Application of ring statistics to characterise graphitisation of carbon fiber heat shields under atmospheric re-entry conditions

Sammanfattning: Carbon fibers submitted to high temperatures (>2000 °C) experience a permanent increasein their thermal conductivity. This change has been attributed to a change in the molecularstructure due to graphitisation. Graphitisation occurs when amorphous carbons are exposed tohigh temperatures (> 1000°C) for a prolonged period of time and describes the process in whichcarbon atoms are rearranged from their amorphous form into structured hexagonal ringed latticesheets. To characterise the extent of this process, one needs to determine certain ring statisticswhich provide information on the bonding structure. In this work, we develop and verify a ringstatistics tool that can be used to analyze the resulting structure of atomistic simulations, and useit in a novel approach to characterise the extent of graphitisation in Molecular Dynamics (MD)simulations of carbon. Different ring definitions, such as Franzblau, Leroux, Hybrid and King arecompared to determine the most appropriate definition for the investigation of carbon structures.A new ring definition, Hybrid, is introduced as an extension of Leroux’s definition, exploiting theefficiency of Leroux’s definition while making the definition more appropriate for carbon systemsby removing shortcuts of length 1. It was found that Franzblau rings most accurately capturecarbon structures, and are most optimal for the investigation of amorphous and graphitisedcarbons. We then apply this tool to two MD simulations of amorphous carbons undergoing anannealing process at 4000K for 300 ps to characterise the extent of graphitisation. We found aprevalence of ∼0.1 hexagonal rings per atom in amorphous carbons prior to annealing, comparedto ∼0.33 hexagonal rings per atom in graphitised carbon after annealing. The likelihood of a ringbeing hexagonal in amorphous carbon was ∼30%, as opposed to ∼75% in graphitised samples.Calculating the ratio in the number of hexagonal rings per atom to the number of hexagonalrings per atom in a fully graphitised system, the extent of graphitisation can be quantified. Sincethis value is normalized by the number of atoms in the simulation this method can be appliedto any domain size. This successful application of the ring statistics tool opens the door toapply it to more realistic and complex systems. The tool has already been expanded to considermulti-component systems and molecule identification. Hence, the tool could already be appliedto more complex cases, such as doped or contaminated systems, investigating the effects on bondstructure. In its current state, the tool could also be used to investigate how the extent andrate of graphitisation changes at different depths in a system. Potentially characterising therate at which graphitisation penetrates a system under various conditions. The tool also hasthe potential to be expanded to consider localisation and identification of defects, bond angles,bond creation and destruction and the structural classification and identification of systems.Combining this tool with MDSuite, a software in development by the Institute for ComputationalPhysics (ICP) at the University of Stuttgart with the collaboration of the von Karman Institutefor Fluid Dynamics (VKI) to analyse MD trajectories, could offer a package that can providedeep system information for minimal cost.