Iron Self-diffusion Research Articles

Nanoscale Kirkendall shift in thin films studied using x-ray waveguide structures

Kirkendall effect has played an important role in developing the understanding of atomic diffusion and mass transport in solids. In thin films and multilayers, in which the microstructure may be far from thermal equilibrium, behavior of a system can be very different from that of the bulk. Therefore, there is a great need to understand the peculiarities of Kirkendall shift occurring at nanometer or sub-nanometer length scale in such systems. In the present work, Kirkendall shift in thin films has been measured with sub-nanometer accuracy, by making use of x-ray planar waveguide structures. Using this technique, we report an apparently counterintuitive result of Kirkendall shift associated with self-diffusion in nanocrystalline iron. The cavity of the waveguide consists of two layers of iron having different microstructures, separated by a thin marker layer of Ag. Thermal annealing results in shift of the Ag marker towards the Fe layer having a coarser grain structure. The effect is established unambiguously by studying two samples with the order of the two Fe layers reversed, and a third sample with the two Fe layers having the same microstructure. The result can be understood in terms of the difference in the microstructure of the two Fe layers; difference in the grain size and hence different concentration of the grain boundaries in the two layers results in a net mass transfer from one region to the other.

Anisotropic diffusion in symmetric tilt grain boundaries in bcc iron: A DFT study

Diffusion analysis at the atomic scale in three orthogonal directions for both low- and high-energy symmetric tilt grain boundaries (GBs) in bcc iron is presented. Using DFT, we report (i) the energetically preferable configurations of point defects in the GBs (112) and (210) as well as in surrounding atomic layers; (ii) the activation barriers for vacancy and self-interstitial hopping in the GB plane and from the GBs to a nearest atomic layer; (iii) the attempt frequencies in each diffusion direction. The obtained values are refined by taking into account the temperature dependence of magnetization. It has been shown that interstitial and combined interstitial-vacancy mechanisms agree with the experimental data on self-diffusion in bcc iron. The temperature dependencies of the diffusion coefficient are obtained as Arrhenius law taking into account transition between ferro- and paramagnetic states. They provide insight into transport processes at relatively low temperatures which can be important for practical applications.

Iron self-diffusion in B2-FeRh thin film

Iron-rhodium thin films are in the center of scientific interest due to their great potential in spintronic, energy harvesting and other forthcoming applications. The structural stability of these materials in industrial applications relies heavily on their ability to withstand temperature variations, therefore it is crucial to gain a thorough understanding of the diffusion processes induced by temperature. To investigate the self-diffusion of iron in FeRh, an isotope-periodic multilayer structure of [nFe50.5Rh49.5(63 Å)/57Fe51.5Rh48.5(46 Å)]10 was prepared by molecular beam epitaxy. By using neutron reflectivity technique, which is capable of detecting atomic-scale diffusion lengths, we determined the pre-exponent factor and activation energy as D0 = (1.19 ± 0.5) × 10−16 m2s−1 and Ea = (1.00 ± 0.03) eV respectively.

Migration behavior of tellurium in bcc iron against typical alloying elements: A first-principles study

The migration behavior of fission product tellurium in bcc iron is investigated by using the first-principles method. The tellurium energetically prefers to stay at the substitutional site, and strong attractive interactions between tellurium and monovacancies are found. The more introduced vacancy does not affect their migration barriers significantly. For their diffusivities in iron, it shows that the migration energy barriers of tellurium are highly affected with relatively larger atomic size of tellurium and strong binding with vacancy. Tellurium exhibits relatively higher diffusivity when compared to that of iron self-diffusion and common alloying elements in stainless steels (e.g. Cr, Mo, Nb, Ti, Al, Co, Cu, Mn, Ni, and W). This study can provide theoretical guidance to understand the vacancy-assisted lattice diffusion mechanisms for tellurium as well as typical alloy elements in iron.

Viscosity of hcp iron at Earth\u2019s inner core conditions from density functional theory

The inner core, extending to 1,221 km above the Earth’s center at pressures between 329 and 364 GPa, is primarily composed of solid iron. Its rheological properties influence both the Earth’s rotation and deformation of the inner core which is a potential source of the observed seismic anisotropy. However, the rheology of the inner core is poorly understood. We propose a mineral physics approach based on the density functional theory to infer the viscosity of hexagonal close packed (hcp) iron at the inner core pressure (P) and temperature (T). As plastic deformation is rate-limited by atomic diffusion under the extreme conditions of the Earth’s center, we quantify self-diffusion in iron non-empirically. The results are applied to model steady-state creep of hcp iron. Here, we show that dislocation creep is a key mechanism driving deformation of hcp iron at inner core conditions. The associated viscosity agrees well with the estimates from geophysical observations supporting that the inner core is significantly less viscous than the Earth’s mantle. Such low viscosity rules out inner core translation, with melting on one side and solidification on the opposite, but allows for the occurrence of the seismically observed fluctuations in inner core differential rotation.

Study of grain boundary self-diffusion in iron with different atomistic models

We studied grain boundary (GB) self-diffusion in body-centered cubic iron using ab initio calculations and molecular dynamics simulations with various interatomic potentials. A combination of different models allowed us to determine the principal characteristics of self-diffusion along different types of GBs. In particular, we found that atomic self-diffusion in symmetric tilt GBs is mostly driven by self-interstitial atoms. In contrast, in general GBs atoms diffuse predominantly via an exchange mechanism that does not involve a particular defect but is similar to diffusion in a liquid. Most observed mechanisms lead to a significant enhancement of self-diffusion along GBs as compared to diffusion in the bulk. The results of simulations are verified by comparison with available experimental data.

Study of Grain Boundary Self-Diffusion in Iron with Different Atomistic Models

We studied grain boundary (GB) self-diffusion in body-centered cubic iron using ab initio calculations and molecular dynamics simulations with various interatomic potentials. A combination of different models allowed us to determine the principal characteristics of self-diffusion along different types of GBs. In particular, we found that atomic self-diffusion in symmetric tilt GBs is mostly driven by self-interstitial atoms. In contrast, in general GBs atoms diffuse predominantly via an exchange mechanism that does not involve a particular defect but is similar to diffusion in a liquid. Most observed mechanisms lead to a significant enhancement of self-diffusion along GBs as compared to diffusion in the bulk. The results of simulations are verified by comparison with available experimental data.

Iron self diffusion in liquid pure iron and iron-carbon alloys

With incoherent quasielastic neutron scattering self-diffusion coefficients in pure iron, and iron-carbon alloys containing 8.7 at% and 16.9 at% carbon have been measured. At the melting point in liquid iron is m2 s−1. For the close-to-eutectic Fe83.1C16.9 composition m2 s−1 at T K. Contradicting conclusions drawn from literature values of tracer diffusion experiments the addition of carbon has only a minor effect on the iron mobility: at a given temperature the self-diffusion coefficient in Fe83.1C16.9 is only 10% larger than in liquid iron, although mixing has a drastic effect on liquidus temperature and phase behavior.

Iron self-diffusion in Fe5Ge3 thin film

Iron-germanides are widely investigated due to their possible application in nanoelectronics and spintronics applications. The feasibility of these materials in industrial application is highly dependent on their structural stability against temperature, therefore it is indispensable to understand temperature induced diffusion processes in this system. In order to study iron self-diffusion, [57Fe5Ge3(36 Å)/nFe5Ge3(62 Å)]10 isotope-periodic multilayer was prepared by molecular beam epitaxy. By using neutron reflectivity technique, which is sensitive to atomic scale diffusion lengths, we have determined the pre-exponent factor and activation energy as D0 = (8.22 ± 3.8) × 10−18 m2 s−1 and Ea = (0.28 ± 0.02) eV respectively.

High-Temperature Corrosion by Carboxylic Acids and Sulfidation under Refinery Conditions—Mechanism, Model, and Simulation

In crude oil refineries, high temperature corrosion in nonaqueous phase, predominantly by carboxylic acids (also known as naphthenic acids in crude oil) and sulfidation, is an old problem and has been studied for almost a century. Despite the large body of laboratory study and field experience, the mechanism of corrosion by naphthenic acids and sulfidation is not fully understood so that models in the public domain are empirical rather than mechanistic. Previously, a protective inner iron oxide scale was found when both naphthenic acids and sulfur compounds were present in our prior corrosion study. In the current study, it is shown that the high-temperature corrosion by naphthenic acids and sulfidation depends on the solid state diffusion of iron through the inner scale. It is postulated that corrosion rates are governed by either chemical kinetics on the surface of the inner scale or self-diffusion of iron through the inner scale. A model was built to simulate this mechanism for corrosion and validated with experimental data from a flow through corrosion test.

First-principles analysis of solute diffusion in dilute bcc Fe- X alloys

The diffusivities of substitutional impurity elements in iron have been computed with ab inito electronic density functional techniques, using exchange-correlation functional PW91. Excess entropies and the attempt frequency for a jump were determined by calculating phonon frequencies in the harmonic approximation. The influence of the degree of spontaneous magnetization on diffusivity is taken into account by means of the Girifalco model. The activation energy for diffusion has been determined by computing the vacancy formation energy, impurity-vacancy binding energies, migration barrier energies, and the effective energy associated with correlation of vacancy-mediated jump. For each type of impurity atom these contributions have been evaluated and analyzed up to and including the fifth nearest-neighbor shell of the impurity atom. It is found that impurities that have a low migration energy tend to have high effective energy associated with vacancy migration correlation, and vice versa, so that the total diffusion activation energies for all impurities are surprisingly close to each other. The strong effect of vacancy migration correlation is found to be associated with the high migration energy for iron self-diffusion, so that movement of vacancies through the iron bulk is in all cases, except cobalt, the limiting factor for impurity diffusion. The diffusivities calculated with the PW91 functional show good agreement with most of the experimental data for a wide range of elements.

Modeling of the Hot Rolling: Towards the Industrial Applicability

A semi-empirical approach to the modeling of the microstructural evolution during the hot rolling of austenite including grain growth, hardening and softening has been discussed in the frame of a generalized energetic expression for related structural processes. The current concept suggests the activation energy of iron self-diffusion in austenite and its dependence upon the chemical composition of the steel for prediction of the particular phenomena. Additionally, the precipitation sequences, the size distribution, Oswald ripening and interaction with softening are also included in the model of the microstructural evolution. The simulation results are reliable to the structural evolution of the low carbon steels microalloyed with Nb and Ti during hot rolling.

Statistical theory of diffusion in concentrated bcc and fcc alloys and concentration dependencies of diffusion coefficients in bcc alloys FeCu, FeMn, FeNi, and FeCr

The statistical theory of diffusion in concentrated bcc and fcc alloys with arbitrary pairwise interatomic interactions based on the master equation approach is developed. Vacancy–atom correlations are described using both the second-shell-jump and the nearest-neighbor-jump approximations which are shown to be usually sufficiently accurate. General expressions for Onsager coefficients in terms of microscopic interatomic interactions and some statistical averages are given. Both the analytical kinetic mean-field and the Monte Carlo methods for finding these averages are described. The theory developed is used to describe sharp concentration dependencies of diffusion coefficients in several iron-based alloy systems. For the bcc alloys FeCu, FeMn, and FeNi, we predict the notable increase of the iron self-diffusion coefficient with solute concentration c, up to several times, even though values of c possible for these alloys do not exceed some percent. For the bcc alloys FeCr at high temperatures T ≳ 1400 K, we show that the very strong and peculiar concentration dependencies of both tracer and chemical diffusion coefficients observed in these alloys can be naturally explained by the theory, without invoking exotic models discussed earlier.

High Temperature Deformation Behavior of P92 Steel

The ferritic-martensitic steels are superior steels based on the potential properties that they possess; especially, the elevated temperature properties. Among these ferritic-martensitic steels, Cr–Mo–W steel is a candidate structural material for high temperature applications such as future advanced reactors and aerospace applications. The hot deformation behavior of P92 steel was carried out at elevated temperatures between 600 and 700 °C and different strain rates of 10−5–10−3 s−1. Thereafter, the hot deformation behavior was analyzed, taking into account the peak stress values for each condition. As a result, the activation energy of P92 steel and the stress exponent were obtained to be 6.7 and 628 kJ/mol, respectively. The activation energy assessed the high-temperature deformation mechanism for this class of steels. Even though, the obtained activation energy was much higher than that of iron self-diffusion, it came in good agreement with the reported values in literature. Subsequently, the relevant hot deformation constitutive equation and the relationship between peak stresses and deformation rate at elevated temperature were developed.

Magnetic diffusion anomaly at the Néel temperature of pyrrhotite, Fe(1-x)S.

Cation diffusion is an important rate-limiting process in the growth of pyrrhotite (Fe1-xS) in passivating films on steels exposed to sulfidic environments, and for proposed synthetic applications of Fe1-xS, for example single-phase magnetic switching devices. Above the Néel temperature TN of 315 °C, where Fe1-xS is paramagnetic and structurally disordered, iron self-diffusivity *DFe predictably follows a standard, established Arrhenius law with temperature. However, we report (57)Fe tracer diffusion measurements below TN, obtained using secondary ion mass spectrometry (SIMS), that demonstrate a 100-fold reduction in diffusion coefficient as compared to the extrapolated, paramagnetic Arrhenius trend at 150 °C. The results can be described by a magnetic diffusion anomaly, where the vacancy migration energy for the spontaneously-magnetized cation sublattice is increased by approximately 40% over the paramagnetic state. These constitute the first set of consistent diffusivity data obtained in magnetic pyrrhotite, allowing more accurate prediction of pyrrhotite growth rates and determination of magnetic properties for synthetic devices.

Correlation between iron self-diffusion and thermal stability in doped iron nitride thin films

Nanocrystalline Fe-X-N thin films (with doping X = 0, 3.1 at. % Al, 1.6 at. % Zr), were deposited using reactive ion beam sputtering. Magnetization study reveals that the deposited films exhibit a perpendicular magnetic anisotropy. Thermal stability of the films was investigated systematically and it was observed that the structural and the magnetic stability gets significantly enhanced with Al doping, whereas Zr doping has only a marginal effect. Fe self-diffusion, obtained using polarized neutron reflectivity, shows a suppression with both additives. A correlation between the thermal stability and the diffusion process gives a direct evidence that the enhancement in the thermal stability is primarily diffusion controlled. A combined picture of diffusion, structural, and magnetic stability has been drawn to understand the obtained results.

On the hot working of FeSi ferritic steels

The high temperature deformation behavior of FeSi electrical steels (ferritic at the testing temperature) was studied under hot compression conditions. The flow curves of these steels exhibit a conventional dynamic recovery behavior. The analysis of the hot working data was carried out by applying the classical hyperbolic-sine equation to derive the peak stress in the flow curve by determining the apparent stress exponent, n, and the activation energy, Q. A modified hyperbolic-sine equation showed a better correlation with experimental data. The modified equation assumes that the rate controlling mechanism is the glide and climb of dislocations. Consequently, Q can be taken equal to the iron self-diffusion in ferrite (Q=239kJ/mol) and the creep exponent can be set equal to 5. The whole flow curves were also characterized by the one variable approach which in turn requires deriving characteristic dynamic recovery and work hardening terms at any processing conditions. A direct relationship between the hardening and softening terms and the Si content of the steels was obtained. Finally all the flow curves were discussed and modeled as a function of the processing parameters and chemical composition. Finally, a universal constitutive equation to describe the high temperature deformation of these steels taking account of the chemical composition is proposed.

Vacancy–carbon complexes in bcc iron: Correlation between carbon content, vacancy concentration and diffusion coefficient

Self-diffusion in face-centered cubic (fcc) iron and hexagonal close-packed cobalt as well as Ni diffusion in bcc iron and Co-diffusion in fcc nickel are all accelerated in the presence of dissolved carbon. This is attributed to an enlarged vacancy concentration due to an attractive vacancy–carbon interaction. The enlarged Ni diffusion in body-centered cubic (bcc) iron contradicts conclusions for self-diffusion in bcc iron obtained from first-principles calculations. This discrepancy is discussed in the present study.

On self-diffusion in iron at very strong compression of crystal

The dependences of the parameters of the formation of vacancies and self-diffusion have been calculated as functions of the degree of compression of iron crystals along isotherms of 300 and 3000 K. It has been shown that, in the range of 1 > V/V0 > (V/V0)min, the suppression of the activation processes occurs upon isothermal compression and, upon isochoric heating, they are strengthened. Here, V/V0 is the ratio of the molar volume of the crystal at a pressure P and temperature T to that at P = 0 and T = 0. However, at V/V0 = (V/V0)min = 0.0548, the probability of the formation of vacancies and the self-diffusion coefficient become minimum and, in the course of the further isothermal compression, the strengthening of activation processes occurs, and the activation parameters cease to depend on temperature. It is indicated that this is due to the quantum subbarrier tunneling of atoms over the volume of the crystal. It has been shown that, at V/V0 (V/V0)min. The isothermal dependence of pressure in bcc iron has been estimated upon its compression to V/V0 = 0.001. Based on the calculated isotherms, the magnitudes of pressure at characteristic points of pressure dependences of the parameters of self-diffusion and surface energy have been estimated.

Lattice dynamics analysis of the thermal properties of liquid iron

Abstract In this paper, the embedded atom method potential and Johnson potential are applied to calculate the thermal properties of liquid iron with an emphasis on a wide rage of temperatures and pressures. The results show that the liquid iron self-diffusion coefficient increases with increasing temperature and decreases with increasing pressure. The calculated self-diffusion coefficient is in good agreement with Protopapas' hard-sphere model at atmospheric pressure. According to the simulation results, we can get the Arrhenius equation between diffusion coefficient, temperature and activation energy. Increasing pressure enlarges the liquid iron activation energy and reduces the movement of atoms in liquid iron. Liquid iron thermal conductivity is computed using non-equilibrium molecular dynamics simulation and the simulation results are consistent with Pottlacher's experimental results with acceptable uncertainty in the 1535–2700 K temperature range.