Activation Energy For Vacancy Diffusion Research Articles

NV centres by vacancies trapping in irradiated diamond: experiments and modelling

Advances in applications of nitrogen-vacancy (NV) spin centres in diamond for sensing and quantum metrology depend critically on the NV fabrication methods. One such technique combines epitaxial diamond growth and electron or ion irradiation (He, C, etc), where NVs are activated by vacancy trapping at the nitrogen donor atoms upon thermal diffusion. In this work we study the efficiency of such method by analyzing NV depth profiles created by 340 keV and also 4 keV He irradiation in high purity CVD and HPHT diamond crystals and subjected to sequent annealing at 950 °C and 1200 °C temperatures. This analysis is coupled with the measurement of NV density in the bulk of CVD diamonds with nitrogen doping at low-ppb and low-ppm levels, exposed to MeV electrons in a wide range of the doses. For data analysis we developed an atomistic model based on probabilistic atomic jumps in a crystal lattice, which considers competitive trapping between di- (V2) or multi-vacancy defects compared to that of NVs. The efficiency of NV formation was defined as a ratio of the corresponding capture cross sections: σ NV vs. σV2 . Applying this model to the experimental data, the σNV/σV2 ratio was estimated about 0.1–0.5, where the activation energy of vacancy diffusion of about 1.7 eV was evaluated by 3D localization of individual NVs in depth profiles in a confocal microscope and sampling their spin coherence properties ( T2 ). In addition, we noted two subsidiary effects also discussed here: (i) reduction of NV density within the stopping range of the implanted He atoms after 1200∘ annealing and, (ii) partial suppression of NVs at near-surface areas visible only at low-dose electron exposures. The results of this study could be helpful to optimize the NV fabrication process reducing the density of ‘collateral’ lattice damage.

Accelerated molecular dynamics simulation of vacancy diffusion in substitutional alloy with collective variable-driven hyperdynamics

It is not straightforward to investigate diffusion-limited phenomena in solid system by molecular dynamics (MD) simulation due to the limitation in time scale. Although many methods have been developed to extend the MD time scale by accelerating infrequent events, there is no established technique to treat diffusion in substitutional solid solution up to now since motions of solute atom, matrix atoms and vacancy interact each other complexly. In this study, an acceleration technique for the MD simulation of diffusion in substitutional solid solution is developed in conjunction with collective variable-driven hyperdynamics (CVHD). This novel technique is applied for the diffusion in Fe-Cr alloy as a representative substitutional alloy. Activation energy of vacancy diffusion from accelerated CVHD simulation basically agrees with that derived from MD simulation without acceleration, which confirms that the accelerated CVHD simulation reproduces the dynamics of vacancy diffusion in substitutional solid solution correctly.

Vacancy formation enthalpy in CoCrFeMnNi high-entropy alloy

In order to determine the vacancy formation enthalpy in a CoCrFeMnNi high entropy alloy, we have performed positron lifetime measurements over a temperature range from 293 to 1423 K. A vacancy formation enthalpy of 1.69 ± 0.13 eV was obtained using a threshold method, similar to the value of 1.72 ± 0.18 eV obtained using an Arrhenius plot. The vacancy formation energies are within the formation enthalpy ranges of the constituent pure metals. The vacancy diffusion activation energy of 2.78 ± 0.08 eV is in excellent agreement with the self-diffusion activation energies reported for the constituent face-centered cubic metals.

The effect of vacancy on the interfacial diffusion in Cu/Sn lead-free solder joints

PurposeThe purpose of this paper is to investigate the diffusion behaviors of different atoms at the Cu/Cu3Sn interface and the vacancy formation energy, diffusion energy barrier and vacancy diffusion activation energy.Design/methodology/approachThe diffusion behaviors of different atoms at the Cu/Cu3Sn interface are analyzed, and the vacancy formation energy, diffusion energy barrier and vacancy diffusion activation energy are obtained using molecular dynamics simulation. The nudged elastic band method is used to evaluate diffusion energy barrier for Cu/Cu3Sn system.FindingsIt is found that the vacancies in the Cu/Cu3Sn interface promote the interfacial diffusion, and the formation energy of Cu vacancy in the Cu crystal is larger than that in Cu3Sn crystal. In addition, the formation energies of Cu1 vacancy and Cu2 vacancy are close to each other in Cu3Sn crystal, and they are all less than the formation energy of Sn vacancy. Furthermore, the vacancy diffusion barrier and vacancy diffusion activation energy of the Cu/Cu3Sn interface are calculated, and the results show that the vacancy diffusion activation energy of Sn was higher than that of Cu. Finally, by comparison of diffusion activation energies of different diffusion mechanisms, Cu→Cu1vac is the most possible migration path at all temperatures.Originality/valueIt is concluded that the vacancies in Cu/Cu3Sn interface promote interfacial diffusion, and the activation energy of vacancy diffusion in most diffusion mechanisms decreases with the increase of temperature.

Ab initio investigations of the phase stability in group IVB and VB transition metal carbides

Using ab-initio calculations, the stability of various stable and metastable group IVB and VB transition metal carbide compounds at ambient pressure and 0K were investigated. By comparing the formation enthalpy, vacancy diffusion activation energy and generalized stacking fault energy of these phases, the thermodynamic competition between vacancy-ordered and stacking-faulted phase formation mechanisms are seen among the carbides. In general, the group IVB carbides have a higher vacancy migration energy than that of the group VB carbides which could explain the difficulty in experimentally forming such vacancy-ordered phases. In addition, the group IVB carbides do not have a stable intrinsic stacking fault (ISF), which is present in the group VB carbides. This ISF is used to rationalize the absence of such faulted phases in the group IVB carbides but their presence in the group VB carbides.

Atomistic Modeling of Sulfur Vacancy Diffusion Near Iron Pyrite Surfaces

Through density functional calculations, we investigated the diffusion of isolated sulfur vacancies (VS) from the bulk of iron pyrite (cubic FeS2) to the (100) and (111) surfaces. The influence of vacancy depth on the vacancy formation energy and the activation energy for vacancy diffusion are discussed. Significantly, we find that VS defects tend to migrate toward stoichiometric and sulfur-rich surfaces through sequential “intra-dimer” and “inter-dimer” hops. We find a pre-exponential constant (D0) of 9 × 10–7 m2 s–1 and an activation energy (E) of 1.95 eV for sulfur vacancy diffusion in bulk pyrite, corresponding to a vacancy diffusion coefficient DV = D0 exp(−E/kT) = 9 × 10–40 m2 s–1 at 25 °C and 5 × 10–18 m2 s–1 at 600 °C. The activation energy is smaller near the surface (e.g., E = 1.5 eV near the stoichiometric (100) surface), resulting in faster vacancy diffusion near the surface than in the bulk. Using the formation enthalpy of VS at the (100) surface, E = 2.37 eV, we find a sulfur diffusivity in bulk pyrite DS = 7 × 10–47 m2 s–1 at 25 °C and 2 × 10–20 m2 s–1 at 600 °C. The calculated DS values are in reasonable agreement with experiment only at intermediate temperatures (∼275–625 °C). Our results show that bulk and near-surface sulfur vacancies can be healed in sulfur-rich conditions at reasonably high temperatures. The mechanism of vacancy diffusion presented here should be useful in managing VS defects during the fabrication of high-quality pyrite samples for solar energy conversion applications.

Visible-light-accelerated oxygen vacancy migration in strontium titanate.

Strontium titanate is a model transition metal oxide that exhibits versatile properties of special interest for both fundamental and applied researches. There is evidence that most of the attractive properties of SrTiO3 are closely associated with oxygen vacancies. Tuning the kinetics of oxygen vacancies is then highly desired. Here we reported on a dramatic tuning of the electro-migration of oxygen vacancies by visible light illumination. It is found that, through depressing activation energy for vacancy diffusion, light illumination remarkably accelerates oxygen vacancies even at room temperature. This effect provides a feasible approach towards the modulation of the anionic processes. The principle proved here can be extended to other perovskite oxides, finding a wide application in oxide electronics.

Modeling defect transport during Cu oxidation

A defect transport model describing Cu oxidation kinetics to Cu2O and CuO is presented. The model supports findings that the dominant defects in Cu2O are singly charged and neutral copper vacancies, and in CuO doubly charged copper vacancies. In this work, CuO is treated as a charge transfer insulator and from the model a reaction enthalpy for Cu vacancies in CuO was estimated to be 250±10kJ/mole. Using the model, defect-diffusion coefficients are extracted from copper oxidation experiments and activation energies for vacancy-diffusion in Cu2O and CuO were found to be 54kJ/mole and 32kJ/mole, respectively.

The effects of electropulsing on the recrystallization behavior of rolled pure tungsten

Abstract

Construction of embedded-atom-method interatomic potentials for alkaline metals (Li, Na, and K) by lattice inversion

The lattice-inversion embedded-atom-method interatomic potential developed previously by us is extended to alkaline metals including Li, Na, and K. It is found that considering interatomic interactions between neighboring atoms of an appropriate distance is a matter of great significance in constructing accurate embedded-atom-method interatomic potentials, especially for the prediction of surface energy. The lattice-inversion embedded-atom-method interatomic potentials for Li, Na, and K are successfully constructed by taking the fourth-neighbor atoms into consideration. These angular-independent potentials markedly promote the accuracy of predicted surface energies, which agree well with experimental results. In addition, the predicted structural stability, elastic constants, formation and migration energies of vacancy, and activation energy of vacancy diffusion are in good agreement with available experimental data and first-principles calculations, and the equilibrium condition is satisfied.

Embedded-atom-method interatomic potentials from lattice inversion

The present work develops a physically reliable procedure for building theembedded-atom-method (EAM) interatomic potentials for the metals with fcc, bcc andhcp structures. This is mainly based on Chen–Möbius lattice inversion (Chen et al 1997 Phys. Rev. E 55 R5) and first-principles calculations. Following Baskes (Baskes et al 2007 Phys. Rev. B 75 094113), this new version of the EAM eliminates all of theprior arbitrary choices in the determination of the atomic electron density andpair potential functions. Parameterizing the universal form deduced from thecalculations within the density-functional scheme for homogeneous electron gas as theembedding function, the new-type EAM potentials for Cu, Fe and Ti metals havesuccessfully been constructed by considering interatomic interactions up to the fifthneighbor, the third neighbor and the seventh neighbor, respectively. The predictionsof elastic constants, structural energy difference, vacancy formation energy andmigration energy, activation energy of vacancy diffusion, latent heat of melting andrelative volume change on melting all satisfactorily agree with the experimentalresults available or first-principles calculations. The predicted surface energies forlow-index crystal faces and the melting point are in agreement with the experimentaldata to the same extent as those calculated by other EAM-type potentials suchas the FBD-EAM, 2NN MEAM and MS-EAM. In addition, the order amongthe predicted low-index surface energies is also consistent with the experimentalinformation.

A computational study of magnesium point defects and diffusion in forsterite

We have studied the formation and migration of point defects within the magnesium sub-lattice in forsterite using a combination of empirical and quantum mechanical modelling methodologies. Empirical models based on a parameterised force field coupled to a high throughput grid computing infrastructure allow rapid evaluation of a very large number of possible defect configurations. An embedded cluster approach reveals more accurate estimates of defect energetics for the most important defect configurations. Considering all defects in their minimum energy, equilibrium positions, we find that the lowest energy intrinsic defect is the magnesium Frenkel type, where a magnesium atom moves from the M1 site to form a split interstitial defect. This defect has 2 four-co-ordinated magnesium atoms located outside opposite triangular faces of an otherwise vacant M1 octahedron. The split interstitial defect is more stable than regular interstitials where magnesium is located in either of the two structurally vacant octahedral sites in the hexagonally close packed oxygen lattice. M1 vacancies are also found to form when iron(II) oxidises to iron(III). The energy of the defects away from the equilibrium positions allows the energy barrier to diffusion to be calculated. We have considered the migration of both magnesium vacancies and interstitials and find that vacancies are more mobile. When the contribution from the formation energy of the defects is included we arrive at activation energies for vacancy diffusion that are in agreement with experiment.

Atomic mechanisms of interdiffusion in metallic multilayers

Interdiffusion data (activation energies and pre-exponential factors) for different metal–metal multilayers (MLs) published in the literature and our own results on Fe/Pt MLs are reviewed. The analysis of the available data suggests that vacancy diffusion is the main interdiffusion mechanism in metallic MLs. An empirical relation between the activation energy for interdiffusion in metallic multilayers, the average activation energy of vacancy diffusion and the activation energy for in-plane grain-boundary diffusion is proposed.

Predicting ionic conductivity of solid oxide fuel cell electrolyte from first principles

First-principles quantum simulations complemented with kinetic Monte Carlo calculations were performed to gain insight into the oxygen vacancy diffusion mechanism and to explain the effect of dopant composition on ionic conductivity in yttria-stabilized zirconia (YSZ). Density-functional theory (DFT) within the local-density approximation with gradient correction was used to calculate a set of energy barriers that oxygen ions encounter during migration in YSZ by a vacancy mechanism. Kinetic Monte Carlo simulations were then performed using Boltzmann probabilities based on the calculated DFT barriers to determine the dopant concentration dependence of the oxygen self-diffusion coefficient in (Y2O3)x(ZrO2)(1−2x) with x increasing from 6% to 15%. The results from the simulations suggest that the maximum conductivity occurs at 7–9mol% Y2O3 at 600–1500K and that the effective activation energy increases at higher Y doping concentrations in good agreement with previously reported literature data. The increase in the effective activation energy for migration arises from the higher-energy barrier for oxygen vacancy diffusion across an Y–Y common edge relative to diffusion across one with a Zr–Y common edge of two adjacent tetrahedra. The binding energies between oxygen vacancies and dopants were extracted up to the fourth nearest-neighbor interaction. Our results reveal that the binding energy is the strongest when the vacancy is in the second nearest-neighbor position relative to the Y dopant atom. The methodology was also applied to scandium-doped zirconia (SDZ). Preliminary results from quantum simulations of SDZ suggest that the effective activation energy for vacancy diffusion in SDZ is lower than that of YSZ, in agreement with experimental observations. The agreement with experimental studies on the two systems analyzed in this paper supports the use of this technique as a predictive tool on electrolyte systems not yet characterized experimentally.

Semiempirical atomic potentials for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, Al, and Pb based on first and second nearest-neighbor modified embedded atom method

Modified embedded atom method (MEAM) potentials for fcc elements Cu, Ag, Au, Ni, Pd, Pt, Al, and Pb have been newly developed using the original first nearest-neighbor MEAM and the recently developed second nearest-neighbor MEAM formalisms. It was found that the original MEAM potentials for fcc elements show some critical shortcomings such as structural instability and incorrect surface reconstructions on (100), (110), and/or (111) surfaces. The newly developed MEAM potentials solve most of the problems and describe the bulk properties (elastic constants, structural energy differences), point defect properties (vacancy and interstitial formation energy and formation volume, activation energy of vacancy diffusion), planar defect properties (stacking fault energy, surface energy, surface relaxation and reconstruction), and thermal properties (thermal expansion coefficients, specific heat, melting point, heat of melting) of the fcc elements considered, in good agreement with relevant experimental information. It has been shown that in the MEAM the degree of many-body screening ${(C}_{\mathrm{min}})$ is an important material property and that structural stability at finite temperatures should be included as a checkpoint during development of semiempirical potentials.

Point-defect properties in HCP rare earth metals with analytic modified embedded atom potentials

The analytic embedded atom method (EAM) type many-body potentials of hcp rare earth metals (Dy, Er, Gd, Ho, Nd, Pr, and Tb) have been constructed. The hcp lattice is shown to be energetically most stable when compared with the fcc and bcc structure, and the hcp lattice with ideal c/a. The mechanical stability of the corresponding hcp lattice with respect to large change of density and c/a ratio is examined. The phonon spectra, stacking fault and surface energy are calculated. The activation energy for vacancy diffusion in these metals has been calculated and the most possible diffusion paths are predicted. Finally, the self-interstitial atom (SIA) formation energy and volume have been evaluated for eight possible sites. This calculation suggests that the crowdion and basal split are the most stable configurations. The SIA formation energy increases linearly with the increase of the melting temperature.

Analytic modified embedded atom potentials for HCP metals

Analytic modified embedded atom method (AMEAM) type many-body potentialshave been constructed for ten hcp metals: Be, Co, Hf, Mg, Re, Ru, Sc, Ti, Yand Zr. The potentials are parametrized using analytic functions and fittedto the cohesive energy, unrelaxed vacancy formation energy, fiveindependent second-order elastic constants and two equilibrium conditions.Hence, each of the constructed potentials represents a stable hexagonalclose-packed lattice with a particular non-ideal c/a ratio. In order totreat the metals with negative Cauchy pressure, a modified term has beenadded to the total energy. For all the metals considered, the hcp latticeis shown to be energetically most stable when compared with the fcc and bccstructure and the hcp lattice with ideal c/a. The activation energy forvacancy diffusion in these metals has been calculated. They agree well withexperimental data available and those calculated by other authors for bothmonovacancy and divacancy mechanisms and the most possible diffusion pathsare predicted. Stacking fault and surface energy have also been calculatedand their values are lower than typical experimental data. Finally, theself-interstitial atom (SIA) formation energy and volume have beenevaluated for eight possible sites. This calculation suggests that thebasal split or crowdion is the most stable configuration for metals with arather large deviation from the ideal c/a value and the non-basaldumbbell (C or S) is the most stable configuration for metals with c/anear ideal. The relationship between SIA formation energy and meltingtemperature roughly obeys a linear relation for most metals except Ru andRe.

Interaction between oxygen vacancies on MgO(100)

Oxygen-deficient MgO(100) surfaces are studied by means of total-energy calculations, within the density-functional theory. Selected surface configurations presenting increasing densities of neutral oxygen vacancies, ranging from 12.5% to 100%, are considered, the missing oxygen being periodically distributed in the surface layer either homogeneously or in a close-packed fashion. We show that the electronic structure is characterized by occupied states in the gap which result either from the hybridization of atomiclike orbitals localized on vacancy sites, or involve surface magnesium orbitals. The latter case occurs at large vacancy concentrations, and the conditions for the apparition of metallicity in the surface layer are derived. The formation energy of oxygen vacancies is calculated as a function of the vacancy concentration and of the particular configuration. A two-body model potential is proposed to account for their interaction. The activation energy for vacancy diffusion at the surface is also computed, thus providing a complete set of parameters for a description of the thermodynamics as well as of the kinetics of oxygen vacancies on a MgO(100) surface.

Anisotropic kinetics of vacancy diffusion and annihilation on Si(001) surfaces studied by scanning reflection electron microscopy

The kinetics of vacancy diffusion and annihilation on Si(001)-2\ifmmode\times\else\texttimes\fi{}1 surfaces are studied by using scanning reflection electron microscopy. The ${\mathrm{S}}_{\mathrm{B}}$ steps, which run across dimer rows, retreat 1.8 times faster than ${\mathrm{S}}_{\mathrm{A}}$ steps during low-energy Ar-ion sputtering at elevated substrate temperatures. This leads to virtual single-domain stabilization in the initial stage of layer-by-layer sputtering. These different types of steps maintain an equilibrium configuration due to a step-step interaction. On wide terraces, elongated vacancy islands with a single atomic height and alternative 2\ifmmode\times\else\texttimes\fi{}1 reconstruction are formed along the dimer rows. These results indicate preferential vacancy annihilation at ${\mathrm{S}}_{\mathrm{B}}$ steps and anisotropic vacancy diffusion depending on the dimer row direction. The diffusion length of the vacancies is estimated from the width of the denuded zones of the vacancy islands, which are formed on both sides of the atomic steps by thermal heating after vacancy introduction at room substrate temperature. The activation energy for vacancy diffusion along the dimer rows is obtained to be 2.3\ifmmode\pm\else\textpm\fi{}0.2 eV. A vacancy diffusion model mediated by dimer vacancy complexes rather than single-dimer vacancies, interprets our experimental results.

Creep Deformation of Dispersion-Strengthened Copper

The creep behavior of an internally oxidized, A12O3 dispersion-strengthened copper alloy, GlidCop Al-15, has been investigated in the temperature range of 745 to 994 K. The results exhibit a high apparent stress exponent (10 to 21) and a high apparent activation energy for creep (253.3 kJ/mole). To describe the creep behavior of this alloy, the Rosler-Arzt model for attractive particle/dislocation interaction is applied. The results are in good agreement with the model when account is taken of the effects of the fine elongated grains and heavily dislocated structures revealed through transmission electron microscopy. The analysis demonstrates that the dislocation/particle interaction is of moderate strength in this alloy, consistent with the observation that the particle/matrix interface is partially coherent. In addition, the analysis reveals that the choice of mechanism and corresponding activation energy for vacancy diffusion has only a small effect on the calculated model parameters. It is argued that the weak dependence of subgrain size on stress demonstrates that creep deformation is particle controlled, rather than subgrain size controlled. In addition, the poorly developed subgrain structure and high dislocation densities are attributed to the presence of the fine oxide particles. Finally, the dependence of rupture time on stress is shown to be consistent with a description of creep fracture based on diffusive cavity growth with continuous nucleation.