Research

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24 pages, 781 KiB

Open AccessFeature PaperArticle

Thermodynamic Modeling of the Uranium–Tellurium System: Estimation of the Uncertainties by a Bayesian Approach

by Christine Guéneau, Eva Lawrence, Thierry Klein and Fabrice Gamboa

Thermo 2022, 2(1), 15-38; https://0-doi-org.brum.beds.ac.uk/10.3390/thermo2010003 - 16 Feb 2022

Cited by 2 | Viewed by 2345

Abstract

Under irradiation, the formation of fission products in the (U,Pu)O

_{2}

fuel with time has a substantial effect on its chemistry. In particular, migration of the most volatile fission products (Cs, Te, I, Mo) from the center to the periphery of the fuel [...] Read more.

Under irradiation, the formation of fission products in the (U,Pu)O

_{2}

fuel with time has a substantial effect on its chemistry. In particular, migration of the most volatile fission products (Cs, Te, I, Mo) from the center to the periphery of the fuel pellet is induced by the large radial thermal gradient. To predict the thermodynamic properties of the irradiated fuel, thermodynamic modeling of the complex multi-component (Cs-I-Te-Mo)–(U-Pu)–O system is performed using the CALPHAD method. In this work, the thermodynamic assessment of the U–Te sub-system is performed. The literature review reveals a lack of experimental data as well as scattering and inconsistency of some of the data. In particular, no thermodynamic data exist on the liquid. From this review, input thermodynamic and phase diagram data are carefully selected. The Gibbs energy functions are then adjusted by fitting these data. An overall good agreement is obtained with all the selected data except for the enthalpy of formation for UTe which is underestimated by 13% by our model. This could be due to an inconsistency between the enthalpy of formation and vapor pressure data. In a second step, the uncertainties on the thermodynamic parameters and their propagation on the calculated thermodynamic and phase diagram data are estimated using a Bayesian approach. The analysis shows that there are too many parameters (22) for too few data points (120 points). The uncertainties are thus large on some of the calculated data. Moreover the inconsistency of some of the data and the lack of thermodynamic data for the liquid makes the model uncertain. New experimental data such as heat capacity, enthalpy of formation for the compounds, and chemical potentials or activities for the liquid phase would improve the reliability of our model. Measurements of phase diagram data in the U–UTe

_{2}

region are also required. However this work provides the first detailed uncertainty analysis of the U–Te CALPHAD model. Moreover our approach, contrary to other Bayesian methods, provides an analytical posterior probability distribution and analytical credible intervals for the calculated thermodynamic quantities. It also speeds up the simulation of the uncertainty estimations on the phase diagram. Full article

(This article belongs to the Special Issue Thermodynamics and Nuclear Materials)

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35 pages, 6321 KiB

Open AccessArticle

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

by Emily Jane Watkinson, Ramy Mesalam, Jean-François Vigier, Ondřej Beneš, Jean-Christophe Griveau, Eric Colineau, Mark Sierig, Daniel Freis, Richard M. Ambrosi, Dragos Staicu and Rudy J. M. Konings

Thermo 2021, 1(3), 297-331; https://0-doi-org.brum.beds.ac.uk/10.3390/thermo1030020 - 15 Oct 2021

Cited by 4 | Viewed by 3121

Abstract

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, T_max, must remain [...] Read more.

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, T_max, must remain below its melting temperature. The current prospected fuel is (Am_0.80U_0.12Np_0.06Pu_0.02)O_1.8. The fuel’s experimental heat capacity, C_p, 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 C_p(T/K) = 55.1189 + 3.46216 × 10² T − 4.58312 × 10⁵ T⁻² (valid up to 1786 K). The RTG/ELHS T_max is estimated as a function of the fuel thermal conductivity, k, and the clad’s inner surface temperature, T_{i 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 C_p, 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 T_max for a ‘standard operating’ RTG is 1120 K. A hypothetical scenario is investigated: an ELHS T_{i cl} = 1973K-the RPSs’ requirements’ maximum permitted temperature. Fuel melting will not occur. Full article

(This article belongs to the Special Issue Thermodynamics and Nuclear Materials)

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11 pages, 922 KiB

Open AccessArticle

Thermochemistry of Polonium Evaporation from LBE

by Alexander Aerts

Thermo 2021, 1(2), 251-261; https://0-doi-org.brum.beds.ac.uk/10.3390/thermo1020017 - 08 Sep 2021

Viewed by 2726

Abstract

Polonium is formed in relatively large quantities in lead-bismuth eutectic (LBE) cooled nuclear systems. Because of its radiotoxicity and volatility, a good understanding of the chemical equilibria governing polonium release from LBE is required. In this work, a set of thermochemical data is [...] Read more.

Polonium is formed in relatively large quantities in lead-bismuth eutectic (LBE) cooled nuclear systems. Because of its radiotoxicity and volatility, a good understanding of the chemical equilibria governing polonium release from LBE is required. In this work, a set of thermochemical data is derived for the chemical species involved in the equilibrium between a solution of polonium in LBE and its vapor in inert conditions. The data were obtained by matching thermochemical models with experimental vapor pressure measurements and ab initio results. The dilute-limit activity coefficient of dissolved polonium in LBE is estimated, as well as the solubility of solid lead polonide in LBE. The results indicate that polonium evaporates from LBE according to the experimentally determined Henry’s law, up to dissolved polonium concentrations well above that expected in LBE cooled nuclear systems. Full article

(This article belongs to the Special Issue Thermodynamics and Nuclear Materials)

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19 pages, 2130 KiB

Open AccessFeature PaperArticle

Thermodynamic Assessment of the NaF-KF-UF₄ System

by Bianca Schacherl, Rachel Eloirdi, Rudy J. M. Konings and Ondrej Beneš

Thermo 2021, 1(2), 232-250; https://0-doi-org.brum.beds.ac.uk/10.3390/thermo1020016 - 27 Aug 2021

Viewed by 3915

Abstract

In the Molten Salt Reactor (MSR) concept, metal fluorides are key components of possible fuel and coolant salts. The fast reactor option opens the possibility for alternatives to the Li based matrix salts, avoiding the costly ⁷Li enrichment and the tritium production [...] Read more.

In the Molten Salt Reactor (MSR) concept, metal fluorides are key components of possible fuel and coolant salts. The fast reactor option opens the possibility for alternatives to the Li based matrix salts, avoiding the costly ⁷Li enrichment and the tritium production from residual ⁶Li. Such alternatives can be based on NaF and KF as matrix components. In this study, two pseudo-binary phase diagrams of NaF-UF₄ and KF-UF₄, and the NaF-KF-UF₄ pseudo-ternary system were experimentally investigated using Differential Scanning Calorimetry (DSC). The obtained data were used to perform a full thermodynamic assessment of the NaF-KF-UF₄ system. The calculated pseudo-ternary eutectic was found at 807 K and a 68.9-7.6-23.5 mol% NaF-KF-UF₄ composition. The comprehensive experimental and modelling data obtained in this work provide further extension of the JRCMSD thermodynamic database describing thermodynamic properties of key fuel and coolant salts for the MSR technology. Full article

(This article belongs to the Special Issue Thermodynamics and Nuclear Materials)

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Graphical abstract

15 pages, 3975 KiB

Open AccessArticle

Thermodynamic Assessment of the AF–CrF₃ (A = Li, Na, K) and CrF₂–CrF₃ Systems

by Thomas Dumaire, Rudy J. M. Konings and Anna Louise Smith

Thermo 2021, 1(2), 205-219; https://0-doi-org.brum.beds.ac.uk/10.3390/thermo1020014 - 18 Aug 2021

Cited by 2 | Viewed by 2727

Abstract

Understanding the corrosion mechanisms and the effect of corrosion products on the basic properties of the salt (e.g., melting point, heat capacity) is fundamental for the safety assessment and durability of molten salt reactor technology. This work focused on the thermodynamic assessment of [...] Read more.

Understanding the corrosion mechanisms and the effect of corrosion products on the basic properties of the salt (e.g., melting point, heat capacity) is fundamental for the safety assessment and durability of molten salt reactor technology. This work focused on the thermodynamic assessment of the CrF₂−CrF₃ system and the binary systems of chromium trifluoride CrF₃ with alkali fluorides (LiF, NaF, KF) using the CALPHAD (computer coupling of phase diagrams and thermochemistry) method. In this work, the modified quasi-chemical model in the quadruplet approximation was used to develop new thermodynamic modelling assessments of the binary solutions, which are highly relevant in assessing the corrosion process in molten salt reactors. The agreement between these assessments and the phase equilibrium data available in the literature is generally good. The excess properties (mixing enthalpies, entropies and Gibbs energies) calculated in this work are consistent with the expected behaviour of decreasing enthalpy and Gibbs energy of mixing with the increasing ionic radius of the alkali cations. Full article

(This article belongs to the Special Issue Thermodynamics and Nuclear Materials)

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11 pages, 1326 KiB

Open AccessArticle

Developing Practical Models of Complex Salts for Molten Salt Reactors

by Theodore M. Besmann and Juliano Schorne-Pinto

Thermo 2021, 1(2), 168-178; https://0-doi-org.brum.beds.ac.uk/10.3390/thermo1020012 - 28 Jul 2021

Cited by 10 | Viewed by 4224

Abstract

Molten salt reactors (MSRs) utilize salts as coolant or as the fuel and coolant together with fissile isotopes dissolved in the salt. It is necessary to therefore understand the behavior of the salts to effectively design, operate, and regulate such reactors, and thus [...] Read more.

Molten salt reactors (MSRs) utilize salts as coolant or as the fuel and coolant together with fissile isotopes dissolved in the salt. It is necessary to therefore understand the behavior of the salts to effectively design, operate, and regulate such reactors, and thus there is a need for thermodynamic models for the salt systems. Molten salts, however, are difficult to represent as they exhibit short-range order that is dependent on both composition and temperature. A widely useful approach is the modified quasichemical model in the quadruplet approximation that provides for consideration of first- and second-nearest-neighbor coordination and interactions. Its use in the CALPHAD approach to system modeling requires fitting parameters using standard thermodynamic data such as phase equilibria, heat capacity, and others. A shortcoming of the model is its inability to directly vary coordination numbers with composition or temperature. Another issue is the difficulty in fitting model parameters using regression methods without already having very good initial values. The proposed paper will discuss these issues and note some practical methods for the effective generation of useful models. Full article

(This article belongs to the Special Issue Thermodynamics and Nuclear Materials)

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12 pages, 404 KiB

Open AccessFeature PaperArticle

Thermodynamic Description of the ACl-ThCl₄ (A = Li, Na, K) Systems

by Jaén A. Ocádiz Flores, Bas A. S. Rooijakkers, Rudy J. M. Konings and Anna Louise Smith

Thermo 2021, 1(2), 122-133; https://0-doi-org.brum.beds.ac.uk/10.3390/thermo1020009 - 16 Jul 2021

Cited by 4 | Viewed by 3392 | Correction

Abstract

The ACl-ThCl

_{4}

(A = Li, Na, K) systems could be of relevance to the nuclear industry in the near future. A thermodynamic investigation of the three binary systems is presented herein. The excess Gibbs energy of the liquid solutions is described using [...] Read more.

The ACl-ThCl

_{4}

(A = Li, Na, K) systems could be of relevance to the nuclear industry in the near future. A thermodynamic investigation of the three binary systems is presented herein. The excess Gibbs energy of the liquid solutions is described using the quasi-chemical formalism in the quadruplet approximation. The phase diagram optimisations are based on the experimental data available in the literature. The thermodynamic stability of the liquid solutions increases in the order Li < Na < K, in agreement with idealised interactions and structural models. Full article

(This article belongs to the Special Issue Thermodynamics and Nuclear Materials)

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Review

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25 pages, 1351 KiB

Open AccessFeature PaperReview

Thermodynamically Informed Nuclear Fuel Codes—A Review and Perspectives

by Markus H. A. Piro

Thermo 2021, 1(2), 262-285; https://0-doi-org.brum.beds.ac.uk/10.3390/thermo1020018 - 09 Sep 2021

Cited by 3 | Viewed by 3343

Abstract

A number of codes are used to predict various aspects of nuclear fuel performance and safety, ranging from conventional fuel performance codes to simulate normal operating conditions to integral engineering codes to simulate severe accident behaviour. There has been a number of reportings [...] Read more.

A number of codes are used to predict various aspects of nuclear fuel performance and safety, ranging from conventional fuel performance codes to simulate normal operating conditions to integral engineering codes to simulate severe accident behaviour. There has been a number of reportings in the open literature of nuclear fuel codes being informed by thermodynamic calculations, ranging from the use of simple thermodynamic correlations to direct coupling of equilibrium thermodynamic software. Progress in expanding predictive capabilities have been reported, which also includes advances in thermodynamic database development to better capture irradiated fuel. However, this progress has been accompanied by several challenges, including effective coupling of different types of physical phenomena in a practical manner and doing so with a reasonable increase in computational expense. This review paper will summarize previous experiences reported in the open literature in coupling thermodynamic calculations with nuclear fuel codes and applications, identify current challenges and limitations, and offer some perspectives for the community to consider moving forward. Full article

(This article belongs to the Special Issue Thermodynamics and Nuclear Materials)

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26 pages, 2739 KiB

Open AccessFeature PaperReview

Corium Experimental Thermodynamics: A Review and Some Perspectives

by Marc Barrachin

Thermo 2021, 1(2), 179-204; https://0-doi-org.brum.beds.ac.uk/10.3390/thermo1020013 - 11 Aug 2021

Cited by 3 | Viewed by 4994

Abstract

More than 30 years ago a specialist meeting was held at Joint Research Center Ispra (Italy) from 15 to 17 January 1990 to review the current understanding of chemistry during severe accidents in light water reactors (LWR). Let us consider that, at the [...] Read more.

More than 30 years ago a specialist meeting was held at Joint Research Center Ispra (Italy) from 15 to 17 January 1990 to review the current understanding of chemistry during severe accidents in light water reactors (LWR). Let us consider that, at the end of the 1980s, thermodynamics introduced in the severe accident codes was really poor. Only some equilibrium constants for a few simple reactions between stoichiometric compounds were used as well as some simple correlations giving estimates of solidus and liquidus temperatures. In the same time, the CALPHAD method was developed and was full of promise to approximate the thermodynamic properties of a complex thermochemical system by the way of a critical assessment of experimental data, a definition of a simple physical model and an optimisation procedure to define the values of the model parameters. It was evident that a nuclear thermodynamic database had to be developed with that new technique to obtain quite rapidly prominent progress in the knowledge of thermochemistry in the severe accident research area. Discussions focused on the important chemical phenomena that could occur across the wide range of conditions of a damaged nuclear plant. The most pressing need for improved chemical models is identified with condensed phase mixtures to model the corium progression. This paper reviews more than 30 years of experimental data production in the field of corium thermodynamics. This work has been conducted through multiple international programs (EURATOM, ISTC, OECD) as well as through more specific studies conducted at the national scale. This research has been capitalised in specific databases such as NUCLEA and TAF-ID, databases developed at IRSN and at CEA, respectively, and are now used in degradation models of the severe accident simulation codes. This research is presented in this paper. In the conclusion, we outline the research perspectives that need to be considered in order to address today’s and tomorrow’s issues. Full article

(This article belongs to the Special Issue Thermodynamics and Nuclear Materials)

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17 pages, 4567 KiB

Open AccessReview

Steam Oxidation of Silicon Carbide at High Temperatures for the Application as Accident Tolerant Fuel Cladding, an Overview

by Hai V. Pham, Masaki Kurata and Martin Steinbrueck

Thermo 2021, 1(2), 151-167; https://0-doi-org.brum.beds.ac.uk/10.3390/thermo1020011 - 27 Jul 2021

Cited by 12 | Viewed by 5457

Abstract

Since the nuclear accident at Fukushima Daiichi Nuclear Power Station in 2011, a considerable number of studies have been conducted to develop accident tolerant fuel (ATF) claddings for safety enhancement of light water reactors. Among many potential ATF claddings, silicon carbide is one [...] Read more.

Since the nuclear accident at Fukushima Daiichi Nuclear Power Station in 2011, a considerable number of studies have been conducted to develop accident tolerant fuel (ATF) claddings for safety enhancement of light water reactors. Among many potential ATF claddings, silicon carbide is one of the most promising candidates with many superior features suitable for nuclear applications. In spite of many potential benefits of SiC cladding, there are some concerns over the oxidation/corrosion resistance of the cladding, especially at extreme temperatures (up to 2000 °C) in severe accidents. However, the study of SiC steam oxidation in conventional test facilities in water vapor atmospheres at temperatures above 1600 °C is very challenging. In recent years, several efforts have been made to modify existing or to develop new advanced test facilities to perform material oxidation tests in steam environments typical of severe accident conditions. In this article, the authors outline the features of SiC oxidation/corrosion at high temperatures, as well as the developments of advanced test facilities in their laboratories, and, finally, give some of the current advances in understanding based on recent data obtained from those advanced test facilities. Full article

(This article belongs to the Special Issue Thermodynamics and Nuclear Materials)

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