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The intermetallic Mn-phase, which precipitates in steels and superalloys, cannoticeably soften the mechanical properties of their matrix. Despite theimportance of developing superalloys and steels, the thermodynamic propertiesand directions of thermal expansion of the Mu-phase are still poorly studied.In this work, the thermal expansion paths, elastic, thermal and thermodynamicproperties of the Fe23Mo16 and Fe7Mo6 Mu-phases have been studied usingfirst-principles based quasi-harmonic Debye-Gruneisen approach. A methodallowing avoids differentiation in many variables is used. The free energiesconsisting of the electronic, vibrational and magnetic energy contributions,calculated along different paths of thermal expansions were compared betweenthemselves. A path with the least free energy was chosen as the trajectory ofthermal expansion. Negative thermal expansion of the Fe7Mo6 compound waspredicted, while the Fe23Mo16 has a conventional thermal expansion and negativeTEC in the parameter c. The thermal expansions of both these compounds are notisotropic. The elastic constants, modulus, heat capacities, Curie and Debyetemperatures were predicted. The obtained results satisfactorily agree with theavailable experimental data. Physical factors affecting the stability ofFe23Mo16 and Fe7Mo6 have been studied. The paper presents an essential featureof thermal expansions of the Mu-phase of the Fe-Mo system, which can provide aninsight into future developments.

Thermal expansion anisotropy of the Fe23Mo16 and Fe7Mo6 Mu-phases predicted from first-principles calculations