TY - JOUR

T1 - Nanoionics from a quantum mechanics point of view

T2 - Mathematical modeling and numerical simulation

AU - Sepúlveda, Paulina

AU - Muga, Ignacio

AU - Sainz, Norberto

AU - Rojas, René G.

AU - Ossandón, Sebastián

N1 - Publisher Copyright:
© 2023 Elsevier B.V.

PY - 2023/3/15

Y1 - 2023/3/15

N2 - Solid nano-structures exhibiting fast ion transport (cations moving in anionic crystal structures) are becoming increasingly relevant in industrial applications. However, it is challenging to model their mechanics due to the presence of electromagnetic couplings. In this paper, a mathematical, physical, and computational framework is introduced, for a cation particle moving through an anion sub-lattice structure in the presence of two electromagnetic fields: an external electromagnetic field; and a self-induced electromagnetic field coming from back-reaction phenomena caused by the relative movement of cations with respect to the mentioned structure. Our approach seeks to incorporate magnetic effects, such as magnetic induction and spin of cations, which are not incorporated in other models, mainly due to the intrinsic difficulty of 3D effects. We propose a quantum mechanical formalism based on a Schrödinger-type equation, where a wave function models the behavior of a cation in presence of an external electromagnetic potential, coupled with transient and self-induced electromagnetic effects. To solve the model, a space–time coupled numerical scheme is presented, which allows the possibility of time-evolving electromagnetic effects. The technique uses finite-elements in space and time-marching schemes in time. While a time-explicit marching scheme is used to update the magnetic and electric-potential fields, a time-implicit marching scheme is used to solve the coupled Schrödinger equation. This strategy allows us to update the electromagnetic contributions and wave functions at each time-step. Numerical examples in one and two spatial dimensions (and evolving in time) have been implemented for some meaningful models obtained from nanoionics literature.

AB - Solid nano-structures exhibiting fast ion transport (cations moving in anionic crystal structures) are becoming increasingly relevant in industrial applications. However, it is challenging to model their mechanics due to the presence of electromagnetic couplings. In this paper, a mathematical, physical, and computational framework is introduced, for a cation particle moving through an anion sub-lattice structure in the presence of two electromagnetic fields: an external electromagnetic field; and a self-induced electromagnetic field coming from back-reaction phenomena caused by the relative movement of cations with respect to the mentioned structure. Our approach seeks to incorporate magnetic effects, such as magnetic induction and spin of cations, which are not incorporated in other models, mainly due to the intrinsic difficulty of 3D effects. We propose a quantum mechanical formalism based on a Schrödinger-type equation, where a wave function models the behavior of a cation in presence of an external electromagnetic potential, coupled with transient and self-induced electromagnetic effects. To solve the model, a space–time coupled numerical scheme is presented, which allows the possibility of time-evolving electromagnetic effects. The technique uses finite-elements in space and time-marching schemes in time. While a time-explicit marching scheme is used to update the magnetic and electric-potential fields, a time-implicit marching scheme is used to solve the coupled Schrödinger equation. This strategy allows us to update the electromagnetic contributions and wave functions at each time-step. Numerical examples in one and two spatial dimensions (and evolving in time) have been implemented for some meaningful models obtained from nanoionics literature.

KW - Electromagnetic coupling

KW - Finite element semi-discretization

KW - Nanoionics

KW - Schrödinger equation

KW - Time-marching schemes

UR - http://www.scopus.com/inward/record.url?scp=85147710707&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2023.115926

DO - 10.1016/j.cma.2023.115926

M3 - Article

AN - SCOPUS:85147710707

SN - 0045-7825

VL - 407

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

M1 - 115926

ER -