Role of Plasticity in Mechanical Failure of Solid ... - ACS Publications

Subscriber access provided by Kaohsiung Medical University

Letter

Role of Plasticity in Mechanical Failure of Solid Electrolyte Interphases on Nanostructured Silicon Electrode: Insight from Continuum Level Modeling Masatomo Tanaka, Justin B. Hooper, and Dmitry Bedrov ACS Appl. Energy Mater., Just Accepted Manuscript • DOI: 10.1021/acsaem.8b00344 • Publication Date (Web): 15 May 2018 Downloaded from http://pubs.acs.org on May 16, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Applied Energy Materials

Role of Plasticity in Mechanical Failure of Solid Electrolyte Interphases on Nanostructured Silicon Electrode: Insight from Continuum Level Modeling. Masatomo Tanaka1, Justin B. Hooper2, Dmitry Bedrov2

1

Murata Manufacturing Co., Ltd., 1-10-1 Higashikotari, Nagaokakyo-shi, Kyoto 617-8555,

Japan.

2

Department of Materials Science & Engineering University of Utah, 122 S. Central Campus

Dr., Salt Lake City, UT 84109, USA.

ABSTRACT

Understanding the failure mechanisms of solid electrolyte interphases (SEI) is important for silicon electrodes because their volume expands substantially during lithiation. This paper discusses material point method simulations of SEI failure during lithiation of silicon nanopillars. We demonstrate that considering SEI films as brittle, elastic materials does not allow fracture that would be consistent with experimental observations. However, constitutive models that include plastic deformation and result in ductile fracture are in very good agreement with trends observed in experiments. The insight gained from these results allows suggestion of possible strategies for design of SEI with improved failure resistance under lithiation-induced electrode expansion, where modification of the SEI leading to increased Young’s modulus and/or strain hardening without compromising the underlying ductility of the material presents a

ACS Paragon Plus Environment

1

ACS Applied Energy Materials 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 18

desirable outcome for chemical and/or processing modifications designed to modify SEI response.

KEYWORDS: silicon, plastic deformation, solid electrolyte interphase, simulations, constitutive model, material point method


2

Page 3 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Lithium-ion batteries are a major power source of portable electronic devices, medical devices, and electric vehicles. Ongoing demand for increased capacity in lithium-ion batteries serves to stimulate searches for novel electrode materials/formulations with increased storage capabilities compared to conventional graphite-based electrodes. For example, the theoretical energy density of a silicon anode is ten times higher than in conventional carbon materials of the same weight.1 However, because the volume of silicon changes by approximately 300% during the charging/discharging processes, the consequent mechanical degradation and loss of capacity with cycling have prevented adoption of these anodes. 2 To mitigate the adverse effects of electrochemical/mechanical coupling, recent research has focused on optimizing the silicon structure by reducing the size of the active silicon materials.3,4,5 Nanostructured active silicon materials and composite silicon-based electrodes have also been intensively studied, leading to substantially improved cycling performance.6-9 However, further development of silicon based energy storage devices requires not only mechanically stable active electrodes, but also a stable interface between the electrolyte and the electrodes.10 The organic electrolytes that are widely used in conventional lithium-ion batteries are reduced on the anode surface, forming a film called the solid electrolyte interphase (SEI). Unfortunately, significant expansion of the active materials forces stress accumulation and eventual breakage of the SEI, with the inevitable subsequent re-formation at newly exposed anode surfaces greatly increasing irreversible lithium and electrolyte consumption and decreasing overall charge capacity. Stabilizing the mechanical properties of the SEI on silicon materials is particularly important. While much research is devoted to the chemical composition and thickness of SEI,11,12 the mechanical properties and failure mode of the SEI are rarely reported and poorly understood. Recently, the mechanical properties of SEI components have been sampled from an atomistic, hybrid molecular dynamics


3


Page 4 of 18

(MD)-Monte Carlo scheme.13 In situ atomic force microscopy has directly observed the breaking of SEI on a silicon nanostructured electrode. 14 However, the mechanisms for initiation and evolution of SEI failure remain unknown. To our knowledge, we present the first computational insight into SEI failure that agrees well with experimental observations. Using simulation provided insight to the correlations between structure, mechanical characteristics and mechanical failure of SEI during silicon expansion/contraction, we can begin to develop strategies that mitigate failure and improve the feasibility for silicon application in high energy density electrodes for lithium-ion batteries. The purpose of this paper is to provide understanding about the nature and character of the overall mechanical behavior of the SEI layer on silicon anodes, using the experimental observations of Kumar et. al.14 as a basis for comparison. Actual SEIs are thought to consist of both inner and outer layers. The inner layer is primarily comprised of the doubly reduced compounds, such as Li2CO3, Li2O, and LiF that form crystalline domains, while the outer SEI layer is thought to be largely a glassy porous phase comprised of alkyl dicarbonate species such as dilithium ethylene dicarbonate (CH2OCO2Li)2 (or Li2EDC) and dilithium butylene dicarbonate (CH2CH2OCO2Li)2 (or Li2BDC).15,16,17 In addition, due to the dynamics of the SEI formation process, contamination from trapped components of the electrolyte are also a substantial possibility. The complexity of such systems requires careful investigations of a number of important phenomena, such as crystallites size and interfacial properties, layer thickness, proportion of inner to outer SEI components, coupling strength between inner SEI/anode and outer SEI/inner SEI. However, attempts to derive reasonable constraints on all of these variables simultaneously, given the current state of knowledge about the exact composition of the SEI, represents an intractable task, as a “bottom up” model would necessarily be


4

Page 5 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


predicated on speculative assumptions about the specific mesoscopic structure of the SEI. In this work, we therefore investigate from a “top down” approach the fundamental question of the overall bulk behavior of the SEI, which is well-suited to the capabilities of continuum level modeling to answer:

Is the fundamental character of the entire SEI strong/weak and

brittle/ductile? Rather than assume SEI components and configurations, we instead eschew such assumptions and seek to determine the necessary macroscopic mechanical models for SEI which lead to reproduction of the observed failure mechanism of an experimental system. Understanding the nature of the overall mechanical behavior of the SEI, in turn, provides a narrowing of scope with which to filter the myriad variables encountered in trying to model a mesoscopically realistic SEI in future work. To elucidate the mechanical failure of the bulk SEI during lithiation, we employ the material point method (MPM), a numerical method of continuum mechanics capable of accurate and efficient calculation when large deformations are involved. 18 Using MPM, Gritton et al. developed a coupled chemical–mechanical lithiation/delithiation model for a silicon nanopillar.19 Based on this model, we employ MPM simulations to investigate deformation of a silicon nanopillar that is surface-coated with a 50-nm thick SEI. The diameter and height of the silicon nanopillar are 250 nm and 50 nm, respectively. The substrate is sized 500 nm × 500 nm × 100 nm. For the calculation, the system is split into cubic (10 nm × 10 nm × 10 nm) grid cells, with 2 material points (MP) in each principal direction within each cell (23 total MP per cubic cell). As the system is axially symmetric, we simulate one-quarter of the whole geometry. A schematic illustration of this system is shown in Figure 1.


5


Page 6 of 18

Figure 1. Schematic illustration and dimensions of investigated system: (a) a quarter of the actual (axially symmetric) domain simulated in the MPM; (b) side view of the system.

The silicon and substrate were simulated using a linear, isotropic strain hardening plasticity model that was adopted for this system by Gritton et al.19 The failure criteria for the silicon nanopillar and substrate are ignored because our main objective is to understand the SEI failure mechanism. We examined the mechanical response of two regimes of bulk SEI bulk, designed to mimic homogenized constitutive properties expected of materials found in the experimental SEI: lithium carbonate (Li2CO3) and polyethylene oxide (PEO). Li2CO3 is believed to be a structured, crystalline component of the inner SEI, while PEO is representative of the outer SEI layer, that has been reported to contain softer, amorphous SEI components. 20 , 21 Dense inorganic components are known to exist at the inner portion of the SEI layer (near the electrode), whereas porous oligomeric/polymeric components mainly occupy the outer portion of the SEI layer.22 However, the domain sizes, domain distributions, and exact ratios of each component are often hard to determine and can strongly depend on a variety of factors. For this reason, for this initial study, we treat the SEI as a single material and examine its mechanical response with two types of SEI mechanical fracture models (see below). The bulk and shear moduli of each SEI component have been investigated in recent works.22


6

Page 7 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Mechanical fracture of SEI was investigated using both brittle and ductile fracture models. In the former, the SEI behavior was modeled as a perfectly elastic material, with failure occurring when the maximum principal stress reaches the yield stress. As the SEI failure stress is unknown, we assumed a typical value from a previous report.23 Table 1 lists the values of the mechanical properties in the brittle fracture model used in our simulations. Table 1. Mechanical properties used in the brittle fracture model

Silicon Substrate PEO Li2CO3

Bulk modulus (GPa)

Shear modulus (GPa)

Yield stress (GPa)

67 180.4 2.4 50.5

31 76 0.89 22.2

1.4 0.7 -

Work hardening modulus (GPa) 1.15 1.15 -

Failure stress (MPa)

Reference number

70 581

19 19 22, 23 22, 23

In the ductile fracture model, the SEI behavior was simulated with the linear, isotropic strain hardening plasticity model, which assumes that material flows plastically after exceeding its yield stress, with plastic deformation occurring in a linear manner with an apparent elastic modulus known as the hardening modulus in the plastic regime. The flow stress is defined as σｙ = σｙ +

(1)

where is the equivalent plastic strain, σｙ is the yield stress and is the work-hardening modulus. As the yield condition, we selected the von Mises criterion. As the yield stress and work-hardening modulus of SEI are unknown, a range of values that yield stress can take was assumed based on a previous report23 and by comparing two different values for the PEO-based SEI layer, respectively. The work-hardening modulus was set to two different values: 0.12 GPa


7


Page 8 of 18

(= 5 % of Young’s modulus) and 1.2 GPa (= 50% of Young’s modulus) for PEO-based SEI layer. The mechanical properties of the plasticity model are listed in Table 2. Table 2. Mechanical properties used in the ductile fracture model

Li2CO3 PEO – 1 PEO – 2 PEO – 3

Bulk modulus (GPa)

Shear modulus (GPa)

Yield stress (MPa)

50.5 2.4 2.4 2.4

22.2 0.89 0.89 0.89

581 70 300 70

Work hardening modulus (MPa) 2.9 0.12 0.12 1.2

Reference number

22, 23 22, 23 22, 23 22, 23

The failure criterion was determined using a porosity model, which limits the maximum volume fraction of voids.24 Based on void nucleation and growth, porosity theory is widely used in ductile fracture analyses. Under plastic deformation, microscopic inclusions may exfoliate from the surrounding matrix and nucleated voids may subsequently grow. The SEI is a passivation layer containing various inorganic and organic electrolyte decomposition products, most of which show ductile behaviors.22 Therefore, the porosity model can reasonably describe SEI failure. The voids evolve through growth and nucleation, with the void evolution, growth and nucleation rates calculated as detailed in the Supplementary Information. In both fracture models, a failed particle is passed to the erosion algorithm and marked as no longer capable of supporting stress. The flux of lithium ions into silicon induced by a voltage difference between the anode and cathode was imitated by a constant flux on the surface of the silicon nanopillar. This approach is indicative of a galvanostatic charging method, whereby the flow of current necessarily includes a corresponding influx of lithium ions to counteract the flow of electrons. As such, our flux coefficient was adjusted to reproduce a charging rate of 0.2C (for


8

Page 9 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


brittle SEIs) or 2.0C (for ductile SEIs) for the anode geometry presented. While the local flux would likely be somewhat different in potentiostatic situations due to the localized stress in the Si anode interacting with the incoming Li+ flux via raising the free energy of insertion, the combination of the sharp diffusion front normally associated with Li infiltration of Si along with the fact that our model does include a pressure dependent transport term, just not a pressure dependent chemical potential of insertion, leads us to believe that the differences would be relatively minor under the assumption that the uniform potential of insertion would be set so as to reproduce the same net charge rate of the system. As discussed in the investigation of the bare silicon anode, the silicon density was increased for enhancement of integration time stepping, and only slightly affects the silicon expansion.19 The densities of the other materials were adjusted by the same order of magnitude as the silicon anode in order to preserve the increased time step for tractable simulation times. The interfaces of all materials were evolved using a constant-velocity contact model, which ensures that the velocity of differing materials across an interface maintain an equivalent value. This contact model therefore represents the strong interface limit of SEI adhesion. More sophisticated contact models that better replicate the contact situation must be explored in future studies. Our MPM calculations were performed in the Uintah computational framework.25 Details of using Uintah to perform MPM calculations are further described in the Uintah User Guide.26 Figure 2 shows the failure evolution of the Li2CO3 SEI layer employing the brittle fracture model with a homogeneous value for the yield stress of 581 MPa. The SEI failure occurred at a 1.0 % state of charge (SOC), progressing from the edge of the silicon nanopillar, where the flux and stress were concentrated (Figure 2a, b). The SEI failure subsequently evolved from the corner, following tensile stress across the large interfacial area (Figure 2b, c). Interestingly, when


9


Page 10 of 18

the SEI was assumed to have an elastic-brittle failure model, its failure evolved from the corner of the silicon nanopillar even after changing the yield stress of the SEI (SI Figure S1) or when assuming a Gaussian distribution of yield stress with variations up to 394 MPa for individual SEI material points (SI Figures S2). Even if the SEI is assumed to have softer, PEO-like mechanical properties with elastic-brittle fracture, its failure evolved from the corner of the silicon nanopillar (SI Figures S3, S4). Therefore, independently of the combination of mechanical characteristics used for SEI layer in our simulations with the elastic-brittle model, the predicted failure of SEI contrasts with the Kumar et al.14 experiments that observed SEI failure on the top surface of the nanopillar some distance interior to the edge of the silicon pillar. This qualitative disagreement suggests that the elastic-brittle fracture SEI model does not capture the mechanical and failure behavior of the SEI during lithiation.

Figure 2. Lithium concentration of silicon nanopillar, stress and failure evolution of the Li2CO3 SEI layer during lithiation in the brittle fracture model at different SOC. Each panel displays an overhead view (left) and a side view (right). (a) normalized lithium concentration of silicon (1.0 corresponds to complete silicon lithiation), (b) principal stress of the Li2CO3 SEI layer, and (c) location of the failed material points in Li2CO3 SEI layer; red and blue regions indicate the failed and non-failed regions in the SEI layer, respectively.


10

Page 11 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 3 shows the simulation results of the Li2CO3 SEI layer employing the ductile fracture model, where failure initiation differed greatly from that in the brittle fracture model. As the silicon expands, the stress applied on the SEI exceeds the yield stress, causing plastic strain. Figure 3 shows that the SEI first starts to delaminate at the silicon–SEI interface, (Figure 3 left (SOC 50 %)), but when the SOC reaches 85% or higher, it fails near, but internal to, the edge of the silicon nanopillar (Figure 3 middle (SOC 85 %) and right (SOC 90 %)). This result qualitatively agrees very well with the failure locations of SEI reported by Kumar et al.14 The PEO-1 SEI layer exhibited a similar tendency, but failed at an earlier SOC (57%; see SI Fig. S6).

Figure 3. Lithium concentration, stress, failure and plastic strain evolution of the Li2CO3 SEI layer in the ductile fracture model. (a) lithium concentration of silicon, (b) effective stress of the Li2CO3 SEI layer, (c) location of the failed material points in the Li2CO3 SEI layer (Red and blue regions indicate the failed and non-failed regions, respectively.) and (d) plastic strain of the Li2CO3 SEI layer.


11


Page 12 of 18

The relative failure behavior of the Li2CO3 and PEO SEI constitutive models at different SOCs can be explained by the different stress and strain evolutions at equivalent states of charge, due to the differing mechanical characteristics in the constitutive models of the SEI. Figure 4a presents the input stress/strain behavior in the Li2CO3 and PEO material models employed in this study. Being the softer SEI material, the PEO layer exhibits larger plastic strains at common SOCs (SI Figures S7), failing earlier than the Li2CO3 layer. To check whether the silicon geometry influences the result, we also examined the rectangular parallelepiped silicon geometry, similar to that investigated in the experimental study.14 Even for this noticeably different geometry, the SEI failure in the ductile fracture model occurred slightly inside the edge of the silicon (SI Figure S8). It is noteworthy that in addition to the interior location of SEI failure, the ductile models predict a much higher overall SOC at failure when compared to the brittle-elastic models due to the ability of the evolved plastic deformation to accommodate significant amounts of strain energy before the SEI is completely transected by fracture. We next examined how magnitude of the yield stress and work-hardening modulus affect SEI failure in the ductile fracture model. The results for PEO SEI layers with the differing material properties (Table 2 and Figure 4a) are shown in Figure 4b at several SOCs. Within the evaluated ranges of yield stresses and work-hardening moduli, increasing the yield stress reduced the overall plastic deformation in the SEI, and increasing the work-hardening modulus reduced both the average value and standard deviation of the plastic strain distribution (SI Table S4). In both parameter evaluations, SEI failure occurred only at the material interface, where the plastic strain was suppressed relative to the reference values employed for the PEO in the PEO/Li2CO3 comparison. To mitigate the SEI failure, therefore, one must effectively suppress the local plastic deformation without losing the plasticity itself, since making the material stiffer and more brittle


12

Page 13 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


seems to make it less capable of attaining high SOC. This finding provides an important guideline for SEI design of silicon active materials.

Figure 4. Material models and simulation results for the differing material characteristics of the SEI layers. (a) stress-strain relation, (b) the side view of failure location in each SEI layer at differing SOCs and (c) the side view of stress distribution in each SEI layer at differing SOCs. In summary, using material point method simulations we investigated the coupling between SEI mechanical characteristics and the SEI failure during charging. Lithiation of the silicon nanopillar imposed an excessive stress (far above the yield stress) on the SEI, causing a large plastic strain in the SEI layer. The results of the ductile fracture model agree well with previous experimental observations, implying that plastic deformation plays an important role in SEI failure. By controlling the yield stress and the work-hardening modulus, the localization of plastic strain during lithiation can be alleviated. This work provides a basis to motivate


13


Page 14 of 18

guidelines for further computational explorations of the SEI mechanical behavior, including calculations involving more realistic approximations of constitutive models, porosity distribution and/or crystallite arrangement/composition variations of a model SEI in future works.

ASSOCIATED CONTENT Supporting Information. Supporting Information is available free of charge on the ACS Publications website as pdf file providing simulation/analysis details and additional data (concentration, stress, and strain distributions; mechanical properties of investigated model materials; description of computational details).

AUTHOR INFORMATION Corresponding Authors. Dmitry Bedrov: [email protected]; Masatomo Tanaka: [email protected] Notes. The authors declare no competing financial interests ACKNOWLEDGMENT Authors would like to acknowledge the support of the joint research project by the Murata Manufacturing Inc. and the support from the project sponsored by the Army Research Laboratory under Cooperative Agreement Number W911NF-12-2-0023. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of ARL or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.

REFERENCES


14

Page 15 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

Larcher, D.; Beattie, S.; Morcrette, M.; Edstroem, K.; Jumas, J. C.; Tarascon, J. M. Recent Findings and Prospects in the Field of Pure Metals as Negative Electrodes for Lithium-ion Batteries. J. Mater. Chem. 2007, 17, 3759–3772. 2

Zhang, W. J. A Review of the Electrochemical Performance of Alloy Anodes for Lithium-Ion Batteries. J. Power Sources 2011, 196, 13−24. 3

Liu, X.; Zhong, L.; Huang, S.; Mao, S. X.; Zhu, T.; Huang, J. Size-Dependent Fracture of Silicon Nanoparticles During Lithiation. ACS Nano 2012, 6, 1522−1531. 4

Wang, X.; Fan, F.; Wang, J.; Wang, H; Tao, S.; Yang, A.; Liu, Y.; Chew, H. B.; Mao, S. X.; Zhu, T.; Xia, S.; High Damage Tolerance of Electrochemically Lithiated Silicon. Nat. Commun. 2015, 6, 8417.

5

Kim, H.; Seo, M.; Park, M. H.; Jaephil Cho, J. A Critical Size of Silicon Nano-Anodes for Lithium Rechargeable Batteries. Angew. Chem., Int. Ed, 2010, 49, 2146–2149. 6

Zhu, Y.; Liu, W.; Zhang, X.; He, J.; Chen, J.; Wang, Y.; Cao, T. Directing Silicon−Graphene Self-Assembly as a Core/Shell Anode for High-Performance Lithium-Ion Batteries. Langmuir. 2013, 29, 744–749. 7

Xiao, Q.; Gu, M.; Yang, H.; Li, B.; Zhang, C.; Liu, Y.; Liu, F.; Dai, F.; Yang, L.; Liu, Z.; Xiao, X.; Liu, G.; Zhao, P.; Zhang, S.; Wang, C.; Lu, Y.; Cai, M. Inward lithium-ion breathing of hierarchically porous silicon anodes. Nat. Commun. 2015, 6, 8844. 8

Wang, X.; Fan, F.; Wang, J.; Wang, H.; Tao, S.; Yang, A.; Liu, Y.; Chew, H. B.; Mao, S. X.; Zhu, T.; Xia, S. Interconnected Silicon Hollow Nanospheres for Lithium-Ion Battery Anodes with Long Cycle Life. Nano Lett. 2011, 11, 2949–2954.

9

Gao, X.; Li, J.; Xie, Y.; Guan, D.; Yuan, C. A Multilayered Silicon-Reduced Graphene Oxide Electrode for High Performance Lithium-Ion Batteries. Mater. Interfaces, 2015, 7, 7855–7862. 10

Gauthier, M.; Carney, T. J.; Grimaud, A.; Giordano, L.; Pour, N.; Chang, H.; Fenning, D. P.; Lux, S. F.; Paschos, O.; Bauer, C.; Maglia, F.; Lupart, S.; Lamp, P.; Shao-Horn, Y. ElectrodeElectrolyte Interface in Lithium-ion Batteries: Current Understanding and New Insights. J. Phys. Chem. Lett. 2015, 6, 4653−4672. 11

Schroder, K.; Alvarado, J.; Yersak, T. A.; Li, J.; Dudney, N.; Webb, L. J.; Meng, Y. S.; Stevenson, K. J. The Effect of Fluoroethylene Carbonate as an Additive on the Solid Electrolyte Interphase on Silicon Lithium-Ion Electrodes. Chem. Mater. 2015, 27, 5531−5542. 12

Verma, P.; Maire, P.; Novák, P. A Review of the Features and Analyses of the Solid Electrolyte Interphase in Lithium-ion Batteries. Electrochim. Acta 2010, 55, 6332–6341.


15


Page 16 of 18

13

Bedrov, D.; Borodin, O.; Hooper, J. B. Li+ Transport and Mechanical Properties of Model Solid Electrolyte Interphases (SEI): Insight from Atomistic Molecular Dynamics Simulations. J. Phys. Chem. C 2017, 121, 16098–16109. 14

Kumar, R.; Tokranov, A.; Sheldon, B. W.; Xiao, X.; Huang, Z.; Li, C.; Mueller, T. In Situ and Operando Investigations of Failure Mechanisms of the Solid Electrolyte interphase on Silicon Electrodes. ACS Energy Lett. 2016, 1, 689−697.

15

Zorba, V.; Syzdek, J.; Mao, X. L.; Russo, R. E.; Kostecki, R. Ultrafast Laser Induced Breakdown Spectroscopy of Electrode/Electrolyte Interfaces. Appl. Phys. Lett. 2012, 100, 234101. 16

Aurbach, D.; Ein-Ely, Y.; Zaban, A. The Surface Chemistry of Lithium Electrodes in Alkyl Carbonate Solutions. J. Electrochem. Soc. 1994, 141, L1-3. 17

Aurbach, D.; Zaban, A.; Schecheter, A.; Ein-Eli, Y.; Zinigrad E.; Markovsky, B. The Study of Electrolyte Solutions Based on Ethylene and Diethyl Carbonates for Rechargeable Li Batteries. I. Li Metal Anodes. J. Electrochem. Soc., 1995, 142, 2873-2882.

18

Sulsky, D.; Zhou, S. J.; Schreyer, H. L. Application of a Particle-in-Cell Method to Solid Mechanics. Comp. Phys. Commun. 1995, 87, 236–252.

19

Gritton, C.; Guilkey, J.; Hooper, J. B.; Bedrov, D.; Kirby, R. M.; Berzins, M. Using the Material Point Method to Model Chemical/Mechanical Coupling in the Deformation of a Silicon Anode. Modelling Simul. Mater. Sci. Eng. 2017, 25, 045005. 20

Tasaki, K.; Goldberg, A.; Lian, J. J.; Walker, M.; Timmons, A.; Harris, S. J.; Solubility of Lithium Salts Formed on the Lithium-Ion Battery Negative Electrode Surface in Organic Solvents. J. Electrochem. Soc. 2009, 156, A1019–A1027. 21

Gachot, G.; Grugeon, S.; Armand, M.; Pilard, S.; Guenot, P.; Tarascon, J. M.; Laruelle, S. Deciphering the Multi-Step Degradation Mechanisms of Carbonate-Based Electrolyte in Li batteries. J. Power Sources 2008, 178, 409–421. 22

Shin, H.; Park, J.; Han, S.; Sastry, A. M.; Lu, W. Component-/Structure-Dependent Elasticity of Solid Electrolyte Interphase Layer in Lithium-ion Batteries: Experimental and computational studies. J. Power Sources 2015, 277, 169–179. 23

Ashby, M. F. Materials Selection in Mechanical Design, 4th ed. Elsevier Ltd, Oxford 2011.

24

Chu, C. C.; Needleman, A. Void Nucleation Effects in Biaxially Stretched Sheets. J. Engineering Materials and Technology 1980, 102, 255.


16

Page 17 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


25

Uintah Computational Framework. http://uintah.utah.edu (accessed Apr 27, 2018).

26

Uintah User Guide. http://uintah-build.sci.utah.edu/trac/wiki/Documentation (accessed Apr 27, 2018).


17


Page 18 of 18

Table of Content Graphics.


18

Role of Plasticity in Mechanical Failure of Solid ... - ACS Publications

Recommend Documents