Triple Junction Mobility: A Molecular Dynamics Study

We present a molecular dynamics simulation study of the migration of individual grain boundary triple junctions. The simulation cell was designed to achieve steady state migration. Observations of the triple junction angle and grain boundary profiles confirm that steady state was achieved. The static, equilibrium grain boundary triple junction angles and the dynamic triple junction angles were measured as a function of grain size and grain boundary misorientation. In most cases, the static and dynamic triple junction angles are nearly identical, while substantial deviations were observed for low boundary misorientations. The intrinsic, steady-state triple junction mobilities were extracted from measurements of the rate of change of grain boundary area in simulations with and without triple junctions. The triple junction velocity is found to be inversely proportional to the grain size width. The normalized triple junction mobility exhibits strong variations with boundary misorientation, with strong minima at misorientations corresponding to orientations corresponding to low values of . The triple junctions create substantial drag on grain boundary migration at these low mobility misorientations.     

Grain Boundary Migration in Metals: Recent Developments

Current research on grain boundary migration in metals is reviewed. For individual grain boundaries the dependence of grain boundary migration on misorientation and impurity content are addressed. Impurity drag theory, extended to include the interaction of adsorbed impurities in the boundary, reasonably accounts quantitatively for the observed concentration dependence of grain boundary mobility. For the first time an experimental study of triple junction motion is presented. The kinetics are quantitatively discussed in terms of a triple junction mobility. Their impact on the kinetics of microstructure evolution during grain growth is outlined.     

Grain Boundary Junctions in Microstructure Generated by Multiple Twinning

The microstructure of a Cu-Ni alloy after static recrystallization was investigated using electron backscatter diffraction in a scanning electron microscope and the existence of orientationally related clusters of crystallites formed by multiple twinning has been established. Grain boundary and triple junction character within the clusters are analyzed. While the outer boundaries of the cluster are crystallographically random, all the inner boundaries have 3 ⁿ misorientations. A newly developed crystallographic theory of triple junctions and multicrystallite ensembles consisting of CSL boundaries is used to describe the structure of the cluster. The presence of an 1 triple junction is confirmed. Apparently, the microstructure of recrystallized materials susceptible to annealing twinning consists of multiple-twinned clusters. The cluster size cannot be reduced to the grain size excluding twins.     

Wetting transition on grain boundaries in Al contacting with a Sn-rich melt

The contact angle at the intersection of a grain boundary in Al bicrystals with the solid Al/liquid Al–Sn interphase boundary has been measured for two symmetric tilt <011> {001} grain boundaries with tilt angles of 32° and 38.5°. The temperature dependencies (T) present the evidence of the grain boundary wetting phase transition at T_w. The observed hysteresis is consistent with the assumption that the wetting transition is of first order. The determined discontinuity in the temperature derivative of the grain boundary energy is–5.6 J/m²K (T w1=617°C) for the boundary with a low energy (=38.5°) and –17 J/m²K (T w2=604°C) for the grain boundary with a high energy (=32°).     

Twin boundaries with 9R zone in Cu and Ag studied by quantitative HRTEM

When highly inclined against the {111} plane of the coherent twin boundary, 3 110 tilt boundaries in Cu or Ag have a complex structure. As the boundary plane approaches the symmetrical {211} orientation, the grain boundaries decompose into two phase boundaries. Between these phase boundaries the metal adopts a rhombohedral crystal structure, denoted as 9R. Not the {211}-oriented boundary, but a boundary inclined by 8° against {211} has the minimum energy in this family of grain boundaries with 9R zone. Using high resolution transmission electron microscopy, we have studied the atomistic structure of this special boundary. An iterative structure refinement based on quantitative image analysis reveals the atomistic structure of the grain boundary at a well-defined level of confidence. Comparing the refined grain boundary structure with a model obtained by molecular statics calculations exposes small, but significant discrepancies. These probably arise because in the model the stacking fault energy is too small and the short distance repulsion is too weak. Grain boundaries of equivalent geometry in Ag and Al exhibit different widths of the 9R zone. Experimental observations support a theory relating the equilibrium width of the 9R slab to the stacking fault energy and the elastic properties of the material.Presented at the Workshop on High-Voltage and High Resolution Electron Microscopy, February 21–24, 1994, Stuttgart, Germany.     

A two-channel model for transport across high T c bicrystal grain boundary junctions

This paper describes an investigation of the microscopic configuration of the barrier which exists at the boundary in high T _c grain boundary junctions. A model for describing the properties of bicrystal and biepitaxial grain boundary junctions is proposed. Two channels for transport currents are assumed, the supercurrent being carrier by one channel only. The measurable macroscopic parameters of a junction, (critical current density and normal state resistance) are computed in terms of the microscopic parameters that appear in this model. The model well describes major features of the characteristics observed for high T _c bicrystal junctions.     

On the Relationship Between Entropy and Enthalpy of Grain Boundary Segregation

An extensive study of anisotropy of grain boundary segregation in -iron, performed in the last decade, confirmed the existence of a linear relationship between entropy and enthalpy of solute segregation at individual grain boundaries. A thermodynamic analysis of this relationship is performed in the present work. It is shown that this dependence defines a compensation temperature and an entropy-like parameter. The compensation temperature is not necessarily connected with a phase transformation, but it represents exclusively a mean temperature at which all boundaries approach to a mean value of the Gibbs free energy of segregation. The most important consequences of this dependence are outlined: a reversed anisotropy of grain boundary segregation at temperatures above the compensation temperature, and a new method for the prediction of the enthalpy and entropy of solute segregation at individual grain boundaries.     

Atomic structure and electronic properties of the ∑37(610) and ∑29(520) [001] tilt grain boundaries in Ge

400 kV high resolution electron microscopy (HREM), deep level transient spectroscopy (DLTS) and steady state electrical measurements have been applied to 37(610) and 29(520) [001] tilt grain boundaries (GBs) in germanium bicrystals. The atomic boundary structures were revealed by experimental HREM images taken under different defocus conditions. Later, structure models were refined by means of a trial-and-error method applying alternatively the image simulation and the molecular static calculation of relaxed structures. The structures were shown to be consistent with the modified structural unit model. Although the structures are different for the two GBs studied, DLTS data and steady state measurements were found to be quite similar for both GBs. Thus, the results point to the extrinsic origin of localized deep states at the GBs. The analysis of DLTS spectra indicates the impurity segregation at the boundary, e.g., the formation of vacancy-type oxygen complexes of a donor-like state at E _c-0.21 eV, which results in the fluctuation of the potential barrier. Defects in the GBs—like facets, atomic steps and secondary grain boundary dislocations—which are characteristic of both boundaries can act as nuclei to the impurity segregation.Presented at the Workshop on High-Voltage and High-Resolution Electron Microscopy, February 21–24, 1994, Stuttgart, Germany.     

Single grain boundary migration

Various driving forces which cause migration of grain boundaries in bicrystals are discussed. The analysis of experimental data for migration of symmetrical tilt grain boundaries 37° <001> 5 in Fe-3 wt. % Si bicrystals indicates that the migration velocity is proportional to the driving force only for relatively fast boundary movement. The observed deviation from linearity might be related to segregation of impurities at the grain boundary.     

Intergranular Stress Corrosion Cracking of Pure Copper 〈111〉 Tilt Bicrystals

Behaviour of stress corrosion cracking (SCC) in a series of pure copper bicrystals with a symmetrical 111-tilt boundary has been investigated. Tests were performed by the slow strain rate technique (SSRT) in 1M NaNO₂ solutions. The small-angle tilt bicrystals fractured in both intergranular and transgranular manners accompanied by a large amount of plastic strain to fracture while the large-angle bicrystals fractured in almost intergranular manner with a smaller plastic strain. Susceptibility of SCC increases with increasing misorientation and becomes relatively constant in large-angle grain boundaries. The local minima appeared at the 7(321) and 3(211) boundaries, suggesting that the susceptibility was partially affected by grain boundary energy. Stress concentration generated by the pile-up of trapped dislocations at the grain boundary could account for the high susceptibility of the intergranular SCC in large-angle grain boundaries.     

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.     

Molecular-Dynamics Method for the Simulation of Grain-Boundary Migration

A molecular-dynamics method for the simulation of the intrinsicmigration behavior of individual, flat grain boundaries is introducedand validated. A constant driving force for grain-boundary migrationis generated by imposing an anisotropic elastic strain on a bicrystalsuch that the elastic-energy densities in its two halves aredifferent. For the model case of a large-planar-unit-cell, high-angle(001) twist boundary in Cu we show that an elastic strain of1%–4% is sufficient to drive thecontinuous, viscous movement of the boundary at temperatures wellbelow the melting point. The driving forces thus generated (at thehigh end of the experimentally accessible range) enable aquantitative evaluation of the migration process during the timeframe of 10^-9 s typically accessible bymolecular-dynamics simulation. For this model high-angle grainboundary we demonstrate that (a) the drift velocity is, indeed,proportional to the applied driving force thus enabling us todetermine the boundary mobility, (b) the activation energy forgrain-boundary migration is distinctly lower than that forgrain-boundary self-diffusion or even self-diffusion in the melt and(c) in agreement with earlier simulations the migration mechanisminvolves the collective reshuffling during local disordering(melting) of small groups of atoms and subsequentresolidification onto the other crystal.     

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.     

Misorientation Dependence of the Grain Boundary Energy in Magnesia

Geometric and crystallographic data obtained from a well annealed magnesia polycrystal have been used to specify the five macroscopic degrees of freedom for 4665 grain boundaries. The results indicate, that for this sample, the five parameter grain boundary character space is fully occupied. A finite series of symmetrized spherical harmonics has been used to approximate the misorientation dependence of the relative grain boundary energy. Best fit coefficients for this series were determined by assuming that the interfacial tensions at each triple junction are balanced. The grain boundary energy function shows Read-Shockley behavior at small misorientations and a broad minimum near the 3 misorientation. Furthermore, misorientations about the ‹100› axis create boundaries with relative energies that are less than those created by misorientations about the ‹110› or ‹111› axes.     

Grain Boundary Wetting Statistic in Zn/Ga System and its Application to Grain Boundary Energy Spectrum Estimation

The grain boundary statistic in zinc polycrystals in contact with saturated Ga(Zn) melt has been studied. The misorientation angle distributions for zinc thin foil and zinc plates were obtained. The influence of the misorientation angle value on the wetting probability p of grain boundaries was observed. The grain boundary energy distribution parameters were obtained by using the p() relationship. The dihedral angles in triple lines of non-wetted zinc samples were also measured and their distribution was used to obtain the grain boundary energy distribution function. The parameters obtained by two different methods correspond to one other.     

Classification of impurities according to their effect on intergranular cohesion of titanium,nickel, and aluminum

Impurities are classified in regard to their effect on the intergranular cohesion of titanium, nickel, and aluminum on the basis of a comparative analysis of the bond energies between the impurity and the grain boundary. Microadditions which bond dangerous impurities into a compound are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, No. 7, pp. 12–15, July, 1987.     

The study of grain orientation distributions and grain boundary misorientation distributions in 304 and 316L stainless steels

Orientation distribution functions in two recrystallized austenitic stainless steels (AISI types 304 and 316L) with known grain boundary misorientation distributions have been studied. Previously obtained data on grain boundary spectra in these steels have been re-examined and analyzed from the point of view of texture analysis.The results obtained have shown that there is no unambiguous relatonship between grain boundary misorientation distribution and grain orientation distribution (ODF) determined by the X-ray analysis in the materials under study. This ambiguity is due to the following reason. In the grain boundary misorientation statistics only nearest-neighbor grains are taken into account, but in the orientation distribution function orientations are averaged over the entire volume of the specimen independent as to whether the grains are adjacent or not. Two main results were established for the steels under study: (i) Textures of the two steels differ, though their grain boundary misorientation distributions are similar; and (ii) misorientations of the majority of grain boundaries can be described as rotations about the axes close to 110.     

Observation of structural units at symmetric [001] tilt boundaries in SrTiO3

Incoherent Z-contrast imaging in the scanning transmission electron microscope allows atom column positions to be deduced directly from the experimental image, including locations where the column separation is less than the resolution limit. Maximum entropy analysis applied to the incoherent image locates the high-Z columns to an accuracy of ±0.2 Å. Oxygen coordination at the boundary plane can be deduced by high spatial resolution electron energy loss spectroscopy, and approximate column positions determined by simple bond-valence sum calculations. Observations of 25° (=85), 36° (=5) and 67° (=13) [001] symmetric tilt grain boundaries in SrTiO₃ bicrystals show that half columns are a ubiquitous feature of grain boundary structural units. The observed structural units can be combined to produce structural models for symmetric tilt boundaries over a 0–90° range. The =17 (410), =5 (310), and =5 (210) are found to be favored boundaries and the structures of all the other tilt boundaries are comprised of these units combined with =1 (100) and =1 (110) structural units. All the proposed boundary models show continuity of grain boundary structure over the entire misorientation range. The =17 (410) structural unit is asymmetric which induces microfacetting on all boundaries less than the =5, 36.87° misorientation.Work Supported by the U.S. Department of Energy under contract DE-Ac05-84OR21400.     

Grain boundary migration in Σ=5 bicrystals of an Fe-3%Si alloy

Migration of differently oriented grain boundaries was studied in the =5, 36.9°[100] tilt bicrystals of an Fe-3mass%Si alloy by the modified reversed-capillary technique. The principles of this method are outlined and discussed in connection with the application of multiple annealing of a single sample. It is shown that the errors introduced by both heating and cooling periods and by possible existence of an incubation period do not exceed the scatter of experimental data. A linear dependence between grain boundary migration velocity and driving force was found in most cases. The measured values of the product of grain boundary mobility and energy for individual grain boundaries differ substantially. The values of activation energy of migration of 332 kJ/mol, 392 kJ/mol, and 97 kJ/mol were found for the, {01}, {02} and (001)/(0 4) grain boundaries, respectively.     

Integration of impurities with large-angle grain boundaries in d-transition metals

The approximation of the liquid model of grain boundaries is used to calculate the bonding energy F of carbon and oxygen interstitial impurities with largeangle grain boundaries in d-transition metals and impurities of d-transition metals in group VIA elements: chromium, molybdenum, and tungsten. It is shown that in the case of interstitial impurities as well as substitutional impurities in d-transition metals the bonding energy is determined by the characteristics of the d-band occupation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 70–75, April, 1979.