Volume 96, Issue 10

A thermodynamic analysis of grain boundary adsorption is presented. From the thermodynamic model developed it follows that in binary polycrystals with identical grain boundaries at some conditions three phases can coexist in equilibrium below the solidus temperature. The model predicts that two solid solutions in the grain and in the grain boundaries coexist below some critical value, X2*$X_2^*$, of solute concentration in the grain. At X2*$X_2^*$ , a compositional phase transition occurs in the GB which is accompanied by a gap in the adsorption isotherm, a change of the slope of the GB tension isotherm, and the formation of a new 2D grain boundary phase. It is shown for three systems (Cu–Sb, Fe –P, and Sn–Bi) that the compositions of the GB phase and the phase in the grain are in close agreement with the predictions.

The structural characteristics of three-dimensional (3-d) irregular networks, such as random polycrystals, are described using scaling arguments based on the properties of Average N-hedra (ANH’s). ANH’s comprise a special set of highly symmetric polyhedral cells that satisfy topological and geometrical criteria demanded in 3-d space-filling networks. All the geometrical properties of ANH’s may be obtained from exact analytical expressions already derived in [1]. The utility and ease of use of these formulas have been carefully checked against accurate simulations of the excess free energy and evolution kinetics of foams and polycrystals. The vertex-to-vertex distance is chosen in this paper as the consistent gauge to estimate an important microstructure feature set presented here for irregular 3-d networks. In the case of annealed polycrystals this includes the total grain boundary area and its associated stored energy per unit volume, the triple line length per unit volume, and the number density of triple lines and quadra-junctions – all of which may be expressed in terms of the polycrystal's grain number density.

Grain boundary networks consisting entirely of Σ3 and Σ9 boundaries (twin-limited microstructures) are analyzed. Analyses of thought examples and theoretical considerations show that there are fundamental differences between two-dimensional and three-dimensional networks. The notion of the upper limit of the fraction of Σ3 boundaries is reassessed, and implications for the concept of grain boundary engineering are discussed.

Grain growth in random and textured 2D polycrystals is modeled under the supposition that all the triple junctions possess limited mobility. In the random polycrystal, the growth kinetics is at first linear and becomes parabolic at later stages if both the triple-junction mobility and the initial grain size are low. The experimental data on triple-junction mobility are used to show that such an effect could be observed in nanocrystalline materials. In the textured polycrystal, triple junctions with limited mobility are found to shift the evolution of the growth process toward abnormal grain growth.

The equilibrium shape of a polycrystalline cylindrical nanowire with bamboo microstructure is determined. It is shown that for a certain ratio of grain boundary and surface energies a critical grain length exists above which the integrity of a nanowire cannot be preserved. Numerical calculations of the kinetics of nanowire shape evolution controlled by surface diffusion are performed. It is shown that the rate of thinning of unstable nanowires in the region of grain boundaries diverges as a break-up event is approached.

Parent-martensite interfaces are modelled in this work as semi-coherent interfaces comprising coherent terraces reticulated by arrays of defects that accommodate coherency strains. It is demonstrated that such interfaces can migrate conservatively if one set of defects is an array of disconnections (transformation dislocations) that can glide along the terraces. The topological character of disconnections (Burgers vector and step height) that can glide in this way is elucidated. Experimental observations of martensitic interfaces in ZrO 2 , Ti-10 wt.% Mo and ferrous alloys are then examined in the light of this understanding. In the cases reviewed, it is found that the interface structures observed are consistent with the terrace/disconnection model proposed.

The existence of the so-called “enthalpy – entropy compensation effect” as an inherent property of a system is proven on the basis of a pure thermodynamic analysis. The compensation effect is documented for the example of grain boundary segregation and migration. It is shown that the changes of the values of characteristic enthalpy and entropy that fulfil the compensation effect are caused by the changes of grain boundary energy via the changes of grain boundary structure and system chemistry: Despite of the nature of such changes, a single linear dependence between the enthalpy and entropy should exist under the same mechanism of the process.

Nanocrystalline materials are polycrystals made up of nanometer-sized grains separated by a network of interfaces – grain or phase boundaries – that generally make a positive contribution to the total energy of the system. Consequently, there exists a thermodynamic driving force for reducing the overall interface area, which renders such systems intrinsically unstable against coarsening. The latter process entails interface migration and the concomitant deterioration of any property enhancements effected by the ultrafine grain size. We describe a strategy for significantly reducing or even eliminating the driving force for grain growth in nanocrystalline materials via the deliberate segregation of solute atoms into the core region of boundaries. Applied to Pd – Zr solid solutions containing up to 20 at.% Zr, the strategy yields nanocrystalline specimens manifesting an unusually high thermal stability with respect to grain growth, extending to the vicinity of the melting point. Parallels are drawn between the migration of grain boundaries in segregation-stabilized systems and antiphase domain boundaries in ordered alloys.

Recently developed models of grain boundary segregation and grain boundary energy, as a function of the 5 macroscopic parameters of grain boundary orientation, have been used to predict the behavior of a simple face centred cubic alloy. It is shown that the equilibrium composition, as well as the composition profile, on one side of a boundary with a given terminating plane, depends on the crystallographic orientation of the terminating plane of the other side of the grain boundary. These predictions are confirmed by recent measurements of Nb segregation to TiO 2 grain boundaries. In addition, the models show stronger solute segregation to higher energy grain boundaries of the pure solvent. This result is also confirmed by the experimental distribution in orientation space of Nb segregation to TiO 2 grain boundaries, when it is compared to the orientation distribution of the grain boundary energy of pure TiO 2 . The overall results are consistent with expectations from the Gibbs adsorption isotherm, and indicate that grain boundary energy anisotropy is decreased by grain boundary segregation.

The faceting and migration of individual triple junctions in Zn tricrystals under a constant driving force was investigated. The triple junction (TJ) was formed by three [101̅0] tilt grain boundaries (GBs) with misorientation angles θ of 43°, 37° and 6°. The stationary shape of the migrating triple junction was studied, and the migration rate was measured in-situ between 670 and 688 K using polarized light. In some experimental runs, a facet was formed on the θ = 37° [101̅0] tilt GB. This facet was parallel to the close-packed plane in the constrained coincidence site lattice (CCSL). The length of this facet decreases with increasing temperature and becomes zero at 688 K. The temperature dependence of the facet length is better described by the mean-field Andreev approximation than by the solid-on-solid model. The step energy estimated in the framework of the Bonzel approximation is about 0.1 eV/atom. In other experimental runs, the θ = 37° [101̅0] tilt GB did not facet and remained rough in the same temperature interval. This fact allowed us to compare the stationary migration of the same TJ with faceted and rough GBs. ATJ formed by faceted GBs migrates one to two orders of magnitude more slowly in comparison with a rough TJ. An unrealistically high value of the apparent migration activation enthalpy of faceted TJs can appear due to the changing geometry of faceted GBs, similar to the case of migration of faceted twin tips.

During grain growth in 2D systems triple junction kinetics may significantly influence not only the rate of grain growth but also the geometric evolution of the grain boundary network. In this contribution we analyse results from in-situ heating experiments coupled with electron backscatter diffraction analysis using a columnar Al foil. It is shown that (a) the von Neumann– Mullins relation is not always satisfied, (b) there is a marked discontinuity and heterogeneity in TJ motion in space and time and (c) grain boundaries evolve from predominately curved to straight boundaries. To interpret these results we introduce 3 main types of triple junctions T c , T p , and T s , which are made up by at least 2 concave, 2 convex, and 3 straight boundaries, respectively. Analyses show that triple junction drag plays a significant role during grain growth. Data suggest that the drag effect of T p is higher than that of T c . In addition, triple junctions with 3 low-angle boundaries are exceptionally stable, while those with at least 2 high-angle boundaries are unstable and tend to disappear during grain growth. Only ~ 20% of grain boundaries exhibit steady state triple junction motion.

Grain boundary motion can be affected by a magnetic field if the anisotropy of the magnetic susceptibility generates a gradient of the magnetic free-energy density across the boundary. Due to this magnetic driving force, annealing of locally deformed single crystals in high magnetic fields results in growth selection. The character distribution of the boundaries connected to growth selection is found to be far from random. If a magnetic energy density gradient as a driving force is superimposed to a curvature driving force during grain growth, this biases the microstructure evolution with regard to grain size and crystallographic texture, as it is demonstrated on polycrystalline zinc and titanium. Analysis of individual orientation data reveals that the observed asymmetrical texture stems to a large extent from a difference in grain numbers of the individual texture components.

Grain boundary mobility has been measured in high-purity aluminum alloyed with 0.03 wt.% Zr using energy stored during plastic deformation as a driving force. In general, the dependence of mobility on grain boundary character was similar to that observed by previous authors with a maximum in mobility in the vicinity of the ∑7 type (38°<111>). The exact location of the mobility maximum varied, however, with temperature in a manner similar to that observed for curvature-driven mobility measurements. Although <111> tilt boundaries exhibit high mobilities in general, the single peak at the ∑7 position at low temperatures changes to a double peak at high temperatures with a local minimum at ∑7. The combination of mobility variation and the thermal activation analysis of the results points to a compensation temperature effect. All these results suggest that grain boundary mobility is a true material property.

In-situ transmission electron microscopy (TEM) observations reveal a permanent chaotic motion of nanosized liquid Pb inclusions embedded in thin aluminum foils. Individual trajectories of the inclusions were analysed to determine the character of their motion. The inclusions moving freely inside a crystal display motion with three-dimensional random walk characteristics while inclusions attached to dislocations display spatially confined random motion localized to the close vicinity of the dislocation lines. The diffusion coefficients of inclusions moving freely in the matrix were determined using Einstein’s classical equation for diffusion of Brownian particles. The diffusion coefficients of inclusions trapped on dislocations were found using an equation based on Smoluchowski’s analysis of Brownian motion of a particle under the action of a linear elastic restoring force. The dependence of the diffusivity on the size of the inclusions suggests that their mobility is controlled by kinetic processes on the inclusion/matrix interfaces. The Arrhenius analysis exhibits two regions with different temperature dependencies. We suppose that this is related to the existence of {111} facets on the inclusion/matrix interfaces.

Non-linear segregation of Ag in Cu grain boundaries (GB) was quantitatively studied by radiotracer GB diffusion measurements on Cu bicrystals with non-special near Σ5 symmetrical [001] tilt boundaries. Bicrystals were used to guarantee a stable GB during the annealing avoiding in this way disturbing effects like GB motion etc. on the measured diffusion penetration profile. The 110m Ag radioisotope with a well-defined specific activity was applied. This allowed to determine quantitatively the amount of Ag solute atoms in a section as a function of the penetration depth. The controlled variation of the total amount of diffusing Ag atoms along the Cu GB resulted in a fundamental change of the GB penetration profile shape from almost linear to strongly curved. The curvature of the penetration profiles was unambiguously shown to be caused by non-linear segregation of Ag in Cu GB. The full Ag segregation isotherm was calculated from the corresponding GB diffusion penetration profile.

Diffusion processes in typical metals are considered to be slow at room temperature but there are many applications for which very long-term use is envisaged and stability needs to be assured over a timescale of 10 000 years, where even slow processes can be important. It is clearly impractical to make diffusion measurements under controlled conditions for this length of time, so it is common to perform accelerated tests at higher temperatures and extrapolate the necessary information from the measurements so obtained. We have tested the validity of this type of extrapolation for room-temperature, grain boundary diffusion in the copper –silver system, by measuring low-temperature diffusion profiles in antique samples of Sheffield Plate. We present experimental measurements and analysis, along with a comparison to modern diffusivity data extrapolated in the usual manner.

We report first results on producing a metal – metal composite by forcing solid aluminium to fill a porous steel preform. This process is akin to forcefill used for filling of vias when producing metallic interconnects in microelectronics. Using scanning electron microscopy with energy-dispersive X-ray spectroscopy, it was shown that for nominal pore size as small as 100 μm, the pores could be filled with aluminium throughout the entire preform used, thus demonstrating the viability of the process. An interesting aspect of this solid state ‘infiltration’ is that the tortuous random paths taken by the plastically flowing Al involve numerous kinks. Some of them may induce large localised shear deformation similar to that produced by equal channel angular pressing, which is used to fabricate bulk ultra-fine-grained materials. It is, therefore, conjectured that towards the exit end of the channels the infiltrating material may develop an ultra-fine grain structure and exhibit enhanced strength. It is suggested that the process described can be used to produce metal– metal (or ceramic – metal) composites with unusual mechanical properties. Thin fibres of the material that has percolated through the porous preform can be expected to have a sub-micron grain structure and to possess improved mechanical properties.

On the basis of in-situ observations of the α/γ phase transformation in an iron-4.2 at.% Cr alloy, it was found that triple junctions with more random boundaries can be preferential sites for nucleation and that a two-stage migration of α/γ interphase boundaries can occur with highly different velocities, i. e. of 0.23 ~ 0.43 μm/sec for the α/γ two phase temperature region and 2.6 ~ 44 μm/sec for the c single phase region. The origin of the observed high migration velocities of α/c interphase boundaries and the generalized K-S orientation relationship between a new phase and the matrix are discussed on the basis of a possible role of {111} γ //{110} α plane matching interphase boundaries in the α/γ phase transformation.

The thermodynamic conditions for spontaneous grain boundary wetting and stress driven liquid metal embrittlement are related to each other and the kinetic mechanism responsible for fast GB penetration under small stress is described. The dissolution – condensation mechanism of liquid metal embrittlement and linear fracture mechanics for calculation of a crack profile are applied to the classical system “Al – liquid Ga”. The results tend to support the idea that the recently observed fast linear penetration of Ga along 150° tilt <110> GB of Al should be considered as propagation of a liquid metal embrittlement crack under a small residual stress rather than as spontaneous grain boundary wetting. With the residual tensile stress σ ≈ 0.5 MPa acting normal to the GB plane, all major findings reported for this model system are explained in a semiquantitative way assuming that the GB spreading coefficient is extremely small by its absolute value, i. e. that the system is near the threshold of spontaneous grain boundary wetting.

The effect of pressure and misorientation on grain boundary wetting in aluminium bicrystals has been investigated. The grain boundaries were of [100] symmetrical tilt type. The wetting liquid was an Sn– Zn alloy. It is shown that the wetting angle is a function of misorientation but not of pressure. The reasons of the above results are discussed, assuming a linear dependence between the interface energy and pressure. It is shown that the difference of energy of the liquid/solid and solid/solid interface as well as the misorientation dependence of energy is simply proportional to the free volume of the interfaces.

This paper describes a combined thermodynamic and micro-mechanical model for the propagation of a grain boundary crack through a solid in which stress concentrations ahead of the crack and plastic deformation around the crack tip are considered. It is shown that critical factors are impurity segregation concentration, grain boundary structure, reflected in the Σ value of the boundary, and temperature. Comparisons of the model predictions are made with other models of grain boundary binding by Sutton. Additionally, the model predictions are compared with several experimental observations of grain boundary fracture strength. It is shown that ductile to brittle transition temperature data for steels are a valuable source of experimental grain boundary fracture information for this important range of commercial materials.