Cu-Au, Ag-Au, Cu-Ag, and Ni-Au intermetallics: First-principles study of temperature-composition phase diagrams and structures

The classic metallurgical systems—noble-metal alloys—that have formed the benchmark for various alloy theories are revisited. First-principles fully relaxed general-potential linearized augmented plane-wave (LAPW) total energies of a few ordered structures are used as input to a mixed-space cluster expansion calculation to study the phase stability, thermodynamic properties, and bond lengths in Cu-Au, Ag-Au, Cu-Ag, and Ni-Au alloys. (i) Our theoretical calculations correctly reproduce the tendencies of Ag-Au and Cu-Au to form compounds and Ni-Au and Cu-Ag to phase separate at $T=0\mathrm{}$ K. (ii) Of all possible structures, ${\mathrm{Cu}}_3\mathrm{Au}$ ${(L1\mathrm{}}_2)$ and CuAu ${(L1\mathrm{}}_0)$ are found to be the most stable low-temperature phases of ${\mathrm{Cu}}_{1-x}{\mathrm{Au}}_x$ with transition temperatures of 530 K and 660 K, respectively, compared to the experimental values 663 K and ≈670 K. The significant improvement over previous first-principles studies is attributed to the more accurate treatment of atomic relaxations in the present work. (iii) LAPW formation enthalpies demonstrate that ${L1\mathrm{}}_2$, the commonly assumed stable phase of ${\mathrm{CuAu}}_3$, is not the ground state for Au-rich alloys, but rather that ordered (100) superlattices are stabilized. (iv) We extract the nonconfigurational (e.g., vibrational) entropies of formation and obtain large values for the size-mismatched systems: 0.48 $k_B$/atom in ${\mathrm{Ni}}_{0.5}{\mathrm{Au}}_{0.5}$ $(T=1100\mathrm{}$ K), 0.37 $k_B$/atom in ${\mathrm{Cu}}_{0.141}{\mathrm{Ag}}_{0.859}$ $(T=1052\mathrm{}$ K), and 0.16 $k_B$/atom in ${\mathrm{Cu}}_{0.5}{\mathrm{Au}}_{0.5}$ $(T=800\mathrm{}$ K). (v) Using 8 atom/cell special quasirandom structures we study the bond lengths in disordered Cu-Au and Ni-Au alloys and obtain good qualitative agreement with recent extended x-ray-absorption fine-structure measurements.