The Nature and Behavior of Grain Boundaries

In order to determine the structure and the energy of grain bounderies in pure metals a relaxation method based upon a minimum free energy criterion has been devised. The principle of the method is very simple; however, its correct application requires various precautions.

This method has been employed to determine the structure and the energy of a number of grain boundaries in aluminium where the boundary planes are either symmetrical or non-symmetrical with respect to the two lattices.

“Special” boundaries having been defined, an investigation has been conducted on boundaries having orientations close to those of the “Special boundaries”. The presence of discontinuity lines in these boundaries, which are sometimes visible in the electron microscope, has been discussed.

The concept of grain boundary dislocations has been refined. In particular, a distinction has been made between “intersection dislocations” and “structural dislocations”. An extension of the Burgers vector and Burgers circuit concepts has been proposed.

Grain boundary dislocations (GBD’s) may be studied conveniently in the electron microscope using specimens which are prepared by welding together two single crystal films having predetermined orientations to produce a thin-film bicrystal slab containing any type of grain boundary. The boundary is then examined at normal incidence. Problems associated with the imaging of GBD’s in both low and high angle boundaries of this type are considered. The following main topics are discussed from both the theoretical and experimental standpoints: (1) the strain field diffraction contrast produced by isolated screw and edge GBD’s under relatively simple conditions where no more than two strong beams exist in the upper crystal, and no more than four strong beams exist in the lower crystal; (2) the effects of superimposed Moiré patterns which are formed when more than one beam enters the objective aperture; (3) the diffraction contrast produced by regular arrays of closely spaced GBD’s and the problem of resolving individual GBD’s in such arrays; and (4) evidence that regular arrays of GBD’s act as twodimensional diffraction gratings which produce extra diffraction spots which may be of use in the direct imaging of finely spaced arrays.

The interaction between a simple tilt boundary made of wedge disclination dipoles and a single edge dislocation is studied. It is found that in general edge dislocations can be generated or absorbed at the wedge disclination dipoles. The dilatation field of such a boundary is calculated and from which the interaction with impurity atoms which cause dilatational distortions of the lattice is studied. The resulting periodic distribution of impurity atoms along the boundary is suggested to play a role in intergranular embrittlement and grain boundary sliding.

Computer simulation has proven to be a powerful tool for determination of atomistic structure in complex zones in metals. This method has been applied to study asymmetric tilt boundaries in γ-iron and their interaction with vacancies and carbon atoms. A program, “GRAINS”, which employs classical equations of motion was used for these experiments. A first neighbor function described the interaction between atom pairs. Volume forces were imposed by the computational cell boundaries. Observations and conclusions of particular interest were: The determination of values for migration and formation energies of vacancies in the vicinity of a grain boundary so vacancy transport and diffusion mechanisms in the boundaries can be estimated more accurately. These values were found to differ appreciably from those in ordered regions. The zone of interaction extends into the grains along close-packed lines from misfit regions much farther than would be anticipated from measurements of grain boundary width. Local ordering in the misfit region of a grain boundary caused by a very few impurity atoms which demonstrated how trace concentrations of impurities could significantly affect the strength of a metal.

Metals and alloys are commonly employed and processed in the form of polycrystalline aggregates. The mechanical strength of such aggregates depends greatly on the strength of the interfaces or grain boundaries that join the individual crystal grains. In general a grain boundary can be expected to be weaker than the grain matrix since the degree of atomic order in the boundary is lower than that in the crystal. Furthermore, the chemical composition with respect to solute components and the diffusive properties of a grain boundary differ from the crystalline matrix.

The absolute grain boundary energies of {011} tilt boundaries in bismuth at a temperature very near the melting point were measured over the range of misorientations 0.5° to 14.5°. A study of the structure of these boundaries was extended as far as 27°. The results at small tilt angles (θ≤6°) can be described accurately in terms of a heterophase dislocation model. This model also correctly predicts the grain boundary energies of [001] tilt boundaries in copper near the melting point, again for tilt angles less than about 6°. The heterophase dislocation model is unique, inasmuch as it permits the calculation of absolute grain boundary energies in terms of usually available thermodynamic and elastic quantities and a simple macroscopic parameter related to the boundary structure. In addition, the theory provides a basis for interpreting the structural transition observed in bismuth tilt boundaries at intermediate misorientations (θ=15°). Finally, the failure of current theories to predict the correct energy-misorientation dependence over a wide range of misorientations is ascribed to linear and nonlinear interactions among the misfit dislocations—interactions which increase rapidly in importance for misorientations above about 5°. For a quantitative description of the energetic behavior of higher angle grain boundaries than are treated at present, a theory which accounts for such interactions appears to be required.

A liquid droplet on a planar grain boundary in a solid is in a position of minimum energy since the grain boundary area must increase if the droplet moves away. Thus a droplet migrating through a polycrystalline solid may either penetrate or be trapped by a grain boundary, depending on whether or not the applied driving force on the droplet is sufficient to propel the droplet out of the energy valley associated with a grain boundary.

A transmission electron microscopy study of 304 stainless steel films has been undertaken to systematically study the interrelationships of the degrees of freedom characterizing a grain boundary. From this study a configurational theory has been developed which is useful in explaining the existence of interfacial torques at twin-grain boundary intersections. The grain boundary misorientation (Θ) is defined as the relative rotation of the <110> directions in the adjacent grains of identical (110) orientation. The two remaining degrees of freedom are represented by the tilt or inclination (θ) and the asymmetry (Φ) of the grain boundary plane. Torques arise because of a difference in grain boundary energy with a change in misorientation or tilt. 90° twin configurations (twin plane along a <112> direction) are essentially high-torque situations, as a result of the change in misorientation (ΔΘ) between the twinned grain and its neighboring grain. 35° twins (twin plane along a <110> direction) are low-torque configurations, but can exhibit high torque anomalies when there is a sufficient variation in tilt across the intersection, Δθ. Misorientation, Θ, appears to be the dominant torque producing parameter for high-torque configurations, and dominates the variations in grain boundary free energy. Also, a functional relationship between Δθ and ΔΦ observed for both high-torque occurrences. Spreads in the histograms for twin boundary-grain boundary energy ratios are due to torque terms or variations in grain boundary energy with changes in grain boundary parameters.

The polycrystalline structure experiences two mechanisms of grain boundary area reduction in the process of grain growth on annealing. One is the readjustment of junction angles on the occurrence of a grain encounter, i.e. the first time “Weting” of two grains. As soon as the threshold of a grain encounter is crossed a rather sharp but localized drop in boundary area ensues. This correction is relatively rapid at first, gradually slowing down as the equilibrium angles for the local junctions are approached. The various junction angles do not necessarily satisfy the angles required by the faces of various polyhedra involved and this discrepancy is satisfied energetically by producing a net spherical curvature of the boundaries. The actual curvature may not always be spherical because there are other geometrical requirements when the polyhedra are not regular or not symmetrical. But the net curvature tends toward spherical curvature because this yields the minimum surface for a given volume, which is dictated by the tendency toward minimization of boundary free energy. The second mechanism takes place as the grains with a net convex curvature diminish in size, the net diffusion favoring atomic escape from such grains. This is a relatively slow process in general but a necessary one, since it leads to further encounters, which repeat the cycle just described. The process may be somewhat rapid for those grains that are approaching extinction.

In order to predict the exact mechanism of grain boundary motion one has to know the atomistic structure of the grain boundary. Although some progress in the understanding of grain boundary structure has been made in recent years, a generally accepted model which is widely applicable is not yet available. In the present paper several alternatives will be treated. First, models will be considered where the boundary is assumed to consist of a distorted zone having a large width compared to the atomic distance. Here thermodynamic formulas can be applied. Secondly, grain boundaries are assumed to have a width of only atomistic dimensions. Here, in particular, the ledge model will be considered. Special emphasis will be given to the impurity drag model and to the orientation dependence of grain boundary motion which is considered largely responsible for the formation of recrystallization textures. Finally a general comparison between theoretical predictions and the various experimental observations of grain boundary motion will be made.

The early stage of isothermal recrystallization of five polycrystalline alloys of zone-refined aluminum containing different amounts of gold and deformed 40% by rolling at 0°C was studied by quantitative metallography. All results could be interpreted in terms of a site-saturated, matrix grain edge nucleation at zero time with subsequent growth controlling the recrystallization kinetics. The length of the matrix edges producing recrystallized colonies depended on the penultimate grain size and was longer the larger that grain size. A modification of the original phenomeno-logical model was proposed which accounted for the observed discrepancies between the measured recrystallization parameters and the ones calculated from the earlier model. The presence of AuAl₂ precipitates had no apparent effect on the nucleation mode. However, the apportionment of gold into a precipitated state caused an enormous (10⁴) increase in boundary migration rate (recrystallization rate). With the exception of an alloy containing 3.4 ppm gold, the activation energy for recrystallization was 25,700 cal/ mole, did not vary with the extent of recrystallization, and was in approximate agreement with the solute drag theory of boundary migration. The migration behavior of the 3.4 ppm gold alloy suggested the possibility of a grain boundary structure transformation. A theory of vacancy-enhanced grain boundary migration during recrystallization of dilute alloys was proposed to account for the observations.

Interaction between conducting electrons and thermally diffusing metal atoms causes a net drift of the atoms in the direction of electron flow. In thin films, where joule heating is minimized by substrate cooling and the temperature is relatively low, this “electromigration” has been shown to be confined mainly to grain boundaries, and, in some cases, surfaces. Because of certain irregularities in the boundary network, the flux of atoms is nonuniform, leading to divergencies and localized depletion. Depletion leads to the formation of grain boundary holes by either void nucleation and growth or by accelerated grain boundary grooving. Decrease in the damage rate is achieved by control of atomic mobility in grain boundaries and surfaces. A particularly effective method of controlling mobility is to introduce a solute species which migrates to appropriate defect sites and effectively inhibits motion of host atoms. The solute, however, being in preferred diffusion paths, is susceptible to electromigration and becomes locally depleted. Restriction of solute depletion is critical for reduction of gross damage by loss of solvent.

The grain boundary transport of aluminum chromium, and copper resulting from electromigration at 175°C in aluminum-chromium and aluminum-copper thin film conductors has been measured. The forces acting on the various types of atoms are estimated from other experiments or from theoretical derivations. It is then possible to calculate the diffusion constants of the different atomic species. The values obtained for aluminum grain boundary diffusion in aluminum-chromium correspond well to values which have been found through different means in the grain boundary of pure silver. It is concluded that chromium does not reduce the rate of grain boundary diffusion of aluminum, but copper reduces this rate by a factor of about 80. The results of a series of electromigration experiments in aluminum-copper thin films are interpreted in terms of the information they yield on the diffusion of adsorbed copper atoms in aluminum-copper grain boundaries. The conclusions reached are compared to the previously reported results on the effect of alloy additions on grain boundary diffusion in a variety of different elements.

Growth selection studies have been performed with 99.9999% cadmium and a cadmium-5 atom p.p.m. lead alloy. After severe local deformation single crystals of a standardized orientation were annealed resulting in the recrystallization of the heavily deformed region, and the competitive growth of these recrystallized grains down the strain gradient into the single crystal matrix. A three dimensional orientation space has been employed to describe the distribution of selected orientations. and six preferred orientations have been identified. The relative preference for these preferred relationships is shown to be dependent on the single crystal orientation, the solute concentration and the annealing temperature.

The preferred orientation relationships between growing grains and strained (4–8 pct in tension) single crystal matrices of 99.999 pct purity copper were observed to be (001) 19° and (111) ~ 30°, identical to those previously found after secondary re-crystallization. Nearly all of the growing grains contained an annealing twin. By considering the orientation of the parent (or twinned) grains, the preferred relationships may be expressed, approximately, in terms of parallelism between the following pairs of orthogonal directions: By considering the matrix during the secondary recrystallization in copper as (001)[100] and its four twin orientations, the present alternative suggests that it is the twin matrices, not the (OOl) [100] orientation, which support the growth of both (001) 19° and (111) 22° secondary grains. When the occurrence of annealing twins is rare, such as in aluminum, it is therefore expected that these two relationships should be absent, as observed experimentally. The findings of only two preferred relationships in the present investigation is in agreement with the alternative offered, but not with the coincidence model, which yields many relationships with a high coincidence density.

Grain boundaries have a profound effect on the strength of metals and alloys. Material properties,can be changed significantly by boundary migration. Studies of grain boundary mobility in matrices of poly- and single-crystals under the conditions of a difference in stored energy across the moving boundary have provided only limited advances towards understanding the behavior of grain boundaries. Primarily, this has been due to uncertainties in the magnitude of the force acting on the boundary during its motion. This difficulty has been avoided by examining boundary motion in wedge-shaped bicrystals in which the boundary migrates under the driving force of its own interfacial energy. The driving force per unit area of the boundary is simply related, in this case, to the specific interfacial energy and to the distance between the boundary and the tip of the wedge. Results of an investigation of the velocities of pure tilt boundaries in zonerefined aluminum and dilute aluminum-magnesium alloy bicrystals of preselected orientations have been presented. The effects of varying driving force and solute concentration on thermally activated boundary motion will be discussed in relation to the postulates of current theories.