Combining phase field crystal methods with a Cahn-Hilliard model for binary alloys

During phase transitions certain properties of a material change, such as composition field and lattice-symmetry distortions. These changes are typically coupled, and affect the microstructures that form in materials. Here, we propose a 2D theoretical framework that couples a Cahn-Hilliard (CH) model describing the composition field of a material system, with a phase field crystal (PFC) model describing its underlying microscopic configurations. We couple the two continuum models via coordinate transformation coefficients. We introduce the transformation coefficients in the PFC method, to describe affine lattice deformations. These transformation coefficients are modeled as functions of the composition field. Using this coupled approach, we explore the effects of coarse-grained lattice symmetry and distortions on a phase transition process. In this paper, we demonstrate the working of the CH-PFC model through three representative examples: First, we describe base cases with hexagonal and square lattice symmetries for two composition fields. Next, we illustrate how the CH-PFC method interpolates lattice symmetry across a diffuse composition phase boundary. Finally, we compute a Cahn-Hilliard type of diffusion and model the accompanying changes to lattice symmetry during a phase transition process.Comment: 9 pages, 5 figure

Religious Roots for the Puritan Morality Laws During the Interregnum

During the decade of the 1650s, England had no King or Queen. Instead, an increasingly monarchical parliamentary system of government reigned. This government was controlled by Puritans, a hardline sect of Protestant Christianity. Although they were a religious minority and their laws relating to morality were unpopular, the Puritans pursued this policies with religious zeal linking seemingly innocuous activities, such as cock-fighting or a may-pole celebration with the supposed evils of Catholicism. Legal documents such as “March 1654: An Ordinance for prohibiting Cock-matches” and..

Modeling Grain Boundaries using a Phase Field Technique

We propose a two dimensional frame-invariant phase field model of grain impingement and coarsening. One dimensional analytical solutions for a stable grain boundary in a bicrystal are obtained, and equilibrium energies are computed. We are able to calculate the rotation rate for a free grain between two grains of fixed orientation. For a particular choice of functional dependencies in the model the grain boundary energy takes the same analytic form as the microscopic (dislocation) model of Read and Shockley.Comment: 4 pages, 2 figure

Li-diffusion accelerates grain growth in intercalation electrodes: a phase-field study

Grain boundary migration is driven by the boundary's curvature and external loads such as temperature and stress. In intercalation electrodes an additional driving force results from Li-diffusion. That is, Li-intercalation induces volume expansion of the host-electrode, which is stored as elastic energy in the system. This stored energy is hypothesized as an additional driving force for grain boundaries and edge dislocations. Here, we apply the 2D Cahn-Hilliard$-$phase-field-crystal (CH-PFC) model to investigate the coupled interactions between highly mobile Li-ions and host-electrode lattice structure, during an electrochemical cycle. We use a polycrystalline FePO$_{4}$/ LiFePO$_{4}$ electrode particle as a model system. We compute grain growth in the FePO$_{4}$ electrode in two parallel studies: In the first study, we electrochemically cycle the electrode and calculate Li-diffusion assisted grain growth. In the second study, we do not cycle the electrode and calculate the curvature-driven grain growth. External loads, such as temperature and stress, did not differ across studies. We find the mean grain-size increases by $\sim11\%$ in the electrochemically cycled electrode particle. By contrast, in the absence of electrochemical cycling, we find the mean grain-size increases by $\sim2\%$ in the electrode particle. These CH-PFC computations suggest that Li-intercalation accelerates grain-boundary migration in the host-electrode particle. The CH-PFC simulations provide atomistic insights on diffusion-induced grain-boundary migration, edge dislocation movement and triple-junction drag-effect in the host-electrode microstructure.Comment: 11 pages, 9 figure

Red Bean Monday

The process of filmmaking starts with an idea and is brought forth to reality through a collaborative effort. This paper will include the process of producing a film through each step from the conception to completion of my thesis film “Red Bean Monday.” I will thoroughly discuss the writing, producing, cinematography, directing, editing, sound, technology, and workflow. I will also discuss things I have learned as a filmmaker through the successes and failures that I determined based on surveys from audience participation

Red Bean Monday

The process of filmmaking starts with an idea and is brought forth to reality through a collaborative effort. This paper will include the process of producing a film through each step from the conception to completion of my thesis film “Red Bean Monday.” I will thoroughly discuss the writing, producing, cinematography, directing, editing, sound, technology, and workflow. I will also discuss things I have learned as a filmmaker through the successes and failures that I determined based on surveys from audience participation

\u27To The Dishonor of God\u27: Religious Roots for Puritan Morality Laws During the Interregnum

During the decade of the 1650s, England had no King or Queen. Instead, an increasingly monarchical parliamentary system of government reigned. This government was controlled by Puritans, a hardline sect of Protestant Christianity. Although they were a religious minority and their laws relating to morality were unpopular, the Puritans pursued these policies with religious zeal linking seemingly innocuous activities, such as cock-fighting or a may-pole celebration with the supposed evils of Catholicism. Legal documents such as “March 1654: An Ordinance for prohibiting Cock-matches” and “June 1657: An Act for the better observation of the Lord’s Day” ban activities based on associations with drinking and gambling, and then in a speech by Oliver Cromwell (1564), those activities are linked with Catholicism. This demonstrates the integral role religious thought played in Puritan laws. This project is the study of how one group with a radical vision of society used language to link domestic and foreign policy to Godliness and sin, despite a lack of popular support or resulting political gain

Economic and Environmental Impacts of Adoption of Genetically Modified Rice in California

Crop Production/Industries, Research and Development/Tech Change/Emerging Technologies,

Thermodynamic phase-field model for microstructure with multiple components and phases: the possibility of metastable phases

A diffuse-interface model for microstructure with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and formalized within a variational framework. The model includes a composition gradient energy to capture solute trapping, and is therefore suited for studying phenomena where the width of the interface plays an important role. Derivation of the inhomogeneous free energy functional from a Taylor expansion of homogeneous free energy reveals how the interfacial properties of each component and phase may be specified under a mass constraint. A diffusion potential for components was defined away from the dilute solution limit, and a multi-obstacle barrier function was used to constrain phase fractions. The model was used to simulate solidification via nucleation, premelting at phase boundaries and triple junctions, the intrinsic instability of small particles, and solutal melting resulting from differing diffusivities in solid and liquid. The shape of metastable free energy surfaces is found to play an important role in microstructure evolution and may explain why some systems premelt at phase boundaries and phase triple junctions while others do not.Comment: 14 pages, 8 figure