  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.
