Fig. 1 a Schematic diagram of X-ray imaging; b schematic diagram of X-ray tomography setup [32]

Fig. 2 Dendritic structure diagram of magnesium alloys obtained by traditional metallographic technique: a Mg-10wt%Zn alloys; b Mg-9Al-0.7Zn alloys

Fig. 3 Reconstructed 3D α-Mg dendrite morphology with 2D livewire algorithm from X-ray tomography a 2D slice; b reconstructed 3D result [33]

Fig. 4 a A reconstructed morphological image of α-Mg dendrite and its growth directions; b, c 3D reconstructed dendrites exactly validate branched structure analysis of a [34]

Fig. 5 Dendritic morphologies of binary magnesium alloys: a Mg-Al alloys [36]; b Mg-Zn alloys [13]; c Mg-Sn alloys [13]

Fig. 6 Whole polycrystalline morphologies of phase-field simulations using alternative preferred orientation [13]

Fig. 7 3D dendritic morphologies in equiaxed growth Mg-30wt% Sn a, b and Mg-30wt% Gd c, d alloys. e and f one dendrite of Mg-30wt% Sn viewed from different perspectives [37]

Fig. 8 Comparison of the dendrite morphology between a phase-field simulation and b X-tomography experiment. Dendrite morphologies view from < 0001 >, < $11\overline{2}0$ >, < $10\overline{1}0$ > and < $11\overline{2}3$ > direction where c-f for simulation and g-j for experiment, respectively [37]

Fig. 9 Dendritic morphology and branching structure in equiaxed solidified Mg-9wt%Ca alloy: a, b dendrites morphology of α-Mg along with the particle clusters (MgO) as nucleation site in equiaxed solidification condition: a 2D slice; b 3D rendering; c-e three types of secondary dendrite growth patterns of α-Mg; dendrites with 5, 4 and 3 branching arms are observed in equiaxed solidification condition; f-h proposed branching structure of primary arms in c-e, respectively [38]

Fig. 10 3D dendritic morphologies and branching mechanism of α-Mg dendrites in Mg-Zn alloys with various additions of Zn; Sect. 1 and Sect. 2 are supposed to be the basal plane and prismatic central plane, respectively. a, a1, a2 Mg-10wt%Zn; b, b1, b2 Mg-25wt%Zn; c, c1, c2 Mg-38wt%Zn; d, d1, d2 Mg-50wt%Zn. a1, a2, b1, b2, c1, c2, d1, d2 share the same scale bar, respectively [14]

Fig. 11 Conclusive figure summary of growth mode of magnesium alloy

Fig. 12 Growth pattern of the α-Mg dendrite in Mg-10wt%Ba alloy. a 2D slice images from synchrotron X-ray tomography experiments, where the primary phase (i.e., α-Mg dendrite) is in dark gray; b the reconstructed morphology of α-Mg dendrite, c the entire 3D growth pattern of the α-Mg dendrite, d relevant sections used to cut the α-Mg dendrite, where P0 is the cross section (i.e., the {0001} basal plane), while P1, P2 and P3 are the longitudinal sections that perpendicular to P0 with the angles between the three longitudinal sections being 60° (i.e., the { $10\overline{1}0$ } non-basal plane), e-h show the corresponding 2D sections of this α-Mg dendrite by P0, P1, P2 and P3 planes, respectively [45]

Fig. 13 Geometrical model describing the 3D growth pattern and outer contour shape of the α-Mg dendrite with hcp lattice structure. a Crystallographic planes related to the growth behavior of the α-Mg dendrite, b relevant crystallographic orientations within the basal plane, c final outer profile composed of those energetically favorable planes with lower surface energy predicted by the ab initio calculations, d outer contour of the ideal shape derived from surface energy and related crystalline anisotropy, e schematic of the 3D growth pattern with eighteen-primary-branches [45]

Fig. 14 Phase-field simulation showing the evolution of an eighteen-branched α-Mg dendrite at different time steps: a 5000, b 10,000, c 15,000, d 20,000, e 25,000, f 30,000 [46]

Fig. 15 Microstructural evolution of Mg-6wt%Gd alloy under different cooling rates: a R = 0.033 K/s, b R = 0.1 K/s and c R = 0.25 K/s at different time, where t0 is the beginning time of solidification [21]

Fig. 16 taken from X-ray radiograms showing the time evolution of the α-Mg primary phase in the Elektron 21 alloy under nearly isothermal conditions at T = 0.0125 K/s [54]

Fig. 17 2D radiograph of microstructure development during AZ91 solidification at a cooling rate of 0.083 K/s [55]

Fig. 18 Two types’ morphology of dendrites in Mg-Gd alloys: a sixfold equiaxed structure, b butterflied structure [56]

Fig. 19 Floating, collision and rotation of dendrites in Mg-Gd alloys when the cooling rate is at about 0.033 K/s under the fixed temperature gradient [56]

Fig. 20 Dendritic morphology of Mg-6wt%Gd alloy of under three different cooling rates R = 0.033 K/s, R = 0.1 K/s and R = 0.25 K/s in directional solidification from the top to bottom, respectively: experimental results a1-a3, simulated results b1-b3 [57]

Fig. 21 2D slices and 3D surface rendering of equiaxed dendrite evolution during solidification of Mg-15wt% Sn for the cooling rates of 3 °C /min a1-a5, b1-b5 12 °C/min c1-c5, d1-d4 [32]

Fig. 22 3D dendritic morphology evolution for Mg-25wt%Zn a1-a4, Mg-38wt%Zn b1-b4 Mg-50wt%Zn c1-c4 alloys [59]

Fig. 23 a Volume normalized specific surface area (Sv) and solid volume fraction (fs) evolution of α-Mg dendrite with time during solidification; b average dendrite tip velocity in the mushy zone as a function of solidification time for Mg-25/38/50wt%Zn alloys; c measured evolution of solid fraction; d specific surface area evolution as a function of solid fraction, and fitted curves using modified Rath and Cahn’s model [32], [59]

Fig. 24 Images showing the evolution of dendritic structures of Mg-25wt%Zn a-1, a-2, b-1, b-2 Mg-38wt%Zn c-1, c-2, d-1, d-2 alloys before (time = 0 s) a-1, b-1, c-1, d-1 after a-2, b-2, c-2, d-2 the isothermal hold stage for coarsening [61]

Fig. 25 Microstructural evolution during solidification of a Mg-25Zn-7Al alloy and a Mg-25 Zn-7Al/SiC nanocomposite material [62]

Fig. 26 Images showing the 3D dendritic evolution of NP-free a-c, g-i NP Mg-25Zn-7Al d-f, j-l alloy [63]