  This computational research study will analyze the multi-physics of lithium
ion insertion into a silicon nanowire in an attempt to explain the
electrochemical kinetics at the nanoscale and quantum level. The electron
coherent states and a quantum field version of photon density waves will be the
joining theories that will explain the electron-photon interaction within the
lithium-silicon lattice structure. These two quantum particles will be
responsible for the photon absorption rate of silicon atoms that are
hypothesized to be the leading cause of breaking diatomic silicon covalent
bonds that ultimately leads to volume expansion. It will be demonstrated
through the combination of Maxwell stress tensor, optical amplification and
path integrals that a stochastic analyze using a variety of Poisson
distributions that the anisotropic expansion rates in the <110>, <111> and
<112> orthogonal directions confirms the findings ascertained in previous works
made by other research groups. The computational findings presented in this
work are similar to those which were discovered experimentally using
transmission electron microscopy (TEM) and simulation models that used density
functional theory (DFT) and molecular dynamics (MD). The refractive index and
electric susceptibility parameters of lithiated silicon are interwoven in the
first principle theoretical equations and appears frequently throughout this
research presentation, which should serve to demonstrate the importance of
these parameters in the understanding of this component in lithium ion
batteries.
