H.J. Frost

The relative rates of secondary and normal grain growth

Abstract It is shown that, if uniform grain boundary energy is the only factor affecting boundary motion, an abnormally large grain in a matrix of normal grains does not grow at a higher relative rate than its neighbors.

The effect of nucleation conditions on the topology and geometry of two-dimensional grain structures

Abstract The geometry and topology of two-dimensional grain structures have been analyzed for different conditions of nucleation and growth to impingement. These conditions include simultaneous nucleation at a fixed number of sites, and continuous nucleation at a constant rate per unit of untransformed area. Intermediate between these cases are conditions in which the nucleation rate declines with time. Another set of conditions are those in which nucleation is excluded in a zone surrounding each pre-existing grain. A constant growth rate is assumed for all conditions. All the conditions modelled result in markedly different structures. The modelling is intended for applications to the study of the nucleation and growth conditions for thin films of metals or semiconductors.

Computer simulation of strain energy effects vs surface and interface energy effects on grain growth in thin films

Abstract A computer simulation of grain growth in two dimensions has been used to model microstructural evolution in Ag (001)Ni thin films. Two orientation dependent driving forces have been included in the simulation: surface and interface energy and strain energy. Surface and interface energy and strain energy do not favor the growth of the same orientations and compete to determine the orientation and microstructure of the film. Growth of grains with (001) texture is favored in highly strained, relatively thick films, while growth of grains with (111) texture is favored by surface and interface energy minimization, especially in very thin films. When a film is constituted of only (001) and (111) grains, (001) texture can develop only if the yield stress of the (111) grains is sufficiently high to prevent yielding at early times. Experimental results confirm that (001) texture can develop in Ag (001)Ni films depending on the state of strain and film thickness.

Simulation of thin film grain structures—II. Abnormal grain growth

Abstract A computer simulation of grain growth in two dimensions has been used to model microstructural evolution in thin films. In a companion paper we have simulated the stagnation of grain-growth due to grain-boundary grooving at the free surface of the film. In this paper we model the effect of driving force variations (due to variations of the free-surface energy among different crystals) on the origination and propagation of abnormal or secondary grain growth. The simulation produces an estimate for the magnitude of the driving force which is required to produce abnormal grain growth. The simulation also indicates that a key requirement for classic abnormal grain growth behavior is that a majority of the grains have free-surface energies which differ very little from each other.

Computer simulation of microstructural evolution in thin films

The nature of the microstructure of a thin film strongly affects its functionality in electronic applications. For example, the rate of electromigration-induced failure is a function not only of the grain size in an interconnect line, but also of the width and shape of the grain size distribution. We are developing techniques which allow prediction of the relationships between the conditions for thin film processing and the topology and geometry of resulting grain structures. We have simulated two-dimensional microstructural evolution by determining the location of grain boundaries after nucleation and growth of crystalline domains. We have allowed for nucleation under a variety of conditions including constant nucleation rates, decreasing nucleation rates and instantaneous saturation of nucleation sites. We have also allowed for increasing and decreasing growth rates which depend in various ways on the domain size. We have simulated grain growth in two-dimensional structures by allowing boundary and triple point motion in order to reduce the total grain boundary area. The rate and nature of the initial stages of grain growth are strongly affected by the conditions for nucleation and growth. Eventually, however, grain growth appears to proceed as expected from analytical treatments.

Cavities in dense random packings

Abstract The structure of dense random packings of hard spheres is analyzed in terms of the polyhedral cavities between spheres. Two different self-consistent schemes of polyhedron classification and identification are presented: polyhedra with all triangular faces, called deltahedra; and local arrangements allowing both triangular and four-edged faces. Two models were analyzed according to these schemes: the mechanical model of Finney Proc. R. Soc. 319A , 479 (1970), and the computer-generated model of Bennett J. appl. Phys. 43 , 2727 (1972). In addition, the number and sizes of the sites for small interstitial spheres were calculated for both models, without regard to the polyhedral classification of the cavities. The structural units described and the results may be applicable to the structure of liquid metals and metallic glasses.

Development of near‐bamboo and bamboo microstructures in thin‐film strips

A two‐dimensional grain growth model is used to study microstructural evolution in thin film strips. We focus on the strip’s transformation to the bamboo structure, in which individual grains transverse the width of the strip. We find that the approach to a fully bamboo structure is exponential, and that the rate of transformation is inversely proportional to the square of the strip width. When the simulation is extended to model grain boundary pinning due to grooving at grain boundary−free surface intersections, we find that there exists a maximum strip width to thickness ratio beyond which the transformation to the bamboo structure does not proceed to completion.

Computer simulation of grain growth

Abstract A variety of computer simulation techniques have been developed to described grain growth in polycrystalline materials and the evolution of cellular patterns in other systems. Most techniques have now been developed to the degree that they can be used to analyze idealized microstructural evolution processes, and, in some cases, answer questions which arise from experimental observations or engineering goals. The development of crystallographic texture, the effect of dispersions of second phase particles, and the nature of grain structure evolution in thermally inhomogeneous environments have also attracted considerable interest.

Grain boundary ordering configurations in the L12 or Ni3Al structure

Abstract A grain boundary in the L1 2 structure (A 3 B ordered f.c.c.) that has a regular repeating structure (which must have a coincidence site lattice misorientation) will have different possible ordering configurations, based on different placements of the A and B atoms within the underlying f.c.c. structure. A general method is presented for determining the number of different ordering configurations for such a boundary, and the implications of these different configurations on the properties of the polycrystal are discussed.

Simulation of the influence of particles on grain structure evolution in two-dimensional systems and thin films

A two-dimensional front-tracking simulation of grain growth has been extended to treat the effects of particles on the evolution of grain structures during annealing. When grain boundaries come into contact with particles, boundary motion is assumed to be pinned. It is found that even a small volume fraction of particles retards grain growth, lowers the ultimate average grain size, and leads to significant changes in the grain-size and number-of-sides distributions. These changes differ in detail from the changes in the grain-size distribution predicted using the Potts model. The changes in the nature of the grain-size distribution are explained by considering the topology of the evolving and of the stagnant grain structures. The average grain size in the stagnant structure scales with the number of particles in a way consistent with a scaling with area fraction of the particles to the power 0.46, in near agreement with the expected dependence from a Zener-pinning analysis in two dimensions. Particle pinning is also simulated in conjunction with the effects of other mechanisms impeding grain growth such as solute drag or grain boundary grooving. In this case it is found that the stagnant grain-size distribution is determined by the competing stagnation forces, and that the Zener-pinning analysis is not obeyed and must be modified.