Fig. 1. The equilibrium phase diagram (a) and the non-equilibrium phase transition process based on the Scheil rule (b).

Fig. 2. The multi-scale dendrites in solidified sample 1. (a) the cooling curve of sample 1; (b) conventional dendrites observed on the top surface; (c) conventional dendrites observed on the section plane; (d) subtle dendrites observed on the surface of a conventional dendritic arm; (e) the amplified subtle dendrites; (f) the altitude map corresponding to (d); (g) subtle dendritic blocks within a conventional dendritic arm on the section plane; (h) and (i) an amplified subtle dendrite lower than surrounding positions; (j) and (k) an amplified subtle dendrite higher than surrounding positions.

Fig. 3. The evolution of multi-scale dendrites in situ and real time observed by the laser confocal microscope. (a-g) the evolution of multi-scale dendrites, with some typical phenomena addressed by red letters; (h) the solidified multi-scale dendrites.

Fig. 4. The fluctuation of temperature during solidification measured by the laser confocal microscope.

Fig. 5. Some subtle dendrites supporting for superimposition mechanism observed in sample 1. (a) clear and slight dendritic patterns on the surface of a conventional dendritic arm; (b) overlapped subtle dendritic patterns on the surface of a conventional dendritic arm; (c) superimposition mechanism sketch for (b); (d) the subtle triangle patterns on the surface of a conventional dendritic arm; (e) superimposition mechanism sketch for (d); (f) circle patterns observed on the surface of a conventional dendritic arm; (g) by sectioning the temperature fluctuations superimposed in three dimensional space, the circle pattern on a spherical surface was shed on a two dimensional plane.

Fig. 6. Some phenomena supporting for superimposition mechanism observed in sample 2. (a) the cooling curve of sample 2; (b-d) the explosive growth and the sudden emergence of sub-structures within traditional dendritic arms; (e) and (f) the emergence and slow movement of segregation strips within the conventional dendritic arm; (g) mechanism sketch for the segregation strips in (e) and (f).

Fig. 7. The variable segregation pattern arisen in the subtle semi-solid matrix of sample 3. (a) the cooling curve of sample 3; (b) a primary segregation pattern emerged in a conventional dendritic arm; (c) and (d) a new segregation pattern substituting the primary segregation pattern.

Fig. 8. The various subtle dendrites within traditional dendritic arms. (a) the comparatively coarse dendrites within the conventional dendritic arm in sample 1; (b) and (c) the comparatively fine dendrites within the conventional dendritic arm in sample 2.

Fig. 9. The influence of cooling rates in the later solidification stage (1270-1000 °C) on the hardness of cast M50 steel.

Fig. 10. The microstructures of cast M50 steel by isothermal treatment at 1250 °C for 60 min during solidification.