Galvanostatic Intermittent Titration Technique for Phase-Transformation ElectrodesYujie Zhu and Chunsheng Wang*Department of Chemical & Biomolecular Engineering, UniVersity of Maryland, College Park, Maryland 20742ReceiVed: NoVember 29, 2009A novel galvanostatic intermittent titration technique (GITT) and a novel potentiostatic intermittent titrationtechnique (PITT) for phase-transformation electrodes were developed by integrating mixed control phase-transformation theory with traditional GITT and PITT methods. The contribution of the strain accommodationenergy to the thermodynamic driving force for phase transformation was assessed. These novel GITT andPITT methods can be used to determine the true ion diffusion coefficient and the interface mobility of phase-transformation electrodes in the two-phase region. To demonstrate the utility of this method, the lithium iondiffusion coefficient and the interface mobility of two LiFePO4samples with different particle sizes wereobtained in the two-phase region. The lithium ion diffusion coefficient in the two-phase region as measuredusing phase-transformation GITT was on the order of 10-13cm2/s in the β phase (Li1-yFePO4) and 10-12cm2/s in the R phase (LixFeO4), which is similar to the diffusion coefficients in the single β and single Rphase regions determined using traditional GITT and PITT. This similarity with the diffusion-coefficient-validated phase-transformation GITT and PITT is expected since traditional GITT/PITT is reliable in thesingle-phase region. The interface mobility of the LiFePO4(about 10-15m mol/J s) increases with decreasingparticle size. The interface mobility of the LiFePO4/FePO4during electrochemical discharge at room temperatureis comparable to that of the martensite-austenite transformation in an Fe-C alloy with a semicoherenceinterface at 350 °C.1. IntroductionRechargeable lithium ion (Li ion) batteries are currently beingused to power an increasingly diverse range of commercialproducts and have been recognized as a critical enablingtechnology for electric vehicles/hybrid electric vehicles (EV/HEV)1and renewable energy storage. Phase-transformationmaterials (such as LiFePO4and Li4Ti5O12) are the mostpromising electrode materials for high-power Li ion batteriesdue to their fast reaction kinetics, safety, low cost, and longlife. The high power density of the carbon-coated nano-LiFePO4electrode is attributed to (i) improved electronic conductivitythrough carbon coating2and supervalent cation doping,3(ii) ashortened ion/electron-transport path through the use of nano-sized materials,4,5and (iii) rapid phase transformation from acoherent or semicoherent interface between Li1-yFePO4andLixFePO4due to a narrow miscibility gap in nanoscaleLiFePO4.6-8However, how the crystal structure, defects, andparticle size affect the diffusion coefficient of lithium ions andthe interface mobility of phase-transformation electrodes is stillnot fully understood6,9-11due to the lack of reliable electroana-lytical techniques for measuring lithium ion transport in phase-transformation materials. All current electroanalytical methods,such as galvanostatic intermittent titration technique (GITT),12potentiostatic intermittent titration technique (PITT),12electro-chemical impedance spectroscopy (EIS),13and cyclic voltam-metry (CV),14can only be used to analyze ion transport in solidsolution electrodes since they all rely on Fick’s law of diffusionwithout considering the effect of interphase boundary movementon ion transport.Using the traditional GITT method, the electrode system issubjected to a small constant current, and potential changes aremeasured as a function of time. Assuming one-dimensionaldiffusion in a solid solution electrode without consideration ofohmic potential drop, double-layer charging, charge-transferkinetics, and phase transformation, the ion diffusion coefficientcan be calculated using Fick’s law through the followingequation12where L (cm) is the characteristic length of electrode materials,F (C/mol) is the Faraday constant, zAis the charge number ofelectroactive species (for a Li ion battery, zA) 1), S (cm2)isthe contact area between the electrode and electrolyte, I (A) isthe applied current, and VM(cm3/mol) is the molar volume ofthe electrode material. The value of dE(t)/dt1/2can be obtainedfrom a plot of the voltage versus the square root of the timeduring constant current pulse, and dE(x)/dx can be measuredby plotting the equilibrium electrode voltage against theelectroactive material composition after each current pulse.Instead of a current pulse as in GITT, a small voltage step isapplied to the system under the PITT method, and the resultingcurrent is measured as a function of time. The diffusioncoefficient of ions in solid solution electrodes can be estimatedbased on Fick’s law using the following equation with the sameassumptions as those made for GITT12* To whom correspondence should be addressed. Tel.: 301-405-0352.Fax: (301)314-9126. E-mail: [email protected])4π(IVMzAFS)[(dE(x)/dx)(dE(t)/d√t)]2(t , L2/DGITT)(1)DPITT)-dlnI(t)dt4L2π2(t . L2/DPITT) (2)J. Phys. Chem. C 2010, 114, 2830–2841283010.1021/jp9113333  2010 American Chemical SocietyPublished on Web 01/22/2010where L (cm) is the characteristic length of the electrode materialand I(t) (A) is the current measured during the constant voltagestep.Since both GITT and PITT are based on the same assumptionof Fick’s law, they are not reliable methods for measuring theion diffusion coefficient in the two-phase region of phase-transformation materials. In the two-phase region, ions aretransported through both movement of an interphase boundaryand ionic diffusion. Using traditional electroanalytical tech-niques, only an apparent diffusion coefficient,15-18rather thanthe true diffusion coefficient, can be obtained in the two-phaseregion, which resulted in considerable controversy.16,19-25Moreover, the apparent Li ion diffusion coefficients of LiFePO4in the two-phase region measured using GITT,19PITT,20andEIS20were 2-3 orders of magnitude lower than those in thesingle-phase region. A reduced apparent diffusion coefficientin the two-phase region was also reported in Li4Ti5O12thin filmsmeasured using traditional PITT and EIS methods.21Since theLi ion diffusion coefficient in the single-phase region measuredusing traditional GITT and PITT is reliable, the significantreduction of the apparent diffusion coefficient in the two-phaseregion should be