Thermodynamics of nano-scale precipitate-strengthened Fe-Cu and Al-transition-metal systems from first-principles calculations

The thermodynamic properties of two nano-scale precipitate-strengthened alloys, Fe-Cu and Al-TM(=Ti, Zr and Hf) systems, are investigated within framework of first-principles thermodynamics methods. In particular, thermodynamic properties of the metastable precipitate phases are calculated, where direct experimental measurements are not available.; Atomic volumes, magnetic moments, mixing energies and elastic properties of bcc Fe1-xCux solid solutions are studied by first-principles calculations based on the cluster expansion (CE) framework. We introduce a generalization of the CE technique for the calculation of concentration-dependent elastic moduli in disordered phase. Calculated mixing energies, atomic volumes and magnetic moments agree well with measurements for metastable alloys prepared through non-equilibrium processing techniques. The variations of the bulk modulus B, shear moduli C44 and C', with respect to copper concentration are calculated for the disordered bcc phase. While the B and C44 are positive for all concentrations, C' is positive only for Cu concentrations less than 50 atomic%. The implications of present results are discussed in relation to the observed metastability of bcc Fe-Cu alloys, and the strengthening mechanism of nanoscale bcc precipitates in an alpha-Fe matrix.; Vibrational entropy, which is often omitted in first-principles phase-diagram calculations, has been shown to be an essential contribution in the phase stability of many Al-based alloys. In this work, we study the effect of lattice vibrations on the solubility limit for Al-TM(=Ti, Zr and Hf) systems. We propose a transferable force constant approach (TFC), in which the relations between bond force constants, bond length and TM composition are assumed to be transferable among different structures, to substantially reduce the heavy computational expense associated with first-principles lattice dynamics calculations. Our results demonstrate that the TFC can predict the vibrational entropy to within ∼15% relative error. Solvus boundary calculations show that the vibrational entropy leads to roughly five to fifteen times increase the computed solubility limit of TM(=Ti, Zr and Hf) in Al. The calculated equilibrium solvus boundaries agree well with available experiments. The solvus boundaries for the metastable phases are also computed, for which direct measurements are not available.