Phase Thermodynamic Properties Research Articles

First-principles thermodynamic investigation on the α phases in TiO and TiNb binary system.

O and Nb are two representative alloying elements of Ti to form high-temperature and corrosion resistance α Ti alloys. The investigation on the thermodynamic characteristics of α Ti-O and Ti-Nb has attracted much attention in recent years. However, in this regard, a satisfied experimental technique or modeling scheme is still yet to be developed due to the appearance of a variety of oxides in Ti-O and the mechanical instability present in Ti-Nb. Herein, we combined first-principles calculations with the cluster expansion method to investigate the ground-state characteristics for α Ti-O and α Ti-Nb systems. The atomic bonding interactions in these two systems were first revealed based on the calculated electronic structures. Afterward, the Debye-Grüneisen model and Monte Carlo simulations were employed together to investigate the thermodynamic properties of α phases in these two systems, and the effect of vibrational entropy on the order-disorder transition temperatures of the phases in α Ti-O system was first examined. A good agreement with experimentally reported phase boundaries is obtained in the Ti-Nb system by handling the mechanical instabilities introduced by the highly distorted structures. In addition, the cluster expansion coefficients for the Ti-O and Ti-Nb system offer a good starting point to investigate the phase equilibrium in Ti-Nb-O ternary alloy. We also believe the insights provided here would be helpful for those who would like to seek an efficient scheme they are confident with to investigate the phase thermodynamic properties of other hcp Ti-based alloys.

Advances in CALPHAD Methodology for Modeling Hydrides: A Comprehensive Review

AbstractHydrides enable handling hydrogen at low pressure and near room temperature, offering higher volumetric densities than compressed or liquid hydrogen and enhancing safety. The CALPHAD method, rooted in the principles of thermodynamics, offers a systematic approach for predicting phase equilibria and thermodynamic properties in multicomponent materials. This comprehensive review paper aims to provide a detailed overview of the application of the CALPHAD method in the realm of metallic and complex hydrides. After an introduction to the fundamental thermodynamic aspects of hydrides, key elements of applying the CALPHAD method to model metal-hydrogen systems and complex hydrides are discussed. Subsequently, recent publications are reviewed, highlighting key findings and recent progresses in the field. Finally, the challenges that must be overcome to achieve further progress in this area are explored.

Comprehensive analysis of the phase stability, optoelectronic, mechanical, thermodynamic, and vibrational properties for prospective optoelectronic applications of novel combinations of chalcogenides XScTe2 (X = Li, Rb) by employing density functional theory

Comprehensive analysis of the phase stability, optoelectronic, mechanical, thermodynamic, and vibrational properties for prospective optoelectronic applications of novel combinations of chalcogenides XScTe2 (X = Li, Rb) by employing density functional theory

Thermodynamic Assessment of the P2O5-Na2O and P2O5-MgO Systems.

Knowledge about the thermodynamic equilibria of the P2O5-Na2O and P2O5-MgO systems is very important for controlling the phosphorus content of steel materials in the process of steelmaking dephosphorization. The phase equilibrium and thermodynamic data of the P2O5-Na2O and P2O5-MgO systems were critically evaluated and re-assessed by the CALPHAD (CAlculation of PHAse Diagram) approach. The liquid phase was described by the ionic two-sublattice model for the first time with the formulas (Na+1)P(O-2, PO3-1, PO4-3, PO5/2)Q and (Mg+2)P(O-2, PO3-1, PO4-3, PO5/2)Q, respectively, and the selection of the species constituting the liquid phase was based on the structure of the phosphate melts. A new and improved self-consistent set of thermodynamic parameters for the P2O5-Na2O and P2O5-MgO systems was finally obtained, and the calculated phase diagram and thermodynamic properties exhibited excellent agreement with the experimental data. The difference in the phase composition of invariant reactions from the experimentally determined values reported in the literature is less than 0.9 mol.%. The present thermodynamic modeling contributes to constructing a multicomponent oxide thermodynamic database in the process of steelmaking dephosphorization.

A Comprehensive Ab Initio Study of the Recently Synthesized Zintl Phase CsGaSb2 Structural, Dynamical Stability, Elastic and Thermodynamic Properties

A Comprehensive Ab Initio Study of the Recently Synthesized Zintl Phase CsGaSb2 Structural, Dynamical Stability, Elastic and Thermodynamic Properties

Thermodynamic assessment of the Cr–Si binary system

A thermodynamic evaluation of the Cr–Si system was performed concerning the latest experimental phase diagram and with the aid of first-principles calculations. The thermodynamic parameters for the Gibbs energy of pure Cr were modified based on the new experimental value of 1861 °C for the melting point of pure Cr, which was previously reported as 1907 °C in the SGTE database. The Gibbs energy descriptions of the Cr3Si and Cr5Si3 phases were revised using Cr3(Cr,Si)- and (Cr,Si)5Si3-type two-sublattice models to reproduce the latest experimental results of their solubility composition ranges, that is, Cr3Si extending toward the Cr-rich side and Cr5Si3 extending toward the Si-rich side from the stoichiometry. The CrSi and CrSi2 phases were considered line compounds with no solubility range, and the solubility of Cr in the Si phase was ignored. A set of self-consistent thermodynamic parameters for the Cr–Si system was obtained using the CALPHAD technique. The phase diagrams calculated using the optimized parameters showed reasonable agreement with the latest phase equilibrium data and thermodynamic property data in the literature, including the enthalpy of mixing, formation enthalpy, and chemical potential diagrams of Cr and Si in the equilibrium phases.

Solid-liquid phase equilibrium and thermodynamic properties analysis of 1,3,5-tribromobenzene in sixteen kinds of organic mono-solvents

Solid-liquid equilibrium solubility of 1,3,5-Tribromobenzene (m-TBB) in 16 pure solvents, including ethyl formate, methyl acetate, ethyl acetate, propyl acetate, butyl acetate, amyl acetate, acetone, 2-butanone, cyclohexanone, 1,2-dichloroethane, chloroform, cyclohexane, toluene, tetrahydrofuran (THF), N,N-dimethylformamide (DMF), and N,N-dimethylacetamide (DMA) were determined by gravimetric method at different temperatures. The solubility of m-TBB increases gradually with the increase of temperature. The order of solubility of m-TBB in alkanes solvents is: chloroform > 1,2-dichloroethane > cyclohexane. The order of solubility of m-TBB in esters solvents is: amyl acetate > butyl acetate > propyl acetate > ethyl acetate > methyl acetate > ethyl formate. The order of solubility of m-TBB in ketones solvents is: cyclohexanone > 2-butanone > acetone. The order of solubility of m-TBB in other solvents is: THF > toluene > DMA > DMF. The KAT-LSER model was selected to explore the solvent effect of m-TBB in the tested solvents. Four thermodynamic models, i.e., the modified Apelblat model, the λh model, the NRTL model and the Wilson model, were selected for correlate the solubility data of m-TBB in 16 mono-solvents. The RAD and the RMSD values of NRTL model were all less than 1.67 × 10-2 and 3.82 × 10-4, respectively. All the four theoretical models can correlate the solubility data of m-TBB well in the selected solvents. The dissolution process of m-TBB were calculated based on the Wilson model. The dissolution process of m-TBB is endothermic, entropy increase and spontaneous. The entropy contributes more to Gibbs free energy.

Solid – phase equilibria and thermodynamic properties of the Sb-Te-S system

The powder X-ray diffraction (PXRD) analysis and the electromotive force (emf) measurements have been used to investigate the Sb–Te–S system in the Sb2S3-Sb2Te3-Te-S composition region at 300–450 K temperatures interval. Relative partial molar functions of antimony in alloys have been calculated and obtained data have been used to get self-consistent sets of the standard Gibbs free energy, standard enthalpy, and standard entropy of the Sb2S3 and Sb2Te2S compounds, as well as the Sb2Te2,4S0,6 and Sb2Te2,7S0,3 solid solutions. The data obtained for Sb2S3 have been compared to the ones available in the literature. Thermodynamic functions of the Sb2Te2S compound, as well as, the Sb2Te2,4S0,6 and Sb2Te2,7S0,3 solid solutions have been determined for the first time.

Phase stabilities and thermodynamic properties of crystalline phases in CaO–SiO2–H2O above 100 °C

The current study revises the phase diagram of the CaO–SiO2–H2O system at saturated steam pressure between 100 and 250 °C by combining experimentally observed phase relations, solubility data and thermodynamic restrictions. A new self-consistent thermodynamic dataset for crystalline C-S-H phases is reported. The dataset revises known thermodynamic properties and derives values for phases for which no data have been published up to now. Chemical compositions and molar volumes of the phases were updated based on recent crystal structure refinements. Additionally, thermodynamic properties are deduced for hydroxylellestadite, scawtite and spurrite as they are relevant for autoclaved concrete and metamorphism/metasomatism of rocks. Portlandite dominates together with hillebrandite, xonotlite and low-quartz the equilibrium phase assemblage up to 250 °C. If the formation of the latter three phases is delayed by kinetic reasons, numerous metastable phases can occur.

Thermodynamic modeling of the Al–Cr–Mo–Ni system

The Al–Cr–Mo–Ni system is of technical interest because it is an essential system for the thermodynamic modeling of systems related to the Ni- and NiAl-based superalloys. The knowledge of phase behaviors and thermodynamic properties of this system will be greatly helpful for the development of related alloys. Thermodynamic modeling of the Al–Cr–Mo–Ni system in the previous effort is not satisfactory. In this study, the Cr–Mo–Ni system was re-optimized with more sophisticated binary databases, and a new thermodynamic database of the Al–Cr–Mo–Ni system was established. A satisfactory agreement between calculated results and experimental data was obtained. The thermodynamic database developed in this study is suitable for assisting the design of both Ni- and NiAl-based superalloys.

Thermo-Calc determination of phase diagram and thermodynamic properties of Ni-Al binary system

Ni-Al alloys have good corrosion-resistant properties making them preferable as a material of choice compared to ordinary metals. A good understanding of the phase diagram and thermodynamic properties of the Ni-Al alloy binary system is essential in determining relevant industrial applications of the system. The Ni-Al phase diagram is being reassessed since those found in the literature are based on old experimental studies. The phase diagram and thermodynamic properties of the Ni-Al alloy is determined using the Thermo-Calc 2022b software over a temperature range of 200 K to 2000 K and 1 atm of pressure. A total of nineteen fields (including elemental Al and Ni) comprising five single solid phases, one liquid phase, and twelve double regions were obtained from the equilibrium calculation. The thermodynamic calculation has six invariant reactions containing two eutectic reactions (914.83 ± 0.025 K and 1641.80 ± 0.025 K), three peritectic reactions (1123.55 ± 0.025 K, 1400.72 ± 0.025 K and 1642.65 ± 0.025 K), and one peritectoid reaction (913.96 ± 0.025 K). The solubility of Al in Ni is also determined. The Gibbs free energy, the molar enthalpy and the activities of Al in Ni are all calculated at temperatures 913 K, 1642 K, and 1953 K. The Thermo-Calc temperature – composition of the Ni-Al alloy is compared with the existing experimental studies to identify the physical properties of the different thermodynamic properties of the Ni-Al alloy binary system.

Thermodynamic descriptions of ternary Al–Si–Yb system and their application to understand solidification behaviors of Yb-modified Al–Si alloys

In this paper, thermodynamic descriptions of binary Si–Yb and ternary Al–Si-Yb system were assessed using the CALculation of PHAse Diagram (CALPHAD) technique, from which insights to the solidification behaviors of Yb-modified Al–Si alloys were attained. Firstly, all the experimental phase equilibria and thermodynamic properties in binary Si–Yb and ternary Al–Si-Yb systems were critically evaluated. Based on evaluated experimental data in the literature, the thermodynamic parameters of binary Si–Yb system were then updated, resulting in a better agreement with the experimental phase equilibrium data in Si-rich part than the previous assessment in the literature. Afterward, the thermodynamic descriptions of ternary Al–Si-Yb system were established on the basis of thermodynamic parameters of three boundary binaries, and their reliability was verified by comprehensively comparing the predicted thermodynamic properties/solidified behaviors with the literature data. Finally, the Scheil-Gulliver solidification simulations of different Yb-modified Al–Si alloys were conducted, from which the effect of Yb additions on the solidification sequences, phase transition temperatures, and phases/structures fractions in Al–Si-Yb alloys was analyzed.

Thermodynamic geometry of STU black holes

This work investigates the phase structure of STU black holes with uniform charges by utilizing the New Thermodynamic Geometry (NTG) approach. The study explores the intriguing relationship between heat capacity phase transitions and curvature singularities, employing the NTG formalism. The analysis encompasses an examination of phase transitions along the T − S and Q − Φ planes, a study of critical exponents, and an assessment of black hole stability. The NTG geometry is applied in both the normal and extended phase spaces, revealing valuable insights into the thermodynamic behavior and stability of STU black holes. Meanwhile, a closer examination of NTG geometry shows a positive correlation in the sign between the extrinsic curvature and the heat capacity, which is incompatible with the curvature singularity. Overall, this study contributes to our understanding of the phase transitions and thermodynamic properties of STU black holes, shedding light on the intricate interplay between curvature singularities and the stability of black holes in diverse thermodynamic scenarios.

Phase Diagram and Quantum Entanglement Properties of a Pentamer S = 1/2 Heisenberg Spin Cluster.

Cluster molecular magnets prove their potential for applications in quantum technologies, encouraging studies of quantum entanglement in spin systems. In the paper we discuss quantum entanglement properties of pentamer cluster composed of spins S=1/2 forming a tetrahedron with additional spin in its center, with geometry reproducing the smallest nonplanar graph. We model the system with isotropic Heisenberg Hamiltonian including external magnetic field and use exact diagonalization approach to explore the ground-state phase diagram and thermodynamic properties within canonical ensemble formalism. We focus the interest on two-spin entanglement quantified by Wootters concurrence. For ground state, we find two states with total cluster spin equal to 3/2 exhibiting entanglement, occurring preferably for antiferromagnetic interactions. For finite temperatures, we predict the presence of magnetic-field-induced entanglement as well as temperature-induced entanglement.

Exploring the phase stability, mechanical and thermodynamic properties of FeCrAl ternary alloy

Although FeCrAl ternary alloy is a promising high-temperature material, the structural features of the FeCrAl remains controversial. To understand the structural features and the related mechanical properties, here, we apply the first-principle method to study the structural stability, mechanical and thermodynamic properties of FeCrAl ternary alloy. Two FeCrAl phases: cubic and orthorhombic structures are designed and discussed. The calculated results show that two FeCrAl ternary alloys are thermodynamically stable at the ground state. In particular, the orthorhombic FeCrAl has better thermodynamically stable in comparison to the cubic FeCrAl. It is found that two FeCrAl ternary alloys exhibit mechanical stability based on the Born stability criteria. Importantly, we predict that two FeCrAl ternary alloys show ductility and plasticity. The orthorhombic FeCrAl shows the stronger volume deformation resistance and higher elastic stiffness in comparison to the cubic FeCrAl. Naturally, the high elastic modulus of the orthorhombic FeCrAl is related to the strong localized hybridization between Fe atom, Cr atom and Al atom in a layered structure. Finally, it is found that the calculated Debye temperature of the orthorhombic FeCrAl is higher than the cubic FeCrAl.

Phase transition and thermodynamic properties of CaV2O6 at high temperature

CaV2O6 is widely utilized in optoelectronic materials, dielectric ceramics, magnetic candidates, and catalytic materials due to its unique physical and chemical properties. CaV2O6 was synthesized by a conventional solid-state reaction technique in this study. The CaV2O6 crystallizes in a monoclinic system belonging to space group C2/m, with the lattice parameters of a = 10.06 Å, b = 3.675 Å, c = 7.039 Å, and β = 104.843°. The congruent melting of CaV2O6 was detected at 1045 K by performing DSC. Enthalpy increments of CaV2O6 were experimentally measured for temperatures ranging from 573 K to 1023 K employing drop calorimetry for the first time. The temperature dependence of the molar heat capacity of CaV2O6 was then calculated on the basis of the enthalpy increments results. Thermodynamic properties (enthalpy change, entropy, and Gibbs free energy) were also calculated in the temperature range of 300–1000 K.

Solid-liquid phase equilibrium and thermodynamic properties analysis of Bazedoxifene acetate in fifteen kinds of mono-solvents

Crystallization is widely used for the isolation and purification of active pharmaceutical ingredients (APIs) in the final manufacturing stage. Bazedoxifene (BZD) acetate, classified as a third-generation selective estrogen receptor modulator, is employed in the treatment of postmenopausal osteoporosis. This work reports the equilibrium solubility data of BZD acetate in fifteen different mono-solvents, including methanol, ethanol, n-propanol, i-propanol, n-butanol, ethyl formate, methyl acetate, ethyl acetate, acetone, 2-butanone, cyclohexanone, tetrahydrofuran (THF), 2-methyltetrahydrofurane (2-MeTHF), 1,4-dioxane and acetonitrile (ACN), within the temperature range “T = 283.15–323.15 K” under p = 0.1 MPa. The solubilities of BZD acetate in various solvents increase with increasing temperature. Among the alcoholic solvents, the solubility order is as follows: methanol > ethanol > n-propanol > n-butanol > i-propanol. In esters solvent, the solubility of BZD acetate decreases in the following order: methyl acetate > ethyl acetate > ethyl formate. For ketones solvent, the solubility decreases in the following order: cyclohexanone > acetone > 2-butanone. The maximum value of BZD acetate solubility was 0.011 mol·mol−1 in tetrahydrofuran at T = 323.15 K, but the least data was found in ethyl formate at 283.15 K. Four thermodynamic models, i.e., the Yaws model, modified Apelblat model, λh model, and Wilson model were applied to fit the solubility data of BZD acetate in different solvents. Among them, the Wilson model represents the most accurate fitting outcomes. Finally, the thermodynamic functions of mixing (including enthalpy, entropy, and Gibbs energy) were calculated, and the results indicate a mixing process that is both spontaneous and driven by entropy. The solubility data, correlated models, and derived thermodynamic functions present essential thermodynamic fundamentals for the industrial production of BZD acetate crystallization, facilitating efficient separation and purification.

Phase stability, mechanical and thermodynamic properties of (Hf, Zr, Ta, M)B2 (M= Nb, Ti, Cr, W) quaternary high-entropy diboride ceramics via first-principles calculations

As the high-entropy design concept applied to the diboride ceramic system, high-entropy diboride ceramics with a wide range of composition control, is expected to become a new high-performance material for extreme high-temperature environments. Herein, the effects of four transition metal elements (Nb, Ti, Cr, W) on the phase stability and properties of (Hf, Zr, Ta)B2-based high-entropy diboride ceramics are systematically investigated via the first-principles calculations. All components were identified as thermodynamically, mechanically and dynamically stable from enthalpy of formation, elastic and phonon spectrum calculations. Among these, compared with the (Hf, Zr, Ta)B2 ceramics, the addition of Nb and Ti on the metal sublattice is beneficial to improve the mechanical properties of ceramics, including Young's modulus, hardness and fracture toughness, while the introduction of Cr and W weakens the strength of covalently and ionic bonds inside the material, reducing its mechanical properties. The predicted thermophysical properties show that the high-entropy diboride ceramics containing Nb and Ti have better high-temperature comprehensive performance, including higher Debye temperature, thermal conductivity and lower thermal expansion characteristics, which is conducive to the application in extreme high-temperature environments. This research will provide important guidance for the design and development of new high-performance high-entropy diboride ceramics.

First-principles calculations of phase transition, elasticity, phonon spectra, and thermodynamic properties for ThO2 polymorphs

First-principles calculations based on density generalized function theory (DFT) were used to determine the structural transformation, phonon spectra, thermodynamic properties, and elastic behavior of ThO2 under compressive and tensile loading in this work. In compressive conditions, the transition pressures and calculation of structural parameters agree with the experiment results. Phase transitions of ThO2 from the Fm3‾m phase to the Pnma, P42/mnm and Pnnm phases under tensile conditions were anticipated to happen at 23.2 GPa, −7.69 GPa, and −7.75 GPa, respectively. Within the range of pressures analyzed, both the Fm3‾m and Pnma phases of ThO2 exhibit mechanical stability, but the P42/mnm phase and Pnnm phase are unstable at high pressures, according to the mechanical stability criteria, which is validated concerning elastic constants. Under ambient pressure, the calculated phonon spectra of the ThO2 polymorphs in this study demonstrate that all of the phases taken into consideration are dynamical stability. Also, the predicted heat capacities, isothermal bulk modulus, Gibbs free energies, and thermal expansion coefficients of ThO2 polymorphs as functions of temperature are analyzed and are in comparison with relevant experiments.

Assessment of phase equilibria and thermodynamic properties in the Fe-RE (RE = rare earth metals) binary systems

This study focuses on investigating phase equilibria and thermodynamic stability of intermetallic compounds made of the transition metal Fe and rare earth (RE) elements. By using the CALPHAD method and reliable experimental information from the literature, the binary systems of Fe-Y, Fe-Er, and Fe-Lu were reassessed. To improve our previous calculations of Fe-RE (RE = Tb and Dy) binary systems, the Gibbs energy expressions of intermetallic compounds Fe2Tb and Fe2Dy were modified to avoid artificial breaks in their heat capacity curves. Thermodynamic parameters obtained are self-consistent, and the Gibbs energies of the Fe-RE (RE = Tb, Dy, Er, Lu, and Y) phases were accurately expressed to reappear available both thermodynamic data and phase equilibria. This work was further combined with the previous calculations of the Fe-RE (RE = La, Ce, Pr, Nd, Sm, Gd, Ho, and Tm) systems to discuss thermodynamic characteristics and phase equilibria of Fe-RE binary systems in detail. A trend was noticed for the change of thermodynamic properties and phase equilibria of the Fe-RE binary systems with RE atomic number. Generally, as the RE atomic number increases, the formation temperatures of the Fe-RE intermetallic compounds increase gradually, and the enthalpy of mixing of liquid Fe-RE (apart from Fe-Y and Fe-Ce) alloys and the enthalpy of formation of the Fe-RE (apart from Fe-Y, Fe-Ce, Fe-Gd, and Fe-Dy) intermetallic compounds become increasingly negative. The results provide a thorough set of thermodynamic parameters of thirteen Fe-RE binary systems, which could serve as a sound basis for developing a thermodynamic database of Fe-RE-based alloy systems.