Fig. 1. Illustration of the location of the chemical elements comprising MAX phases in the periodic table, and the projection of the unit cell along <11$\bar{2}$0 > . Blue, red and black balls denote the M, A and X atoms, respectively.

Fig. 2. Atomic-scale high-angle annual dark-field scanning transmission electron microscopy images of (a) Ti3AlC2, (b) Mo2Ga2C [45], (c) Ti2Au2C2 [46] and (d) Ti3Au2C2 [47] along <11$\bar{2}$0 > . Selected area electron diffraction patterns along (e) [0001], (f) [1$\bar{2}$10], (g) [0$\bar{1}$10] and (h) [hki0] of Nb12Al3C8 [14]. Convergent beam electron diffraction patterns along (i) [0001] and (j) [hki0]. “m” and “c*” mark the mirror and [0001] in the reciprocal space.

Fig. 3. (a) Disordered carbon vacancy on (0001). Black balls and squares are carbon atoms and vacancies. Gray and blue balls represent Nb atoms above and below the carbon layer. Carbon vacancy becomes ordered on the left-hand side in (b), where the red and black hexagons outline the sub-lattice of Nb12Al3C8 and carbon-vacancy-disordered Nb4AlC3?x. The sub-lattice of carbon vacancy on the left side and right side in (c) has no relative shifts during the ordering process. (d) The sub-lattice of carbon vacancy on the left side and right side are shifted by 1/3<$\bar{1}$010> (Nb12Al3C8 lattice), as illustrated by the yellow arrows. A domain boundary forms in the region highlighted in pink. (e) Misorientation-angle plot of as-synthesized Nb4AlC3?x. The inset is the distribution of the rotation axis plotted in inverse pole figure. (f) Electron back-scattered diffraction orientation map. The 30°/[0001] boundaries are highlighted with black lines [95].

Fig. 4. Typical dislocation configurations in MAX phases. (a) Dislocation wall in Ti3SiC2 [125], (b) dislocation arrays (denoted as D) in Ti3SiC2 piled up near the grain boundary (marked by the arrow) [128], (c) non-regular dislocations and dislocation networks formed by dislocation reactions in Ti2AlN [124], (d) dislocation cells in Ti3AlC2. (e)?(i) Diffraction contrast analysis of the dislocation reactions. The diffraction vectors used for the imaging in (e)?(h) are provided at the lower right corner of each subfigure [124]. (i) Illustration of the dislocation reactions. The Burgers vector for dislocation segments 1 and 3 is 1/3[$\bar{1}$$\bar{1}$20], that for 2, 4, 6 and 7 is 1/3[$\bar{1}$2$\bar{1}$0], and that for 5 is 1/3[$\bar{2}$110]. (j) Non-basal slip dislocations (arrow) in Ti3AlC2. Black dots illustrate the basal plane [129].

Fig. 5. (a) Projection of the Nb12Al3C8 unit cell along < 011-0 >. (b-d), (e-g) are the atomic configurations displaced along the α and β basal plane, respectively. The displacement was introduced by shifting the part right above α or β plane with respect to the lower part by (b, e) 0, (c, g) 1/3[011-0], (d) [011-0], (f) 1/6[011-0]. (h) Atomic resolution HAADF?STEM image of a mixed type dislocation superimposed with the strain map generated by geometric phase analysis. The Burgers circuit illustrated in (h) starts at S and ends at F, indicating a disregistry of 1/6<11$\bar{2}$0 . The inset is the εyy strain map. The figures are adapted from Ref. [95].

Fig. 6. (a) TEM morphology of SFs in Nb12Al3C8. The dotted line illustrates the basal plane. (b) Statistic histogram of the spacing between SFs. (c-f) SFs and dislocations in Ti3SiC2 [128]. (c) and (d) are recorded with g=(0$\bar{1}$14) and g=(1$\bar{2}$10), respectively. G1, G2, and G3 denote different grains. The SF is marked by arrows. (e, f) Typical bright field TEM morphologies of SFs which are bounded by partial dislocations (D) and grain boundaries (not shown here). (f) The SFs are out of contrast and only partial dislocations are visible. (g) Atomic-scale HAADF?STEM image of SF in Ti3AlC2. “3” represents the normal stacking of Ti3AlC2, while “2” denotes the wrong stacking formed by the extraction of one “TiC” layer. The bright and dim dots are Ti and Al atoms respectively. (h-j) Formation of SF in Ti3AlC2, where the red and blue lines are A and M plane, respectively. The dislocations are marked by ˫. (k) Typical TEM morphologies of SFs in Ti4AlN3 [137], including those running through the grain (A), bounded by partial dislocations (B) and perpendicular to the basal plane (C).

Fig. 7. (a) Inverse pole figure map of Ti2AlC with y-axis in the vertical direction. Grain boundary maps of the as-prepared (b) and cyclically compressed sample (c). The low- and high-angle grain boundaries are marked by red and black lines, respectively. (d)?(f) Misorientation profiles and unit cell orientations. Inserts show magnified Schmid factor maps for the corresponding grains with low- (red lines) and high-angle (black lines) grain boundaries. The figures are adapted from Ref. [153].

Fig. 8. (a) Scanning electron microscopy morphology of kink in Ti3SiC2 [157]. The delamination results in cracks. (b) TEM morphology of kink in Ti3SiC2 [123]. The kink boundary has both tilt (about 15°) and twist (about 2°) components. (c) Lattice fringe images showing the dislocation walls marked by the arrows in (b). The dislocations are b2 or b3 type full dislocations. The length of the observed Burgers vector is 1.54 Å. (d) Illustration of dislocation configuration comprising the kink boundary [123]. The left part illustrates the projection of HCP lattice on (0001), where the dislocation line, observed Burgers vector (bobs) for the dislocation in (c), b1, b2, and b3 are shown. The right part shows possible arrangements of mixed dislocations b2 and b3 in a dislocation wall. The screw components contributed by each dislocation in ① are in the same directions. The screw components in the neighboring dislocation in ② are in opposite directions and cancel each other. An error of the arrangement in ② gives a net twist component in ③. The stable configuration is ② or ③.

Fig. 9. (a) A typical TEM morphology of hexagonal screw dislocation networks. (b) Strain dependence of the length of hexagon edge and twist angle. (c) Crystallographic directions of the diffraction vectors and Burgers vectors. TEM dark field images are recorded with a diffraction vector (d) g1, (e) g2 and (f) g3. Solid and dotted lines illustrate the dislocations in and out of contrast, respectively. White arrows denote the Burgers vectors of the dislocation segments out of contrast. The figures are adapted from Ref. [156].

Fig. 10. SAED patterns along of (a-c) Cr2AlC [178] and (d-i) Ti2AlN [182] irradiated with 1 M Au ions at (a, d, g) 1 × 1014 cm-2, (b) 3 × 1014 cm-2, (c) 5 × 1015 cm-2, (e, h) 1 × 1015 cm-2 and (f, i) 1 × 1016 cm-2. The zone axis of (a-f) and (g-i) is <11$\bar{2}$0> and <10$\bar{1}$0> of “211” MAX phases. (j) The unit cell of (Ti2/3Al1/3)3N (left) and simulated electron diffraction patterns (middle and right). The corresponding SAED patterns are inserted. Red, blue, black and white balls denote Al, Ti, N and N vacancy. (k) Illustration of the formation of (Ti3/4Al1/4)4C2. The top three sketches are the projections of Ti3C2 slab on (0001). Blue and green balls are Ti atoms on and below the projection plane. The green balls with a cross are Ti atoms above the projection plane. Al atoms stacked above the Ti atoms marked with a cross are represented by the red ball (middle and right). The bottom three projections along <11$\bar{2}$0> demonstrate the formation of Ti3AlC2 polytype (left), TiAl and AlTi antisite pairs and C vacancies (middle) and (Ti3/4Al1/4)4C2. Since no superlattice diffractions have been observed, the N and C vacancies were treated as a random distribution.

Fig. 11. (a) Illustration of the typical process from MAX phases to MXenes [188]. (b) Atomic resolution HAADF?STEM image from single-layer Ti3C2Tx MXene synthesized using etchants with 2.7 wt.% HF aqueous solutions. Red circles indicate Ti vacancies. (c) The dependence of defect concentration (percentage) on HF concentrations [210]. (d, e) Atomic resolution HAADF?STEM image from (Mo2/3Y1/3)2AlC MXene after etching with 48 wt.% HF aqueous solution for 12 h [212]. Three left-column subfigures in (e) are enlarged from the framed regions in (d). The right columns are composites of the experimental images and projections of the structural model. Mo, Y and C atoms are denoted by purple, green and dark balls. (f) Projections of single-layer (M12/3M21/3)2C (upper left) and (M12/3)2C (upper right) MXenes along [0001]. M1 (Mo,W) and M2 (Y, Sc) are represented by small and large blue balls. The bottom subfigure is the atomic resolution HAADF?STEM image of (Mo2/3)2C [59]. (g-h) Atomic resolution HAADF?STEM image of the Ti3C2Tx monolayer at room temperature (g), at 500 °C (h) and 1000 °C (i) [215]. Areas containing Ti vacancies in (g) are marked by white dots. Composite of experimental image and projections of the Ti3C2Tx structural model is inserted in (g). The black areas in (h) are pores. In (h, i), areas framed by green, blue, and black dashed lines are the substrate Ti3C2, Ti4C3, and Ti5C4, respectively.