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

Abstract

The technological performances of metallic compounds are largely influenced by atomic ordering. Although there is a general consensus that successful theories of metallic systems should account for the quantum nature of the electronic glue, existing non-perturbative 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. By taking advantage of a coarse grained formulation of the density functional theory [Bruno et al., Phys. Rev. B 77, 155108 (2008)] we develop a MonteCarlo technique, based on an ab initio Hamiltonian, that allows for the efficient evaluation of finite temperature statistical averages. Calculations of the relevant thermodynamic quantities and of the electronic structures for CuZn and Ni3V support that our theory provides an appropriate description of orderdisorder phase transitions. PACS numbers:Nowadays ground state properties of metallic alloys are routinely calculated by using Density Functional (DF) [1, 2] theory which appropriately incorporates electronic correlations. However, most finite temperature status of art calculations [3] are based on classical Ising models which allow the accurate evaluation of phase equilibria, but are not able to predict the electronic properties. A theory able to cope with both tasks must incorporate quantum mechanics and should be able to explore the very large space of alloy configurations [4] in order to give reliable statistical averages. Unfortunately, quantum simulations as the Car-Parrinello Molecular Dynamics [5] (CPMD) are very hard for the problem at hand and the application of such methods the phase equilibria of metallic alloys seems beyond the capabilities of existing hardware and software. In this Letter we shall outline a new approach to the problem, which, similarly to CPMD is based on the DF theory and the Born-Oppenheimer approximation, but where the relevant quantities shall be obtained as statistical averages (by sampling the space of alloy configurations) rather than as Boltzmann time averages.Although the generalization to n-ary systems is straightforward, in this Letter we focus on binary metallic alloys A c B 1−c . They shall be studied in the (T, c) statistical ensemble defined by the temperature, T , and the mean atomic concentration, c. In order to have a tractable problem, we shall limit ourselves to the solid state and the normal metal regime or, equivalently, to the temperatures between the superconducting and the melting transitions, T SC < T < T M . Furthermore, martensitic and magnetic phenomena shall not be considered.Our first crucial step is to obtain a coarse grained version of the Hohenberg-Kohn DF. If the ions constituting the system are considered frozen on the sites of a simple lattice at their equilibrium positions, R i , then the electrostatic contribution to the DF can be written as a sum of local terms plus some bilinear terms...

Lattice charge models and core level shifts in disordered alloys

“…However, the strength of the CEFM comes from the fact that, as mentioned earlier, the free parameters are seemingly transferable between systems with the same species concentrations and underlying crystal lattice. Hence the CEFM is an efficient method for evaluating differences in the charge distribution 24,25 and energies 26 between such systems, with potential applications including Monte Carlo simulations 27 . The layout of this paper is as follows.…”