Dorel Moldovan

Mechanisms of grain growth in nanocrystalline fcc metals by molecular-dynamics simulation.

To elucidate the mechanisms of grain growth in nanocrystalline fcc metals, we have performed fully three-dimensional molecular-dynamics simulations with a columnar grain structure and an average grain diameter of 15 nm. Based on the study of coarse-grained materials, the conventional picture is that grain growth is governed by curvature-driven grain-boundary migration. However, our simulations reveal that in a nanocrystalline material grain rotations play an equally important role, at least during the early stages of grain growth. By eliminating the grain boundary between neighboring grains, such rotations lead to grain coalescence and the consequent formation of highly elongated grains. A detailed analysis exposes an intricate coupling between this mechanism and the conventional grain-boundary-migration dominated mechanism. Incorporation of these insights into mesoscopic models should enable more realistic mesoscopic simulations of grain growth in nanocrystalline materials. (A short movie showing the overall evolution of the grain microstructure can be viewed at http://www.msd.anl.gov/im/movies/graingrowth.html.)

Stress-enhanced grain growth in a nanocrystalline material by molecular-dynamics simulation.

Molecular-dynamics simulations are used to elucidate the coupling between grain growth and grain-boundary diffusion creep in a polycrystal consisting of 25 grains with an average grain size of about 15 nm and a columnar grain shape. Consistent with our earlier simulations of grain-boundary diffusion creep, albeit in the absence of grain growth, we find that initially, i.e. prior to the onset of significant grain growth, the deformation proceeds via the mechanism of Coble creep. Also, consistent with our earlier grain-growth simulations in the absence of stress, two growth mechanisms are observed during the deformation: growth due to curvature-driven GB migration and growth resulting from grain rotation-induced grain coalescence. The comparison of the grain growth observed in the presence of the applied stress with that solely in response to temperature as the driving force enables us to identify the mechanisms by which external stress affects grain growth. In particular, we find that both GB migration and grain rotation are accelerated by the deformation.

Theory of diffusion-accommodated grain rotation in columnar polycrystalline microstructures

Abstract A dynamical theory of grain rotation in columnar polycrystalline microstructures is developed based on the theory of diffusion-accommodated grain-boundary sliding by Raj and Ashby. The driving force for rotation of any given grain is given by the aggregate torque on the grain, i.e., by the weighted sum of the energy derivatives with respect to the misorientations of all the grain boundaries delimiting the grain. Analogous to the Raj–Ashby theory, grain rotation is viewed as a sliding problem on the periphery of the grain; the necessary changes in the grain shape during rotation are assumed to be accommodated by diffusion either through the grain boundaries or through the grain interiors. Our main result is an analytic expression for the rate of rotation of a grain of arbitrary shape as a function of the grain size and temperature. This expression reduces to an earlier result of Harris et al . for the special case of a regular-hexagonal grain shape.

Role of grain rotation during grain growth in a columnar microstructure by mesoscale simulation

We use a mesoscopic simulation approach to study the coupling and competition between grain-boundary-curvature driven and grain-rotation-coalescence induced grain growth in a {l_angle}001{r_angle} textured columnar microstructure. The well-known variational formulation for the total dissipated power, due to Needleman and Rice, provides the formal basis for our two-dimensional simulations. A stochastic velocity Monte-Carlo algorithm is used to minimize the functional in each time step. The competition between grain-boundary migration and grain rotation introduces a physical length scale, Rc, into the system, enabling the growth process to be characterized by two regimes. If the average grain size is smaller than Rc, as is the case in nanocrystalline materials, grain growth is dominated by the grain-rotation-coalescence mechanism. By contrast, if the average grain size is greater than Rc, then growth is dominated by curvature-driven grain-boundary migration. The growth exponents characterizing the power-law time dependence of the average grain size are different for the two growth regimes. An extended von Neumann-Mullins relation, based on averaged grain-boundary properties, is further extended to include the effect of grain rotations.

Combined atomistic and mesoscale simulation of grain growth in nanocrystalline thin films

We have combined molecular-dynamics (MD) simulations with mesoscale simulations to elucidate the mechanism and kinetics of grain growth in nanocrystalline palladium with a columnar grain structure. The conventional picture of grain growth assumes that the process is governed by curvature-driven grain-boundary (GB) migration. Our MD simulations demonstrate that, at least in a nanocrystalline material, grain growth can also be triggered by the coordinated rotations of neighboring grains so as to eliminate the common GB between them. Such rotation-coalescence events result in the formation of highly elongated, unstable grains which then grow via the GB migration mechanism. These insights can be incorporated into mesoscale simulations in which, instead of the atoms, the objects that evolve in space and time are discretized GBs, grain junctions and the grain orientations, with a time scale controlled by that associated with grain rotation and GB migration and with a length scale given by the grain size. These mesoscale simulations, with physical insight and input materials parameters obtained by MD simulation, enable the investigation of the topology and long-time grain-growth behavior in a physically more realistic manner than via mesoscale simulations alone.

Mesoscopic simulation of two-dimensional grain growth with anisotropic grain-boundary properties

Abstract Grain-boundary (GB) properties in a polycrystalline system are generally anisotropic; in particular, both the GB energy and the mobility depend on the GB misorientation. Here the effect of anisotropic GB properties on two- dimensional grain growth is investigated by computer simulation. A stochastic velocity Monte Carlo algorithm based on a variational formulation for the dissipated power is implemented. The simulations show that grain growth leads to an increase in the fraction of small-angle GBs during the growth process. The average grain area is found to grow with a smaller exponent than in a system with isotropic GB properties. An extended von Neumann-Mullins relation based on averaged GB properties is proposed.

Linking atomistic and mesoscale simulations of nanocrystalline materials: quantitative validation for the case of grain growth

Using grain growth in nanocrystalline palladium as a simple case study, we demonstrate how a novel mesoscale approach for simulating microstructural evolution in polycrystalline materials can be validated directly against atomic-level simulations of the same system. We first describe molecular dynamics simulations of grain growth in a columnar model microstructure. The atomic-level insights into the grain-growth mechanism gained from these simulations, particularly in the role of grain rotations, are captured theoretically for incorporation into the mesoscale approach, in which the objects evolving in space and time are the grain boundaries and grain junctions rather than the atoms. With all the input parameters to the mesoscale being physically well defined and obtained directly from the atomic-level simulations, the mesoscale simulations are fully prescribed. We find that the morphology of the mesoscale system evolves in an almost identical manner with that of the molecular dynamics simulation, demonstrating that the length- and time-scale linking has been performed correctly. When applied to systems containing large numbers of grains, the now validated mesoscale simulation approach allows the growth topology and long-time growth kinetics to be determined. As an outlook, we describe how the effects of applied stress can be incorporated.

Grain-boundary diffusion controlled stress concentration in polycrystals.

Mesoscopic simulations are used to elucidate the fundamental effects of microstructural inhomogeneity in polycrystalline materials on grain-boundary diffusion creep (Coble creep). Considering two-dimensional model micro-structures with a distribution in the grain sizes and grain-boundary diffusivities, we determine the stress distribution along the grain boundaries during diffusion creep. Our simulations reveal that two distinct types of microstructural inhomogeneity have similar effects on the diffusion creep. The purely topological inhomogeneities, arising from the presence of the distributions in the grain sizes and grain shapes, cause the larger grains to experience much higher stresses than the smaller grains do. Moreover, even in a topologically uniform microstructure, a distribution in the grain-boundary diffusivities can lead to even higher stress concentrations than those caused by the topological inhomogeneities alone.

Grain Rotation as a Mechanism of Grain Growth in Nanocrystalline Materials

Grain-boundary (GB) properties in a polycrystalline system are generally anisotropic; in particular, both the GB energy and mobility depend on the GB misorientation. Moreover, in nanocrystalline materials, in which the grain size is less than 100 nm, grain rotations leading to the coalescence of neighboring grains via elimination of the common GB between them may provide a new mechanism for grain growth. Here we investigate the combined effect of curvature-driven GB migration and grain-rotation grain-coalescence on the kinetics, topology and morphology of grain growth. A stochastic velocity-Monte-Carlo algorithm based on a variational formulation for the dissipated power is implemented. The presence of both growth mechanisms introduces a physical length scale RC into the system, enabling the growth process to be characterized by two regimes. If the average grain size is smaller than RC, grain growth is dominated by the grain-rotation-coalescence mechanism. By contrast, if the average grain size is greater than RC, growth is dominated by curvature-driven GB migration. The values of the growth exponents, different for the two growth regimes and different from a system with isotropic GB properties, are rationalized in terms of the detailed growth mechanism and the continuous change of the fraction of low-angle GBs in the system. An extended von Neumann-Mullins relation based on averaged GB properties is proposed and verified.

Multiscale simulation of grain growth in nanocrystalline materials

Publisher Summary In this chapter, grain growth is used as a simple case study to illustrate a novel multiscale approach for the simulation of microstructural evolution in poly crystalline materials. By linking atomic-level, mesoscale, and continuum simulation methods, all the relevant length and time scales of the problem are incorporated. For the simple model case of grain growth, it illustrates a rigorous computational and theoretical framework that permits physical insights gained from atomic-level simulations to be transferred into the mesoscale and then linked to the continuum level. This transfer requires quantification of the results of the atomic-level simulations by formulation of a theoretical model. This then enables examination of the statistical mechanics of the process in a realistic system. It describes the way the effects of applied stress are incorporated into multiscale approach. By meshing the grain interiors in a way that the grain-interior nodes link up with the already discretized grain-boundary (GBs) and grain junctions delimiting each grain, the inhomogeneous stress distribution arising from some externally applied stress can be computed using the finite-element approach. In an elastically anisotropic system, these stresses provide a driving force for GB migration, in addition to or acting against the driving force because of the GB curvature.