Jump Attempt Frequency Research Articles

Machine learning based on-the-fly kinetic Monte Carlo simulations of sluggish diffusion in Ni-Fe concentrated alloys

Defect diffusion in concentrated alloys plays a key role on governing their unique mechanical and physical properties. In such alloys, defect diffusion depends on its complex local atomic environment and varies from site to site due to the chemical disorder. On-the-fly determination of the defect migration barrier at every site using the standard nudged elastic band (NEB) method is computationally expensive and often impractical. In this work, we couple machine learning and kinetic Monte Carlo (KMC) to study vacancy-mediated sluggish diffusion in concentrated Ni-Fe model alloys. Based on about 32,000 pre-calculated NEB barriers, an artificial neural network (ANN) based machine learning model is developed to accurately predict the vacancy migration barriers for arbitrary local atomic environments, including both random solution configurations and alloys with short-range orders. The ANN model is then coupled with KMC (ANN-KMC) to determine the vacancy migration barriers on-the-fly, enabling an efficient study of the vacancy diffusion in the full composition range at a wide range of temperatures. In addition, a composition and temperature dependent jump attempt frequency model is developed. Upon calibration, the ANN-KMC modeling can predict nearly identical vacancy diffusivities as those obtained from independent molecular dynamics (MD) and temperature accelerated dynamics (TAD) simulations at their accessible temperatures. The sluggish diffusion mechanisms in this specific alloy system at both high and low temperatures are discussed based on the ANN-KMC results.

Design Principles for Rotational Cluster Anion [BH4]− Promote Superionic Conductivity in Sodium-Rich Antiperovskite Na3OBH4

The ionic conductivity is determined by the activation energies and the jump attempt frequencies of carrier migrations between adjacent sites. However, few works in the past have considered the influence of the attempt frequency. In this work, the attempt frequencies of carrier migrations in Na3OBH4 and Na3OBr are calculated using density functional theory and written as the contribution of each element using frequency analysis, which can be used to calculate the conductivity of a carrier in combination with the defect concentration, migration barrier of carrier migration in equilibrium. The results show that the conductivity of sodium cations can be greatly improved by substituting Br− with the [BH4]− tetrahedral anion in an antiperovskite structure due to two reasons: (1) the paddle-wheel mechanism (PWM) of the [BH4]− anionic groups can effectively reduce the activation energy and (2) the [BH4]− anionic groups with a high vibration frequency undoubtedly improve the carrier jump attempt frequency by the buffering effect. The quasi-harmonic approximation (QHA) is used to describe the isobaric behavior of Na3OBH4 and Na3OBr, and the results show that carriers have a higher jump attempt frequency in the zero-pressure compared with the constant volume. The ionic conductivity (σ) in Na3OBr and Na3OBH4 are obtained from the Arrhenius equation. The results show that the calculated sodium ionic conductivity of Na3OBH4 is 3–4 orders of magnitude higher than that of Na3OBr at room temperature. The calculated sodium ionic conductivity is lower than the experimental measurement, and the discrepancy is attributed to the overestimation of the calculated migration barrier and the underestimation of the defect concentration.

Effect of Zn Concentration on the Structure, Morphology, and Magnetic Behavior of Ni1 − xZnxFe2O4 Ferrofluid

In this work, we investigated the effect of doping zinc ions onto nickel ferrite upon the structure, morphology, and magnetic properties of Ni1 − xZnxFe2O4 ferrite nanoparticles (x = 0, 0.25, and 0.75) prepared via co-precipitation method. X-ray diffraction analysis showed the presence of the most intense peak corresponding to the (311) crystallographic orientation of NiFe2O4 cubic spinel phase, and the crystallite size obtained from Scherrer formula increased from 6.8 to 11.2 nm when the Zn concentration increases from x = 0 to x = 0.75. Fourier transform infrared spectroscopy analysis confirmed the presence of a prominent band associated to the vibrations of metal ions, as a feature of spinel ferrite phase formation, observing that their band positions were very sensitive to Zn doping concentration. Transmission electron microscopy studies allowed to determinate that for all Zn concentrations, the particle sizes are around 15 nm. The magnetic properties were studied by using the vibrating sample magnetometer at room temperature. The results reveal superparamagnetic behavior determined by the shape of the hysteresis loop, presenting decreased coercive magnetic field and increased saturation magnetization, with increased zinc concentration. Additionally, from field cooling and zero field cooling curves, we can observe the typical behavior of the blocking process assembly of superparamagnetic nanoparticles. Alternate current susceptibility measurements show that the blocking temperature is frequency dependent and shifts toward higher temperatures by increasing the frequency, a characteristic of superparamagnetic, and glassy systems. Furthermore, τ0, related to the jump attempt frequency of the magnetic moment of the nanoparticle between the opposite directions of the magnetization easy axis, is in the range of 2 × 10−10 and 7 × 10−13 s for the three different Zn concentrations, which agrees with characteristic of non-interacting superparamagnetic systems.

Study of dynamic behaviors for nano Fe-doped MgB2 superconductor via ac-susceptibility measurements

Nano-sized superconducting polycrystalline particles of Mg1-xFexB2 (0.00 ≤ x ≤ 0.04; space group P6/mmm) were synthesized through the solid state reaction route. The effect of nano-Fe substitution on ac-susceptibility at varying frequency range from 1 to 3 kHz in addition with ac-amplitude (Hac) and dc-applied field (Hdc) were explored. The dynamical behavior of nano-particles shows the strong magnetic interaction between the nano-clusters with the increase of doping content. This is due to the successful inclusion of Fe3+ ions in the matrix of MgB2. X-ray powder diffraction (XRD) reveals the reduction of average grain size with increasing the doping level. Neel-Arrhenius (N-A) and Vogel-Fulcher (V-F) models were discussed to distinguish the dynamical behaviors of the nano-particles. Remarkably, the V-F model elucidates the experimental results much better than N-A model with the support of some parameters like jump attempt frequency, activation energy, magnetic anisotropy constant and V-F temperature.

Structural deformation and transformation of θ′-Al2Cu precipitate in Al matrix via interfacial diffusion

Metastable θ′-Al2Cu precipitates enhance mechanical properties of Al alloy, but gradually transform to θ phase due to diffusion related coarsening at higher temperatures (>200 °C). To improve understanding of the phase instability and transformation of θ′-Al2Cu, we investigated the interfacial atomic mobility of θ′-Al2Cu precipitate in Al matrix via molecular dynamics (MD). To characterize the interfacial atomic mobility, diffusion properties (activation energy, diffusivity, and jump attempt frequency) with respect to atomic species, interfacial structure, and temperature are calculated using atomic trajectories from MD. For the enhanced accuracy of this analysis, especially at low temperatures, temporal scale of molecular dynamics is significantly extended by employing the parallel replica dynamics. This study, as the first MD investigation on atomic diffusion of θ′-Al2Cu in Al matrix, suggests and discusses (i) structural deformation activated at the semi-coherent θ′-Al2Cu/Al interfaces, (ii) transformation initiated at the edge of the coherent θ′-Al2Cu/Al interface, and (iii) directional dependence of diffusion properties. These findings are expected to be employed in a larger scale phase-field modeling of precipitate growth, and to contribute to the understanding of phase transformation process and the development of alloys with θ′-phase retained to higher temperatures.

Ab initio calculation of the attempt frequency of oxygen diffusion in pure and samarium doped ceria.

The rate of oxygen ion jumps in a solid oxide depends not only on the activation energy but also on the pre-exponential factor of diffusion. In order to allow a fully ab initio prediction of the oxygen ion conductivity in pure and samarium doped ceria, we calculated the attempt frequency for an oxygen ion jump from first principles combining DFT+U, the NEB method, phonon calculations and the transition state theory. Different definitions of the jump attempt frequency are presented. The equivalence of the Eyring and the Vineyard method is shown without restriction to the Gamma point. Convergence checks of the phonon mesh reveal that the common reduction to the Gamma point is not sufficient to calculate the attempt frequency. Calculations of Sm doped ceria revealed an increase of the prefactor. The attempt frequency for the constant pressure case in quasi-harmonic approximation is larger than the attempt frequency at constant volume in harmonic approximation. The calculated electronic energies, enthalpies and entropies of migration are in agreement with the experimental diffusion coefficients and activation energies.

Critical effect of local pressure on jump frequencies in intermetallics

Through an extensive atomic-scale investigation of NiAl 3 , a cementite-like structure, we show that only a proper account of saddle-point pressures leads to unambiguous jump attempt frequency spectra. We also demonstrate that attempt frequencies can spread over ranges exceeding five orders of magnitude and therefore cannot be realistically described by simplified few-valued schemes, as commonly assumed. These issues cast doubt on generally admitted assumptions in kinetic simulations, which may have critical consequences on their accuracy.

Modeling of the Diffusion of Hydrogen in Porous Graphite

The graphite used in fusion devices as first wall material is porous and consists of granules and voids. The 1–10 µm granules are further composed of graphitic micro-crystallites (5–10 nm), which are separated by micro-voids. Understanding the hydrogen transport and trapping in such granules is an important aspect of understanding the effect of a realistic graphite structure on hydrogen recycling and hydrocarbon formation in graphite. We use Kinetic Monte Carlo (KMC) to study the diffusion of hydrogen in a typical granule of graphite. We use molecular dynamics (MD) to obtain the jump attempt frequency ωo and the migration energy Em of interstitial graphite which are inputs to the KMC. A consistent parameterization of MD within KMC is presented. The diffusion shows a non-Arrhenius behavior which can be explained with two types of different jump processes within the graphite crystal. The porous granule structure is constructed using statistical distributions for the crystallite dimensions and for crystallite orientations at a given porosity. The hydrogen trapping at inter-crystallite micro-voids are modeled by assuming that a fraction of the hydrogen atom flux transiting through the micro-void is trapped. We present a parametric study of the diffusion and trapping of hydrogen within the granule for various trapping fractions at the inter-crystallite micro-voids.

Direct determination of the vortex jump attempt frequency in high temperature superconductors

We show that the frequency dependence of the effective critical current, resulting from thermally activated flux motion, may be used to evaluates the jump attempt frequency f o of over vortices over their pinning potential wells. We apply this analysis to estimate f o for a Nd 1.85Ce 0.15CuO 4−y single crystal. The obtained value, f o≈10 9Hz, is in agreement with the theoretical estimates; furthermore, this high value, together with the experimental activation energies U(T,H,J), allow to explain the important thermally activated flux motion effects in these superconductors, observed at low temperatures or high frequencies.

A molecular dynamics simulation of the diffusion of sodium on a Cu(001) surface

A molecular dynamics simulation of the diffusion of sodium adatoms on a Cu(001) surface has been performed. A pairwise Morse potential, fitted to the adatom adsorption geometry, binding energy, vibrational frequencies and activation energy for diffusion is used to model the sodium-copper interaction. Good agreement is obtained with quasielastic helium scattering data for the system, confirming the interpretation that sodium diffuses by jumps from one four-fold hollow site to another with an effective activation energy of 51 meV and a jump attempt frequency of 0.53 THz. The measured jump rate is lower than that predicted by transition state theory. The MD simulation suggests that this discrepancy arises because the rate of energy transfer between the adatom and the substrate is so slow that it controls the attempt rate rather than the vibrational frequencies of the adatom as transition state theory would predict.

Observation of jump diffusion of isolated sodium atoms on a Cu(001) surface by helium atom scattering.

The diffusion of sodium adatoms on a Cu(001) surface has been studied with quasielastic helium atom scattering. A jump mechanism was found with activation energy 51 meV, jump length 2.56 \AA{}, and jump attempt frequency ${\ensuremath{\nu}}_{0}$ 0.53 THz. The adatom vibrational frequency parallel to the surface is measured to be 1.23 THz. The data are interpreted with the aid of a realistic molecular-dynamics simulation which reveals that ${\ensuremath{\nu}}_{0}$ is governed by the rate of energy exchange between the adatoms and the substrate, and not, as transition state theory would predict, by the vibrational frequencies of the adatom.

Nuclear magnetic resonance survey of hydrogen motion and electronic structure in α-phase (NbMo)-H alloys

The results of a proton nuclear magnetic resonance (NMR) survey of hydrogen motion and electronic structure in the solid solution (α) phase of niobium rich Nb1−yMoyHx alloys are reported (y ⩽ 0.2, x ⩽ 0.2). Measurements of the temperature dependence of the proton spin-lattice relaxation time T1 over the range 20 ⩽ T ⩽ 800 K were analyzed to yield values of the activation energy Ea and jump attempt frequency v0 for hydrogen diffusive hopping and of the product T1eT = Ce indicative of the electronic density-of-states at the Fermi level, N(EF), where T1e is that contribution to T1. The T1vs. T behavior shows features characteristic of hydrogen in random alloys, reflecting a distribution of Ea and v0 values. At high temperatures (~ 500 K), T1 exhibits anomalous behavior, passing through a maximum and decreasing again at higher temperatures in the same manner found in the NbH and (NbV)-H systems.

Hydrogen dynamics in hydro-sodalite Na8 [AlSiO4]6 (OH)2 by inelastic and quasielastic neutron scattering

The dynamical properties of hydrogen in the sodalite Na8[AlSiO4]6 (OH)2 were investigated by quasielastic and inelastic neutron scattering techniques. The data were analyzed with a jump model for the hydrogen motion (OH reorientation). The characteristic time of the jump process is 2.1 ps at 295 K, the frequency of the local vibration (jump attempt frequency) is 17.4 THz. The detailed analysis shows that the hydrogen environment in the (Na4OH)3+ complex cation has lower than tetrahedral symmetry.

The compensation law for conductivity of ionic crystals

The conductivity prefactor A is specified as a function of the conductivity activation energy E A for a large series of alkali halide type crystals and of superionic conductors (SIC). A linear dependence of the form log A = 2.1 E A + 5.3 is observed for classical ionic conductors (CIC) with values of E A > 0.9 eV, as well as for SIC with E A > 0.4 eV. Such behavior, known as the compensation law (CL) cannot be understood within the framework of the conventional assumption of temperature-dependent E A values. It is demonstrated that the CL is characteristic for defect formation as well as for defect migration processes, with corresponding isokinetic temperatures T 0 = 2.8 × 10 3 K and T μ = 2.1 × 10 3 K, respectively. For lower values of E A ( E A < 0.9 eV for CIC and E A < 0.4 eV for SIC) a considerable decrease in the prefactor is observed. This is interpreted in terms of melting or positional disordering of mobile ions in the cation sublattice of the crystal. This means that entropy change for mobility S μ is quite small, or even vanishes for these crystals. It is demonstrated that the conventional practice of using as the jump attempt frequency ν 0 the Debye frequency ν D for the mobile ion seems to be invalid. We propose to use instead the expression suggested by Rice and Roth: ν 0 = ( 1 π ) · √ 2H μ a 2m .

Molecular-dynamics studies of grain-boundary diffusion. II. Vacancy migration, diffusion mechanism, and kinetics

Vacancy jumps in a bicrystal model of $\ensuremath{\Sigma}=5$ (36.9\ifmmode^\circ\else\textdegree\fi{}) [001] tilt boundary in bcc Fe have been simulated at temperatures of 1300, 1400, and 1500 K by molecular dynamics with the use of the empirical Johnson potential. The results confirm the dominance of a vacancy mechanism in grain-boundary diffusion. An activation energy of 0.51 eV for vacancy migration has been obtained along with a reasonable value of the jump-attempt frequency. Analysis of the jump directions shows a preferential bias along the tilt axis. The relation between diffusivity and atomic mean-square displacement is examined. It is suggested that the structure dependence of grain-boundary diffusion may be expressed through a matrix of transition probability for vacancy jumps among the various discrete sites.

Fast-proton transport in hydrazine sulphate. II. NMR linewidth and relaxation studies

For pt.I see ibid., vol.16, no.16, p.3081 (1983). The proton mobility has been observed in hydrazine sulphate (H2H6SO4) from NMR studies. The linewidth has been measured as a function of temperature. It shows a sudden line narrowing at 150K indicating that the H+ are mobile at temperatures higher than this. Further, a minor hump in the linewidth curve is obtained at 228K which indicates a structural change. The relaxation time measurement (T1 and T2) also confirms the above conclusion. From the linewidth data at different temperatures, the jump attempt frequency is estimated to be about 1011 s-1. The low attempt frequency of about 1011 s-1 is nearly the proton tunnelling frequency suggesting H+ motion.

Measurement of hydrogen diffusion in Mg 2NiH 2 using nuclear magnetic resonance

We measured the nuclear spin-lattice relaxation time T 1 of protons in Mg 2NiH 4 and determined the hydrogen diffusion parameters, yielding an activation energy E a = 10.6 ± 0.4 kcal mol −1 (0.46 ± 0.02 eV) and a jump attempt frequency ν 0= 6.6 × 10 13 Hz in the temperature region 210 – 480 K.

NMR study of hydrogen diffusion in the three different phases of the titanium-hydrogen system

The proton spin lattice relaxation time T 1 has been measured by an NMR pulse technique at 19.00 MHz as a function of temperature in the range 25°–500°C for a series of samples in the α, β and γ phases of titanium hydride. The relaxation mechanism in the α and γ phases was governed primarily by hydrogen diffusion over most of the temperature range. The diffusional activation energy in the γ phase was found to be constant with respect to the hydrogen concentration, having a value of 11.77 ± 0.4 kcal mole , and the attempt jump frequency was found to be proportional to the available local vacancies. The activation energy behavior is discussed in relation to a previously proposed model for hydrogen diffusion in titanium and the jump attempt frequency is compared to available data on the optical mode of the hydrogen vibrations. Evidence was found for a uniform distribution in the γ phase when the ratio of hydrogen to titanium, x, is greater than 1.6 while clustering takes place at lower ratios. The low temperature γ phase transition concentration at x = 1.6 was found to be related to the electronic structure from ( T 1) e data. The conduction electrons were the primary cause of relaxation in the γ phase near room temperature and the contribution of this mechanism to the relaxation rate increased with increase in hydrogen concentration. ( T 1) e T ranged from 190 ± 4sec-°K to 62.5 ± 2 sec −°K as x (the ratio of hydrogen to titanium atoms) varied from 1.55 to 1.90. The α + gg, γ phase boundary was found between 25° and 100°C. Diffusion parameters were measured for the α phase and the gradual transition from the α + γ to γ region observed. The transition from the α + γ to the β phase was observed and a heating-cooling hysteresis effect was displayed. T 1, for the β phase near 450°C of TiH 0.78 was governed mainly by the conduction electrons and a value of( T 1) e T = 58±5 sec −° K was found.