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 K. (ii) Of all possible structures, Cu3Au (L1(2)) and CuAu (L1(0)) are found to be the most stable low-temperature phases of Cu1-xAux with transition temperatures of 530 K and 660 K, respectively, compared to the experimental values 663 K and approximate to 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(2), the commonly assumed stable phase of CuAu,, 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 Ni0.5Au0.5 (T=1100 K), 0.37 k(B)/atom in Cu0.141Ag0.859 (T=1052 K), and 0.16 k(B)/atom in Cu0.5Au0.5 (T=800 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.