Phase Thermodynamic Properties Research Articles

The Al–Ca System, Part 2: Calorimetrie Measurements and Thermodynamic Assessment

Abstract Drop solution calorimetry was performed to determine the enthalpies of formation of the binary Al2Ca and Al3Ca8 phases and the partial enthalpy of mixing at infinite dilution of calcium in liquid aluminum. A consistent thermodynamic model of the Al–Ca system was constructed for the four stoichiometric compounds Al4Ca, Al2Ca, AlCa and Al3Ca8 and for the liquid phase with a sub-subregular solution model. Optimization of the thermodynamic parameters using the Calphad method was done by incorporating all available experimental data on phase equilibria, enthalpies of formation and mixing and the activity coefficients in the liquid. A consistent description of the phase diagram and thermodynamic properties is presented which is well supported by the experimental data. The Ca-rich part of the phase diagram differs substantially from previous reports, mainly because of the two newly discovered phases AlCa and Al3Ca8.

System Pr –Pd–O: Phase Diagram and Thermodynamic Properties of Ternary Oxides Using Solid-State Cells with Special Features

Abstract An isothermal section of the phase diagram for the system Pr– Pd–O at 1223 K has been established by equilibration of samples representing 13 different compositions, and phase identification after quenching by optical and scanning electron microscopy (SEM), X-ray diffraction (XRD), and energy dispersive analysis of X-rays (EDX). The binary oxide PdO was not stable at 1223 K. Three oxide phases were stable along the binary Pr– O; Pr2O3, Pr7O12 and a phase of variable composition between these two oxides designated as σ. Two ternary oxides Pr4PdO7 and Pr2Pd2O5 were identified and their crystal structures were determined. Liquid alloy, the intermetallic compounds PrPd, Pr3Pd4, PrPd3, PrPd5, and Pd-rich solid solution (Pds.s.) were found to be in equilibrium with Pr2O3. Based on the phase relations, two solid-state cells were designed to measure the Gibbs energies of formation of the two ternary oxides. An advanced version of the solid-state cell incorporating a buffer electrode was used for high temperature thermodynamic measurements. The function of the buffer electrode, placed between reference and working electrodes, was to absorb the electrochemical flux of the mobile species through the solid electrolyte caused by trace electronic conductivity. The buffer electrode prevented polarization of the measuring electrode and ensured accurate data. Yttria-stabilized zirconia was used as the solid electrolyte and pure oxygen gas at a pressure of 0.1 MPa as the reference electrode. Electromotive force measurements, conducted in the temperature range 925 – 1400 K, indicated the presence of a third ternary oxide Pr2PdO4, stable below 1150 ± 9 K. Additional solid state cells were designed to study this compound. The standard Gibbs energy of formation of the interoxide compounds from their component binary oxides Pr2O3 and PdO can be represented by the following equations: Pr 4 PdO 7 : Δ f ( ox ) G o /J ⋅ mol − 1 = − 43 540 + 0.74 T ( ± 150 ) Pr 2 PdO 4 : Δ f ( ox ) G o /J ⋅ mol − 1 = − 38 805 + 1.91 T ( ± 120 ) Pr 2 Pd 2 O 5 : Δ f ( ox ) G o /J ⋅ mol − 1 = − 68 640 + 1.28 T ( ± 270 ) $$\eqalign{ & {\rm{P}}{{\rm{r}}_4}{\rm{Pd}}{{\rm{O}}_7}:{{\rm{\Delta }}_{{\rm{f}}\left( {{\rm{ox}}} \right)}}{G^{\rm{o}}}{\rm{/J}} \cdot {\rm{mo}}{{\rm{l}}^{ - 1}} = - 43\,540 + 0.74\,T\left( { \pm 150} \right) \cr & {\rm{P}}{{\rm{r}}_2}{\rm{Pd}}{{\rm{O}}_4}:{{\rm{\Delta }}_{{\rm{f}}\left( {{\rm{ox}}} \right)}}{G^{\rm{o}}}{\rm{/J}} \cdot {\rm{mo}}{{\rm{l}}^{ - 1}} = - 38\,805 + 1.91\,T\left( { \pm 120} \right) \cr & {\rm{P}}{{\rm{r}}_2}{\rm{P}}{{\rm{d}}_2}{{\rm{O}}_5}:{{\rm{\Delta }}_{{\rm{f}}\left( {{\rm{ox}}} \right)}}{G^{\rm{o}}}{\rm{/J}} \cdot {\rm{mo}}{{\rm{l}}^{ - 1}} = - 68\,640 + 1.28T\left( { \pm 270} \right) \cr} $$ Crystallographic data for all three ternary oxides have been determined based on the thermodynamic information, isobaric phase diagrams and isothermal chemical potential diagrams for the system Pr–Pd –O are developed.

Thermodynamic assessment of the Al2O3–ZrO2, CaO–Al2O3–ZrO2, and Al2O3–SiO2–ZrO2 systems

All available thermodynamic data and phase diagram data in the Al2O3–ZrO2, CaO–Al2O3–ZrO2, and Al2O3–SiO2–ZrO2 systems at 1 bar total pressure were critically evaluated and assessed simultaneously to obtain a set of the optimized Gibbs energies of all phases in the systems. Due to the lack of reliable data on the mutual solubility of Al2O3 and ZrO2, key phase diagram experiments in the Al2O3–ZrO2 binary system were carried out by using a classical phase equilibrium and quenching technique followed by the EPMA phase analysis. Based on the optimized Gibbs energies, the reliable experimental phase diagram and thermodynamic property data of the Al2O3–ZrO2, CaO–Al2O3–ZrO2, and Al2O3–SiO2–ZrO2 systems are well reproduced, and unknown phase diagram and thermodynamic properties are predicted.

Thermodynamic assessment of the systems La2O3–Al2O3 and La2O3–Y2O3

Abstract The thermodynamic parameters of the systems La2O3– Al2O3 and La2O3–Y2O3 are assessed using the Calphad technique. The available phase equilibrium data and calorimetric measurements for the LaAlO3, perovskite phase have been used. The calculated phase diagrams are in reasonable agreement with experimental results. However, experimental data for the La2O3–Y2O3 system demonstrated large uncertainty and new experimental study of solid state reactions would be useful to verify the calculated diagram. Experimental investigations of thermodynamic properties are necessary for both systems to verify the calculated phase diagrams and thermodynamic properties.

Liquid Immiscibility and Thermodynamic Assessment of the Al2O3\u2013TiO2\u2013SiO2 System

Phase equilibria in the TiO2–SiO2 system have been studied experimentally using DTA and SEM/EDX. The thermodynamic parameters for the TiO2–SiO2 system have been assessed considering new experimental data of the present work and from the literature. Moreover, the miscibility of the liquid in the Al2O3–TiO2–SiO2 system has been studied at 2013 K in air and shrinkage of the miscibility gap at 3.8 mol% Al2O3 has been demonstrated. The experimental data obtained in the present work and literature as well as the thermodynamic databases for the binary Al2O3–TiO2, TiO2–SiO2, and Al2O3–SiO2 systems have been used to derive the thermodynamic description of the Al2O3–TiO2–SiO2 system using the CALPHAD approach. Solid phases have been modeled using the compound energy formalism. The liquid phase has been described by the two-sublattice partially ionic liquid model. A set of self-consistent parameters have been proposed, which resulted in a reasonably good agreement between the calculated and experimental data on the phase equilibria, liquid immiscibility, and thermodynamic properties in the Al2O3–TiO2–SiO2 system.

The Fe-Si-C system at extreme P-T conditions: A possible core crystallization pathway for reduced planets

Several characteristics of a planet, including its internal dynamics, hinge on the composition and crystallization regime of the core, which, in turn, depends on the phase relations, melting behaviour and thermodynamic properties of constituent materials. The Fe-Si-C ternary system can serve as a proxy for core composition and formation processes under reducing conditions. We conducted laser-heated diamond anvil cell experiments coupled with in situ X-ray diffraction and electron microscopy analysis of the recovered samples, on four different starting compositions in the Fe-Si-C ternary system. Phase relations up to 200 GPa and up to 4000 K were determined. An FeSi phase with a B2 structure and iron carbides with different stoichiometries (i.e., Fe3C and Fe7C3) are the main observed phases, along with pure C (diamond) that has an extended stability field in the subsolidus regime. Carbon is largely soluble in B2-structured FeSi, whereas Si does not partition into the carbides. The melting curve determined for the starting material containing the least amount of light elements is consistent with the one for the Fe-C system. The other starting materials display higher melting temperatures than that of Fe-C, suggesting the existence of at least two different invariant points in the Fe-Si-C system. Applied to planetary interiors, our observations highlight how a small variation in light elements content would deeply affect the solidification style of a core. Bottom-up (Fe-enriched systems) and top-down regimes (C-rich systems), as well as solidification of a crystal mush (Si-enriched systems). These three crystallization regimes influence significantly the possibility of starting and sustaining a dynamo. Our results provide new insights into the differentiation of terrestrial planets in the Solar System and beyond, contributing to the study of planetary diversity.

Thermodynamic calculation of phase equilibria of rare earth metals with boron binary systems

Abstract In order to develop novel materials based on rare earth (RE) boride and/or transition metals, phase equilibria and thermodynamic information of the RE–B based alloys are indispensable. On the basis of experimental phase equilibria and thermodynamic properties, thermodynamic assessments of the RE–B (RE = La, Sm, Gd and Tb) binary systems were carried out by the CALPHAD (Calculation of Phase Diagram) method. Self-consistent parameters of the RE–B (RE = La, Sm, Gd and Tb) binary systems were obtained, which can be used to reproduce well the experimental data. Furthermore, in combination with the previous assessments of the RE–B binary systems in the literature, phase equilibria and thermodynamic properties of the RE–B (RE = La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm and Lu) binary systems are discussed systematically. The tendency of phase equilibria and thermodynamic information as a function of RE atomic number is demonstrated. In general, the enthalpy of mixing of liquid RE–B alloys and the enthalpy of formation of the RE–B intermetallic compounds become more and more negative with the increase in RE atomic number (except for La, Ce, Pr and Nd), while the phase transition temperatures for the RE–B intermetallic compounds increase gradually.

Design, processing, and assessment of additive manufacturing by laser powder bed fusion: A case study on INCONEL 718 alloy

During the designing stage of the laser powder bed fusion (LPBF) process for the production from a new material system, the operating variables form a large experimental parametric space. An efficient method to find the optimal parametric window of the variables is needed to enhance the essential advantage of the additive manufacturing technology – rapid prototyping. This article presents a simple analytical method to generate an optimal parametric window by estimating the melt pool dimension during the process of LPBF. By treating the well-studied INCONEL™ 718 as a new system, the phase diagram, thermodynamic and thermophysical properties of the material were derived from the information available to the general public. Based on these data, a 4 × 4 parametric matrix was designed for a laser with focal diameter of 0.085 mm and 16 samples were built. The metallographic examinations of these as-built samples were performed to study the melt pool dimensions and microstructures of the samples. From the initial assessments on the structural quality of the as-built samples manufactured by the parametric matrix, it is proposed that the laser energy ranging from 45 mJ to 60 mJ, or the linear energy density from 0.53 J/mm to 0.71 J/mm, on an 85 µm × 85 µm area was the optimal operating window. From the study, it was concluded that the results of analytical calculations on the INCONEL™ 718 material system agreed reasonably well with the experimental findings and the method can be applied to other new material systems to establish the optimal parametric window.

Thermodynamic analysis of high-temperature heazlewoodite

Abstract Experimental data for phase equilibria and thermodynamic properties have been used for thermodynamic analysis of the high-temperature heazlewoodite. A two-sublattice model in the framework of the Compound Energy Formalism is proposed for the Gibbs energy of a second high-temperature heazlewoodite phase around the composition Ni3S4. Optimized model parameters have been obtained which reproduce all data simultaneously within experimental error limits. The Gibbs energy modeling is carried out consistently with the recent assessment by the author of the nickel – sulfur system at 1 bar pressure over the entire composition range for temperatures from 25 °C to above the liquidus.

Phase transitions in a two-dimensional antiferromagnetic Potts model on a kagome lattice

The phase transitions and thermodynamic properties of the two-dimensional antiferromagnetic Potts model with the number of spin states q=4 on the kagome lattice are studied by the Monte Carlo method, taking into account the exchange interactions of the first J1 and second J2 nearest neighbors. The studies were carried out for the value of the interaction of the second nearest neighbors in the interval -1.0≤ J_2≤0.0. An analysis of the character of phase transitions has been carried out. It is shown that in the interval -1.0≤ J_2≤-0.1, a second-order phase transition is observed, while at J_2=0.0, frustrations disturb the order in the system and lead to the disappearance of the phase transition Keywords: Frustration, phase transition, Monte Carlo method, Potts model.

Исследование влияния слабых магнитных полей на термодинамические свойства модели Поттса с числом состояний спина q=4 на гексагональной решетке

The replica exchange algorithm of the Monte Carlo method was used to study phase transitions and thermodynamic properties of the two-dimensional Potts model with the number of spin states q = 4 on a hexagonal lattice in weak magnetic fields. The studies were carried out for the interval of the magnetic field value 0.0 ≤ Н ≤ 3.0 with a step of 1.0. It is found that a first-order phase transition is observed in the considered range of field values.

Investigation of the influence of weak magnetic fields on thermodynamic properties of the Potts model with the number of spin states q=4 on a hexagonal lattice

The replica exchange algorithm of the Monte Carlo method was used to study phase transitions and thermodynamic properties of the two-dimensional Potts model with the number of spin states q=4 on a hexagonal lattice in weak magnetic fields. The studies were carried out for the interval of the magnetic field value 0.0≤ H≤3.0 with a step of 1.0. It is found that a first-order phase transition is observed in the considered range of field values. Keywords: Frustration, Phase transitions, Monte Carlo method, Potts model.

Фазовые переходы в двумерной антиферромагнитной модели Поттса на решетке кагоме

The phase transitions and thermodynamic properties of the two-dimensional antiferromagnetic Potts model with the number of spin states q = 4 on the kagome lattice are studied by the Monte Carlo method, taking into account the exchange interactions of the first J1 and second J2 nearest neighbors. The studies were carried out for the value of the interaction of the second nearest neighbors in the interval -1.0 ≤ J2 ≤ 0.0. An analysis of the character of phase transitions has been carried out. It is shown that in the interval -1.0 ≤ J2 ≤ -0.1, a second-order phase transition is observed, while at J2 = 0.0, frustrations disturb the order in the system and lead to the disappearance of the phase transition.

High pressure structural phase transition and thermodynamic properties of SnO2 polymorphs: First principles calculation

The scientific community has shown interest in the field of high pressure studies in recent years due to the feasibility of several nano synthesis techniques in modern technology. The high-pressure phase transition of tin dioxide (SnO2) polymorphs was investigated using the density functional theory (DFT) plane-wave pseudopotential method. Researchers are interested in SnO2 because it has a variety of intriguing structural transformations. Under hydrostatic pressure, we observed the structural phase transition of seven SnO2 polymorphs. These findings were in line with those of other AO2 oxide structures. The thermodynamic parameters of these polymorphs were also determined as a function of temperature in the range of 0–1000 K, including heat capacity, entropy, vibrational free energy, and Debye temperature.

Phase diagram, thermodynamic properties and long-term isothermal stability of quaternary molten nitrate salts for thermal energy storage

Thermal energy storage (TES) is a vastly growing technique that allows for the generation of dispatchable electricity in modern concentrating solar power (CSP) plants. In solar tower systems the key to success is the use of a heat transfer fluid (HTF) and storage medium known as Solar Salt. This nitrate salt mixture of NaNO3 and KNO3 is considered thermally stable, non-toxic and environmentally friendly. In line-focusing CSP plants Solar Salt is still not being used as heat transfer fluid due to the inherent risk of freezing and related systematic failure. Accordingly, there is a need to develop nitrate salts with lower melting temperatures but yet acceptably high thermal stability. The information on molten nitrate mixtures with low melting points (⪅100 °C) is limited, especially in terms of isothermal stability tests. This work presents thermo-physical data of the complex quaternary Ca,Li,Na,K//NO3 system. Melting temperatures of more than 100 mixtures were assessed and compositions with melting points below 100 °C were identified. The heat capacity of selected mixtures was in the range of 1.5–1.6 kJ/kg K and generally increased with increasing Li-content. Thermal stability, with Solar Salt as reference salt, indicated that the stability of all mixtures did not exceed 500 °C but that the achievable ΔT was 360 °C, about 90 °C higher than that of Solar Salt. Some compositions are therefore are potential HTF and storage media but the overall Ca-content plays a crucial role in the decomposition of the quaternary mixtures during operation at high temperatures.

Thermodynamic Stability of Fenclorim and Clopyralid.

The present work reports an experimental thermodynamic study of two nitrogen heterocyclic organic compounds, fenclorim and clopyralid, that have been used as herbicides. The sublimation vapor pressures of fenclorim (4,6-dichloro-2-phenylpyrimidine) and of clopyralid (3,6-dichloro-2-pyridinecarboxylic acid) were measured, at different temperatures, using a Knudsen mass-loss effusion technique. The vapor pressures of both crystalline and liquid (including supercooled liquid) phases of fenclorim were also determined using a static method based on capacitance diaphragm manometers. The experimental results enabled accurate determination of the standard molar enthalpies, entropies and Gibbs energies of sublimation for both compounds and of vaporization for fenclorim, allowing a phase diagram representation of the (p,T) results, in the neighborhood of the triple point of this compound. The temperatures and molar enthalpies of fusion of the two compounds studied were determined using differential scanning calorimetry. The standard isobaric molar heat capacities of the two crystalline compounds were determined at 298.15 K, using drop calorimetry. The gas phase thermodynamic properties of the two compounds were estimated through ab initio calculations, at the G3(MP2)//B3LYP level, and their thermodynamic stability was evaluated in the gaseous and crystalline phases, considering the calculated values of the standard Gibbs energies of formation, at 298.15 K. All these data, together with other physical and chemical properties, will be useful to predict the mobility and environmental distribution of these two compounds.

Компьютерное моделирование двумерной модели Поттса с конкурирующими обменными взаимодействиями

The phase transitions and thermodynamic properties of the two-dimensional Potts model with the number of spin states $q = 4$ on a hexagonal lattice with competing exchange interactions have been investigated on the basis of the Wang-Landau algorithm by the Monte Carlo method. It is shown that taking into account the antiferromagnetic interactions of the next-nearest neighbors leads to a violation of the magnetic ordering and to the appearance of frustration.

First-principles calculations of phase transition, elasticity, phonon spectra, and thermodynamic properties for CeO2 polymorphs

In this work, the structural transformation, elastic behavior, phonon spectra and thermodynamic properties of CeO2 under compressive and tensile loading were investigated by first-principles calculations based on density generalized function theory (DFT). Our calculated structural parameters and transition pressure under compressive condition are in good agreement with the experimental values. Under tensile condition, the phase transitions of CeO2 from fluorite-type (space group Fm3¯m) phase to cotunnite-type (space group Pnma), rutile-type (space group P 42/mnm) and marcasite-type (space group Pnnm) phases were predicted to occur at 23.2 ​GPa, −7.69 ​GPa, and −7.75 ​GPa respectively. The mechanical stability criteria are verified in terms of elastic constants and shows that the cotunnite and fluorite structures of CeO2 are mechanically stable in the studied pressure range, while the rutile and marcasite structures turn out to be mechanical unstable under high pressure. The calculated phonon spectra of CeO2 polymorphs demonstrate that all phases considered in present work are dynamically stable under ambient pressure. Furthermore, the calculated heat capacity, isothermal bulk modulus, Gibbs free energy, thermally expanding coefficient of CeO2 polymorphs as a function of temperature are discussed and compared with available experimental data.

First-principles study of pressure-induced phase transitions, mechanical and thermodynamic properties of ThBC

First-principles calculations and particle swarm optimization algorithm are combined to predict the crystal structures in the pressure range from 0 to 100 GPa. Four phases of ThBC are determined, including the P4122, Cmcm, Cmce and Immm phases, in which the Cmcm, Cmce and Immm phases are newly predicted structures. The mechanical, electronic and thermodynamic properties of the four phases are investigated. According to the enthalpy–pressure and volume–pressure curves, the phase transition pressure from the P4122 phase to the Cmcm phase is 15 GPa, the Cmcm to the Cmce is 36 GPa and the Cmce to the Immm is 69 GPa. All the transitions belong to the first-order phase transition. Based on the calculated elastic constants, the P4122, Cmcm, Cmce and Immm phases exhibit brittle nature. The Young’s moduli show that the P4122 phase has the largest degree of anisotropy, and the Immm phase has the smallest. The calculated density of states reveal that the P4122, Cmcm, Cmce and Immm phases are all metallic.

The elastic anisotropy, electronic and thermodynamic properties of TM5Si4 (TM= Sc, Y, Ti, Zr and Hf) silicides from first-principles calculations

In recent years, transition-metal silicon-based high temperature materials have attracted more and more attention due to their excellent physical and chemical properties. In this paper, we explored the phase stability, mechanical, anisotropy and thermodynamic properties of TM5Si4 (TM = Sc, Y, Ti, Zr and Hf) compounds by first-principles calculations. The results indicate that TM5Si4 compounds exhibit the thermodynamical and dynamical stability. And Hf5Si4 exhibits the best phase stability among five compounds. The orthorhombic Sc5Si4 and Y5Si4 are ductile, but the tetragonal Ti5Si4, Zr5Si4 and Hf5Si4 are brittle. The elastic anisotropies of TM5Si4 were demonstrated by the 3D contours and 2D projections of elastic modulus. The results confirm that the order of anisotropy is as follows: Zr5Si4 < Hf5Si4 < Ti5Si4 < Sc5Si4 < Y5Si4. TM-Si bonds can be formed in TM5Si4 silicides for the strong localized hybridization between TM-d and Si-3p states. Moreover, the thermal parameters confirm that five TM5Si4 silicides display the better thermal stability at elevated temperature.