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Density functional theory is used to provide theoretical insights into the ternary nanolaminated and layered transition metal boride (MAB phase) of MoAlB, with calculations of crystal structure, electronic structure, lattice dynamics and elastic properties, including a corresponding hypothetical MAX phase compound Mo2AlC for comparison. The calculated atomic configuration matches well with experiment. The metal-like electronic structure contributes to the physical origin of the high electrical conductivity of MoAlB. Strong covalent bonding is present between the B atoms, as well as between the Mo and B atoms, and significantly the much weaker Al Al bonds are consistent with the high fracture toughness and damage tolerance seen in MoAlB. With increasing pressure, the shrinkage is highest along the b axis, and lowest along the c axis. From the calculated second-order elastic constants, the bulk moduli B, shear moduli G, Young's moduli E and Poisson ratio μ are 207 GPa, 137 GPa, 336 GPa and 0.23, respectively. The G/B ratio of 0.66—similar in magnitude to values in MAX phases –demonstrate similarities in properties between MAB and MAX phases. Lattice dynamics are examined in detail, with 9 Raman-active modes and 6 infrared-active modes identified and analyzed in terms of their atomic motion and wavenumbers.

The newly discovered MAX phase, Ti4GaC3, can exist in one of three polymorphs, α, β and γ, all with the space group P63/mmc. The Ti and Ga (underlined) atomic arrangements are, respectively, AB A BACB C BC, AC A CACA C AC and AB C BACB A BC. Herein first-principles calculations are used to investigate the phase stabilities, electronic structures, elastic properties and compressibilities of the three polymorphs. Since the α- to γ-phase transition only involves shuffling of the A-atoms, it occurs much more easily than those to β-Ti4GaC3 despite the fact that the latter is thermodynamically less stable than γ-Ti4GaC3. For α-Ti4GaC3, the total density of states, TDOS, around the Fermi energy, Ef, lies in a local minimum; for the two other polymorphs, the TDOS is near a local minimum. The electrons occupy all the bonding states for α-Ti4GaC3, but the bonding states are partially occupied for both β- and γ-Ti4GaC3. Both bond stiffness and bond angle play an important role in the compressibility. In general, with increasing pressure, all the bonds become shorter, and the rate of increase in bond stiffness also increases. The bulk moduli of the α-, β- and γ-polymorphs were calculated to be 178, 174 and 169 GPa, respectively. The corresponding theoretical densities are 5.14, 5.12 and 5.11 g cm−3.