Fig. 1 Picture of Ce: LYSO scintillation crystals prepared by innovative fast crystal lifting growth technique based on the chemical bonding theory of crystalline growth[9]

Fig. 2 In-situ optical microscope crystallization images of KDP growth (a) By optical microscope; (b) By camera

Fig. 3 Crystallization spectrum of hydrated calcium carbonate[31] (a) FTIR spectra of calcium carbonate monohydrate (blue spectrum) and aCCM (black spectrum); (b) Schematic representation of different vibrational modes; (c) FTIR spectra of aCCM recrystallized in acetonitrile mixture after different intervals; (d) Rectangle area in (c) showing hydroxyl stretching band region during recrystallization of aCCM after different intervals

Fig. 4 Raman spectra and microstructure evolution of LCB crystal growth (a) Raman spectra of LCB crystals at room temperature and LCB-grown raw material powders at different temperatures; (b, c) Molecular structural evolution in LCB-grown melts[38]

Fig. 5 Energy dispersive X-ray diffraction patterns of melamine at different pressures[55]

Fig. 6 Time-resolved WAXS and SAXS data of ACC crystallization[65] (a) 3D representation of the time resolved WAXS modes in the experiment; (b) Stacked time series of the SAXS modes with time in minutes, and the arrows indicating positions of peaks caused by scattering from the growing vaterite crystallites, 1 Å =0.1 nm

Fig. 7 Based on artificial intelligence, the average prediction time of the growth furnace state reaching 0.0003 s[78]

Fig. 8 Time and space dimensions of multi-scale calculation method for materials[79]

Fig. 9 Lithium niobate structure, defects and formation energy of different point defects as a function of Fermi energy[82] (a, b) Crystallographic structures of stoichiometric LN and congruent LN with anti-site NbLi4+ and VLi− defects. Green octahedra indicate NbO6 and LiO6; (c) Formation energies of different point defects (NbLi4+, VLi−, and NbLi4+ + VNb5−) in LN as a function of Fermi energy

Fig. 10 Atomic structure (left) and electron localization functions (right) of CaH6[83]

Fig. 11 Displacement of atoms in the interface layer during energy minimization[92] (a) Al atoms; (b) Ni atoms

Fig. 12 Variation of crystal growth rate V⊥with temperature[93] Error bars represent the standard deviation of growth velocity measurements. The system can still maintain the maximum growth rate in deep and supercooled region without temperature change

Fig. 13 Structural snapshots and relationship between energy and GSW of the optimal route for C60 dimer binding by the path search method[94] (a-f) Structural snapshots and relationship between energy and GSW steps; (g) GSW in the 0, 5, 15, 25, 40, and 80 GSW steps. Red and green represent two carbon atoms in C60, respectively

Fig. 14 Phase-field simulation of the solidification of Al-1% Cu alloy at a cooling rate of 0.1 K/s[97] (a1-a4) Solid fraction of the 2D system at 0.9; (b1-b4) Substantial fraction of the 3D system at 0.2; (b1-b4)3D systems corresponding to (a1-a4), respectively, containing different numbers of grains