J. M. Rickman

Stress calculation in atomistic simulations of perfect and imperfect solids

We analyze a real-space expression for the local stress tensor. This tensor rigorously satisfies conservation of linear momentum. From this expression a coarse-grained tensor is obtained for use in atomistic simulations of solids. Our formulation is then validated by considering both a homogeneously strained crystalline solid and one containing an oversized inclusion. In the latter case a direct comparison is made with results from anisotropic elasticity theory. We find that we are able to obtain good agreement with the suitably averaged continuum solutions in the far-field regime. Moreover, the coarse-grained tensor derived here appears to offer superior accuracy as compared to a stress tensor that has been widely used in atomistic analysis.

Role of segregating dopants on the improved creep resistance of aluminum oxide

Recent studies have demonstrated that p.p.m. levels of rare-earth dopant ions (e.g. Y, La, Nd) wield a beneficial and highly potent influence on the creep properties of alumina. In addition, codoping with ions of disparate sizes (Nd, Zr) resulted in even further enhancement of the creep behavior. In all cases, the dopant ions were found to strongly segregate to grain boundaries. Creep rates were not influenced by the presence of second phase precipitates, verifying that the creep improvement is a solid solution effect. In an attempt to clarify the exact mechanism(s) that controls creep behavior of the doped aluminas, various advanced characterization techniques have been applied including: secondary ion mass spectrometry, scanning transmission electron microscopy, orientation image microscopy, and extended X-ray absorption fine structure as well as atomistic computer simulation and studies of the creep kinetics. Although no definitive mechanism has been established, a logical explanation is that outsize ions segregate to more energetically favorable grain boundary sites, and improve creep resistance by blocking a few critical diffusive pathways. This mechanism is sufficiently general that it may be applicable to other ceramic systems.

Impact of heterogeneous boundary nucleation on transformation kinetics and microstructure

Abstract We examine quantitatively the impact of heterogenous nucleation on the temporal evolution of a phase transformation with particular emphasis on the correlation of nucleation site distribution and product phase microstructure. This is accomplished by investigating the spatial correlations in the transforming system via the calculation of several non-equilibrium,n-point correlation functions and thereby defining associated transformation fractions and correlation lengths. Computer simulations of transformations are also employed in order to validate the theoretical description and to relate the microstructural features of the evolving phase to relevant length and time scales in the problem. Finally, our findings are related to the results of experimental calorimetric studies of phase formation in thin films.

A methodology for automated quantitative microstructural analysis of transmission electron micrographs

It is generally recognized that proper quantification of microstructural behavior is necessary for the optimization of materials properties. In the specific case of polycrystalline thin films, transmission electron microscopy (TEM) is required for microstructural interrogation due to the small (nm–μm) inherent length scales in these systems. While a meaningful study requires large grain populations, typical data sets are relatively small due to the need for human interpretation of the contrast in TEM micrographs. To overcome this limitation, a general methodology has been developed to fully automate the grain boundary identification procedure by using a combination of both conventional and newly developed image processing algorithms to extract and combine information from multiple, optimized TEM micrographs. This technique has been validated by systematically analyzing microstructures of thin Al films, as obtained from TEM micrographs, and comparing these results with those obtained by a conventional, man...

Twinning in thin films—I. Elastic analysis

Abstract We examine the elastic energy contributions to the thermodynamics of twinning of a coherent film on a substrate and a thin layer, sandwiched within the bulk. Using linear elasticity, we obtain exact analytical results for the elastic energy release and stress fields associated with the formation of a periodic array of twinned domains, as well as for a single embedded twin domain. The corresponding results are also obtained for twinning within the bulk and these results facilitate comparisons between twinning in a constrained environment as opposed to twinning in an environment with a traction free boundary. An asymptotic analysis of the substrate stress fields far from the film—substrate interface reveals that the domains can be represented as idealized defects in terms of elastic line force dipoles. While the analysis is applicable to general misfit strain tensors, we present detailed results for the energetics of domain formation for a tetragonal film on a cubic substrate; a case commonly encountered in ferroelectric films. The elastic energy release, derived in this paper, is incorporated into a thermodynamic analysis of twinning and the equilibrium microstructures are determined as a function of the film thickness, interfacial energy, transformation strains and the elastic constants in the following paper.

MICROSTRUCTURAL STABILITY OF STRESSED LAMELLAR AND FIBER COMPOSITES

Abstract Microstructural stability can be modified by the presence of internal or applied stresses. We employ a linear stability analysis to examine the effect of stresses on the interface diffusion controlled morphological stability of lamellar (plate-like) and fibrous (rod-like phase) eutectic microstructures. These stresses can be either due to misfit strains and/or externally applied loads. For misfitting plates, the nominally flat plate-matrix interface is unstable with respect to the growth of perturbations with wavelengths greater than a critical wavelength, provided that the plates are elastically stiffer than the surrounding matrix. In contrast, for stresses generated by externally applied loads, the flat plate-matrix interface is always unstable as long as the plate modulus and the matrix modulus are different. In addition, the present analysis shows that misfit strains can either counteract or enhance the destabilizing influence of applied loads, depending on the elastic properties of the plate and the matrix and the volume fraction of the two phases. For misfitting rods, the nominally cylindrical rod-matrix interface in an isotropic matrix is unstable with or without elastic effects. However, the elastic effects can decrease (increase) the maximally unstable wavelength over that predicted by curvature effects alone provided that the rods are elastically stiffer (softer) than the surrounding matrix. Stresses generated by externally applied loads, on the other hand, always lead to a decrease in the instability wavelength compared with the Rayleigh instability wavelength. Stability diagrams are presented which identify the material properties and operating conditions required to maintain a stable interface in these eutectic microstructures.

Dislocation motion in the presence of diffusing solutes: a computer simulation study

A discrete lattice, kinetic Monte Carlo model is developed to simulate the motion of an edge dislocation in the presence of interacting, diffusing solute atoms that have a misfit with respect to the matrix. The simulation self-consistently determines the solute concentration profile (in two spatial dimensions), as well as the associated dislocation velocity. The solute segregation profile around the moving dislocation is characterized at low velocity by a condensed solute cloud near and on one side of the dislocation core, a region depleted of solute on the opposite side and a diffuse solute (Cottrell) atmosphere further from the core. At high velocity, no condensed solute cloud forms. The relation between the dislocation velocity and the applied stress shows a low-velocity, solute drag branch and a high-velocity branch, typified by no solute cloud but with occasional solute trapping. At intermediate velocities, the dislocation stochastically jumps between these two branches.

Twinning in thin films-II. Equilibrium microstructures

Abstract We consider the energetics of twinning in misfitting films. While the analysis is general, we consider the case of a misfitting coherent thin film with a cubic crystal structure which transforms to a tetragonal crystal structure on an initially lattice matched cubic substrate; a commonly occurring phase transformation in ferroelectric films. The strain energy change upon twinning, estimated in Paper 1, along with the interfacial energy contributions are incorporated into a thermodynamic analysis of twinning and the equilibrium twinned microstructure is determined as a function of the film thickness, lattice misfit, elastic properties of the film—substrate system, the film surface energy, the film—substrate interface energy and the domain (twin) boundary energy. We develop stability diagrams that examine the role of these parameters in determining the equilibrium microstructure. Our results show that for like variants, a periodic array of domains is always energetically favorable compared to a monovariant film and therefore there is no critical thickness below which the monovariant film is stable. However, the equilibrium wavelength of the twinning microstructure depends on the normalized film thickness as well as the orientation of the domain boundaries with respect to the cubic substrate. Examination of the elastic energy as a function of domain boundary orientation shows that boundaries oriented parallel to the (110) plane of the substrate are preferred. However, (100) oriented boundaries are likely favorable from an interfacial energy viewpoint. The equilibrium wavelength of the microstructure scales as the exponential of the inverse film thickness for small thicknesses, and is either independent of film thickness or proportional to the square root of film thickness at large film thicknesses for the (100) and (110) oriented boundaries, respectively. For the unlike variants case, there is a critical thickness below which the monovariant film is energetically favored. This critical thickness depends on the relative misfit strains, the normalized domain (twin) boundary energy, and the normalized film—substrate interface energy and the normalized surface energies. Finally, we modify this thermodynamic analysis to account for externally applied stress fields and examine their effect on the equilibrium domain structure. Using these results, we derive an expression for the applied stress required to inhibit twinning in these films.

Multilayer film stability

We apply a linear stability analysis to examine the effect of misfit stress on the interface diffusion controlled morphological stability of multilayer microstructures. The stresses could be the result of misfit strains between the individual film layers and/or between film and substrate. We find that misfit between the layers in the film can destabilize the multilayer structure in cases where the thinner layer is elastically stiffer than the thicker layer. The rate at which these instabilities develop increase with increasing misfit and decreasing interfacial energy. Even when there is no misfit between layers, the misfit between the multilayer film and substrate can destabilize the interfaces. This type of instability occurs whether the thinner layers are stiffer or more compliant than the thicker ones. By appropriate choice of the elastic moduli mismatch between layers and relative layer thicknesses, the presence of an interlayer misfit can suppress the instability caused by the substrate misfit. We pr...

Issues associated with the analysis and acquisition of thin-film grain size data

Reliable quantification of microstructural parameters via microscopy is of primary importance for the optimization of materials properties, especially for thin films such as those used in microelectronics or magnetic storage applications. Thus, we present a grain-size analysis for an Al thin-film microstructure consisting of the order of 104 grains for the purpose of examining the predictions of various grain growth models. The microstructural information was acquired with a recently developed automated grain recognition methodology, and the relatively large population obtained here permits a meaningful comparison of tabulated grain-size distributions with those inherent in theoretical models. Finally, we consider the role of grain identification criteria in determining grain-size distributions.