Statistical kinetics of phase-transforming nanoparticles in LiFePO4 porous electrodes

Abstract Using a simple mathematical model, we demonstrate that statistical kinetics of phase-transforming nanoparticles in porous electrodes results in macroscopic non-monotonic transient currents, which could be misinterpreted as the nucleation and growth mechanism by the Kolmogorov–Johnson–Mehl–Avrami (KJMA) theory. Our model decouples the roles of nucleation and surface reaction in the electrochemically driven phase-transformation process by a special activation rate and the mean particle-filling speed of active nanoparticles, which can be extracted from the responses of porous electrodes to identify the dynamics in single composing nanoparticles.

[1]  D. Aurbach,et al.  Comparison between Cottrell diffusion and moving boundary models for determination of the chemical diffusion coefficients in ion-insertion electrodes , 2005 .

[2]  Martin Z. Bazant,et al.  Coherency Strain and the Kinetics of Phase Separation in LiFePO [subscript 4] , 2012 .

[3]  Lijun Wu,et al.  A new in situ synchrotron X-ray diffraction technique to study the chemical delithiation of LiFePO4. , 2011, Chemical communications.

[4]  Daniel A. Cogswell,et al.  Suppression of phase separation in LiFePO₄ nanoparticles during battery discharge. , 2011, Nano letters.

[5]  Wei Lai,et al.  Thermodynamics and kinetics of phase transformation in intercalation battery electrodes – phenomenological modeling , 2010 .

[6]  Wolfgang Dreyer,et al.  The thermodynamic origin of hysteresis in insertion batteries. , 2010, Nature materials.

[7]  Thomas J. Richardson,et al.  Electron Microscopy Study of the LiFePO4 to FePO4 Phase Transition , 2006 .

[8]  J. E. Hilliard,et al.  Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .

[9]  A. Shiryayev.  On The Statistical Theory of Metal Crystallization , 1992 .

[10]  Xufeng Zhou,et al.  Morphology-controlled solvothermal synthesis of LiFePO4 as a cathode material for lithium-ion batteries , 2010 .

[11]  P. D'ajello,et al.  Transient equations for multiple nucleation on solid electrodes: A stochastic description , 1999 .

[12]  Venkat Srinivasan,et al.  Discharge Model for the Lithium Iron-Phosphate Electrode , 2004 .

[13]  W. Craig Carter,et al.  Overpotential-Dependent Phase Transformation Pathways in Lithium Iron Phosphate Battery Electrodes , 2010 .

[14]  Daniel A. Cogswell,et al.  Coherency strain and the kinetics of phase separation in LiFePO4 nanoparticles. , 2011, ACS nano.

[15]  Nae-Lih Wu,et al.  Study on dynamics of structural transformation during charge/discharge of LiFePO4 cathode , 2008 .

[16]  Wolfgang Dreyer,et al.  The behavior of a many-particle electrode in a lithium-ion battery , 2011 .

[17]  R. Compton,et al.  A review of the analysis of multiple nucleation with diffusion controlled growth , 2003 .

[18]  Robert W. Balluffi,et al.  Kinetics Of Materials , 2005 .

[19]  Oliver C. Ibe,et al.  Markov processes for stochastic modeling , 2008 .

[20]  Haoshen Zhou,et al.  Fast Li-Ion insertion into nanosized LiMn(2)O(4) without domain boundaries. , 2010, ACS nano.

[21]  Stéphanie Belin,et al.  An Electrochemical Cell for Operando Study of Lithium Batteries Using Synchrotron Radiation , 2010 .

[22]  M. Avrami.  Kinetics of Phase Change. I General Theory , 1939 .

[23]  A. Milchev.  Electrochemical nucleation on active sites—what do we measure in reality? Part II , 1998 .

[24]  E. F. Rauch,et al.  Confirmation of the domino-cascade model by lifepo4/fepo 4 precession electron diffraction , 2011 .

[25]  M. Avrami.  Kinetics of Phase Change. II Transformation‐Time Relations for Random Distribution of Nuclei , 1940 .

[26]  Bastien Chopard,et al.  Cellular Automata Modeling of Physical Systems , 1999, Encyclopedia of Complexity and Systems Science.

[27]  Charles Delacourt,et al.  Study of the LiFePO4/FePO4 Two-Phase System by High-Resolution Electron Energy Loss Spectroscopy , 2006 .

[28]  N. Sharma,et al.  Direct evidence of concurrent solid-solution and two-phase reactions and the nonequilibrium structural evolution of LiFePO4. , 2012, Journal of the American Chemical Society.

[29]  Gernot Kostorz,et al.  Phase Transformations in Materials , 2001 .

[30]  C. Delmas,et al.  Lithium deintercalation in LiFePO4 nanoparticles via a domino-cascade model. , 2008, Nature materials.

[31]  Wei Lai,et al.  Electrochemical modeling of single particle intercalation battery materials with different thermodynamics , 2011 .

[32]  S. Fletcher.  Nucleation on active sites: Part III. Nucleation modelled as a pure birth process and nucleation modelled as a birth-and-death process , 1986 .

[33]  Steven Dargaville,et al.  Predicting Active Material Utilization in LiFePO4 Electrodes Using a Multiscale Mathematical Model , 2010 .

[34]  Xiao‐Qing Yang,et al.  Investigation of the structural changes in Li1−xFePO4 upon charging by synchrotron radiation techniques , 2011 .

[35]  K. S. Nanjundaswamy,et al.  Phospho‐olivines as Positive‐Electrode Materials for Rechargeable Lithium Batteries , 1997 .

[36]  H. Jang,et al.  Rate performance and structural change of Cr-doped LiFePO4/C during cycling , 2008 .

[37]  J. Newman,et al.  Porous‐electrode theory with battery applications , 1975 .

[38]  Rahul Malik,et al.  Kinetics of non-equilibrium lithium incorporation in LiFePO4. , 2011, Nature materials.

[39]  Yuki Yamada,et al.  Kinetics of Nucleation and Growth in Two-Phase Electrochemical Reaction of LixFePO4 , 2012 .

[40]  Some new insights into the old Avrami’s equation , 1992 .

[41]  Jeff Wolfenstine,et al.  Kinetic Study of the Electrochemical FePO 4 to LiFePO 4 Phase Transition , 2007 .

[42]  Lin Gu,et al.  Direct observation of lithium staging in partially delithiated LiFePO4 at atomic resolution. , 2011, Journal of the American Chemical Society.

[43]  Yadong Li,et al.  Solvothermal synthesis of lithium iron phosphate nanoplates , 2011 .

[44]  Ho Jang,et al.  Asymmetry between charge and discharge during high rate cycling in LiFePO4 – In Situ X-ray diffraction study , 2008 .

[45]  Martin Z. Bazant,et al.  Nonequilibrium Thermodynamics of Porous Electrodes , 2012, 1204.2934.

[46]  Ruhul Amin,et al.  Phase boundary propagation in large LiFePO4 single crystals on delithiation. , 2012, Journal of the American Chemical Society.

[47]  Dane Morgan,et al.  Li Conductivity in Li x MPO 4 ( M = Mn , Fe , Co , Ni ) Olivine Materials , 2004 .