[Paper Review] Investigating finite-size effects in molecular dynamics simulations of ion diffusion, heat transport, and thermal motion in superionic materials

Federico Grasselli|arXiv (Cornell University)|Jan 1, 2022

Advanced Battery Materials and Technologies68 references36 citations

TL;DR

This study investigates finite-size effects in equilibrium molecular dynamics simulations of superionic materials using empirical force fields. It reveals that ion diffusivity in type-II superionics (PbF2, CaF2, UO2) is strongly size-dependent, with smaller boxes shifting the superionic transition to higher temperatures, while effects are weaker in type-I α-AgI. The work establishes that simulations of at least several hundred atoms are necessary to capture the experimentally observed change in activation energy at the order-disorder transition.

ABSTRACT

The effects of the finite size of the simulation box in equilibrium molecular dynamics simulations are investigated for prototypical superionic conductors of different types, namely the fluorite-structure materials PbF2, CaF2, and UO2 (type-II), and the {\alpha} phase of AgI (type I). Largely validated empirical force-fields are employed to run ns-long simulations and extract general trends for several properties, at increasing size and in a wide temperature range. This work shows that, for the considered type-II superionic conductors, the diffusivity dramatically depends on the system size and that the superionic regime is shifted to larger temperatures in smaller cells. Furthermore, only simulations of several hundred atoms are able to capture the experimentally-observed, characteristic change in the activation energy of the diffusion process, occurring at the order-disorder transition to the superionic regime. Finite-size effects on ion diffusion are instead much weaker in {\alpha}-AgI. The thermal conductivity is found generally smaller for smaller cells, where the temperature-independent (Allen-Feldman) regime is also reached at significantly lower temperatures. The finite-size effects on the thermal motion of the non-mobile ions composing the solid matrix follow the simple law which holds for solids.

Motivation & Objective

• To investigate how finite simulation box size affects key transport and dynamic properties in superionic materials.
• To determine whether small system sizes in molecular dynamics simulations lead to unphysical shifts in the superionic transition temperature.
• To assess the reliability of diffusivity, thermal conductivity, and Debye-Waller factors in small-box simulations compared to bulk behavior.
• To compare finite-size effects between type-I (α-AgI) and type-II (fluorite-structured) superionics, where diffusion mechanisms differ fundamentally.
• To provide guidance on minimum system size required to accurately capture the activation energy change at the order-disorder transition.

Proposed method

• Equilibrium molecular dynamics simulations using well-validated empirical force fields for PbF2, CaF2, UO2 (type-II), and α-AgI (type-I).
• Systematic variation of simulation box size by replicating the cubic unit cell ℓ times in each direction, maintaining stoichiometry and periodic boundary conditions.
• Calculation of ionic diffusivity via mean-square displacement analysis of mobile ions over ns-long trajectories.
• Thermal conductivity computed using the Green-Kubo formalism with heat current correlation functions.
• Debye-Waller B-factors extracted from atomic mean-square displacements to probe thermal motion of non-mobile ions.
• Analysis of size dependence across a wide temperature range to identify shifts in transition temperatures and changes in activation energy.

Experimental results

Research questions

• RQ1 How does the finite size of the simulation box affect the ionic diffusivity in type-II superionic materials like PbF2, CaF2, and UO2?
• RQ2 Does the superionic transition temperature shift with system size in type-II superionics, and if so, in which direction?
• RQ3 To what extent do finite-size effects influence the thermal conductivity and the onset of the Allen-Feldman regime in superionics?
• RQ4 How do finite-size effects differ between type-I (α-AgI) and type-II superionics due to differences in diffusion mechanisms?
• RQ5 Can simulations with fewer than a few hundred atoms reliably reproduce the experimentally observed change in activation energy at the order-disorder transition?

Key findings

• For type-II superionics (PbF2, CaF2, UO2), the superionic transition temperature increases significantly with decreasing system size, indicating a strong finite-size effect on the phase transition.
• Only simulations with several hundred atoms or more capture the experimentally observed change in activation energy for ion diffusion at the order-disorder transition.
• Finite-size effects on ionic diffusivity are dramatically stronger in type-II superionics than in type-I α-AgI, where the large site degeneracy reduces size dependence.
• Thermal conductivity is systematically underestimated in smaller boxes, and the temperature-independent Allen-Feldman regime is reached at significantly lower temperatures.
• The thermal motion of non-mobile ions (Debye-Waller factors) follows the standard size-scaling law for solids, indicating that this property is less sensitive to finite-size effects.
• The study demonstrates that ns-scale simulations with empirical potentials can reliably reveal finite-size artifacts in transport properties, especially in cooperative diffusion systems.