Abstract
Using first-principles alloy theory, we perform a systematic study of the Co-Cu phase diagram. Calculations are carried out for ferromagnetic and paramagnetic ${\mathrm{Co}}_{1\ensuremath{-}x}{\mathrm{Cu}}_{x}$ solid solutions with face-centered-cubic (fcc) crystal structure. We find that the equilibrium volumes and magnetic states are crucial for a quantitative description of the thermodynamics of the Co-Cu system at temperatures up to 1400 K. In particular, the paramagnetic state of Cu-rich alloys with persisting local magnetic moments is shown to be responsible for the solubility of a small amount of Co in fcc Cu whereas the excess entropy in the ferromagnetic Co-rich region critically depends on the adopted lattice parameters. None of the common local or semilocal density functional theory approximations have the necessary accuracy for the lattice parameters when compared to the experimental data. The predicted ab initio Co-Cu phase diagram is in good agreement with the measurements and CALPHAD data, making it possible to gain a deep insight into the various contributions to the Gibbs free energy. The present study provides an atomic-level description of the thermodynamic quantities controlling the limited mutual solubility of Co and Cu and highlights the importance of high-temperature magnetism.
Highlights
A fundamental factor in applying first-principles methods to material design is the accurate description of the thermomechanics [1,2,3]
The present exact muffin-tin orbitals (EMTO) (PBE and quasi-nonuniform approximation (QNA)) results for the equilibrium lattice constants obtained for the FM and PM states are plotted, as well as the grid-based projector augmented-wave (GPAW)-PBE results with and without lattice relaxation
Recalling the fact that QNA by construction is practically exact for pure elements, the nearly composition independent shift relative to the linear rule of mixture can be ascribed to the neglected thermal effects
Summary
A fundamental factor in applying first-principles methods to material design is the accurate description of the thermomechanics [1,2,3]. Computations based on density functional theory (DFT) have been widely used to calculate properties such as equilibrium volume, elastic moduli, and formation enthalpy at static (0 K) state [4,5,6,7], using first-principles methods to capture high-temperature properties of materials is very challenging [8]. First-principles calculations are often used to establish the equilibrium phase diagram at static condition via the calculations of the phase stability for various structures or phases. Such calculations provide important information missing in the experimental phase diagrams at the low-temperature part.
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