Phase diagrams and mechanical properties of TiC-SiC solid solutions from first-principles

First-principles calculations were carried out in order to investigate the stability and properties of the random Ti_1-xSi_xC solid solutions (alloys) with both the B1 and B3 structures. Lattice parameter, total energy, formation energy, phonon spectra, and elastic properties were studied as functions of composition. The phase diagram, in particular, binodal and spinodal curves were calculated. It was established that at 0 K the B1 alloys are energetically favorable at 0 ≤ x < 0.5, while the B3 alloys are favorable at 0.5 ≤ x ≤ 1.0. It was found that the contribution to the Gibbs free energy coming from the lattice vibrations strongly reduces the critical temperature of stabilization of the solid solutions. Calculated elastic moduli, Debye temperature, and Vickers hardness do not point to any strength enhancement of the alloys compared to TiC and SiC. Analysis of the spatial distribution of the Young and shear moduli shows that the B3 alloys exhibit much more spatial anisotropy of the elastic moduli than the B1 alloys.     

Structure, elastic and thermodynamic properties of the Ni-P system from first-principles calculations

A systematic investigation concerned with the structure, elastic, and finite-temperature thermodynamic properties of Ni₃P, Ni₁₂P₅, Ni₂P, Ni₅P₄, NiP, cubic NiP₂ (C- NiP₂), monoclinic NiP₂ (M- NiP₂), and NiP₃ in the Ni-P system is carried out via first-principles calculations. The elastic stiffness tensors and associated macroscopic elastic properties of these Ni-P compounds including the bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio are calculated. Within the framework of the quasi-harmonic approach, the finite-temperature thermodynamic properties of these Ni-P compounds including the Helmholtz free energy, entropy, heat capacity at constant pressure and enthalpy are predicted. The acquired thermodynamic properties are expected to be utilized for the thermodynamic modelling of the Ni-P system.     

First-principles calculations of binary Al compounds: Enthalpies of formation and elastic properties

Systematic first-principles calculations of energy vs. volume (E-V) and single crystal elastic stiffness constants (c_ij’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 c_ij’s are determined by an efficient strain-stress method. The calculated lattice parameters, enthalpies of formation, and c_ij’s of these binary compounds are compared with the available experimental data in the literature. In addition, elastic properties of polycrystalline aggregates including bulk modulus (B), shear modulus (G), Young’s modulus (E), B/G (bulk/shear) ratio, and anisotropy ratio are calculated and compared with the experimental and theoretical results available in the literature. The systematic predictions of elastic properties and enthalpies of formation for Al-X compounds provide an insight into the understanding and design of Al-based alloys.     

Phase equilibria and microstructure development in Mg-rich Mg-Gd-Sr alloys: Experiments and CALPHAD assessment

Mg-Sr alloys are promising to fabricate orthopedic implants. The alloying of rare earth elements such as Gd may improve the comprehensive mechanical properties of Mg-Sr alloys. The information on the phase diagram and the microstructure development are required to design chemical composition and microstructure of Gd alloyed Mg-Sr alloys. The phase equilibria and the microstructure development in Mg-rich Mg-Gd-Sr alloys (Gd, Sr < 30 at. %) are experimentally investigated via phase identification, chemical analysis, and microstructure observation with respect to the annealed ternary alloys. The onset temperatures of liquid formation are measured by differential scanning calorimetry. A thermodynamic database of the Mg-rich Mg–Gd–Sr ternary system is developed for the first time via CALPHAD (CALculation of PHAse Diagram) approach assisted by First-Principles calculations. The thermodynamic calculations with the developed database enable a well reproduction of the experimental findings and the physical-metallurgical understanding of the microstructure formation in solidification and annealing.     

Phase equilibria of the Zn-Ti system: Experiments,first-principles calculations and Calphad assessment

The phase equilibria and thermodynamic properties of the Zn-Ti system have been investigated by experiments, first-principles calculations and Calphad assessment. Differential scanning calorimetry measurement and microstructure characterization confirmed the Zn richest eutectic reaction to occur at 691.3 ± 0.4 K with about 0.27 at% Ti in the liquid. Density functional theory (DFT) calculations have been performed to calculate the finite-temperature heat capacity (C_p) of the intermetallics, providing also the absolute entropies. A full thermodynamic assessment of the Zn-Ti system has been performed by using the experimental and DFT results obtained in this work together with the collection of all available data from previous publications. In the present work, the Calphad results show good agreement not only in thermodynamic properties with DFT data, but also phase equilibria data with experimental results, especially in the Zn-rich side, which significantly improved from previous Calphad assessment. Phase diagrams including the gas phase have also been calculated and discussed.     

An overview on phase equilibria and thermodynamic modeling in multicomponent Al alloys: Focusing on the Al-Cu-Fe-Mg-Mn-Ni-Si-Zn system

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 important Al alloys (focusing on the Al-Cu-Fe-Mg-Mn-Ni-Si-Zn system, which covers the major elements in most commercial Al alloys) is reviewed with an emphasis on the need of the integrated approach. Second, the major experimental methods (X-ray diffraction, metallography, electron probe microanalysis, differential thermal analysis, diffusion couple method, and calorimetry), which are widely employed to provide phase diagram and thermodynamic data, are briefly described. Third, the basics of the first-principles calculations and CALPHAD are presented focusing on the integration of these two computational approaches. Case study for the representative Al-Fe-Ni ternary system is then demonstrated, followed by a thermodynamic modeling of the quinary Al-Fe-Mg-Mn-Si system and a brief summary to our recent activities on investigations of phase equilibria in multicomponent Al alloys.     

Thermodynamic assessment of the Sr–In and Sr–Bi systems supported by first-principles calculations

Based on the available experimental phase equilibria and thermodynamic data, the Sr–In and Sr–Bi systems have been assessed by means of the CALPHAD technique. The solution phases (Liquid, (αSr), (βSr), (In) and (Bi)) were modeled with the Redlich–Kister polynomial. All the intermetallic compounds (SrIn₅, SrIn₃, Sr₂In₅, SrIn₂, Sr₂In₃, SrIn, Sr₅In₃, Sr₃In, SrBi₃, Sr₁₁Bi₁₀, αSr₅Bi₃, βSr₅Bi₃ and Sr₂Bi) were treated as stoichiometric compounds. The enthalpies of formation at 0 K for SrIn₅, SrIn₃, SrIn₂, SrIn, Sr₅In₃, Sr₃In, SrBi₃, αSr₅Bi₃, βSr₅Bi₃ and Sr₂Bi were computed by first-principles calculations in order to assist the thermodynamic modeling. A set of self-consistent thermodynamic parameters for each of the two systems has been obtained, and the present calculations can satisfactorily reproduce the available experimental data.     

Thermodynamic modeling of the Si-Y system aided by first-principles and phonon calculations

Thermodynamic modeling of the Si-Y binary system has been performed by the CALPHAD (CALculation of PHAse Diagram) method based on phase diagram and thermochemical data in the literature combined with Gibbs energies of end-members of compounds predicted by first-principles phonon calculations. In particular, non-stoichiometric compounds Si₂Y and Si₃Y₅ are modelled to accommodate their homogeneity ranges in terms of two-sublattice models (Si,Y)₂(Si,Y) and (Si)₃(Si,Y)₅, respectively. Formation of SiY is treated as a peritectic reaction according to experimental results, instead of an eutectic one as described in the previous models. The calculated phase equilibriums and thermodynamic properties are in a satisfactory agreement with available experimental data.     

A first-principles study on the electromechanical effect of graphene nanoribbon

The electromechanical effect of graphene nanoribbons (GNRs) is investigated via a first-principles method. The deformations of GNRs with zigzag shaped edges (ZGNR) and armchair shaped edges (AGNR) are considered. The nonlinear stress–strain relations are found for both of the AGNRs and the ZGNRs. The AGNRs seem to be stiffer than the ZGNRs as concluded from inspecting the Young's modulus and the ideal strength of GNRs. It is found that a mechanical deformation will affect the electronic structures of GNRs. The band gap of AGNRs exhibits sawtooth oscillations under strains and the oscillating strength is up to 1 eV. On the contrary, the band gap of ZGNRs is insensitive to strain. However, the band gap of ZGNRs will be reduced dramatically to zero as the compressive strain is greater than 0.17. The large variation of the band gap of AGNRs under strain indicates that deformation can provide an opportunity for tuning the band gap of an AGNR.     

Thermodynamic modeling of Laves phases in the Cr–Hf and Cr–Ti systems: Reassessment using first-principles results

The Cr–Hf and Cr–Ti belong to interesting systems exhibiting the existence of all polytypes of Laves phases, i.e. lower-temperature cubic C15 and higher-temperature hexagonal C14 and C36, although in the Cr–Hf phase diagram only C14 and C15 phases occur. Comparison of total energies of these structures calculated from first principles with the total energy of the ideal mixture of elemental constituents reveals the relative stability of Laves phases in these systems. The effect of magnetic order in the Laves phases is also briefly discussed.     

Thermodynamic assessment of the Ga–X (X=B,Ca, Sr,Ba) systems supported by first-principles calculations

Thermodynamic modeling of the Ga–X (X=B, Ca, Sr, Ba) systems was performed based on the available experimental information and first-principles calculations. Enthalpies of formation for the compounds (Ca₂₈Ga₁₁, Ca₅Ga₃, Ca₁₁Ga₇, CaGa, Ca₃Ga₅, CaGa₂, Ca₃Ga₈, CaGa₄, Ga₄Sr, Ga₂Sr, Ga₇Sr₈, Ba₈Ga₇, BaGa₂ and BaGa₄) at 0 K were computed by ab initio methods, and were used to improve the accuracy of the present assessment. A set of self-consistent thermodynamic parameters was obtained. The computed phase diagrams and thermodynamic properties of the Ga–X (X=B, Ca, Sr, Ba) systems agree well with the experimental data and first-principles calculations.     

Critical evaluation of ternary phase diagram data: Important considerations in the scrutiny of the correctness,coherence, and interpretation

Thermodynamic optimization of ternary phase diagrams via Calphad approach is a complex procedure. The success and quality of such a Calphad optimization depend on the reliability of the experimental data and on the scrutiny of the critical evaluation of the experimental datasets. With this in mind, we provide a set of recommendations that might facilitate the critical evaluation procedure and improve the quality of the thermodynamic datasets for the calculations of the phase diagrams. The particulars regarding the consistency between binary and ternary phase diagrams as well as the internal agreement between the different ternary datasets, are discussed.