Vacancy-mediated Diffusion Research Articles

Formation characteristics of CaTiO3 in the vicinity of the calcium ferrite/TiO2 interface

Calcium ferrite-TiO 2 (C x F-TiO 2 ) diffusion couples were prepared to investigate the reaction between TiO 2 and CaO of calcium ferrite during sintering vanadium‑titanium magnetite. The distribution, species, and number of phases in the vicinity of the C x F/TiO 2 interface were characterized by electron probe microanalysis (EPMA), Fourier transform-infrared (FT-IR) spectroscopy, and X-ray diffraction (XRD) that could select the scanning location. The phases generated from the C x F side to the TiO 2 side are 66.66% CaFe 2 O 4 + 33.33% Fe 2 O 3 , 100% CaTiO 3 , 66.66% CaTiO 3 + 33.33% Fe 2 O 3 , and 75% CaTiO 3 + 25% Fe 2 O 3 , respectively. The isothermal section was plotted using the experimental data. The diffusion thickness decreased from 90.2 to 8.1 μm as the temperature decreased from 1323 to 1173 K, and increaesed from 47.4 to 121.4 μm as the annealing time increased from 1 to 4 h. The linear relationship between the diffusion thickness and the square root of the annealing time indicates that the formation of CaTiO 3 was controlled by the diffusion process. Vacancy-mediated diffusion mechanism, which was widely used to describe the diffusion-controlled process, was introduced to describe the formation of CaTiO 3 in the vicinity of the C x F/TiO 2 interface. The Ti 4+ in the TiO 2 layer jumped and diffused through the Ti 4+ vacancies in the CaTiO 3 + Fe 2 O 3 layer to the CaFe 2 O 4 + Fe 2 O 3 /CaTiO 3 interface, and reacted with CaFe 2 O 4 and O 2− to generate CaTiO 3 . The concentration data across the C x F/TiO 2 interface were applied in the modified Boltzmann-Matano method to calculate the interdiffusion coefficient. The average interdiffusion coefficients of various Ti concentrations increased with temperature: 2.51 × 10 −10 , 7.49 × 10 −10 , 2.56 × 10 −9 , and 8.06 × 10 −9 cm 2 ·s −1 at 1173, 1223, 1273, and 1323 K, respectively. The relationship between the logarithm of the interdiffusion coefficient and the reciprocal of the temperature was empirically described by the Arrhenius expression. Linear regression analysis showed that the diffusion activation energy of CaTiO 3 formation is 300.14 kJ/mol. • CaFe 2 O 4 , CaTiO 3, and Fe 2 O 3 generate at the calcium ferrite/TiO 2 interface. • CaTiO 3 forms thorough vacancy-mediated diffusion mechanism. • Diffusion of Ti 4+ governs the CaTiO 3 formation in the calcium ferrite-TiO 2 system. • Diffusion thickness and interdiffusion coefficient increase with temperature. • CaTiO 3 formation requires approximately activation energy of 314 kJ/mol.

Thermodynamically Driven Formation of Intercalated Cu Carpets from Supported Cu Pyramids on MoS2.

Thermodynamic and kinetic analyses based on our first-principles density functional theory calculations are used to interpret the experimentally observed formation of Cu carpets intercalated under the top layer of a 2H-MoS2 substrate. Spontaneous Cu transport from Cu pyramids on top of the MoS2 substrate through surface point defects to the growing Cu carpet is shown to be driven by a slightly lower chemical potential for the Cu carpet. We demonstrate that the competition between a preference for a thicker Cu carpet and the cost of elastic stretching of the top MoS2 layer results in a selected Cu carpet thickness. We also propose that Cu transport occurs primarily via vacancy-mediated diffusion through constricting point defect portals.

Self-diffusion in carbon-alloyed CoCrFeMnNi high entropy alloys

Tracer diffusion of the substitutional components in interstitial (CoCrFeNiMn)1-xCx high-entropy alloys with nominally x = 0.002, 0.005 and 0.008 (in at. fractions) is measured at elevated temperatures from 1173 to 1373 K. Two different characteristic effects of interstitial carbon addition on substitutional diffusion in these FCC alloys are distinguished. At the highest temperature of 1373 K, alloying by C with relatively low concentrations (x = 0.002) retards diffusion of the substitutional elements with respect to those in the C-free alloy. At lower temperatures and/or higher C concentrations (x ≥ 0.005), an enhancement of the diffusion rates of all substitutional elements is seen. A model is suggested that relates the self-diffusivities in the CoCrFeMnNi–C alloys with the lattice distortion imposed by interstitially dissolved carbon. The experimental results are interpreted in terms of a decrease of the migration barriers for vacancy-mediated diffusion due to the presence of interstitial C atoms.

Vacancy-mediated suppression of phase separation in a model two-dimensional surface alloy by the difference of the atomic jump rates

A vacancy-mediated collective diffusion model is used to compute a thermally-induced (spinodal) phase separation in a typical fcc bi-metallic surface alloy at low median concentration of vacancies, focusing on the effect of the ratio, Γ=ΓA/ΓB, of the jump rates to the vacant sites of the two types of atoms. The model is formulated for the diffusion of one atomic species and vacancies, employing the kinetic transport coefficients derived by Moleko et al. (Phil. Mag. A 59, 141 (1989)). It is demonstrated that for A0.7B0.3 alloy, Γ∼50 results in suppression of phase separation, whereas very small Γ values result in mild phase separation (i.e., the suppression is incomplete).

Diffusion in polymer-derived Si–(B–)C–N ceramics, particularly amorphous Si29B9C41N21

Abstract The diffusion coefficients (D) of implanted radioisotopes – 71Ge, 31Si, and 11C – in the polymer-derived amorphous (a-)Si29B9C41N21 ceramic have been measured as functions of temperature (T) in different as-pyrolysed states (71Ge) or after pre-diffusion annealing at 1600 °C for 2 h (71Ge, 31Si, and 11C) by means of radiotracer techniques, in which serial sectioning was done by ion-beam sputtering. In the cases of 31Si (half-life t 1/2 = 2.6 h) and 11C (t 1/2 = 20.4 min), implantation, diffusion annealing, and sputter-sectioning were done on beamline and in situ of a novel set-up specially constructed for diffusion studies of short-lived radiotracer atoms. In all cases, the T-dependencies of D are of Arrhenius type. Comparing the Arrhenius parameters of D(71Ge) to previous data on diffusion in (B-free) a-Si28C36N36, it is concluded that the diffusion of 71Ge in the a-Si29B9C41N21 ceramic is controlled by vacancies in its a-Si3N4 –y C y phase which become increasingly smeared out when the C-content y decreases as a result of pre-annealing. The coincidence of D(31Si) and D(11C) in pre-annealed a-Si29B9C41N21 at all temperatures investigated is enforced by vacancy-mediated diffusion through SiC crystallites embedded in the a-Si3N4 –y C y phase.

Accurate Determination of Vacancy-Mediated Diffusion Coefficients Under the Influence of Short-Range Ordering in Multiprincipal Elemental Alloys

Accurate Determination of Vacancy-Mediated Diffusion Coefficients Under the Influence of Short-Range Ordering in Multiprincipal Elemental Alloys

Rapid Atomic Ordering Transformation toward Intermetallic Nanoparticles.

Chemically ordered intermetallic nanoparticles are promising candidates for energy-related applications such as electrocatalysis. However, the synthesis of intermetallics generally requires long annealing (several hours) to achieve the ordered structure, which causes nanoparticles agglomeration and diminished performance, particularly for catalysis. Herein, we demonstrate a new rapid Joule heating approach that can synthesize highly ordered and well-dispersed intermetallic nanoparticles. As a proof-of-concept, we synthesized fully ordered Pd3Pb intermetallic nanoparticles that feature small size distribution (∼6 nm). Computational analysis of the L12 Pd3Pb material suggests that this rapid atomic ordering transformation can be attributed to a vacancy-mediated diffusion mechanism. Moreover, the nanoparticles demonstrate excellent electrocatalytic activity and exceptional stability for the oxygen reduction reaction (ORR), retaining >95% of the current density over 10 h of chronoamperometry test with negligible structural and compositional changes. This study demonstrates a new strategy of providing a new direction for intermetallic synthesis and catalyst discovery.

Short-range order localizing diffusion in multi-principal element alloys

The impact of chemical short-range order (SRO) on diffusion is computationally studied and theoretically analyzed in two classes of multi-principal elements alloys, fcc CrCoNi and bcc MoNbTa. We find the presence of SRO considerably reduces and localizes vacancy-mediated diffusion. The diffusivity reduction is induced by an increase of migration barrier (decreasing jump frequency) and enhanced diffusion correlation that lowers the effectiveness of atomic jumps. By sampling the diffusion pathways and associated energy barriers, a picture of SRO-stretched potential energy landscape is conceived that elucidates an increasing backward jumps and vacancy trapping effect stemming from chemical ordering. The results imply controlling the ordering in chemistry can act as a potential approach for manipulating diffusional behaviors in multi-principal elements alloys.

Impurity diffusion in magic-size icosahedral clusters.

Atomic diffusion is at the basis of chemical ordering transformations in nanoalloys. Understanding the diffusion mechanisms at the atomic level is therefore a key issue in the study of the thermodynamic behavior of these systems and, in particular, of their evolution from out-of-equilibrium chemical ordering types often obtained in the experiments. Here, the diffusion is studied in the case of a single-atom impurity of Ag or Au moving within otherwise pure magic-size icosahedral clusters of Cu or Co by means of two different computational techniques, i.e., molecular dynamics and metadynamics. Our simulations reveal unexpected diffusion pathways, in which the displacement of the impurity is coupled with the creation of vacancies in the central part of the cluster. We show that the observed mechanism is quite different from the vacancy-mediated diffusion processes identified so far, and we demonstrate that it can be related to the presence of non-homogeneous compressive stress in the inner part of the icosahedral structure.

Vacancy-Mediated Diffusion and Diffusion-Controlled Processes in Ordered Binary Intermetallics by Kinetic Monte Carlo Simulations

We review the results of our Monte Carlo simulation studies carried out within the past two decades in the area of atomic-migration-controlled phenomena in intermetallic compounds. The review aims at showing the high potential of Monte Carlo methods in modelling both the equilibrium states of the systems and the kinetics of the running processes. We focus on three particular problems: (i) the atomistic origin of the complexity of the ‘order-order’ relaxations in γ’-Ni3Al; (ii) surface-induced ordering phenomena in γ-FePt and (iii) ‘order—order’ kinetics and self-diffusion in the ‘triple-defect’ β-NiAl. The latter investigation demonstrated how diverse Monte Carlo techniques may be used to model the phenomena where equilibrium thermodynamics interplays and competes with kinetic effects.

Self-diffusion of Fe and Pt in L10-Ordered FePt: Molecular Dynamics simulation

Vacancy-mediated lattice diffusion coefficients of Fe and Pt atoms in the chemically ordered L10-FePt phase at temperatures between 1300 and 1600 K were evaluated by means of Molecular Dynamics (MD) simulations. Due to the anisotropic structure of the L10-ordered FePt phase, Fe and Pt diffusion fluxes and the resulting self-diffusion coefficients were considered along and perpendicular to the [001] crystallographic direction. In view of a very low vacancy concentration in real FePt single crystals, steady state conditions of the simulated process were approximated by specifically scaling the self-diffusion coefficients estimated for higher vacancy concentrations to the equilibrium vacancy concentration. This procedure involved the calculation of vacancy formation energies which appeared temperature dependent. The validity of this approach was thoroughly tested and the final results were analyzed and compared to the relevant literature data. The evaluated temperature dependent Fe and Pt self-diffusion coefficients showed Arrhenius behavior, however, their values were much lower than the reported experimental ones. Apart from the inevitable effect of the applied quasi-empirical potentials, the discrepancies might originate from the fact that while the MD simulations addressed a single crystal of FePt defected exclusively with vacancies and antisites, the existence of fast diffusion paths along linear and planar defects cannot be excluded in real materials.

Solubility and vacancy-mediated inter-diffusion in the Zr-Nb-Cr system

To better understand the microstructural evolution of Cr-coated Zr alloy cladding, we investigate, using density functional theory calculations, the vacancy-mediated diffusion behaviour of Zr and Nb solutes in BCC-Cr as well as Zr and Cr solutes in BCC-Nb. The calculated vacancy formation and migration energies are in good agreement with available literature, as are the self-diffusivities. We show that in BCC-Cr both Nb and Zr are faster diffusers than Cr (vacancy-mediated self-diffusion). It was also found that both Zr and Nb segregate towards vacancy sinks in BCC-Cr at normal reactor operating temperatures, but at elevated temperatures their flux is expected to be in opposite directions. In BCC-Nb, we show that Cr is a slower diffuser than Nb self-diffusion, while Zr is faster; and both Zr and Cr are expected to decorate vacancy sinks in BCC-Nb at all temperatures relevant to reactor operation. A similar behaviour is likely to occur in β-Nb phase found in Zr-Nb alloys. The implications of these findings for Cr-coated Zr alloy cladding are discussed.

Directed long-range transport of a nearly pure component atom clusters by the electromigration of a binary surface alloy

Assuming a vacancy-mediated diffusion, a continuum model for electromigration-driven transport of an embedded atom cluster across a surface terrace of a phase-separating A$_x$B$_{1-x}$ surface alloy, such as fcc AgPt(111), is presented. Computations show that the electron wind carries the cluster over hundreds of lattice spacings and in the set direction, while the cluster grows and its purity improves during the drift. Impacts of the current density, the diffusion anisotropy, the magnitude and sign of the ratio of the effective charges $q_A/q_B$, and the jump frequencies ratio $\Gamma_A/\Gamma_B$ on the cluster's drift speed, drift direction, purity and shape are demonstrated.

Predicting activation energies for vacancy-mediated diffusion in alloys using a transition-state cluster expansion

Kinetic Monte Carlo models parameterized by first principles calculations are widely used to simulate atomic diffusion. However, accurately predicting the activation energies for diffusion in substitutional alloys remains challenging due to the wide variety of local environments that may exist around the diffusing atom. We address this challenge using a cluster expansion model that explicitly includes a sublattice of sites representing transition states and assess its accuracy in comparison with other models, such as the broken bond model and a model related to Marcus theory, by modeling vacancy-mediated diffusion in Pt-Ni nanoparticles. We find that the prediction error of the cluster expansion is similar to that of other models for small training sets, but with larger training sets the cluster expansion has a significantly lower prediction error than the other models with comparable execution speed. Of the simpler models, the model related to Marcus theory yields predictions of nanoparticle evolution that are most similar to those of the cluster expansion, and a weighted average of the two approaches has the lowest prediction error for activation energies across all training set sizes.

M-Site Vacancy-Mediated Adsorption and Diffusion of Sodium on Ti2CO2 MXene

MXenes is a promising electrode material for Na ion batteries. To achieve better electrode performance in different aspects, we provide theoretical insight into vacancy engineering of a common MXen...

Multicomponent diffusion in ionic crystals: theoretical model and application to combined tracer- and interdiffusion in alkali feldspar

We present a model for multicomponent diffusion in ionic crystals. The model accounts for vacancy-mediated diffusion on a sub-lattice and for diffusion due to binary exchange of different ionic species without involvement of vacancies on the same sub-lattice. The diffusive flux of a specific ionic species depends on the self-diffusion coefficients, on the diffusion coefficients related to the binary exchanges, and on the site fractions of all ionic species. The model delivers explicit expressions for these dependencies, which lead to a set of coupled non-linear diffusion equations. We applied the model to diffusion of ^{23}Na, ^{39}K, and ^{41}K in alkali feldspar. To this end, gem-quality crystals of alkali feldspar were used together with ^{41}K doped KCl salt as diffusion couples, which were annealed at temperatures between 800^circ and 950^circC. Concentration-distance data for ^{23}Na, ^{39}K, and ^{41}K were obtained by Time of Flight Secondary Ion Mass Spectrometry. Over the entire investigated temperature range the Na self-diffusion coefficient is by a factor of ge 500 higher than the K self-diffusion coefficient. Diffusion mediated by binary ^{39}K–^{41}K exchange is required for obtaining satisfactory fits of the model curves to the experimental data, and the respective kinetic coefficient is well constrained.

Vacancy-mediated diffusion of atoms at Ge/Si interfaces: An atomistic perspective

The diffusive transport of atoms at the interface between germanium and silicon is a phenomenon of key importance in understanding the electronic, thermal, and structural behavior of many hetero-epitaxial semiconductor devices and superlattices. Here we explore this phenomenon from the perspective of vacancy-diffusion at the Ge/Si interfaces. By employing the atomistic nudged elastic band method, we obtain the diffusion enthalpies, transition pathways, and activation barriers for the vacancy-mediated diffusion of interfacial atoms. In particular, the {100}, {111}-glide, and {111}-shuffle pseudomorphic interfaces have been examined, and the tendency of a vacancy to cross the interface has been evaluated. Such calculations facilitate the identification of paths and interfaces with minimum and maximum resistance against the vacancy-mediated migration of interfacial atoms. Our computations reveal that the {111}-glide interface exhibits the least tendency of interface-crossing diffusion of vacancies, whereas the {111}-shuffle interface promotes such diffusion. In addition, the atomistic calculations also reveal a unique stable state of Ge monovacancy at the Ge/Si {111}-shuffle interface.

Vacancy- and interstitial-mediated self-diffusion coefficients determined from the analysis of observed self-diffusion coefficients in silicon crystals

We clarify the mechanisms of self-diffusion mediated by both vacancies and interstitials in silicon crystals. Südkamp and Bracht published carefully measured self-diffusion data for silicon and determined the vacancy-mediated diffusion coefficients from the difference between their new data and previous data of metal diffusion under consideration of a correlation factor. Instead, we analyzed their data using the vacancy properties: the formation energy was obtained from quenching experiments of silicon crystals in a hydrogen atmosphere, and the migration energy determined from low-temperature electron irradiation. The self-diffusion coefficient is given by the sum of the diffusion coefficients of the vacancy mechanism, 0.90 exp (−4.30 eV/kBT), and the interstitial mechanism, 6.9 × 102 exp (−4.8 eV/kBT) cm2 s−1.

A comprehensive theoretical picture of E centers in silicon: From optical properties to vacancy-mediated dopant diffusion

Among the common vacancy-related point defects in silicon, the E center is one of the most prominent due to its degrading effect in silicon-based technology. Even though it has been the subject of extensive experimental and theoretical studies, a comprehensive theoretical model capable of reproducing the experimental evidence for all three dopants (P, As, and Sb) is still missing. Guided by a Jahn-Teller model, we are able to reproduce the absorption bands and the transition probability between equivalent geometries of the defect at low temperatures by including many-body-perturbation corrections based on the GW approximation on top of the density functional theory. At higher temperatures, vacancies become mobile centers, enabling the reorientation of the whole defect and contributing to the dopant diffusion. The underlying mechanisms of the vacancy-mediated dopant diffusion are revisited, characterizing the activation energies of such technologically relevant processes and obtaining quantitative results in good agreement with experiment.

Ionic and Electronic Conduction in TiNb2O7.

TiNb2O7 is a Wadsley–Roth phase with a crystallographic shear structure and is a promising candidate for high-rate lithium ion energy storage. The fundamental aspects of the lithium insertion mechanism and conduction in TiNb2O7, however, are not well-characterized. Herein, experimental and computational insights are combined to understand the inherent properties of bulk TiNb2O7. The results show an increase in electronic conductivity of seven orders of magnitude upon lithiation and indicate that electrons exhibit both localized and delocalized character, with a maximum Curie constant and Li NMR paramagnetic shift near a composition of Li0.60TiNb2O7. Square-planar or distorted-five-coordinate lithium sites are calculated to invert between thermodynamic minima or transition states. Lithium diffusion in the single-redox region (i.e., x ≤ 3 in LixTiNb2O7) is rapid with low activation barriers from NMR and DLi = 10–11 m2 s–1 at the temperature of the observed T1 minima of 525–650 K for x ≥ 0.75. DFT calculations predict that ionic diffusion, like electronic conduction, is anisotropic with activation barriers for lithium hopping of 100–200 meV down the tunnels but ca. 700–1000 meV across the blocks. Lithium mobility is hindered in the multiredox region (i.e., x > 3 in LixTiNb2O7), related to a transition from interstitial-mediated to vacancy-mediated diffusion. Overall, lithium insertion leads to effective n-type self-doping of TiNb2O7 and high-rate conduction, while ionic motion is eventually hindered at high lithiation. Transition-state searching with beyond Li chemistries (Na+, K+, Mg2+) in TiNb2O7 reveals high diffusion barriers of 1–3 eV, indicating that this structure is specifically suited to Li+ mobility.