Neumann-Kopp Rule Research Articles

Evaluation and thermodynamic optimization of phase diagram of lithium niobate tantalate solid solutions

The lithium niobate–lithium tantalate solid solution’s phase diagram was investigated using experimental data from differential thermal analysis (DTA) and crystal growth. We used XRF analysis to determine the elemental composition of the crystals. The Neumann–Kopp rule provided essential data for the end members lithium niobate (LN) and lithium tantalate (LT). The heats of fusion of the end members, given by DTA measurements, are 103 kJ/mol at 1531 K for LN and 289 kJ/mol at 1913 K for LT. These values were used as input parameters to generate the data. This data served as the basis for calculating a phase diagram for LN-LT solid solutions. Finally, based on the experimental data and a thermodynamic solution model, the Calphad Factsage module optimized the phase diagram. We also generated thermodynamic parameters for Gibbs’ excess energy of the solid solution. A plot of the segregation coefficient as a function of Ta concentration was derived from the phase diagram.

Revisiting thermodynamics in (LiF, NaF, KF, CrF2)–CrF3 by first-principles calculations and CALPHAD modeling

The thermodynamic description of the (LiF, NaF, KF, CrF2)–CrF3 systems has been revisited, aiming for a better understanding of the effects of Cr on the FLiNaK molten salt. First-principles calculations based on density functional theory (DFT) were performed to determine the electronic and structural properties of each compound, including the formation enthalpy, volume, and bulk modulus. DFT-based phonon calculations were carried out to determine the thermodynamic properties of compounds, for example, enthalpy, entropy, and heat capacity as functions of temperature. Phonon-based thermodynamic properties show a good agreement with experimental data of binary compounds LiF, NaF, KF, CrF3, and CrF2, establishing a solid foundation to determine thermodynamic properties of ternary compounds as well as to verify results estimated by the Neumann-Kopp rule. Additionally, DFT-based ab initio molecular dynamics (AIMD) simulations were employed to predict the mixing enthalpies of liquid salts. Using DFT-based results and experimental data in the literature, the (LiF, NaF, KF, CrF2)–CrF3 system has been remodeled in terms of the CALculation of PHAse Diagrams (CALPHAD) approach using the modified quasichemical model with quadruplet approximation (MQMQA) for liquid. Calculated phase stability in the present work shows an excellent agreement with experiments, indicating the effectiveness of combining DFT-based total energy, phonon, and AIMD calculations, and CALPHAD modeling to provide the thermodynamic description in complex molten salt systems.

Chemistry Informed Machine Learning-Based Heat Capacity Prediction of Solid Mixed Oxides.

Knowing heat capacity is crucial for modeling temperature changes with the absorption and release of heat and for calculating the thermal energy storage capacity of oxide mixtures with energy applications. The current prediction methods (ab initio simulations, computational thermodynamics, and the Neumann-Kopp rule) are computationally expensive, not fully generalizable, or inaccurate. Machine learning has the potential of being fast, accurate, and generalizable, but it has been scarcely used to predict mixture properties, particularly for mixed oxides. Here, we demonstrate a method for the generalizable prediction of heat capacity of solid oxide pseudobinary mixtures using heat capacity data obtained from computational thermodynamics and descriptors from ab initio databases. Models trained through this workflow achieved an error (mean absolute error of 0.43 J mol-1 K-1) lower than the uncertainty in differential scanning calorimetry measurements, and the workflow can be extended to predict other properties derived from the Gibbs free energy and for higher-order oxide mixtures.

Thermodynamic data of a promising cathode material NaV6O15 and its synthesis/decomposition thermodynamic analysis

Sodium-ion batteries have emerged as a promising alternative to lithium-ion batteries due to their lower cost and similar electrochemical properties. The development of high-capacity and long-life electrode materials is crucial for advancing sodium-ion battery research. A significant amount of research has been conducted on the electrochemical properties of NaV6O15, however, there remains a dearth of data on its thermodynamic properties. Herein, NaV6O15 was synthesized using the solid-phase sintering method and thoroughly characterized. Thermodynamic data in the temperature ranges of 298.15–900 K, 15–303 K, and 573–873 K were determined using the Neumann-Kopp rule, low-temperature physical property measurement system, and MHTC 96 line, respectively. The heat capacity equation of NaV6O15 was derived and its enthalpy, entropy, and Gibbs free energy (298.15–800 K) were calculated. Moreover, the thermodynamics of NaV6O15-related formation and decomposition reactions were analyzed. The obtained heat capacity equation of NaV6O15 was Cp=517.05524+0.08612T−1.25053×107T−2(J/mol·K)(298.15∼873K). This study addresses the thermodynamic knowledge gaps of NaV6O15 and provides valuable insights for its preparation and decomposition in manufacturing processes.

INFLUENCE OF THE DIAMETER OF CYLINDRICAL SAMPLES MADE OF DIFFERENT GRADES OF ALUMINUM ON THE COOLING KINETICS

The influence of the diameter of cylindrical samples from various grades of technical aluminum (A0, A5, A6), aviation AB98 and high-purity aluminum A5N on their characteristic cooling times and rates, as well as on heat transfer processes in a wide temperature range, was studied. It was revealed that cooling of the samples occurs due to convective heat transfer and radiation, which have characteristic times. An assessment of the magnitude of characteristic cooling times due to convective heat transfer and radiation has been carried out. It is shown that the characteristic cooling time due to radiation is less than the characteristic cooling time due to convection. Using experimental data on the cooling rate of the studied samples and theoretically calculated values of their heat capacity according to the Neumann-Kopp rule, heat transfer coefficients for the processes of convective heat transfer and radiation depending on temperature were determined. It has been established that with increasing temperature, the contribution of radiation to the total heat transfer coefficient increases, and the coefficient of convective heat transfer with increasing temperature first increases, then after passing a maximum it decreases. The contribution to the overall heat transfer coefficient from radiation is noticeable at high temperatures. It was revealed that the characteristic cooling times due to radiation and convection increase nonlinearly with increasing sample diameter (V/S). This dependence is explained by a decrease in the heat transfer coefficient with increasing sample diameter. Compared with the patterns of influence of sample size on the thermophysical properties of spherical samples. It was revealed that spherical samples cool faster than cylindrical samples of the same mass, and the heat transfer coefficients are higher.

The specific heat of Al-based compounds, evaluation of the Neumann-Kopp rule and proposal for a modified Neumann-Kopp rule

Application of the Neumann-Kopp rule to aluminum containing compounds produces a kink in the specific heat caused by the description of pure aluminum in the SGTE Unary database. Two ways to get rid of this problem are investigated. In a first step, we tried to redefine the description of aluminum above its melting point using a reverse Neumann-Kopp approach. After a systematic review of the experimental Cp data for all the aluminum based compounds, we could evaluate the accuracy of the Neumann-Kopp rule. We could find a nearly systematic overestimation of the Cp of the order of 15%. This makes the use of the reverse Neumann-Kopp approach inapplicable. In a second step, based on this analysis of the available data, we propose another approach consisting in defining the Cp of a compound by a composition average of the Cp of the pure elements, not at the same temperature as in the Neumann-Kopp rule, but rather at a temperature normalized to the melting point of each pure element and the compound. Not only are the results in much better agreement with the experimental data than the conventional Neumann-Kopp rule, but also, there is no longer a need to define the Cp of aluminum above its melting point.

Thermodynamic properties study of polyoxometalate Na7[H2PV14O42

Lithium-ion batteries (LIBs) are widely used in electronic applications because of their high voltage, high specific energy, long lifespan, and other characteristics. Electrode materials have garnered interest as an indispensable component of LIBs. Na7[H2PV14O42] is used as an electrode material because of its excellent properties. In this study, Na7[H2PV14O42] was synthesized by the water bath method using NaVO3 as the raw material, experimentally characterized, and its thermodynamic data were measured using the Neumann-Kopp rule from 298.15 to 843K, a Physical Property Measurement System from 15 to 309K, and the MHTC 96 line from 473 to 773K. The data were fitted to the Debye-Einstein heat capacity equation at low temperatures and a polynomial function at higher temperatures. The heat capacity equation of Na7[H2PV14O42] was obtained from the fitted curves. The corresponding enthalpy (▵298.15 THm), entropy (▵298.15 TSm), and Gibbs energy (▵298.15 TGm) (from 298.15 to 800K) were calculated according to the heat capacity equation. The obtained heat capacity of Na7[H2PV14O42], as a function of temperature, was modeled as Cp = 1502.30 + 0.27T - 2.44E7T-2J mol-1K-1 (473-773K). This study can compensate for the thermodynamic deficiency of Na7[H2PV14O42].

Thermodynamic properties of KCaCl(NO3)2 compound and influence of kinetic effects

The thermodynamic properties of the intermediate compound KCaCl(NO3)2 are important for the thermochemical description of the KCl–CaCl2–KNO3–Ca(NO3)2 reciprocal system, for its utilization as a phase change material or heat transfer fluid in thermal energy storage. The formation of KCaCl(NO3)2 as intermediate compound in this reciprocal system was confirmed by X-Ray diffraction analysis. Aside from the main phase of KCaCl(NO3)2, other crystalline phases were also identified. Kinetic effects were observed during the study of this compound. For example, the enthalpy of fusion of the 50KCl–50Ca(NO3)2 mixture depends on the cooling rate of the previous cycle. The samples, which crystallized with 10 K/min, show higher enthalpy of fusion (22.4 kJ/mol) compared to samples cooled with 0.5 K/min - 16.3 kJ/mol. This effect is related to the different ratio of crystallized phases (KCaCl(NO3)2, KCaCl3, Ca(NO3)2 and various Potassium Calcium nitrates) in this mixture. The heat capacity and enthalpy increment of the KCaCl(NO3)2 compound in solid and liquid phases are determined with two different DSC instruments. The selected value of the fusion enthalpy for KCaCl(NO3)2 compound is 22.4 ± 1.2 kJ/mol, which was obtained after fast (10 K/min) cooling. The comparison of the experimental results with calculated values based on Neumann-Kopp rule confirms the reliability of the obtained data.

The Heat Capacity of PuO2 at High Temperature: Molecular Dynamics Calculations

Abstract A new generation of fast breeder reactors (FBRs) is under development with the objective of making nuclear energy more sustainable. Most promising reactor designs are loaded, at least during their early phase of deployment, with UO2–PuO2 mixed oxide fuel (MOX). Concentrations of plutonium dioxide that are foreseen for FBRs range up to 30 mol%. This highlights the need for a sound and deep knowledge of the thermophysical properties of PuO2. This statement is valid in the case of heat capacity, as evaluations on MOX fuel are usually carried out by using the Neumann–Kopp rule. Heat capacity is relevant for thermal conductivity and performance under transient conditions. However, measurements on the heat capacity of plutonium dioxide are scarce or even lacking at high temperature. Numerical methodologies such as molecular dynamics (MD) calculations have been employed to overcome the difficulties encountered in experimental measurements. Besides numerical also theoretical models have been applied as valuable tools for interpretation of enthalpy measurements. Nevertheless, due to the mentioned lack of experimental measurement issues such as the existence of the Bredig transition and the formation of defects at high temperatures are still debated in nuclear fuel research. Excess enthalpy seen in measurements of actinides oxides has been explained by means of either electronic disorder or anion disorder. In the case of plutonium dioxide, a common consensus has been reached on the hypothesis that anion disorder leads to a significant increase in heat capacity at high temperature. Konings and Beneš have developed a model that accounts for this phenomenon. Their correlation has been often included in models of heat capacity and employed for recommendations. However, in the high-temperature region, MD calculations showed an underestimation of model predictions that was not compensated by the presence of a peak of heat capacity that has been interpreted as the Bredig transition. Based on these observations, this paper presents MD evaluations on the heat capacity of PuO2 at high temperature that are mostly focused on the formation energy of oxygen Frenkel pairs (OFPs) and its correlation with the model proposed by Konings and Beneš. Besides an interatomic potential published in the open literature and developed in compliance with the experimental thermal expansion of PuO2, a second interatomic potential has been applied in calculations. This latter is featured by a lower formation energy of OFP. The contribution due to defects formation was calculated by means of a simplified theoretical model of heat capacity. Results of calculations in the very high-temperature domain showed an increase in the contribution due to OFP defects consistent with the model by Konings and Beneš. Predictions suggest the onset of a premelting transition around 85% of melting temperature without the presence of a peak of heat capacity. Major deviations from the recommended model have been noted in the intermediate temperature region where the effect of clustering of defects should play a significant role. Therefore, the value of formation energy of OFP proposed by Konings and Beneš could be interpreted as an effective value that accounts for the two processes (defects clustering and premelting transition) that could contribute, according to our results, to the heat capacity of plutonium dioxide at high temperature. This conclusion is consistent with the numerical evaluations of OFP formation energy that are in general higher than proposed by Konings and Beneš.

Molar heat capacity of liquid Ti, Al20Ti80 and Al50Ti50 measured in electromagnetic levitation

Temperature dependent isobaric molar heat capacity cP was measured in a containerless way for liquid Ti and two AlTi binary liquid alloys. The technique of electromagnetic levitation was used in combination with laser modulation calorimetry. In all cases, linear temperature dependencies were found: At the corresponding liquidus temperatures, cP equals 49.75(±2.0) J∙K-1mol-1, 57.43(±2.9) J∙K-1mol-1, and 42.60(±2.2) J∙K-1mol-1, for Ti, Al20Ti80 and Al50Ti50, respectively. The respective temperature coefficients amount to -1.67∙10-2J∙K-2mol-1, -2.73∙10-2J∙K-2mol-1, and +7.83∙10-2J∙K-2mol-1. For liquid Ti, there is a good agreement with existing literature data. The results are discussed in relation to the Neumann-Kopp rule.

Synthesis Method and Thermodynamic Characteristics of Anode Material Li3FeN2 for Application in Lithium-Ion Batteries.

Li3FeN2 material was synthesized by the two-step solid-state method from Li3N (adiabatic camera) and FeN2 (tube furnace) powders. Phase investigation of Li3N, FeN2, and Li3FeN2 was carried out. The discharge capacity of Li3FeN2 is 343 mAh g−1, which is about 44.7% of the theoretic capacity. The ternary nitride Li3FeN2 molar heat capacity is calculated using the formula Cp,m = 77.831 + 0.130 × T − 6289 × T−2, (T is absolute temperature, temperature range is 298–900 K, pressure is constant). The thermodynamic characteristics of Li3FeN2 have the following values: entropy S0298 = 116.2 J mol−1 K−1, molar enthalpy of dissolution ΔdHLFN = −206.537 ± 2.8 kJ mol−1, the standard enthalpy of formation ΔfH0 = −291.331 ± 5.7 kJ mol−1, entropy S0298 = 113.2 J mol−1 K−1 (Neumann–Kopp rule) and 116.2 J mol−1 K−1 (W. Herz rule), the standard Gibbs free energy of formation ΔfG0298 = −276.7 kJ mol−1.

A Combined Experimental and First-Principles Based Assessment of Finite-Temperature Thermodynamic Properties of Intermetallic Al3Sc.

We present a first-principles assessment of the finite-temperature thermodynamic properties of the intermetallic AlSc phase including the complete spectrum of excitations and compare the theoretical findings with our dilatometric and calorimetric measurements. While significant electronic contributions to the heat capacity and thermal expansion are observed near the melting temperature, anharmonic contributions, and electron–phonon coupling effects are found to be relatively small. On the one hand, these accurate methods are used to demonstrate shortcomings of empirical predictions of phase stabilities such as the Neumann–Kopp rule. On the other hand, their combination with elasticity theory was found to provide an upper limit for the size of AlSc nanoprecipitates needed to maintain coherency with the host matrix. The chemo-mechanical coupling being responsible for the coherency loss of strengthening precipitates is revealed by a combination of state-of-the-art simulations and dedicated experiments. These findings can be exploited to fine-tune the microstructure of Al-Sc-based alloys to approach optimum mechanical properties.

Thermodynamic evaluation and optimization of LiNO3–KNO3–NaNO3 ternary system

The phase diagram of LiNO3–KNO3 system was investigated with differential scanning calorimetry. Phase transitions data of LiNO3–KNO3 system were obtained. Using the measured phase equilibrium data as well as other available phase equilibrium and thermodynamic data in literature, the thermodynamic optimization of parameters for all phases and compounds in the LiNO3–NaNO3–KNO3 system was performed. The Modified Quasichemical Model was applied for the liquid phase, and Compound Energy Formalism was used for the NaNO3–KNO3 solid solutions. The compound KNO3·LiNO3 was treated with Neumann-Kopp rule. The optimized parameters were used to predict the phase diagram of LiNO3–NaNO3–KNO3 ternary system and the predicted ternary invariant points were experimentally verified.

Phonons and thermophysical properties of U1−yPuyO2 mixed oxide (MOX) fuels

The phonon and thermophysical properties of uranium-plutonium mixed oxides (MOX) fuels are investigated. We have applied Hubbard corrected density functional theory (DFT + U) and empirical potentials (EP) coupled to the Boltzmann transport equation (BTE) to investigate the harmonic and anharmonic lattice vibrational properties. The specific heat, entropy and thermal conductivity, were analyzed to investigate the effect of actinide composition on the thermal properties in pure and mixed oxides. Our results indicate a relative increase in the anharmonicity of phonons in mixed oxides compared to the parent oxides. We discuss the decrease in the lattice thermal conductivity in the MOX in terms of the increase in the Grüneisen parameter, group velocity and phonon-phonon scattering, in comparison to the parent oxides. Furthermore, we demonstrate that the differences in the specific heat of actinide oxides, and thus the Neumann-Kopp rule for MOX, which is the rule of mixtures, are originated from the contribution of the crystal electric field at the actinide cations.

Thermodynamic modeling of Cr–Al–C and Ni–Al–C systems for low-density steels

The so-called low-density steels have generated a lot of interests with their high specific strength and ductility due to the addition of the light element Al. In order to accelerate the low-density steel design, a thermodynamic database has been developed within the present author group. Two Al-containing systems, i.e., Cr–Al–C and Ni–Al–C, were modeled and optimized with CALPHAD approach based on the reliable binary descriptions. For Cr–Al–C system, the Gibbs energy of Cr2AlC phase was described by a temperature-dependent polynomial with the aid of the experimental data on the heat capacity, instead of estimating heat capacity from Neumann–Kopp rule. The incongruent melting temperature of Cr2AlC is 1762 K with the invariant reaction of liquid + Cr3C2 + Al4C3 → Cr2AlC. The phase equilibria between Cr2AlC and binary phases were well reproduced by using the present model parameters. For Ni–Al–C system, the liquid, fcc and bcc phases have been optimized to fit the carbon solubility in these three phases. A good agreement between the calculated and experimental data has been obtained using the present description of Ni–Al–C system. The reliable descriptions of the two ternary systems developed in the present work can be implemented into the thermodynamic database for low-density steels.

Enthalpies of formation of the solid solutions of ZrxY0.5−x/2Ta0.5−x/2O2 (0 ≤ x ≤ 0.2 and 0.65 ≤ x ≤ 1)

Abstract

Thermophysical properties of M′-LuTaO4: Structural and calorimetric studies

Lutetium orthotantalate with M′-fergusonite type structure was synthesized using a reverse coprecipitation method. Phase and chemical composition, as well as microstructure of the synthesized sample, were characterized by X-ray diffraction (XRD), μ-X-ray fluorescence and Fourier-transform infrared spectroscopies, and scanning electron microscopy. Heat capacity of M′-LuTaO4 was first studied by adiabatic and differential scanning calorimetry (DSC) in the temperature range from 10 to 1300 K. Using a temperature dependence of heat capacity, the standard thermodynamic functions (entropy Smo(T), enthalpy change Hmo(T)–Hmo(0) and derived Gibbs energy Фmo(T)) were calculated in the range of T→0–1300 K. The standard molar entropy of M′-LuTaO4 at 298.15 K is 123.12 ± 0.50 J K−1 mol−1. A comparison of the experimental heat capacity values, obtained by DSC, with those calculated using the empirical Neumann-Kopp rule showed a reasonable agreement between the two sets of data only up to ≈1000 K. The high-temperature evolution of the lattice parameters for M′-LuTaO4 was studied by high-temperature XRD (HTXRD). According to the high-temperature heat capacity study and the HTXRD measurements, there were no phase transformations up to 1300 K. Based on the HTXRD data, the linear and volume thermal expansion coefficients were obtained for the first time.

Thermodynamic properties of YRhO3 and phase relations of the system Y-Rh-O

As part of a larger program of research on physico-chemical aspects of processing Rh catalysts, thermodynamic properties of the ternary oxide YRhO3 are determined in the temperature range from 900 to 1300 K using a solid-state electrochemical cell incorporating yttria-stabilized zirconia as the electrolyte. The standard Gibbs energy of formation of orthorhombically-distorted perovskite YRhO3 from its component binary oxides Y2O3 and Rh2O3 is calculated.Assuming Neumann-Kopp rule, the standard entropy of YRhO3 at 298.15 K is evaluated as 83.51(±1.5) J K−1 mol−1. The standard enthalpy of formation of the compound from elements at 298.15 K is obtained as −1219.2(±2.8) kJ mol−1. Using isothermal equilibration technique, YRhO3 is identified as the only inter-oxide compound in the system Y2O3-Rh2O3. Existence of a three-phase field involving Rh + Y2O3 + YRhO3 is confirmed. Based on thermodynamic data phase relations in the system Y-Rh-O are computed at 1200 K. Various phase diagrams at 1200 K are presented.

Experimental investigation and thermodynamic assessment of the RbCl[sbnd]CsCl[sbnd]ZnCl2 system and its subsystems

The RbClZnCl2 and CsClZnCl2 binary systems with different proportions are firstly prepared to determine the phase equilibrium relation using differential scanning calorimetry (DSC) and X-ray diffraction (XRD) methods. The phase diagrams of RbClZnCl2, CsClZnCl2 and RbClCsCl are thus critically optimized by thermodynamic modeling based on the available experimental values. The associate solution model (ASM) is used to describe the liquid phases of RbClZnCl2 and CsClZnCl2 binary system, and the substitutional solution model (SSM) is applied for the RbClCsCl binary system. All Gibbs energies of intermediate compounds are treated with the Neumann-Kopp rule. In light of this, a set of self-consistent thermodynamic database is obtained and applied to predict the thermodynamic properties of the RbClCsClZnCl2 ternary system by merging the Gibbs energies in its subsystems via the Kohler-Toop interpolation method. These results could provide effective data supporting for the selection and optimization of multi-component molten salts for the concentrating solar power (CSP) plants.

Synthesis of pure intermetallic phases on the example of the ternary phase τ1 in the system Al-Fe-Ni

An experimental method for the synthesis of the ternary τ1 Al9(Fe,Ni)2 phase in the Al-Fe-Ni system in quantities of up to several grams is presented. The resolidification of the mushy zone in a stationary temperature gradient is employed. In a temperature gradient, solidifying phases may form spatially separated in a sequence following the two-phase equilibria liquid/solid in the equilibrium phase diagram. An initial composition different from that of the desired intermetallic phase needs to be chosen. A suitable concentration for synthesizing τ1 was identified on the basis of a preliminary ternary phase diagram in combination with solid/liquid coarsening experiments. After confirmation of the single-phase state of τ1 using XRD, the heat capacity of τ1 was measured, and the thermodynamic description of τ1 was re-assessed. The Neumann-Kopp rule that is frequently employed for the thermodynamic description of the heat capacity is found to be inadequate in the case of τ1, and the problem appears to be of some generality.