.

Multiscale simulation on electromigration of the oxygen vacancies in metal oxides

The energetics and dynamics of electromigration of the oxygen vacancy is investigated with first-principles calculations and kinetic Monte Carlo methods. To simulate the charged oxygen vacancy under external fields within the first-principles approach, we introduce a slab model with electron-accepting dopants in the surface. The analysis of the density of states confirms that the oxygen vacancies are positively charged. When the external field is applied, the total energy of the slab linearly changes with respect to the position of the charged vacancy in the field direction, which allows for probing local permittivity around the vacancy site. The activation energy of vacancy migration is lowered along the field direction in a manner that the charge state of the vacancy is maintained along the migration path. Kinetic Monte Carlo simulations based on the first-principles inputs are also carried out and it is shown that the high-temperature condition is important for the fast redistribution of charged vacancies.

Activation energies for vacancy migration, clustering and annealing in silicon

A series of measurements have been performed at the University of Bath to study the evolution of vacancy-type structures in silicon. Isothermal annealing performed during positron beam-based Doppler broadening measurements have yielded activation energies for vacancy cluster formation and evaporation in silicon of approximately 2.5 and 3.7 eV, respectively. The clusters, which could predominantly be the stable hexavacancy, appear to form between 400-500°C, and anneal at ∼ 600°C. A similar technique applied to low-temperature in situ measurements have yielded the migration energies for the silicon monovacancy and interstitial (of ∼ 0.5 and 0.08 eV, respectively). Interesting observations of positronium formation at the surface of the samples studied during isothermal annealing are presented.

First-principles Study of Defect Migration in RE-doped Ceria (RE = Pr, Gd)

ABSTRACTOxygen vacancy formation and migration in ceria is central to its performance as an ionic conductor. Ceria doped with suitable aliovalent dopants has enhanced oxygen ion conductivity – higher than that of yttria stabilized zirconia (YSZ), the most widely used electrolyte material in solid oxide fuel cells (SOFC). To gain insight into atomic defect migration in this class of promising electrolyte materials, we have performed total energy calculations within the framework of density functional theory (DFT+U) to study oxygen vacancy migration in ceria, Pr-doped ceria (PDC) and Gd-doped ceria (GDC). We report activation energies for various oxygen vacancy migration pathways in PDC and GDC. Results pertaining to the preferred oxygen vacancy formation sites and migration pathways in these materials will be discussed in detail. Overall, the presence of Pr and Gd ions significantly affects oxygen vacancy formation and migration, in a complex manner requiring the investigation of many different migration events. We propose a relationship that explains the role of additional dopants in lowering the activation energy for vacancy migration in PDC and GDC.

Oxygen vacancy migration in ceria and Pr-doped ceria: A DFT+U study

Oxygen vacancy formation and migration in ceria (CeO(2)) is central to its performance as an ionic conductor. It has been observed that ceria doped with suitable aliovalent cationic dopants improves its ionic conductivity. To investigate this phenomenon, we present total energy calculations within the framework of density functional theory to study oxygen vacancy migration in ceria and Pr-doped ceria (PDC). We report activation energies for oxygen vacancy formation and migration in undoped ceria and for different migration pathways in PDC. The activation energy value for oxygen vacancy migration in undoped ceria was found to be in reasonable agreement with the available experimental and theoretical results. Conductivity values for reduced undoped ceria calculated using theoretical activation energy and attempt frequency were found in reasonably good agreement with the experimental data. For PDC, oxygen vacancy formation and migration were investigated at first, second, and third nearest neighbor positions to a Pr ion. The second nearest neighbor site is found to be the most favorable vacancy formation site. Vacancy migration between first, second, and third nearest neighbors was calculated (nine possible jumps), with activation energies ranging from 0.41 to 0.78 eV for first-nearest-neighbor jumps. Overall, the presence of Pr significantly affects vacancy formation and migration, in a complex manner requiring the investigation of many different migration events. We propose a relationship illuminating the role of additional dopants toward lowering the activation energy for vacancy migration in PDC.

Defect recovery in proton irradiated Ti-modified stainless steel probed by positron annihilation

The defect recovery in proton irradiated Ti-modified D9 steel has been studied by positron annihilation isochronal and isothermal annealing measurements. D9 samples have been irradiated with 3 MeV protons followed by isochronal annealing at various temperatures in the range of 323 to 1273 K. The dramatic decrease in positron annihilation parameters, viz. positron lifetime and Doppler S-parameter, around 500 K indicates the recovery of vacancy-defects. A clear difference in the recovery beyond 700 K is observed between solution annealed and cold worked state of D9 steel due to the precipitation of TiC in the latter. Isothermal annealing studies have been carried out at the temperature wherein vacancies distinctly migrate. Assuming a singly activated process for defect annealing, the effective activation energy for vacancy migration is estimated to be 1.13 ± 0.08 eV.

Validity of Activation Energy for Vacancy Migration Obtained by Integrating Force–Distance Curve

Kuramoto et al. calculated the activation energy for dislocation loop migration by integrating the force-distance curve. Their method has a great potential for the determination of migration energy in many cases. However, the validity of the application of their method to point defect migration has not yet been proved, because the migration of point defects is a thermally activated process and the physical meaning of the force in the force-distance curve has not been clarified. In this study, the validity was investigated by three methods to calculate the vacancy migration energy. In the first method, the migration energy was obtained by definition from the difference in potential energy between the equilibrium configuration before migration and the saddle point configuration (Method 1) using a statistic lattice relaxation method. The second method involved a molecular dynamics simulation based on an absolute reaction rate theory (Method 2). The third method involved the integration of the force-distance curve obtained by the statistic lattice relaxation method mentioned above (Method 3). The calculation model used was a two-dimensional hexagonal lattice and the Morse potential for Cu was used. The migration energies obtained by Methods 1, 2 and 3 were 0.391 eV, 0.394 ± 0.009 eV and 0.392 eV, respectively. As these values were similar, the validity of Method 3 was demonstrated.

Activation energy for vacancy migration in [001] tilt boundaries in nickel

The activation energy for vacancy migration in [001] tilt boundaries in nickel under the action of homogeneous tensile stress in the presence of a grain-boundary dislocation (GBD) was calculated with the help of atomistic computer simulation by the molecular-statics method using embedded-atom-method potentials. The Σ=5 (ϑ=36.9°) special boundary as well as the boundary with a misorientation angle of ϑ=37.9° whose period contains 20 structural units of the Σ=5 (ϑ=36.9°) boundary and one structural unit of the Σ=5 (ϑ=53.1°) boundary simulating a GBD have been investigated. High applied stresses and long-range GBD-induced stresses are shown to exert no significant effect on the activation energy for vacancy migration. An analysis using calculated data on the energy for vacancy formation [1] shows that, due to the internal stresses in ordered boundaries, the diffusion coefficient along grain boundaries may increase only slightly.

Atomistic Simulation of Pipe Diffusion in AlCu Alloys

Activation energies for solute diffusion along dislocations are difficult to measure experimentally. The aim of this work is to provide insight into pipe diffusion with the help of atomistic simulations. The distribution of vacancy formation energy and the activation energy for copper migration are determined in the core of an edge dislocation in aluminum. The Dimer method is used to find activation energies for vacancy migration. The activated region around the dislocation where a very high diffusivity is observed and the activation energy for copper diffusion associated with this region are interpreted with regard to the contribution of the dislocation and the contribution of the alloying.

Order–disorder transformation in the Ni–4.49 at.% Al alloy

The order–disorder transformation in the Ni–4.49 at.% Al alloy was studied using electrical resistivity measurements, microhardness measurements, differential scanning calorimetry (DSC) and transmission electron microscopy (TEM). The results confirmed the ordering behavior expected for Ni–Al dilute alloys and the suggested relation between resistivity changes and microhardness changes with anti-ferromagnetic spin ordering. The higher value obtained for the activation energy of vacancy migration was associated with a decrease in the Al concentration gradient near solute-depleted regions.

Precipitation and Dissolution Reactions in a 6061 Aluminum Alloy

The aging processes in a 6061 commercial aluminum alloy during continuous heating at various heating rates have been studied by means of DSC measurements. Eight reactions have been detected, six exothermic and two endothermic. The activation energy for the first exothermic peak observed at about 373 K at a heating rate of 10 K min -1 is 79 kJ mol -1 , almost the same as the activation energy for vacancy migration. Considering the excess vacancies exist in the as-quenched condition, this reaction can be explained in terms of vacancy cluster formation. The second and the third exothermic reactions within the large endothermic peak are thought to arise from the formation of solute atom clusters involving silicon and magnesium. The endothermic reaction is probably due to the dissolution of these atomic clusters. The activation energy for this process is close to those for the bulk diffusion of magnesium and silicon atoms in aluminum. A large and sharp exothermic peak at temperatures around 500-550 K is due to the precipitation of intermediate β needles. The activation energy for this process is significantly smaller than that for bulk diffusion. The reason for it is not clear at present, but may arise from the needlelike shape of the precipitates. The following two exothermic reactions which are difficult to separate clearly from the peak at 500-550 K are probably due to the precipitation of β' needles and the stable β phase, respectively. The dissolution of stable β phase occurs at higher temperatures.

Investigation of point defects in TiAl alloy

The many-body potentials of TiAl alloy were constructed by empirical fitting to the properties of the L10TiAl tetragonal phase and the pressure–volume relationship. The properties and stable configurations for point defects and their aggregates, and the activation energies for vacancy migration are simulated in TiAl intermetallic compounds using molecular dynamics.