Multi-walled carbon nanotubes formed by condensed-phase conversions of Fe-C-based nanopowder in vacuum

We describe the formation of multi-walled carbon nanotubes (MWCNTs) which have grown during annealing at 800 °C of Fe-C-based nanopowder in vacuum. The Fe-C-based nanopowder was produced by a laser pyrolysis of gas-phase reactants. The as-synthesized and annealed samples were characterised by TEM, XRD, Mössbauer spectroscopy, Raman spectroscopy, and magnetic measurements. Under the TEM, MWCNTs were observed in the annealed sample. In addition, larger particles with the graphitic shells and various graphitic structures were found. XRD and Mössbauer analysis confirmed that only two iron phases were present in the annealed sample: α-Fe and Fe₃C. Phase transformations taking place during the thermal treatment of the sample are discussed.     

Cooperation in dividing the cake

This paper defines models of cooperation among players partitioning a completely divisible good (such as a cake or a piece of land). The novelty of our approach lies in the players’ ability to form coalitions before the actual division of the good with the aim to maximize the average utility of the coalition. A social welfare function which takes into account coalitions drives the division. In addition, we derive a cooperative game which measures the performance of each coalition. This game is compared with the game in which players start cooperating only after the good has been portioned and has been allocated among the players. We show that a modified version of the game played before the division outperforms the game played after the division.