Diffusion and coupled fluxes in concentrated alloys under irradiation: a self-consistent mean-field approach

When an alloy is irradiated, atomic transport can occur through the two types of defects which are created: vacancies and interstitials. Recent developments of the self-consistent mean field (SCMF) kinetic theory could treat within the same formalism diffusion due to vacancies and interstitials in a multi-component alloy. It starts from a microscopic model of the atomic transport via vacancies and interstitials and yields the fluxes with a complete Onsager matrix of the phenomenological coefficients. The jump frequencies depend on the local environment through a ‘broken bond model’ such that the large range of frequencies involved in concentrated alloys is produced by a small number of thermodynamic and kinetic parameters. Kinetic correlations are accounted for through a set of time-dependent effective interactions within a non-equilibrium distribution function of the system. The different approximations of the SCMF theory recover most of the previous diffusion models. Recent improvements of the theory were to extend the multi-frequency approach usually restricted to dilute alloys to diffusion in concentrated alloys with jump frequencies depending on local concentrations and to generalize the formalism first developed for the vacancy diffusion mechanism to the more complex diffusion mechanism of the interstitial in the dumbbell configuration. To cite this article: M. Nastar, C. R. Physique 9 (2008).     

Observations of glide and decomposition of a⟨101⟩ dislocations at high temperatures in Ni-Al single crystals deformed along the hard orientation

Ni-44 at.% Al and Ni-50 at.% Al single crystals were tested in compression in the hard d001 ¢orientation. The dislocation processes and deformation behaviour were studied as a function of temperature, strain and strain rate. A slip transition in NiAl occurs from a?111? slip to non-a?111? slip at intermediate temperatures. In Ni-50 at.% Al single crystals, only a?010? dislocations are observed above the slip transition temperature. In contrast, a a?101?{101} glide has been observed to control deformation beyond the slip transition temperature in Ni-44 at.% Al. a?101? dislocations are observed primarily along both ?111? directions in the glide plane. High-resolution transmission electron microscopy observations show that the core of the a?101? dislocations along these directions is decomposed into two a?010? dislocations, separated by a distance of approximately 2 nm. The temperature window of stability for these a?101? dislocations depends upon the strain rate. At a strain rate of 1.4 210^?4 s^?1, a?101? dislocations are observed between 800 and 1000 K. Complete decomposition of a?101? dislocations into a?010? dislocations occurs beyond 1000 K, leading to a?010? climb as the deformation mode at higher temperatures. At lower strain rates, decomposition of a?101? dislocations has been observed to occur along the edge orientation at temperatures below 1000 K. Embedded-atom method calculations and experimental results indicate that a?101? dislocations have a large Peierls stress at low temperatures. Based on the present microstructural observations and a survey of the literature with respect to vacancy content and diffusion in NiAl, a model is proposed for a?101?{101} glide in Ni-44 at.% Al, and for the observed yield strength versus temperature behaviour of Ni-Al alloys at intermediate and high temperatures.     

Simulation of diffusion instability of a mercury atomic distribution in the cadmium-mercury-tellurium alloy

The formation of inhomogeneities in Cd_xHg_1-x Te alloys upon post-growth cooling or upon low-temperature annealing is simulated numerically. The mechanism of the formation of inhomogeneities is based on the diffusion instability in a system involving mercury atoms located at lattice sites, interstitial mercury atoms, and cation vacancies. It is revealed that, upon prolonged annealing of the Cd_xHg_1-x Te alloys with a cadmium content x = 0.2 at a temperature of ∼200°C, the concentrations of mercury atoms at lattice sites, interstitial mercury atoms, and vacancies are characterized by an inhomogeneous nearly periodical distribution arising from a small fluctuation when the initial equilibrium concentration of interstitial mercury atoms exceeds a threshold value (∼3 × 10¹⁷ cm⁻³). The spatial and time scales of the concentration distribution are determined primarily by the equilibrium concentration of vacancies and do not depend on the type of fluctuation involved. The spatial period of the concentration distribution increases linearly from 0.01 to 3.00 μm as the equilibrium concentration of vacancies changes from 10¹⁹ to 10¹⁴ cm⁻³. At lower concentrations of vacancies, the periodic structure is formed for a considerably longer time.     

The Manning factor for direct exchange and ring diffusion mechanisms

Abstract

In this paper, we consider lattice-based diffusion kinetics for the direct exchange and ring mechanisms as possible proxy diffusion mechanisms for diffusion in liquid alloys. For these mechanisms, we assessed the Manning factor that arises from the Darken–Manning relation relating the interdiffusion coefficient and tracer diffusion coefficients and which can be obtained experimentally. The maximum values of the Manning factor for these two mechanisms occur when the exchange only takes place between the atoms of different type but not between the atoms of the same type. These values have strong composition dependence and reach a value of 2 (ignoring tracer correlation factors) for the direct exchange mechanism at equal compositions of the two components in binary alloys. But for the three atom ring mechanism, these values as a function of composition have a much more complicated form that sits below the direct exchange mechanism for compositions between 10 and 90%. When all exchanges (allowed by a mechanism) occur with approximately the same probability, then the Manning factor is about unity for all compositions.     

Analysis of interdiffusion via vacancy-pairs in strongly ionic solids

In this paper, we analyse chemical interdiffusion via Schottky vacancy-pairs in strongly ionic crystals for diffusion couples (AY–BY), where A and B take the same valence. We derive a sum-rule relating the phenomenological coefficients that is based on an earlier sum-rule derived by Moleko and Allnatt (Phil. Mag. A, 58 () 677) for diffusion in the multicomponent random alloy via the agency of isolated vacancies. With this sum-rule and other relationships derived by us, we show that the ratio of the intrinsic diffusivities can be expressed in exactly the same simple form as the case for diffusion via isolated vacancies. The functional form for the interdiffusion coefficient when expressed in terms of atom-vacancy exchange frequencies for diffusion is found to be essentially the same as that for isolated vacancies. The difference centres only on the relative differences of the local jump coordination of the vacancies in each case.     

Analysis of the effect of interatomic interaction energy in V-Fe alloys with different iron concentrations on segregation and swelling processes after ion irradiation

Comparative analysis of iron segregation profiles near the free surfaces of V-(2, 5, 7) at % Fe alloys irradiated with 50-keV V⁺ ions at temperatures 30–40°C with doses from 1 × 10¹⁹ to 1 × 10²¹ ions/m² has been performed. Data on the change in the moduli of normal elasticity and the values of swelling of these alloys with a change in Fe concentration in them are reported. A correlation between the character of the concentration dependence of the degree of Fe segregation, partial diffusion coefficients of the alloy components, the Young moduli, and the preference factors for vacancies and interstitials between dislocations and voids in these alloys is established.     

In-situ study of deformation-enhanced atomic diffusion in NaCl by nuclear magnetic resonance

Abstract

Enhancements in atomic diffusion during deformation are investigated by ²³Na rotating frame nuclear spin relaxation measurements on pure NaCl single crystals. The enhanced diffusion is shown to arise from deformation-induced excess concentration of vacancies. Evaluation of the data yields the concentration of these vacancies as a function of temperature and strain rate.     

Solid solutions of paradichlorobenzene in paradibromobenzene with vacancies present in their structure

The results of polarization studies of the low-frequency optical Raman spectra of solid solutions of paradibromobenzene with p-dichlorobenzene (10% paradichlorobenzene) are reported. The spectra of lattice vibrations of the mixed crystals are calculated, and it is shown that vacancies can be present in their structure, in agreement with the experimental spectra. The existence of vacancies is manifested by the appearance of secondary lines in the low-frequency spectrum, in the vicinity of 70 cm⁻¹. The intensities of the lines are related to the number of vacancies. The diffusion activation energies in mixed crystals of paradibromobenzene with paradichlorobenzene with vacancies present in their structure are calculated at different temperatures on the basis of the method of atom-atom potentials. It is shown that the activation energy in these mixed crystals is not as dependent on the temperature variation and the crystallographic direction as in crystals of the constituent components. Fiz. Tverd. Tela (St. Petersburg) 39, 1564–1566 (September 1997)     

Comparison of Monte Carlo simulations and macroscopic theories of diffusion in systems with non-ideal sources and sinks for vacancies

A new concept of generation and annihilation of vacancies at non-ideal dense sources and sinks for vacancies is incorporated into the standard Monte Carlo model for vacancy-mediated diffusion. This model enables to treat the vacancy wind as well as the deformation of the specimen and the shift of the Kirkendall plane. The Monte Carlo model is used for testing the recent macroscopic theories of diffusion by Darken [Trans. Am. Inst. Min. Eng. 175 184 (1948)], Manning [Phys. Rev. B 4 1111 (1971)] and Moleko et al. [Phil. Mag. A 59 141 (1989)]. The agreement with the self-consistent Moleko et al. theory is excellent. On the other hand, the agreement with the classical Darken theory frequently used in the open literature for the explanation of the Kirkendall effect is rather poor.     

Structural defects in Ni-Ti alloys in the region of B2-phase homogeneity

A comparison is made of the x-ray and pycnometric densities of Ti-Ni alloys, with a high nickel content relative to the equiatomic composition, when the alloys are quenched outside the region of -phase homogeneity. An analysis is made of the possibility of the formation of vacancies, interstitial atoms, triple defects, and substitutional defects in the alloys. It is concluded that substitutional defects are formed: nickel atoms which are excess atoms relative to those found at the lattice points in the CsCl superstructure are located in the titanium sublattice. An evaluation showed that in the formation of alloys near the equiatomic composition of TiNi, the atomic volumes of titanium and nickel are about 1.8 and 7.4% smaller than for the pure components, respectively.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 45–50, November, 1987.     

Ionic transport in potassium chloride and a possible trwacancy contribution to it (oral presentation)

Abstract

The ionic transport properties of potassium chloride are discussed in light of the recent measurements of the electrical conductivity and chlorine ion diffusion in KCl and KCl: SrCl₂ single crystals. These measurements were analyzed using as a model a perfect crystal perturbed by five defects: isolated anion vacancies. isolated cation vacancies, divalent cation impurities, divalent-cation-impurity-cation-vacancy-complexes, and vacancy pairs. This analysis revealed nonrandom deviations between the theoretical and experimental values of the transport properties. Possible explanations of these deviations are discussed. The possibility of a trivacancy mechanism making a contribution to the conductivity is considered. The concentration and migration of trivacancies is examined.     

ESCA studies of Ni-Cr alloys

ESCA examination on Ni-Cr alloys has shown that a thin passive film was formed after 24 h immersion in 0.1 M NaCl. The film contained only chromium oxide in the form of Cr₂O₃. Electrochemical techniques according to ASTM G59 and ASTM G5 were used for the determination of the relative corrosion rate of the alloys. Both Ni-10 wt. % Cr and Ni-20 wt. % Cr alloys showed a slightly higher corrosion rate than the Ni-40 wt. % Cr alloy.The present ESCA study of the Ni-Cr system is part of our programme which involves an examination of the four binary alloy systems Fe-Si, Cr-Co, Ni-Cr, and Mo-Ni [1]. The aim is to correlate the structure and composition of the passive films formed in 0.1 M NaCl to the corrosion behaviour in the same solution.     

Erbium-induced interdiffusion of gallium and aluminum in GaAs/AlGaAs quantum-well structures

Incorporation of erbium into GaAs/AlGaAs quantum-well structures in the course of their MBE growth has been shown experimentally to initiate effective Ga and Al interdiffusion and Er diffusion due to the erbium-induced enhanced vacancy formation. A mechanism for the formation of cation vacancies is proposed, which is based on the generation of local strains by the incorporating erbium. It is shown that erbium interacts with aluminum to produce in AlGaAs aluminum-enriched, erbium-containing clusters. Fiz. Tverd. Tela (St. Petersburg) 41, 540–544 (March 1999)     

Vacancy‐induced minority‐spin states in half‐metallic Heusler alloys

Ferromagnetic full Heusler alloys containing Co are amongst the most studied half‐metallic systems. Several studies recently have been concentrated on the effect of defects and impurities. We focus in this Letter on the case of vacancies in these alloys. We show that the occurrence of vacancies at the sites occupied by Co atoms can destroy half‐metallicity and alters the Slater–Pauling rule. Such defects are likely to occur since they result to the C1_b lattice structure of the semi‐Heusler alloys. Contrary, the appearance of vacancies at the other sites keeps the half‐metallic character of the parent alloys. Thus for realistic devices it is important to prevent the appearance of vacancies during the growth of thin films. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Kinetic model and mechanism of Y3Al5O12 formation in hydrothermal and thermovaporous synthesis

Abstract

Kinetics and mechanism of fine-crystalline yttrium-aluminum garnet (YAG) formation under hydrothermal and thermovaporous treatment were investigated. It was synthesized from the stoichiomctric mixture of oxides in the temperature range 200-400°C at pressures of water vapor 4.0-26MPa. It was established that in quasiequilibrium with water vapor conditions the synthesis of YAG proceeds with formation of intermediate substance with Y(OH)₃ structure and amorphous aluminous component. The diffusion of this aluminous component into the Y(OH)₃ matrix resulted in the reorganization of oxygen sublattice accompanied with dehydroxylation. The kinetics of YAG formation is described by the equation of solid-phase transformation with the limiting stage of nucleation. Synthesized YAG contains 5-7% of water, which corresponds to a hydrogarnet structure. The study of luminescence properties of YAG doped with Nd³⁺ or Cr³⁺ ions has allowed to determine the positions of hydroxyl groups and oxygen vacancies in the structure.     

Surface segregation measurements during electron irradiation

Abstract

The growth of Ni3Si surface films on Ni-12.7at%Si alloys has been measured during lMeV electron irradiation. Stereoscopic techniques were used to determine film thickness from dark field images formed from Ni₃Si superlattice reflections. Parabolic growth kinetics are observed at lower temperatures. However, at higher temperatures, deviations from parabolic kinetics are observed after short irradiation times. Such deviations have not been observed in bulk specimens during bombardment with energetic ions and, therefore, may be due to foil thickness effects.     

Point-defect concentrations in B2 NiAl alloys under pressure

The pressure dependence of point-defect concentrations is calculated on the basis of two recently published models. It is demonstrated that the effective formation volume of vacancies shows asymmetrical character about stoichiometry. For Ni-rich and stoichiometric compositions, the concentration of Ni vacancies versus pressure can be described by a simple exponential function. The concentration of Ni antisite defects is independent of pressure. For Al-rich compositions, the concentration of Ni vacancies shows a more complex behaviour. At low pressures the vacancy concentration is independent of pressure, the effective formation volume is zero, while above a critical pressure the vacancy concentration becomes pressure dependent. This can be explained by the annihilation reaction of Ni vacancies. The pressure of complete replacement depends on the stoichiometry and has proved to be very sensitive to the input parameters used in the different models. The changes expected in diffusion activation energy and activation volume with composition are discussed on the basis of calculated temperature and pressure dependence of Ni vacancy concentration, assuming vacancy-mediated diffusion. The pressure effect on the boundary that separates regions in which triple defects or interbranch defects dominate was also investigated. It was observed that pressure expands the region in which Al interbranch defects dominate.     

NMR investigation of defect properties in single crystal SrTiO3

Abstract

⁴⁹Ti and ⁸⁷Sr nuclear magnetic resonance measurements were performed in single crystalline SrTiO₃ between 90 K and 1800 K at various oxygen partical pressures. The NMR lines are found to be shifted with rising temperature due to oxygen vacancies acting as donors. Furthermore, three distinct motion-induced nuclear spin relaxation rates could be observed. The corresponding jump rates are attributed to the following processes: translational jumps of charged oxygen vacancies between oxygen sites, localized motion of oxygen vacancies in Fe-vacancy complexes, self diffusion of Sr²⁺.     

Density functional theory-based cluster expansion to simulate thermal annealing in FeCrW alloys

Abstract

In this work, we develop a rigid lattice cluster expansion as an ultimate goal to track the micro-structural evolution of Eurofer steel under neutron irradiation. The fact that all (defect) structures are mapped upon a rigid lattice allows a simplified computation and fitting procedure, thus enabling alloys of large chemical complexity to be modelled. As a first step towards the chemical complexity of Eurofer steels, we develop a cluster expansion (CE) for the FeCrW-vacancy system based on density functional theory (DFT) calculations in the dilute alloy limit. The DFT calculations suggest that only CrW clusters containing vacancies are stabilised. The cluster expansion was used to simulate thermal annealing in Fe–20Cr–xW alloys at 773 K. It is found that the addition of W to the alloy results in a non-linear decrease in the precipitation kinetics. The CE was found suitable to describe the energetics of the FeCrW-vacancy system in the Fe-rich limit.