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.     

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.     

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.     

Grain Boundary Grooving as an Indicator of Grain Boundary Phase Transformations

The atomic force microscopy (AFM) was used to study the grain boundary (GB) groove profiles far away from the melting temperature T _m. It is shown that AFM allows one to measure the temperature dependence of the GB energy in a rather broad temperature interval (from 0.85 T _m to T _m). The GB energy and GB segregation of Bi were measured at 1123 K in the interval of the Bi bulk concentration x ^v _Bi from 5 to 140 ppm Bi. The transition from monolayer to multilayer adsorption is observed for the 19a GB at 1123 K and x ^v _Bi = 60 at. ppm Bi. At the same point (1123 K and x ^v _Bi = 60 at. ppm Bi) a discontinuity of the first derivative of the GB energy is observed. These features were explained using the model of GB prewetting phase transformation developed previously.     

Grain Boundary Channel Formation During Interdiffusion in Alloys

We present results of an experimental study of a new phenomenon accompanying grain boundary (GB) interdiffusion: the hole channel formation along GBs. The objects for study were plates of a homogeneous Cu-5 at.% Sn alloy, which were annealed at 800°C in purified hydrogen. Porous zones were found with GB hole channels perpendicular to the surface and practically equidistant from one another. The porous zone propagation and the average pore size growth at early stages of annealing obey a parabolic law. The observed processes are caused by nucleation and growth of the Cu₃Sn phase at the free surface. The new phase works as diffusion pump pumping out Sn atoms from the alloy towards the growing compound layer. The GB channel formation has been described as a relaxation process accompanying GB interdiffusion of Sn and Cu atoms with unequal partial diffusion coefficients (D _Sn>D _Cu). Excessive vacancies appearing at the GBs due to the inequality between D _Sn and D _Cu are absorbed by bulk and GB sinks, and tensile stresses appear near the GBs stimulating hole channels or groove formation.     

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.     

Grain growth in ultrafine titanium powders during sintering

Grain growth behaviour of fine (∼3 μm) and attrition milled nanocrystalline (∼32 nm) titanium powers during sintering have been studied. The activation energies of grain growth (Q _g) in fine titanium were found to be 192.9 and 142.4 kJ/mol at lower and higher temperature ranges, respectively. The nanocrystalline titanium showed very low values of Q _g (54.6 kJ/mol) at lower temperatures and it increased to 273.2 kJ/mol at higher temperatures. The constant (n) in nano Ti system was found to have unusually very high values of 6.5–8.2. The grain boundary rotation along with the diffusional processes could be the grain growth mechanism in nanocrystalline and in fine titanium powders.     

Ion mixing and thermochemical properties of markers in Cu

Markers of Nb, Ru, Ag, In, Sb, Hf, Pt, Au, and Bi in Cu were mixed by irradiation with 750 keV Kr at 77 K and analyzed in situ by backscattering of 1.9 MeV He⁺. Cu with Pt and Au markers were also irradiated and analyzed at 7 K. The results were identical to those obtained at 77 K results. The measured mixing efficienciesDt/øF _D , for the various markers correlate with their respective impurity tracer diffusivities and impurity-vacancy binding energies in Cu. The correlation suggests that diffusion by a vacancy mechanism during a thermal spike as an important process in ion mixing of marker atoms in Cu.     

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.     

Experimental determination of U diffusion in α-Ti

α-spectrometry was used in order to measure the diffusion of U in bulk α-Ti in the temperature range 863–1123?K (540–850?°C). A straight Arrhenius plot was found, giving diffusion parameters Q?=?297?kJ/mol and D ₀?=?5?×?10^?3?m²/s, which are similar to the α-Ti self-diffusion ones, when measured in Ti samples with a similar impurity content than presently. This behaviour is compatible with the hypothesis of U diffusing via a vacancy-assisted mechanism in the α-Ti lattice and contrasts with older results in which the activation energy is almost a third the self-diffusion one, even lower than the vacancy formation energy.     

Compensation Effect for Grain Boundary Diffusion in a Bicrystalline Experiment

The paper is devoted to the problem of the compensation effect for grain boundary (GB) diffusion, i.e. the linear dependence of the pre-exponential factor of the GB diffusion coefficient on the activation energy. Specific features of GB diffusion as a thermally activated process namely, the influence of segregation factor, K, and variation of the GB width, d, on the diffusion rate are discussed. A special diffusion experiment was designed to estimate the contribution of the separate component parts of the triple product, KdD_GB (D_GB is the GB diffusion coefficient). The experiment was performed with Al bicrystals. The variation of the GB width d, and a value of the segregation factor K, due to GB structure change are estimated. It is concluded that D_GB is the main GB structure-sensitive parameter in the triple product. This circumstance allows us to consider the GBs in Al bicrystals as a series of uniform objects and to describe the kinetics of GB diffusion in terms of the compensation temperature T_c and a “barrier” phase. The value of T_c for GB diffusion of Zn and Ge in Al bicrystals is practically the same and equals 709 and 706 K, respectively. The character of the “barrier” phase is discussed.     

N.M.R. study of solid perfluorocyclobutane

spin-lattice relaxation times and linewidth measurements for fluorine nuclei in solid perfluorocyclobutane are presented. The results are discussed in terms of D _2d molecular species performing fast internal motion. The relaxation measurements corroborate the existance of four solid-solid phase transitions and give some insight into their nature. The activation energies for molecular reorientation and self-diffusion processes are found to be 28·0 and 32·2 kJ mol^-1, respectively.     

Correlation of Grain Boundary Character with Wetting Behavior

Wetting of 975 grain boundaries (GB's) by liquid Cu in an iron-based alloy has been studied as a function of the five macroscopic degrees of freedom (DoF's) of grain boundary character. In addition, models of GB energy in terms of all five DoF's, and of anisotropic solid-liquid interfacial energy have been developed. The experimentally observed wetting behavior is interpreted in terms of the model, and it is shown that reasonable overall agreement is obtained between experimental results and model predictions.     

Computer simulation of symmetrical tilt grain boundaries in noble metals with MAEAM

This paper reports that an atomic scale study of [\bar {1}10] symmetrical tilt grain boundary (STGB) has been made with modified analytical embedded atom method (MAEAM) for 44 planes in three noble metals Au, Ag and Cu. For each metal, the energies of two crystals ideally joined together are unrealistically high due to very short distance between atoms near the grain boundary (GB) plane. A relative slide between grains in the GB plane results in a significant decrease in GB energy and a minimum value is obtained at specific translation distance. The minimum energy of Cu is much higher than that of Ag and Au, while the minimum energy of Ag is slightly higher than that of Au. For all the three metals, the three lowest energies correspond to identical (111), \mbox(113) and \mbox(331) boundary successively for two translations considered; from minimization of GB energy, these boundaries should be preferable in [\bar {1}10] STGB for noble metals. This is consistent with the experimental results. In addition, the minimum energy increases with increasing reciprocal planar coincidence density \Sigma, but decreases with increasing relative interplanar distance d /a.     

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.     

Self-diffusion of aluminium in the intermetallic compound Fe-48 at.% Al

The self-diffusion coefficient of Al in the B2-type intermetallic compound Fe-48 at.% Al has been determined using the intrinsic diffusion coefficients of Fe and Al and the self-diffusion coefficient of Fe with the help of the Darken-Manning relation. The self-diffusion coefficient of Al in Fe-48 at.% Al is estimated to be a factor of about 0.6 smaller than that of Fe, and the activation energy for the self-diffusion of Al is obtained to be 280 kJ mol^?1 which is a little larger than the value of 262 kJ mol^?1 for the self-diffusion of Fe, indicating that the diffusion mechanisms for both components are nearly equal.     

Diffusion of gold in silicon studied by means of neutron-activation analysis and spreading-resistance measurements

In- and out-diffusion of gold in silicon were investigated with the aid of a neutronactivation analysis in combination with mechanical sectioning or by the spreadingresistance technique. In-diffusion profiles in the range 1371–1073 K show that Au diffuses in Si mainly via the so-called kick-out mechanism. From the Au diffusion and solubility measurements the interstitialcy contributionD _I ^SD to the Si self-diffusion coefficient was determined, which shows that the self-diffusion occurs to a considerable extent via selfinterstitials. Out-diffusion profiles at 1173 K were measured on wafers homogeneously supersaturated with Au. The observed decrease of the electrical activity of Au in the bulk indicates that during the out-diffusion anneal the majority of Au atoms originally dissolved substitutionally changes its configuration.     

Correlation of Grain Boundary Character with Wetting Behavior

Wetting of grain boundaries (GB's) by liquid Cu in an Fe-30wt%Mn-10wt%Cu alloy has been studied as a function of the five macroscopic degrees of freedom (DoF's) of grain boundary character. These were chosen to consist of two grain boundary normals (or bounding planes) and a twist angle. The five DoF's of 975 GB's were determined by electron backscattering patterns and serial sectioning, after annealing at 1120°C, and each GB was categorized as being either wet, dry, or mixed (i.e. partly wet and partly dry). Interpretation of the wetting behavior by means of a model of GB energy, which includes consideration of the five macroscopic DoF's, led to correct predictions of wet and dry behavior in 80% of the GB's studied.     

High Ni2+-mobility in the Chevrel phase Ni2Mo6S8: a quasielastic neutron scattering study

A quasielastic neutron scattering study of Ni₂Mo₆S₈ has established relatively fast long-range motion of the intercalated Ni²⁺ ions, with a diffusion constantD=3×10^–9 cm² s^–1. A model with a jump distance of about 2.1 Å and an activation energy of 24 kJ/mol is favoured. A critical consideration of the information contained in fixed window measurements is given.