Multiscale Modeling of Solid-State Interfaces and Microstructures in High-Temperature Water Splitting Materials


Lawrence Livermore National Laboratory (LLNL)

Capability Expert

Tae Wook Heo, Brandon C. Wood, Timofey Frolov


Computational Tools and Modeling

Node Readiness Category

2: High-Temperature Electrolysis (HTE)
2: Solar Thermochemical (STCH)


Previous capability name: "Mesoscale Kinetic Modeling of Water Splitting and Corrosion Processes."

LLNL maintains a comprehensive multiscale modeling framework for simulating solid-state interfaces and their impacts on mass transport and phase microstructure evolution kinetics, which play significant roles in determining high-temperature water splitting performances of STCH and HTE materials. For example, the kinetics of interconversion between oxidized and reduced phases, which is often controlled by diffusion, is a key determiner of STCH efficiency. Formation of undesired phases in HTE materials in service can activate thermomechanical failure modes that significantly limit their lifetime and operability.

Mass Transport and Microstructural Evolution

LLNL maintains the MesoMicro code, which has modules for mass transport and phase evolution modeling based on the mesoscopic phase-field approach. This highly flexible approach uses a diffuse-interface theory to describe the dynamics of the diffusing species and a phase boundary (or reaction front) in response to a local thermodynamic driving force. It is a powerful approach for modeling multiple concurrent physical, chemical, and materials processes under nonequilibrium reaction conditions. Computational models for the following processes are integrated:

  1. Mass transport through complex microstructures
  2. Solute-grain boundary interactions
  3. Interfacial chemical reactions
  4. Inhomogeneous elastic interactions in polycrystals
  5. Diffusional and/or structural phase transformations.

Necessary thermodynamic and kinetic input parameters include diffusivities of species through bulk and grain boundaries, interfacial or grain boundary energies (which can be obtained using the approach described below), interfacial chemical reactivity, elastic moduli and lattice parameters, and thermodynamic free energies. These inputs can be derived from relevant experiments or atomistic DFT calculations.

Solid-State Interface Energetics

One of the most difficult parameters to obtain is the interfacial free energy. LLNL in collaboration with external partners has established a computational method for predicting structures and energetics of complex interfaces in solid-state materials. The method is based on combining evolutionary structure search with machine learning techniques that can identify distinct grain boundary phases [1]. The search algorithm is based on the USPEX structure prediction code was recently extended to grain and phase boundaries [1]. In addition to the ground state interfacial structures, we utilize LAMMPS code [2-3] to model high-temperature behavior of the structures.

Capability Bounds‎

The interface energy prediction methodology is currently limited to the systems for which empirical potentials are available. The mesoscale models using the MesoMicro code are based on a continuum description that relies on effective parameters rather than direct simulation of physical and/or chemical pathways. The predictive capabilities of the models are dependent upon the accuracy of these input parameters. Improved methods for extracting these parameters from a combination of theoretical and experimental studies are currently under development.

Unique Aspects‎

The approaches require high-performance computing capabilities and leverage resources available through the national laboratories. Application of the phase-field mesoscale modeling approach is new to water splitting applications, and the corresponding framework is not generally available in the community. The method is capable of integrating the kinetics of various processes that are usually simulated independently, yet measured as a collective process. boundaries. The recent advances of LLNL’s phase-field method to complex polycrystals [4-6] enable the modeling of the relevant kinetic processes, including mass transport and microstructure evolution, in more realistic polycrystalline STCH and HTE materials. The interfacial structure prediction methodology is a unique capability, as predictive modeling of interfaces in complex hydrogen production materials is extremely challenging and no similar codes are publicly available.


The MesoMicro code for mesoscopic mass transport and phase evolution has been well tested and used to study the non-equilibrium evolution of hydrogen storage materials [9] and battery electrode materials [10,11]. The interface structure prediction code is distributed as a part of USPEX code, and has been tested for metallic alloys [1,7,8]. As of yet, neither code has been applied directly to hydrogen production applications; however, it is expected that similarities with hydrogen storage processes can be leveraged for extending the models to STCH and HTE. The codes are mature and can be run on the high-performance computing facilities at LLNL.


The mesoscopic modeling capability will allow for integrated kinetic simulations of water-splitting devices that can simultaneously account for possible rate limitations in carrier transport, diffusion, interfacial chemistry, and phase transformation within a unified computational framework. It can therefore be used for sensitivity studies to devise specific device optimization strategies. It can also be used to model mass transport and microstructure evolution in polycrystalline materials, which is underrepresented in this field but important for understanding kinetics and failure modes in high-temperature water-splitting materials. The addition of the interfacial structure prediction capability will allow for predicting possible atomistic structures and associated energetics of interfaces these materials, which is a critical input parameter for the phase-field codes that is not trivially obtainable from other available experimental and/or modeling methodologies. Predicted results can inform other simulation capabilities for further modeling of atomistic (vacancy or impurity) diffusion mechanisms through relevant interfaces.


Figure 1a. New grain boundary phases and a structural transition predicted by USPEX. Energies of the grain boundary structures generated by USPEX.

Figure 1b. (Left) Mesoscopic effective diffusivity calculations incorporating microstructures and internal stress impacts for Mg-H [12], and (Right) Phase-field simulations of diffusional [6] and structural phase transformations [7] in the presence of grain boundaries.


  1. Q. Zhu, A. Samanta, B. Li, R.E. Rudd, “Predicting phase behaviour of grain boundaries with evolutionary algorithms and machine learning”, Nature Communications, 9, 467 (2018)
  2. T. Frolov, D. L. Olmsted, M. Asta and Y. Mishin, “Structural phase transformations in metallic grain boundaries, Nature Communications”, Nature Communications, 4, 1899, (2013).
  3. T. Frolov, S. V. Divinski, M. Asta and Y. Mishin, “Effect of interface phase transformations on diffusion and segregation in high-angle grain boundaries”, Physical Review Letters, 110, 255502 (2013).
  4. T.W. Heo, S. Bhattacharyya, and L.-Q. Chen, “A phase field study of strain energy effects on solute-grain boundary interactions”, Acta Materialia, 59, 7800 (2011)
  5. T.W. Heo, S. Bhattacharyya, and L.-Q. Chen, “A phase-field model for elastically anisotropic polycrystalline binary solid solutions”, Philosophical Magazine, 93, 1468 (2013)
  6. T.W. Heo and L.-Q. Chen, “Phase-field modeling of displacive phase transformations in elastically anisotropic and inhomogeneous polycrystals”, Acta Materialia, 76, 68 (2014)
  7. T. Folov, W. Setyawan, R. J. Kurtz, J. Marian, A. R. Oganov, R. E. Rudd and Q. Zhu, “Grain boundary phases in bcc metals”, Nanoscale, 10, 8253 (2018)
  8. T. Frolov, Q. Zhu, T. Oppelstrup, J. Marian, R. E. Rudd, “Structures and Transitions in bcc tungsten grain boundaries and their role in the adsorption of point defects”, Acta Materialia (2018)
  9. B.C. Wood, T.W. Heo, T. Ogitsu, S. Bonev, S. Kang, J.R.I. Lee, A. Baker, P. Shea, K.G. Ray, T. Baumann, “HyMARC: LLNL Technical Effort”, Proceedings of the DOE Hydrogen Program Annual Merit Review (2018).
  10. T.W. Heo, L.-Q. Chen, and B.C. Wood, “Phase-field modeling of diffusional phase behaviors of solid surfaces: A study of phase-separating LixFePO4 electrode particles,” Computational Materials Science, 108, 323 (2015).
  11. T.W. Heo, M. Tang, L.-Q. Chen, and B.C. Wood, “Defects, entropy, and the stabilization of alternative phase boundary orientations in battery electrode particles,” Advanced Energy Materials, 6, 1501759 (2016).