Thermodynamic variational method for liquid alloys with chemical short-range order

Abstract

We present a first-principles study of chemical short-range ordering in liquid (s,p)-bonded alloys. Our approach is based on an optimized pseudopotential technique for the construction of the interatomic potentials and a thermodynamic variational technique based on the Gibbs-Bogoliubov inequality and hard-sphere Yukawa reference potentials (we use the analytical solution of the mean spherical solution for the equal-diameter case). The analysis of the redistribution of the valence electrons upon alloying allows us to elucidate the electronic origin of the ordering potential. In the case of a moderately strong ordering interaction, the application of the Gibbs-Bogoliubov variational technique yields a reasonably accurate prediction of the structure factors and of the thermodynamic excess functions. For very strong ordering potentials, a free minimization of the variational upper bound to the exact free energy gives unrealistic results. This is a consequence of the complete decoupling of number-density and concentration fluctuations in the mean-spherical approximation to the equal-diameter hard-sphere Yukawa mixture. We find that realistic solutions may be found by imposing the condition that the exact and the reference-system ordering potentials be the same at the mean effective atomic diameter. This constrained minimization of the variational free energy yields good results for the structure factors, but rather bad ones for the thermodynamic excess functions. We are able to show that this is due to a neglect of the finite electronic mean free path of the electrons in those concentration regions where it is comparable to the mean interatomic distance.