Energy Formalism Research Articles

Defect energy formalism for CALPHAD thermodynamics of dilute point defects

Defect energy formalism for CALPHAD thermodynamics of dilute point defects

Extracting metal oxide redox thermodynamics from TGA measurements requires moving beyond the linearized van ‘t Hoff approach

Thermodynamic modeling of metal oxide reduction is crucial for optimizing chemical processes and materials in systems dependent on off-stoichiometric reduction/re-oxidation cycling. Two prevalent methods for extracting reduction thermodynamics from thermogravimetric data are linearized van ‘t Hoff (VH) analysis and the compound energy formalism (CEF). This work evaluates the accuracy of these methods by constructing invertible ground truth thermodynamic models, generating hypothetical thermogravimetric data, and determining the reduction thermodynamic using both VH and CEF methods. Our findings reveal that the VH method produces absolute errors 3–5 times higher than the CEF in kJ/mol O or J/mol O K for enthalpy and entropy of reduction, respectively. In contrast, the CrossFit CEF (CF-CEF) method yields errors often less than 10 kJ/mol O or J/mol O K. Moreover, the CF-CEF method provides models based on mole fraction, temperature, and extent of reduction, while a typical VH analysis provides thermodynamics of only the specific compositions measured. Although simple to implement, the VH method suffers from significant, non-systematic errors due to entropy/enthalpy compensation and defect modeling. Consequently, we recommend the more complex but robust, CF-CEF method for extracting redox thermodynamics from thermogravimetric measurements.

Critical Evaluation and Thermodynamic Optimization of the Cr–P and Cr–Fe–P Systems

Existing thermodynamic descriptions of the whole Cr–Fe–P system are insufficiently accurate for understanding the thermodynamic behavior of the Cr–Fe–P materials during the manufacturing process. To construct a more precise and consistent thermodynamic database of the Cr–Fe–P system, thermodynamic modeling of the Cr–P and Cr–Fe–P systems was conducted using the CALculation of PHAse Diagrams (CALPHAD) approach based on critical evaluation of the experimental data. The modified quasichemical model and compound energy formalism were employed to describe the liquid and solid solutions, respectively. The Gibbs energies of stoichiometric compounds Cr3P(s), Cr2P(s), CrP(s), and CrP2(s) were carefully determined based on reliable experimental data. The ternary (Cr,Fe)3P, (Cr,Fe)2P, and (Cr,Fe)P phosphides were modeled as solid solutions considering mutual substitution between Cr and Fe atoms. In addition, the phase equilibria of BCC_A2 and FCC_A1 solutions and the liquid phase of the ternary Cr–Fe–P system were also optimized for more accurate descriptions of existing phase equilibria and thermodynamic properties data. As an application of the present database, the experimentally unexplored thermodynamic properties and phase diagrams of the Cr–Fe–P system are predicted.

Experimental investigations and thermodynamic modelling of the ternary system Pb-Mo-O

A combined experimental and modelling study into the Pb-Mo-O system has been conducted in view of the safety analysis for lead-cooled nuclear systems. The thermal expansion and low-temperature heat capacity of the ternary compounds PbMoO4 and Pb2MoO5 have been determined experimentally, as well as the melting enthalpy of PbMoO4. Moreover, XANES measurements have confirmed the hexavalent oxidation state of Mo in PbMoO4 and Pb2MoO5.A thermodynamic model of the ternary system including the ternary phases PbMoO4, Pb2MoO5 and Pb5MoO8 has also been developed in this work based on the CALPHAD methodology. For the first time, an ionic two-sublattice model is used for the liquid phase, while the compound energy formalism is used for the solid phases.

Thermodynamic modeling of Bi2Te3 in the defect energy formalism

Bi2Te3 is a promising thermoelectric material that is often touted as one of the best-performing low-temperature thermoelectric materials. As a result, it has been widely used commercially, both for clean energy generation and in cooling devices. Like many other thermoelectric materials, defects play a key role in the performance of Bi2Te3. As a result, numerous studies have attempted to experimentally and computationally map out the dominant defects in the phase, these include efforts to determine the dominant defect, estimate defect energies, and predict their concentration. The computer coupling of phase diagrams and thermochemistry (CALPHAD) is one of many tools under the auspices of the materials genome initiative (MGI) that enables the rapid design of new functional materials with improved properties. The Defect energy formalism (DEF) with a charged sublattice, an offshoot of the Compound energy formalism (CEF), provides a way to directly include first-principle defect energy calculations into CALPHAD descriptions of solid phases. The introduction of the charge sublattice enables the estimation of the free carrier concentrations in the phase. Here we apply the DEF to the Bi2Te3 system, emphasizing the robustness of the DEF in describing meaningful endmembers and the elimination of fitting parameters. Unlike previous assessments using the Wagner–Schottky defect model, we include the description of the charged defects in our assessment. The DEF with a charged sublattice provides a good prediction of the non-stoichiometry of the phase when compared with experimental data and also predicts a thermodynamic defect concentration at low temperature that is physically reasonable.

The formation of the magnetic symbiotic star FN Sgr

Context. There are several symbiotic stars (e.g., BF Cyg, Z And, and FN Sgr) in which periodic signals of tens of minutes have been detected. These periods have been interpreted as the spin period of magnetic white dwarfs that accrete through a magnetic stream originating from a truncated accretion disc. Aims. To shed light on the origin of magnetic symbiotic stars, we investigated the system FN Sgr in detail. We searched for a reasonable formation pathway to explain its stellar and binary parameters including the magnetic field of the accreting white dwarf. Methods. We used the MESA code to carry out pre-CE and post-CE binary evolution and determined the outcome of CE evolution assuming the energy formalism. For the origin and evolution of the white dwarf magnetic field, we adopted the crystallization scenario. Results. We found that FN Sgr can be explained as follows. First, a non-magnetic white dwarf is formed through CE evolution. Later, during post-CE evolution, the white dwarf starts to crystallize and a weak magnetic field is generated. After a few hundred million years, the magnetic field penetrates the white dwarf surface and becomes detectable. Meanwhile, its companion evolves and becomes an evolved red giant. Subsequently, the white dwarf accretes part of the angular momentum from the red giant stellar winds. As a result, the white dwarf spin period decreases and its magnetic field reaches super-equipartition, getting amplified due to a rotation- and crystallization-driven dynamo. The binary then evolves into a symbiotic star, with a magnetic white dwarf accreting from an evolved red giant through atmospheric Roche-lobe overflow. Conclusions. We conclude that the rotation- and crystallization-driven dynamo scenario, or any age-dependent scenario, can explain the origin of magnetic symbiotic stars reasonably well. This adds another piece to the pile of evidence supporting this scenario. If our formation channel is correct, our findings suggest that white dwarfs in most symbiotic stars formed through CE evolution might be magnetic, provided that the red giant has spent ≳3 Gyr as a main-sequence star.

Modeling Charged Defects Using the Defect Energy Formalism With a Charge Sublattice Within a CALPHAD Framework

AbstractThe non‐stoichiometry of material compounds significantly influences their functional properties. In semiconductors, point defects determine whether a material is n‐type or p‐type and the concentration of charge carriers. Even in structural alloys and ion conductors used in batteries and fuel cells, non‐stoichiometry and dilute defects play an integral role in their function. The design of metal alloys has advanced rapidly with the aid of thermodynamic modeling using calculation of phase diagrams (CALPHAD) to predict the phases produced during different processing conditions. While thermodynamic modeling has been done previously by fitting experimental data, the advent of first‐principle techniques has enabled the computational prediction of material properties. The defect energy formalism (DEF) is described for modeling charged and uncharged defects in compounds, showing that it accurately predicts non‐stoichiometry using density functional theory (DFT), without fitting experiments. The model reproduces the expected defect and free‐charge carrier concentrations using the statistical mechanics approach commonly used in most DFT defect studies. Finally, the model is used to accurately predict the single‐phase region of PbTe with no fitting to measured defect concentrations. This method can revolutionize materials development of insulators, semiconductors, and even metals by allowing rapid DFT calculations to replace laborious experiments when dilute defects are involved.

Atomic-Scale Description of the Magnetic TiN|FeCo Multilayers.

Motivated by the experimental findings of Wolff et al., we investigated the TiN|FeCo multilayers at the atomic scale. Four different models were employed to investigate the interface, considering both Fe and Co surface terminations of the FeCo compounds. The interface formation energy formalism was employed to study the thermodynamic stability of these models. The results show that an interface mediated by Co atoms is most likely to appear in the experiment. Also, the Fe surface termination is more viable than a Co surface termination. The magnetic moments of Co at the interface are 1.48 μB/atom, which denotes a decay compared to bulk (1.76 μB/atom). Besides, Ti acquires a very small induced magnetization of -0.05 μB/atom. Our proposed atomistic model of the TiN|FeCo multilayer system fits perfectly with the structure obtained in experiments, and it is a step forward in the theoretical-experimental design of wear-resistant coatings with outstanding magnetic and mechanical properties.

Coupled Experimental Study and Thermodynamic Modeling of the Fe–Si–N System

Some key experiments are carried out to determine the solubility of N in Fe–Si liquid solutions at various compositions, temperatures, and N2 pressures using the sampling method. The Fe–Si–N system is thermodynamically modeled using the CALculation of PHAse Diagrams (CALPHAD) approach for the first time based on critical evaluation of all available experimental data. In the present thermodynamic modeling, the liquid and solid solutions of the Fe–Si–N system are described using the modified quasichemical model and compound energy formalism, respectively. In particular, the Gibbs energies of liquid, FCC_A1, and BCC_A2 solutions are carefully determined to resolve the discrepancies among existing experimental data. The solubility product of β‐Si3N4(s) in Si steels and ferrosilicon alloys, activity coefficients, and interaction parameters of N in liquid and solid Fe–Si–N solutions are determined over a wide temperature range. As an application of the database, the N solubility in Si steels and phase constitution of nitrided ferrosilicon alloys in a wide composition, temperature, and N2 pressure ranges are predicted.

Nuclear structure properties and weak interaction rates of even–even Fe isotopes

Nuclear structure properties and weak interaction rates of neutron-rich even–even iron (Fe) isotopes (A = 50 – 70) are investigated using the Interacting Boson Model-1 (IBM-1) and the proton–neutron Quasiparticle Random Phase Approximation (pn-QRPA) model. The IBM-1 is used for the calculation of energy levels and the B(E2) values of neutron-rich Fe isotopes. Later their geometry was predicted within the potential energy formalism of the IBM-1 model. Weak interaction rates on neutron-rich nuclei are needed for the modeling and simulation of presupernova evolution of massive stars. In the current study, we investigate the possible effect of nuclear deformation on stellar rates of even–even Fe isotopes. The pn-QRPA model is applied to calculate the weak interaction rates of selected Fe isotopes using three different values of deformation parameter. It is noted that, in general, bigger deformation values led to smaller total strength and larger centroid values of the resulting Gamow–Teller distributions. This later translated to smaller computed weak interaction rates. The current finding warrants further investigation before it may be generalized. The reported stellar rates are up to 4 orders of magnitude smaller than previous calculations and may bear astrophysical significance.

Ab Initio Conformational Analysis of 3,7-Diacetyl-3,7-Diazabicyclo[3.3.1]Nonanes

Introduction: The importance of the conformational behavior comprehension for proper prediction of properties for a certain compound or for a class of compounds is indisputable. For 3,7-diacylbispidines (3,7-diacyl-3,7-diazabicyclo[3.3.1]nonanes), only “double chair” (CC) conformers were prior found experimentally in the condensed phase, which differ only in the acyl groups relative orientation, “parallel,” pa or “antiparallel,” ap. However, 2 other conformer families, “boat-chair,” BC and “double twist,” TT, are known for other bicyclo[3.3.1]nonane derivatives. Features of these conformers would be useful for the accurate prediction of properties and activities of the compounds. Methods: Second-order perturbation theory ab initio techniques (MP2) in the triple-zeta correlation-consistent orbital basis set cc-pVTZ was employed to optimize the electronic energy for structures, to characterize the optimized structures as potential energy surface minima by energy hessian eigenvalue calculations and to calculate zero-point energy corrections for the minima using the “rigid rotor-harmonic oscillator” approximation to model the molecular ensemble thermodynamics. Additionally, the computational chemical thermodynamics benefits much from the concept of the molecular strain and its energy assessed successfully through the bond separation energy formalism. We combine both approaches in our investigation to find and consistently characterize the conformers previously unknown for the compounds under the studies. Results: Six possible conformers were found for the investigated 3,7-diacetyl-3,7-diazabicyclo[3.3.1]nonanes 1-4, formed by combining the skeletal conformation changes with the internal rotation of acyl substituents. The conformational behavior is quite similar for all investigated molecules. In all cases, the CC conformation is optimal for the bicyclic skeleton and ap orientation prevails over pa for 2 acetyl groups. This prevalence is 4-5 kcal mol−1 in CC and less than 1 kcal mol−1 in other skeletal forms, making rotation of 2 acyl groups in BC and TT almost independent. Concerning the skeletal conformations, the common energy sequence CC < BC < TT is found. While the relative BC energy is 6-7 kcal mol−1 over the optimal CC structure, TT forms are all strained by more than 12 kcal mol−1. Conclusions: For the first time, both BC and TT conformers of 3,7-diacetylbispidines were characterized by their strain and conformation energies together with known less strained CC forms. On the basis of our calculations, the relative energies of BC conformers are expected to be close to those of the CC acetyl amide bond rotamers found previously in experiment, therefore, their exclusion from the conformational behavior would look unjustified. On the contrary, TT conformers are found to be much more strained enough to be neglected in the conformational ensemble modeling.

Experimental Investigation and Thermodynamic Modeling of the Li2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}O–Al2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}O3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_3$$\\end{document} System

In the present work, phase equilibria in the Li2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}O–Al2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}O3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_3$$\\end{document} system were experimentally studied and calorimetric measurements were performed. Based on obtained results and data from literature, thermodynamic parameters of the system were assessed. The solid solution phases were modeled using Compound Energy Formalism (CEF) and liquid phase was described by two-sublattice partially ionic liquid model. The experimental investigations for selected compositions of isothermally heat-treated samples were performed using x-ray Diffraction (XRD) and Scanning Electron Microscopy (SEM). Differential Thermal Analysis (DTA) and Differential Scanning Calorimetry (DSC) were used to measure the temperature of the reactions as well as the heat capacities, respectively. After DTA, the microstructure was analyzed using SEM. Temperature of peritectic melting of h-LiAl5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_5$$\\end{document}O8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_8$$\\end{document} was determined to be 2222 K and temperature of eutectic reaction Liq ↔\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\leftrightarrow$$\\end{document}γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma$$\\end{document}-LiAlO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} + h-LiAl5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_5$$\\end{document}O8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_8$$\\end{document} to be 1965 K. Heat capacity of LiAlO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} and LiAl5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_5$$\\end{document}O8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_8$$\\end{document} was measured in the temperature range of 100-1300 K. The degree of inversion of spinel phase (Al+3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{+3}$$\\end{document}, Li+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{+1}$$\\end{document})1T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_1^T$$\\end{document}:(Al+3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{+3}$$\\end{document}, Li+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{+1}$$\\end{document}, Va)2O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2^O$$\\end{document}:O4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_4$$\\end{document} was modelled assuming Al+3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{+3}$$\\end{document} and Li+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{+1}$$\\end{document} can occupy tetrahedral (T) and octahedral (O) cationic sublattices while its composition extension in Al2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}O3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_3$$\\end{document} enriched region was described by introducing vacancies in octahedral sites. Thermodynamic description derived in the present study reproduces the degree of inversion close to that of the high-temperature spinel phase, which means that Al+3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{+3}$$\\end{document} ions preferentially occupy the tetrahedral sites. The calculated phase diagram satisfactorily agrees with the experimental results. Available experimental thermodynamic data are also reproduced within uncertainty limits.

Experimental investigation and thermodynamic assessment of the Na2O–Al2O3–CaO system

Thermodynamic investigation of the Na2O–Al2O3–CaO system plays an important role in the applications of HACs and refractory. However, the phase relationships in the Al2O3-rich corner of the isothermal section at 1473 K for this system are uncertain. Key experimental investigation was performed and an improved method was developed to prepare the samples. Four three-phase regions of NC3A8+CA2+β-Al2O3, CA2+CA6+β-Al2O3, CA6+β-Al2O3+Al2O3 and NC3A8+NA6+β-Al2O3 were confirmed by X-ray diffraction. The Na2O–Al2O3 system was reassessed by CALPHAD method and the Na2O–Al2O3–CaO system was optimized by using the ionic two-sublattice liquid model (Na+1,Al+3,Ca+2)P(AlO2−1,O−2)Q to describe the liquid phase and a sublattice compound energy formalism model (Na+1)2(Ca+2,Na+1)1(Al+3)4(O−2)8(Va,Na+1)1 to describe the ternary compound NCA2. A set of self-consistent thermodynamic parameters was finally obtained, satisfactorily reproducing the experimental data and predicting the liquidus projection and primary phase regions. The present thermodynamic investigation of the Na2O–Al2O3–CaO system contributes to compositional design in HACs and refractory.

Phase equilibria of advanced technology uranium silicide-based nuclear fuel

The phases in uranium-silicide binary system were evaluated in regards to their stabilities, phase boundaries, crystal structures, and phase transitions. The results from this study were used in combination with a well assessed literature to optimize the U-Si phase diagram using the CALPHAD method. A thermodynamic database was developed, which could be used to guide nuclear fuel fabrication, could be incorporated into other nuclear fuel thermodynamic databases, or could be used to generate data required by fuel performance codes to model fuel behavior in normal or off-normal reactor operations. The U3Si2 and U3Si5 phases were modeled using the Compound Energy Formalism model with 3 sublattices to account for the variation in composition. The crystal structure used for the USi phase was the tetragonal with an I4/mmm space. Above 450°C, the U3Si5 phase was modeled. The composition of the USi2 phase was adjusted to USi1.84. The calculated invariant reactions and the enthalpy of formation for the stoichiometric phases were in agreement with experimental data.

Analytical energy formalism and kinetic effects of grain boundaries: A case study of graphene

Grain boundaries (GBs), inherent in polycrystalline materials, manifest a diverse array of features that substantially affect material properties. However, the incomplete knowledge of the relevance between structures and energetics of GBs impedes the understanding of their effects. Here, taking graphene as an example, we propose an analytical energy formula for GBs in grain-boundary angle space. Our study reveals that any given GB can be characterized by a geometric combination of symmetric GBs, adhering to the principle of uniformly distributing their dislocation cores along straight trajectories. The formation probability of GBs, as predicted by our theoretical derivation, aligns well with both high-throughput calculations and experimental statistics. Furthermore, we unveil the elusive kinetic effects on GBs by contrasting experimental statistics with energy-dependent thermodynamic effects. This study not only presents a robust model to describe energetically favorable GBs in graphene, offering insight into the formation of GBs in two-dimensional materials, but also reveals the kinetic effects of GBs in material synthesizing process.

Applying the Effective Bond Energy Formalism (EBEF) to Describe the Sigma (σ) Phase in the Co-Cr-Ni-Re System

Applying the Effective Bond Energy Formalism (EBEF) to Describe the Sigma (σ) Phase in the Co-Cr-Ni-Re System

Optimized laser photoionization scheme of separation of complex isotopes in the separator devices

An effective approach to determining parameters of optimal schemes of the method of laser selective photoionization of heavy isotopes, in particular, lanthanides (Gd atoms as the example) with ionization at the final stage by a pulsed electric field, autoionization through the narrow autoionization resonances and due to collisions is developed for separation of heavy isotopes in the separator devices. On the basis of the theory of optimal control and previously developed theoretical quantum approaches (the energy formalism and the relativistic many-body perturbation theory with the Dirac-Kohn-Sham-Sturm zeroth approximation for computing the parameters of elementary atomic processes such as excitation, ionization amplitudes, cross-sections, energies, widths of autoionization resonances etc.) an optimized scheme for the separation of Gd isotopes by the method of 3-stage laser photoionization with ionization at the final stage by a pulsed electric field, ionization through narrow autoionization resonances is presented. For the first time, there are theoretically calculated parameters of the narrow autoionization resonances for Gd in a sufficiently weak electric field, which are in physically reasonable agreement with data of the known experiment by Letokhov et al. Narrow-width autoionization resonances in Gd (in general in spectra of any lanthanide & actinide atom) have a relatively long lifetime, correspondingly, their excitation, ionization cross sections have the same order as the excitation one at the initial stage of separation scheme. Therefore, the use of these long-lived states can ensure the optimal implementation of a laser scheme for the separation of heavy isotopes. The obtained results for Gd with using models of optimal governing confirm the perspective of construction of the optimized schemes of the laser photoionization method with ionization at the final stage by a pulsed electric field, autoionization and allow determining the optimal parameters of the separation scheme, including diagram of atomic transitions, shape of laser pulses, etc. It is hoped that this work will also provide new opportunities for further development of laser chemistry of lanthanides, as well as actinides, taking into account new physics of autoionization resonances in their spectra.

Mn induces a 1×3 reconstruction in the ferromagnetic L21 Mn2FeGa (001) surface

The Mn2FeGa compound is an ordered ferrimagnetic Heusler alloy characterized by its unique inverse magnetostriction and exceptional magnetic properties. In this study, we employ density functional theory (DFT) to conduct a theoretical analysis of the atomic structure of the (001) surface of Mn2FeGa. We utilize the surface energy formalism to systematically evaluate and compare the stability of various surface atomic configurations under different chemical potential conditions. Notably, our investigation identifies three energetically stable surfaces: MnGa-terminated, Ga-terminated, and MnGa2-terminated surfaces, featuring a 3×1 surface reconstruction, prevalent under Ga-rich conditions. Understanding the atomic arrangements and surface effects of Mn2FeGa is pivotal for optimizing its properties for specific device applications.

Thermodynamic study of the Ca-Cu-Zn ternary system with key experimental measurements

Zinc-based alloys, particularly those alloyed with elements like Ca, Cu, and others, have emerged as promising candidates for biodegradable implants. Therefore, the purpose of this study was to investigate the phase equilibrium relationship of the Ca-Cu-Zn ternary system in the Cu-Zn rich region for Zn-based biodegradable materials development. In this work, 21 and 19 samples were prepared and annealed at the temperatures of 350 and 400 °C, respectively. And Then, these samples were analyzed using analytical techniques including scanning electron microscopy (SEM) coupled with energy dispersion spectroscopy (EDS), electron probe microanalysis (EPMA), and powder X-ray diffraction analysis (XRD). The present obtained results indicate the existence of five regions exhibiting three-phase equilibrium and sixteen regions exhibiting two-phase equilibrium within these two isothermal sections. Additionally, differential scanning calorimetry (DSC) was utilized to determine the phase transition temperatures of alloys with constant values of 12 at% Cu and 40 at% Ca, respectively. Moreover, the CALPHAD method was employed to optimize the thermodynamic parameters of the phases of Ca-Cu-Zn ternary system. The model of the liquid phase was performed using the modified quasi-chemical model (MQM). The compound energy formalism (CEF) model was used to represent the Gibbs free energy of the solid phases. Finally, the experimental measured results could be reproduced well using the present obtained thermodynamic parameters.

Development of a flexible quasi-harmonic-based approach for fast generation of self-consistent thermodynamic properties used in computational thermochemistry

We present in this work a new formalism for the rapid and accurate evaluation of the thermodynamic properties of compounds and solid solution end-members which are required in the high-throughput computational thermochemistry discovery of new materials. The method is based on the Debye approximation and is fully thermodynamically self-consistent. It considers several energetic contributions, such as the vibrational free energy (including both implicit and explicit anharmonicity), the defect-free energy (via the introduction of thermal vacancies), the energetic effect of thermal excitation of electrons (for metallic solids) as well as other excess terms to precisely reproduce experimental data. Sets of fully self-consistent pressure- and temperature-dependent thermodynamic properties are evaluated from the exact differentiation of this complete free energy formalism. This strategy allows the formalism to be fully integrated in the CALPHAD framework for the development of large thermodynamic databases of both stable and metastable compounds which may form in multicomponent/high-order systems. An emphasis is put in this work on the analysis and precise description of anharmonic vibrational contributions. Finally, sets of self-consistent thermodynamic and thermo-physical properties have been predicted as a function of temperature and compared with both experiments and classical QHA for pure elements (i.e. Ag, Li, V, Al, and C) and stoichiometric compounds of different chemical nature (i.e. MgO, CaO, Al2O3, NaCl, LiFePO4 and InP). The impact of various input parameters of the formalism on the free energy and the derived thermodynamic properties for these solids is analyzed. A better predictive capability and the enhanced flexibility of the proposed formalism are demonstrated.