Electronic structures of LiFePO4 and related materials - Wake Forest ...

Electronic structures ofLiFePO 4 and related materials aNatalie HolzwarthWake Forest University, Winston-Salem, NC, USA• Introduction and motivation• Calculational methods• Electronic structure results• Summary and Conclusionsa Ph. D. thesis work of Ping Tang, with help from YaojunDu and Xiao Xu. Supported by NSF grants DMR-0405456 andDMR-0427055.1

Performance comparison of different rechargeable AA-size (or equivalent)batteries at 20 o C. (Figure from Interface 15:1, 18 (2006).)2

Diagram of discharge operation for a Li-ionbatteryLi +− +Cathode Electrolyte Anodee −V = IRI3

CathodesLiCoO 2LiMn 2 O 4LiFePO 4Some battery materialsElectrolytesLiPF 6 (liquid)PEO & other polymersLiPON ( Li 3 PO 4 glass)AnodesLi metalLiAl alloyLiC 64

J. Electrochem. Soc. 144 1188, (1997)5

Accumulated number of papers on LiFePO 4(Estimated from the number of citations of the original articles:“Phospho-olivines as positive-electrode materials for rechargeable lithium batteries”, A. K.Padhi, K. S. Nanjundaswamy, and J. B. Goodenough, JECS 144 1188, (1997); “Effect ofstructure on the Fe 3+ /Fe 2+ redox couple in iron phosphates”, A. K. Padhi, K. S.Nanjundaswamy, C. Masquelier, S. Okada, and J. B. Goodenough, JECS 144 1609, (1997)400Accumulated citations300200100019982000year2002200420066

Commercial use of LiFePO 4 ???(pure speculation)In 2001, Professor Yet-Ming Chiang, Department of Materials Science andEngineering, M. I. T. co-founded A123Systems, a startup company involved withdeveloping, manufacturing, and marketing batteries based on lithium metalphosphate. (http://www.a123systems.com)Watertown, Mass. November 2,2005:A123Systems, developer of a new generationof Lithium-ion batteries, today unveiledits technology and announced thatit is delivering batteries with unprecedentedpower, safety, and life as comparedto conventional Lithium technology.A123Systems first battery is now in productionand being delivered to the Black& Decker Corporation (NYSE: BDK). Itwill be first utilized by the corporation’sDEWALT brand, a leading manufacturerof power tools.7

What can computer simulations do to advanceour understanding of LiFePO 4 materials?The role of computation in electrochemical research is not as prominent as it isin the semiconductor and catalysis fields. Our work was inspired by a talk givenby Professor Gerbrand Ceder of M. I. T. given at the Fourteenth AnnualWorkshop on Recent Developments in Electronic Structure Methods – ES2002 inwhich he summarized his pioneering work on the cathode materials LiCoO 2 ,LiNiO 2 , and LiMn 2 O 4 . (More recently, Ceder and his group have made majoradvances in the understanding of the LiFePO 4 family as well.)Outline of our work• Introduction to the general features of the electronic structures of theelectrochemically active forms of LiFePO 4 and FePO 4 .• Comparison of the electrochemically active form of FePO 4 with 3 othermeta-stable crystalline structures.• Beginning work on Li-ion diffusion mechanisms in Li 3 PO 4 .8

Calculational methodsMethodPAWpwpaw - pwpaw.wfu.edusocorro - dft.sandia.gov/socorroabinit - www.abinit.orgLAPWwien2k - www.wien2k.atPWscfpwscf - www.pwscf.orgCommentsWorks well for moderately large unit cells,but variable unit cell optimization not yet implementedin pwpaw and socorro. Need toconstruct and test PAW basis and projectorfunctions.Works well for smaller unit cells; variable unitcell optimization not implemented. Need tochoose non-overlapping muffin tin radii andavoid “ghost” solutions.Works well for large unit cells and includesvariable unit cell optimization. Need to constructand test soft pseudopotential functions.9

Secret recipe of calculational parametersr c (bohr)Atomic basisFePAW ∗ 1.90 3s, 4s, 3p, 4p, 3d, ɛdPWscf † 1.90 3s, 4s, 3p, 4p, 3d, ɛdLAPW 1.95 3s, ɛs, 3p, ɛp, ɛdOPAW ∗ 1.41 2s, ɛs, 2p, ɛpPWscf † 1.40 2s, ɛs, 2p, ɛpLAPW 1.28 2s, ɛs, ɛpPPAW ∗ 1.51 2s, 3s, 2p, 3pPWscf † 1.50 3s, ɛs, 3p, ɛp, ɛdLAPW 1.38 ɛs, 2p, ɛp∗ PAW basis and projector functions generated by atompaw code.† Ultra-soft pseudopotentials generated by uspp code of David Vanderbilt.10

Details on constructing the PAW basis and projector functionsFor each all-electron basis function φ i (r), we need to construct corresponding pseudo-basisfunctions ˜φ i (r) and projector functions ˜p i (r). Two slightly different variations:• Blöchl’s scheme (PR B 50, 17953 (1994)): choose shape of ˜p i (r) and derive ˜φ i (r).• Vanderbilt’s scheme (PR B 41, 7892 (1990)): choose shape of ˜φ i (r) and derive ˜p i (r).Example for 3d functions of Fe:30.152.52p(r)~Bloechl schemeVanderbilt scheme0.1Bloechl schemeVanderbilt scheme1.5F(q)1φ(r)0.050.5~φ(r)00 0.5 1r (bohr)1.5 200 2 4 6q (bohr) -1Basis and projector functions F (q) ≡ ¯˜p(q)¯˜φ(q)q211

Other computational details• Spin polarized calculations performed assuming full crystal symmetry(“ferromagnetic” spin configuration).• Exchange-correlation functionals –LDA: J. Perdew and Y. Wang, Phys. Rev. B 45, 13244 (1992)GGA: J. Perdew, K. Burke, and M. Ernzerhof, PRL 77, 3865 (1996)12

Test results for simple oxides∆E (eV)0.50.40.3GGAPWscfPAWLAPWLi 2OLDAPWscfPAWLAPW∆E (eV)0.50.40.3FeOGGAPWscfPAWLAPWLDAPWscfPAWLAPW∆E (eV)1.210.80.6GGAPWscfPAWLAPWPO 4LDAPWscfPAWLAPW0.20.20.40.10.10.208 8.5 9 9.5a (bohr)07.5 7.75 8 8.25 8.5 8.75a (bohr)02.8 2.9 3 3.1b (bohr)Fluorite structure NaCl structure Tetrahedral moleculeNote: This kind of consistency is generally not possible withparameters taken “off the shelf”.13

Introduction to general features of the electronicstructures of the electrochemically active forms ofLiFePO 4 and FePO 4Ref: “Electronic structures of FePO4, LiFePO4, and related materials”, Ping Tangand N. A. W. Holzwarth, Phys. Rev. B 68, 165107 (2003)14

FePO 4 and LiFePO 4in olivine (Pnma) structureFePO 4 LiFePO 415

LSDA partial densities of states for olivine materials42FePO 4N(E) (states/(eV. spin . sphere))02442024LiFePO 4LiFePO-10 -5 0 5 10E (eV)16

Partial densities for majority spin FePO 4states4 I II III FeP2O0-10 -5 0 5E (eV)I: −9.9 ≤ E ≤ −6.2 eV II: −6.2 ≤ E ≤ −2.3 eV III: −2.3 ≤ E ≤ −0.1 eV17

Partial densities for majority spin LiFePO 4states4 I II III LiFe2PO0-10 -5 0 5E (eV)I: −11.1 ≤ E ≤ −7.7 eV II: −7.7 ≤ E ≤ −3.4 eV III: −3.3 ≤ E ≤ −1.2 eV18

Summary of results for FePO 4 and LiFePO 4FePO 4 – Fe +3 ⇐⇒ Fe 3d 5 ↑ ; strong hybridization of Fe 3d ↑ and O2p ↑ bandsLiFePO 4 – Fe +2 ⇐⇒ Fe 3d 5 ↑ d1 ↓; Fe 3d states form narrow bandswith very little O 2p character19

Comparison of the electrochemically active formof FePO 4 with 3 other crystalline structuresSummary of experimental situation:• FePO 4 in its “olivine” structure is the delithiated product of LiFePO 4 ,known as a promising cathode material for rechargeable Li ion batteries.(Padhi,Nanjundaswamy, Goodenough, J. Electrochem. Soc. 144, 1188(1997))• Yang, Song, Zavalij, and Whittingham (Electrochem. Comm. 4, 239 (2002))showed that olivine FePO 4 irreversibly transforms to a quartz-like structureat ≈ 600 o C.• Song, Zavalij, Suzuki, and Whittingham (Inorg. Chem. 41, 5778 (2002))investigated the structural and electrochemical properties of severalcrystalline forms of FePO 4 .• Iyer, Delacourt, Masquelier, Tarascon, and Navrotsky (Electrochem.Solid-State Lett. 9, A46 (2006)) showed that that the olivine structure ismore stable than the quartz structure.20

Computational challenge1. Can we reliably predict the most stable structure?2. If so:(a) Can we understand what factors control thestructural stability?(b) Can we understand what factors control theelectrochemical activity? can we understandwhat determines its structural stability?21

Crystal structures“Olivine”Space group: PnmaMineral names: olivine, heterositeProperties: Li ion cathode (LiFePO 4 )“Quartz”Space group: P3 1 21Mineral names: α-quartz, berliniteProperties: Catalyst, electrochemically inactiveForms at 600 o C from olivine phase22

Crystal structures – continued“CrVO 4 -type”Space group: CmcmSynthesized at high pressure from quartz formProperties: Electrochemically inactiveArroyo-de Dompablo, Gallardo-Amores, Amador,Electrochem. Solid-State Lett. 8, A564 (2005)“Monoclinic”Space group: P2 1 /nSynthesized by dehydrating phosphosideriteProperties: Partial electrochemical activitySong, Zavalij, Suzuki, Whittingham,Inorg. Chem. 41, 5778, 200223

Crystal volumes – optimized and experimental(in units of Å 3 /FePO 4 )Crystal LDA GGA ExpOlivine 67.9(LAPW) 67.5 74.5(PAW) 74.5(PWscf) 68.1 74.0Quartz 82.4(LAPW) 79.9 91.9(PAW) 91.9(PWscf) 79.8 91.3CrVO 4 -type 64.2(LAPW) 62.3(PWscf) 62.8 68.6Monoclinic 82.1(LAPW) 81.3 91.4(PWscf) 81.9 88.424

Internal Energy Differences(in units of eV/FePO 4 )Crystal LDA GGA ExpOlivine 0.00 0.00 0.00Quartz0.12 ∗(LAPW) 0.09 −0.35(PAW) 0.05 −0.27(PWscf) 0.09 −0.25CrVO 4 -type(LAPW) −0.10(PAW) −0.11 0.07(PWscf) −0.07 0.07Monoclinic(LAPW) 0.02 −0.19(PAW) −0.01 −0.16(PWscf) −0.02 −0.17∗ Iyer, Delacourt, Masquelier, Tarascon, and Navrotsky,Electrochemical and Solid-State Letters 9, A46 (2006).25

LDSA partial densities of states for FePO 44Olivine4Monoclinic22N(E) (states/(eV . spin . sphere))002244Quartz44CrVO 4FePO22002244-8 -6 -4 -2 0 2 4 6 8E (eV)-8 -6 -4 -2 0 2 4 6 8E (eV)26

LSDA band gaps and widths for FePO 4 crystals(Band widths refer to Fe 3d majority spin states)Crystal Band gap (eV) Band width (eV)Olivine 0.1 8.1Quartz 0.8 5.2CrVO 4 -type 0.0 8.9Monoclinic 0.4 6.027

Results so far for FePO 41. Can we reliably predict the most stable structure? no2. If not, what is missing from our simulations?(a) We suspect the electron self-interaction error to be the mostimportant contribution, especially for the very localized Fe 3dstates.(b) Possibly, electron correlation effects could also be significant.28

Li-ion diffusion mechanisms in electrolyte material Li 3 PO 4LiFePO 4 γ-Li 3 PO 4(cathode)(electrolyte)29

Li + diffusion by possible interstitial mechanism in γ- Li 3 PO 4Relaxed structures about two meta-stable interstitial sites. (Arrows indicatemagnitude and direction of distortion relative to perfect crystal. Darker greenball indicates interstitial position.)Site 1 Site 230

Li + diffusion by possible vacancy mechanism in γ- Li 3 PO 4Relaxed structures about two meta-stable vacancy sites. (Arrows indicatemagnitude and direction of distortion relative to perfect crystal, scaled by 2×relative to interstitial case. Light green ball indicates vacancy position.)Site 1 Site 231

Results so far for Li-ion diffusion mechanisms in γ-Li 3 PO 4• Found several meta-stable interstitial and vacancy configurations.• Currently investigating the barriers for diffusion between thesesites along several likely paths.32

Summary• With careful attention to calculational details, we are able to obtain nearlyidentical results using independent software packages.• Investigated general features of the electronic structures of theelectrochemically active forms of LiFePO 4 and FePO 4 .• Compared of the electrochemically active form of FePO 4 with 3 othermeta-stable crystalline structures. Need to estimate electron self-interactionerror.• Currently studying Li-ion diffusion mechanisms in the electrolyte materialLi 3 PO 4 .33

Collaborators:Ph. D. Thesis: Ping TangPostdoc: Yaojun DuAcknowledgmentsBeginning Grad. Student: Xiao XuFunding:• NSF DMR-0405456• NSF DMR-0427055Graphics software:• XCrySDen (http://www.xcrysden.org), written by Anton Kokalj• dx (http://www.opendx.org) (based on Data Explorer, a general purposevisualization package originally developed at IBM.)34