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.

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We examine the influence of different forms of the free-energy functionals used in the phase-field-crystal ͑PFC͒ model, and compare them with the second-order density-functional theory ͑DFT͒ of freezing, by using bcc iron as an example case. We show that there are large differences between the PFC and the DFT and it is difficult to obtain reasonable parameters for existing PFC models directly from the DFT. Therefore, we propose a way of expanding the correlation function in terms of gradients that allows us to incorporate the bulk modulus of the liquid as an additional parameter in the theory. We show that this functional reproduces reasonable values for both bulk and surface properties of bcc iron, and therefore it should be useful in modeling bcc materials. As a further demonstration, we also calculate the grain boundary energy as a function of misorientation for a symmetric tilt boundary close to the melting transition.