Next Article in Journal
New Scientific Contribution on the 2-D Subdomain Technique in Polar Coordinates: Taking into Account of Iron Parts
Previous Article in Journal
Sensitivity Analysis Based on Markovian Integration by Parts Formula
Open AccessArticle

Quantum Coherent States and Path Integral Method to Stochastically Determine the Anisotropic Volume Expansion in Lithiated Silicon Nanowires

Nanoscience Research Institute, 4423 Lehigh Road Suite 371, College Park, MD 20740, USA
Math. Comput. Appl. 2017, 22(4), 41; https://doi.org/10.3390/mca22040041
Received: 6 June 2017 / Revised: 21 July 2017 / Accepted: 26 July 2017 / Published: 23 October 2017
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. View Full-Text
Keywords: silicon; nanowire; lithium; quantum; refractive index silicon; nanowire; lithium; quantum; refractive index
Show Figures

Figure 1

MDPI and ACS Style

Boone, D.C. Quantum Coherent States and Path Integral Method to Stochastically Determine the Anisotropic Volume Expansion in Lithiated Silicon Nanowires. Math. Comput. Appl. 2017, 22, 41.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop