the modeling of the subsystems, especially Al-Co-Ni and Co-Cr-Ni, necessary in building a coherent Al-Co-Cr-Ni quaternary description. Some modifications are made in the description of the Al-Co-Cr [5] system and are discussed in detail later in the manuscript. The quaternary Al-Co-Cr-Ni system is studied in a separate publication [8].While B2 (β, , simple cubic type) and fcc-A1 (γ, , disordered f.c.c.) are the desired phases in MCrAlY coatings, all other phases must be modeled to give an accurate overall description of phase stability in the system. These include bcc-A2 (α, , disordered b.c.c.), 3 Pm m 3 Fm m 3 Im m 3 hcp-A3 (ε, , disordered h.c.p.), L1 2 (γ', , simple cubic type), sigma (σ, , Frank-Kasper, Figure 1 (a)) and the binary intermetallics. The present paper focuses on evaluating and modeling the important ternary alloy systems found in the Al-Co-Cr-Ni quaternary in order to produce meaningful extrapolations without the need of excessive higher order parameters. First-principles calculations based on density functional theory (DFT) are performed to supplement the lack of experimentally measured thermochemical data. By effectively combining these results with experimental information from the literature, energetically accurate parameters in the lower order systems are evaluated. Ultimately, this model will be used in the construction of a multicomponent Al-Co-Cr-Ni database in future work. 2 Literature review 2.1 Binary models used in the present workThe assessment of the Al-Co binary by Dupin and Ansara [9] reproduces all experimental results available in the literature satisfactorily and is hence adopted in the present work. The model for B2 in the original Al-Co binary was asymmetrical and was changed to the orderdisorder model by Liu et al. in previous work on the system [5], which is adopted here. The Al-Cr assessment by Saunders, which can be found in the COST507 [10] database, is also accepted without modification. The assessment for the Al-Ni binary by Ansara et al. [11], (later modified by Dupin et al. [6]) has been used extensively previously and is, therefore, adopted in the present work. There are two descriptions of the Co-Cr binary available which both reproduce certain experiments well, one by Oikawa et al. [12] and another by Kusoffsky et al. [13]. However, it 3 6/ P mmc 3 Pm m 2 4/ P mnm 4 has been found that the Oikawa description has σ end-member energies which disagree with experiments by Downie and Arslan [14] though it was adopted in the previous modeling of Al-Co-Cr [5]. It is important to have correct energies in the binary subsystems to produce accurate extrapolations to the higher order systems and for this reason, the model by Kusoffsky et al. [13] is used here. The Co-Ni and Cr-Ni binary descriptions are taken from SGTE [15], based on works by Guillermet [16] and Lee [17], respectively. In addition, the present Cr-Ni description includes a metastable description of σ following the work by Gustafson [18] in the ternary Ni-Cr-W system which is later modified by Kattner [7]. Re...

A thermodynamic database for the Al–Co–Cr–Ni system is built via the Calphad method by extrapolating re-assessed ternary subsystems. A minimum number of quaternary parameters are included, which are optimized using experimental phase equilibrium data obtained by electron probe micro-analysis and x-ray diffraction analysis of NiCoCrAlY alloys spanning a wide compositional range, after annealing at 900 °C, 1100 °C and 1200 °C, and water quenching. These temperatures are relevant to oxidation and corrosion resistant MCrAlY coatings, where M corresponds to some combination of nickel and cobalt. Comparisons of calculated and measured phase compositions show excellent agreement for the β–γ equilibrium, and good agreement for three-phase β–γ–σ and β–γ–α equilibria. An extensive comparison with existing Ni-base databases (TCNI6, TTNI8, NIST) is presented in terms of phase compositions.

A vast number of materials properties and phenomena are regulated by diffusion. However, diffusion coefficients from experiments and calculations are far from complete. Here, we report a compilation of vacancy formation energies ( ), vacancy migration energies ( ), vacancy activation energies ( ), vacancy concentrations (C Va ), and vacancy-mediated self-diffusion coefficients (D Va ) as a function of temperature for 82 pure elements in bcc, fcc, and hcp structures by means of a comprehensive first-principles study. We assess the accuracy of four exchange-correlation (X-C) functionals for first-principles calculations, including the local density approximation (LDA), two generalized gradient approximations (PW91 and PBE), andPBEsol  the focus of the present work. To gain temperature-dependent diffusion properties, transition state structure searches are performed by the climbing image nudged elastic band

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