Subscriber access provided by UNIV TORONTO
Article
Multi-Physics Simulations of LithiationInduced Stress in Li TiO Electrode Particles 1+x
2
4
Tonghu Jiang, Shiva Rudraraju, Anindya Roy, Anton Van der Ven, Krishna Garikipati, and Michael L. Falk J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b09775 • Publication Date (Web): 22 Nov 2016 Downloaded from http://pubs.acs.org on November 23, 2016
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 free 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 accessible to all readers and 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.
The Journal of Physical Chemistry C 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 37
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
The Journal of Physical Chemistry
Multi-Physics Simulations of Lithiation-Induced Stress in Li1+xTi2O4 Electrode Particles Tonghu Jiang,† Shiva Rudraraju,‡ Anindya Roy,† Anton Van der Ven,¶ Krishna Garikipati,‡,§ and Michael L. Falk∗,†,k †Department of Materials Science and Engineering, Johns Hopkins University, Baltimore, MD 21218 USA ‡Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109 USA ¶Materials Department, University of California, Santa Barbara, CA 93106 USA §Department of Mathematics, University of Michigan, Ann Arbor, MI 48109 USA kDepartment of Mechanical Engineering and Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218 USA E-mail:
[email protected] 1
ACS Paragon Plus Environment
The Journal of Physical Chemistry
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
Abstract Cubic spinel Li1+x Ti2 O4 is a promising electrode material as it exhibits a high lithium diffusivity and undergoes minimal changes in lattice parameters during lithiation and delithiation, thereby ensuring favorable cycleability. The present work is a multi-physics and multi-scale study of Li1+x Ti2 O4 that combines first principles computations of thermodynamic and kinetic properties with continuum scale modeling of lithiation-delithiation kinetics. Density functional theory calculations and statistical mechanics methods are used to calculate lattice parameters, elastic coefficients, thermodynamic potentials, migration barriers and Li diffusion coefficients. These computations were performed at a temperature of 800 K to magnify the kinetic effects. These quantities then inform a phase field framework to model the coupled chemomechanical evolution of electrode particles. Several case studies accounting for either homogeneous or heterogeneous nucleation are considered to explore the temporal evolution of maximum principle stress values, which serve to indicate stress localization and the potential for crack initiation, during lithiation and delithiation.
1
Introduction
Scientists and engineers are exploring a vast materials space for cheaper, higher energydensity, and reliable battery materials, in response to the growing demand of portable electronics and electric vehicles. 1 Understanding the suitability of the cathode and anode materials, both computationally and experimentally, has been central to battery research. Li-ion batteries are the most used rechargeable batteries today, and a considerable fraction of battery research is focused on improving the characteristics of Li-ion batteries and finding better candidates for the electrodes. In this work, we are interested in Li1+x Ti2 O4 for its possible use as an electrode material. Li1+x Ti2 O4 is known to form different polymorphs upon lithium insertion, and the common phases include rutile, anatase, spinel, and brookite. 2,3 The electric potential for 2
ACS Paragon Plus Environment
Page 2 of 37
Page 3 of 37
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
The Journal of Physical Chemistry
lithium insertion into these structures is relatively low (∼1.5V ), enhancing the suitability of Li1+x Ti2 O4 as an anode material. Cubic spinel Li1+x Ti2 O4 and Li4/3 Ti5/3 O4 have been shown in experiments to exhibit high lithium diffusivity, and a negligible change of lattice parameter during (dis)charging. 4–6 A large change in stress during the charging process can result, via the elastic coefficients, from significant changes in lattice parameters. The high stress can initiate fracture, limiting cycleability. Low variations in lattice parameters can thus promote better cycleability. This work presents a multi-physics and multi-scale case-study in which we investigated Li1+x Ti2 O4 computationally, with the aim of predicting, from first principles, the stresses that will arise within the material during repeated charging and discharging of electrode particles. In particular, we are interested in spinel Li1+x Ti2 O4 , which belongs to the space group F d¯3m. In spinel Li1+x Ti2 O4 , 16d and 32e sites are occupied by Ti and O, respectively. We emphasize that the goal of the present work is to demonstrate how the various computational techniques at different length scales could be applied in tandem, and we used a high temperature of 800 K to magnify the kinetic effects. While specific quantitative predictions regarding electrode failure are not possible without continued development of these methods, the work presented here demonstrates that interesting insights into the chemo-mechanical processes that can limit cycleability can nonetheless be obtained. During charge and discharge, Li1+x Ti2 O4 undergoes first order phase transformations. For x
