1. The 15th Annual Spring Meeting of the NASA-Missouri Space Grant Consortium Faceted Carbon and Coherence Effects in Presolar Graphenes Eric Mandell University of Missouri – St. Louis Advisor: Dr. Phil Fraundorf

2. I would like to thank: Dr. Phil Fraundorf, University of Missouri - St. Louis Nathan Hunton, University of Missouri – St. Louis The Missouri-NASA Space Grant Consortium The Department of Physics and Astronomy, UM – St. Louis All those involved in the preparation of the specimens Acknowledgements

3. These grains are spherical, ~ 1[μm] in diameter, and are characterized by their core-rim structure. Presolar Graphite Spherules The rims are concentric graphitic layers (~ 0.34[nm] apart), similar to a carbon onion 0.34[nm] Graphite spherules are presolar in origin, as characterized by their heavy isotopic ratios (i.e. with 12 C/ 13 C < solar = 89). The cores are comprised primarily of unlayered graphene. This is evidenced in diffraction by the occurrence of (hk0) graphitic ordering only, and the high frequency tails following each periodicity, characteristic of atom-thick crystals.

4. (100) (110) (200) (210) (300) (220) Graphite Spherule Diffraction - Observe the absence of any inner ring, corresponding to graphitic layering. - The rings correspond to the in-plane (hk0) graphite periodicities. - The peak shapes are characteristic of atom-thick structures; sharp rises followed by high frequency tails

5. Debye Scattering Profile and Flat-Sheet Fitting Routine In order to see how these effects manifest in diffraction data, we compute azimuthally averaged diffraction data using a Debye model Create a fitting routine that finds the best fit to experimental data using a flat sheet model - Extra scattering on the leading edge of the (100) and (110) peaks. - Extra scattering at the graphene spacings Neither two sheet sizes, nor a log-normal distribution of sheet sizes, improves upon the single-size graphene model.

6. - It was previously thought that there could be a second component with graphene-like spacings contributing to diffraction to account for the residuals. - Another possibility, however, is that there is extra scattering, and a slight broadening and shifting of the peaks, occurring due to coherence effects between nearby or adjoined sheets. - Let’s look at the faceted carbon nanocone as an example of where this would occur Diffraction Coherence Effects

7. One Facet versus Two Facets - To further investigate the strength of these effects, we consider Debye profiles for a single facet, or flat sheet, and two adjacent facets of a cone. - Observe that there is some extra scattering at the graphene spacings and the satellite peak as predicted.

8. Model Ensembles of Graphene Sheets - We create ensembles of sheets, or sheets and nanocones, and calculate Debye profiles for the ensembles. - Then use the fitting routine and compare deviations from a flat sheet model to the experimental case. Ensemble of randomly-oriented flat sheets, 1754 atoms Experimental data

9. Model Ensembles of Graphene Sheets - While this looks great, there are some reservations to consider when we have only flat graphene in our ensemble. - Given a larger ensemble of graphene, these coherence effects should be less visible and we should approach a flat sheet model Randomly-Oriented Flat Sheets 10,299 atoms ~200 Sheets ~100,000 atoms contribute in a set of experimental data

10. The Failing of Flat Sheets Alone This can be seen mathematically by looking at a 1D case where a real function, f(r), representing a sheet, and its Fourier transform, can be used to write and equation for the 1D power spectrum of a collection of N such objects, This formula reduces to, where the cosine term vanishes when there are enough sheets to sufficiently randomize the part of the phase,

11. Faceting Suggested by Diffraction The full randomizing of these phases would not occur if we had an ensemble of faceted structures. Thus, both electron diffraction and HRTEM imaging tell us there is faceting between graphene layers in the core, With no other significant crystal ordering

12. Competing Formation Models Three primary competing models for the formation of the core material: 1.Grains are formed one atom at a time, where carbon atoms will be able to relax with few nearest neighbors as they are added. Layering is prevented by the high temperature environment, and knock-on damage. 2.Cores may form through the agglomeration of PAHs (polycyclic aromatic hydrocarbons), or other graphene sheets/cones flying around in the stellar atmosphere. Here, any relaxation occurs prior to the ensemble forming. 3.Perhaps these cores are the result of an ultra-fast solidification of a carbon liquid droplet. In this scenario, dendritic sheet growth takes place throughout the droplet, where pentagonal defects occasionally occur. Some relaxation is possible, though the many nearest neighbors suppress layering and full relaxation, resulting in faceted structures.

13. Conclusions Presolar graphene cores present an interesting challenge in elucidating molecular structure and modeling formation. By comparing deviations from a flat sheet model in experimental core diffraction data and model ensembles of randomly-oriented graphene sheets, we find coherence effects in the models show residuals similar to those in the experimental case. Coherence effects can manifest in diffraction data from collections of nanocrystals, when there is some type of regular coordination between the scatterers. Faceting or some type of regular coordination between graphene within the presolar cores is required for the coherence effects to remain in the large experimentally sampled area.

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