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 (Fe
x
C
y
, 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(P63
mc) 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.