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Failures of Miedema’s model to predict enthalpies of formation for binary Zr-based compounds are attributed to the original choice of the parameter for electronegativity, ϕ∗=3.45 V, for Zr. By refinement procedures based on (1) ab initio enthalpies of formation, (2) reliable calorimetric data for the compounds, and (3) data for elemental metallic Zr we suggest that ϕ∗=3.62 V is a reasonable choice...
Enthalpies of mixing for ternary fcc solid solutions in Al–Cu–Mg, Al–Cu–Si, and Al–Mg–Si systems are calculated from first-principles study of ternary fcc Special Quasirandom Structures (SQS) whose correlation functions are close to those of completely random fcc solid solutions. It is shown that ternary fcc SQSs calculations at four different compositions in each system, i.e. xA=xB=xC=13; xA=12,...
In this paper we have used a combined first principles and Calphad approach to calculate phase diagrams in the titanium–carbon–nitrogen system, with particular focus on the vacancy-induced ordering of the substoichiometric carbonitride phase, TiC x N y (x+y≤1). Results from earlier Monte Carlo simulations of the low-temperature binary phase diagrams are used in order to formulate sublattice...
The thermodynamic description of the Cu–Si system has been updated with first-principles calculations of the ϵ-Cu 15 Si 4 phase and solid solution phases. Calculated enthalpy of formation for the ϵ-phase indicates that enthalpies of formation for intermetallic compounds in Cu–Si must be negative, which were evaluated as positive in the previous thermodynamic modelings. Enthalpies of...
A calorimetric study of alloys along the section TiZn 3 –TiAl 3 is carried out to determine their heat of formation (ΔfH∘) at 300 K using a high temperature direct drop calorimeter. The target compositions of the alloys lie in the range of 10–65 at.% Al. The structure and composition of the reacted samples are characterized by X-ray diffraction and electron probe microanalysis. The...
A thermodynamic database has been produced for the Al–Co–Ni–Y quaternary system, with an emphasis on the Al-rich region of the Al–Ni–Y ternary system. The database was created using the CALPHAD method, combining existing binary systems with relevant experimental and first-principles information for selected Al–Ni–Y and Co-containing compounds. The thermodynamic database was used to produce equilibrium...
The Sn–V binary system was thermodynamically modeled using the CALPHAD approach combined with first-principles calculations. The predicted Gibbs free energy of the end-members in sublattice models of “ V 3 Sn” phase by the first-principles calculations was used to describe the lattice stabilities. A set of thermodynamic parameters for the Sn–V system was obtained using the PanOptimizer program...
Thermodynamic modeling of the Si–Sr system was carried out using the CALPHAD method. In this system, three of the intermetallic compounds, Sr 2 Si,Sr 5 Si 3 ,SrSi, were considered to be stoichiometric and SrSi 2 was modeled as a non-stoichiometric phase. For the liquid phase, two different models were used. In one case, Sr and Si were assumed to constitute a random...
The Pt–Ga–Ge ternary system was thermodynamically assessed by the CALPHAD (CALculaton of PHAse Diagram) approach with help of first-principles calculations. Firstly, the formation enthalpies of the Pt–Ge and Pt–Ga compounds were calculated by the first-principles method. Subsequently, the Pt–Ge system was modeled and the Pt–Ga system was re-assessed. The solution phases, Liquid, Diamond_A4 (Ge) and...
The Ge–Sr system is investigated via a hybrid approach of CALPHAD and first-principles calculations. The experimental phase diagram and thermodynamic data available in the literature are critically reviewed and assessed by using thermodynamic models for the Gibbs energies of the individual phases. The enthalpies of formation for Ge 2 Sr, GeSr, Ge 3 Sr 5 , and GeSr 2 ...
The V–Zn system was investigated by a combination of CALPHAD modeling with key experiments and first-principles calculations. Based on a critical literature review, one diffusion couple and nine alloys were designed to reinvestigate the stabilities of the phases reported in the literature. The samples were annealed and cooled under different conditions, followed by examination with X-ray diffraction...
Using first-principles total energies and frozen phonon calculations, we predict the thermodynamic properties (enthalpies of formation and vibrational entropies) for three phases in the Al–Mg–Si system: the stable phase (β-Mg 2 Si), and two metastable precipitate phases (β′-Mg18Si10 and β″-Mg5Si6). The stable fcc/β and the metastable fcc/β′ and fcc/β″ phase boundaries are obtained from a combination...
Thermodynamic description of the Cs–In system has been developed by the CALPHAD modeling combined with first-principles calculations. From first-principles calculations, the enthalpies of formation of CsIn 3 and Cs 2 In 3 are predicted to be −14.76 and −16.79 kJ/mol atom, respectively. With these enthalpies of formation and phase equilibrium data, Gibbs energy functions of...
A thermodynamic analysis of the phase equilibria in the Cr–Mo–B ternary system has been carried out by combining first-principles calculations with the CALPHAD approach. The thermodynamic descriptions of three binary systems relevant to this ternary phase diagram were taken from previous studies. The enthalpy of formation of the (Cr,Mo) 2 B (Al 2 Cu-type, tI12, space group I4/mcm),...
Various experimentally measured diffusivities of fcc Al–Mg, Cu–Mg and Al–Cu–Mg alloys available in the literature are critically reviewed in the present work. The first-principles calculations coupled with a semi-empirical correlation is employed to derive the temperature dependence of impurity diffusivity for Mg in fcc Cu. Atomic mobilities for the above fcc alloys are then evaluated as a function...
Thermodynamic description of the Al–Pt binary system is modeled by combining first-principles calculations with the CALPHAD method. The four-sublattice and two-sublattice compound energy formalisms are used to model the ordered L1 2 and B2 phases, respectively. The modeling includes the solution phases and the stoichiometric Al 21 Pt 5 , Al 21 Pt 8 , Al ...
Knowledge of thermodynamics and phase diagram is a prerequisite for understanding many scientific and technological disciplines. To establish a reliable thermodynamic database, an integrated approach of key experiments and thermodynamic modeling, supplemented with first-principles calculations, can be utilized. In this paper, first investigations of phase diagram and thermodynamics of technologically...
Systematic first-principles calculations of energy vs. volume (E–V) and single crystal elastic stiffness constants (cij’s) have been performed for 50 Al binary compounds in the Al–X (X = Co, Cu, Hf, Mg, Mn, Ni, Sr, V, Ti, Y, and Zr) systems. The E–V equations of state are fitted by a four-parameter Birch–Murnaghan equation, and the cij’s are determined by an efficient strain–stress method. The calculated...
The total energies of intermetallic compounds in the Si–Zr system are calculated employing electronic density-functional theory (DFT). The calculated zero-temperature lattice parameters and internal parameters of the stable intermetallic compounds agree well with those obtained experimentally at ambient temperature. The calculated formation enthalpies are in good agreement with the most recent available...
We propose a cluster expansion (CE) technique that can be applied to any atomic arrangement on alloy systems in their polymorphs. The proposed CE introduces virtual vacancy sites in the starting structure in order to describe the atomic positions for a variety of lattices. We derive the general condition for obtaining effective interactions in the present CE, which results in rigorous expansion of...
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