Carol A. Handwerker

Overview No. 98 I—Geometric models of crystal growth

Abstract Recent theoretical advances in the mathematical treatment of geometric interface motion make more tractable the theory of a wide variety of materials science problems where the interface velocity is not controlled by long-range-diffusion. Among the interface motion problems that can be modelled as geometric are certain types of phase changes, crystal growth, domain growth, grain growth, ion beam and chemical etching, and coherency stress driven interface migration. We provide an introduction to nine mathematical methods for solving such problems, give the limits of applicability of the methods, and discuss the relations among them theoretically and their uses in computation. Comparisons of some of them are made by displaying how the same physical problems are treated in the various applicable methods.

Reactive Wetting and Intermetallic Formation

Despite its apparent simplicity, the spreading of molten solder on copper or on solder-coated copper to form a solder joint involves many complex physical processes. Poor solderability of electronic components, while infrequent in absolute numbers, can cause significant manufacturing difficulties when acceptable performance requires less than one failure in 106 joints. An assessment of solderability involves consideration of the entire soldering process including the details of the soldering equipment, the design of the joint geometry, and the wettability of the surfaces to be joined. Wettability involves consideration of the intrinsic rate and extent that solder can spread on a particular surface and is the primary focus of this chapter. Thus we need only consider macroscopically simple geometries of wetting; we will focus on the fundamental physical processes involved in solder wetting and spreading. The ultimate goal is to determine those processes that are most important in order to provide a scientific basis for the analysis of engineering problems in solder technology.

Equilibrium geometries of anisotropic surfaces and interfaces

Abstract The geometries of anisotropic surfaces or interfaces in polyphase or polycrystalline microstructures can display a variety of shapes that are locally in equilibrium. Anisotropy introduces edges, corners, and flat facets, as well as new types of multigrain junctions, and requires a re-examination of how we represent geometrical equilibrium. The traditional approach, that begins with the interfacial free energy γ( n ) as a function of interface normal n , assumes knowledge of data that are unlikely to over be available with the required accuracy. However, transforms of γ( n ), notably the Wulff shape W itself, can be easily obtained by experiment and will give many of the same predictions as γ( n ). A particularly useful representation of these data is the n -diagram, a stereographic projection of the interface orientations present at equilibrium. In this paper various examples illustrate the use of these concepts.

Effect of chemical composition on sintering of ceramics

Abstract Recent advances have been made in the understanding of sintering of ceramics. The primary advances have been in the modelling of grain boundary and surface properties and in the measurement of the effect of low levels of impurities and dopants on the energies and properties of interfaces. These results indicate that sintering is strongly affected by crystalline anisotropy, multiple transport mechanisms, complex geometries and impurity effects. In particular the effect of variable concentrations of impurities at the trace level have been found to mask the effects of changing most other systems parameters in ceramics with low intrinsic concentrations of defects. Experiments are described which can be used to isolate specific parameters or processes involved in sintering, such as the surface-grain boundary dihedral angle. Specific examples of impurity effects in MgO and α-Al 2 O 3 are presented.

Thermodynamics and kinetics of reactions at interfaces in composites

Abstract Composites are complex engineering systems in which the constituent materials are not in thermodynamic equilibrium during initial fabrication, during production of components or in use. Diffusion, phase transformations and roughening at interfaces can occur at any of these stages. By the use of thermodynamic and kinetic concepts, changes in the interface morphology in composite systems can be predicted and thus controlled. Two features which govern interfacial reactions, compositions, phases and structures are described: (1) surface energy effects at interfaces, including nucleation, and (2) stress effects accompanying diffusion at interfaces. Through both theory and experiment, small departures from equilibrium, even without the formation of new phases, are shown to cause large-scale changes in diffusion near the interface and interface morphology. These theoretical concepts are used to examine reactions in the AlSiC system and control of phase formation and interface structure in Al2O3Cr2O3Cr metal composites.

Observations on crystal defects associated with diffusion induced grain boundary migration in CuZn

Abstract Standard TEM techniques have been applied to the study of crystal defects associated with DIGM in copper foil exposed to zinc vapor. The experimental results have been compared to the coherency strain theory (as discussed for liquid film migration (15, 16) and the Balluffi/Cahn GB Kirkendall effect theory (11). There are indications that coherency strain may play a role in the initiation of DIGM but the observation of a high density of GB steps suggests GBD climb is also a viable mechanism. However, neither model can explain all the experimental results. None of the current theories can be proved or disproved on the basis of the results presented here. The observations do, however, suggest the possibility that more than a single mechanism or driving force may be responsible for all the morphological changes associated with DIGM. We hope that this paper will serve to stimulate further TEM analysis of the DIGM process, particularly in the area of grain boundary structure and matrix dislocation densities.

Formation of alumina-chromia-chromium composites by a partial reduction reaction

Abstract Metal-ceramic matrix composites were formed by the partial reduction of Al 2 O 3 -Cr 2 O 3 solid solutions to form Cr metal particles in an Al 2 O 3 -Cr 2 O 3 matrix which had a lower Cr 2 O 3 concentration. In Al 2 O 3 -Cr 2 O 3 solid solutions containing 10 and 25 wt.% Cr 2 O 3 , the microstructures produced by reduction are different from that expected from simple models of internal reduction or oxide scale formation. Grain boundary diffusion of individual grains. Small Cr particles were then observed to coarsen along some, but not all, grain boundaries by concomitant process known as ‘discontinuous coarsening’. The mechanisms controlling microstructural evolution in this system were examined.

Composition control of the microstructure of Ba2YCu3O6+x

Abstract Although Ba 2 YCu 3 O 6+ x exhibits superconductivity at high temperatures, the critical current density ( J c ) in bulk polycrystallin e materials, prepared by sintering, is several orders of magnitude below useful values. One possible source of low J c in polycrystalline materials is the presence of resistive grain boundary junctions resulting from second phases or impurity segregation. Chemical composition plays a major role in determining the phases present and hence the grain boundary characteristics. Preliminary composition measurements of Ba 2 YCu 3 O 6+ x include the ratio of major elements, impurity concentrations at the trace level, compositional mapping of major elements by electron probe microanalyses, and observations of sintered microstructures. Results on liquid phase formation and carbon contamination introduced during powder processing and from exposure to atmospheric CO 2 indicate that a great degree of compositional control is required for any meaningful characterization of the Ba-Y-Cu-O system.

Phase Stability and Interface Reactions in the Al-SiC System

The Al-SiC system has been used as a model system in an examination of phase stability in the presence of a liquid phase and microstructure development in metal-matrix composites. The Al-Si-C phase diagram has been calculated for temperatures between 500°C and 1500°C. The phases formed between Al(liquid) and SiC at 920°C have been determined experimentally, using analytical electron microscopy, in both fiber and particulate composites and compared with what is predicted from the equilibrium phase diagram. The morphologies and the spatial distributions of phases have also been examined in addition to the phase analysis. The only phases found were Al, Al 4 C 3 , SiC, and Si. Although Al 4 SiC 4 is calculated to be stable at 920°C, it was not found. The SiC grain structure was found to influence strongly the morphology of the Al 4 C 3 -SiC and Al-SiC interfaces.

Sintering of Ceramics

The primary goal of sintering research is the controlled manipulation of microstructure. Out of the entire range of microstructures which are theoretically possible, each material system will be able to achieve only a subset of them, depending on the intrinsic material properties. Within these material constraints, the aim is to produce microstructures which enhance specific properties. Our understanding of the relationships among materials processing, microstructure, and properties is just beginning to emerge, and is producing unexpected results. For example, in a recent study of toughness in Al2O3 by Bennison and Lawn, microstructures with platy grains and a bimodal grain size distribution in undoped Al2O3 exhibited a greater resistance to crack propagation than did the more uniform microstructures in MgO-doped Al2O3 [1]. As a result of this emerging understanding, the focus of sintering science is changing from the modification of microstructures in incremental ways for correspondingly incremental improvement in properties to more effectual manipulation of microstructures to optimize properties. However, the production of the optimum microstructure will be dependent on both the material and the application and may require radically different processing routes for different materials. In this review paper, we have examined the research in sintering science over the past five years which has advanced the goal of microstructure manipulation.