Ab initio prediction for the thermal properties of the Al- and Si-containing MAB phases

This study employs first-principles calculations to predict and analyze the heat capacity (c_p) and thermal expansion coefficient (TEC) of 29 Al- and Si-containing stable MAB phases in the framework of quasi-harmonic approximation including the contributions from electronic excitation and magnetism, covering temperature ranges up to 1500 K, consistent with the present and previous experimental ones available. Generally, electronic excitation slightly increases c_p above 300 K, while the magnetic contribution becomes significant near the Curie temperature (T_C), with a peak that increases with higher T_C and magnetic moments. The Sicontaining MAB phases generally possess higher c_p, which can be explained by Kopp's law, and lower TEC due to stronger chemical bonding. Similar to c_p, TEC is affected by the valence electron concentration (VEC) and electronic shell number of transition metals. Notably, the TEC of magnetic MAB phases exhibits abrupt changes near T_C, while Cr₄AlB₄ shows an abnormally low TEC. Furthermore, these MAB phases have relatively high Debye temperature (θ_D), reflecting their strong bond stiffness, which decreases with increasing VEC. The Grüneisen parameter (γ) suggests these MAB phases exhibit low lattice anharmonicity, similar with MAX phases.