Simulation of Metal Electrodeposition Using the Kinetic Monte Carlo and Embedded-Atom Methods

The effects of the microstructure of metal films on electric component performance and longevity have become increasingly important with the recent advances in nanotechnology. Depending on the application of the metal films and interconnects, certain microscopic structures and properties are preferred over others. A common method to produce these films and interconnects is through electrodeposition. As with every process, the ability to control the end product requires a detailed understanding of the system and the effect of operating conditions on the resulting product. To address this problem, a three-dimensional on-lattice kinetic Monte Carlo (KMC) method is developed to conduct atomistic simulations of single crystal and polycrystalline metal electrodeposition. The method utilizes the semi-empirical multi-body embedded-atom method (EAM) potential that accounts for the cohesive forces in a metallic system. The resulting computational method, KMC-EAM, enables highly descriptive simulations of electrodeposition processes to be performed over experimentally relevant scales. In this work, kinetically controlled copper electrodeposition onto single crystal copper under galvanostatic direct-current conditions and polycrystalline copper under potentiostatic direct-current conditions is modelled using the aforementioned KMC method. Four types of surface processes are considered during electrodeposition: deposition, dissolution, surface diffusion and grain boundary diffusion. The equilibrium microstructures from single crystal experiments were validated using molecular dynamics (MD) simulations through the comparison of energy per atom and average coordination number. The growth mode observed is in agreement with experimental results for the same orientation of copper. MD simulation relaxes constraints and approximations resulting from the use of KMC. Results indicate that collective diffusion mechanisms are essential in order to accurately model the evolution of coating morphology during electrodeposition. In the polycrystalline simulations, the effect of surface energy is taken into account in the propensities of deposition and dissolution. Sub-surface grain volume measurements were obtained from simulation results and the grain volume evolution with time is in agreement with both qualitative observations based on the deposit morphology and surface energy calculations. Simulations of polycrystalline deposition agree with findings from experimental studies that the evolution of the root-mean-squared roughness of the deposit during the early stages of deposition follows a power law relationship with respect to time $\approx t^{n}$. Furthermore, the power law exponent on time is determined to be $n \approx 0.5$, also in agreement with the experimental values reported in the literature

Diffuse Solid-Fluid Interface Method for Dispersed Multiphase Flows

Industrial chemical engineering processes such as bubble columns, reactors and separators involve multiphase flows of two or more fluids. In order to improve the design and operation of these processes, an understanding of their multiphase hydrodynamics is essential. An emergent tool in studying multiphase flow systems that is becoming readily accessible to researchers is computational fluid dynamics (CFD) simulation. CFD simulations of multiphase flow systems enable researchers to explore the effect of different combinations of operating conditions and designs on pressure drop, separation efficiency, and heat and mass transfer without the cost and safety issues incurred by experimental design and pilot studies. Consequently, CFD simulations are increasingly relevant for the design and optimization of chemical process equipment. The multiphase hydrodynamic model that is often used to study chemical engineering processes is the two-fluid (Euler-Euler) model. In this model, the fluids are treated as inter-penetrating continua and fluid phase fractions are used to describe the average spatial composition of the multiphase fluid. Generally, the physical boundaries (e.g. vessel walls, reactor internals, \textit{etc.}) in numerical simulations using the two-fluid model are defined by the mesh or grid, i.e. the mesh/grid boundaries correspond to an approximation of the physical boundaries of the system. The resulting conformal mesh/grid could potentially contain a large number of skewed elements, which is undesirable in numerical simulations. One approach to address this issue involves approximation of solid boundaries using a diffuse solid-fluid interface approximation. This approach allows for a structured mesh to be used while still capturing the desired solid-fluid boundaries. The diffuse-interface method also allows for the simulation of moving boundaries without the need for manipulation of the underlying mesh/grid or interpolation of boundary variables to the nearest node. This allows for the geometry of the domain of interest (i.e. process equipment) to be easily modified during the process of simulation-assisted design and optimization. In the two-fluid model, phase fractions are used to describe the composition of the mixture and are bounded quantities. Consequently, numerical solution methods used in simulations must preserve boundedness for accuracy and physical fidelity. Firstly, a phase-bounded numerical method for the two-fluid model is developed in which phase fraction inequality constraints are imposed through the use of an implicit variational nonlinear inequality solver. The numerical method is verified and compared to an established explicit numerical method. The effect of using separate phasic pressure fields as opposed to the commonly used single-pressure assumption is also found to be non-negligible in dilute dispersed flows (less than 3% gas fraction). Subsequently, the phase-bounded numerical method is extended to support a diffuse-interface method for the imposition of solid-fluid boundaries. The diffuse-interface is used to define physical boundaries and boundary conditions are imposed by blending conservation equations from the two-fluid model with the solid boundary condition. Simulations of two-dimensional channel flow and flow past a stationary cylinder are used to validate the diffuse-interface method. This is achieved by comparing the bubble plume width and time evolution of the overall gas hold-up from the diffuse-interface simulations with results obtained using boundary-conformal meshes. The results from the channel flow simulations are found to be in agreement with the boundary-conformal mesh solution when the interface width is sufficiently small. In the case of flow past a stationary cylinder, similar flow features are observed in both diffuse-interface and reference simulations

On the use of physical boundary conditions for two-phase flow simulations: Integration of control feedback

The final publication is available at Elsevier via https://dx.doi.org/10.1016/j.compchemeng.2018.08.012 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/The sensitivity of two-phase flow simulations using the Euler–Euler model on the inlet boundary conditions (BCs) is studied. Specifically, the physical relevance of Dirichlet uniform inlet velocity BCs is studied which are widely used due their simplicity and the lack of a priori knowledge of the slip velocity between the phases. It is found that flow patterns obtained with the more physically realistic uniform inlet pressure BCs are radically different from the results obtained with Dirichlet inlet velocity BCs, refuting the argument frequently put forward that Dirichlet uniform inlet velocity BCs can be interchangeably used because the terminal slip velocity is reached after a short entrance region. A comparison with experimental data is performed to assess the relevance of the flows obtained numerically. Additionally, a multivariable feedback control method is demonstrated to be ideal for enforcing desired flow rates for simulations using pressure BCs.Natural Sciences and Engineering Research Council of Canad

Diffuse-interface blended method for the imposition of physical boundaries in two-fluid flows

Multiphase flows are commonly found in chemical engineering processes such as distillation columns, bubble columns, fluidized beds and heat exchangers. Physical boundaries in numerical simulations of multiphase flows are generally defined by a mesh that conforms to the physical boundaries of the system. Depending on the complexity of the physical system, generating the conformal mesh can be time-consuming and the resulting mesh could potentially contain a large number of skewed elements, which is undesirable. The diffuse-interface approach allows for a structured mesh to be used while still capturing the desired solid-fluid boundaries. In this work, a diffuse-interface method for the imposition of physical boundaries is developed for two-fluid incompressible flow systems. The diffuse-interface is used to define the physical boundaries and the boundary conditions are imposed by blending the conservation equations from the two-fluid model with that of the solid. The results from the diffuse-interface method and mesh-defined boundaries are found to be in good agreement at small diffuse-interface widths.Comment: Submitted to International Journal of Multiphase Flo