Fig. 1 a TEM image of the precipitates in the Ti-W sample after the deformation and stress relaxation for 200 s followed by water quenching, EDS results (at.%) of b Type 1 precipitate, c Type 2 precipitate and d Type 3 precipitate marked in (a). The peaks of Cu are from the Cu grid that supports the carbon replica. It should be noted that the distribution of ultrafine carbides is not uniform, and the number of carbides in the regions marked by yellow lines are obviously less than that in other regions

Fig. 2 High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image and EDS mapping analysis of a precipitate Type 1, b precipitate Type 2, and c precipitate Type 3. The white dashed lines surround the particles

Fig. 3 a Three-dimensional atom maps of Ti-W-bearing steel after stress relaxation for 60 s at 925 ℃ followed by water quenching, b an atom map of one (Ti, W)C nanoprecipitate and one-dimensional concentration profiles along three perpendicular directions, and c HAADF-STEM image of the Type 1 precipitate with the core-shell structure. In c, the contrast at the edge of the particle is bright, which reflects the large atomic number, showing a clear W-enriched shell. It should be noted that the contents of elements in the carbide shown in b are found to be less than 6 at.%, which is much lower than the theoretical percentage of MC (~ 50 at.% M and 50 at.% C). Such phenomenon should be caused by local magnification effects in APT measurements [39]

Fig. 4 TEM analysis of a Type 1 particle in the Ti-W-bearing steel: a schematic diagram showing the projection geometry of a particle with octahedral shape, b TEM image and c SAED of a Type 1 particle, d HRTEM, e IFFT and f FFT lattice images of the lower-right corner of the particle marked with white rectangle in b, g isopach map of the projection of the (Ti, W)C particle shown in b, h HAADF-STEM image of the (Ti, W)C particle, and i sublattice fraction measured by nanobeam EDS (spot size 1.0 nm) of Ti, W, and Fe along one diagonal of the (Ti, W)C particle as shown in h

Fig. 5 a An atomic-resolution HAADF-STEM image of the Type 2 particle, and b isopach map of the projection of the (Ti, W)C particle as shown in (a)

Fig. 6 a Metallic sublattice fraction of Ti, W, and Fe determined by EDS as a function of particle size, b product of metallic sublattice fraction with particle size as a function of particle size

Fig. 7 Structure analysis of fine carbide particles: a HRTEM image of several ultrafine particles in the Ti-W steel, b the corresponding SAED and calibration of diffractive ring, c HRTEM image of a carbide particle with a composite structure, d magnified image of this particle in c, and e FFT image of the particle in d

Fig. 8 a-d TEM images of the precipitates formed in the Ti-W steel after the deformation at 925 °C and stress relaxation for various holding time: a 60 s, b 200 s, c 1800s and d 3000 s. e-h TEM images of the precipitates formed in the Ti steel after the deformation at 925 °C and stress relaxation for various holding times: e 60 s, f 200 s [18], g 1800s and h 3000 s

Fig. 9 Variation of average size of carbide particles with coarsening time

Fig. 10 Fe/MC supercell structure having eight Fe atoms, four M atoms (M = Fe, Ti and W), and four C atoms

Fig. 11 Calculated formation energies of MCy B1 structure carbide with M = W, Fe and Ti and y are the octahedral interstitial sublattice fraction

Fig. 12 Calculated lattice parameters of MCy B1-structure carbide with M = W, Fe and Ti, and y are the octahedral interstitial sublattice fraction

Fig. 13 Interfacial chemical energies of MC/γ. “MC0.5-C Inside” indicates the configuration where the C atoms are away from MC/γ interface, and “MC0.5-C Interface” denotes the configuration where the C atoms are located at the MC/γ interface. The symbol “○” represents interstitial vacancy