Lithiated Silicon Nanowires Research Articles

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

This research will examine the computational methods to calculate the nonlinear optical process of second harmonic generation (SHG) that will be hypothesized to be present during lithium ion insertion into silicon nanowires. First it will be determined whether the medium in which SHG is conveyed is non-centrosymmetric or whether the medium is inversion symmetric where SHG as a part of the second-order nonlinear optical phenomenon does not exist. It will be demonstrated that the main interaction that determines SHG is multiphoton absorption on lithium ions. The quantum harmonic oscillator (QHO) is used as the background that generates coherent states for electrons and photons that transverse the length of the silicon nanowire. The matrix elements of the Hamiltonian which represents the energy of the system will be used to calculate the probability density of second-order nonlinear optical interactions which includes collectively SHG, sum-frequency generation (SFG) and difference-frequency generation (DFG). As a result, it will be seen that at varies concentrations of lithium ions (Li+) within the crystallized silicon (c-Si) matrix the second-order nonlinear optical process has probabilities substantial enough to create second harmonic generation that could possibly be used for such applications as second harmonic imaging microscopy.

The quantum transport properties of silicon nanowires are affected upon lithiation

Density functional theory shows that electrical performance in lithiated silicon nanowires remains acceptable even with surface roughness and disorder.

Influence of disorder and surface roughness on the electrical and thermal properties of lithiated silicon nanowires

We use density functional theory and reactive-force-field methods to investigate the electrical and thermal transport properties of long disordered lithiated silicon nanowires. The latter could build the core of future lithium ion batteries with enhanced storage capacity. Due to the amorphous nature of these nanowires, disorder and surface roughness effects inevitably arise, affecting the lithiation process. It is found that the electrical conductivity of the nanowires steadily increases as a function of the lithium concentration, despite the presence of disorder, while the thermal conductivity follows the opposite trend and decreases significantly with reduced heat evacuation capabilities as a consequence. This behavior can be attributed to the influence of Li ions, which on one hand tend to metallize Si nanowires and thus enhance their electron mobility. On the other hand, the random distribution of Li atoms perturbs the phonon propagation through the nanowire, explaining the decrease in thermal conductivity.

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

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 works to be ten times greater charge capacity than carbon base anode material for lithium ion batteries.

In Situ Transmission Electron Microsopy of Oxide Shell-Induced Pore Formation in (De)lithiated Silicon Nanowires

Silicon (Si) nanowires with a silicon oxide (SiOx) shell undergoing lithiation and delithiation were examined by in situ transmission electron microscopy (TEM). Large pores formed in the nanowires during the delithiation cycle. We found that the oxide shell constrains the expansion of the Si nanowires during lithitation and then induces pore formation in the nanowires. We propose that the SiOx shell prevents the vacancies that result from the loss of lithium from escaping the Si core, leading to pore nucleation and growth. It is also possible that the difference in mechanical properties of the expanding and contracting Si nanowire and SiOx shell contribute to the observed pore formation. This in situ study reaffirms the need to directly observe structural changes that occur during cycling in battery materials, especially when modified by coatings.

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

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.

Maxwell stress to explain the mechanism for the anisotropic expansion in lithiated silicon nanowires

This computational research study attempts to explain the process that leads to volume expansion during insertion of lithium ions into a silicon nanowire. During lithiation, electrons flow through the nanowire in the opposing direction of lithium ions insertion. This causes an applied electromagnetic field which is described as being a quantum mechanical version of photon density wave theory. A series of events are calculated as the individual electrons and photons travels through the lithiated silicon nanowire. The hypothesis that will be presented employs the Maxwell stress tensor to calculate the refractive indices in three orthogonal directions during lithiation. The quantum harmonic oscillator and the electromagnetic intensity will be utilized in this presentation to calculate the energy of electrons and optical amplification of the electromagnetic field respectively. The main focus of this research study will use electron scattering theory, spontaneous and stimulated emission theory to model the breaking of cohesion bonds between silicon atoms that ultimately leads to excessive volume expansion that is witnessed during the lithiation process in Si nanowires.

Exotic reaction front migration and stage structure in lithiated silicon nanowires.

Nanostructured silicon anodes, which possess extremely high energy density and accommodate large strain without pulverization, have been developed rapidly for high-power lithium ion batteries. Here, using in situ transmission electron microscopy, the lithiation behavior of silicon nanowires with diameters smaller than 60 nm was investigated. The study demonstrated a direct dependence of the self-limiting lithiation on the pristine diameter. A "punch-through" lithiation process at the core of nanowires with pristine diameters slightly larger than the self-limiting threshold is suggested to occur with the consequent formation of a stage structure. Our work demonstrates the crucial role of mechanical stress and local defects in determining the migration and geometry of the reaction front at the mesoscopic scale. This intriguing finding holds critical significance for the application of silicon nanostructures in high-power lithium ion batteries.

The Role of Elasto-Plasticity on Phase Kinetics in Lithiated Silicon Nanowires: Phase Field Simulation

Silicon (Si) is a promising anode material for Li-ion batteries, since it absorbs large amounts of Li. In addition to volumetric expansion, huge stresses, and fracture, recent experiments reveal that the kinetics of Li insertion and extraction, which critically control the rates of charging and discharging, are of great importance for the high performance of LIBs. Here, we first propose a phase field model coupled to elasto-plasticity to study the lithiation kinetics in individual Si nanowires. In contrast to other models, the proposed phase field model is thermodynamically consistent, and the corresponding thermodynamic and kinetics parameters can be obtained from the experiments or Density function theory (DFT) calculations. The developed model describes well the experimental known self-limiting lithiation phenomenon, which is attributed to the retardation effect of the lithiation-induced stress. Further, the proposed model has general character and is applicable to any electrode systems.

In situ tensile and creep testing of lithiated silicon nanowires

We present experimental results for uniaxial tensile and creep testing of fully lithiated silicon nanowires. A reduction in the elastic modulus is observed when silicon nanowires are alloyed with lithium and plastic deformation becomes possible when the wires are saturated with lithium. Creep testing was performed at fixed force levels above and below the tensile strength of the material. A linear dependence of the strain-rate on the applied stress was evident below the yield stress of the alloy, indicating viscous deformation behavior. The observed inverse exponential relationship between wire radius and strain rate below the yield stress indicates that material transport was controlled by diffusion. At stress levels approaching the yield strength of fully lithiated silicon, power-law creep appears to govern the strain-rate dependence on stress. These results have direct implications on the cycling conditions, rate-capabilities, and charge capacity of silicon and should prove useful for the design and construction of future silicon-based electrodes.

Quantitative Fracture Strength and Plasticity Measurements of Lithiated Silicon Nanowires by In Situ TEM Tensile Experiments

We report in situ tensile strength measurement of fully lithiated Si (Li-Si alloy) nanowires inside a transmission electron microscope. A specially designed dual probe with an atomic force microscopy cantilever and a scanning tunneling microscopy electrode was used to conduct lithiation of Si nanowires and then perform in situ tension of the lithiated nanowires. The axial tensile strength decreased from the initial value of 3.6 GPa for the pristine unlithiated Si nanowires to 0.72 GPa for the lithiated Li-Si alloy. We observed large fracture strain ranging from 8% to 16% for Li-Si alloy, 70% of which remained permanent after fracture. This indicates a certain degree of tensile plasticity in the lithiated silicon before fracture, important for constitutive modeling of the lithium-ion battery cyclability. We also compare the ab initio computed ideal strengths with our measured strengths and attribute the differences to the morphology and flaws in the lithiated nanowires.

Orientation-Dependent Interfacial Mobility Governs the Anisotropic Swelling in Lithiated Silicon Nanowires

Recent independent experiments demonstrated that the lithiation-induced volume expansion in silicon nanowires, nanopillars, and microslabs is highly anisotropic, with predominant expansion along the <110> direction but negligibly small expansion along the <111> direction. The origin of such anisotropic behavior remains elusive. Here, we develop a chemomechanical model to study the phase evolution and morphological changes in lithiated silicon nanowires. The model couples the diffusive reaction of lithium with the lithiation-induced elasto-plastic deformation. We show that the apparent anisotropic swelling is critically controlled by the orientation-dependent mobility of the core-shell interface, i.e., the lithiation reaction rate at the atomically sharp phase boundary between the crystalline core and the amorphous shell. Our results also underscore the importance of structural relaxation by plastic flow behind the moving phase boundary, which is essential to quantitative prediction of the experimentally observed morphologies of lithiated silicon nanowires. The study sheds light on the lithiation-mediated failure in nanowire-based electrodes, and the modeling framework provides a basis for simulating the morphological evolution, stress generation, and fracture in high-capacity electrodes for the next-generation lithium-ion batteries.