Crystal Structure Prediction Approach to Explore the Iron Carbide Phases: Novel Crystal Structures and Unexpected Magnetic Properties

Using our proposed structure prediction algorithm coupled with first-principles calculations, we performed crystal structure prediction on a series of iron-rich iron carbide phases (FexCy, 1 ≤ y ≤ x ≤ 7, 0 < y/x ≤ 1) with not more than 32 total number of atoms per cell at T = 0 K and P = 0 GPa. The experimentally well-known structures in the region (0 < y/x ≤ 0.5 and y/x = 1) for η-Fe2C(Pnnm), θ-Fe3C(Pnma), χ-Fe5C2(C2/c), and h-Fe7C3(P63mc) have been successfully reproduced, and more stable phases of Fe4C(Fdd2) and FeC(Pnnm) are found. For the unknown region (0.5 < y/x < 1), we have predicted the lowest-enthalpy structures for Fe7C5(C2), Fe4C3(Cmcm), Fe5C4(C2/m), Fe6C5(Imm2), and Fe7C6(P63/m). We have examined the structural, thermodynamic, and mechanical stabilities of all predicted structures. The local structure of the new region is quite different from that of the known region. Atomic magnetic moments and magnetic hyperfine field parameters are drastically reduced in the new region, which are unexpected in iron carbides so far. We qualitatively analyze the relationship between the local atomic structure and magnetic moment and further quantitatively establish a high-accuracy model using the machine learning method with small root-mean-square errors for training set (0.079μB) and validation set (0.083μB). Our work can not only help us to enrich the understanding of iron carbide phases and provide a new method for the correlation of local structure and magnetism but also provide a new way for the discovery and design of novel iron-based materials.