A 314-type MAB phase V₃PB₄ with hexagonal crystal structure is synthesized by self-propagating high temperature combustion synthesis (SHS), with the help of the full first-principles predictions for the phase stability and adiabatic combustion temperature of SHS. Using XRD and TEM, V₃PB₄ crystallizes in the space group of P6m2, with the lattice parameters a = 3.030 Å and c = 9.148 Å, of much interest, well with the predicted one. Furthermore, the electronic structure, chemical bonding, and elastic properties of hex-V₃PB₄ are predicted by first-principles. No bandgap around Fermi energy indicates its electronic conductor. And the strong covalent bonding is present between the B and V atoms with, significantly, much weaker V-P bond. With the help of the theoretical model of bond stiffness, the significantly high ratio of bond stiffness of weakest bonds to the strongest ones (0.873) of hex-V₃PB₄ indicates its poor damage tolerance and fracture toughness. The high bond stiffness results in its high moduli in comparison with other MAB phases. As the number of inserted P atoms increases, the engineering elastic modulus decrease, without the price of an increase in density.

To respond the recent experimental advances, the phase stability, mechanical properties, phonon as well as infrared- and Raman-active modes, thermal expansion and heat capacity were investigated by density functional theory for the S-containing MAX carbides and borides (M from Ⅲ B to Ⅷ B), of importance, well consistent with the available experimental results. After examining the thermodynamic competition with all the competing phases and intrinsic stability by their lattice dynamics, 18 MAX phases were screened out from 138 ones. Using the “bond stiffness” model as well as the associated criterion for damage tolerance and fracture toughness, the ratio of bond stiffness of weakest M−S to the strongest M-X bonds (k_min/k_max) over 1/2 indicates their intrinsic brittleness of all S-containing MAX phases except Nb₄SC₃. Including the contributions from phonon and electrons, their linear thermal expansion coefficients [(8.1–13.6)×10⁻⁶ K⁻¹, 300–1,300 K] and heat capacities (C_p) as a function of temperature are predicted. Of much interest, a well-established relationship between molar C_p of the MAX and MX phases is theoretically deduced in the present work.

MoAlB as a typical member of MAB phases has attracted much-growing attention due to its unique properties. However, the low production of MoAlB powders limits its further development and potential applications. In the present work, the ultra-fast preparation of high-purity MoAlB powders in a few seconds is achieved by self-propagating high-temperature synthesis (SHS) using a raw powder mixture at an atomic ratio of Mo : Al : B = 1 : 1.3 : 1. SHS reaction mechanism is obtained by analyzing the corresponding composition changes of starting materials. Furthermore, the thermodynamic prediction for the SHS reaction is consistent with the present experiments, where the preparation of MoAlB also conforms to two common self-propagating conditions of the SHS. The enthalpy vs. temperature curve shows that the adiabatic temperature of the reaction decreases with the amount of excuse Al increasing but increases when pre-heating the reactants. Also, this thermodynamic calculation provides a new idea for the preparation of other MAB phases by the SHS.

Mo₂Ga₂C is a new MAX phase with a stacking Ga-bilayer as well as possible unusual properties. To understand this unique MAX phase structure and promote possible future applications, the structure, chemical bonding, and mechanical and thermodynamic properties of Mo₂Ga₂C were investigated by first-principles. Using the "bond stiffness" model, the strongest covalent bonding (1162 GPa) was formed between Mo and C atoms in Mo₂Ga₂C, while the weakest Ga-Ga (389 GPa) bonding was formed between two Ga-atomic layers, different from other typical MAX phases. The ratio of the bond stiffness of the weakest bond to the strongest bond (0.33) was lower than 1/2, indicating the high damage tolerance and fracture toughness of Mo₂Ga₂C, which was confirmed by indentation without any cracks. The high-temperature heat capacity and thermal expansion of Mo₂Ga₂C were calculated in the framework of quasi-harmonic approximation from 0 to 1300 K. Because of the metal-like electronic structure, the electronic excitation contribution became more significant with increasing temperature above 300 K.