Nghi Q. Lam

A theory of radiation-induced segregation in concentrated alloys☆

Abstract A new and simple theory for radiation-induced segregation in concentrated alloys is presented. The coupling between defect fluxes and atom fluxes is accounted for by the concept of preferential migration of vacancies and interstitials via A-atoms or B-atoms in a binary A-B alloy. Similarly, atom fluxes are partitioned into those occurring via vacancies and via interstitials. This approach permits expression of the defect fluxes and atom fluxes in terms of partial diffusivity coeffi- cients and concentration gradients of defects and alloy components. The time and space dependence of the defect concen- trations and composition of a binary alloy is described by a set of three coupled partial differential equations containing four partial diffusivity coefficients, i.e., those of A-atoms and B-atoms diffusing via vacancies and via interstitials. The set of differential equations has been integrated for some model binary alloys with complete miscibility, utilizing the geometry of a thin foil. The sample calculations are in good qualitative agreement with the general features of radiation-induced segregation as deduced from experiments. The temperature, dose and dose-rate dependencies of segregation in concentrated alloys are found to be similar to those predicted by the Johnson-Lam model for dilute alloys.

Physics of Crystal-to-Glass Transformations

Publisher Summary This chapter focuses on the relationship between melting and solid-state amorphization. It discusses that amorphization is a disorder-driven melting process, occurring below the glass transition temperature, and that a unified approach to heating- and disorder-induced melting is found in the generalized version of the Lindemann melting hypothesis. This hypothesis assumes that the melting of a defective crystal occurs when the sum of the static and thermal mean-square displacements reaches a critical fraction of the interatomic spacing, which was shown to be equivalent to a generalized T o -concept resulting from a disorder-induced softening of the shear modulus. Comparisons with available experimental data and with the predictions of microscopic defect-mediated melting models were made to establish the validity of the generalized Lindemann melting criterion. The chapter explores that the disorder-induced melting concept provides a new thermodynamic approach to understand other materials problems, including brittle fracture and stress-corrosion cracking. Stress-corrosion cracking is viewed as premelting of high-energy grain boundaries, because of the combined effects of applied stresses and the segregation of insoluble impurities in lowering the melting temperature of grain boundaries to the ambient temperature. Stress-induced melting may also occur in the vicinity of moving crack tips. However, as revealed by atomistic simulations, the local melting is a transient phenomenon at elevated temperatures and, hence it is observable only at temperatures below the glass transition temperature where the liquid phase persists indefinitely as a glass.

Steady-state point-defect diffusion profiles in solids during irradiation

Abstract The steady-state distribution of mobile point defects in a monatomic solid under irradiation has been calculated for a semi-infinite solid and for a foil. The calculation was performed for defect annihilation by mutual recombination, at internal sinks, and by diffusion to the surface. Simple approximations, accurate to within 5%, have been developed for the analytical solutions to the differential rate equations.

Solute segregation and precipitation under heavy-ion bombardment

Abstract Solute segregation and precipitation in dilute Ni-base binary alloys during heavy-ion bombardment were studied using a kinetic model. Spatially-dependent defect—production rates corresponding to 75-keV and 3-MeV Ni+ ion bombardment and various defect—solute interactions were considered in the calculations. For strong interstitial—solute binding, solutes in the peak-damage region are transported to the sample surface and into the bulk beyond the damage range, resulting in a solute depletion at the damage peak. However, for a vacancy—solute binding energy of ~0.05 eV, the solute-segregation trends are reversed from the strong interstitial—solute interaction case. With larger vacancy—solute binding energies, solute enrichment occurs at the surface. The present theoretical predictions are qualitatively compared with recent experimental measurements of the temperature and spatial dependence of radiation-induced segregation of undersize and oversize solutes in Ni-base alloys.

Disorder-induced amorphization

Many crystalline materials undergo a crystalline-to-amorphous (c-a) phase transition when subjected to energetic particle irradiation at low temperatures. By focusing on the mean-square static atomic displacement as a generic measure of chemical and topological disorder, we are led quite naturally to a generalized version of the Lindemann melting criterion as a conceptual framework for a unified thermodynamic approach to solid-state amorphizing transformations. In its simplest form, the generalized Lindemann criterion assumes that the sum of the static and dynamic mean-square atomic displacements is constant along the polymorphous melting curve so that c-a transformations can be understood simply as melting of a critically-disordered crystal at temperatures below the glass transition temperature where the supercooled liquid can persist indefinitely in a configurationally-frozen state. Evidence in support of the generalized Lindemann melting criterion for amorphization is provided by a large variety of experimental observations and by molecular dynamics simulations of heat-induced melting and of defect-induced amorphization of intermetallic compounds.

Bombardment-induced segregation and redistribution

During ion bombardment, a number of processes can alter the compositional distribution and microstructure in near-surface regions of alloys. The relative importance of each process depends principally on the target composition, temperature, and ion characteristics. In addition to displacement mixing leading to a randomization of atomic locations, and preferential loss of alloying elements by sputtering, which are dominant at relatively low temperatures, several thermally-activated processes, including radiation-enhanced diffusion, radiation-induced segregation and Gibbsian adsorption, also play important roles. At elevated temperatures, nonequilibrium point defects induced by ion impacts become mobile and tend to anneal out by recombination and diffusion to extended sinks, such as dislocations, grain boundaries and free surfaces. The high defect concentrations, far exceeding the thermodynamic equilibrium values, can enhance diffusion-controlled processes, while persistent defect fluxes, originating from the spatial non-uniformity in defect production and annihilation, give rise to local redistribution of alloy constituents because of radiation-induced segregation. Moreover, when the alloy is maintained at high temperature, Gibbsian adsorption, driven by the reduction in free energy of the system, occurs even without irradiation; it involves a compositional perturbation in a few atom layers near the alloy surface. The combination of these processes leads to the complex development of a compositionally-modified layer in the subsurface region. Considerable progress has been made recently in identifying and understanding the relative contributions from the individual processes under various irradiation conditions. In the present paper, selected examples of these different phenomena and their synergistic effects on the evolution of the near-surface compositions of alloys during sputtering and ion implantation at elevated temperatures are discussed.

Solute segregation under irradiation

Abstract Recent calculations of substitutional solute segregation to planar surfaces, voids, and dislocations in fcc metals during irradiation are reviewed. The calculations were based on a kinetic model that included the effects of vacancy and dumbellinterstitial diffusional encounters with solute atoms, diffusion of point defects and bound complexes, and spatially dependent reaction terms. Solute segregation is found to be significant in the temperature range from 0.2 to 0.6 T m . The temperature for maximum segregation is appreciably higher for heavy-ion bombardment or high-voltage-electron-microscope irradiation rates than for fast-reactor irradiation rates. Segregation is also found to be maximum when the interstitialsolute binding energy is sufficiently high so that the migration energies of the vacancy and interstitial-solute complex become comparable. Furthermore, the magnitude of the segregation effect varies with foil thickness, void size, void number density, dislocation-capture radius, and dislocation density.

Effects of solute segregation and precipitation on void swelling in irradiated alloys

Abstract A model of radiation-induced segregation of substitutional solutes has been used to study the effects of solute segregation and precipitation on void swelling behavior in metals and alloys. If the binding energies between point defects and solute atoms are sufficiently large, significant solute segregation takes place during irradiation, giving rise to a solute depletion or enrichment at defect sinks and a nonuniform distribution of defect-trapping centers in the matrix. The swelling reduction, which results from trapping of point defects by minor additions of alloying elements, is affected by radiationinduced solute redistribution in alloys. The effects of either dominant interstitial-solute interactions or dominant vacancy-solute interactions on segregation and swelling were studied. The present calculations are in good qualitative agreement with experimental results.

Sputter-induced surface composition changes in alloys

Abstract Radiation-induced redistribution of alloying elements in the near-surface region of dilute binary alloys during low-energy Ar+ ion sputtering was calculated using a kinetic model that includes the effects of radiation-induced segregation and preferential sputtering. Changes in the alloy surface composition were calculated as functions of sputtering time, temperature, ion flux and initial alloy composition for Ni-based model alloys. In the temperature range 200–850°C, radiation-induced segregation is dominant initially and the surface is enriched with or depleted of solutes whose fluxes are coupled predominantly to interstitial or vacancy fluxes, respectively. As the bombardment time increases, the effects of preferential sputtering become dominant and the surface composition approaches a steady-state value determined by the sputtering coefficients of the alloy components. Below 200 and above 850°C, the surface composition is altered by preferential sputtering because radiation-induced segregation is insignificant. The time required to achieve steady state increases with increasing temperature and decreasing ion flux. The present calculations may be of importance in the areas of sputter depth-profiling, sputter etching, and plasma contamination in fusion reactors.

Relationship between segregation-induced intergranular fracture and melting in the nickel–sulfur system

The effect of S segregation to grain boundaries on the intergranular embrittlement of Ni has been studied at room temperature using Auger electron spectroscopy and slow strain rate tensile tests. The grain-boundary S concentration was varied by time-controlled annealing of dilute Ni–S alloy specimens at 625 °C. The ductile-to-brittle transition in Ni, as determined from percent integranular fracture and reduction-in-area measurements, occurred over a narrow range of S concentrations centered on 15.5±3.4 at. % S. This critical S concentration for 50% intergranular fracture of polycrystalline Ni is similar to the 14.2±3.3 at. % S required to induce 50% amorphization of single-crystal Ni by S+-ion implantation. This suggests that segregation-induced intergranular fracture, like implantation-induced amorphization, may be a disorder-induced polymorphous melting process. In agreement with experimental observations, the polymorphous melting curve for the Ni–S solid solution on the phase diagram drops rapidly to ...