Changes in the potential and vibrational energies upon the formation of vacancies in the oxygen-alloyed cores of crystallite-conjugation regions of polycrystalline Cr, Cu, and Ir

The changes in the potential and vibrational energies upon the formation of vacancies in the oxygen-alloyed (OA) cores of crystallite-conjugation regions (CCRs) in polycrystals of d transition metals Cr, Cu, and Ir have been determined. The potential energy increases upon the formation of vacancies (upon the formation of complexes of vacancies with oxygen atoms) in the OA cores of CCRs in the polycrystalline Cr, Cu, and Ir. However, the vibrational energy decreases upon the formation of vacancies in the OA cores of CCRs in these polycrystals, as in the OA cores of CCRs in polycrystals of the 4d and 5d transition bcc metals Mo, Ta, and W. The volume of the OA cores of CCRs in polycrystals of Cr, Cu, and Ir decreases upon the formation of vacancies. The changes in the interatomic interactions and dynamic properties in the regions of vacancy localization in the OA cores of CCRs coincide with analogous changes introduced into the lattices of metals by split interstitials.     

Changes in the potential and vibrational energies upon the formation of vacancies in oxygen-doped cores of crystallite-conjugation regions of polycrystalline 4d and 5d BCC transition metals

The changes in the potential (u _cmpl) and vibrational (?_cmpl) energies and the signs of changes in the interatomic spacings (Δa _cmpl) upon the formation of vacancies in oxygen-alloyed (OA) cores of crystallite-conjugation regions (CCR) in polycrystalline 4d and 5d transition metals Mo, Ta, and W have been determined. The potential energy upon the formation of vacancies (upon the formation of vacancy complexes with oxygen atoms—vacO complexes) in the OA cores of CCRs in polycrystalline Mo, Ta, and W increases (u _cmpl are positive), as upon the formation of vacancies in pure CCR cores of transition bcc d metals. The vibrational energy upon the formation of vacancies in OA CCR cores in polycrystalline Mo, Ta, and W decreases (?_vacO are negative). The negative sign of changes in the vibrational energy upon the formation of vacancies in the OA CCR cores in Mo, Ta, and W (?_vacO < 0) agrees with the independent determinations of the sign of changes in the vibrational energy in the OA CCR cores in polycrystalline tungsten (?_vacO)_W using Mössbauer measurements of the Debye temperature. The signs of changes in the interatomic spacings upon the formation of vacancies in the OA CCR cores in polycrystals of Mo, Ta and W are negative (Δa _VacO < 0), in contrast to positive (0 < Δa _BCC) changes in the interatomic distances in the nearest neighborhood of vacancies formed in pure CCR cores in Mo, Ta, and W.     

Changes in the potential energy upon the formation of vacancies in the volume and in the cores of crystallite-conjugation regions in cubic polycrystalline metals

Changes in the potential energy of atoms that constitute the nearest neighborhood of vacancies formed in the bulk of d transition and precious cubic metals have been determined. These changes agree with the available first-principles calculations of changes in the potential energy of atoms of the nearest neighborhood of vacancies. In the cores of crystallite-conjugation regions (CCRs) of bcc polycrystalline d transition metals, the formation of vacancies is accompanied by positive changes in the potential energy of atoms of their nearest neighborhood. The absolute magnitudes of these changes are several times less than the changes in the potential energy of atoms of the nearest neighborhood of vacancies in the bulk of these metals, in accordance with the relationship between the enthalpies of formation of vacancies in these regions of polycrystals. The changes in the potential energy of atoms of the nearest neighborhood of vacancies formed in the cores of CCRs of fcc polycrystalline metals are negative because of the split structure of vacancies in the CCR cores of such metals.     

Crystallite-conjugation regions and adjacent lattice regions in polycrystalline iridium: III. Enthalpies of formation of vacancies and the energies of interaction of partners in vacancy complexes with oxygen formed in the cores of crystallite-conjugation regions in polycrystalline iridium

The interatomic spacings in the cores of crystallite-conjugation regions (CCRs) and adjacent lattice regions (ALRs) of polycrystals either decrease or increase upon alloying of nominally pure metals with oxygen and vacancy complexes with oxygen (mVacO, where m is the number of vacancies in the complex) that are formed during annealing. These changes in the interatomic spacings lead to an increase or decrease in the isomer shifts δ of the components of the Mössbauer spectra of atomic probes ⁵⁷Fe that are localized in the CCR cores and ALRs of polycrystals [1–6]. The enthalpies Q _mcmpl1, of formation of vacancy-oxygen complexes mVacO in the CCR cores have been measured for Ir and Cr polycrystals, and the enthalpies Q _Vac,1 of formation of vacancies in CCR cores have been determined for Ta, W, Ir, and Cr polycrystals. The enthalpies E _mcmpl of the interaction between the partners of the complexes increase with increasing number m of vacancies in the complexes.     

Crystallite-conjugation regions and adjacent lattice regions in polycrystalline iridium: II. Composition and properties of cores of crystallite-conjugation regions in polycrystalline iridium during annealing in an ultrahigh vacuum

Composition and properties of cores of crystallite-conjugation regions (CCRs) formed during annealing of polycrystalline iridium (poly-Ir) in an ultrahigh vacuum (UHV) have been studied using the method of intercrystalline diffusion in combination with Mössbauer spectroscopy (ID+MS) that has been developed in our previous works. Upon annealing in a UHV, poly-Ir is doped with oxygen from the atmosphere of the vacuum chamber. Complexes containing two vacancies per oxygen atom are formed in the CCR cores of poly-Ir because of a rearrangement of the atomic structure of the CCR cores upon their doping with oxygen. Using the ID+MS method, we for the first time revealed a “compensated” state of CCR cores in poly-Ir samples annealed in a UHV and of CCR cores in poly-Cr annealed in technical vacuum. The cause of the appearance of “compensated” states in CCR cores is the mutual compensation of relaxation volumes with opposite signs characteristic of different point defects. The relaxation volume of an oxygen atom in the CCR core of poly-Ir is by an order of magnitude greater than that in poly-Cr.     

Effects of crystallographic structure and Cr on the rate of void nucleation in BCC Fe: An atomistic simulation study

Atomistic Monte Carlo simulations based on modified embedded-atom method (MEAM) interatomic potentials have been carried out to clarify the differences in swelling rates between bcc and fcc Fe and between pure bcc Fe and bcc Fe−Cr alloys. Assuming that the transient regimes prior to the onset of steady-state swelling correspond to the void nucleation stage, the effect of crystallographic structure (bcc vs. fcc) or Cr alloying on the void nucleation rate under a given amount of supersaturated vacancies was examined. It was found that the void nucleation rate is much higher in fcc Fe than in bcc Fe. Randomly distributed Cr atoms slightly increase the void nucleation rate in bcc Fe, but microstructural evolutions such as the precipitation of Cr-rich phase have more decisive effects, serving as a vacancy sink. The reasons for the individual results are rationalized in terms of the binding energy of vacancy clusters and the size difference between Fe and Cr atoms.     

ATOMISTIC SIMULATION OF POINT DEFECTS IN NiAl ALLOY

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Interpretation of viscous deformation of Zr-based bulk metallic glass alloys based on Nabarro-Herring creep model

Superplastic-like viscous deformation of bulk metallic glass alloys around the glass transition temperature (Tg) was analyzed based on the Nabarro-Herring creep model, a classical creep model, where the diffusional motion of atoms or vacancies through the lattice (atomic configuration) is considered. The amorphous matrix of bulk metallic glasses that has a randomly-packed atomic configuration was assumed to behave in a manner similar to the grain boundary in polycrystalline metals so as to approximate the diffusivity of the major constituent element. In spite of rough approximation of the parameters in the Nabarro-Herring creep equation, a reasonable value of the diffusion path (d) could be obtained from the experimentally-obtained metal flow data, including the steady state stress and the strain rate. Due to the absence of vacancy sources such as grain boundaries in homogeneous metallic glasses, the diffusion path, which, in polycrystalline materials, generally is the average distance between vacancy sources such as grain boundaries, was considered in this work as the average distance between tunneling centers in bulk metallic glass alloys. The calculated diffusion path was comparable to the density of tunneling centers around Tg, proposed by M. H. Cohen and G. S. Grest based on free volume theory. The calculated diffusion path showed monotonous decrease with temperature over Tg for Zr-based bulk metallic glass alloys. Based on this analysis, a schematic model for viscous deformation of bulk metallic glass was proposed.     

A modified embedded-atom method interatomic potential for the Fe–H system

A modified embedded-atom method (MEAM) interatomic potential for the Fe–H binary system has been developed using previously developed MEAM potentials of Fe and H. The potential parameters were determined by fitting to experimental data on the dilute heat of solution of hydrogen in body-centered cubic (bcc) and face-centered cubic (fcc) Fe, the vacancy–hydrogen binding energy in bcc Fe, and to a first-principles calculation for the lattice parameter and bulk modulus of a hypothetical NaCl-type FeH. The potential accurately reproduces the known physical properties of hydrogen as an interstitial solute element in bcc and fcc Fe. The applicability of the potential to atomistic approaches for investigating interactions between hydrogen atoms and other defects such as vacancies, dislocations and grain boundaries, and also for investigating the effects of hydrogen on various deformation and mechanical behaviors of iron is demonstrated.     

Simulation of characteristics determining pressure effects on the concentration and diffusivity of vacancies in BCC metals: A new approach

This work is devoted to the development of a new model (based on the molecular-statics method) for studying the diffusion properties of point defects in metals. In the model, a new algorithm is realized, which makes it possible in a self-consistent manner to calculate the atomic structure in the vicinity of a defect and the constants which determine atomic displacements in the elastic medium surrounding the computational cell. We also took into account the fact that the energy of the system depends on pressure. This dependence is different in the case of an ideal system and a system with a defect, which gives an additional contribution to the volumes of formation and migration. Furthermore, we took into consideration that the time required for an atom to jump into a vacancy is about that required for an atom to execute only a few vibrations in a lattice site. In this period, only atoms that are located in the immediate proximity to the center of dilation have time to respond for the disturbances arising in the system; therefore, when calculating the volume for the vacancy migration we carried out only a partial relaxation of the system. Within the framework of this model, we calculated the energies and volumes of vacancy formation and migration in different bcc metals.     

Crystallite-conjugation regions and adjacent lattice regions in polycrystalline iridium: I. Composition and properties of adjacent lattice regions formed in polycrystalline iridium during annealing in an ultrahigh vacuum

In this work, we have studied the characteristics of regions in which atomic probes (APs) ⁵⁷Co(⁵⁷Fe) were diffusionally localized in polycrystalline iridium (poly-Ir) using a previously developed method based on Mössbauer spectroscopy. Poly-Ir becomes alloyed with oxygen during annealing even in an ultrahigh vacuum already at a temperature of 0.18T _m (T _m is the melting point of the matrix). After the annealing temperature reaches a certain value, there arises a “compensated” state of lattice regions adjacent to crystallite-conjugation regions (“adjacent zones,” or AZs) in poly-Ir. Such a state of AZs arises due to the mutual compensation of positive relaxation volumes of oxygen atoms and negative relaxation volumes of oxygen-vacancy complexes that are formed during each annealing. Therefore, in the “compensated” state of AZs the isomer shifts δ₂ of components 2 of Mössbauer spectra of ⁵⁷Fe APs become equal to “intrinsic” isomer shifts δ_{intrs, 2} of the Mössbauer spectra of ⁵⁷Fe APs located in the AZs of impurity-free metals. The “intrinsic” isomer shifts depend parabolically on the charges Z of the matrix-atom nuclei.     

Semigrand Canonical and Kinetic Monte Carlo simulations of binary B2-ordered nano-films with triple defects

Equilibrium atomic configurations and the kinetics of “order–order” and surface segregation processes in B2-ordering stoichiometric A-50 at.%B binary thin films are investigated by means of Semigrand Canonical Monte Carlo (SGCMC) and Kinetic Monte Carlo (KMC) simulations. The (100)-oriented films are modeled with an Ising-type Hamiltonian with previously evaluated pair-interaction energy parameters yielding the effect of “triple-defect disordering”. The SGCMC simulations provide equilibrium vacancy concentration and atomic configuration in the films with B-atom termination of both free surfaces achieved at high temperatures by the generation of an antiphase boundary. Despite strong vacancy surface segregation, the thermodynamic activation energy for their formation inside the films is the same as in the bulk material. KMC simulations implemented with the SGCMC-determined equilibrium vacancy concentration reveal very slow relaxation of the films towards equilibrium configuration. The B-termination of the (100) free surfaces is produced by A-atom diffusion inwards into the films mediated by vacancies segregating on surfaces.     

Anomalous diffusion in dilute solid solutions

Diffusion in metals and alloys encapsulates many different physical phenomena and a range of time and length scales, and consequently, a hierarchical combination of simulation methods is required to study diffusion. We develop such methods to study the role interaction among defects and diffusants, and local association effects, play in diffusion in metals. We use Fe impurity diffusion in Al as an example. Using recently developed, accurate, interatomic potentials for the Fe–Al system, we calculate migration energies for atom–vacancy exchange in a variety of local atomic configurations, using lattice statics methods. These are used in a kinetic Monte-Carlo framework to calculate diffusivities. Two different activation regimes are observed at temperatures above and below 550 K. We explain this anomalous, non-Arrhenius behavior of the diffusion activation energy in terms of the interaction among vacancies and Fe atoms, and local association/ordering effects.     

Solute and vacancy segregation to a/4<1 1 1> and a/2<1 0 0> antiphase domain boundaries in Fe3Al

Segregation of solute atoms and vacancies to antiphase domain boundaries (APDBs) in Fe–Al alloys near the stoichiometry Fe₃Al (Fe–22–28 at.% Al) was studied using a phase-field model based on the Bragg–Williams approximation. Local equilibrium vacancy concentration was determined from experimental data for vacancy formation enthalpy and the configurational entropy of vacancies assuming that the formation enthalpy is independent of long-range order and chemical composition. Fe atoms and vacancies segregate to APDB with the phase-shift vector a/2<1 0 0>(D0₃-APDB) in crystals with stoichiometric composition (Fe–25 at.% Al) and with the Fe-rich composition, whereas both of them tend to be depleted in Al-rich crystals. On the other hand, Fe atoms and vacancies both segregate on APDBs with the phase-shift vector a/4<1 1 1>(B2-APDB) in all compositions studied. The effects of vacancy segregation on APDB energy and thickness is negligibly small; however, the vacancy concentration at the center of APDBs can be up to 80% larger than in the bulk, and therefore it is anticipated that the mobility of APDBs can be significantly affected by the segregation of vacancies as well as by that of solute atoms.     

A finite difference calculation of vacancy migration under non-steady state conditions

The hydrogenation of metals, often a rapid process, may lead to the production of high vacancy concentrations in the solid when equilibrium is reached. The achievement of equilibrium in this “upquenching” process depends, at least in part, upon the migration of vacancies from the surface into the interior of the solid. Because individual vacancy jump frequencies may depend on position within the vacancy density gradient, particularly when the solid is under an applied stress, analytical solutions of Fick's second law are not appropriate. A finite difference method has been developed to treat such vacancy diffusion problems and applied to vacancy migration in nickel.     

Vacancy-driven stress relaxation in layers

The role of vacancies together with their generally non-ideal sources and sinks has been investigated previously in the context of multi-component diffusion. This concept is applied to a thin layer on a substrate subjected to an initial eigenstress state. The surface of the layer is assumed to act as an ideal source and sink for vacancies. The interface may act either as an ideal or as no source and sink for vacancies. Non-ideal sources and sinks are supposed in the bulk. The formation of a vacancy site fraction profile across the layer due to active sources and sinks and due to diffusion is studied, provoking a relaxation of the residual eigenstress state. A set of two nonlinear partial differential equations for both the vacancy site fraction and the eigenstress distributions is developed. The problem is reformulated in dimension-free quantities. The relation between the diffusivity and the activity of sources and sinks for vacancies in the bulk is characterized by a vacancy intensity parameter k. Numerical solutions are presented, and the influence of nonlinear terms in the evolution equations is evaluated. The simulations provide the evolution of the vacancy site fraction and of the hydrostatic stress profiles in the layer. The development of a film of newly deposited or removed atoms at the layer surface and of the total thickness of the layer is also calculated. The results of simulations are discussed.     

Shear susceptibility – A universal integral parameter relating the shear softening,heat effects,anharmonicity of interatomic interaction and “defect” structure of metallic glasses

We studied shear modulus relaxation and heat effects occurring upon structural relaxation of La-, Zr- and Pd-based bulk metallic glasses. On this basis, we suggest a new method for the determination of the shear susceptibility, which appears to constitute a universal integral parameter relating different physical phenomena – shear softening, heat effects and anharmonicity of interatomic interaction – with the “defect” structure of metallic glasses.     

Lattice gas decomposition model for vacancy formation correlated with B2 atomic ordering in intermetallics

Thermal vacancy formation correlated with atomic ordering was modelled in B2-ordering A–B binary intermetallics. Ising Hamiltonian was implemented with a specific Bragg–Williams-type thermodynamic formalism for thermal vacancy formation based on the phase equilibria in a lattice gas composed of atoms and vacancies. It has been demonstrated that for pair-interaction energetics favouring vacancy formation on A-atom sublattice, equilibrium concentrations of vacancies and antisite defects result mutually proportional in well defined temperature ranges. The effect observed in both stoichiometric and non-stoichiometric binary alloys was interpreted as a tendency for triple defect formation. In B-rich non-stoichiometric binary alloys vacancy concentration did not extrapolate to zero at temperature approaching zero, which indicated the formation of constitutional vacancies. Energetic conditions for the occurrence of the effects were analysed in detail.     

Molecular dynamics simulation of diffusion in a (110) B2-NiAl film

We report on the first direct molecular dynamics study of diffusion in B2-NiAl using one of the most reliable embedded-atom method potentials for this phase. The simulation is performed for near the stoichiometric composition at a temperature just below the melting temperature of the model. In the molecular dynamics simulation, an equilibrium point-defect concentration is generated and maintained by using a film sample with periodic boundary conditions only in two directions and free surfaces in the third direction. Two types of point defects – Ni vacancies and Ni antisites – are found in the bulk of the model. It is demonstrated that isolated Ni vacancies strongly dominate in concentration over all of their bound complexes with Ni antisites. Although we predict that some attractive interactions should occur between point defects to form bound Ni vacancy-Ni antisite pairs and bound Ni antisite-Ni vacancy-Ni antisite complexes, only about 2% of Ni vacancies and 1% of Ni antisites statistically randomly associate to form bound Ni vacancy-Ni antisite-Ni vacancy complexes (the so-called bound triple-defect complex). As a result, it is deduced that the triple-defect diffusion mechanism is not likely to be the dominant diffusion mechanism in the bulk of the model because this diffusion mechanism effectively requires that the Ni vacancies and Ni antisites must form bound triple-defect complexes. Furthermore, it is found that Ni atoms diffuse in the bulk of the model on average about 2.5 times faster than Al atoms. Therefore, we suggest that isolated Ni vacancies are likely to play a key role in atomic diffusion of both Ni and Al near the stoichiometric composition of B2-NiAl and, consequently, the most plausible and widely accepted candidate for dominant diffusion mechanism in B2-NiAl can be considered to be six-jump cycles of a Ni vacancy. Furthermore, we can suppose that additional next-nearest-neighbor jumps of a Ni vacancy may cause that Ni atoms diffuse faster than Al atoms.     

The influence of metal lattice vacancies on the oxidation of high temperature materials

When an oxide scale grows on a metal by the outward diffusion of cations, it is anticipated theoretically that lattice vacancies will be injected into the metal substrate. Experiments are reviewed which provide direct evidence for vacancy injection, including X-ray and electron microscope observations of the growth of vacancy dislocation loops and optical microscopy of voids. The influence of a vacancy supersaturation on the kinetics of oxidation is discussed in detail, but the effects are shown to be small in practical cases. The main consequence of vacancy injection is shown to be the eventual breakdown of the initial scale and subsequent growth of a duplex porous oxide. In some cases, this transition has undesirable consequences such as carburization/decarburization of the underlying metal and “breakaway” oxidation.