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M. Todt, R.D. Bitsche, M.A. Hartmann, F.D. Fischer, F. G. Rammerstorfer:
"Growth Limit of Carbon Onions - A Continuum Mechanical Study";
International Journal of Solids and Structures, 51 (2014), 3-4; 706 - 715.

The growth of carbon onions is simulated using continuum mechanical shell models. With this models it is shown that, if a carbon onion has grown to a critical size, the formation of an additional layer leads to the occurrence of a structural instability. This instability inhibits further growth of carbon onions and, thus, can be a reason for the limited size of such particles. The loss of stability is mainly evoked by van der Waals interactions between misfitting neighboring layers leading to self-equilibrating stress states in the layers due to mutual accommodation. The influence of the curvature induced surface energy and its consequential stress state is investigated and found to be rather negligible. Furthermore, it is shown that the nonlinear character of the van der Waals interactions has to be considered to obtain maximum layer numbers comparable to experimental observations. The proposed model gives insight into mechanisms which are assumed to limit the size of carbon onions and can serve as basis for further investigations, e.g., of the formation of nanodiamonds in the center of carbon onions.

http://dx.doi.org/10.1016/j.ijsolstr.2013.10.038