Nitrogen and carbon play an important role in the oxidation of Ti-Al intermetallic alloys in air. The insertion and diffusion of these elements in the $\gamma$-TiAl phase are investigated by first-principle computations. The accommodation of C and N atoms in several likely interstitial positions has been evaluated using density functional theory (DFT) calculations. The results show that both carbon and nitrogen prefer Ti-rich environments. Then, considering the possible jumps among the stable and metastable interstitial sites, the diffusion coefficients have also been obtained from ab initio calculations. According to the Transitional State Theory, in order to compute atomic jump rates, diffusion energy barriers and vibrational modes need to be known. Herein, barrier energies are obtained using the Climbing Image Nudged Elastic Band method. Vibrational properties are computed using the finite displacement method. Finally, diffusion coefficients are obtained solving the transport equation in the infinite time limit, using an analytical approach. The obtained results are compared to the diffusion of oxygen in $\gamma$-TiAl, investigated in previous studies. An anisotropic diffusion is obtained for all the interstitial species.

氮和碳在 Ti-Al 金属间合金在空气中的氧化中起重要作用。这些元素的插入和扩散$\gamma$-TiAl 相通过第一性原理计算进行研究。已经使用密度泛函理论 (DFT) 计算评估了 C 和 N 原子在几个可能的间隙位置中的适应。结果表明，碳和氮都喜欢富钛环境。然后，考虑到稳定和亚稳定间隙位点之间可能的跳跃，扩散系数也已经从ab initio获得计算。根据过渡态理论，为了计算原子跳跃率，需要知道扩散能垒和振动模式。在此，势垒能量是使用 Climbing Image Nudged Elastic Band 方法获得的。使用有限位移方法计算振动特性。最后，使用解析方法求解无限时限内的输运方程，得到扩散系数。将所得结果与氧气在$\gamma$-TiAl，在之前的研究中进行了调查。对于所有间隙物质获得各向异性扩散。