Simulation of chemical bond distributions and phase transformation in   carbon chains
  In the present work we develop a Monte Carlo algorithm of the carbon chains ordered into 2D hexagonal array. The chemical bond of the chained carbon is computed from 1K to 1300K. Our model confirms that the beta phase is more energetic preferable at low temperatures but the system prefers the alpha phase at high temperatures. Based on the thermal effect on the bond distributions and 3D atomic vibrations in the carbon chains, the bond softening temperature is observed at 500K. The bond softening temperature is higher in the presence of interstitial doping but it does not change with the length of nanowire. The elastic modulus of the carbon chains is 1.7TPa at 5K and the thermal expansion is +7 x 10-5 K-1 at 300K via monitoring the collective atomic vibrations and bond distributions. Thermal fluctuation in terms of heat capacity as a function of temperatures is computed in order to study the phase transition across melting point. The heat capacity anomaly initiates around 3800K. 
C.H.Wong, E.A. Buntov, V.N. Rychkov, M.B. Guseva, A.F. Zatsepin
cond-mat.mtrl-sci