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Register a new userDoubly Degenerate Diffuse Interface Models of Surface Diffusion
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We discuss two doubly degenerate Cahn-Hilliard (DDCH) models for isotropic surface diffusion. Degeneracy is introduced in both the mobility function and a restriction function associated to the chemical potential. Our computational results suggest that the restriction functions yield more accurate approximations of surface diffusion. We consider a slight generalization of a model that has appeared before, which is non-variational, meaning there is no clear energy that is dissipated along the solution trajectories. We also introduce a new variational and, more precisely, energy dissipative model, which can be related to the generalized non-variational model. For both models we use formal matched asymptotics to show the convergence to the sharp interface limit of surface diffusion.
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We extend the doubly degenerate Cahn-Hilliard (DDCH) models for isotropic surface diffusion, which yield more accurate approximations than classical degenerate Cahn-Hilliard (DCH) models, to the anisotropic case. We consider both weak and strong anisotropies and demonstrate the capabilities of the approach for these cases numerically. The proposed model provides a variational and energy dissipative approach for anisotropic surface diffusion, enabling large scale simulations with material-specific parameters.
In solid-state physics, energies of crystals are usually computed with a plane-wave discretization of Kohn-Sham equations. However the presence of Coulomb singularities requires the use of large plane-wave cut-offs to produce accurate numerical results. In this paper, an analysis of the plane-wave convergence of the eigenvalues of periodic linear Hamiltonians with Coulomb potentials using the variational projector-augmented wave (VPAW) method is presented. In the VPAW method, an invertible transformation is applied to the original eigenvalue problem, acting locally in balls centered at the singularities. In this setting, a generalized eigenvalue problem needs to be solved using plane-waves. We show that cusps of the eigenfunctions of the VPAW eigenvalue problem at the positions of the nuclei are significantly reduced. These eigenfunctions have however a higher-order derivative discontinuity at the spheres centered at the nuclei. By balancing both sources of error, we show that the VPAW method can drastically improve the plane-wave convergence of the eigenvalues with a minor additional computational cost. Numerical tests are provided confirming the efficiency of the method to treat Coulomb singularities.
Monolayer FeSe on SrTiO$_3$ superconducts with reported $T_mathrm{c}$ as high as 100 K, but the dramatic interfacial $T_mathrm{c}$ enhancement remains poorly understood. Oxygen vacancies in SrTiO$_3$ are known to enhance the interfacial electron doping, electron-phonon coupling, and superconducting gap, but the detailed mechanism is unclear. Here we apply scanning transmission electron microscopy (STEM) and electron energy loss spectroscopy (EELS) to FeSe/SrTiO$_3$ to image the diffusion of selenium into SrTiO$_3$ to an unexpected depth of several unit cells, consistent with the simultaneously observed depth profile of oxygen vacancies. Our density functional theory (DFT) calculations support the crucial role of oxygen vacancies in facilitating the thermally driven Se diffusion. In contrast to excess Se in the FeSe monolayer or FeSe/SrTiO$_3$ interface that is typically removed during post-growth annealing, the diffused Se remains in the top few unit cells of the SrTiO$_3$ bulk after the extended post-growth annealing that is necessary to achieve superconductivity. Thus the unexpected Se in SrTiO$_3$ may contribute to the interfacial electron doping and electron-phonon coupling that enhance $T_mathrm{c}$, suggesting another important role for oxygen vacancies as facilitators of Se diffusion.
The standard way of modeling plasticity in polycrystals is by using the crystal plasticity model for single crystals in each grain, and imposing suitable traction and slip boundary conditions across grain boundaries. In this fashion, the system is modeled as a collection of boundary-value problems with matching boundary conditions. In this paper, we develop a diffuse-interface crystal plasticity model for polycrystalline materials that results in a single boundary-value problem with a single crystal as the reference configuration. Using a multiplicative decomposition of the deformation gradient into lattice and plastic parts, i.e. F(X,t) = F^L(X,t) F^P(X,t), an initial stress-free polycrystal is constructed by imposing F^L to be a piecewise constant rotation field R^0(X), and F^P = R^0(X)^T, thereby having F(X,0) = I, and zero elastic strain. This model serves as a precursor to higher order crystal plasticity models with grain boundary energy and evolution.
Notched components are commonly used in engineering structures, where stress concentration may easily lead to crack initiation and development. The main goal of this work is to develop a simple numerical method to predict the structural strength and crack-growth-path of U-notched specimens made of brittle materials. For this purpose, the Fragile Points Method (FPM), as previously proposed by the authors, has been augmented by an interface damage model at the interfaces of the FPM domains, to simulate crack initiation and development. The formulations of FPM are based on a discontinuous Galerkin weak form where point-based piece-wise-continuous polynomial test and trial functions are used instead of element-based basis functions. In this work, the numerical fluxes introduced across interior interfaces between subdomains are postulated as the tractions acting on the interface derived from an interface damage model. The interface damage is triggered when the numerical flux reaches the interface strength, and the process of crack-surface separation is governed by the fracture energy. In this way, arbitrary crack initiation and propagation can be naturally simulated without the need for knowing the fracture-patch before-hand. Additionally, a small penalty parameter is sufficient to enforce the weak-form continuity condition before damage initiation, without causing problems such as artificial compliance and numerical ill-conditioning. As validations, the proposed FPM method with the interface damage model is used to predict the structural strength and crack-development from U-notched structures made of brittle materials, which is useful but challenging in engineering structural design practices.
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