Fig. 1. Fifty-one substitutional alloying atoms (in groups 1-16 and periods 2-6) in bcc Fe. The atomic names indicate the recommended standard potentials supplied by VASP. The extensions sv, pv, and d mean that the semi-core s, p, and d states are treated as valence states as well, respectively. The B, C, N, O, S, Ba and Se atoms are not calculated here, as the first five atoms are interstitial atoms in bcc Fe and the energies for the last two solute atoms are not convergent under the current calculation conditions.

Fig. 2. (a) Atomistic configuration of supercell containing 123 Fe atoms (denoted by the solid cycle), 1 solute atom (denoted by the dashed square) and 1 monovacancy (denoted by the solid cycle embed the sign “×”), where the substitutional solute atom exchanges its position with the vacancy at the nearest-neighbor site. (b) Illustration of the vacancy jump along the atomic dense-packing direction (the black arrow) in the atomic dense-packing plane (gray plane) in bcc Fe. (c) Three key positions during solute-vacancy exchange, i.e. the initial, the middle and the final positions.

Fig. 3. Relaxed structures for (a) ∑3(112), (b) ∑5(310) and (c) ∑5(210) GBs. The black and white circles represent Fe atoms lying on two adjacent atomic layers along rotation axis [1 $\bar{1}$ 0] for ∑3(112), and [001] for ∑5(310) and ∑5(210). The dashed squares denote the solute atoms.

Fig. 4. Evolution of (a) solute-vacancy bonding energy ΔQb calculated by Eq. (10), (b) migration energy ΔQm calculated by Eq. (12) and (c) activation energy for bulk diffusion Qb calculated by Eq. (9), with group number for fifty-one substitutional solute atoms. The vacancy formation energy for all substitutional solute atoms is same as 2.13 eV and thus is not plotted here. The reader can find the values of ΔQb, ΔQm and Qb of fifty-one solute atoms in Supplementary IV.

Fig. 5. Evolution of segregation enthalpy Hseg calculated by Eq. (13) with group number for (a) ∑3 (112), (b) ∑5 (310) and (c) ∑5 (210) GBs. Obviously, the values of segregation enthalpy are strongly dependent on the types of GBs. The reader can find the values of Hseg of fifty-one solute atoms in Supplementary V.

Fig. 6. Evolution of thermal stability calculated by Eq. (8) with group number for (a) ∑3 (112), (b) ∑5(310) and (c) ∑5 (210) GBs. Obviously, the values of thermal stability are strongly dependent on the types of GBs. (d) Evolution of averaged thermal stability for ∑3(112) , ∑5(310) and ∑5 (210) GBs with group number, with the aim to conveniently compare the thermal stability between different solute atoms. The reader can find the values of thermal stability and averaged thermal stability of fifty-one solute atoms for the three types of GBs in Supplementary VI.

Fig. 7. (a) Comparison of evolved grain sizes as function of annealing temperature between different NC alloys, i.e., Fe-1at.%Y (obtained in current work), pure Fe [63], Fe-1at.%Ni [63], Fe-1at.%Zr [64], Fe-10 wt.%Cr [62] and Fe-1.8at.%Ag [68]. (b) Comparison of X-ray diffraction scans of Fe-1at.%Y powders between the as-milled (denoted by black curve) state, the heat-treated state for 1 h at 800 °C (denoted by red curve), and the heat-treated state for 1 h at 1000 °C (denoted by blue curve). Bright field TEM micrograph of heat-treated Fe-1at.%Y powders for 1 h at (c) 800 °C and (d) 1000 °C.

Fig. 8. (a) Calculated thermal stability vs. activation energy for bulk diffusion for ∑3(112) (green signs “Δ”), ∑5(310) (red signs “?”) and ∑5(210) (blue signs “▽”) GBs. (b) Calculated thermal stability vs. segregation enthalpy for ∑3 (112) (green signs “△”), ∑5(310) (red signs “?”) and ∑5(210) (blue signs “▽”) GBs. The inset shows a comparison between the thermal stability from thermo-kinetic contribution (green signs “△”) and that from thermodynamic contribution (blue solid line), for ∑3 (112) GB, where the difference between the two curves corresponds to thermal stability from kinetic contribution. The values of activation energy for bulk diffusion, segregation enthalpy and thermal stability can be found in Supplementary IV, V and VI, respectively.

Fig. 9. (a) Thermal stability is plotted as function of Qb and Hseg numerically calculated by Eq. (8). The green surface is calculated using the parameters of set 1: D =30 nm, T =25 °C, AmGB = 1.18 ?2/atom, γ0 = 0.76 J/m2, Q0 = 1.3 eV/atom and x0 = 0.01, and the blue surface is calculated using the parameters of set 2: D = 15 nm, T = 1100 °C, AmGB = 0.68 × 1.18 ?2/atom, γ0 = 0.68 × 0.76 J/m2, Q0 = 0.68 × 1.3 eV/atom and x0 = 0.01. The intersection between the two surfaces is denoted by red solid line. a-f mark six dots with different Qb and Hseg. (b) The intersections between the thermal stability surfaces (the green and the blue surfaces) and the plane A (left) and plane B (right).