In the present work we develop a Monte Carlo algorithm of the carbon chainsordered into 2D hexagonal array. The chemical bond of the chained carbon iscomputed from 1K to 1300K. Our model confirms that the beta phase is moreenergetic preferable at low temperatures but the system prefers the alpha phaseat high temperatures. Based on the thermal effect on the bond distributions and3D atomic vibrations in the carbon chains, the bond softening temperature isobserved at 500K. The bond softening temperature is higher in the presence ofinterstitial doping but it does not change with the length of nanowire. Theelastic modulus of the carbon chains is 1.7TPa at 5K and the thermal expansionis +7 x 10-5 K-1 at 300K via monitoring the collective atomic vibrations andbond distributions. Thermal fluctuation in terms of heat capacity as a functionof temperatures is computed in order to study the phase transition acrossmelting point. The heat capacity anomaly initiates around 3800K.
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机译：在本工作中，我们开发了将碳链排序为二维六边形阵列的蒙特卡洛算法。链碳的化学键计算范围为1K至1300K。我们的模型证实，在低温下，β相的能量更高，但在高温下，系统更倾向于α相。基于对碳链中键分布和3D原子振动的热效应，观察到键软化温度为500K。在存在间隙掺杂的情况下，键软化温度较高，但不会随纳米线的长度而变化。通过监测集体原子振动和键分布，碳链的弹性模量在5K时为1.7TPa，在300K时热膨胀为+7 x 10-5 K-1。为了研究跨熔点的相变，计算了以热容量作为温度函数的热波动。热容量异常在3800K附近启动。
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