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The elastic properties of $Cu-Al-Mn$ alloys with compositions along the$Cu_3Al \to Cu_2AlMn$ line and $bcc$-based structures, are studied by means offirst-principles calculations. From the calculated elastic constants, theZener's anisotropy, sound velocities and Debye temperature are determined. Thetheoretical results compare well with the available experimental data. Theinfluence of vibrations is introduced through the quasi-harmonic Debye model,and different properties are studied as functions of temperature andcomposition.

Mechanical and thermodynamical properties of $\beta-Cu-Al-Mn$ alloys along the $Cu_3Al \to Cu_2AlMn$ compositional line