High-temperature Drop Calorimetry Research Articles

A new methodology for measuring the enthalpies of mixing and heat capacities of molten chloride salts using high temperature drop calorimetry.

Molten salt reactors (MSRs) are a promising alternative to conventional nuclear reactors as they may offer more efficient fuel utilization, lower waste generation, and improved safety. The state of knowledge of the properties of liquid salts is far from complete. In order to develop the MSR concept, it is essential to develop a fundamental understanding of the thermodynamic properties, including the heat capacities (Cp) and enthalpies of mixing (ΔHmix), of molten salts at MSR operating conditions. Historically, the Cp values of molten salts were determined by drop-calorimetry or differential scanning calorimetry, whereas their ΔHmix values were typically measured using specialized high temperature calorimeters. In this work, a new methodology for measuring both the Cp and the ΔHmix of molten chloride salts was developed. This novel method involves sealing a chloride salt sample in a nickel capsule and performing conventional transposed temperature drop calorimetry using a commercially available Setaram AlexSYS-800 Tian-Calvet twin microcalorimeter. This methodology may be applied to calorimetric measurements of more complex salt mixtures, especially mixtures containing actinides and fission products.

Thermodynamic investigation of the NaCl-KCl salt system from 25 to 950 °C

NaCl-KCl molten salt system has been proposed as a primary component of several promising heat transfer eutectics and fuel host for Generation IV molten salt reactors (MSR). In this work, several key thermodynamic parameters, including high temperature enthalpies, isobaric heat capacities (Cp) and molar enthalpies of mixing (ΔHmix), of the NaCl-KCl system (NaCl, 75 mol% NaCl – 25 mol% KCl, 51 mol% NaCl – 49 mol% KCl, 25 mol% NaCl – 75 mol% KCl, and KCl) were measured by high temperature drop calorimetry (HTDC) utilizing laser sealed nickel and aluminum crucibles. Salts were checked for phase purity by X-ray diffraction (XRD), and water content by Karl Fischer coulometric titrimetry and thermogravimetric analysis (TGA). Thermo-mechanical analysis (TMA) utilizing custom-built boron nitride (BN) crucibles was employed to determine temperatures of phase transitions (solid → liquid) for the salts and plotted against the pseudobinary phase diagram for the NaCl-KCl system. Small deviations (3–10 %) were found among Cp values obtained from HTDC, differential scanning calorimetry (DSC), and NIST, comparable to the average uncertainty based on two standard deviations of measured data that are ∼6% for DSC and ∼3% for HTDC. Additionally, the measured enthalpies and Cp values of mixed NaCl-KCl salts (e.g., 51 mol% NaCl – 49 mol% KCl eutectic) were shown to behave as a nearly statistical mixtures of its pure endmembers, consistent with ΔHmix = −1.324 kJ/mol at 800 °C, and a regular interaction parameter of Ω = 4.77 ± 0.79 kJ/mol. This study represents a step towards improved accuracy and precision in determinations of thermodynamic parameters of molten salts by using DSC, TMA, and HTDC, in completion of the Molten Salt Thermal Properties Database (MSTDB).

Density, Thermal Expansion, Enthalpy, Heat Capacity, and Thermal Conductivity of Calcium in the Temperature Range 720–1290 K

Thermophysical properties of solid and liquid calcium (99.75 wt % pure) were experimentally studied with high accuracy in the temperature range 720–1290 K using dilatometer measurements, gamma-ray attenuation measurements (the gamma-ray method), high-temperature drop calorimetry, and the laser flash method. The behaviors of the density, enthalpy, and thermal conductivity of calcium in the fusion–crystallization region were studied. The enthalpy of fusion was measured as 8075 J/mol, the relative density change upon fusion as 3.3%, and the relative change in thermal conductivity upon fusion as 26%. The results were compared to the respective values in the related literature. The measurements at temperatures above 720 K either significantly amend the available literature data, or are currently unique. The constancy of the heat capacity of liquid calcium in the temperature range 1115–1290 K was verified. Fitting equations were derived, and recommended values of the investigated properties of calcium were tabulated for 720–1290 K, the temperature range where calcium is in the condensed state.

The magnesium-ytterbium system: A contribution to the thermodynamics of solid alloys

Abstract Magnesium-ytterbium alloys were investigated in order to determine the enthalpy of formation of YbMg2 and to check the phase diagram of the system. The system was investigated by using differential scanning calorimetry, electron microscopy, electron microprobe analysis, and X-ray diffraction analysis. The enthalpy of formation was measured by high temperature drop calorimetry. A value of – 13.5 ± 0.5 kJ/mol of atoms was obtained for the standard formation enthalpy of YbMg2.

Thermal Properties and Behaviour of Am-Bearing Fuel in European Space Radioisotope Power Systems

The European Space Agency is funding the research and development of 241Am-bearing oxide-fuelled radioisotope power systems (RPSs) including radioisotope thermoelectric generators (RTGs) and European Large Heat Sources (ELHSs). The RPSs’ requirements include that the fuel’s maximum temperature, Tmax, must remain below its melting temperature. The current prospected fuel is (Am0.80U0.12Np0.06Pu0.02)O1.8. The fuel’s experimental heat capacity, Cp, is determined between 20 K and 1786 K based on direct low temperature heat capacity measurements and high temperature drop calorimetry measurements. The recommended high temperature equation is Cp(T/K) = 55.1189 + 3.46216 × 102 T − 4.58312 × 105 T−2 (valid up to 1786 K). The RTG/ELHS Tmax is estimated as a function of the fuel thermal conductivity, k, and the clad’s inner surface temperature, Ti cl, using a new analytical thermal model. Estimated bounds, based on conduction-only and radiation-only conditions between the fuel and clad, are established. Estimates for k (80–100% T.D.) are made using Cp, and estimates of thermal diffusivity and thermal expansion estimates of americium/uranium oxides. The lowest melting temperature of americium/uranium oxides is assumed. The lowest k estimates are assumed (80% T.D.). The highest estimated Tmax for a ‘standard operating’ RTG is 1120 K. A hypothetical scenario is investigated: an ELHS Ti cl = 1973K-the RPSs’ requirements’ maximum permitted temperature. Fuel melting will not occur.

Experimental results of the Li-Pb-Pt system obtained by the high temperature drop calorimetry

The integral enthalpy of mixing of the ternary Li-Pb-Pt system was measured using high temperature drop calorimetry. Four independent series of fixed mole ratios of Li to Pb equaled to 1/3, 1, 3, and Pb to Pt equaled to 4 were conducted at 1026 K. The measurements were divided into three continuous parts. Firstly, the calorimeter was calibrated by dropping the pieces of Pb, subsequently, pieces of the second component (Li or Pt) were added to form a binary alloy, and then the study of the integral enthalpy of mixing of ternary Li-Pb-Pt began. The thermodynamic results are characterized by negative deviations to the ideal solution in the entire measured concentration range. Based on the experimental data for the Li-Pb-Pt solutions and on the integral enthalpy of mixing of the binary Li-Pb, Li-Pt and Pb-Pt solutions the ternary interaction parameters were determined and presented.

Defect structure and thermochemistry of YBaCo2O6-δ

The defect structure analysis of the oxygen deficient YBaCo2O6-δ double perovskite cobaltite confirms that the model proposed earlier for RBaCo2O6-δ (R – Pr, Gd, La) holds also for YBaCo2O6-δ. In particular, a good agreement between the pO2(T, δ) model function and experimental pO2 – T – δ data is obtained for this oxide. By means of high-temperature drop calorimetry, the enthalpy increments of YBaCo2O6-δ samples with different initial oxygen contents (0.67 ≤ δ ≤ 1) were measured in air in the (1123–1273) K temperature range. The results obtained for YBaCo2O5.0 were fitted using a Maier-Kelley function. The smoothed values of Δ298.15TH∘, Cp(T), and Δ298.15TS∘ were calculated for thermodynamically stable YBaCo2O5.0 in the temperature range 1150 ≤ T, K ≤ 1350. The drop calorimetric results for the metastable YBaCo2O5.33 were used to evaluate the standard enthalpy of its reduction at 298.15 K, ΔHred∘, as (161 ± 15) kJ·(mol O2)-1 (expanded uncertainty with ≈0.95 level of confidence), which is significantly less endothermic than ΔHred∘ of some other double perovskite cobaltites, RBaCo2O6-δ (R – Pr, Gd), within similar oxygen nonstoichiometry ranges (0.5 ≤ δ ≤ 1.0).

Calorimetric and phase diagram studies of the Ga-In-Zn system

Partial and integral enthalpies of mixing of liquid Ga-In-Zn alloys at a temperature of 720 K were measured by high-temperature drop calorimetry. Calorimetric measurements were performed along four intersections as follows: xGa/xZn = 3/1, xGa/xZn = 1/1, xGa/xZn = 1/3 and xGa/xIn =1/3. Based on obtained thermodynamic results and those available in the literature the thermodynamic optimization was done using Thermo-Calc software. Next, the phase equilibria in the binary and ternary systems were calculated and the results were compared with those obtained using different experimental techniques.

Crystal structure and high-temperature thermodynamic properties of Pr-doped barium zirconates, BaZr1–xPrxO3 (x = 0.1, 0.5)

The crystal structure of BaZr1–xPrxO3 (x = 0.1, 0.5) perovskites was studied by means of X-ray powder diffraction (XRD). It was found that, at room temperature, BaZr0.9Pr0.1O3 possesses cubic (Pm3‾m) crystal structure, whereas BaZr0.5Pr0.5O3 is rhombohedral (R3‾c). High-temperature XRD study revealed that rhombohedral distortions in the BaZr0.5Pr0.5O3 lattice gradually decrease upon heating. As a result, BaZr0.5Pr0.5O3 becomes ideally cubic (Pm3‾m) at temperatures higher than 723 K. The enthalpy increments, Δ298.15TH○, of the perovskites BaZr1–xPrxO3 (x = 0.1, 0.5) were measured by high-temperature drop calorimetry in the temperature range (373–1273) K in air. The Δ298.15TH○ data for BaZr1–xPrxO3 (x = 0.1, 0.5) were approximated using one Einstein term with, for BaZr0.5Pr0.5O3, an addition of the exponential terms describing the influence of the R3‾c→Pm3‾m transition. The high- and low-temperature thermodynamic properties of BaZrO3 reported in the literature were reevaluated and its heat capacity, Cp(T), was approximated with one Einstein term as well. Thus, analytical Cp(T) dependences are reported for BaZr1–xPrxO3 (x = 0, 0.1, 0.5). While the Cp(T) of BaZrO3 and BaZr0.9Pr0.1O3 are very close to each other, the values of Cp(T) of BaZr0.5Pr0.5O3 are higher, mostly because of the phase transition and the differences in the crystal structure. Using the thermodynamic data obtained in this work along with those reported earlier, it was shown that addition of praseodymium leads to decreasing relative stability of BaZr1–xPrxO3 towards interaction with CO2 and gaseous H2O.

Thermodynamic properties of synthetic zeolite – Mordenite

The thermal behaviour of zeolites is of an important consideration for evaluating the consequences of temperature changes in geologic, experimental, and engineered systems. Calorimetric measurements have been carried out on a synthetic sample of mordenite having the composition Na1.51Al1.51Si10.49O24·4.60 H2O. High-temperature drop calorimetry has been used to derive the thermochemical properties: enthalpy of formation and enthalpy of dehydration. New additive thermodynamic model for zeolites thermodynamic properties prediction was used to estimate the heat capacity, entropy and heat content of mordenite in wide temperature range. This study is a part of a program to determine calorimetrically the thermodynamic properties of synthetic zeolites.

Calorimetric studies of mixing enthalpy in the liquid system Ga-Li, and Ga-Li-Sn

Partial enthalpies of mixing for the liquid phase of the binary Ga-Li and ternary Ga-Li-Sn systems at a temperature of 1081 K were measured by high-temperature drop calorimetry. The binary system was investigated to a maximum lithium content of x(Li) = 0.59. In the ternary, seven composition sections were investigated: x(Ga)/(x(Ga) + x(Sn)) = 0.15, 0.45, 0.70, 0.85, and x(Ga)/(x(Ga) + x(Li)) = 0.80, 0.50, 0.40. It is shown, that the binary sub-system Ga-Li shows a strong exothermic behavior with a molar liquid mixing enthalpy of ΔmixH = −22.4 kJ·mol−1 at x(Li) = 0.58 (1081 K). In accordance with an even more negative molar mixing enthalpy of ΔmixH = −36.82 kJ·mol−1 at x(Li) = 0.7 (1081 K) in the binary sub-system Li-Sn, the ternary Ga-Li-Sn system is characterized by a strong exothermic behavior. Our experimental values for the binary Ga-Li system agree well with literature data and ΔmixH against composition was described by a Redlich-Kister polynomial. It is shown, that for the ternary Ga-Li-Sn system the extrapolation model of Toop is sufficient enough to describe the mixing enthalpy of the liquid phase. Moreover, our experimental ternary data were numerically fitted on the basis of an extended Redlich-Kister-Muggianu model which was designed for the excess energy of the substitutional-regular-solution model.

Enthalpy of formation of U3Si2: A high-temperature drop calorimetry study

U3Si2 is presently receiving consideration as a high density light water reactor fuel. A reliable knowledge of the formation enthalpy of U3Si2 not only helps study the thermal stability but also facilitate the modeling efforts by serving as a benchmark parameter for thermodynamic calculations of phase equilibria at high temperatures. Previous high temperature thermal analysis on U3Si2 laid the basis for us to conduct two types of high-temperature drop calorimetric measurements to determine its enthalpy of formation: oxide-melt drop-solution calorimetry and transposed temperature drop calorimetry, from which the results obtained are consistent. The determined standard enthalpy of formation of U3Si2 per mole atom, −33.2 ± 3.1 kJ/mol⋅at.%, is in good agreement with previously reported values obtained by other techniques. Our drop calorimetry methods will be used for thermodynamic studies of other U-Si compounds whose enthalpies of formation are not available.

High temperature drop calorimetry measurements of enthalpy increment in Ti–xTa (x=5, 10, 15, 20 mass%) alloys

The enthalpy increment for a series of Ti–xTa (x=5, 10, 15, 20 mass%) alloys, having α(hcp)+β(bcc) two phase microstructure has been measured using inverse drop calorimetry in the temperature range 463–1257K. The studies clearly revealed the occurrence of α→β diffusional phase transformation. Both the α→β transformation onset temperatures and the measured transformation enthalpy Δ0Htrα→β exhibit progressively lower values with increasing Ta content. It is found that the measured enthalpy in the transformation region is constituted of two principal contributions namely, (i) the enthalpy due to untransformed α and coexisting β phases and (ii) the transformation enthalpy due to α→β phase change. Since the fractional extent of α→β transformation varies continuously with temperature, the measured enthalpy variation in the transformation domain has been modeled using Kolmogorov–Johnson–Mehl–Avrami formalism for the diffusional transformation kinetics. The thermodynamic quantities for all the alloys have been derived.

Enthalpy of SmAlO3 in the range 472–2252 K

The enthalpy increment of SmAlO3 is measured for the first time using high-temperature drop calorimetry in the temperature range 472–2252 K. The enthalpy values are used to determine other thermodynamic functions, such as heat capacity, entropy, and reduced Gibbs energy. Phase transitions from orthorhombic to trigonal structure and from trigonal to cubic structure are observed at 1055 and 2103 K, respectively. The phase transition at 1055 K is studied by differential thermal analysis. The enthalpies and entropies of phase transitions are determined.

Premelting at fusion of titanite CaTiSiO5: a calorimetric study

An extensive anomalously rapid increase of relative enthalpy H(T) − H(298 K) of crystalline CaTiSiO5 was observed by means of high-temperature drop calorimetry when melting point is approached. X-ray diffraction analysis of the quenched products after drop in calorimeter shows that this effect is related to premelting. The determined excess enthalpy of crystals near the melting point reaches up to 115 kJ mol−1, that is about 82 % of the total enthalpy of melting, indicating that the premelting effect reflects configurational changes in the bulk of the crystals rather than a surface melting or any other type of partial melting. The obtained results support the presumption that calorimetrically measured premelting effect in titanite reflects the energy-consuming temperature-induced disordering of the framework elements, Si and Ti, which are strongly bonded to oxygen.

High temperature thermal properties of UFe2

High temperature drop calorimetry measurements of enthalpy increment have been made on phase pure UFe2 compound for temperatures up to 1,473 K. The measured data agreed well with the earlier reported data that are available only up to 1,000 K. An integrated modelling of the present heat capacity data has been made using the framework of quasi-harmonic Debye-Gruneisen formalism, the input parameters for which have been obtained after a critical appraisal of the available thermophysical data. The modelling yielded fully consistent estimates of both heat capacity and volume thermal expansivity, for the complete temperature range, 0–1,273 K.

Enthalpies of mixing of liquid systems for lead free soldering: Co–Sb–Sn

The partial and integral enthalpy of mixing of molten ternary Co–Sb–Sn alloys was determined performing high temperature drop calorimetry in a large compositional range at 1273 K. Measurements have been done along five sections, xSb/xSn ≈ 1:1, xSb/xSn ≈ 1:3, xSb/xSn ≈ 3:1, xCo/xSn ≈ 1:4, and xCo/xSb ≈ 1:5. Additionally, binary alloys of the constituent systems Co–Sb and Co–Sn were investigated at the same temperature. All the binary data were evaluated by means of a standard Redlich–Kister polynomial fit whereas ternary data were fitted on the basis of an extended Redlich–Kister–Muggianu model for substitutional solutions. An iso-enthalpy plot of the ternary system was constructed. In addition, the extrapolation Model of Toop was applied and compared to our data.

Heat capacity measurements and XPS studies on uranium–lanthanum mixed oxides

Heat capacity measurements were carried out on (U 1− y La y )O 2± x ( y = 0.2, 0.4, 0.6, and 0.8) using differential scanning calorimeter (DSC) in the temperature range 298–800 K. Enthalpy increment measurements were carried out on the above solid solutions using high temperature drop calorimetry in the temperature range 800–1800 K. Chemical states of U and La in the solid solutions of mixed oxides were determined using X-ray photoelectron spectroscopy (XPS). Oxygen to metal ratios of (U 1− y La y )O 2± x were estimated from the ratios of different chemical states of U present in the sample. Anomalous increase in the heat capacity is observed for (U 1− y La y )O 2± x ( y = 0.4, 0.6 and 0.8) with onset temperatures in the range of 1000–1200 K. The anomalous increase in the heat capacity is attributed to certain thermal excitation process, namely, Frenkel pair defect of oxygen. The heat capacity value of (U 1− y La y )O 2± x ( y = 0.2, 0.4, 0.6, and 0.8) at 298 K are 65.3, 64.1, 57.7, 51.9 J K −1 mol −1, respectively. From the XPS investigations, it was observed that the O/M ratios at the surface are higher than that in the bulk. In uranium rich mixed oxide samples, the surface O/M ratios are greater than 2 whereas that in La rich mixed oxides, they are less than 2, though the bulk O/M in all the samples are less than 2.

Heat capacity of the AuZr compound obtained by high-temperature drop calorimetry

The enthalpy increments of the Zr 0.50Au 0.50 phase have been measured by high-temperature drop calorimetry in the temperature range 372–1245 K. From these results, heat capacities of ZrAu have been derived and two changes of the C p values have been observed, in agreement with the existence of three crystalline forms of ZrAu. No latent heat was observed for the low-temperature (564 K) transition, whereas the enthalpy change at high temperature (841 K) was estimated at 1.55 kJ·mol −1, from enthalpy increments obtained by drop calorimetry. These results are discussed in relation to the crystal modifications already reported for the ZrAu compound.

Experimental study and thermodynamic assessment of the ZrO2–DyO1.5 system

Abstract The phase equilibria and thermodynamic properties in the ZrO2 – DyO1.5 system have been studied using the experimental methods of X-ray diffraction, scanning electron microscopy, energy dispersive X-ray spectroscopy, differential thermal analysis and high temperature drop calorimetry. The tetragonal + fluorite and fluorite + C-Dy2O3 phase equilibria between 1400 °C and 1700 °C have been determined, together with the enthalpy increments of the materials with 30 mol.% and 50 mol.% DyO1.5 in the temperature range 200 – 1400 °C. Furthermore, the martensitic transformation temperatures (As, Ms) have been measured for the samples with 1 and 2 mol.% DyO1.5. Finally, thermodynamic assessment has been carried out using the experimental results obtained and literature data.