Workforce of the Future:

1. DEVCOM Army Research Laboratory, Aberdeen Proving Ground, MD 21005, United States
2. Applied Research Laboratory, The Pennsylvania State University, University Park, PA 16802, United States

As a result of their high melting temperatures, high thermal conductivities, low thermal expansion, and strong oxidation resistance, ultra-high temperature ceramics (UHTC) are materials of considerable interest in the area of aero-propulsion.^1–4 These qualities also make them promising materials for hypersonic flight applications. Transition metal carbides and borides are well-suited for use as leading edge materials, which will be necessary to increase efficiency and stability of aircraft in the future.³ These material qualities can be further improved by integrating SiC into composites to make ultra-high temperature ceramic matrix composites (UHTCMC)^2,3,5,6.

The chemical reactions that occur at the surfaces of UHTCMC have parabolic kinetics at high temperatures, and these reactions are generally distinct from those that take place at low temperatures.^3,7 The systems in question are mostly unreactive at their typical operating temperatures (e.g., below 1,500 °C to 1,800 °C). However, at high temperatures, a tremendous amount of thermal energy is applied to the systems which reduces the energy barriers for unfavorable reaction kinetics.^4,5,7 The propensity of these materials to oxidize at necessary high operating temperatures is regarded as the primary impediment in the research and development of these materials for aero-propulsion, and is the primary contributor to the lack of progress in developing new materials for these applications. This phenomenon is particularly common in composite systems which incorporate both ionic and covalent bonds, or if the melting points of the various components in the system vary much from one another. It is hypothesized that the physical chemistry at the oxidation site and the transport of the reactants to this site are crucial to the oxidation behavior of these materials.^1,6,7 Furthermore, this project’s goal is to create an atomistic ablative model to better comprehend the thermal and mechanical features of the UHTCMC environment. This will be done by studying the causes of SiC ablation failure under harsh conditions of hypersonic flight with the goal of improving performance and extending UHTC lifespan.

Classical molecular dynamics (MD) simulations were performed to determine the thermomechanical and oxidation properties of the UHTC. These atomic simulations were run using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) code developed at Sandia National Laboratory.⁸ Newton’s equation of motion was used in the MD simulations to track the atomic-level dynamics of a system through time. In order to carry out and comprehend the oxidation processes of the UHTC using MD, the interatomic potential used must allow for charge transfer and the formation of new species; thus, a reactive interatomic potential is required.⁹ To accomplish this, the ReaxFF interatomic potential and charge equilibration, already implemented in the LAMMPS source code, were used. The ReaxFF potential energy of the system is depicted in the following simplified equation of the atoms with physical bonds, non-bonded interacting atoms, and the charge transfer scheme.^9,10

Polycrystalline SiC surfaces were exposed to oxidation at high temperatures and pressures in these MD simulations. From these simulations, the initial molecular species that ablate from the oxidized polycrystalline SiC surface were depicted. The temperature of hypersonic environments in the MD simulations was controlled with a Langevin thermostat with a timestep of 0.25 femtoseconds.^11,12 Using these simulations, the initial oxidation and ablation behavior for the deposition of molecular and atomic oxygen onto the surface of the polycrystalline SiC was predicted. In the model, the system was brought from 3 Bar to 30 Bar as the simulation environment was heated from 26 C to 1726 C. Atomic and molecular oxygen were then added to the simulation with an initial velocity of Mach 10 which was quickly decreased to Mach 0.1 by the shock boundary layer where oxidation of the SiC surface occurs. If the oxidized species formed moves to the top of the simulation box, the atoms are deleted from the simulation to represent species being ablated from the surface. The atoms at the bottom of the simulation box are kept fixed while the rest of the atoms are under a thermostat (Figure 1). In these simulations, the rates of oxidation of different SiC grain surfaces and grain boundaries can be predicted, which will help reduce the number of experimental oxidation tests needed. Polyhedral Template Mapping was used in conjunction with coordination analysis to systematically identify hexagonal bulk crystal structures from grain boundaries and defective areas (Figure 1). Visualization for the MD simulations was done using the OVITO code.¹³

Figure 1 – Visual image of the initial MD simulation for the polycrystalline SiC, with color coordinated atoms. Polyhedral template mapping was used to depict the individual grains and grain boundaries. The rightmost image depicts the initial MD simulation build and indicates which atoms were thermostat and which were kept fixed during the simulation to stabilize the potential energy of the system.

Through classical MD simulations, the oxidization of α-SiC was observed for polycrystalline structures. An illustration of the initial oxidization of the α-SiC is shown in Figure 2. As oxygen atoms collide with the α-SiC surface in the shock boundary layer of the hypersonic environments, a new active oxide film is formed. The oxidation of polycrystalline α-SiC may be broken down into three stages, first the oxidation of the unordered grain boundary α-SiC surfaces, then the oxidation of the surface terminations, and lastly oxygen diffusion through the SiO2 layer occurs. Segregation of SiO and C rich regions was observed in the oxide layer. There was also an increase in the oxide layer thickness on the α-SiC surface as the simulation pressure and temperature increased.

These simulations allowed us to predict the ablation behavior of individual molecules of SiO₃, CO, CO₂, C₂O₂, and C₂O₃ as they evaporated from the surface of the polycrystalline a-SiC (Figures 3 and 4). These simulations will allow for future in-depth examination of UHTC oxidation behaviors to better comprehend the peculiar parabolic reaction kinetics that occur in such severe settings.^2,3,7

Figure 2 – MD simulation with the initial atomic oxidation of the hypersonic environment.

Figure 3 – Visual depiction of the ablation of CO, CO₂, C₂O₂, and C₂O₃ molecules during the oxidation of polycrystalline a-SiC. A pressure of 30 Bar and a temperature of 1726 °C were used in the simulation.

Figure 4 – Visual depiction of the ablation of SiO₃, CO, CO₂, and C₂O₂ molecules during the oxidation of polycrystalline a-SiC. A pressure of 30 Bar and a temperature of 1526 °C were used in the simulation.

The purpose of the next generation of high temperature propulsion material systems is to provide our military with strong overmatch capability for operation in all extreme environmental conditions. In this work, the ReaxFF interatomic potential was used to develop a fundamental kinetic model to understand the atomistic ablation of UHTC in hypersonic conditions. Using structural characterization and kinetic modelling, we predict the production of a silicon oxide layer on the surface of α-SiC and its structure in hypersonic environments. The ablation of SiO₃, CO, CO₂, C₂O₂, and C₂O₃ molecules from the α-SiC surface is also predicted at different temperatures.

Further investigation of traditional UHTC compositions is needed to better understand their thermomechanical properties regarding oxidization resistance in extreme environments. Next steps include the oxidation of additional transition metal carbides and borides as the current interatomic potentials developed for other possible UHTC are non reactive, which does not allow for charge transfer as is required for oxidation simulations. The ReaxFF interatomic potential must be parameterized for the remaining components in the target systems before oxide simulations can be run. To verify the new interatomic potentials for the new systems, density functional theory (DFT) computations must be performed. These calculations will be used to determine defect energies, formation energies, the equations of state for volume relaxations, adsorption energies, and the mechanical properties of the individual and composite systems. This will allow researchers to examine the effects of chemical bonding, defect density, composition, microstruture, and other factors on the oxidation behaviors of UHTC and UHTCMC.

The authors acknowledge financial support from the US Army Research Laboratory, the DOD High-Performance Computing Modernization Program (HPCMP), and the HPC Internship Program (HIP). The computations were run on the Narwhal supercomputer, which was kindly provided by the Department of Navy Research and Development Center. Dr. Slapikas would like to thank his advisors at the Army Research Laboratory, especially Drs. Ghoshal, Bravo, Murugan, and McGowan, for helping learn and grow professionally and academically during this project. He would also like to give thanks to Dr. Douglas Wolfe, his Ph.D. adviser at Penn State, for helping refine the simulations and his mentorship in the laboratory.

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