Abstract
When two materials interact, the processes between the phases determine the functional properties of the compound. Pivotal interface phenomena are diffusion and redistribution of atoms (molecules). This is especially of interest in Lithium ion batteries where the interfacial kinetics determines the battery performance and impact cycling stability. A new phase field model, which links the atomistic processes at the interface to the mesoscale transport by a redistribution flux controlled by the so called ’interface permeability’ was developed. The model was validated with experimental data from diffusion couples. Calculations of the concentration profiles of the species at the electrode-electrolyte interface are reported. Active particle size, morphology and spatial arrangement were put in correlation with diffusion behavior for use in reverse engineering.
Similar content being viewed by others
References
M.S. Whittingham: Electrical energy storage and intercalation chemistry. Science 192, 1126–1127 (1976).
W.J. Boettinger, J.A. Warren, C. Beckermann, and A. Karma: Phase field simulation of solidification. Ann. Rev. Mater. Res. 32, 163–194 (2002).
L.-Q. Chen: Phase field models for microstructure evolution. Ann. Rev. Mater. Res. 32, 113–140 (2002).
S.L Wang, R.F. Sekerka, A.A. Wheeler, B.T. Murray, S.R. Coriell, R. J. Braun, and G.B. McFadden: Thermodynamically consistent phase field models for solidification. Physica D: Nonlinear Phenomena 69, 189–200 (1993).
I. Steinbach: Phase-field models in materials science. Model. Simul. Mater. Sci. Eng. 17, 073001 (2009).
V.I. Levitas and A.M. Roy: Multiphase phase field theory for temperature-and stress induced phase transformations. Phys. Rev. B 91, 174109 (2015).
K. Momeni and V.I. Levitas: A phase-field approach to nonequilibrium phase transformations in elastic solids via an intermediate phase (melt) allowing for interface stresses. Phys. Chem. Chem. Phys. 18, 12183–12203 (2016).
C. Denouai and A. Vattré: A phase field approach with a reaction pathways-based potential to model reconstructive martensitic transformations with a large number of variants. J. Mech. Phys. Solids 90, 91–107 (2016).
V.I. Levitas and K. Samani: Size and mechanics effects in surface-induced melting of nanoparticles. Nat. Commun. 2, 284 (2011).
K. Momeni, VI. Levitas, and J.A. Warren: The strong influence of internal stresses on the nucleation of a nanosized, deeply undercooled melt at a solid-solid phase interface. Nano Lett. 15, 2298–2303 (2015).
L.-Q. Chen and W. Yang: Computer simulation of the domain dynamics of quenched system with a large number of nonconserved order parameters: the grain-growth kinetics. Phys. Rev. B 50, 15752 (1994).
E. Miyoshia and T. Takaki: Validation of a novel higher-order multi-phase-field model for grain-growth simulations using anisotropic grain-boundary properties. Comput. Mater. Sci. 112, 44–51 (2016).
L. Chen and S. Hu: Solute segregation and coherent nucleation and growth near a dislocation: a phase-field model integrating defect and phase microstructures. Acta Mater. 49, 463–472 (2001).
D. Rodney, Y. Le Bouar, and A. Finel: Phase field methods and dislocations. Acta Mater. 51, 17–30 (2003).
L. Wang, Z. Liu and Z. Zhuang: Developing micro-scale crystal plasticity model based on phase field theory for modeling dislocations in heteroe-pitaxial structures. Int. J. Plasticity 81, 267–283 (2016).
Y. Jin, Y. Wang, and A. Khachaturyan: Three-dimensional phase field microelasticity theory and modelling of multiple cracks and voids. Appl. Phys. Lett. 79, 3071 (2001).
H. Levine and H. Henry: Dynamic instabilities of fracture under biaxial strain using a phase field model. Phys. Rev. Lett. 93, 105504 (2004).
B. Pattern, A. Kazaryan, and Y. Wang: Generalized phase field approach for computer simulation of sintering: incorporation of rigid-body motion. Scripta Mater. 41, 487–492 (1999).
X.N. Jing, J.H. Zhao, G. Subhash, and X.L. Gao: Anisotropic grain growth with pore drag under applied loads. Mater. Sci. Eng. A 412, 271–278 (2005).
Y. Wang: Computer modeling and simulation of solid-state sintering: a phase field approach. Acta Mater. 54, 953–961 (2006).
Q. Du, C. Liu, and X. Wang: Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions. J. Comput. Phys. 212, 757–777 (2006).
T. Biben, K. Kassner, and C. Misbah: Phase-field approach to three dimensional vesicle dynamics. Phys. Rev. Ell, 041921 (2005).
J. Guyer, W. Boettinger, J. Warren, and G. McFadden: Phase field modeling of electrochemistry I: equilibrium. Phys. Rev. E 69, 021603 (2004).
J. Guyer, W. Boettinger, J. Warren, and G. McFadden: Phase field modeling of electrochemistry II: kinetics. Phys. Rev. E 69, 021604 (2004).
W. Pongsaksawad, A.C. Powell, and D. Dussault: Phase-field modeling of transport-limited electrolysis in solid and liquid states. J. Electrochem. Soc. 154, F122 (2007).
Y. Shibuta, Y. Okajima, and T. Suzuki: Phase field modeling for electrode-position process. Sci. Technol. Adv. Mater. 8, 511–518 (2007).
I. Steinbach, L. Zhang, and M. Plapp: Phase-field model with finite interface dissipation. Acta Mater. 60, 2689–2701 (2012).
L Zhang and I. Steinbach: Phase-field model with finite interface dissipation: extension to multi-component multi-phase alloys. Acta Mater. Elsevier Ltd. 60, 2702–2710 (2012).
U. Preiss, E. Borukhovich, N. Alemayehu, and I. Steinbach: A permeation model for the electrochemical interface. Model. Simul. Mater. Sci. Eng. 21, 4006 (2013).
I. Steinbach and M. Apel: Phase-field simulation of rapid crystallization of silicon on substrate. Mater. Sci. Eng. A, Elsevier Sci. SA, Lausanne 449, 95–98 (2007).
I. Steinbach: Phase field model for microstructure evolution at the mesoscopic scale. Ann. Rev. Mater. Res. 43, 89–107 (2013).
J. Tiaden, B. Nestler, H.J. Diepers, and I. Steinbach: The multiphase-field model with an integrated concept for modelling solute diffusion. Physica D: Nonlinear Phenomena 115, 73–86 (1998).
I. Steinbach, F. Pezzolla, B. Nestler, M. Seesselberg, R. Prieler, G.J. Schmitz, and J.L.L. Rezende: A phase field concept for multiphase systems. Physica D: Nonlinear Phenomena 94, 135–147 (1996).
I. Steinbach and F. Pezzolla: A generalized field method for multiphase transformations using interface fields. Physica D: Nonlinear Phenomenal, 385–393 (1999).
I. Steinbach, B. Boetinger, J. Eiken, N. Warnken, and S.G. Fries: CALPHAD and phase-field modeling: a successful Liaison. J. Phase Equilibria Diff. 28, 101–106 (2007).
J. Eiken, B. Boetiger, and I. Steinbach: Multiphase-field approach for mul-ticomponent alloys with extrapolation scheme for numerical application. Phys. Rev. £73, 066122 (2006).
W.J. Boettinger and J.A. Warren: Simulation of the cell to plane front transition during directional solidification at high velocity. J. Cryst. Growth 200, 583–591 (1999).
J.W. Gahn and J.C. Baker: Solute trapping by rapid solidification. Acta. Metall. 17, 575 (1969).
J.A. Kittl, P.G. Sanders, M.J. Aziz, D.P. Brunco, and M.O. Thompson: Complete experimental test for kinetic models of rapid alloy solidification. Acta Mater. 48, 4797 (2000).
C.-W. Wang and A.M. Sastry: Mesoscale modeling of a Li-ion polymer cell. J. Electrochem. Soc. 154, A1035–A1047 (2007).
G.K. Singh, G. Ceder, and M.Z. Bazant: Intercalation dynamics in rechargeable battery materials: General theory and phase transformation in LiFePO4. Electrochim. Acta S3, 7599–7613 (2008).
M.Z. Bazant: Theory of chemical kinetics and charge transfer based on nonequilibrium thermodynamics. Acc. Chem. Res. 46, 1144–1160 (2013).
V. Noel and M. Rajendran: A comprehensive model for cyclic voltammetric study of intercalation/de-intercalation. J. Power Sources 88, 243–249 (2000).
S. Flandrois: Graphite intercalation compounds as electrode materials in batteries. Synth. Met. 4, 255 (1982).
J.R. Macdonald: Impedance spectroscopy. Ann. Biomed. Eng. 20, 289–305 (1992).
S.M. Park and J.S. Yoo: Electrochemical impedance spectroscopy for better electro-chemical measurements. Anal. Chem. 75, 455A–461A (2003).
A. Lasia: Electrochemical impedance spectroscopy and its applications. Modern Asp. Electrochem. 32, 143–248 (1999).
C. Wang and J. Hong: Ionic/electronic conducting characteristics of LiFePO4 cathode materials. Electrochem. Solid-State Lett. 10, A65–A69 (2007).
W. Vielstich, C.H. Hamann, and A. Hamnett: Electrochemistry (Wiley-VCH, Weinheim, 2007).
Y. Zhu and C. Wang: Novel CV for phase transformation electrodes. J. Phys. Chem. C 115, 823–832 (2011).
E. Katz and I. Willner: Probing biomolecular interactions at conductive and semi-conductive surfaces by impedance spectroscopy: routes to impedimetric immunosensors, DNA-sensors, and enzyme biosensors. Electroanalysis 15, 913–947 (2003).
P. Paolo, M. Lisi, D. Zane and M. Pasquali: Determination of the chemical diffusion coefficient of lithium in LiFePO4. Solid State Ionics 148, 45–51 (2002).
S. Wang, Q. Wang, J. Liu, Z. Cheng, D. Si, and B. Geng: Kinetic manipulation of the morphology evolution of FePO4 microcrystals: from rugbies to porous microspheres. Cryst. Eng. Commun. 11, 2510 (2009).
B.L. Ellis, W.R. Michael Makahnouk, W.N. Rowan-Weetaluktuk, D.H. Ryan, and L.F. Nazar: Crystal structure and electrochemical properties of A2MPO4F fluorophosphates (A=Na, Li; M=Fe, Mn, Co, Ni). Chem. Mater. 22, 1059–1070 (2010).
B.L. Ellis, K.T. Lee, and L.F. Nazar: Positive electrode materials for Li-ion and Li-batteries. Chem. Mater. 22, 691–714 (2010).
R. Malik, D. Burch, M. Bazant, and G. Ceder: Particle size dependence of the ionic diffusivity. Nano Lett. 10, 4123–4127 (2010).
N.N. Sinha and N. Munichandraiah: The effect of particle size on performance of cathode materials of Li-ion batteries. J. Indian Inst. Sci. 89, 381–392 (2009).
K.T. Lee and J. Cho: Roles of nanosize in lithium reactive nanomaterials for lithium ion batteries. Nano Todays, 28–41 (2011).
K. Kai, Y. Kobayashi, H. Miyashiro, G. Oyama, S. Nishimura, M. Okubo, and A. Yamada: Particle-size effects on the entropy behavior of a LixFePO4 electrode. Chem. Phys Chem 15, 2156–2161 (2014).
W. Dua, A. Gupta, X. Zhang, A.M. Sastry, and W. Shyy: Effect of cycling rate, particle size and transport properties on lithium-ion cathode performance. Int. J. Heat Mass Transf. 53, 3552–3561 (2010).
I. Bloom, B.W. Cole, J.J. Sohn, S.A. Jones, E.G. Polzin, V.S. Battaglia, G.L. Henriksen, C. Motloch, R. Richardson, T. Unkelhaeuser, D. Ingersoll, and H.L. Case: An accelerated calendar and cycle life study of Li-ion cells. J. Power Sources 101, 238–247 (2001).
P. Ramadass, B. Haran, R. White, and B.N. Popov: Mathematical modeling of the capacity fades of Li-ion cells. J. Power Sources 123, 230–240 (2003).
R.P. Ramasamy, R.E. White, and B.N. Popov: Calendar life performance of pouch lithium-ion cells. J. Power Sources 141, 298–306 (2005).
D.P. Abraham, J. Liu, C.H. Chen, Y.E. Hyung, M. Stall, N. Elsen, S. MacLaren, R. Twesten, R. Haasch, E. Sammann, I. Petrov, K. Amine, and G. Henriksen: Diagnosis of power fade mechanisms in high-power lithium-ion cells. J. Power Sources 119, 511–516 (2003).
Acknowledgments
The authors like to thank Dr. Ulrich Preiss for contributing to the model development and for useful discussions. We acknowledge financial support through the International Max Planck Institute for Surface and Interface Engineering of Materials (IMPRS-SurMat) and ICAMS and Addis Ababa University for supporting the preparation of this manuscript.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zerihun, N.A., Steinbach, I. Phase field modeling of intercalation kinetics: a finite interface dissipation approach. MRS Communications 6, 270–282 (2016). https://doi.org/10.1557/mrc.2016.31
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1557/mrc.2016.31