The present study describes the thermodynamic assessment of three pseudo-binary systems relevant to CsI solubility in molten iodide salts: KI-CsI, NaI-CsI, and NaF-CsI. The motivation for this study was to corroborate a single previously reported data set of the NaI-CsI system, resolve inconsistencies reported by two different data-sets of the KI-CsI system, and generate new experimental data on the NaF-CsI system. Equilibrium data for all systems were obtained using Differential Scanning Calorimetry. Thermodynamic treatments of the three pseudo-binary systems were revised using the CALPHAD method with the thermodynamic software FactSage and Thermochimica. Both experimental and computational investigations provide increased confidence in the thermochemical behaviour of CsI in Molten Salt Reactor nuclear systems.

MELCOR is a state-of-the-art code used to model severe accidents in conventional nuclear reactors Humphries et al., 2021. The purpose of this work was to enhance the material modelling in MELCOR via one-way coupling to the equilibrium thermodynamics code Thermochimica. One-way coupling from MELCOR to Thermochimica was implemented to allow Thermochimica to predict the phase fractions and compositions within each simulation cell. Two test case scenarios were simulated in MELCOR using a generic boiling water reactor design that included either conventional Zircaloy-2 or accident-tolerant FeCrAl fuel cladding/canister material. FeCrAl cladding/canister material was examined in the second case because the improved oxidation kinetics make FeCrAl a potential choice for future accident-tolerate cladding material. The results from these two cases were analysed with Thermochimica to demonstrate potential areas for improvement of MELCOR’s material modelling capabilities.

Molten Salt Reactor (MSR) systems can be divided into two basic categories: liquid-fueled MSRs in which the fuel is dissolved in the salt, and solid-fueled systems such as the Fluoride-salt-cooled High-temperature Reactor (FHR). The molten salt provides an impediment to fission product release as actinides and many fission products are soluble in molten salt. Nonetheless, under accident conditions, some radionuclides may escape the salt by vaporization and aerosol formation, which may lead to release into the environment. We present recent enhancements to MELCOR to represent the transport of radionuclides in the salt and releases from the salt. Some soluble but volatile radionuclides may vaporize and subsequently condense to aerosol. Insoluble fission products can deposit on structures. Thermochimica, an open-source Gibbs Energy Minimization (GEM) code, has been integrated into MELCOR. With the appropriate thermochemical database, Thermochimica provides the solubility and vapor pressure of species as a function of temperature, pressure, and composition, which are needed to characterize the vaporization rate and the state of the salt with fission products. Since thermochemical databases are still under active development for molten salt systems, thermodynamic data for fission product solubility and vapor pressure may be user specified. This enables preliminary assessments of fission product transport in molten salt systems. In this paper, we discuss modeling of soluble and insoluble fission product releases in a MSR with Thermochimica incorporated into MELCOR. Separate-effects experiments performed as part of the Molten Salt Reactor Experiment in which radioactive aerosol was released are discussed as needed for determining the source term.

The modified quasichemical model in the quadruplet approximation (MQMQA) considers the first- and the second-nearest-neighbor coordination and interactions, particularly useful in describing short-range ordering in complex liquids such as molten salts, slag in metal processing, and electrolytic solutions. The present work implements the MQMQA into the Python based open-source software PyCalphad for thermodynamic calculations. This endeavor facilitates the development of MQMQA-based thermodynamic database with uncertainty quantification (UQ) using the open-source software ESPEI. A new database structure based on Extensible Markup Language (XML) is proposed for ESPEI evaluation of MQMQA model parameters. Using the KF-NiF2 system as an example, we demonstrate the successful implementation of MQMQA in PyCalphad through thermodynamic calculations of Gibbs energy, equilibrium quadruplet fractions, and phase diagram, as well as database development with UQ using ESPEI. The present implementation offers an open-source capability for performing CALPHAD modeling for complex liquids with short-range ordering using MQMQA.

The atomic scale computation of dislocation core structures has become an essential tool in the development of models for the plasticity of metals. Competing dislocation core structures are often analyzed at T = 0 K (with T the temperature), and the dislocation core structure with the lowest energy is assumed to be the structure dictating the dynamics of the individual dislocation at finite temperatures. It is shown here that, for some hexagonalclose-packed (HCP) metals, this approach may be too simplistic. As a prototypical example, < a >-type screw dislocations within HCP Ti modeled using an empirical interatomic potential are considered. It is shown using molecular dynamics simulations that, at room temperature and above, the core structure of the dislocation is remarkably complex and variable. The implications of this complexity for the dynamics of the dislocations are discussed.

An exactly solvable thermodynamic model for the core structure of (a)-type screw dislocations in alpha-Ti is introduced and used to explore the role in which polymorphic core spreading contributes to the free energy of the dislocation. Each segment of the dislocation core is assumed to be in one of three possible configurations, and the free energy differences per segment between dislocation core spreadings are taken as parameters. It is shown that thermal fluctuations between the core spreadings should be common, even at room temperature, and that these fluctuations can contribute significantly to the free energy. It is also shown that under some circumstances, the core structures can display morphological switching wherein the stable core spreading changes morphology with a change in temperature. The implications for dislocation dynamics and for modeling finite temperature dislocation core properties using molecular dynamics simulations are considered.

A mechanistic-based mass accountancy model in the context of liquid-fueled molten salt reactors was implemented in the dynamic systems modeling software library TRANSFORM by way of coupling with the equilibrium thermodynamics code Thermochimica. Liquid-fueled molten salt reactors present new challenges for mass accountancy because of the dissolution of fuel and evolved fission products, which may be soluble in the salt, off gas, or precipitate. Two cases of mass loss from the molten salt were addressed: off-gassing and precipitation. The software implementation was tested through a series of increasingly complex demonstration problems, culminating in a model of the primary fuel and primary coolant loops of the molten salt demonstration reactor. Analysis shows that negligible mass was lost from the salt under normal operating conditions, but an overheating event caused by partial loss of fuel loop cooling resulted in release of measurable amounts of uranium (among other elements) via off-gassing. The tools developed here are primarily aimed at capability development but are readily available for use in further modeling of molten salt reactor concepts. These tools have not yet been validated, and future experimental work to perform this validation is recommended.

An effective numerical method is presented for optimizing model parameters that can be applied to any type of system of non-linear equations and any number of data-points, which does not require explicit formulation of the objective function or its partial derivatives. The numerics are reduced to solving a non-linear least squares problem, which uses the Levenberg-Marquardt algorithm and the Jacobian is approximated by applying rank-one updates using Broyden's method. An advantage of this methodology over conventional approaches is that the partial derivatives of the objective function do not have to be analytically calculated. For instance, there may be situations where one cannot formulate the partial derivatives, such as cases involving an objective function that itself contains a nested optimization problem. Moreover, a line search algorithm is also described that ensures that the Armijo conditions are satisfied and that convergence is assured, which makes the success of the approach insensitive to the initial estimates of the model parameters. The foregoing numerical methods are described with respect to the development of the Optima software to solve inverse problems, which are reduced to non-linear least squares problems. This computational approach has proven to be particularly useful at solving inverse problems of very complex physical models that cannot be optimized directly in a practical way.

The bypassing of an oxygen interstitial by < a >-type screw dislocations in Ti is studied as a function of the dislocation core structure using an empirical potential and the nudged elastic band method. It is shown that an interstitial oxygen will be pushed from the octahedral site into a new interstitial site in the dislocation core. From there, with the passage of a dislocation spread primarily on the prismatic plane there is a high energy barrier for oxygen to return to the octahedral site. Instead, it is likely to shuffle into the neighboring hexahedral site, a transition expected to lead to slip plane softening. For dislocations spread primarily within the pyramidal planes, the octahedral to hexahedral transition is much less likely as there is little to no barrier for the oxygen to return to the original octahedral site. This difference in barriers is then explained by a reduction in the attraction between the hexahedral site and the dislocation core, calculated within micromechanics, as the core transitions from a prismatic to a pyramidal state.

The modified quasi-chemical model in the quadruplet approximation has been implemented in the open-source equilibrium thermodynamics library Thermochimica, enabling single point equilibrium calculations and sophisticated multi-physics simulations of molten salt nuclear reactor systems. Here, the derivations necessary to obtain the chemical potentials of the quadruplet species required for Gibbs energy minimization are provided. The implementation is verified via code-to-code benchmarking against FactSage. A scheme to increase computational efficiency of multi-physics simulations including Thermochimica is described and its effectiveness for molten salt systems demonstrated. Finally, a multi-physics simulation of a molten salt nuclear fuel system is presented as a demonstration problem: ORIGEN-S is used to calculate the isotopic evolution of a fuel-loaded FLiBe mixture with fission and activation products as Thermochimica predicts the phase evolution and number of moles of Cs in various phases.

Modern computational thermodynamics methods rely on the use of numerical models that represent chemical systems. Typically, these models are formulated in terms of the Gibbs energy, which must be minimised to find the conditions of thermodynamic equilibrium. Numerous thermodynamic models have been developed to capture the behaviour of regular solid and liquid solutions, ionic ceramics, multi-sublattice metallic alloys, short and long range ordering, and much more. Some classes of commonly used thermodynamic models include substitutional solutions and compound energy formalism. The mathematical formulation of the Gibbs energy of a solution phase represented by any of the aforementioned models takes on a unique form, which requires special consideration for obtaining the partial derivatives in the Hessian matrix of a Gibbs energy minimiser. This paper provides derivations of the partial molar excess Gibbs energy of mixing of some common classes of thermodynamic models for use in a Gibbs energy minimiser.

New multiphysics coupling capabilities for molten salt reactor (MSR) analysis have been developed in the Virtual Environment for Reactor Applications (VERA). This development consisted of two main efforts. First, a generic species transport module was added in the CTF code, which is the thermal-hydraulics (TH) code for VERA. This module uses the velocity fields for which CTF solves during the TH calculation to transport species through the core and around the primary loop. Additionally, a gas sparging model has been added to CTF to model the movement of certain species, namely, fission products such as xenon gas, to transport between the molten salt and gas bubbles present in the salt. The second effort in this development was coupling this capability to VERA's neutron transport code MPACT. This effort focused on coupling the detailed TH transport models in CTF to MPACT to account for feedback effects in the neutron transport calculations. Finally, the thermochemistry code Thermochimica has also been coupled to VERA. Thermochimica performs pointwise calculations for chemical potential and Gibbs free energy and determines what phases are produced by the temperature, pressure, and elemental concentrations at different locations in the primary loop.These capabilities are demonstrated using a model of the Molten Salt Reactor Experiment (MSRE). This reactor operated at Oak Ridge National Laboratory in the 1960s, providing sources of experimental data that were used to develop the model. Various combinations of species were modeled using VERA's new multiphysics coupling capabilities. Species distributions and reactivity effects behaved as expected for the MSRE model, demonstrating that the coupling is behaving correctly and causing appropriate feedback. The results of these calculations show the potential for VERA to be used for a wide variety of MSR analyses.

A new formulation for redistribution of constituents in metallic U-Pu-Zr nuclear fuel is presented that can incorporate the contributions from fission products. The formulation is based on the thermodynamic driving forces derived from the generalized chemical potential that includes effects of composition and temperature. As a result, the redistribution model can readily account for the composition changes due to the generation of fission products while using only a limited set of transport coefficients. The thermodynamic model for the metallic fuel and thermochemistry solver Thermochimica were coupled with the nuclear fuel performance code BISON to implement the redistribution model. The simulations reproduce an experimentally observed Zr-depletion zone in the mid-radius region of an irradiated fuel slug. The generation of fission products during burnup is shown to have a stabilizing effect on the fuel chemistry, slowing the rate of U-Zr interdiffusion and reducing the size of the Zr-depleted zone. The overall objective of the work is to advance predictive capabilities of fission product behaviour in U-Zr metallic fuel in the context of fuel performance and safety.

Nuclear materials are highly complex multiscale, multiphysics systems, and an effective prediction of nuclear reactor performance and safety requires simulation capabilities that tightly couple different physical phenomena. The Idaho National Laboratory’s Multiphysics Object Oriented Simulation Environment (MOOSE) provides the computational foundation for performing such simulations and currently consists of the continuum scale fuel performance code Bison and the mesoscale phase-field code Marmot. With the move towards advanced reactors that employ high temperature fluids compared to conventional reactors, corrosion has become a problem of great interest. A new application called Yellowjacket is under development to directly couple thermodynamic equilibrium and kinetics with phase field models in order to model corrosion in advanced reactors. As part of Yellowjacket, a thermochemistry code is being developed to perform thermochemical equilibrium calculations for a range of different materials, which is currently in its infancy. This paper describes the recent progress towards the development of Yellowjacket and presents the plans for developing capabilities of practical interest to the nuclear industry.

The current work presents investigations of flow through a 37-element CANDU nuclear fuel bundle residing within a deformed pressure tube. This scenario simulates the long-term effects of aging, whereby the pressure tube may experience up to 6% diametral creep, resulting in flow bypass and the concomitant increase in fuel temperature due to local undercooling. This work examines in high spatial detail the three-dimensional, three-component fluid velocity field through the fuel channel. A companion paper is dedicated to the experimental component of this work, which is based on Magnetic Resonance Velocimetry. In the present paper, computational fluid dynamic simulations have been performed with HYDRA using an implicit large eddy simulation to predict turbulent flow behavior. Together, an improved understanding has been gained in quantifying flow bypass, the evolution of geometry-induced inter-subchannel mixing, and various turbulent effects, such as recirculation, swirl, and separated flow. These capabilities are not possible with conventional experimental techniques or thermal-hydraulic codes. The overall goal of the combined works is to continue developing experimental and computational capabilities for future investigations to support nuclear reactor performance and safety.

The performance of the open-source thermochemical software library Thermochimica has been enhanced by developing a re-initialization algorithm to make use of data from previous calculations to reduce the number of convergence steps in the Gibbs energy minimization procedure. This algorithm has been tested in the context of stand-alone Thermochimica calculations, and speedups in the range of 2x-3x achieved for cases with chemistries resembling those of irradiated nuclear fuels. Routines to make use of this re-initialization procedure have been implemented in Bison, in which each node uses the results of the previous calculation at that node as the initial conditions for the following Thermochimica call. Examples based on calculating the diffusion of oxygen in UO$_2$ LWR fuel in 1D and 3D have been tested, with speedups up to 7.38x demonstrated.

The open-source equilibrium thermochemistry library Thermochimica has previously been employed to study uranium dioxide nuclear fuel for light-water reactor (LWR) applications. Recently, significant improvements to the efficiency and range of applications of Thermochimica have been made. We will discuss these advances and demonstrate applications of Thermochimica for LWRs and next-generation nuclear technologies, such as Molten Salt Reactors (MSRs). Calculations on popular molten salt fuel materials, such as FliNaK, FliBe, and fission product containing salts, have been enabled through the implementation of the quadruplet approximation to the modified quasichemical model in Thermochimica, which takes into account first- and second-nearest-neighbor short-range ordering contributions to the Gibbs energies of liquid solution phases. Coupling of Thermochimica to various other software packages, such as the Multi-physics Object-Oriented Simulation Environment (MOOSE) app Bison and Oak Ridge Isotope GENeration (ORIGEN), for nuclear fuel applications will also be demonstrated. Future work will include further software coupling, such as with Coolant-Boiling in Rod Arrays-Two Fluids (CTF) and the Virtual Environment for Reactor Applications (VERA).

We have developed a formulation for oxygen transport in uranium dioxide nuclear fuel that accounts for the effects of irradiation. The overall simulation combines the evolving isotopic composition, thermochemistry, and oxygen transport in irradiated fuel. The driving forces for oxygen transport are computed from local thermodynamic equilibrium calculations and account for the effects of temperature gradients and composition, including fission products. The proposed method provides a mechanism for including complex thermodynamic models of nuclear fuel in modeling of mass redistribution, and alleviates difficulties associated with the common thermodiffusion formulation. The transport model has been implemented within the nuclear fuel performance code BISON utilizing the thermochemistry code Thermochimica, with burnup calculations provided by the ORIGEN isotopic transmutation code.