The thermodynamic ordering transformation of tetragonal FeNi system is investigated by the Exact Muffin-Tin Orbitals (EMTO) method. The tetragonal distortion of the unit cell is taken into account and the free energy is calculated as a function of long-range order and includes the configurational, vibrational, electronic and magnetic contributions. We find that both configurational and vibrational effects are important and that the vibrational effect lowers the predicted transformation temperature by about 480 K compared to the value obtained merely from the configurational free energy. The predicted temperature is in excellent agreement with the experimental value when all contributions are taken into account. We also perform spin dynamics calculations for the magnetic transition temperature and find it to be in agreement with the experiments. The present research opens new opportunities for quantum-mechanical engineering of the chemical and magnetic ordering in tetrataenite.

Semilocal density functional approximations occupy the second rung of the Jacob's ladder model and are thus expected to have certain limits to their applicability. Recently, it has been hypothesized that the formation energy, being one of the key quantities in alloy theory, would be beyond the grasp of semilocal Density Functional Theory (DFT). Here we explore the physics of semilocal DFT formation energies and shed light on the connection between the accuracy of the formation energy and the ability of a semilocal approximation to produce accurate lattice constants. We demonstrate that semilocal functionals designed to perform well for alloy constituents can concomitantly solve the problem of alloy formation energies.PACS numbers: 71.15. Mb, 71.20.Be, 64.30.Ef, Density Functional Theory (DFT) with its various practical approximate forms has come to have a deep impact on many different fields of science. The local and semilocal exchange-correlation (XC) schemes, such as the Local Density Approximation (LDA) and the Generalized Gradient Approximation (GGA) [1], are two of the most important levels (first and second rungs of the Jacob's ladder model [2]) on the DFT XC approximation gamut. Recently, there has also been important developments in meta-GGAs (third rung of the Jacob's ladder), where the functional also includes dependence on the kinetic energy density. Empirical meta-GGAs, e.g. the M06 family [3][4][5], and recent nonempirical meta-GGAs, such as MGGA-MS2 [6] and SCAN [7], can lead to significant improvements in both structure and energetics [8].The computational efficiency of the first three rungs of the Jacob's ladder is superior compared to most of the more sophisticated approaches. Naturally, for this reason semilocal XC approximations are in many instances preferred, especially when large amounts of individual calculations are involved. Therefore, it is vitally important to establish a clear picture of the limits and capabilities of semilocal approximations.In a recent Letter by Zhang et al.[9], it was surmised that conventional semilocal DFT simply falls short of being able to accurately predict key properties in alloy theory, such as the formation energy. One of the most spectacular failures happens with the well-known Cu-Au system showing a series of intermetallic compounds. Zhang et al. found that the experimental formation energies of these intermetallics are far smaller in magnitude than their (semi)local DFT counterparts and concluded that nonlocal exchange interaction schemes, such as the HeydScuseria-Ernzerhof (HSE) hybrid functional [10,11], are necessary in order to mitigate the delocalization error of standard approximations and to increase the accuracy of the theoretical predictions. This finding has raised strong doubts concerning the scope of (semi)local DFT and in particular the applicability of LDA or PerdewBurke-Ernzerhof (PBE) [12] GGA to Cu-Au and similar important members of the highly versatile class of metallic alloys.In this Letter, we adopt an energy functional perspective a...

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In our previous study [Phys. Rev. B 86, 201104 (2012)] we introduced the so called quasi-non-uniform gradient-level exchange-correlation approximation (QNA) and demonstrated it's strength in producing highly accurate equilibrium volumes for metals and their alloys within the density-functional theory. In this paper we extend the scheme to include the accuracy of bulk modulus as an additional figure of merit and show that this scheme is flexible enough as to allow the computation of accurate equilibrium volumes and bulk moduli at the same time. The power and feasibility of this scheme is demonstrated on NiAl and FeV binary alloys