The M n+1 AX n , or MAX, phases are layered, hexagonal, early transition-metal carbides and nitrides, where n = 1, 2, or 3 ''M'' is an early transition metal, ''A'' is an A-group (mostly groups 13 and 14) element, and ''X'' is C and/or N. In every case, near-close-packed M layers are interleaved with layers of pure group-A element with the X atoms filling the octahedral sites between the former (Figure 1.1a-c). The M 6 X octahedra are edge-sharing and are identical to those found in the rock salt structure. The A-group elements are located at the center of trigonal prisms that are larger than the octahedral sites and thus better able to accommodate the larger A atoms. The main difference between the structures with various n values ( Figure 1.1a-c) is in the number of M layers separating the A layers: in the M 2 AX, or 211, phases, there are two; in the M 3 AX 2 , or 312, phases there are three; and in the M 4 AX 3 , or 413, phases, there are four. As discussed in more detail in later chapters, this layering is crucial and fundamental to understanding MAX-phase properties in general, and their mechanical properties in particular. Currently, the MAX phases number over 60 (Figure 1.2) with new ones, especially 413s and solid solutions, still being discovered.Most of the MAX phases are 211 phases, some are 312s, and the rest are 413s. The M group elements include Ti, V, Cr, Zr, Nb, Mo, Hf, and Ta. The A elements include Al, Si, P, S, Ga, Ge, As, Cd, In, Sn, Tl, and Pb. The X elements are either C and/or N.Thermally, elastically, and electrically, the MAX phases share many of the advantageous attributes of their respective binary metal carbides or nitrides: they are elastically stiff, and electrically and thermally conductive. Mechanically, however, they cannot be more different: they are readily machinable -remarkably a simple hack-saw will do (Figure 1.3) -relatively soft, resistant to thermal shock, and unusually damage-tolerant. They are the only polycrystalline solids that deform by a combination of kink and shear band formation, together with the delaminations of individual grains. Dislocations multiply and are mobile at room temperature, glide exclusively on the basal planes, and are overwhelmingly arranged either MAX Phases: Properties of Machinable Ternary Carbides and Nitrides, First Edition. Michel W. Barsoum.