1. The Thermochemistry Library THERMOCHIMICA Markus H.A. Piro, April 2014

2. Outline Introduction Background Applications and capabilities Example problem Numerical methods and algorithms Accessing software Future plans Summary

3. Introduction THERMOCHIMICA is an open-source software library for computing thermodynamic equilibria with the primary purpose of direct integration into multi-physics codes. The software is written in Fortran and it can be called from a Fortran, C, or C++ Application Programming Interfaces (API) on a desktop workstation or high performance computing environment. Software development began during PhD at RMC*, it evolved during a Post- Doctoral fellowship at ORNL and it is currently being maintained by M.H.A. Piro. * M.H.A. Piro, “Computation of Thermodynamic Equilibria Pertinent to Nuclear Materials in Multi-Physics Codes,” PhD Thesis, Royal Military College of Canada (2011).

4. Brief Background Conditions for thermodynamic equilibrium: – Gibbs’ Phase rule, – Conservation of mass, and – Gibbs energy of a closed system at constant T & P is a global minimum (derived from first and second laws of thermodynamics). Thermodynamic equilibrium is assumed (i.e., time dependency is not considered). – The appropriateness of this assumption is problem specific. This is generally a good assumption when temperature is high and time scale is long. * M.H.A. Piro, “Computation of Thermodynamic Equilibria Pertinent to Nuclear Materials in Multi-Physics Codes,” PhD Thesis, Royal Military College of Canada (2011).

5. Applications The software is intended to provide input to material properties and boundary conditions for continuum mechanics and phase field simulations. THERMOCHIMICA can be used for various applications: – Combustion – Metallurgy – Geochemistry – Batteries – Nuclear materials

6. Applications of Thermochimica to Nuclear Engineering Applications Fuel performance and safety analysis: – Fuel chemistry (akin to previous slides), – Fuel melting, – Fission gas retention (predicting fission product speciation), – Iodine-induced stress corrosion cracking (I-SCC) / Pellet-cladding interaction (PCI), and – Zirconium hydriding. Potential applications (more development needed): – Aqueous chemistry: CRUD formation, fuel storage, fuel transportation.

7. Species mole fraction Chemical Potential Element Mass Database Gibbs energy Moles of Phases Enthalpy Heat capacity Pressure THERMOCHIMICA Temper- ature Input Output I/O

8. Capabilities Parse ChemSage data-files as input. Data-files containing a maximum of 48 chemical elements, 1500 chemical species and 24 solution phases. Thermodynamic models: – Pure condensed phases, – Ideal solution phases, – Substitutional Kohler-Toop model with regular polynomials, – Substitutional Redlich-Kister-Muggiano model with Legendre polynomials, and – Compound energy formalism with Legendre polynomials (up to 5 sublattices).

9. Compound Energy Formalism – UO 2 Fluorite Crystal Structure M.H.A. Piro, PhD Thesis, Royal Military College, 2011. Reproduced from D.R. Olander, U.S. Dept. of Commerce, 1976.

10. Compound Energy Formalism – UO 2 Fluorite Crystal Structure M.H.A. Piro, PhD Thesis, Royal Military College, 2011. Reproduced from D.R. Olander, U.S. Dept. of Commerce, 1976. Non-stoichiometric UO 2±x (U 3+, U 4+, U 5+, O 2- ) Modelled with three sublattices by C. Gueneau et al, J. Nucl. Mater., 419 (2011) 145-167. This treatment is being expanded to represent irradiated fuel by T.M. Besmann et al, to be published.

11. Example – Nuclear Fuel Thermochemistry Engineering motivation: – Extend PWR fuel to very high burnup (i.e., ~ 100 GWd/t(U)). Maximize performance and safety. – Experiments are extremely time-consuming (i.e., 10 years in reactor), expensive and dangerous. Simulations may help guide/minimize experiments. Description of problem: – Fuel irradiated in European PWR to 100 GWd/t(U). – Oxidation and compositional measurements performed at ITU. – Numerical simulations predict fuel behaviour (chemistry, isotopic evolution and heat transfer). – Coupled: AMP, Origen-S and Thermochimica. M.H.A. Piro, J. Banfield, K.T. Clarno, S. Simunovic, T.M. Besmann, B.J. Lewis and W.T. Thompson, J. Nucl. Mater., in press.

12. Example – Nuclear Fuel Thermochemistry Cont… Oxygen partial pressure predictions with Thermochimica are in very good agreement with experimental measurements. Most codes that account for fuel chemistry assume “fresh fuel.” M.H.A. Piro, J. Banfield, K.T. Clarno, S. Simunovic, T.M. Besmann, B.J. Lewis and W.T. Thompson, J. Nucl. Mater., in press.

13. Example – Nuclear Fuel Thermochemistry Cont… O/M cannot be measured directly. Experimentally inferred values for O/M were derived by ICP-MS, EPMA and assumptions regarding phase equilibria. M.H.A. Piro, J. Banfield, K.T. Clarno, S. Simunovic, T.M. Besmann, B.J. Lewis and W.T. Thompson, J. Nucl. Mater., in press.

14. Example – Nuclear Fuel Thermochemistry Cont… SEM in high burnup structure [~75 GWd/t(U)] Noble metal HCP “white phase” Figure kindly provided by T. Wiss and V.V. Rondinella (ITU) M.H.A. Piro, J. Banfield, K.T. Clarno, S. Simunovic, T.M. Besmann, B.J. Lewis and W.T. Thompson, J. Nucl. Mater., in press.

15. Numerical Methods From a mathematical point of view, this is a numerical optimization problem of a non-convex function with linear and non-linear equality and inequality constraints. Also, the active set of constraints change throughout the iteration process. The overall objective is to minimize the integral Gibbs energy of the system subject to the mass balance constraints and Gibbs’ Phase Rule. Numerical methods employed by THERMOCHIMICA are described in the literature (1-4). 1. M.H.A. Piro and S. Simunovic, CALPHAD, 39 (2012) 104-110. 2. M.H.A. Piro, S. Simunovic, T.M. Besmann, B.J. Lewis and W.T. Thompson, Comp. Mater. Sci., 67 (2013) 266-272. 3. M.H.A. Piro, T.M. Besmann, S. Simunovic, B.J. Lewis and W.T. Thompson, J. Nucl. Mater., 414 (2011) 399-407. 4. M.H.A. Piro and B. Sundman, to be published.

16. Numerical Methods – Local Minimization Minimize the integral Gibbs energy of the system (i.e., 1 st and 2 nd law of thermodynamics): Subject to the following linear equality constraints (i.e., conservation of mass): and inequality constraints (i.e., non-negative mass and Gibbs’ Phase Rule): M.H.A. Piro, S. Simunovic, T.M. Besmann, B.J. Lewis and W.T. Thompson, Comp. Mater. Sci., 67 (2013) 266-272.

17. Numerical Methods – Global Minimization At thermodynamic equilibrium, the following linear equality constraints must be satisfied for all stables phases: and the following non-linear inequality constraints must hold true for all other phases in the system (i.e., the system is not metastable. Equivalently, a global minimum has been reached and not a local minima): A modified branch and bound approach has been adopted for the non-linear inequality constraints. This is tested when a local minima has been reached. M.H.A. Piro and B. Sundman, to be published.

18. Accessing the code The software is maintained on a Subversion (SVN) repository and can be accessed online: – https://sites.google.com/site/thermochimica/ https://sites.google.com/site/thermochimica/ Prerequisites: – BLAS / LAPACK linear algebra libraries – Fortran compiler (gfortran/Intel) Operating system: – Intended for Linux/Mac OS-X

19. Current and Future plans (Piro) A database conversion tool is under development to convert between various established formats (i.e., TDB, DAT). A thermodynamic model optimization tool is being developed to facilitate model development.

20. Summary THERMOCHIMICA is an open-source thermodynamic equilibrium solver for integration into multi-physics codes to provide material properties and boundary conditions. THERMOCHIMICA can be used for a multitude of applications, including combustion, metallurgy, geochemistry, nuclear materials and batteries. Please feel free to contact me (markuspiro@gmail.com) should you have any questions.markuspiro@gmail.com