Bridging Atomistic and Continuum Space Charge Models in Solid Electrolytes

Student thesis: Doctoral ThesisPhD


The use of solid state electrolytes in electrochemical devices has become paramount in recent decades. The increased utilisation is due to the provision of important advantages with respect to the conventional industrial processes of the relevant technologies. In particular, the use of solid electrolytes offer for technologies such as batteries, increased safety and potentially higher ionic conductivities, and for solid oxide fuel cells, high energy conversion efficiency, improved robustness and greater fuel flexibility. Solid electrolytes have the ability to conduct due to defects in the crystal lattice. These defects include ionic vacancies where an ions are removed from their explicit sites creating diffusion paths throughout the material.

Most solid electrolytes used in solid state electrochemical devices are polycrystalline, with regions of crystallographic disorder (grain boundaries) separating regions that are perfectly crystalline (bulk). The structural distortion in the grain boundaries creates a difference in chemical potential compared to the bulk which in turn causes variations in defect segregation energies (the change in free energy associated with moving a defect from the bulk to a boundary). Non-zero segregation energies indicates spontaneous redistribution of defects from the bulk to, or away from, the grain boundaries.

Segregation of defects to, or away from grain boundaries results in the formation of space charge. Space charge comprises of a charged grain boundary core, where defects are accumulated or depleted respectively and adjacent space charge
regions where electrostatic forces dictate a region of depleted or accumulated charge carriers respectively. The variation of charge carriers in these regions can result in a large variation in ionic conductivity throughout the material.

The formation and resulting effects of space charge regions can be studied mathematically by solving Poisson’s equation. In this thesis we discuss a mathematical framework and the associated open source software produced throughout the project for modelling space charge formation on a site explicit basis, and the effect on the ionic conductivity under a range of conditions. The simulations carried out include, different materials, different grain boundary orientations and different inter-grain boundary separations under a variety of conditions including, but not limited to, the effect of defect concentrations and temperatures.
Date of Award24 Jun 2020
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorBenjamin Morgan (Supervisor) & Steve Parker (Supervisor)


  • Solid electrolytes
  • Space charge formation
  • Poisson-Boltzmann
  • Python

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