Jonathan E. Guyer

FiPy: Partial Differential Equations with Python

Many existing partial differential equation solver packages focus on the important, but arcane, task of numerically solving the linearized set of algebraic equations that result from discretizing a set of PDEs. Many researchers, however, need something higher level than that.

Phase field modeling of electrochemistry. I. Equilibrium

A diffuse interface (phase field) model for an electrochemical system is developed. We describe the minimal set of components needed to model an electrochemical interface and present a variational derivation of the governing equations. With a simple set of assumptions: mass and volume constraints, Poissons equation, ideal solution thermodynamics in the bulk, and a simple description of the competing energies in the interface, the model captures the charge separation associated with the equilibrium double layer at the electrochemical interface. The decay of the electrostatic potential in the electrolyte agrees with the classical Gouy-Chapman and Debye-Hückel theories. We calculate the surface free energy, surface charge, and differential capacitance as functions of potential and find qualitative agreement between the model and existing theories and experiments. In particular, the differential capacitance curves exhibit complex shapes with multiple extrema, as exhibited in many electrochemical systems.

Morphological stability and compositional uniformity of alloy thin films

Abstract Alloy thin films differ from pure materials in two respects: the alloy components may be prone to phase separation and the lattice parameter of the film is generally a function of the alloy composition. Both of these characteristics affect the compositional uniformity of the film, which has implications for the films mechanical and opto-electronic properties. To explore these phenomena, we present a linear stability analysis of alloy film growth, which accounts for the stresses generated by both film–substrate misfit and compositional nonuniformities. We find that, when compositional stresses are considered, an instability can be present and that this instability is generic to alloy crystal growth. This instability is due to the deposition process, along with compositionally generated stresses, and occurs even in the absence of a film–substrate misfit. We compare our predictions to other related models and to the experimental literature.

Application of Finite Element, Phase-field, and CALPHAD-based Methods to Additive Manufacturing of Ni-based Superalloys

Numerical simulations are used in this work to investigate aspects of microstructure and microseg-regation during rapid solidification of a Ni-based superalloy in a laser powder bed fusion additive manufacturing process. Thermal modeling by finite element analysis simulates the laser melt pool, with surface temperatures in agreement with in situ thermographic measurements on Inconel 625. Geometric and thermal features of the simulated melt pools are extracted and used in subsequent mesoscale simulations. Solidification in the melt pool is simulated on two length scales. For the multicomponent alloy Inconel 625, microsegregation between dendrite arms is calculated using the Scheil-Gulliver solidification model and DICTRA software. Phase-field simulations, using Ni-Nb as a binary analogue to Inconel 625, produced microstructures with primary cellular/dendritic arm spacings in agreement with measured spacings in experimentally observed microstructures and a lesser extent of microsegregation than predicted by DICTRA simulations. The composition profiles are used to compare thermodynamic driving forces for nucleation against experimentally observed precipitates identified by electron and X-ray diffraction analyses. Our analysis lists the precipitates that may form from FCC phase of enriched interdendritic compositions and compares these against experimentally observed phases from 1 h heat treatments at two temperatures: stress relief at 1143 K (870 °C) or homogenization at 1423 K (1150 °C).

Diffusion under temperature gradient: A phase-field model study

A diffuse interface model was devised and employed to investigate the effect of thermotransport (a.k.a., thermomigration) process in single-phase and two-phase alloys of a binary system. Simulation results show that an applied temperature gradient can cause significant redistribution of constituent elements and phases in the alloy. The magnitude and the direction of the redistribution depend on the initial composition, the atomic mobility and the heat of transport of the respective elements. In two-phase alloys, the thermomigration effect can cause the formation of single-element rich phases at the cold and hot ends of the alloy (i.e., demixing).

Computation of the Kirkendall velocity and displacement fields in a one-dimensional binary diffusion couple with a moving interface

The moving interface problem in a one-dimensional binary α/β diffusion couple is studied using sharp and diffuse interface (Cahn–Hilliard) approaches. With both methods, we calculate the solute field and the Kirkendall marker velocity and displacement fields. In the sharp interface treatment, the velocity field is generally discontinuous at the interphase boundary, but can be integrated to obtain a displacement field that is continuous everywhere. The diffuse interface approach avoids this discontinuity, simplifies the integration and yet gives the same qualitative behaviour. Special features observed experimentally and reported in the literature are also studied with the two methods: (i) multiple Kirkendall planes, where markers placed on the initial compositional discontinuity of the diffusion couple bifurcate into two locations, and (ii) a Kirkendall plane that coincides with the interphase interface. These situations occur with special values of the interdiffusion coefficients and starting couple compositions. The details of the deformation in these special situations are given using both methods and are discussed in terms of the stress-free strain rate associated with the Kirkendall effect.

On the primary spacing and microsegregation of cellular dendrites in laser deposited Ni-Nb alloys

In this study, an alloy phase-field model is used to simulate solidification microstructures at different locations within a solidified molten pool. The temperature gradient

Benchmark problems for numerical implementations of phase field models

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Three dimensionally structured interdigitated back contact thin film heterojunction solar cells

and the solidification velocity

Windowless CdSe/CdTe solar cells with differentiated back contacts: J-V, EQE, and photocurrent mapping.

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