Phase-Field Crystal Model Development

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The phase-field crystal (PFC) model is an exciting new method for simulating crystalline materials with atomic resolution over diffusional time scales. Unfortunately, applications of the model have been severely limited by the requirement that novel free energies must be constructed for each new material of interest. This thesis describes three different methods by which the basic PFC model has been extended to simulate additional materials and also demonstrates that these new models capture some of the physics of real materials.', 'The first extension is the development of a PFC model for a multicomponent ordered crystal. As a test case, a generic B2 compound is investigated. This model produces a line of either first-order or second-order order-disorder phase transitions, depending on parameters. This B2 model is then used to study antiphase boundaries (APBs), which are shown to reproduce classical mean field behavior. Lastly, we found through dynamical simulations of ordering across small-angle grain boundaries that the model predicts that dislocation cores pin the evolution of APBs.', 'The second extension is a method that, utilizing a numerically tractable three-point correlation function, creates an array of new complex three- and two-dimensional crystal structures. The three-point correlation function is designed in order to energetically favor the principal interplanar angles of a target crystal structure. This is achieved via an analysis performed by examining the crystal’s structure factor. This approach successfully yields energetically stable simple cubic, diamond cubic, simple hexagonal, graphene layers, and CaF2 crystals. To illustrate the ability of the method to yield a particularly complex and technologically important crystal structure, this three-point correlation function method is used to generate perovskite crystals.', 'The last extension is for a two-component PFC model that undergoes displacive phase transitions. When the intercomponent free energy in the model is a simple polynomial, the crystal undergoes displacive transitions in <10> and <11> directions. When the interaction is a correlation function however, displacements in any direction can occur. This displacive phase-field crystal (DPFC) model also maps to Landau-Ginzburg-Devonshire (LGD) theories for ferroelectrics, and the DPFC and LGD models are compared in terms of phase transitions and domain walls. The DPFC model also displays stable quadrijunctions and pinning of domain wall evolution by dislocation cores.

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  • 10/28/2019
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