Thermodynamic and kinetic properties of carbon (C) atoms in body-centered tetragonal iron (Fe) are investigated by using Monte Carlo (MC) simulations. Pairwise interactions between carbon atoms are obtained by combining the linear elasticity theory and the state-of-the-art results from density functional theory (DFT). This energy database is applied to MC simulations to predict the equilibrium carbon configuration and the collective kinetic motion of carbon atoms in an as-quenched martensite. From the metropolis MC simulation, we obtain a novel equilibrium phase of Fe${}_6$C${}_2$ structure. However, according to the kinetic MC simulations, it is difficult to reach this equilibrium phase during the martensite ageing because, at room temperature or below, the carbon diffusivity is so slow that it will take an unrealistically long time for the system to achieve the equilibrium; and at higher temperature, even though the kinetics are accelerated, the carbon concentration of the predicted equilibrium phase is so high that other metastable carbides can be formed before such equilibrium is reached. Moreover, the effects of the temperature, the applied stress, and the initial state on the ageing kinetics are highlighted. The evolution of the carbon cluster concentration and the time scale of the ageing kinetics are in good agreement with some existing experimental results.

通过使用蒙特卡罗 (MC) 模拟研究了体心四方铁 (Fe) 中碳 (C) 原子的热力学和动力学性质。碳原子之间的成对相互作用是通过结合线性弹性理论和密度泛函理论 (DFT) 的最新结果获得的。该能量数据库应用于 MC 模拟，以预测淬火马氏体中碳原子的平衡碳构型和集体动能。从都市 MC 模拟中，我们获得了 Fe 的新平衡相${}_{\mathrm{6个}}$C${}_{\mathrm{2个}}$结构。然而，根据动力学 MC 模拟，在马氏体时效过程中很难达到这个平衡阶段，因为在室温或更低温度下，碳扩散率非常慢，系统需要很长时间才能达到平衡; 在更高的温度下，即使动力学加速，预测的平衡相的碳浓度如此之高，以至于在达到这种平衡之前可以形成其他亚稳态碳化物。此外，还强调了温度、施加的应力和初始状态对老化动力学的影响。碳簇浓度的演变和老化动力学的时间尺度与一些现有的实验结果非常吻合。