Abstract
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.
Highlights
The research work that will be presented is a continuation from a study that examined how energy was transformed within an electron flux that transverse a cubic silicon crystal lattice in the opposing direction of lithium ion diffusion [1]
As a result, when electrons enter the lithiated silicon from crystalline silicon (c-Si), there is a high probability that they will transition to the minimum conduction band E0 at which time photons are emitted that will aid in the spontaneous and stimulated emission process of lithium ions that was described earlier
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Summary
The research work that will be presented is a continuation from a study that examined how energy was transformed within an electron flux that transverse a cubic silicon crystal lattice in the opposing direction of lithium ion diffusion [1]. The variable nc is defined as the negative charge differential within the quantum harmonic oscillator conduction bands per unit volume which is the difference between the electrons that are traveling in the conduction bands and the number of positively charged lithium ions within silicon cubic lattice model. When a particular electron obtains enough energy due to photon absorption during optical amplification of the EM field, the electron transition from the minimum conduction band E0 to an available energy state in E1 (Figure 7c). As a result, when electrons enter the lithiated silicon from c-Si, there is a high probability that they will transition to the minimum conduction band E0 at which time photons are emitted that will aid in the spontaneous and stimulated emission process of lithium ions that was described earlier. Whehnen nc==6,6d, idreircetciotinonhahsasa ammaxaixmimuummEEMMeenneerrggyyooffaapppprrooxxiimmaatteellyy 3t3hh00aeveeVeVcotaahrnnrededscapoaorCr〈neds1pi1〉n0ogonofdf0i.0n〈3.g5355C〉35=.31S.1i01mS.2imi5=la4irl60aly.r2,lay5fon,4rfd6otrhaneth〈d.3=0(=n60c21.33=,)0a61rn2e3,sd)pralwy=(,int2wch1i)=thadn2iar1en)EctdEMioiMrneesce,ntniweoernerggshy,yawvooeeff aapppprrooxxiimmaatteellyy 3300 eeVV ((FFiigguurree 88))
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