Diffusion Of Interstitial Atoms Research Articles

Calculations for Diffusion Probability and Diffusivity of Interstitial Atom in one Lattice for γ-TiAl Alloy

The motion of interstitial atoms (one of the point defects) in material is random under certain temperature. However, the diffusion of interstitial atoms has priority along some certain directions to the others, so it is necessary to reveal the phenomenon (the phenomenon also can be called anisotropic). In order to illustrate the anisotropic and reveal the magnitude of probability of the micro crack formation along crystal axes, some formulae derived from former literatures have been adopted, and the values of diffusion probability and diffusivity of interstitial atoms-Ti or Al along 〈110〉and〈100〉have been calculated. The conclusion that the diffusion of interstitial atoms along different crystal axis has different diffusivity is verified by the comparison of the results of calculations.

Determination of depths of traps for interstitials from thermodynamic data: a new view on carbon trapping and diffusion

Traps, such as dislocation cores, foreign atoms, surfaces of nano-precipitates, etc, can significantly influence the kinetics of diffusion of interstitial atoms in a crystal lattice. Trapping is reflected in the chemical diffusion coefficient, whose value can be up to several orders of magnitude lower than the corresponding diffusion coefficient in a trap-free system. If we consider trapping only at dilute foreign atoms, we may assume only one sort of traps in the system, the depth of which is characterized by ΔE (trapping enthalpy) given by the decrease in energy due to trapping of one mole of interstitials. In this paper, a rigorous thermodynamically based concept is offered to extract the value of trapping enthalpy ΔE from chemical potentials of interstitial atoms which are, for instance, available in the form of CALPHAD-type thermodynamic databases. Exemplarily, the values of ΔE for C-trapping at Cr impurities are evaluated. For comparison, trapping enthalpies of C at various typical alloying elements in steel are also extracted and compared with literature values. The chemical diffusion coefficient of C in an Fe–Cr–C system at 500 °C is calculated for different mole fractions of C and Cr atoms. The influence of traps on diffusion becomes evident from this analysis.

Beyond Sieverts' law: A comprehensive microkinetic model of hydrogen permeation in dense metal membranes

There is much ongoing research on developing dense metal membranes based on palladium and its alloys for producing high purity hydrogen, e.g., for fuel cells. Such membranes are almost exclusively permeable to hydrogen in a feed gas mixture via the following steps: (s1) dissociative adsorption on the surface; (s2) sub-surface dissolution; (s3) diffusion of interstitial hydrogen atoms within the bulk metal matrix; (s4) evolution from the bulk metal to its permeate side surface; and finally, (s5) associative desorption of hydrogen. The flux is commonly described by the so-called “Sieverts' law,” which expresses the flux as a membrane permeance times the difference in square root of hydrogen pressure on the feed side and that on the permeate side. It is derived by assuming that diffusion (step s3) is controlling, and hydrogen concentration in metal is low, which strictly limits its applicability to relatively high temperatures, thick membranes, and low hydrogen pressures. We describe a comprehensive microkinetic model that includes all five steps, and is shown to be suitable for Pd over a broad range of conditions. It also describes non-ideal hydrogen solution due to phase-transition in Pd, which explains the sharp peak at intermediate temperatures in hydrogen flux observed experimentally, but not so far explained theoretically. The model includes effect of metal surface roughness, not commonly considered so far. Use of an electrical analogy and comparison of step resistances allows a reduction to a three-step (adsorption, diffusion, and desorption control) model that also adequately describes hydrogen permeation over a broad range of conditions.

Comparative Study of Hardening Mechanisms During Aging of a 304 Stainless Steel Containing α′-Martensite

Strain aging and hardening behaviors of a 304 stainless steel containing deformation-induced martensite were investigated by examining mechanical properties and microstructural evolution for different aging temperature and time. Introduced age hardening mechanisms of a cold rolled 304 stainless steel were the additional formation of α′-martensite, hardening of α′-martensite, and hardening of deformed austenite. The increased amount of α′-martensite at an aging temperature of 450 °C confirmed the additional formation of α′-martensite as a hardening mechanism in a cold rolled 304 stainless steel. Additionally, the increased hardness in both α′-martensite and austenite phases with aging temperature proved that hardening of both α′-martensite and austenite phases would be effective as hardening mechanisms in cold rolled and aged 304 stainless steels. The results suggested that among hardening mechanisms, hardening of an α′-martensite phase, including the diffusion of interstitial solute carbon atoms to dislocations and the precipitation of fine carbide particles would become a major hardening mechanism during aging of cold rolled 304 stainless steels.

Effects of grain boundary and boundary inclination on hydrogen diffusion in α-iron

Abstract

Coefficient of Diffusion in Crystals of Si<sub>1-x</sub>Ge<sub>x</sub>: Role of Preexponential Factor

In the present work the results of theoretical analysis of the process of diffusion of covalently bonded atoms (interstitial oxygen atoms) in Si1-xGex alloys are presented. The diffusion coefficient (activation energy and pre-exponential factor) was calculated by means of quantum-chemical simulations (Hartree–Fock, NDDO, PM5) and the dependences of the activation energy and pre-exponential factor on Ge atoms concentration (x) were analyzed with the use of the percolation theory. The study has revealed that the diffusivity of impurities (defects) in alloys can decrease considerably at low concentration (x<0.05) of a minor alloy component and this variation results from the fact that the pre-exponential factor depends on the concentration of component elements of the alloy. The alloy-induced decrease in the pre-exponential factor is associated with removal of the degeneracy of the number of equivalent diffusion paths. It is found that a sharp decrease in the pre-exponential factor causes experimentally observed decreases in the coefficient of diffusion of interstitial oxygen atoms and in the rate of formation of oxygen thermal donors in Si1‑xGex crystals at x~0.01.

High efficiency white luminescence of alumina doped ZnO

The application of alumina-doped ZnO (AZO) films as luminescent material for large area lighting sources has been evaluated. Thin films were grown on quartz using magnetron sputtering and subsequently annealed under argon atmosphere in a rapid thermal annealing experiment. Below 550 °C, red-shift of the optical band gap and increase of the visible emission are observed in agreement with Al diffusion and formation of interstitial oxygen atoms. At temperatures higher than 800 °C, diffusion is activated and Ostwald ripening leads to the formation of larger grains and an increase of the crystalline phase. The photoluminescence (PL) intensity is enhanced, specifically in the UV range. As a result the emission spectrum of AZO thin films can be adjusted by the annealing conditions, with equal contributions from the UV and orange parts of the PL spectrum resulting in an efficient white emission as quantified using the color space map of the Commission Internationale de l'Éclairage.

Mechanisms of bulk diffusion at “high” and “low” temperatures

A phenomenological model has been proposed for bulk self-diffusion and diffusion of interstitial atoms in the ranges of high (T > T D) and low (T < T D) temperatures (where T D is Debye temperature). It has been shown that the mechanisms of diffusion at high and low temperatures differ significantly. In the high-temperature range, the diffusion is provided by fluctuations, which can be described in terms of local melting, i.e., the formation of a “liquid diffusion channel.” In the low-temperature range, when melting for some reasons is hindered, the diffusion is due to the fluctuation formation of a “hollow diffusion channel.” The calculation of the activation energies of these processes in the case of self-diffusion agrees well with the experiment in the temperature range T > T D and has demonstrated that the activation energy increases significantly at T < T D. The calculation of the activation energy for diffusion of interstitial atoms in bcc metals agrees well with the experiment in the entire temperature range and provides an explanation of the decrease in the activation energy of diffusion at low temperatures.

Quantumchemical simulation of diffusion in alloys: diffusion of interstitial oxygen atoms in Si1‐xGex

AbstractIn the present work the results of theoretical analysis of the process of diffusion of covalently bonded atoms (interstitial oxygen atoms) in Si1‐xGex alloys are presented. The diffusion coefficient (activation energy and preexponential factor) was calculated by means of quantumchemical simulations (NDDO PM5) and the dependences of the activation energy and preexponential factor on Ge atoms concentration (x) were analyzed with the use of the percolation theory. It is shown that a significant decrease in the diffusion coefficient of interstitial oxygen atoms in Si1‐xGex (x&lt;0.05) compared to the value in pure silicon is caused not only by changes in activation energy but also by a decrease of the preexponential factor. The alloy‐induced decrease in the preexponential factor is associated with removal of the degeneracy of the number of equivalent diffusion paths. The dependences obtained describe well experimentally observed changes in the diffusion coefficient of interstitial oxygen atoms and in the formation rate of oxygen‐related thermal donors in Si1‐xGex alloys. (© 2011 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Effects of Lithium Ions on Dye-Sensitized ZnO Aggregate Solar Cells

We report on the synthesis of ZnO nanocrystallite aggregates in the presence of lithium ions and films consisting of these aggregates for dye-sensitized solar cell applications. A maximum overall conversion efficiency of 6.1% has been achieved with these films. This value is much higher than the 4.0% obtained for the films that are comprised of ZnO aggregates synthesized in the absence of lithium ions. The lithium ions were found to have an influence on the growth and assembly of ZnO nanocrystallites, leading to an increase in the nanocrystallite size and a polydisperse distribution in the size of the aggregates. The increase in the nanocrystallite size is due to a lithium-induced increase in the diffusivity of interstitial zinc atoms, which leads to an improvement in the crystallinity. This, in turn, yields an oxygen-enriched ZnO surface, which acts to suppress the dissolution of zinc atoms at the ZnO surface in the case of an acidic dye. As such, the formation of a Zn2+/dye complex is avoided. This coll...

Intrinsic damping, relaxation processes, and internal friction in vibrating systems.

Vibrations lose energy because of (1) coupling of the system to other systems or to the environment or of (2) intrinsic damping within the system itself. The present paper attempts to survey the current state of understanding for the principal mechanisms of the latter type with explicit physics (rather than purely phenomenological considerations), as simply as practical. Some mechanisms are evidenced in the attenuation of waves in unbounded homogeneous media, others are caused by the presence of boundaries. Some explicitly require quantum-mechanical concepts for their explanation, others can be explained in terms of classical mechanics and thermodynamics. Specific mechanisms that are to be discussed include those associated with thermal conductivity, grain and domain boundary effects, interstitial atom diffusion, relaxation by diffusion, inter-grain diffusion, micro-eddy current losses, hysteresis losses, thermoelastic internal friction, thermal damping associated with transverse vibrations of thin bodies, phonon-phonon interactions, phonon-electron interactions, internal fluids, and dislocations. The concept of relaxation often provides a convenient unified description. Rather than use the local averaged particle displacement as a sole description of the local vibrations, one considers additional local variables, loosely referred to as hidden variables. Each such variable, when disturbed, relaxes to its equilibrium value with a characteristic relaxation time.

Mechanisms of bulk diffusion at high and low temperatures

A phenomenological model has been proposed for bulk self-diffusion and diffusion of interstitial atoms in the ranges of high (T > T D) and low (T T D and has demonstrated that the activation energy increases significantly at T < T D. The calculation of the activation energy for diffusion of interstitial atoms in bcc metals agrees well with the experiment in the entire temperature range and provides an explanation of the decrease in the activation energy of diffusion at low temperatures.

Interstitial diffusion under conditions of trapping of interstitial impurity atoms

Abstract The diffusion equation for nonequilibrium interstitial impurity atoms in the form convenient for numerical solution has been obtained. The proposed equation takes into account all different charge states of interstitial atoms and drift of all mobile charged species in the built-in electric field, although only the concentration of the neutral impurity interstitials must be obtained to solve the equation. The absorption of impurity interstitials by immobile sinks, mobile vacancies, and due to the passivation of dopant atoms is also taken into account. The derived effective coefficients that describe diffusion and trapping of impurity interstitials have the following characteristic features: (i) their dependences on the concentration of substitutionally dissolved dopant atoms are smooth and monotone; (ii) these concentration dependences are obtained in the form traditionally used for the approximation of effective diffusivity of substitutionally dissolved dopant atoms in processing-simulation codes. To illustrate the usability and efficiency of the derived equation for simulation of diffusion of nonequilibrium interstitial impurity atoms, the migration of deuterium interstitials in the silicon substrate doped with boron has been simulated. The calculated profile of deuterium concentration in the passivated region agrees well with the experimental data.

Simulation of Material Fracture in the Field of Thermal Stresses

Internal stresses occur within a material in the presence of non-uniform deformation. The main types of the internal stresses are thermal, residual and those due to structural defects. These stresses affect diffusion (of interstitial impurities such as hydrogen and oxygen) resulting in damage induced degradation of mechanical material properties, such as the yield point. There are various mechanisms of material property changes, e.g., the decrease of the energy of surface fracture, and corrosion cracking and hydrogen embrittlement. In this paper, a theoretical formulation for thermal stress fields due to diffusion-induced fracture is presented. The kinetics of interstitial atom diffusion (e.g., hydrogen) is described by an equation of the parabolic type with corresponding initial and boundary conditions.

Model of High-Temperature Diffusion of Interstitial Silicon Atoms in Silicon

Problem statement: Correct description of the anomalous phenomena determined by self-point defects in implanted silicon desires knowledge of their properties. Interstitial Si atoms themselves display anomalies in their behavior and firstly in existence of two very different values of the diffusion coefficient. Approach: We analyzed experimental results and proposed the model of diffusion of interstitial Si atoms in silicon in two shapes. Results: At low saturation Si atoms diffuse as isolated atoms with a low diffusion coefficient (~10-12 cm2 sec-1 at 900°C). At high supersaturation interstitial atoms diffused as Si-Si pairs, which had lower activation energy of migration and higher diffusion coefficients (~10-7 cm2 sec-1). Conclusion: The high diffusivity pairs were formed when two Si atoms hit in the same interstice. The atoms were not bound to one another by covalent bond. In a pair atoms were retained by a potential relief of the crystal.

Macroscopic description of the diffusion of interstitial impurity atoms considering the influence of elastic stress on the drift of interstitial species

The diffusion equation for non-equilibrium interstitial impurity atoms taking into account their charge states and drift of all mobile interstitial species in the built-in electric field and in the field of elastic stress is obtained. The obtained generalized equation is equivalent to the set of diffusion equations written for the interstitial impurity atoms in each individual charge state. Due to a number of characteristic features the generalized equation is more convenient for numerical solution than the original system of separate diffusion equations. On this basis, the macroscopic description of stress-mediated impurity diffusion due to a kick-out mechanism is obtained. It is supposed that the interstitial impurity atom makes a number of jumps before conversion to the substitutional position. At the same time, local equilibrium prevails between substitutionally dissolved impurity atoms, non-equilibrium self-interstitials, and interstitial impurity atoms. Also, the derived equation for impurity diffusion due to the kick-out mechanism takes into account all charge states of interstitial impurity atoms as well as drift of interstitial species in the electric field and in the field of elastic stress. Moreover, this equation exactly matches the equation of stress-mediated impurity diffusion due to the generation, migration, and dissociation of the equilibrium ‘impurity atom–self-interstitial’ pairs.

Al-induced reduction of the oxygen diffusion inHfO2: an ab initio study

Using first-principles calculations we have studied the effect of Aladdition on the diffusion of interstitial oxygen atoms and ions inHfO2.Calculated results show that interstitial oxygen ions in the singly negatively charged state easily diffusein HfO2 via exchange with lattice oxygen atoms, due to the lower diffusion barrier as compared to thosefor neutral interstitial oxygen atoms and interstitial oxygen ions in the doubly negativelycharged state. The addition of Al raises the diffusion barrier for interstitial oxygen becausethe interstitial oxygen is strongly attracted by its neighboring Al atoms. The electronicstructure analysis further reveals that the bonding between interstitial oxygen andlattice oxygen atoms is strengthened for each charge state of interstitial oxygen inHfO2 with the addition of Al.

Diffusion of Light Elements in BCC, FCC and HCP Metals

The mechanisms of formation of activated states upon diffusion of impurity interstitial atoms in metals have been identified, which allows formulation of the theoretical criterion for reliability of corresponding experimental data. This criterion is valid for almost all experimental results gained using precise techniques for bcc, fcc, and hcp metals. In case of hydrogen, oxygen, and nitrogen, most adequate are the models of potential diffusion barrier that are based on the elasticity theory. For carbon and boron, a less energy-taking mechanism is realized which involves the electron system rearrangement in a crystal during the diffusion jump. The accuracy of the theoretical criterion is in line with the capacities of modern precision techniques.

Nonlinear diffusion of interstitial atoms

A nonlinear kinetic discrete model for interstitial diffusion in a nonuniform system is presented, based on Martin's deterministic model and Hillert's sublattice theory, where the diffusion coefficient of interstitial atoms strongly depends on their local concentration. The nonlinear diffusion of interstitial atoms is characterized by the concentration-dependent correlation coefficient $\ensuremath{\gamma}$ and the relaxation time $\ensuremath{\tau}$, which are determined by the pair interaction energies between interstitial atoms and between interstitial atoms and matrix atoms, respectively. This model exceeds the range of validity of the traditional Fick's law, and allows of an extension of Fick's law to diffusion on the nanoscale.

Comments on the paper of V. L. Gapontsev and V. M. Koloskov “Nonequilibrium vacancy-stimulated diffusion (induced diffusion) as the main mechanism of activated alloy formation”

The authors of the considered paper in their study are focusing on systems of metal phases that can be called substitution phases. Presumably, in this case a variation of the mixture composition in the course of reaction is of less significance, since here in diffusion we observe point defects of the same sort (vacancies). It would be interesting to investigate the diffusion of interstitial atoms for some real objects. Due to the low values of diffusion activation energy for interstitial atoms, we could expect an improved sensitivity of the methods to composition variation (a higher diffusion coefficient). In any case it appears necessary to discuss the role of interstitial atoms in the preservation of the vacancy concentration with respect to annihilation processes. It follows from the theory proposed by V. Indenbom and A. Orlov that plastic deformation under low temperatures and significant loads, which are typical for high-energy mills, leads to the formation of interstitial atoms. The considered paper gives several examples of the practical use of mechanochemical synthesis. It would be important for the description of particular examples to include all parameters of synthesis, as well as selection, calculation of quantities, and methods of introduction of material, in particular, for so-called nonequilibrium vacancies. Below are certain considerations regarding the state of an activated alloy.