Coarse-grained density functional theory of order-disorder phase transitions in metallic alloys

The technological performances of metallic compounds are largely influenced by atomic ordering. At finite temperatures metallic alloys are not perfectly ordered nor ideally disordered. Although there is a general consensus that successful theories of metallic systems should account for the quantum nature of the electronic glue, existing nonperturbative high-temperature treatments are based on effective classical atomic Hamiltonians. We propose a solution for the above paradox and offer a fully quantum mechanical, though approximate, theory that on equal footing deals with both electrons and ions. Thus, the amount of order and the electronic properties of metallic alloys are self-consistently determined as a function of the temperature. Our formulation is based on a coarse-grained version of the density functional theory and a Monte Carlo technique, which are jointly implemented allowing for the efficient evaluation of finite temperature statistical averages. Calculations of the relevant thermodynamic quantities and of the electronic structures for CuZn and ${\text{Ni}}_{3}\text{V}$ support that our theory provides an appropriate description of order-disorder phase transitions.