Dumbbell Interstitials Research Articles

Interrelationship between the shear modulus of a metallic glass, concentration of frozen-in defects, and shear modulus of the parent crystal

The Interstitialcy theory assumes that major structural defects defining the properties of glass are similar to dumbbell interstitials in crystalline metals. Within the framework of this approach, we showed that at a constant defect concentration, the temperature coefficient of the shear modulus of glass equals to that of the parent crystal, in agreement with the theory. Relaxation of the defect system leads to either positive or negative variation of this coefficient, depending on the sign of defect concentration change. A full map of the defect concentration for initial, relaxed, and quasi-equilibrium states of a Pd-based glass is presented.

Molecular dynamics simulations of displacement cascades in Fe-10%Cr systems

Molecular dynamics simulations of the displacement cascades in Fe−10%Cr systems are used to simulate the primary knocked-on atom events of the irradiation damage at temperatures 300, 600, and 750 K with primary knocked-on atom energies between 1 and 15 keV. The results indicate that the vacancies produced by the cascade are all in the central region of the displacement cascade. During the cascade, all recoil Fe and Cr atoms combine with each other to form Fe—Cr or Fe—Fe interstitial dumbbells as well as interstitial clusters. The number and the size of interstitial clusters increase with the energy of the primary knocked-on atom and the temperature. A few large clusters consist of a large number of Fe interstitials with a few Cr atoms, the rest are Fe—Cr clusters with small and medium sizes. The interstitial dumbbells of Fe—Fe and Fe—Cr are in the (111) and (110) series directions, respectively.

Structural relaxation and related viscous flow of Zr–Cu–Al-based bulk glasses produced from the melts with different glass-forming ability

The relaxation ability of Zr 46(Cu 4/5Ag 1/5) 46Al 8 and Zr 46Cu 46Al 8 bulk glasses displaying different glass-forming ability (GFA) in the liquid state has been studied by measurements of the shear modulus, creep and stress relaxation. It has been found that the four-component alloy with higher GFA always displays higher relaxation ability in the glassy state. This fact does not seem to correlate with the amount of the frozen-in free volume as dependent on the GFA. It has been argued that the relaxation centers responsible for structural relaxation and related viscous flow are similar to dumbbell interstitials in simple metals. Such an approach precisely describes the kinetics of shear modulus relaxation and reasonably agrees with a phenomenological interpretation of structural relaxation-induced viscoelastic phenomena in metallic glasses.

Irradiation-Driven Compositional Changes in Alloys

ABSTRACTA model to study the formation of compositional patterns in concentrated binary alloys under irradiation is presented. In this model, six atomic and defect species are considered: regular lattice atoms (A and B), dumbbell interstitials (AA, BB and AB) and vacancies. In addition to long range diffusion of these species, local defect-defect (vacancy-interstitial recombination) and defect-atom (dumbbell-atom) reactions have also been considered. The model tracks simultaneous evolution of all the species in reaction-diffusion formalism. Irradiation events are modeled as a stochastic point process which changes the concentration of all the species instantaneously in a random fashion. In each irradiation event, a spatial distribution of point defects (core-shell distribution: core dominated by vacancies and shell by interstitials) has been introduced in the system which drives the kinetics of diffusion and reaction. The model has been non-dimensionalized with respect to intrinsic length and time scales of the material system and solved numerically using finite difference technique. Applying this model to CuAu solid solution, we have shown that the alloy exhibits spinodal-like decomposition with specific steady state wavelengths that depend on the irradiation conditions.

Melting, thermal expansion, and the Lindemann rule for elemental substances

An interpretation of a long-standing problem—the Lindemann melting rule—has been suggested within the framework of the interstitialcy theory. Melting is considered to be due to the rapid generation of thermodynamically equilibrium defects—dumbbell interstitials, which drastically decrease the shear modulus at the melting point. An analytical expression for the relationship between the thermal expansion coefficient and melting temperature coinciding with the Lindemann melting rule has been derived. The obtained results agree with available data on elemental substances. A correlation between the melting temperature and shear modulus has been discovered and explained within the framework of the same approach.

First-principles study of uranium carbide: Accommodation of point defects and of helium, xenon, and oxygen impurities

Point defects and volatile impurities (helium, xenon, oxygen) in uranium monocarbide UC are studied by first-principles calculations. Preliminarily, bulk properties of UC and of two other uranium carbide phases, ${\text{UC}}_{2}$ and ${\text{U}}_{2}{\text{C}}_{3}$, are calculated in order to compare them to experimental data and to get confidence in the use of the generalized gradient approximation for this class of compounds. The subsequent study of different types of point defects shows that the carbon sublattice best accommodates the defects. The perturbation of the crystal structure induced by the defects is weak and the interaction between defects is found short range. Interstitial carbon dumbbells possibly play an important role in the diffusion of carbon atoms. The most favorable location of diluted helium, xenon, and oxygen impurities in the UC crystal lattice is then determined. The rare-gas atoms occupy preferably a uranium substitution site or a uranium site in a U-C bivacancy. But their incorporation in UC is, however, not energetically favorable, especially for xenon, suggesting their propensity to diffuse in the material and/or form bubbles. On the other hand, oxygen atoms are very favorably incorporated as diluted atoms in the UC lattice, confirming the easy oxidation of UC. The oxygen atoms preferably occupy a carbon substitution site or the carbon site of a U-C bivacancy. Our results are compared to available experimental data on UC and to similar studies by first-principles calculations for other carbides and nitrides with the rock-salt structure.

Evidence of Distributed Interstitialcy-Like Relaxation of the Shear Modulus due to Structural Relaxation of Metallic Glasses

The interstitialcy theory is used to calculate the kinetics of shear modulus relaxation induced by structural relaxation of metallic glasses. A continuous distribution of activation energies is shown to be a salient feature of the relaxation. High precision in situ contactless electromagnetic acoustic-transformation shear modulus (600- kHz) measurements performed on a Zr-based bulk metallic glass are found to strongly support the approach under consideration. It is revealed that the activation energy spectra derived from isothermal and isochronal shear modulus measurements are in good agreement with each other. It is concluded that the increase of the shear modulus during structural relaxation can be understood as a decrease of the concentration of structural defects similar to dumbbell interstitials in simple crystalline metals.

Interstitials in FeCr alloys studied by density functional theory

Density functional theory calculations have been used to study relaxed interstitial configurations in FeCr alloys. The ionic and electronic ground states of 69 interstitial structures have been determined. Interstitials were placed in alloys with up to $14\phantom{\rule{0.3em}{0ex}}\mathrm{at.}\phantom{\rule{0.2em}{0ex}}%$ Cr. Cr atoms were either monatomically dispersed or clustered together within a periodically repeated supercell consisting of $4\ifmmode\times\else\texttimes\fi{}4\ifmmode\times\else\texttimes\fi{}4$ cubes of bcc unit cells. The distance between the interstitials and Cr atoms was varied within the supercells. It is shown that Cr atoms beyond third-nearest-neighbor distance from the interstitial can still have an interaction with it of up to $0.9\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The multibody nature of the Cr-Cr interactions causes the Cr-interstitial interaction to be strongly concentration dependent. The Cr-Cr interaction in defect-free alloys is also dependent on the overall Cr concentration. The effective Cr-Cr repulsion is weaker in alloys than in an environment of pure Fe. Apart from the Cr concentration, the Cr-interstitial interaction also depends on the dispersion level of Cr atoms beyond third-nearest-neighbor distance from the interstitial. The formation energy differences between dumbbell interstitials with different orientations are independent of the Cr concentration. We show that the long-range influence of Cr atoms on the interstitial is not due to the interstitial strain field protruding into Cr-rich parts of the supercells. The Fermi-level and band energies were found not to be the sole governing parameter in determining the formation energies. Implications for the construction of empirical potentials are discussed.

Molecular dynamics simulation of irradiation damage in tungsten

Molecular dynamics (MD) simulations have been performed for the radiation damage of tungsten using a modified Finnis-Sinclair type many-body interatomic potential. The interstitial defects and vacancies are distinguished by the Wigner–Seitz cell method and the types of the interstitial dumbbells are also identified by the azimuth and polar angles of dumbbell line vectors. It is observed that the number of interstitial defects and vacancies initially sharply increases and passing through the peak position, relaxes to the steady state for all PKA energies and that all residual interstitial dumbbells at the steady state are the <111>-oriented. Based on the variation of the orientation angles of dumbbells during the radiation damage simulation, it is found that the recombination of the <111>-oriented dumbbells with the vacancies is much faster than that of two other types of dumbbells and that the population of the <100> dumbbells is much larger than that of the <110> ones in spite of its higher formation energy, the reason of which is explained with the dynamics of the individual dumbbell.

Influence of Cu, Cr and C on the irradiation defect in Fe: A molecular dynamics simulation study

The effects of alloying elements, Cu, Cr and C, on the number of residual point defects (vacancies and interstitials), their clustering tendency and constitution have been investigated by performing molecular dynamics cascade simulations on pure Fe, Fe–0.5 at.% Cu, Fe–10 at.% Cr and Fe–0.1 at.% C alloys using MEAM interatomic potentials. Both Cu and Cr form Fe–M and M–M interstitial dumbbells, but have no significant effect on the number and clustering tendency of point defects. Carbon has no effect on the formation and clustering of point defects neither, but shows a strong binding with vacancies and interstitial dumbbells. By combining the simulation results and calculated binding energies between individual point defects, effects of solute atoms on the long-term irradiation-induced microstructure evolution are deduced. Details of cascade simulation results and binding energies between point defects are presented, and influence of solute elements on long-term irradiation defect such as void swelling and formation of solute-rich precipitates are discussed.

Synergistic effects of PKA and helium on primary damage formation in Fe–0.1%He

Molecular dynamics (MD) simulation of displacement cascades in Fe–0.1%He are used to investigate the synergistic effects of primary knock-on atoms (PKA) and He on the irradiation damage production at temperatures between 10 K and 523 K. The results indicate that the vacancies produced by cascades are all in the central region of displacement cascade. The presence of He does not influence Frenkel pair production. During cascade evolution all displaced Fe and He atoms combine with each other to form Fe–He or Fe–Fe interstitials dumbbell as well as interstitial clusters. The number and size of interstitial clusters increase with the PKA energy and temperature. A few large clusters consisting of a large number of Fe interstitials with a few helium atoms are formed, the rest being Fe–He clusters at small and medium sizes. The interstitial dumbbell of Fe–Fe and Fe–He are in the 〈1 0 0〉 and 〈1 1 0〉 lattice direction, respectively.

Molecular dynamics simulations of point defect interactions in Fe–Cr alloys

Predicting the performance of Fe–Cr ferritic martensitic steels in fusion energy environments requires an understanding of point defect properties, including the influence of solutes, impurities and other defects on their migration behavior. This paper presents molecular dynamics simulations of the effect of Cr on the diffusion of single, di- and tri-interstitials in Fe–10%Cr alloys. Two Finnis–Sinclair-type potentials were used to model the Fe–Cr alloys, which alternately describe Cr as under- or over-sized in body-centered cubic Fe. In general, the diffusivity of the single interstitials and di- and tri-interstitial clusters was reduced in the Fe–10%Cr alloys, irrespective of interatomic potential, although the underlying mechanism was different. When Cr is undersized, interstitial diffusion is retarded through a trapping mechanism associated with bound Cr-interstitial (mixed dumbbell) complexes, whereas oversized Cr atoms retard interstitial diffusion by enhancing the rotation frequency away from one-dimensionally mobile 〈1 1 1〉 interstitial dumbbell configurations.

Molecular dynamics simulation of radiation damage in bcc tungsten

Molecular dynamics (MD) simulations are performed to assess the primary damage due to high-energy neutron irradiation in bcc tungsten. For short-range interactions two different universal potentials are used, while for long-range interactions, two empirical embedded atom method (EAM) tungsten potentials are used. The short-range and long-range potentials are smoothly connected. Additionally, truncation of the electron density function at low distances is used. Statistically meaningful Frenkel pairs (FP) are counted and interstitial dumbbell orientations and interstitial or vacancy cluster counts are obtained. In addition, an approach to assess the volume influenced by the cascades based on a standard deviation ellipsoid is presented. A critical review of present and existing MD results is performed, and an attempt is made to clarify the roles played by the empirical potentials and by the temperature.

Formation and recovery of irradiation and mechanical damage in stabilized δ-plutonium alloys

Based on the results of thermal expansion measurements of aged δ-phase Pu–Ga alloys and comparisons with historical bulk density, thermal expansion, and X-ray diffraction data of δ-phase Pu–Al and Pu–Ga alloys, it is being proposed that Pu-solute atom mixed 〈1 0 0〉 dumbbell interstitials, generated by damage processes, induce volumetric swelling and impede δ → α′ Martensitic transformation in these alloys. Damage induced volumetric swelling in δ-phase Pu–Al and Pu–Ga alloys is distinct from swelling induced by He bubble formation in that it appears to saturate as a function of damage eventually reaching a constant value which is linearly dependent on solute element atomic concentration. Based on arguments offered in this work, each Pu-solute atom mixed 〈1 0 0〉 dumbbell interstitial creates a strain field of approximately 4.8 times the Pu atomic volume over some 20 Å in extent. As the interstitial concentration increases with damage, so does the volumetric swelling up to the point of saturation with a concentration of 1% of the solute atomic concentration. These interstitials appear to anneal out at temperatures of 150 to 200 °C. This relatively high thermal stability is possibly due to an altered local bonding environment for the Pu-solute atom interstitial pair and first-nearest neighbors in response to reduced coordination number and lattice strain field.

Diffusion and conversion of interstitial dumbbells in segregated ternary alloys under irradiation

A radiation-induced segregation model for concentrated alloys based on the inverse Kirkendall effect is successfully used to predict element segregation in model alloys under irradiation conditions. In this model the segregation is the result of preferential atom-vacancy jumps. But under conditions of high irradiation flux or wide temperature range, a description of interstitial migration must be included in the model. In the present work the rate theory was used to simulate radiation-induced segregation near the grain boundary in Fe–Cr–Ni alloys. A model of diffusion and conversion of a mixed interstitial dumbbell was applied to describe the flux of interstitial. Six types of interstitial dumbbells and their conversion by a jump of one of its constituent atoms to a neighbouring site to form a dumbbell of different orientation, were considered. The vacancy flux was described similarly to the Wiedersich–Okamoto–Lam model, considering its migration through position exchange with a lattice atom.

Self-diffusion and solute diffusion in alloys under irradiation: Influence of ballistic jumps

We have studied the influence of ballistic jumps on thermal and total diffusion of solvent and solute atoms in dilute fcc alloys under irradiation. For the diffusion components that result from vacancy migration, we introduce generalized five-frequency models, and show that ballistic jumps produce decorrelation effects that have a moderate impact on self-diffusion but that can enhance or suppress solute diffusion by several orders of magnitude. These could lead to new irradiation-induced transformations, especially in the case of subthreshold irradiation conditions. We also show that the mutual influence of thermal and ballistic jumps results in a nonadditivity of partial diffusion coefficients: the total diffusion coefficient under irradiation may be less than the sum of the thermal and ballistic diffusion coefficients. These predictions are confirmed by kinetic Monte Carlo simulations. Finally, it is shown that the method introduced here can be extended to take into account the effect of ballistic jumps on the diffusion of dumbbell interstitials in dilute alloys.

Phenomenological coefficients for transport by dumbbell mechanisms in a dilute random bcc alloy

Abstract Onsager phenomenological coefficients for matter transport are calculated for models of interstitial dumbbell jump mechanism appropriate to dilute binary bcc transition-metal alloys. By use of a refinement of a kinetic equation method earlier employed for dilute and concentrated fcc alloy models, the linear response expressions are reduced to expressions containing defect jump frequencies and concentrations and certain Brillouin integrals. An example of the final form for the case where one particular mechanism operates alone is described in more detail. Monte Carlo simulation results are in satisfactory agreement with the theoretical predictions. Comparison is also made with the pair association calculations by Barbu and Lidiard (1996, Phil. Mag. A, 74, 709). It is shown that, even when all mechanisms operate simultaneously, simple relationships exist between parts of the three independent phenomenological coefficients. The relationship to the earlier calculation of the impurity and defect coeff...

Percolation problem in atomic transport inHg1−xCdxTe

Using high-resolution x-ray diffraction for precise measurements of structural modifications in boron-implanted ${\mathrm{Hg}}_{1\ensuremath{-}x}{\mathrm{Cd}}_{x}\mathrm{Te}$ layers, we found a percolation problem in the long-range diffusion of Cd interstitials through the Cd, Hg sublattice. The percolation threshold ${x}_{c}=0.265$ is in agreement with the calculated one, ${x}_{\mathrm{th}}=0.278,$ for dumbbell interstitials diffusion in the fcc lattice [J. Bocquet, Phys. Rev. B 50, 16 386 (1994)]. These findings were supported by high-resolution scanning electron microscopy images, taken under magnification \ifmmode\times\else\texttimes\fi{}400 000, in which very different post-implantation surface recovery (due to a flux of interstitials from an interior to the crystal surface) was observed below and above ${x=x}_{c}.$ Measurements of x-ray-diffraction profiles in samples, implanted and annealed at 150\char21{}350 \ifmmode^\circ\else\textdegree\fi{}C, allowed us to determine an energy barrier, $\ensuremath{\Delta}E=0.31\mathrm{eV},$ between Cd-Cd and Cd-Hg dumbbell configurations.

Hetero-epitaxial growth of CoSi 2 thin films on Si(1 0 0): : template effects and epitaxial orientations

This HREM investigation focuses on the influence of point defects on the final epitaxial relation and atomic interface configuration in a CoSi 2/Si(1 0 0) heterostructure. A two-step SPE–MBE grown CoSi 2/Si(1 0 0) system is used and, by altering the number of deposited Co monolayers in the template layer, the point defect behavior is studied. We propose a film growth model in which the knowledge about the reconstructed (2×1) : Si(1 0 0) surface, the point defect behavior in the presence of an interface, especially a silicide interface, the migration of point defects through a lattice by formation of 〈1 0 0〉-split interstitial (dumbbell) atomic configurations, and a new type of extended defect configurations in diamond type materials will all amalgamate.

A model for radiation-induced segregation in fcc binary alloys

A model is presented for radiation-induced segregation (RIS) in a face-centered cubic (fcc) binary alloy containing A- and B-atoms. Assuming that the interstitial in an fcc crystal takes the configuration of the 〈100〉 dumbbell, three types of interstitial dumbbells, AA-, BB- and AB-type, are considered. The present model includes the diffusion and conversion of the three types of interstitial dumbbells via an interstitialcy migration, their recombination with a vacancy, and vacancy diffusion by position exchange with a lattice atom. The fraction of AA-, BB- and AB-type dumbbells is determined through the conversions, and the AB-type mixed dumbbell plays an important role in the determination of the segregation direction. When a large number of mixed dumbbells moves toward the sinks, enrichment of the lower concentration element occurs, because the AB-dumbbell includes the same number of A- and B-atoms. When mixed dumbbell migration is rare, on the other hand, the lower concentration element can be depleted, even if the self-interstitial dumbbell composed of that element moves more quickly. Consequently, the direction of RIS depends on the mobility of point defects as well as alloy compositions. When the RIS kinetics of a Cu Au alloy is calculated with the model, good agreement is obtained with experimental results.