Diffusion kinetics in an ensemble of intersecting grain boundaries. The role of a size factor

The quasi-steady state Fisher model is used to analyze the efficiency of delivery of a diffusing matter to a triple junction point in an ensemble of three intersecting grain boundaries. A version of grain boundary ensemble is considered in which two grains adjacent to a surface containing a diffusion source are at a tilt angle of 30° and the third boundary is normal to the surface. This configuration of grain boundaries corresponds to a triple junction angle of 120°. It is shown that the efficiency of delivery of a matter to the triple point depends on the ratio of the diffusion length of grain boundaries adjacent to the surface containing a diffusion source to the triple junction depth and on the relation between the grain boundary diffusion coefficients of each grain boundary in the ensemble. The conditions are found under which enhanced diffusion as compared to diffusion in a single boundary takes place in an ensemble of grain boundaries.     

Penetration of liquid tin along grain boundaries and triple grain-boundary junctions of aluminum

A new procedure for investigation of liquid-metal etching grooves that form owing to wetting and penetration of the liquid phase along the triple grain-boundary junctions (triple junction) and grain boundaries in the Al-Sn system is described. The investigations were carried out by the method of layer-by-layer polishing of the end surface of the wetted sample. The obtained slices were investigated by methods of optical and electron scanning microscopy. It was shown that the groove depth is virtually invariable along a single grain boundary and increases as the groove approaches the triple junction. The penetration depth of Sn along the triple junctions is much larger than along the grain boundaries. It is shown that, owing to wetting processes in the triple junction, as in the grain boundaries, the Sn-based alloy is formed.     

Investigation of Interfaces by Atom Probe Tomography

We investigated the thermodynamic and transport properties of buried interfaces with atom probe tomography. Owing to the 3D subnanometer resolution and single atom sensitivity of the method, it is possible to obtain composition profiles with high accuracy both along or normal to the interfaces. We have shown that the width of the chemical interface between the Fe and Cr system follows the Cahn–Hilliard relation with a gradient energy coefficient of 1.86 × 10^?22 J nm². Sharpening of the Ni/Cu interface as a result of kinetic control was directly observed. We investigated the grain boundary and triple junction transport in Fe/Cr and Ni/Cu. Cr segregation enthalpy into Fe triple junctions was found to be 0.076 eV, which falls in between the surface (0.159 eV) and grain boundary (0.03 eV) segregation enthalpies. In the investigated 563 K to 643 K (290 °C to 370 °C) range, Ni transport is 200 to 300 times faster in the triple junctions of Cu than in the grain boundaries. The diffusion activation enthalpy in the triple junctions is two-thirds that of the grain boundaries (0.86 and 1.24 eV, respectively). These investigations have shown that triple junctions are defects in their own right with characteristic segregation and diffusion properties: They are preferred segregation sites and can be considered as a diffusion shortcut in the grain boundary network.     

Quasi-static intergranular brittle fracture at 0.5 tm: A non-equilibrium segregation mechanism of sulphur embrittlement in stress-relief cracking of low-alloy steels

A theory of elastic-plastic-diffusive crack growth along grain boundaries is developed and compared with experimental observations of stress-relief cracking of low-alloy steels. Intergranular decohesion advances atomistically by coupled surface and grain-boundary diffusion, while the macroscopic plain-strain crack grows quasi-statistically by maintaining a deformation field in small-scale yielding. Near an advancing crack tip, a surface diffusion distance is found within which steady-state diffusion is driven by a sharp curvature, while a corresponding boundary diffusion distance is found within which diffusion plating overtakes elastic-plastic stretching to smooth out the stress concentration. Diffusional and elastic-plastic processes at an extending crack tip are thus coupled to each other and to the loading parameter at distance. Fast diffusants are predicted to accumulate near the crack tip on both surfaces and grain boundary, confirming a recent scanning Auger observation of sulphur segregation by Hippsley et al. Considerations of non-equilibrium interfacial energies and fracture work reveal the embrittling role of sulphur, both as a fast diffusant and as a strong surface segregant. Predictions of growth rates are in excellent agreement with the data of Shin and McMahon, over the entire range of stress intensity factor and temperature studied. Metallurgical factors promoting brittle stress-relief cracking in the heat-affected zones of welding of low-alloy steels, including sulfide distribution, hot yield strength, and notch sensitivity, are explained.     

Capillary instabilities in thin films: A model of thermal pitting at grain boundary vertices

The equation describing surface topographic evolution by surface diffusion is adapted to describe the thermal pitting of a surface in the vicinity of a grain boundary vertex (triple junction of three boundaries) in order to model experimental observations of hole formation in thin films; isotropy of surface properties is assumed. An analytic solution for the evolution of an initially flat surface is obtained for a sector between two intersecting boundaries (of a triple junction) with an included angle ϕ=90°, and numerical solutions are calculated for several other values of ϕ. The results show that the surface shape is time-independent with linear dimensions that are proportional to $\text{t}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$. For a given angle at the root of the groove, the calculations show that the rate of pit deepening increases as ϕ decreases and show that, typically, pitting is appreciably faster than thermal grooving.     

The effect of triple junction type on grain-boundary sliding and accomodation in aluminium tricrystals

The topological method of analysis of grain boundary triple junctions during deformation of polycrystals is proposed in our work. The method is based on the mutual orientation of all the boundaries forming junctions and of the loading axis. Comparative investigations of grain boundary sliding and accomodation behaviour of two types of aluminium tricrystals under high temperature creep conditions have been carried out from the point of view of the proposed classification of triple junctions. It is shown that the type of junction not only affects the kinetics of sliding but also determines the variety of the primary accomodation which proves to be constant when loading and temperature change.     

Analysis of mean square penetration depth in grain boundary diffusion

Exact and approximate expressions for mean square penetration depth (MSPD) in grain boundary diffusion are derived. The MSPDs in boundary diffusion are functionally different from those in lattice diffusion. The quantitative results obtained provide more reliable estimates for the penetration depth of a diffusant in polycrystalline materials, thin films, and bicrystals.     

Grain boundary diffusion mechanisms in metals

In recent years it has become well established that fast diffusion along grain boundaries plays a key role in many important metallurgical processes including cases where net mass is transported along boundaries which act as sources and/or sinks for the fluxes of atoms. In addition, considerable advances have been made in understanding grain boundary structure, and new techniques have become available for studying kinetic phenomena in grain boundaries. This lecture will attempt to review our current knowledge of the atomistic mechanisms responsible for these grain boundary diffusion phenomena. Relevant aspects of the structure of grain boundaries and the point and line defects which may exist in grain boundaries are described first. The important experimental observations are then discussed. Diffusion models are then taken up, and it is concluded that the atomic migration occurs by a point defect exchange mechanism which, in at least the vast majority of boundaries in simple metals, most likely involves grain boundary vacancies. The grain boundary sources and/or sinks required to support divergences in the atomic (vacancy) fluxes are grain boundary dislocations. Phenomena therefore occur which resemble the Kirkendall Effect in the bulk lattice in certain respects. Additional topics are discussed which include effects of boundary structure on boundary diffusion and the question of whether or not boundary diffusion is faster along migrating than stationary boundaries.     

Measurements of the grain boundary energy and anisotropy in tin

The three-dimensional (3-D) geometry of the triple junction formed between two solid Sn-rich particles and a Pb-rich liquid matrix is used to measure the interfacial energy and its anisotropy for individual grain boundaries. The anisotropy is determined using a Cahn-Hoffman capillarity vector analysis of the energy balance at a triple junction. The absolute solid-solid grain bondary energy for each individual boundary is then determined by using the known value for the solid-liquid energy. A total of 136 boundaries are analyzed, with 46 of them forming grain boundaries. The remaining boundaries are found to be wetted boundaries with thin-liquid films formed between the two particles. A correlation between the low interfacial energy and the probability of occurrence for that disorientation is also observed. We also show that the anisotropy, as quantified by the magnitude of the torque term, is a significant portion of the total interfacial energy, especially for low energy boundaries. The degree of twist vs tilt of the boundaries is also analyzed. As expected, there are more tilt boundaries within the system than twist boundaries and most of the low energy boundaries have a mixed tilt-twist character.     

SIMS study of hydrogen at the surface and grain boundaries of nickel bicrystals

The distribution of deuterium at the surface and at grain boundaries of cathodically charged nickel bicrystals was studied using Secondary Ion Mass Spectrometry. Both high energy and low energy boundaries were studied under conditions where deuteride formation occurred during charging. The formation of the deuteride along the grain boundaries was compared to that in the adjacent grains and interpreted in terms of the deuterium diffusion in the lattice and along the grain boundaries. Decomposition of the deuteride was also studied. The results are interpreted in terms of the dependence of diffusion along grain boundaries on the structure of the boundary.     

Faceting transformation and energy of a Σ3 grain boundary in silver

Grain boundary facets forming at the intersection between a grain boundary and the free surface in diffusion bonded Σ3〈011〉Ag bicrystals during prologed annealing have been characterized crystallographically by metallographic methods. It is shown that the observed faceting has qualitatively the same character as that in Σ3〈011〉 grain boundaries in Cu. The energy of an incoherent Σ3 grain boundary in Ag (210 mJ/m²) is determined from the dihedral angle of the thermal groove and the extrapolated literature data on the surface tension of Ag. The facet geometry is discussed with respect to computer simulation data on the inclination dependence of the energy of Σ3 grain boundaries in Cu. The geometrical stability of a grain boundary near the free surface is considered.     

The effect of small plastic deformation and annealing on the properties of polycrystals: Part II. Theoretical model for the transformation of nonequilibrium grain boundaries

The nonequilibrium grain boundary state which has a high energy state is the result of absorption of a certain density of extrinsic grain boundary dislocations (EGBD’s). The equilibrium of such a boundary occurs by annealing at higher temperatures. A model has been proposed in this paper which assumes that the equilibrium of a nonequilibrium grain boundary involves the annihilation of EGBD’s by climbvia lattice diffusion of vacancies at the triple points. Due to the stress field of the EGBD’s, there is a vacancy concentration gradient around the triple points. The profile of the vacancy concentration gradient is derived by assuming a steady state flux of vacancies. Using this vacancy concentration profile, the expressions for the rate of climb of EGBD’s are derived. The proposed model predicts that the time required for the equilibration of nonequilibrium grain boundaries is dependent not only on the annealing temperature but also on the initial density of EGBD’s and the boundary length (which is related to the grain size). It has also been shown that the equilibrium behavior predicted by our model is in good agreement with the experimental results obtained for 316L stainless steel.     

Grain boundary diffusion mechanisms in metals

In recent years it has become well established that fast diffusion along grain boundaries plays a key role in many important metallurgical processes including cases where net mass is transported along boundaries which act as sources and/or sinks for the fluxes of atoms. In addition, considerable advances have been made in understanding grain boundary structure, and new techniques have become available for studying kinetic phenomena in grain boundaries. This lecture will attempt to review our current knowledge of the atomistic mechanisms responsible for these grain boundary diffusion phenomena. Relevant aspects of the structure of grain boundaries and the point and line defects which may exist in grain boundaries are described first. The important experimental observations are then discussed. Diffusion models are then taken up, and it is concluded that the atomic migration occurs by a point defect exchange mechanism which, in at least the vast majority of boundaries in simple metals, most likely involves grain boundary vacancies. The grain boundary sources and/or sinks required to support divergences in the atomic (vacancy) fluxes are grain boundary dislocations. Phenomena therefore occur which resemblethe Kirkendall Effect in the bulk lattice in certain respects. Additional topics are discussed which include effects of boundary structure on boundary diffusion and the question of whether or not boundary diffusion is faster along migrating than stationary boundaries. The Institute of Metals Lecture was established in 1921, at which time the Institute of Metals Division was the only professional Division within the American Institute of Mining and Metallurgical Engineers. It has been given annually since 1922 by distinguished men from this country and abroad. Beginning in 1973 and thereafter, the person selected to deliver the lecture will be known as the “Institute of Metals Division Lecturer and R. F. Mehl Medalist” for that year.     

Microstructural changes during wear by plastic deformation of cemented carbide and cermet cutting inserts

The microstructure of one WC-Co and two Ti(C,N)-WC-Co cutting inserts has been studied before and after plastic deformation, caused by high-speed turning. It was found that after deformation, the binder phase had infiltrated some of the grain boundaries and formed lamellae between the hard phase grains. The infiltration of grain boundaries was assumed to occur by a stress-induced dissolution along the grain boundaries of the hard phase grains as a wide front of binder phase, rather than gradually by Co grain boundary diffusion. Some localized dissolution of the hard phase could also be seen as faceting of grains in WC-Co and at triple points in cermets. It was concluded that the plastic deformation occurs by grain boundary infiltration with simultaneous grain boundary sliding. The rate of deformation is controlled by grain boundary infiltration through dissolution of the hard phase grains.     

Shrinkage and splitting of microcracks under pressure simulated by the finite-element method

The two-dimensional finite-element method is applied to analyze the shrinkage and splitting of microcracks regularly arranged on or perpendicular to a grain boundary under pressure. Grain-boundary and surface diffusions are coupled by the boundary conditions at the triple point of the microcrack surface and the grain boundary. The shrinkage and splitting processes for the two kinds of microcracks are revealed by detailed finite-element analyses. For the microcrack lying on a grain boundary, it first shrinks to a small void shape, then the void is split by the grain boundary and the two split voids assume a cylindrical shape under the capillary force of the surface. For the microcrack perpendicular to the grain boundary, it is split into two segments by the grain boundary during the early stage of shrinkage. Then, the split microcracks stop shrinking and evolve into two cylindrical channels with a circular section by the capillary force of the surface. These evolution processes are controlled by the applied pressure, microcrack spacing, ratio of grain-boundary diffusion to surface diffusion, and equilibrium dihedral angle, defined by surface and grain-boundary tensions. The influences of these controlled parameters on the evolution processes are numerically clarified based on a great number of finite-element analyses.     

Theory of coble creep for irregular grain structures

Coble creep occurs by the diffusion of matter along grain boundaries. Under the action of an externally applied stress, matter diffuses from grain boundaries in compression to those in tension. Individual grains elongate and macroscopic creep ensues. To date, Coble creep has been derived only for simple periodic grain structures. In this work we show how to solve the Coble creep problem for irregular, two-dimensional grain structures consisting of straight grain boundary segments connected by triple points. Since the normal stress distributions at the grain boundaries are represented by cubic polynomials, 4n_gb constants have to be determined for a two-dimensional grain structure consisting of n_gb grain boundary segments. We show how the corresponding system of 4n_gb equations can be set up for freely chosen boundary conditions at the grain boundary-surface intersections. Several calculated examples with clusters consisting of 25 grains illustrate the power of the technique.     

Discontinuous γ′ coarsening in a Ni-Al-Mo base superalloy

Discontinuous coarsening in a Ni-AI-Mo base superalloy was studied emphasizing the influence of grain boundary misorientation. Nucleation and growth rates were determined as a function of temperature, time, and degree of misorientation for (001) twist boundaries. Both nucleation and growth were controlled by grain boundary diffusion and increased with twist angle and temperature. Grain boundary diffusivities (calculated assuming reduced γ′ surface energy as the driving force) were more than one order of magnitude greater than those reported for static boundaries of similar misorientation. Consideration of atomic jump frequencies in static and dynamic boundaries indicated that the high diffusivities cannot be attributed to motion enhanced grain boundary diffusion. Rather, the high calculated diffusivities are interpreted to indicate the presence of additional driving forces for discontinuous coarsening in the Ni-AI-Mo base superalloys. Potential sources of additional driving force are presented.     

Measuring Grain Junction Angles in Discretized Microstructures

Grain junction angles control microstructural morphology and evolution, but because they are difficult to measure, they are reported rarely. We have developed a method, based on the optimization of the Pearson’s correlation coefficient, to measure grain junction angles in planar discretized microstructures without converting or remeshing the original data. We find that the grain junction angle distribution of equiaxed, relatively isotropic, three-dimensional (3D) microstructures is a Gaussian distribution centered about 120 deg, with a larger width than predicted primarily because of boundary energy anisotropy. Short boundary segments, which occur primarily in sections of 3D microstructures, cause anomalous peaks in the grain junction angle distribution that provide a marker for sample dimensionality. The grain junction angle distribution is a characterization metric for digitized microstructures, revealing the effects of grain boundary energy anisotropy, simulation parameters, and dimensionality.     

The Distribution of Grain Boundary Planes in Interstitial Free Steel

The grain boundary character distribution in a commercial IF steel has been measured as a function of lattice misorientation and boundary plane orientation. The grain boundary plane distribution revealed a relatively low anisotropy with a tendency for grain boundaries to terminate on low index planes having relatively low surface energy and large interplanar spacings. Although the most common grain boundary plane orientation was (111), grain boundaries terminated on higher index planes were sometimes found. For instance, at a misorientation angle of 60?deg about [111], symmetric {112} tilt boundaries were far more populous than [111] twist boundaries. The current observation revealed an inverse relationship between the measured populations and the previously reported grain boundary energies.     

The influence of grain junctions and boundaries on superplastic deformation

The crystallography of the grain boundary/grain junction network has been analysed in an aluminium—lithium alloy after 1100% superplastic deformation. The grain junctions were classified as “I-lines” or “U-lines” as defined by an extension to the O-lattice model. Overall there were 38% I-lines in the sample population which compares to a predicted 4% for random generation. It was shown that the grain orientation distribution alone was not responsible for the high proportion of I-lines. The occurrence of intergranular cavities in the microstructure was associated with high angle boundaries and U-lines. Cavities arrested at I-lines, which highlights the structural differences between the two junction types. With regard to the mechanisms of superplastic flow, it was argued that the two recognised competing mechanisms for grain accommodation, diffusion creep and dislocation creep, are associated with U- and I-lines respectively, which accounts for the observed proportions of these defects.