Migration Enthalpy Research Articles

Formation and Migration Enthalpy from Elemental and Cooperative Diffusion in Lead Silicate Supercooled Liquid and Glass

Formation and Migration Enthalpy from Elemental and Cooperative Diffusion in Lead Silicate Supercooled Liquid and Glass

Revisiting the diffusion coefficient calculation of Mg in face centred cubic aluminium

The trajectory along the diffusion path is determined by structure repetitions, or images, within the Nudged Elastic Band methodology. In the literature using a single image, among the initial and final position of the vacancy site, is well accepted to determine the transition state, and hence, the enthalpy of migration to model diffusion within aluminium. Scaling the number of evolving images, in the Nudged Elastic Band methodology, is performed for the first time to our knowledge, to determine transition states for the diffusion of magnesium in face centred cubic aluminium. Since a single image locates the transition state away from the expected middle place, along the diffusion path. With an odd number of evolving images is possible to clearly place the saddle point exactly halfway, in between extremal positions, as the enthalpy of migration converges its magnitude. Adjusting the number of evolving images consolidates then a scheme to accurately determine transition states, within the methodology to compute macroscopic diffusion factors, and the results also demonstrate that single image calculations provide a coarse result for diffusion parameters, meanwhile, the converged number of images locates the Arrhenius plot in good agreement with previous ab-initio calculations and experimental measurements.

Silicon diffusion in AlN

In this study, we investigate the diffusion of Si donors in AlN. Amorphous Si1−xNx sputtered on the surface of bulk AlN with low dislocation density is used as a Si source. The diffusion experiments are conducted through isochronal and isothermal annealing in a protective N2 atmosphere at temperatures between 1500 and 1700 °C. The Si depth profiles measured by secondary ion mass spectrometry exhibit a convex box-like shape with a steep diffusion front. These concentration profiles are best described with a diffusion coefficient that depends on the square of local Si concentration. From the characteristic box-shaped Si profiles, we conclude that diffusion of Si in AlN is mediated by singly negatively charged dopant–vacancy pairs SiAlVAl−. The strong concentration dependence of Si diffusion is due to the electric field associated with the incorporation of Si donors (SiAl+1) on substitutional Al lattice sites and reflects that Si is fully electrically active at diffusion temperature. The experimentally obtained extrinsic Si diffusion coefficient is reduced to intrinsic doping conditions. The temperature dependence of Si diffusion for intrinsic conditions is described by an activation enthalpy of (10.34±0.32)eV and a pre-exponential factor of 235−203+1485cm2s−1. The migration enthalpy of the donor–vacancy pair SiAlVAl− is estimated to be around 3.5 eV. This estimation is based on the activation enthalpy of the transport capacity of SiAlVAl− and theoretical results concerning the formation energy of negatively charged vacancies on Al-sites in AlN.

The Sluggish Diffusion of Cations in CeO2 Probed through Molecular Dynamics and Metadynamics Simulations

Cation diffusion in fluorite‐structured CeO2, though far slower than anion diffusion, is an important, high‐temperature process because it governs diverse fabrication and degradation phenomena. Herein, cation diffusion is studied by means of classical molecular dynamics and metadynamics simulations. Three different mechanisms are examined: migration involving an isolated cerium vacancy, migration involving a cerium vacancy in a defect associate with an oxygen vacancy, and migration involving a cation divacancy. For each mechanism, defect diffusion coefficients are calculated as a function of temperature, from which the respective activation enthalpy of defect migration is obtained. Through comparisons with experimental cation diffusion data (specifically, of the absolute magnitude of the cation diffusivity as well as its activation enthalpy), it is concluded that cation diffusion takes place predominantly neither by isolated vacancies nor by cation vacancy–oxygen vacancy associates but by cation divacancies.

Effect of Lithium Iodide on transport phenomenon in Lithium Borophosphate glass Electrolyte

Ion transport study for the lithium iodide doped Lithium Borophosphate (LBP) glass electrolyte x(LiI):[(100−x).(60Li2O:8B2O3:32P2O5)] has been carried out over a range of composition (x=0 to 25 wt.%). The electrical conductivity has been measured by complex impedance spectroscopy from 303 K to 423 K temperature. The physical parameter and conductivity study indicate to obey the Arrhenius relationship and the frequency dependent conductivity is in consonance with Jonscher's universal power law. The Correlated Barrier Hopping (CBH) model for ion transport is observed to follow in the present glass system. Further investigation of the conductivity has also been carried out to calculate the hopping frequency (ωp), relaxation time (τ), power-law exponent (n) and decoupling index (Rτ). The enthalpy for migration and free energy have been estimated using the frequency-dependent power-law exponent (n) behaviour. Charge dynamics between local states due to the activated hopping process has been discussed according to Anderson- Drago and Elliot's model. To reinforce the Lithium ion transport study, several physical parameters such as density (ρ), molar volume (VO), oxygen packing density (OPD), cation concentration (NLi), the mean distance between cations (R′LiI) and the total number of energy states per unit volume at Fermi level N(Ef) have been calculated using various empirical formulae to discuss the present LBP ionic glass system.

Vacancies in thermal equilibrium and ferromagnetism near the Curie temperature

Abstract In several refractory body-centred cubic metals (α-Fe, V, Nb, Ta) the binding energy of positrons (e+) trapped in vacancies is too small to permit accurate determinations of the enthalpy of formation of monovacancies, H 1V F , $ H_{{\rm{1V}}}^{\rm{F}},$ by high-temperature positron annihilation. Owing to their larger mass, trapped positive muons (μ+) and π-mesons (π+) are much more firmly bound to vacancies. It is argued that the lattice steering (channelling or blocking) of their charged decay products (e+ or μ+) allows us to obtain accurate H 1V F $ H_{{\rm{1V}}}^{\rm{F}}$ values of the refractory bcc metals. In ferromagnets with high Curie temperatures T C, such as α-Fe, Co, and FeCo alloys, H 1V F $ H_{{\rm{1V}}}^{\rm{F}}$ may also be deduced from muon spin rotation (μ+SR) measurements. However, in Fe and Co this approach is limited by the strong sensitivity of the spontaneous magnetization against temperature fluctuations near T C. The reduction of this sensitivity in the so-called asymptotic critical regime by applying sufficiently strong external magnetic fields is investigated on the basis of the Arrott– Noakes equation. A method for determining the critical amplitudes occurring in this equation is proposed. In disordered Fe1–xCox alloys (0.2 ≤ x ≤ 0.75) the Curie temperatures are sufficiently high for the spontaneous magnetization in the bcc phase not to be critically affected by temperature fluctuations, hence these alloys are well suited for μ+SR investigations of thermal vacancies. From an analysis of the available positron-annihilation and self-diffusion data the vacancy migration enthalpy in disordered Fe0.5Co0.5 is found to be (1.1 ± 0.2) eV, in good agreement with quenching data and with the value established for α-Fe.

Conduction Mechanism and Dielectric Properties in Polyaniline/Titanium Dioxide Composites

The conductivity and dielectric properties of polyaniline (PANI) and PANI/TiO2 composites have been studied over a temperature range (313-393 K) and frequency range (25 Hz- 50 MHz). The nature of temperature and frequency-dependent conductivity can be explained by Jonscher’s universal power law and used to find the related parameters such as frequency exponent (s), dc conductivity (σdc), and crossover frequency (ωH). Besides, the frequency exponent analysis through a distinct model suggests that the conduction occurred through small polaron tunnelling in all compositions and at different temperatures. On the other hand, the enthalpy of migration (Hm), dissociation enthalpy of cation from its indigenous location alongside a compensating center (Hf), and the activation energy were also calculated using the Arrhenius relation. The temperature-dependent dc conductivity was examined in the framework of the theoretical model; Mott’s variable range hopping model (VRH) and experimental results were in good agreement with the 3-dimensional VRH model. As a function of temperature, dielectric constants (ε’ and ε”) increase while decreasing with an increasing dopant. Being such a high dielectric constant value, these composites can be used as frequency converters, modulators, and dielectric amplifiers.

Ion transport mechanism in anhydrous lithium thiocyanate LiSCN Part I: ionic conductivity and defect chemistry.

This work reports on the ion transport properties and defect chemistry in anhydrous lithium thiocyanate Li(SCN), which is a pseudo-halide Li+ cation conductor. An extensive doping study was conducted, employing magnesium, zinc and cobalt thiocyanate as donor dopants to systematically vary the conductivity and derive a defect model. The investigations are based on impedance measurements and supported by other analytical techniques such as X-ray powder diffraction (XRPD), infrared (IR) spectroscopy, and density functional theory (DFT) calculations. The material was identified as Schottky disordered with lithium vacancies being the majority mobile charge carriers. In the case of Mg2+ as dopant, defect association with lithium vacancies was observed at low temperatures. Despite a comparably low Schottky defect formation enthalpy of (0.6 ± 0.3) eV, the unexpectedly high lithium vacancy migration enthalpy of (0.89 ± 0.08) eV distinguishes Li(SCN) from the chemically related lithium halides. A detailed defect model of Li(SCN) is presented and respective thermodynamic and kinetic data are given. The thiocyanate anion (SCN)- has a significant impact on ion mobility due to its anisotropic structure and bifunctionality in forming both Li-N and Li-S bonds. More details about the impact on ion dynamics at local and global scale, and on the defect chemical analysis of the premelting regime at high temperatures are given in separate publications (Part II and Part III).

Investigation of the effect of local atomic polarization on field-enhanced ion transport in insulating binary oxides: The case of CeO2

Over the course of more than 70 years, several theoretical models for electric field-enhanced ion diffusion in crystalline insulators have been presented. However, there is no assessment of the validity of these models despite the urge to have a correct description of field-enhanced ion diffusion in several emerging technologies. Herein, an assessment of five models was carried out by computing the field-dependent migration enthalpy $\mathrm{\ensuremath{\Delta}}{H}_{\mathrm{mig}}(E)$ for the oxide ion in ${\mathrm{CeO}}_{2}$. The input to these models is the zero-field and zero-temperature migration pathway and/or the activation barrier obtained from an interatomic potential. $\mathrm{\ensuremath{\Delta}}{H}_{\mathrm{mig}}(E)$ from these models was compared with reference values obtained from a set of classical molecular-dynamics simulations in the temperature range of $1000\phantom{\rule{4pt}{0ex}}\ensuremath{\le}T\ensuremath{\le}1600\phantom{\rule{4pt}{0ex}}\mathrm{K}$ and the electric field range of $0\phantom{\rule{4pt}{0ex}}\ensuremath{\le}E\ensuremath{\le}30\phantom{\rule{4pt}{0ex}}\mathrm{MV}/\mathrm{cm}$. It is revealed that the most successful theoretical models are those that consider local polarization effects induced in the diffusing ion itself and its vicinity. However, all the models did not account for the effect of the electric field and finite temperature on the local polarization, leading to discrepancies between the predicted and the reference $\mathrm{\ensuremath{\Delta}}{H}_{\mathrm{mig}}(E)$, particularly at high fields. By comparing results from a rigid-ion potential and a polarizable core-shell potential, it is concluded that an intraionic polarization degree of freedom in the polarizable potential is an important factor in predicting $\mathrm{\ensuremath{\Delta}}{H}_{\mathrm{mig}}(E)$, regardless of the field-enhanced diffusion model particularly for low to moderate field. Future more accurate treatments should consider the field- and temperature-dependent interionic and intraionic local polarization effects.

Metadynamics simulations of strontium-vacancy diffusion in SrTiO3

The sluggish diffusion of strontium vacancies in the perovskite-oxide ${\mathrm{SrTiO}}_{3}$ was studied by means of classical metadynamics simulations. Two different mechanisms were examined: the migration of an isolated strontium vacancy and the migration of a strontium vacancy in a defect associate with an oxygen vacancy. Combining activation Gibbs energies of migration with the appropriate temperature-dependent pre-exponential terms, we obtained diffusivities of strontium vacancies by the two mechanisms for the temperature range $1000\ensuremath{\le}T/K\ensuremath{\le}2000$. Comparisons with experimental data (where available) yield excellent agreement, both in terms of the effective activation enthalpy of migration as well as the absolute rate of diffusion. In this way we demonstrate the ability of classical metadynamics simulations to predict diffusion coefficients quantitatively for extremely slow-moving defects in oxides, and we highlight the complexity of cation diffusion in perovskite materials.

Impact of Oxygen Non‐Stoichiometry on Near‐Ambient Temperature Ionic Mobility in Polaronic Mixed‐Ionic‐Electronic Conducting Thin Films

AbstractEnhanced ionic mobility in mixed ionic and electronic conducting solids contributes to improved performance of memristive memory, energy storage and conversion, and catalytic devices. Ionic mobility can be significantly depressed at reduced temperatures, for example, due to defect association and therefore needs to be monitored. Measurements of ionic transport in mixed conductors, however, proves to be difficult due to dominant electronic conductivity. This study examines the impact of different levels of quenched‐in oxygen deficiency on the oxygen vacancy mobility near room temperature. A praseodymium doped ceria (Pr0.1Ce0.9O2–δ ) film is grown by pulsed laser deposition and annealed in various oxygen partial pressures to modify its oxygen vacancy concentration. Changes in film non‐stoichiometry are monitored by tracking the optical absorption related to the oxidation state of Pr ions. A 13‐fold increase in ionic mobility at 60 °C for increases in oxygen non‐stoichiometry from 0.032 to 0.042 is detected with negligible changes in migration enthalpy and large changes in pre‐factor. Several factors potentially contributing to the large pre‐factor changes are examined and discussed. Insights into how ionic defect concentration can markedly impact ionic mobility should help in elucidating the origins of variations seen in nanoionic devices.

Vacancy diffusion in palladium hydrides.

The self-diffusion coefficients of palladium in PdHx (x = 0, 0.25, 0.5, 0.75, 1) were studied using density functional theory to obtain the required thermodynamic and kinetic parameters. The enthalpy of migration decreased from 0.95 eV for Pd to 0.78 eV for PdH. The enthalpy of vacancy formation exhibited a substantial decrease from about 1.1 eV in Pd to 0.4 eV in PdH, which was ascribed to successive filling of antibonding states weakening the Pd-Pd bonds. Concurrently, the Arrhenius pre-exponential was significantly reduced from 4.75 × 10-3 cm2 s-1 for Pd to 5.67 × 10-9 cm2 s-1 for PdH due to softening of the vibrational modes that determine the entropy of vacancy formation and initial/transition state frequencies. A linear correlation between the logarithm of the pre-exponential and the activation energy was interpreted as enthalpy-entropy compensation (Meyer-Neldel rule). The Pd self-diffusion coefficients in the hydrides were within 1 order of magnitude of that in pure palladium above 200 °C for hydrogen pressures up to at least 107 Pa.

Defect chemistry and transport properties of perovskite-type oxides La1−xCaxFeO3−δ

Correlating the migration enthalpy of oxygen in perovskite-type oxides La1−xCaxFeO3−δ with the formation enthalpy of oxygen vacancies.

Determination of the vacancy migration enthalpy in a ternary Fe54Cr16Ni30 alloy, by Monte Carlo simulation of ordering kinetic, using a vacancy diffusion mechanism

We determined the vacancy migration enthalpy in a Fe54Cr16Ni30 stainless steel with a face-centered cubic structure by Monte Carlo simulation of the kinetic ordering by a vacancy diffusion mechanism. We have calculated isothermal curves of electrical resistivity variation as a function of time, at two different temperatures T1 = 700 K and T2 = 800 K (Barkani et al., 2007) [1], (Belkadi et al., 2019) [2]. The vacancy migration enthalpy determined in our work ΔHVM = (1.10 ± 0.031) eV, is higher than that determined by Yoshihiro Sekio et al. [3] in an alloy with a composition close to that of our alloy, and which is 0.77 eV. It is slightly lower than that determined by Dimitrov et al. [4] who found a value of 1.17 eV, independent of nickel content for Fe-Cr-Ni steels containing 16% Cr and a nickel concentration ranging from 20%Ni to 45%Ni.

The Effects of Severe Plastic Deformation and/or Thermal Treatment on the Mechanical Properties of Biodegradable Mg-Alloys

In this study, five MgZnCa alloys with low alloy content and high biocorrosion resistance were investigated during thermomechanical processing. As documented by microhardness and tensile tests, high pressure torsion (HPT)-processing and subsequent heat treatments led to strength increases of up to 250%; as much as about 1/3 of this increase was due to the heat treatment. Microstructural analyses by electron microscopy revealed a significant density of precipitates, but estimates of the Orowan strength exhibited values much smaller than the strength increases observed. Calculations using Kirchner’s model of vacancy hardening, however, showed that vacancy concentrations of 10−⁵ could have accounted for the extensive hardening observed, at least when they formed vacancy agglomerates with sizes around 50–100 nm. While such an effect has been suggested for a selected Mg-alloy already in a previous paper of the authors, in this study the effect was substantiated by combined quantitative evaluations from differential scanning calorimetry and X-ray line profile analysis. Those exhibited vacancy concentrations of up to about 10−3 with a marked percentage being part of vacancy agglomerates, which has been confirmed by evaluations of defect specific activation migration enthalpies. The variations of Young’s modulus during HPT-processing and during the subsequent thermal treatments were small. Additionally, the corrosion rate did not markedly change compared to that of the homogenized state.

Insight into understanding the jump frequency of diffusion in solids

In view of the diversity and ambiguity of the interpretation of the physical nature contributing to the jump frequency of diffusion in solids, the fundamental of jump frequency is reexamined with special attention toward enthalpy and entropy aspects. The present model, extending the approaches of Burke and Shewmon, provides an insight into understanding the jump frequency of diffusion in solids. The entropy term involved in the frequency or pre-exponential factor basically stems from the change in the vibration frequency of the atoms in a transitional complex. Migration enthalpy is the sum of the thermal energy required for the vibration amplitude of the jumping atom to reach the critical amplitude and the elastic energy of minimal local deformation developed in a transitional complex.

Low-frequency noise and thermal equilibrium properties of vacancies

A model explaining Lorentzian low-frequency noise spectra observed in electronic interconnects is presented. The model is based on the interaction of electrons with vacancies, whose thermodynamic equilibrium properties determine the temperature dependence of the noise. The model, therefore, allows calculating vacancy formation and migration enthalpies. It is experimentally verified on copper and tungsten interconnects; the sum of formation and migration enthalpies matches the electromigration activation energy obtained using standard accelerated tests.

Highest Ionic Conductivity of BIMEVOX (ME = 10% Cu, 10% Ga, 20% Ta): Computational Modeling and Simulation

BIMEVOX had the potential to play an important role in solid oxide fuel cell, especially as the electrolyte due to their high ionic conductivity. In this work, oxide ion migrations of γ-Bi2VO5.5 and BIMEVOX were simulated using density function theory (DFT), Mott-Littleton method, and molecular dynamic simulation. In γ-Bi2VO5.5, there were oxygen vacancies at the equatorial position in the vanadate layers. These vacancies could facilitate oxide ions migration. The Enthalpy of the oxide migration for γ-Bi2VO5.5 based on DFT calculation was 0.38 eV, which was in a good agreement with experimental results. The γ-Bi2VO5.5 can be stabilized by partial substitution of V5+ with Cu2+, Ga3+, and Ta5+. Defect simulation results using the Mott-Littleton method showed that the total maximum energies of region II were achieved at concentrations of 10, 10, and 20%, respectively for Cu2+, Ga3+, and Ta5+. The calculated concentration of Cu2+, Ga3+, and Ta5+ were in a good agreement with those of experiment results, where the highest ionic conductivity obtained. The results of the molecular dynamics simulation showed that the activation energies of oxide ion migration in γ-Bi2VO5.5 and BIMEVOX (ME = Cu and Ta) respectively were 0.19, 0.21, and 0.10 eV, close to experimental values.

Oxygen ion conductivity in ceria-based electrolytes co-doped with samarium and gadolinium

In a systematic study, two compositional series of ceria-based oxides, both co-doped with Sm and Gd, were synthesised using a low temperature method and evaluated as oxygen ion-conducting electrolytes for Intermediate Temperature Solid Oxide Fuel Cells (IT-SOFCs). Series one, Ce1-2xSmxGdxO2-x, had equal concentrations of Sm and Gd but varying total dopant concentration. Series two, Ce0.825SmxGd0.175-xO1.9125, had a fixed total dopant concentration but the Sm:Gd concentration ratio was varied. The materials were characterised using scanning and transmission electron microscopy, inductively coupled plasma mass spectrometry and X-ray diffraction. Impedance spectra were recorded on dense pellets of these materials. From these, total, bulk and grain boundary conductivities and capacitances along with activation energies, pre-exponential constants and enthalpies of ion migration and defect association were obtained. These gave a detailed insight into the fundamental conduction processes in the materials. Ce0.825Sm0.0875Gd0.0875O1.9125 had the highest total ionic conductivity at temperatures of 550 °C and above and also demonstrated an enhanced conductivity with respect to its singly-doped parent compounds, Ce0.825Sm0.175O1.9125 and Ce0.825Gd0.175O1.9125, at 400 °C and above. This compares favourably with previously-reported values and has promising implications for the development of IT-SOFCs.

The usefulness of molecular-dynamics simulations in clarifying the activation enthalpy of oxygen-vacancy migration in the perovskite oxide BaTiO3

We employed molecular-dynamics simulations with interatomic pair-potentials to examine oxygen-vacancy diffusion in the cubic phase of perovskite BaTiO3 as a function of temperature. By comparing the absolute rate of vacancy diffusion as well as its temperature dependence with experimental data, we are able to narrow down the activation enthalpy of migration to 0.70-0.76 eV.