Grain Boundary Diffusion and Segregation in Interstitial Solid Solutions Based on BCC Transition Metals: Carbon in Niobium

Bulk and grain boundary (GB) diffusion of ¹⁴C in Nb has been studied by the radiotracer serial sectioning technique. B and C kinetic regimes were realized for GB diffusion in the temperature range from 800 to 1173 K. The values of P = sD _gb, D _gb and s follow the Arrhenius dependencies: P = 5.15 × 10^–15 exp[–(83.1 kJ/mol)/RT] m³/s (973–1173 K), D _gb = 2.3 × 10^–6 exp[–(133.0 kJ/mol)/RT] m²/s (800–950 K), and s = 4.7 exp[(49.9 kJ/mol)/RT].The increase in the GB diffusion compared with self-diffusion is very large despite the probable retardation effect due to the strong segregation.The results for GB diffusion of C in Nb as well as for other interstitial solutes (P, S) in bcc transition metals (- Fe, Mo) are discussed in the framework of the transition state theory. It is assumed that GB segregation decreases the energy of the ground state whereas the change in the diffusion mechanism (e.g. from vacancy to interstitial) leads to a strong decrease of the transition state energy. This change in the diffusion mechanism results in a fast GB diffusion of interstitial solutes in spite of their large tendency to segregate to GBs.     

Grain Boundary Migration in Solid State Discontinuous Reactions

Discontinuous reactions are a special class of solid state moving boundary reactions characterized by a discontinuous change in orientation and composition across the migrating reaction front that provides a short circuit path of solute transport. Grain boundary migration in discontinuous reactions is both of technological as well as fundamental interest. In this paper, the initiation/growth mechanism, product morphology, driving force, reaction kinetics, and effect of external parameters on the major discontinuous reactions, namely, discontinuous precipitation, coarsening, dissolution, and diffusion induced grain boundary migration have been discussed. In addition, a number of interesting features about boundary migration in discontinuous reactions has been analyzed. Finally, the scope and necessity of continued research attention in this area have been highlighted.     

On the accommodation of extrinsic dislocations in grain boundaries

The relaxation of the extrinsic grain boundary dislocation (EGBD) stresses, created by interaction of lattice dislocations with grain boundaries (GBs), is a phenomenon which plays an important role in recrystallization and high temperature deformation of materials. The kinetics of this phenomenon, controlled by GB diffusion, are relatively well established. On the contrary, the processes which operate in order the GBs return to equilibrium are still controversed in vicinal and general GBs.The decomposition in discrete products and the rapid motion of the glissile components observed by High Resolution Electron Microscopy (HREM) in symmetrical tilt GBs support the recent incorporation model of EGBD accommodation. But, until now, these observations and this model are restricted to GBs described by the Structural Unit/Grain Boundary Dislocation (SU/GBD) model. Otherwise, the Spreading phenomenon generally observed by Transmission Electron Microscopy (TEM) in vicinal and general GBs is not clearly understood.This paper is an attempt to review the different EGBD accommodation models and to raise up the question of their relevance to account for the stress relaxation in any grain boundary.     

Grain Boundary Diffusion and Linear and Non-Linear Segregation of Ag in Cu

Ag grain boundary (GB) diffusion was measured in the Cu-0.2at%Ag alloy in a wide temperature range from 473 to 970 K. The direct measurements of Ag GB diffusivity D ^alloy _gb under conditions of the Harrison C regime revealed that D ^alloy _gb is almost identical to D ^pure _gb determined earlier for Ag diffusion in high-purity Cu (Divinski, Lohmann, and Herzig, 2001). The penetration profiles determined in the Harrison B regime showed a complex, multi-stage shape. This diffusion behavior can be rationalized assuming that besides GBs significantly covered by segregated Ag atoms, some fraction of GBs remains almost free from Ag atoms in the studied temperature interval. The total amount of pure GBs drastically decreases with decreasing temperature. This hypothesis was proven by measurements of Ag GB diffusion in Cu near 5 bicrystals, which allowed us to analyze in detail the non-linear segregation of Ag in Cu GBs.     

The Effect of Pressure on Indium Diffusion along 〈001〉 Tilt Grain Boundaries in Copper Bicrystals

The effect of pressure on the diffusion of indium along two grain boundaries (GBs) in copper bicrystals has been investigated. The GBs studied were of symmetrical tilt type with a 001 misorientation axis. The tilt angle of one GB was 36.5°, which corresponds to the near 5 coincidence orientation, where is the inverse density of the coincidence sites in the two misoriented crystal lattices. The other GB was a general boundary with a tilt angle of 45°. The diffusion along the 001 tilt axis has taken place at the temperature of 923 K and under argon gas pressures up to 1 GPa. The following activation volumes have been found: 0.94±0.11 _Cu for bulk diffusion,–0.5 ±0.7 _Cu for the diffusivity of the near 5 GB and –0.6±0.3 _Cu for the diffusivity of the 45° 100 GB, where _Cu is the atomic volume of copper. Two interpretations of this result seem plausible. The first interpretation is that the In atoms diffuse along the 001 tilt axis by an instertitialcy mechanism. It is known that for such a diffusion mechanism the activation volume is close to zero. The alternative explanation bases on the observation that the parameter measured is the GB diffusivity, which depends on the product of the GB diffusion coefficient and the segregation factor. An enhancement of the In segregation under pressure would lead to an increase of the GB diffusivity. It seems plausible that both interpretations are true and the fact that the atomic volume of In is a factor of 2.2 larger than that of Cu plays an important role both for the increased segregation of In under pressure and the diffusion mechanism.     

The Impact of Grain Boundary Diffusion on the Low Temperature Reoxidation Mechanism in Nanocrystalline TiO2−δ Films

The redox reaction TiO₂ TiO_2- + /2O_2(gas) can modify the oxygen deficiency and electrical conductivity of TiO_2– upon changing the ambient oxygen pressure. It is found that in nanocrystalline films this leads to significant changes in even at relatively low temperatures (200–325°C) that were previously considered too low to modify TiO₂ defect chemistry. This unusual phenomenon is attributed to the fine-grained structure and the important role of grain boundary (GB) diffusion in these films. A phenomenological model of the low temperature redox mechanism in nanocrystalline TiO_2– films is elaborated. Taking into account the impact of GB diffusion and considering time-dependent decay of the volume fraction of GB diffusion sites, we derive a modified parabolic law for the redox reaction kinetics. It is demonstrated that this law describes very well the electrical response kinetics of nanocrystalline TiO_2– thin films during exposure to oxygen between 200 and 325°C. From the fitting between the experimental results and this formula the activation energy of chemical diffusion in TiO_2– bulk and GBs is evaluated, obtaining 0.69 and 0.52 eV, respectively.     

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.     

Effect of Grain Boundary Segregation and Migration on Diffusion Profiles: Analysis and Experiments

In many experimental studies, curved penetration profiles are observed for grain boundary diffusion performed in the B kinetics regime in contrast to the shape expected from the solutions of the second Fick's equation. To explain these curvatures the effects of grain boundary structure, grain boundary migration, and grain boundary segregation have been successively proposed in the literature. Using previous data for Cu–Ag and Cu–Ni and new ones on Cu–Fe and Cu–Zn systems we will show how it is possible to separate all these possible contributions and how, knowing the true origin of the curvature, one can deduce much quantitative information impossible (or very difficult) to obtain by other techniques.     

Thermodynamics of Vacancies and Impurities at Grain Boundaries

The thermodynamics of vacancy and impurity adsorption at interfaces and grain boundaries (GBs) in solids is considered. Theoretical expressions are derived for the GB/interface free energy change caused by various levels of vacancy or impurity adsorption. This information is used to predict the behavior of vacancies at interfaces and GBs in a stress gradient and to forecast the effect of impurities on GB fracture strength. The latter predictions provide an interpretation of intergranular fracture behavior in terms of impurity adsorption and GB structural parameters such as GB width and value.     

Interdiffusion in two-layer Pd/Ag films II. “Cold” homogenization mechanisms

Interdiffusion processes in thin epitaxial polycrystalline Pd/Ag films in the temperature range 20–500°C are studied by transmission electron microscopy, electron diffraction and electrical resistance methods. Homogenization is investigated both during condensation and under conditions of postcondensation annealing.The basic processes of homogenization associated with GB diffusion along migrating boundaries. It is found that in real polycrystal films with wide spectrum of grain sizes few mechanisms can occur simultaneously or subsequently: recrystallization induced diffusion, diffusion induced grain boundary migration, activation of bulk diffusion in fine grain clusters, bulk diffusion through interphase boundary. The conditions for prevailing one of them can be provided by changing condensation and postcondensation annealing temperatures or by choosing certain grain size.     

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.     

On grain boundary character distribution in materials with cubic structure

From analysis of numerous experimental data on grain boundary (GB) statistics in polycrystals it has been established that certain groups of materials with cubic structure reveal similar GB character distributions (GBCD) (distribution of GBs by reciprocal density of coincidence sites ). It has been shown that GBCD can be described with an empirical low with different parameters for various groups. Several criteria for classification of materials by these groups (the stacking fault energy value, hierarchy of GB energies and mechanism of replacement of high-energy GBs with low-energy ones) have been considered. It has been found that peculiarities of electronic structure of materials are correlated with the classification proposed.     

Progress in the Investigations of Grain Boundary Relaxation

Internal friction (or damping) is a measure of energy dissipation during mechanical vibration. The internal friction peak induced by grain boundary (GB) relaxation was discovered by Kê in polycrystals in 1947. The GB internal friction and related anelastic effects have been successfully interpreted by Zener's anelastic theory and viscous sliding model. Since then, the GB internal friction peak has been widely used to study the dynamic process of GBs, impurity segregation at GBs and relevant processes in materials science.

Previously, the GB internal friction was mostly studied with polycrystalline materials, in which mixed contributions of different types of GBs are involved. Since the microstructures and behaviors for different types of GBs are different, the detailed mechanism of the GB peak in polycryatals has not been clearly clarified.

From the beginning of the 21th century, the internal friction in bicrystals (each has a single boundary) with different misorientations and rotation axes has been systematically investigated. The results indicate that the internal friction can be used to distinguish the individual behavior of different types of GBs and applied to the practice of “GB engineering.”

Moreover, the coupling effect and compensation effect involved in GB relaxation has been recently observed and explained. The coupling effect means a correlated atomic motion occurred in GB relaxation. The compensation effect indicates that the apparent activation enthalpy is linearly related to the activation entropy in GB relaxation. These findings improve the understanding of the mechanism of GB internal friction.

This article attempts to give a comprehensive review to the investigations of GB internal friction in polycrystals, bamboo-crystals, and bicrystals. The microscopic mechanisms and the further applications of GB internal friction are discussed and prospected.     

Tracer Diffusion of 63Ni in Nano-γ-FeNi Produced by Powder Metallurgical Method: Systematic Investigations in the C, B, and A Diffusion Regimes

⁶³Ni radiotracer diffusion in a well-compacted nanocrystalline (grain size d 80 to 100 nm) -Fe–40wt%Ni alloy was measured by the serial sectioning technique in an extended temperature range from about 610 to 1010 K. Since the material microstructure reveals two different length scales with nano-size grains forming micrometer-size clusters (or agglomerates), three main diffusion paths determine the diffusion behavior: the nanocrystalline grain interior, the nanocrystalline grain boundaries (GB), and the inter-agglomerate interfaces. The systematics of diffusion in a compacted nanostructured material with such a bimodal distribution of interface characteristics was elaborated and the experimental data were analyzed in dependence on the diffusion regime. The absolute values and the Arrhenius parameters of Ni GB diffusion in the nano--Fe–40wt%Ni alloy (D ₀ = 9.3 × 10^–4 m² s^–1 and Q = 177 kJ/mol) are similar to the Ni GB diffusivity in coarse-grained poly-crystalline -Fe. Accordingly, the nanocrystalline GBs are concluded to have quasi-equilibrium structures, particularly because of a pronounced grain growth (from about 30 to about 100 nm) during the production stage of the nanomaterial. In contrast, the inter-agglomerate interfaces, which present the fastest diffusion path in the present investigation (D ₀ = 1.9 × 10^–3 m² s^–1 and Q = 134 kJ/mol), are likely to be in a non-equilibrium state due to specific features of the applied powder metallurgical process.     

Relationship between Electrical Activity and Grain Boundary Structural Configuration in Polycrystalline Silicon

Temperature dependent electron beam induced current (EBIC) technique has been applied to investigate the electrical activities of grain boundaries (GBs) in polycrystalline silicon. The GB character, misorientation and orientation of GB plane, were analyzed using a FE-SEM/EBSP/OIM system prior to the EBIC measurements. The EBIC contrasts were found to depend on GB character; low GBs showed weak contrasts compared with general GBs at any temperatures, and also demonstrated to vary at GB irregularities such as boundary steps. These results indicate that electrical properties depend on the orientation of the GB plane as well as the misorientation. On the other hand, there existed less differences in temperature dependence of EBIC contrast irrespective of GB characters. The EBIC contrast decreased with increasing temperature, showed a minimum around 250 K, then increased again with further increasing temperature. The resulting temperature dependence of EBIC contrast probably comes from the combination of two types of recombination processes of carriers. One is related to a shallow level associated with an inherent GB structure, though the exact energy levels also would probably depend on GB structures, and the other to a deep level associated with impurities segregated at GBs, which acts as recombination center.     

Kinetic pathways of diffusion and solid-state reactions in nanostructured thin films

Mass transport and solid-state reactions in nanocrystalline thin films are reviewed. It is illustrated that diffusion along different grain boundaries (GBs) can have important effects on the overall intermixing process between two pure films. These processes can be well characterized by a bimodal GB network, with different (fast and slow) diffusivities. First the atoms migrate along fast GBs and accumulate at the film surface. These accumulated atoms form a secondary diffusion source for back diffusion along slow boundaries. Thus the different GBs of the thin films can be gradually filled up with the diffusing atoms and composition depth profiles reflect the result of these processes. Similar processes can be observed in binary systems with intermetallic layers: instead of nucleation and growth of the reaction layer at the initial interface, the reaction takes place in the GBs and the amount of the product phase grows by the motion of its interfaces perpendicular to the GBs. Thus, the entire layer of the pure parent films can be consumed by this GB diffusion-induced solid-state reaction (GBDIREAC), and a fully homogeneous product layer can be obtained.     

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 = 5/(002)/ = 36.89° symmetrical twist and the = 5/(310)/ = 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.     

Evolution of Pore Ensembles Located at the Grain Boundaries in Cu and Cu-5 at.% Sn

The kinetics of pore coalescence in ensembles located at the grain boundaries in Cu and Cu-5 at. % Sn has been studied by optical and scanning electron microscopy at 500 and 800°C. In the case of pure Cu the evolution of the pore ensemble followed the kinetical law ¯4 t, where ¯ is the average pore radius and t is the ageing time. This law is typical for a grain boundary diffusion controlled process. However, in the case of the Cu-5 at. % Sn alloy the kinetical law obeyed the ¯3 t relationship, which is characteristic for a reaction controlled process. The reaction in question is the generation of vacancies on the surfaces of the pores. The importance of the surface reaction controlled mass transfer process in alloys is discussed. The grain boundary self-diffusivity and the kinetical coefficients of the reaction are determined and analyzed.     

Microstructure Observations for Diffusion Induced Recrystallization and Diffusion Induced Grain Boundary Migration on Surfaces of Zincified Cu Bicrystals With [1 1 0] Twist Boundaries

The formation behavior of the fine-grain region alloyed with Zn due to diffusion induced recrystallization (DIR) in the Cu(Zn) system was experimentally examined for the surfaces polished in different manners using a Cu bicrystal containing a [1 1 0] twist boundary with a misorientation angle of = 46° zincified at 673 K for 2.88 × 10⁴ s with Cu-15 wt% Zn and Cu-30 wt% Zn alloys by a capsule zincification technique. The extent and morphology of the fine-grain DIR region vary depending on the surface conditions and the composition of the Zn-source Cu-Zn alloy. For the specimen with the surface electrolytically polished in an etchant consisting of 20 vol% of nitric acid and 80 vol% of methanol, no DIR region was formed on the whole surface when the Cu-15 wt% Zn alloy was used as a Zn source.In order to observe the morphology of the moving grain boundary owing to diffusion induced grain boundary migration (DIGM) without influences of DIR, Cu bicrystals with [1 1 0] twist boundaries of = 32 ( 27), 39 ( 9), 46, 51 ( 11) and 55° were electrolytically polished in the etchant mentioned above. The polished Cu bicrystals were zincified at 673 K for 2.88 × 10⁴ s using the Cu-15 wt% Zn alloy as a Zn source. Remarkable surface relief and clear slip bands were recognized on the surfaces due to DIGM for the specimens with the 32 ( 27) and 46° boundaries. The moving boundary became zigzag owing to the slip bands parallel to the moving direction. On the other hand, such surface relief and slip bands were not observed for the specimens with the 39 ( 9), 51 ( 11) and 55° boundaries. The moving boundary was considerably irregular for = 39° whereas rather smooth for = 51 ( 11) and 55°. The migration behavior of the grain boundary was not affected by the interruption of the zincification.