A continuum field theory approach is presented for modeling elastic and plastic deformation, free surfaces, and multiple crystal orientations in nonequilibrium processing phenomena. Many basic properties of the model are calculated analytically, and numerical simulations are presented for a number of important applications including, epitaxial growth, material hardness, grain growth, reconstructive phase transitions, and crack propagation.

A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to time scales much larger than conventional atomic methods. The model is shown to be consistent with the predictions of Read and Shockley for grain boundary energy, and Matthews and Blakeslee for misfit dislocations in epitaxial growth. DOI: 10.1103/PhysRevLett.88.245701 PACS numbers: 64.60.Cn, 05.70.Ln, 64.60.My, 81.30.Hd The appearance and growth of crystal phases occurs in many technologically important processes including epitaxial growth and zone refinement. While a plethora of models have been constructed to examine various aspects of these phenomena, it has proven difficult to develop a computationally efficient model that can be used for a wide range of applications. For example, standard molecular dynamics simulations include the necessary physics but are limited by atomic sizes (Å) and phonon time scales (ps). Conversely, continuum field theories can access longer length (i.e., correlation length) and time (i.e., diffusive) scales, but are difficult to incorporate with the appropriate physics. In this paper a new model is presented that includes the essential physics and is not limited by atomic time scales.To illustrate the features that must be incorporated, it is useful to consider two examples. First, consider the nucleation and growth of crystals from a pure supercooled liquid or vapor phase. In such a process, small crystallites nucleate (heterogeneously or homogeneously) and grow in arbitrary locations and orientations. Eventually, the crystallites impinge on one another and grain boundaries are formed. Further growth is then determined by the evolution of grain boundaries. Now consider the growth of a thin crystal film on a substrate of a different crystal structure. The substrate stresses the overlying film which can destabilize the growing film and cause an elastic defect-free morphological deformation [1,2], plastic deformation involving misfit dislocations [3], or a combination of both. Thus, the model must be able to nucleate crystallites at arbitrary locations and orientations and contain elastic and plastic deformations. While all these features are naturally incorporated in atomistic descriptions, they are much more difficult to include in continuum or phase field models.Historically, many continuum models have been developed to describe certain aspects of crystal growth and liquid/solid transitions in general. At the simplest level, "model A" in the Halperin and Hohenberg [4] classification scheme has been used to describe liquid/solid transitions. This model treats all solids equivalently and does not introduce any crystal anisotropy. Extensions to this basic model have been developed to incorporate a solid phase that has multiple states that represent multiple orientations [5,6] or, recently [7], an infinite number of orientations. Unfortunately, these models ...

In this paper the relationship between the classical density functional theory of freezing and phase-field modeling is examined. More specifically a connection is made between the correlation functions that enter density functional theory and the free energy functionals used in phase-field crystal modeling and standard models of binary alloys ͑i.e., regular solution model͒. To demonstrate the properties of the phase-field crystal formalism a simple model of binary alloy crystallization is derived and shown to simultaneously model solidification, phase segregation, grain growth, elastic and plastic deformations in anisotropic systems with multiple crystal orientations on diffusive time scales.

We model friction acting on the tip of an atomic force microscope as it is dragged across a surface at nonzero temperatures. We find that stick-slip motion occurs and that the average frictional force follows jlnyj 2͞3 , where y is the tip velocity. This compares well to recent experimental work, permitting the quantitative extraction of all microscopic parameters. We calculate the scaled form of the average frictional force's dependence on both temperature and tip speed as well as the form of the friction-force distribution function.

A theoretical approach to the Ostwald ripening of droplets is presented in dimension D_2. A mean-field theory is constructed to incorporate screening effects in the competing many-droplet system. The mean-field equations are solved to infinite order in the volume fraction and provide analytic expressions for the coarsening rate, the time-dependent droplet-distribution function, and the time evolution of the total number of droplets. These results are in good agreement with experiments in three dimensions and with a very large scale and extensive numerical study in both two and three dimensions presented in this paper. The numerical study also provides the time evolution of the structure factors, which scale with the only length scale, the average droplet radius