Grain Boundary Sites Research Articles

Computational study of carbon segregation and diffusion within a nickel grain boundary

Using density functional theory, we study the segregation and diffusion of carbon interstitials at a nickel Σ3 ( 1 1 2 ¯ ) tilt grain boundary (GB) as a function of C coverage and Ni magnetic state. We find that segregation is most favorable for a “checkerboard” configuration at a coverage of 1 2 monolayer in both non-magnetic (NM) and ferromagnetic (FM) states, with FM (NM) heats of segregation approaching −0.5 (−0.3) eV per C atom. Segregation is 0.1–0.2 eV stronger in the FM state, because C interstitials suppress Ni magnetism, and this suppression is minimized when C resides at the boundary. Carbon GB diffusion is predicted to be highly anisotropic: calculated energy barriers ( E a) for migration parallel to the [ 1 1 ¯ 0 ] tilt axis are significantly smaller ( E a = 0.44–0.77 eV) than for lattice diffusion ( E a = 1.62 eV), while barriers perpendicular to [ 1 1 ¯ 0 ] are comparable to those of lattice diffusion. Changes in barrier height due to Ni magnetism are (with one exception) relatively small, and are evident only when the diffusion pathway bisects highly compressed GB sites.

First-Principles Study on Segregation Energy and Embrittling Potency of Hydrogen in NiΣ5(012) Tilt Grain Boundary

The electronic structures of Σ5(012) symmetrical tilt grain boundary (GB) and (012) free surface (FS) systems for nickel including hydrogen are calculated by the full-potential linearized augmented plane wave method with the generalized gradient approximation. The GB/FS energy and the binding energy of hydrogen at an inner bulk site and GB/FS site are calculated. The calculated binding energy of hydrogen on Ni(111) surface is in good agreement with experiment. The difference of the binding energies between the Σ5(012) GB/FS site and the inner bulk site is obtained as the GB/FS segregation energy, and the difference between GB and FS segregation energies as the embrittling potency energy. The segregation position of hydrogen atom is determined by the force minimization. We find that hydrogen atom prefers Σ5(012) GB to inner bulk energetically by about 0.3 eV/H, while it prefers (012) FS to the GB by about 0.3–0.4 eV/H. The open space at GB may be occupied by an additional interstitial Ni atom since it increases the GB energy by only about 10%. In this case, the GB segregation energy of hydrogen reduces, which makes the segregation difficult. The calculated zero-point energies of hydrogen at inner bulk, GB, and FS sites are within 0.12–0.16 eV/H. The difference of the zero-point energies is within 0.04 eV/H, which is small comparing with the segregation energy and embrittling potency.

Structure and energetics of clean and hydrogenated Ni surfaces and symmetrical tilt grain boundaries using the embedded-atom method

Multilayer relaxations, surface/interface energies, and hydrogen binding sites and energies were systematically studied using the embedded-atom method, for a series of the clean and hydrogenated Ni surfaces and symmetrical tilt Ni grain boundaries. The hydrogen binding energies were in the range of 2.7--2.9 eV at the surface sites while 2.1--2.6 eV at the grain-boundary sites, both being larger than at the fcc crystal interior site, 2.1 eV. These data are consistent with the conclusions from ab initio calculations that intergranular embrittlement is seen by hydrogen segregation at the Ni grain boundaries. It was found that multilayer relaxation of Ni plays a key role in trapping hydrogen at the grain boundaries.

Atomistic Modeling of Point Defects and Diffusion in Copper Grain Boundaries

The atomic structure of several symmetrical tilt grain boundaries (GBs) in Cu and their interaction with vacancies and interstitials as well as self-diffusion are studied by molecular statics, molecular dynamics, kinetic Monte Carlo (KMC), and other atomistic simulation methods. Point defect formation energy in the GBs is on average lower than in the lattice but variations from site to site within the GB core are very significant. The formation energies of vacancies and interstitials are close to one another, which makes the defects equally important for GB diffusion. Vacancies show interesting effects such as delocalization and instability at certain GB sites. They move in GBs by simple vacancy-atom exchanges or by “long jumps” involving several atoms. Interstitial atoms can occupy relatively open positions between atoms, form split dumbbell configurations, or form highly delocalized displacement zones. They diffuse by direct jumps or by the indirect mechanism involving a collective displacement of several atoms. Diffusion coefficients in the GBs have been calculated by KMC simulations using defect jump rates determined within the transition state theory. GB diffusion can be dominated by vacancies or interstitials, depending on the GB structure. The diffusion anisotropy also depends on the GB structure, with diffusion along the tilt axis being either faster or slower than diffusion normal to the tilt axis. In agreement with Borisov's correlation, the activation energy of GB diffusion tends to decrease with the GB energy.

Interaction of Point Defects with Grain Boundaries in fcc Metals

Structures of several symmetrical tilt grain boundaries (GBs) with different tilt axes in Cu and Al and their interaction with vacancies and interstitials are studied using atomistic computer simulations with embedded-atom potentials. The lowest defect formation energy in a GB is found to correlate with the GB energy in both Cu and Al. Importantly, vacancies and self-interstitials in GBs have comparable formation energies, suggesting that both defects are equally important for GB diffusion and other properties. Vacancies in GBs can be either localized at certain sites or be delocalized over several sites. Some GB sites do not support a stable vacancy at all. Self-interstitial atoms can occupy relatively open interatomic positions, form split dumbbell configurations, or give rise to highly delocalized displacement zones. These structural forms of point defects have been observed across the whole set of twelve GBs in Cu and six GBs in Al studied in this paper as well as in our previous work [Interface Science 11, 131–148 (2003)]. It is suggested that these structural forms are general to all GBs in fcc metals. They can be explained by the existence of internal stresses and alternating tension and compression regions in the GB core.

Diffusion mechanisms in Cu grain boundaries

We investigate atomic mechanisms of grain boundary (GB) diffusion by combining molecular dynamics (MD), molecular statics, the harmonic approximation to atomic vibrations, and kinetic Monte Carlo (KMC) simulations. The most important aspects of this approach are the basin-constrained implementation of MD and an automated location of transition states using the nudged elastic band method. We study two $\ensuremath{\Sigma}=5$ [001] symmetric tilt GB's in Cu, with atomic interactions described by an embedded-atom potential. Our simulations demonstrate that GB's support both vacancies and interstitials, and that vacancies can show interesting effects such as delocalization and instability at certain GB sites. Besides simple vacancy-atom exchanges, vacancies move by ``long jumps'' involving a concerted motion of two atoms. Interstitials move through concerted displacements of two or more atoms. More complex mechanisms (such as ring processes) involving larger groups of atoms have also been found. The obtained point defect formation energies and entropies, as well as their migration rate constants calculated within harmonic transition state theory, are used as input to KMC simulations of GB diffusion. The simulations show that GB diffusion can be dominated by either vacancy or interstitial-related mechanisms depending on the GB structure. The KMC simulations also reveal interesting effects such as temperature-dependent correlation factors and the trapping effect. Using the same simulation approach we study mechanisms of point defect generation in GB's and show that such mechanisms also involve collective transitions.

Investigations of grain boundaries in copper using emission Mössbauer spectroscopy

Grain boundaries (GBs) in pure Cu specimens were studied by means of 57Fe emission Mossbauer spectroscopy. A spectrum component which can be ascribed to iron atoms at GBs is represented by the single line with isomer shift 0.67 ± 0.05 mm/s. It is interpreted as iron atoms at GB sites with expanded atomic volumes and highly symmetric distribution of surrounding atoms.

The identification of hydrogen trapping states in an Al-Li-Cu-Zr alloy using thermal desorption spectroscopy

Thermal desorption spectroscopy (TDS) was utilized to identify several metallurgical states in an Al -2Li - 2Cu-0.1Zr (wt pct) alloy, which trap absorbed hydrogen. Six distinct metallurgical desorption states for hydrogen were observed for tempers varying from the T3 to peakaged condition. Lower energy thermal desorption states were correlated with interstitial sites, lithium in solid solution, and δ′ (Al3Li) precipitates. These states have trap-binding energies ≤25.2 kJ/mol. Under the charging conditions utilized, approximately 4 pct of the total (e.g., trapped and lattice) hydrogen content was associated with interstitial sites, consistent with the view that the intrinsic lattice solubility of hydrogen in aluminum is very low. In contrast, dislocations, grain boundaries, and T1 (Al2CuLi) particles were found to be higher energy-trap states with trap-binding energies ≥31.7 kJ/mol. Approximately 78 pct of all absorbed hydrogen occupied these states. Moreover, greater than 13 pct of the available trap sites at grain boundaries were occupied. Such a high hydrogen coverage at grain-boundary sites supports the notion that hydrogen contributes to grain-boundary environmental cracking in Al-Li-Cu-Zr alloys. Also, it points out the error in assuming that hydrogen cannot play a major role in cracking of Al-based alloys due to the low lattice solubility.

A new investigation of copper's role in enhancing Al–Cu interconnect electromigration resistance from an atomistic view

An explanation of why Cu prolongs the electromigration lifetime of Al–Cu interconnects in comparison to Al is provided based on atomistic calculations. Copper preferentially segregates to the grain-boundary (GB) interstitial sites. The overall GB diffusivity is reduced with Cu segregation at GB sites. Calculation results predict that in Al(Cu) lines, Cu will diffuse first, with Al diffusion essentially suppressed because of a higher diffusion activation energy. The activation energy for Cu incubation diffusion is calculated to be 0.95 eV. The predictions are in excellent agreement with experiments.

Grain-boundary segregation in Al–10%Mg alloys at hot working temperatures

Monte-Carlo simulations are done to determine Mg enrichment at various grain-boundaries of Al–10%Mg alloys at hot working temperatures. The interatomic potentials used in the simulations are developed using the force-matching method. The Mg segregation levels at the grain-boundaries are found to vary from 20% to 40%. The segregation enrichment differences at different grain-boundary sites are explained in terms of atomic size and local hydrostatic stress. The segregation level varies strongly with [110] tilt boundaries from low to high angle while showing minimal variation with [100] twist boundaries. Segregation levels are found to have some correlation with grain-boundary energy. The effect on grain-boundary decohesion due to Mg segregation is found to be a modest (10--35%) reduction in fracture energy compared to the fracture energy in pure Al.

Nickel and selenium grain boundary solute diffusion and segregation in silver

For the first time, the grain boundary (GB) solute diffusion of Ni and Se in Ag polycrystals was investigated systematically by the radiotracer serial sectioning technique using 63Ni and 75Se isotopes. Measurements in the temperature ranges 589–989 K for Ni and 371–877 K for Se were carried out in Harrison's type B regime at high temperatures and in type C regime at low temperatures. In the B regime, the product sδD GB was determined ( s being the solute GB segregation factor, δ the GB width, D GB the GB diffusion coefficient), while in the C-regime D GB values were measured directly. The solid solubility of both solutes, Ni and Se, in Ag is very small. The equilibrium phase diagrams, however, are quite different: Se forms an intermetallic compound whereas Ni does not form any compound with Ag, which indicates dominating Se–Ag and Ni–Ni bonds, respectively. Comparing the solute D GB values with C regime measurements of GB self-diffusion in Ag, a drastic decrease of the Ni diffusivity and an increased activation enthalpy of Ni diffusion, H GB Ni, in Ag GBs is observed. This behaviour is discussed in terms of repulsive Ni-vacancy interactions and decreased jump frequencies of the Ni atoms which are mainly located at low energy positions in the GB. The measured D GB values of Se, on the other hand, are comparatively close to GB self-diffusion, whereas H GB Se is again larger than H GB Ag of GB self-diffusion. This behaviour is explained in terms of the formation of “embryos” of two-dimensional phases at high energy GB sites. Combining the obtained sδD GB and D GB values and assuming δ=0.5 nm, the GB segregation factors and segregation enthalpies of Ni ( H s Ni=−39.7 kJ/mol) and Se ( H s Se=−21.4 kJ/mol) in Ag were evaluated.

Monte Carlo Simulation of the Concentration Dependence of Segregation at Vicinal Grain Boundaries

Using the Metropolis algorithm Monte Carlo technique solute-atom segregation is studied at two vicinal grain boundaries (GBs)—the Σ = 5/(002)/θ = 36.89° symmetrical twist and the Σ = 5/(310)/θ = 53.13° symmetrical tilt—at 850 K on the Ni-rich side of the Ni-Pt phase diagram, over the concentration range 0–10 at.% Pt. Unlike the Pt-rich side of the phase diagram the structures of both GBs remain stable in this concentration range. The dilute limit behavior for most GB sites extends to at least 0.1 at. %. At higher concentrations the effective segregation energies steadily decrease with increasing solute concentrations, due to solute-solute interactions between segregated atoms, until saturation occurs. It is argued that simple statistical mechanical models, e.g., the Fowler-Guggenheim model do not work well, even in the case of simple vicinal GBs.

Solute-atom segregation to 〈110〉 symmetric tilt grain boundaries

Segregation of substitutional, oversized solute atoms to both equilibrium and metastable structures of twenty-one 〈110〉 symmetric tilt grain boundaries (GBs) in an f.c.c. binary alloy is investigated with atomistic simulations. The Monte Carlo technique is employed to determine the interfacial excess and the solute distribution in GB structures for a bulk solute concentration of 4 at.%. Results from these simulations are used to demonstrate the shortcomings of simple geometric GB parameters for predicting variations in the interfacial excess from GB to GB. The interfacial excess is also found to vary from one structure to another for the same GB. An example of a segregation-induced congruent GB phase transition is also presented. Accurate segregation free energies for individual sites in GBs are calculated with the overlapping distributions Monte Carlo technique. Segregation entropies are determined and are found to be a linear function of the segregation internal energies for the same GB sites.

The atomic structure of a ?=5[001]/(310) grain-boundary in an Al-5% Mg alloy by high-resolution electron microscopy

A symmetrical tilt Σ=5[001]/(310) grain-boundary and its surrounding matrix in an Al-5% Mg alloy, as prepared by cold rolling and annealing, have been studied by conventional transmission electron microscopy, high-resolution electron microscopy, and analytical electron microscopy. EDS measurements of the Mg concentration in the bulk and at grain boundaries indicate variations of Mg content ranging between 4 to 11 atomic percent. This variation is attributed to local ordering of Mg atoms in the alloy. HREM images show that the boundary runs parallel to the median of (310) and contains segments primarily composed of two types of structural unit. One unit contains seven atomic sites, while the other contains eight. In both types of unit, the grain-boundary coincident site lattice is continuous across the interface and exhibits periodicity in its core structure. The core structure, which is characterized by “kite-like” structural units containing seven atoms, conforms well with the structure of Σ=5 grain boundaries in pure FCC materials. The presence of atomic-scale ordering of Mg atoms along [001] of the boundary core is associated with the existence of the structural unit possessing eight atomic sites.

Grain boundary compositions in stoichiometric and off-stoichiometric Y 1Ba 2Cu 3O 7−x

The grain boundary segregation behavior of stoichiometric and off-stoichiometric YBa 2Cu 3O 7− x has been studied with analytical electron microscopy (AEM) to complement previous results obtained with Auger electron spectroscopy (AES). It was observed that the grain boundary segregation levels varied from boundary to boundary. In stoichiometry material, excess copper and deficient oxygen were observed at the grain boundaries. In materials containing excess barium, excess yttrium and deficient copper levels were observed at the grain boundaries. The grain boundary segregation levels in the materials containing excess barium can be related to the resistivity and critical current density results. Preferential segregation to specific sites in grain boundaries was observed by AEM. The effect of grain boundary segregation on the superconducting properties of these materials is discussed in terms of the weak link behavior and a possible percolative mechanism in order to maintain a continuous current path.

An auger electron spectroscopy study of low temperature segregation of silicon at aluminum surface

Abstract Low temperature surface segregation of silicon out of refined aluminum samples is studied by AES. The analysis of kinetics data gives an Arrhenius type diffusivity with an activation energy equal to 65 kJ mol−1 (0.68 eV atom−1). The pre-exponential factor is of the order of 3 × 10−6 m2 s−1. These results fit well within the limits of grain boundaries and dislocation diffusivities, as compiled from the literature by Hwang and Balluffi, and show that the segregation proceeds from distorted sites in grain boundaries and dislocations, rather than from bulk undistorted sites. The analysis of data obtained from a slow-cooling-rate experiment gives a segregation energy of −60 kJ mol−1 (−0.63 eV atom−1) and shows that the silicon surface concentration limit is not a monolayer, but rather unexpectedly about 8%. This may be related to LEED observation of silicon adsorption on various faces of aluminum by Jona and suggests that long range repulsive forces are effective to saturate silicon condensation on aluminum at a low coverage value.

An auger electron spectroscopy study of low temperature segregation of silicon at aluminum surface

Low temperature surface segregation of silicon out of refined aluminum samples is studied by AES. The analysis of kinetics data gives an Arrhenius type diffusivity with an activation energy equal to 65 kJ mol −1 (0.68 eV atom −1). The pre-exponential factor is of the order of 3 × 10 −6 m 2 s −1. These results fit well within the limits of grain boundaries and dislocation diffusivities, as compiled from the literature by Hwang and Balluffi, and show that the segregation proceeds from distorted sites in grain boundaries and dislocations, rather than from bulk undistorted sites. The analysis of data obtained from a slow-cooling-rate experiment gives a segregation energy of −60 kJ mol −1 (−0.63 eV atom −1) and shows that the silicon surface concentration limit is not a monolayer, but rather unexpectedly about 8%. This may be related to LEED observation of silicon adsorption on various faces of aluminum by Jona and suggests that long range repulsive forces are effective to saturate silicon condensation on aluminum at a low coverage value.

Recrystallization in cold-rolled Fe–V–C alloy containing fine carbides

AbstractCold rolling an Fe–1V–0·23C alloy contaInIng ∼1 vol.-% of fine interphase V4C3 particles results in the formation of shear bands at rolling reductions greater than 20%. Although in general the dislocation distribution is homogenized by the presence of the particles, the shear bands provide potent sites for nucleation of recrystallization on subsequent annealing. In 60% cold-rolled samples, annealing at 706°C resulted in the onset of recrystallization within 15 min, but the recrystallization process was still incomplete after 1000 h. This is consistent with the exhaustion of shear-band and grain-boundary sites at a relatively small volume fraction of recrystallized grains, and the severe retardation of both nucleation and growth rates by the precipitate dispersion. The low rate of recrystallization is associated with the pinning effect of the V4C3 precipitates on boundaries of both recrystallized grains and subgrains. Coarsening of the pinning particles controls the rate of migration of the recryst...

On the possible significance of the density of coincidence sites in grain boundaries

On the possible significance of the density of coincidence sites in grain boundaries

Comments on “the density of coincidence sites in grain boundaries.”

Comments on “the density of coincidence sites in grain boundaries.”