First-principles all-electron theory of atomic short-range ordering in metallic alloys:D022- versusL12-like correlations

We use a ‘‘first-principles’’ concentration-wave approach based on a finite-temperature, electronic density-functional, mean-field, grand potential of the random alloy to investigate the high-temperature atomic short-range order (ASRO) in ${\mathrm{Ni}}_{75}$ ${\mathrm{V}}_{25}$ and ${\mathrm{Pd}}_{75}$ ${\mathrm{V}}_{25}$ solid solutions. Experimentally, these similar alloys both develop D$0_{22}$-type long-range order at low temperatures but different ASRO at high temperatures. Our calculations describe the measured ASRO well. We compare these results with those found for a hypothetical ${\mathrm{Co}}_{75}$ ${\mathrm{Ti}}_{25}$ solid solution. Since this alloy orders directly from the melt into the L$1_2$ phase, it should exhibit strong L$1_2$-like ASRO, as we find in our calculations. We analyze the features in the calculated diffuse intensities in terms of various factors in each alloy’s electronic structure. Because we have assumed that the atoms are fixed to the Bravais lattice, we discuss two additional examples, ${\mathrm{Al}}_{75}$ ${\mathrm{Ti}}_{25}$ and ${\mathrm{Ni}}_{50}$ ${\mathrm{Pt}}_{50}$, to show the limitations of neglecting atomic displacements. Notably, the Onsager cavity fields have been incorporated into the theory to conserve the diffuse scattering intensity over the Brillouin zone and to provide a better description of the long-ranged, electrostatic screening effects.