Solid State Ionics 112 (1998) 255–259

First-principles prediction of voltages of lithiated oxides forlithium-ion batteries

a , a 1 ,a a b*´L’ubomır Benco , Jean-Luc Barras , Michail Atanasov , Claude A. Daul , Erich Deissa ´Institute of Inorganic Chemistry, University of Fribourg, Perolles, CH-1700, Fribourg, Switzerland

bDepartment of General Energy Research, Paul Scherrer Institute, CH-5232 Villigen, Switzerland

Received 7 July 1998; accepted 20 July 1998

Abstract

The average intercalation voltages (AIV) of cathode materials for rechargeable lithium-ion batteries are calculated fromfirst principles using the LAPW method for both trigonal layered (LiMO ) and cubic spinel (LiM O ) structures. All2 2 4

calculated AIV are in good agreement with corresponding plateaus of measured open circuit voltages. It is shown that theAIV is directly related to the change of bonding occurring upon the intercalation of lithium. With increasing atomic numberof the transition metal up to Co the increase of the AIV is caused by the increase in Li–O stabilizing interaction, which inturn is induced by increasing covalency of M–O bonding. The AIV is demonstrated not to depend on the structure but onlyon the oxidation state of the transition metal. 1998 Elsevier Science B.V. All rights reserved.

Keywords: Li-ion batteries; Average voltage; Intercalation compounds; First-principles calculations; Enthalpies of formation

PACS: 71.20.T; 71.15.Nc; 71.15.Ap

Over the last two decades there has been consider- average intercalation voltage (AIV) for Li inserted inable development activity toward the lithium-ion various compounds [4–6]. The average voltage Ebattery technology based on the insertion of lithium can be calculated as the change of the Gibbs energy

Tinto structures of transition metal oxides (TMO). DG between products and reactants divided by theLithium-ion cells designed for repeated insertion and Faraday number F,extraction reactions at ambient temperatures yield TE 5 DG /F (1)inexpensive high energy density rechargeable bat-teries [1–3]. Recent applications of computational T

DG 5 DU 1 pDV2 TDS (2)chemistry tools have shown that methods based onfirst principles can provide good prediction of the

It was demonstrated by Deiss et al. [4] andAydinol et al. [5,6] that acceptable values of AIVs

*Corresponding author. Address for correspondence: Institute are obtained when both the volume ( p.DV ) and theT´ ´of Inorganic Chemistry, Slovak Academy of Sciences, Dubravska entropy (T.DS) components of the DG are neg-

cesta 9, SK-84236 Bratislava, Slovakia. Tel.: 1421 7 3782010;lected. This means that dominant part of the DG of aFax: 1421 7 373541; E-mail: benco@savba.sk

1 chemical reaction between solids originates from thePermanent address: Institute of General and Inorganic Chemistry,Bulgarian Academy of Sciences, B1.11, 1113 Sofia, Bulgaria. change in internal energy DU. In this communica-

0167-2738/98/$ – see front matter 1998 Elsevier Science B.V. All rights reserved.PI I : S0167-2738( 98 )00232-X

256 L. Benco et al. / Solid State Ionics 112 (1998) 255 –259

tion, we present a bond analysis which goes beyondprevious evaluations and considerably enhances ourunderstanding of chemical reactions in solids. Weshow the influence of both the structure and thetransition metal (TM) on bonding and final AIVs anddemonstrate the predictive power of our conclusionsfor compounds not yet synthesized. The analysis,focused on energy relations and their dependence onthe covalency/ ionicity of bonding, is presented fortwo reactions which are important in battery technol-ogy.

Charge DischargeLi 1 MO ↔ LiMO (trigonal) (3)2 2

Li 1 2MO ↔LiM O (spinel) (4)2 2 4

Using the first-principles all-electron full-potentialLAPW method [7] we performed geometry optimi-zation of cubic spinel (LiM O ) structures of three2 4

TM compounds (M5Ti, Mn, Co) and of layeredtrigonal (LiMO ) structures of two TM compounds2

(M5Ti, Mn) as well as of the corresponding de-lithiated structures. Computational details are givenin Ref. [8].

Subtracting energies of the free atoms from thetotal energies of the solid compounds we calculateenthalpies of formation (EOF) of reactants andproducts and AIVs of the chemical reaction. Weshow for the first time to our knowledge that the AIV

Fig. 1. Enthalpies of formation (EOF) of TMO structures,between two solids originates from the difference ofdifferences of the enthalpies of formation (DEOF), and energy

EOF between reactants and products. Based on the levels of free atoms. (a) The EOFs for spinel structures LiM O2 4interaction scheme obtained from the calculated (M5Ti, Mn, and Co); (b) the DEOFs for spinel and trigonal

structures (according to Eq. (5) and Eq. (6)); (c) 2s (Li), 2p(O),electronic structures [9], we show the trend ofand 4s (TM) and 3d (TM) atomic energy levels of the first rowchanges in EOFs and corresponding AIVs for theTMs.series of first row TM compounds (M5Ti, . . . Co)

within the two structure types.calculated AIVs are in good agreement with ex-Fig. 1a shows our calculated EOFs of Li extractedperimental values available for LiMnO , LiTi O(circles) and Li inserted (squares) TMO spinel struc- 2 2 4

and LiMn O . A spinel Co structure does not existtures, and Fig. 1b shows the difference of EOFs of 2 4

[15], but we used the calculated value thus obtainedthree spinel structuresto indicate the trend of EOFs within structures for

DEOF 5 EOF(LiM O ) 2 2EOF(MO ) (5)2 4 2 higher TMs. Similarly, the non-existing trigonalLiTiO structure is calculated to reveal the same(M5Ti, Mn, Co), as well as of two trigonal struc- 2

trend for trigonal structures. The dashed line in Fig.tures1b mimics for the trigonal structure the trend of the

DEOF 5 EOF(LiMO ) 2 EOF(MO ) (6)2 2 DEOF that was found in the case of the spinel(M5Ti, Mn). The comparison of calculated and structure and indicates the estimated value of theexperimental AIVs is presented in Table 1. The DEOF of trigonal LiCoO (dashed circle).2

L. Benco et al. / Solid State Ionics 112 (1998) 255 –259 257

Table 1Average intercalation voltages of trigonal LiMO and spinel LiM O (in V)2 2 4

Trigonal structures (layered) Cubic structures (spinels)

LiTiO LiMnO LiCoO LiTi O LiMn O LiCo O2 2 2 2 4 2 4 2 4

a bAIV 1.81 3.00 |3.9 2.90 3.78 4.70c dAIV 2.14 3.13 3.75 3.9

e,f g h iAIV (exp.) – 3.08 3.9 2.6–3.0 4.00 –a This work.b Estimated from Fig. 1b.c,d References [5] and [6].e–i Plateaus of potential curves from References [10–14].

Fig. 1a shows that the EOF of the Li inserted (upper) components. Note that in solids, the t band2g

structure is higher than that of the Li extracted TMO. is stabilised and the e band is destabilised asg

During discharge of the battery Li atoms therefore compared to the position of the d level for freespontaneously intercalate into the structure of the atoms. In the interaction schemes (Fig. 2), theTMO (cf. Eqs. (3) and (4)). The structures of higher splitting of atomic levels into bonding and antibond-TMs show a steady decrease of the EOF values of ing components is indicated by interaction lines. Allboth intercalated and deintercalated compounds rela- states of the p band are Ti-to-O bonding. But notetive to the Ti structures. Electronic arguments ex- that states of both d bands are Ti-to-O antibonding,plaining this phenomenon are displayed in terms of because they are higher in energy than the atomic Othe interaction schemes in Fig. 2. For the two 2p level. At this point we must stress that the patternschemes constructed for spinels TiO and LiTi O , of the bonding displayed in Fig. 2 for spinels (TiO2 2 4 2

the distribution of energy states in the solid is and LiTi O ) is retained also in the layered trigonal2 4

compared with energy levels of free atoms [9]. Both Ti structures as well as in compounds of the higherthe s and the p bands, which are completely filled in TMs [8].the two compounds, are shifted toward more nega- For TiO structures, electrons only occupy bond-2

tive energies, i.e. stabilized as compared to atomic s ing states. Hence, the EOF of all TiO structures is2

and p levels. The d bands, which are empty in TiO high. In TMOs of higher TMs, electrons also occupy2

and only slightly filled in LiTi O (cf. positions of antibonding states which causes a decrease of the2 4

the Fermi levels in the two compounds), are dis- EOFs. The EOFs of Li inserted Mn oxides aretinguished by symmetry into t (lower) and e decreased compared to Ti structures for the same2g g

reasons, i.e. filling of antibonding states. The de-crease of the EOFs of LiM O in Fig. 1a, however,2 4

is less steep than the decrease for the correspondingdelithiated MO structure, due to an additional2

stabilization of Li in the TMO structures. Theincreasing difference of EOFs of Li intercalated andLi extracted structures displayed in Fig. 1b is respon-sible for the increasing voltage of compounds withhigher TMs.

A question which still cannot be answered is, whythe highly ionic Li atoms are more strongly stabilisedin structures involving higher TMs, in spite of thefact, that the highest negative charge is located onthe O atoms in Ti structures? All compounds arecomposed of MO octahedral structural units and6

Fig. 2. Interaction schemes of TiO and LiTi O . retain the same bonding pattern as shown in Fig. 2.2 2 4

258 L. Benco et al. / Solid State Ionics 112 (1998) 255 –259

In order to understand different features of bonding tion of Li is the downward shift of the d bands,in higher TMOs, two kinds of bonding must be which is proportional to the lowering of atomic dclearly distinguished. The M-to-O bonding, which is level. This shift increases the ionicity of the Li-to-Overy strong and is responsible for the observed interaction (cf. arrows in Fig. 1c indicatingdistribution of energy states (cf. Fig. 2), and O-to-Li DE ) and makes the transfer of the LiLi 2s–M 3d

bonding which is weak and where Li electron density electron density to the d band more stable. In Fig. 2basically fills energy states delineated by the former the empty arrow shows the transfer of the Li atomicbonding. electron density to the t band, where it occupies the2g

A good tool to analyse the bonding is the refer- empty states up to the Fermi level.ence to atomic energy levels relevant to the bonding. The capacity of the lower d band (t ) to accom-2g

They include 2p (O), 3d (M), and 2s (Li) levels (cf. modate electrons is 6. The complete filling of thisFig. 2). The role of M 4s electrons was shown to be band and occupation of the upper d band (e ), whichg

practically negligible. Calculated atomic energy is destabilised compared to the atomic d level (Fig.levels [7] are displayed in Fig. 1c. The difference of 2), occurs in nickel oxides [5]. Due to this ‘bandenergy levels indicates the degree of ionicity of the structure effect’, the EOFs and AIVs of nickelbonding [8,9]. The M-to-O bonding is therefore the compounds show deviations from the behaviour ofmost ionic in Ti compounds (DE 54.8 eV). All the DEOF indicated in Fig. 1b for spinels. In thepd

electron density is accommodated in bonding states series of TMOs from Ti to Co in which the electronand concentrated mostly between the atoms of TiO density supplied by intercalated Li fills the t band,6 2g

octahedra. Since Li atoms are situated outside of however, the trend of the DEOF is quite smooth. Theoctahedra, the Li-to-O bonding is therefore rather same behaviour of the DEOF is expected also for thelimited. In compounds including higher TMs’ the 2p series of trigonal structures. Before all values are(O) and 3d (M) levels are getting closer (cf. Fig. 1c) calculated, we estimate the DEOF for the trigonaland the M-to-O bonding is becoming more covalent. LiCoO compound directly from Fig. 1b and present2

With increasing covalency the admixture of 3d (M) the corresponding AIV in Table 1. This value is instates to the p band increases, and so does the very good agreement with experiment.number of 2p (O) states which are pushed out of the Fig. 1a and b show that the occupation ofp band into antibonding bands. Thus, increased antibonding states in the same structure, whichcovalency of the M-to-O bonding causes that a larger occurs due to the increased number of electrons infraction of 2p (O) states to become antibonding. higher TMs, causes a steady decrease of the EOFsThese states are admixed into the d bands. In oxides and an almost linear increase of the DEOF. Theof higher TMs the filling up of the d bands therefore continuous filling of antibonding states, however,increases the fraction of the oxygen electron density occurs also in structures of the same TM due tooccupying antibonding orbitals. Similarly, the addi- increasing content of inserted Li. The EOF of thetional electron density supplied by Li upon its lithiated structure, therefore, decreases with in-intercalation into oxides of higher TMs is transferred creased Li content and with decreasing oxidationto the TM, and to much higher extent also to O state of the TM. At small Li /TM ratios the oxidationantibonding states as shown in the difference density state of the TM is only slightly lowered from itsmaps published by Aydinol et al. [5,6]. The increase initial value of IV, and Li atoms are stronglyof the partial charge on O due to the intercalation of stabilized. The EOF of such a compound is thereforeLi, which we calculate to be 0.027, 0.037, and 0.046 large and the AIV is at its upper limit. Withfor LiTi O , LiMn O , and LiCo O , respectively, increasing Li /TM ratio the progressive filling of2 4 2 4 2 4

is in line with the evaluations by Aydinol et al. [5,6]. antibonding states causes a continuous decrease ofBecause the antibonding density is oriented out of the EOF and AIV.the MO octahedra, it is available for interaction The dependence of the AIV on the Li /TM ratio for6

with Li atoms and is responsible for larger stabiliza- Li MnO compounds, constructed from four ex-x 2

tion of Li in structures of higher TMs. perimental [14] and two calculated values, is dis-Another factor which does influence the stabilisa- played in Fig. 3. Usually only three values are

L. Benco et al. / Solid State Ionics 112 (1998) 255 –259 259

the help with structural data, P. Blaha for numerousdiscussions on the computer code WIEN97, and M.Ziegler for helpful discussions. We acknowledgeCSCS (Manno) for computer time.

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