Reduction of Anisotropic Volume Expansion and the Optimization of Specific Charge Capacity in Lithiated Silicon Nanowires

Abstract

This computational research study analyzes the increase of the specific charge capacity that comes with the reduction of the anisotropic volume expansion during lithium ion insertion within silicon nanowires. This research paper is a continuation from previous work that studied the expansion rate and volume increase. It has been determined that when the lithium ion concentration is decreased by regulating the amount of Li ion flux, the lithium ions to silicon atoms ratio, represented by x, decreases within the amorphous lithiated silicon (a-LixSi) material. This results in a decrease in the volumetric strain of the lithiated silicon nanowire as well as a reduction in Maxwell stress that was calculated and Young’s elastic module that was measured experimentally using nanoindentation. The conclusion as will be seen is that as there is a decrease in lithium ion concentration there is a corresponding decrease in anisotropic volume and a resulting increase in specific charge capacity. In fact the amplification of the electromagnetic field due to the electron flux that created detrimental effects for a fully lithiated silicon nanowire at x = 3.75 which resulted in over a 300% volume expansion becomes beneficial with the decrease in lithium ion flux as x approaches 0.75 which leads to a marginal volume increase of ~25 percent. This could lead to the use of crystalline silicon, c-Si, as an anode material that has been demonstrated in many previous research work to be ten times greater charge capacity than carbon base anode material for lithium ion batteries.

Quantum Mechanical Comparison between Lithiated and Sodiated Silicon Nanowires

“…where ϵ Li and ϵ Na are the volumetric strain for lithiated and sodiated silicon nanowires respectively. The volumetric stains are constant in this study because both silicon nanowires are at their maximum volume during the computational analysis [13]. The minimum g Li (2) is related to the maximum SCC for lithium as shown in figures 4 and 5 respectively.…”

Second Harmonic Generation in Lithiated Silicon Nanowires: Derivations and Computational Methods <strong> </strong>

“…Several scaling coefficients are displayed in figure 2. The scaling coefficient is linear due to the QHO when the lithiated silicon nanowire experiences approximately 20 percent volume expansion or less [6]. As the volume increases with greater lithium ion concentration x, Sn-Li remains linear with the energy states within the conduction bands becoming more energetic.…”

Second Harmonic Generation in Lithiated Silicon Nanowires: Derivations and Computational Methods

“…2. The scaling coefficient 𝑆 𝑛 𝐿𝑖 is linear due to the QHO when the lithiated silicon nanowire experiences approximately 20% volume expansion or less [6]. As the volume increases with greater lithium ion concentration x, Sn-Li remains linear with the energy states within the conduction bands becoming more energetic.…”

“…When multiple photons are absorbed by a lithium ion, the ion experiences an excitation that transitions the lithium ion from the ground state to an excited state. Once the lithium ion transitions to an elevated energy state, it is subjected to the spontaneous emission process [6].…”