Mathematical and computational models for nanostructured coating using electron beam-physical vapor deposition (EB-PVD)

Open Access
Baek, Seungyup
Graduate Program:
Industrial Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
November 20, 2006
Committee Members:
  • Vittaldas V Prabhu, Committee Chair
  • Richard Allen Wysk, Committee Member
  • Robert Carl Voigt, Committee Member
  • Jogender Singh, Committee Member
  • Multiobjective optimization problem
  • Simulation
  • Level set method
  • Nanostructured coating
  • EB-PVD
  • Feedback control
Nanostructured coatings offer substantial improvement over conventional coatings in physical and mechanical properties such as hardness, strength, toughness and thermal conductivity. There are numerous applications where nanostructured coatings have been found to beneficial including bio-mechanical implants, semiconductor thin films, propulsion, and power generation. In aircraft and power generation turbines, nanostructured thermal barrier coating (TBC) can significantly reduce fuel costs. There has been an acute need for a science base, such as dynamic models of nanostructured coating processes. Modeling the processes presents significant challenges because the physical variables are highly coupled and interact in a nonlinear manner. Real-time control of this process poses additional challenges because of the high vacuum, high temperature, and generally hostile environment for making in-situ measurements, which further motivates the need for good process models. This research proposes unified models for controlling nanostructured coating process using electron beam physical vapor deposition (EB-PVD). Specifically, the following three dynamical models have been developed: 1. Machine Dynamics Model – combines models of various component dynamics in the EB-PVD machine such as cathode heating, ingot melting, and evaporation. 2. Deposition Process Model – mathematically characterizes the physical relationship between process parameters and the micro/nanostructure of the coating. 3. Substrate Kinematics Model – geometric models that are computationally efficient for modeling the kinematics of substrate and manipulator motion. One of the main contributions of this work is the use of partial differential equations for the deposition process model to characterize the evolution of the coated surface. This has been used to characterize surface evolution at the macro-level (1 micrometer), at the meso-level (50 nanometers), and with limited fidelity at the nano-level (1 nanometer). The underlying partial differential equations have been solved using numerical techniques on a cluster of computers, and solutions have been found to agree well with experimental results published by independent researchers. A multi-criteria technique has also been developed to determine EB-PVD parameters by solving a optimization problem including four criteria: production cost, process efficiency, coating uniformity, and coating life-time. The technique combines a fuzzy-logic approach with a continuous variable control approach to enable interactive optimization. A simplified model of the EB-PVD process has been developed to relate current input to the EB gun to the coating thickness. This model has been used to design and simulate a real-time PID controller. Simulation results indicate that the controller performs well in terms of disturbance-rejection in input power. The controller requires real-time feedback from quartz-crystal microbalance sensors, which makes it practically feasible and serve as a basis for spatial composition control. Anticipated benefits of this research are the development of a science base for controlling nanostructured coating processes using the EB-PVD through reduced-order mathematical models and efficient computational models. This can be expected to lead to systematically engineered processes with high repeatability and low variance instead of the current “trial and error/recipe-based methods” used in industry. This can be expected to have a significant short-term and long-term impact in several vertical industry sectors including energy, transportation, medical, and semi-conductor.