X-ray computed microtomography (X-CT) and U-net convolutional neural network (U-net CNN) were used to characterize and segment the three-dimensional structure of MC and M₂₃C₆ carbides. The volume fraction of MC and M₂₃C₆ carbides, the percentage of MC carbides in all carbides, and the size of MC carbides were statistically analyzed. We found that the MC carbides were mainly distributed at the interface between γ dendrites and the interdendritic γ’ phase. The M₂₃C₆ carbide grows from the MC carbide to the interdendritic region. Combing with the finite element simulation of the directional solidification process, it was shown that the cooling rate had a significant influence on the carbide growth of superalloys. The faster the cooling rate, the smaller the MC carbides volume percentage and size, the larger the M₂₃C₆ carbides volume percentage, and the faster carbides growth. Based on the simulation results and thermodynamic calculations, we developed the relationship between the carbon addition, cooling rate, and volume fraction of carbides by regression models. The results show that the volume fraction of carbides in nickel-based single crystal superalloys increases linearly with the increase of carbon content and gradually increases with the rise of cooling rates.

X射线计算机显微断层扫描（X-CT）和U-net卷积神经网络（U-net CNN）被用来表征和分割MC和M ₂₃ C ₆碳化物的三维结构。统计分析了MC和M ₂₃ C ₆碳化物的体积分数、MC碳化物在所有碳化物中的百分比以及MC碳化物的尺寸。我们发现MC碳化物主要分布在γ枝晶和枝晶间γ'相之间的界面处。M ₂₃ C ₆碳化物从 MC 碳化物生长到枝晶间区域。结合定向凝固过程的有限元模拟表明，冷却速度对高温合金碳化物生长有显着影响。冷却速度越快，MC碳化物体积百分比和尺寸越小，M ₂₃ C ₆越大碳化物体积百分比，且碳化物生长较快。基于模拟结果和热力学计算，我们通过回归模型建立了碳添加量、冷却速度和碳化物体积分数之间的关系。结果表明，镍基单晶高温合金中碳化物的体积分数随着碳含量的增加呈线性增加，随着冷却速度的增加而逐渐增加。