  The intermetallic Mn-phase, which precipitates in steels and superalloys, can
noticeably soften the mechanical properties of their matrix. Despite the
importance of developing superalloys and steels, the thermodynamic properties
and directions of thermal expansion of the Mu-phase are still poorly studied.
In this work, the thermal expansion paths, elastic, thermal and thermodynamic
properties of the Fe23Mo16 and Fe7Mo6 Mu-phases have been studied using
first-principles based quasi-harmonic Debye-Gruneisen approach. A method
allowing avoids differentiation in many variables is used. The free energies
consisting of the electronic, vibrational and magnetic energy contributions,
calculated along different paths of thermal expansions were compared between
themselves. A path with the least free energy was chosen as the trajectory of
thermal expansion. Negative thermal expansion of the Fe7Mo6 compound was
predicted, while the Fe23Mo16 has a conventional thermal expansion and negative
TEC in the parameter c. The thermal expansions of both these compounds are not
isotropic. The elastic constants, modulus, heat capacities, Curie and Debye
temperatures were predicted. The obtained results satisfactorily agree with the
available experimental data. Physical factors affecting the stability of
Fe23Mo16 and Fe7Mo6 have been studied. The paper presents an essential feature
of thermal expansions of the Mu-phase of the Fe-Mo system, which can provide an
insight into future developments.
