Role of Electronic Structure in the Susceptibility of...

Role of Electronic Structure in the Susceptibility of MetastableTransition-Metal Oxide Structures to Transformation

John Reed and Gerbrand Ceder*

Department of Materials Science and Engineering, Massachusetts Institute of Technology, Building 13-5056, 77 Massachusetts Avenue,Cambridge, Massachusetts 02139

Received March 1, 2004

Contents1. Introduction 45132. Transformation Mechanisms 45143. Density Functional Theory 45164. Comparison between the Activation Barriers for

Co and Mn Migration4516

5. Valence of Co and Mn during Migration 45176. Ligand-Field Effects on the Energetics of

Migrating Co and Mn4518

7. Summary of Important Factors Influencing Coand Mn Site Preference in ccp Oxides

4520

8. Effect of Chemical Substitutions on Mn SitePreference

4521

8.1. Electronic Structure Model for the Energeticsof Mn Oxides

4524

9. Qualitative Ionization Scale 452610. Effect of Valence on Site Preference of Other 3d

Transition Metals4527

10.1. Ti 452810.2. V 452810.3. Cr 452910.4. Mn 452910.5. Fe 452910.6. Co 453010.7. Ni 453010.8. Cu 4530

10.11. Overall Trends for 3d Metals 453011. Conclusions 453112. Acknowledgments 453213. References 4532

1. Introduction

Kinetic stability is a key aspect of Li-insertioncompounds used in rechargeable Li batteries. Toobtain high capacity, the Li ions need to be cycledover a wide range of concentrations within the hoststructure of the insertion compound. This almostinvariably brings the host structure outside its rangeof thermodynamic stability at some stage of theelectrochemical cycle. Maintaining a desirable hoststructure over repeated electrochemical cycles oftenhinges upon the host structures resistance against

transforming into more stable phases when it be-comes thermodynamically metastable. The ability toresist phase transformation can have an importantimpact on the overall performance of a Li-insertioncompound used as an electrode material in a Lirechargeable battery.

The focus of this paper is on the role electronicstructure plays in determining the site preferenceand mobility of 3d transition-metal ions in an oxideand how these factors in turn affect the resistanceof metastable 3d transition-metal oxides againsttransformation. This is a relevant topic to the Lirechargeable battery field because 3d transition-metal oxides are often used as positive electrodematerials.

Lithium manganese oxide structures serve as themain prototype of a 3d transition-metal oxide systemused in this investigation. Lithium manganese oxideshave been intensely researched as candidate positiveelectrode materials for use in Li rechargeable bat-teries because they offer the possibility of highcapacity combined with good safety. This desirablecombination is a consequence of the relative stabilityof the fully charged MnO2 structures. Mn is also lessexpensive than Co, the transition metal commonlyused today in positive electrode materials for re-chargeable Li batteries.1

The Mn oxide structures that have received themost attention as possible positive electrode materi-als are spinel,2-4 R-NaFeO2-type layered,5-9 andorthorhombic (Pmnm).2,3 All three of these structureshave a close-packed (sometimes slightly distorted)oxygen array in a fcc-like stacking with Mn occupyingoctahedral sites and Li occupying either octahedralor tetrahedral sites. Unfortunately, each of thesestructures has problems that have hindered theirpractical use in Li rechargeable batteries thusfar.2,3,5,10,11 For the R-NaFeO2-type layered and ortho-rhombic (Pmnm) structures the primary problem isthat they undergo structural transformation withelectrochemical cycling. As such the Mn oxides are agood prototype for investigating the relationshipbetween transformation kinetics and electronic struc-ture.

One advantage that spinel-like LixMn2O4 (s-Lix-Mn2O4) has over the other candidates is that it is notsusceptible to any major structural transformationupon electrochemical cycling over the 0 e XLi e 2range.2 This is due in part to s-LixMn2O4 being

* To whom correspondence should be addressed. Phone: (617) 253-1581. Fax: (617) 258 6534. E-mail [email protected].

4513Chem. Rev. 2004, 104, 4513−4534

10.1021/cr020733x CCC: $48.50 © 2004 American Chemical SocietyPublished on Web 09/28/2004

thermodynamically stable at XLi ) 1. Additionallys-LixMn2O4 retains its structural integrity at high andlow lithiation even though it becomes energeticallymetastable at those compositions.2

The low energy of the spinel structure at theLiMn2O4 composition is not unique to Mn. For the3d transition metals from Ti to Cu, the energy of thespinel structure is lower than the energy of thelayered structure.12,13 This is not too surprising sincethere is a greater separation between neighboringpositively charged Li and M cations (M ≡ 3d transi-tion-metal ion) in the spinel structureswhere the Lioccupy tetrahedral sites and the M octahedral sitessthan in the layered structureswhere both Li and Moccupy octahedral sites.2

As mentioned previously, both R-NaFeO2-type lay-ered (l-LixMnO2) and orthorhombic (o-LixMnO2) losetheir structural integrity with electrochemical cy-cling, in contrast to s-LixMn2O4, and rapidly trans-form to a spinel-like material at partial lithiation.9,14-17

This results in a substantial drop in capacity overthe first few charge/discharge cycles.8 However,capacity is recovered with additional cycling as thetransformation to spinel moves toward completion.18

The transformed spinel-like material is reported tohave properties such as reduced Jahn-Teller distor-tion and greater durability that are actually superiorto conventionally synthesized s-LixMn2O4 spinel.15,18,19

Nonetheless, there remains an interest in makinglayered manganates that can resist transforming intospinel.

Although spinel is energetically favored at theLi1/2MO2 composition for all of the 3d transitionmetals from Ti to Cu, the rate at which the layeredstructure transforms to spinel varies substantiallyfor each 3d metal. For LixMnO2 the transformationfrom layered to spinel occurs rapidly at room tem-perature. In the case of LixNiO2, heating is requiredin order for layered to rapidly transform to spinel.20

While for LixCoO2 the transformation of layered tospinel appears to be even more difficult, with theconversion only detected by TEM in the surfacelayers of highly cycled l-LixCoO2.21,22 In the followingsections the transformation of the layered R-NaFeO2structure to spinel will be focused upon as anexample (with significant relevance to the batteryfield) that illustrates the influence of electronicstructure on the transformation kinetics of 3d transi-tion-metal oxides.

2. Transformation Mechanisms

The transformation of l-LixMO2 or o-LixMO2 intos-LixM2O4 (M ≡ 3d transition-metal ions) does notrequire oxygen rearrangement since all the struc-tures share a cubic closed-packed (ccp) oxygen anionsublattice. In all three structures M ions occupyoctahedral interstitial positions while the Li occupyeither octahedral or tetrahedral interstices.2 Hence,the transformation of l-LixMnO2 or o-LixMnO2 to s-Lix-Mn2O4 involves a rearrangement of Mn from the setof octahedral sites characterizing l-LiMnO2 or o-LiMnO2 to the set of octahedral sites characterizings-LiMnO2 (as well as rearrangement of the Li ions).

Formation of spinel from l-LixMnO2 requires themovement of one-fourth of the Mn ions from the Mn(111) plane into the Li (111) plane as can be seen byexamining Figure 1.

John Reed received his Ph.D. degree in Materials Science and Engineeringfrom the Massachusetts Institute of Technology in 2003. Currently he isdoing postdoctoral work for the Massachusetts Institute of Technology inaddition to being a visiting scientist at Lawrence Berkeley NationalLaboratory. His current interests are energy technologies and utilizationof computational methods to analyze materials used in these technologies,as well as identification of new candidate materials. His primary researchfocus to date has been on transition-metal oxide materials used in thepositive electrodes of Li rechargeable batteries and the physics andchemistry that govern their properties.

Gerbrand Ceder is the R. P. Simmons Professor of Materials Scienceand Engineering at the Massachusetts Institute of Technology. He receivedhis engineering degree in Metallurgy and Applied Materials Science fromthe University of Leuven, Belgium, in 1988, and his Ph.D. degree inMaterials Science from the University of California at Berkeley in 1991,at which time he joined the MIT faculty. Ceder’s research interests lie incomputational modeling of material properties and design of novelmaterials. He has published over 160 scientific papers in the fields ofalloy theory, oxide phase stability, high-temperature superconductors, andLi-battery materials, and holds three current or pending U.S. patents. Hehas received numerous awards among which a Career Award from theNational Science Foundation, the Robert Lansing Hardy Award from TheMetals, Minerals and Materials Society for “exceptional promise for asuccessful career”, the 2004 Battery Research Award from the Electro-chemical Society, and an award from the graduate students at MIT forbest teaching. He has worked with several U.S. and international materialscompanies to use modeling to design and optimize materials for high-performance applications. He is also a co-founder of ComputationalModeling Consultants, which provides first-principles materials modelingservices to industry. He is currently head of the Theory and ModelingDivision of the Institute for Soldier Nano Technology at MIT and a groupleader for the Research Program on High Performance Power Sourcesin the Center for Materials Science and Engineering.

4514 Chemical Reviews, 2004, Vol. 104, No. 10 Reed and Ceder

For o-LixMnO2, 50% of the Mn ions need to changeposition in order to form spinel.2 The characteristicsof the orthorhombic, R-NaFeO2-type layered, andspinel structures as well as many other ordered rock-salt structures have been covered in detail by Thack-eray.2

Given that the structural transformation of theR-NaFeO2-type layered and orthorhombic structuresto spinel only requires cation migration, the varyingresistance of transition-metal compositions againstthe transformation (i.e., low resistance for Mn, highfor Co) is most likely connected to the diffusionkinetics of the respective 3d transition-metal ions.

An ion can take two extreme paths in migratingbetween octahedral sites of a ccp oxygen framework,as occurs during the transformation of l-LixMnO2 oro-LixMnO2 to s-LixMn2O4. These two paths are shownin Figure 2. The most direct path travels straightthrough the edge shared by neighboring octahedra,i.e., the Oh f Oh path through E shown in Figure 2.This path, while short, brings the cation in closeproximity to the coordinating oxygen anions. A moreopen but longer path is through a nearest neighbor(n.n.) tetrahedral site via the faces (F) it shares withthe neighboring octahedra (i.e., path Oh f Td f Ohin Figure 2).

While the octahedra shown in Figure 2 are undis-torted, this is generally not the case in structuressuch as l-LixMnO2 and o-LixMnO2. In these cases theoctahedra are distorted by both the cationic orderingwhich breaks the cubic symmetry of the underlyingoxygen sublattice and the Jahn-Teller distortionwhen Mn3+ is present. Consequently, not all of theoctahedral edges (E) or faces (F) that Mn can passthrough are equivalent in l-LixMnO2 and o-LixMnO2.

Generally, the activation barrier for a transition-metal ion passing through the triangular oxygen face(F) along a Oh f Td f Oh type path is expected to beless than the barrier to pass through the oxygen edge(E) along a Oh f Oh type path. The separationbetween cation and oxygen is about 15% greater atF than at E (assuming an undistorted octahedron).Hence, there should be less Pauli repulsion from theelectron clouds of the oxygen when the cation passesthrough the octahedral face (F) than when passingthrough the octahedral edge (E). Previous work hasshown that Li favors a Oh f Td f Oh type path whendiffusing in the Li layer of l-LixCoO2.23 It is expectedthat 3d metal ions will typically take Oh f Td f Ohtype paths (Figure 2) as well when diffusing througha ccp oxygen framework, such as during the trans-formation of l-LixMnO2 or o-LixMnO2 to s-LixMn2O4.The results of first-principles calculations discussedin the following sections support this view.

A notable exception to the general favorability ofOh f Td f Oh type paths for cation migration is caseswhere the intermediate tetrahedral site (Td) sharesa face with an octahedral site occupied by anothercation. The passage of a 3d metal ion through suchtetrahedral sites is typically calculated to be high inenergy, in some cases higher than the energy forpassing through the octahedral edge (i.e., the Oh fOh path).24 This is due to the small separation andhence strong repulsion between face-sharing cationsin a ccp oxygen framework.

In the following sections it will be shown that first-principles calculations and ligand-field theory indi-cate that the energetics for the passage of a 3d ionlike Mn through intermediate triangular (F) andtetrahedral (Td) sites is highly effected by its oxida-tion state.76 This suggests that the kinetics of phase

Figure 1. l-LixMO2 (layered) and s-LiM2O4 (spinel) struc-tures (M ≡ 3d transition metal). M occupy octahedral sitesin both structures. In l-LixMO2, M and Li (and/or vacancies)alternately occupy (111) planes of the ccp oxygen sublattice.The (111) plane parallel to the M layers is indicated bythe black line between the layered and spinel structures.The [111] direction is shown as well. In s-Li1/2MnO2, (111)planes with three-fourths of the Mn alternate with (111)planes with one-fourth of the Mn. Li ions occupy tetra-hedral sites in the planes with one-fourth of the Mn. Theplanes with three-fourths of the Mn are free of Li. In fullylithiated spinel-like s-Li2Mn2O4, the Li move into octahe-dral sites. Three-fourths of the Li are in the (111) planewith one-fourth of the Mn, and one-fourth of the Li are inthe plane with three-fourths of the Mn.

Figure 2. The most direct path an octahedral Mn canfollow to a vacant nearest neighbor octahedral site (Oh) isthrough the edge (E) shared by the two sites. This path(Oh f Oh) is also the most constricted in terms of separationbetween the migrating Mn and the surrounding oxygenanions. The minimum separation occurs as Mn passesthrough the center of the octahedral edge labeled E. A moreopen path between octahedral sites is via a nearestneighbor (n.n.) tetrahedral site (Td). Along this path (Ohf Td f Oh) the minimum separation between a migratingMn and surrounding oxygens occurs as Mn passes throughthe center of the shared triangular face between the n.n.octahedron and tetrahedron (F). In a perfect octahedronthe distance between the corner oxygens and the center ofthe triangular face (i.e., distance from O to F) is 1.155 timesthe distance from corner oxygens to the center of the edge(i.e., distance from O to E in Figure 2).

Metastable Transition-Metal Oxide Structures Chemical Reviews, 2004, Vol. 104, No. 10 4515

transformations involving 3d ion rearrangements ina ccp oxygen framework will depend strongly uponoxidation state. Since the maintenance of structuralintegrity is a desirable feature for an electrodematerial, the effect of valence on ionic mobility is animportant consideration when designing electrodes.For multivalent TM ions it is possible that the TMion could have a low mobility in one valence,- but ahigh mobility in another, which could make the hoststructure vulnerable to transformation during elec-trochemical cycling.

3. Density Functional Theory

Much of the quantitative information in this paperis derived from first-principles calculations based ondensity functional theory (DFT).25-27 Experimentallyit is difficult to determine ion migration paths andenergy barriers along migration paths in structuraltransformations such as from l-LixMnO2 to s-LiMn2O4.Examining the atomic-scale ionic movements thatcould occur in such a transformation using first-principles calculations can therefore be informative.

For characteristics of TM oxides such as LixMnO2or LixCoO2 that can be experimentally determined,it is found that the calculated results presented inthis paper are in good agreement with experiment.77

Additionally, previous studies have found that vari-ous properties of 3d TM oxides can be determinedwith good accuracy using DFT-based methods.13,28,29

This gives credibility to the findings of this paperwhich rely upon the rich and precise atomic-scaledetail provided by first-principles calculations.

The density functional calculations were performedusing the Vienna Ab Initio Simulation Package(VASP).30 The spin-polarized generalized gradientapproximation,31,32 Perdue-Wang exchange correla-tion function, and ultrasoft pseudopotentials wereused.33

Defects can be calculated in supercells that aremultiples of the unit cell for the underlying undefec-ted structure (e.g., l-Li1/2MnO2). If the supercell islarge enough, the periodic images of the defect willhave negligible interaction, giving an approximationof an isolated lone defect.

Such an approximation of periodicity was made forthe calculations discussed in the next section (section4). The supercells for these calculations were com-posed of either 12 or 32 primitive LixMO2 unit cells(M ≡ 3d TM ion; 0 e x e 1) that contained variousM defects. The lattice parameters of the supercellswere kept constant at the parameters for the unde-fected structure, while the ionic coordinates wereallowed to relax. A 2 × 2 × 2 k-point mesh was usedfor the calculations on the 12-unit supercells and a1 × 1 × 1 k-point mesh for the 32-unit supercells.The primitive LixMO2 unit cells used to construct thesuper cells had previously been calculated with fullrelaxation of lattice parameters as well as ioniccoordinates.

Later sections will draw upon the results of calcu-lations on l-LixMO2, s-LixM2O4, and related meta-stable crystalline structures. For these calculationsa LixM4O8 (0 e x e 4) unit cell and a 4 × 4 × 4 k-point

mesh were used. Both the lattice parameters and theionic coordinates were allowed to fully relax.

The bulk of the calculations in this study wereperformed on Mn oxide structures; however, as areference, many equivalent calculations were alsocarried out for LixCoO2 (0 e x e 1). This system waschosen for comparison with LixMnO2 because in thelayered form it is does not undergo significant phasetransformations with electrochemical cycling despitebecoming energetically metastable relative to spinelat partial lithiation.34-37 This resistance to transfor-mation has allowed layered LixCoO2 to become thestandard positive electrode material for use in com-mercial Li rechargeable batteries.

Finally, some calculations equivalent to thoseperformed with Mn and Co were carried out foroxides of the other 3d transition metals, from Ti toCu, to demonstrate some general principles govern-ing this class of materials.

4. Comparison between the Activation Barriersfor Co and Mn Migration

Figures 3 and 4 show the energy barriers calcu-lated for Mn and Co movements out of a TM layeroctahedron and into the Li/vacancy layer of thelayered R-NaFeO2-type structure (recall that the TMcations have to migrate into the Li/vacancy layer forthe transformation to spinel). The cation positionsused in these calculations follow the Oh f Oh (Figure3) and Oh f Td f Oh (Figure 4) type paths shown inFigure 2.

Figure 3 shows the calculated energy barrier forMn and Co hopping directly through an octahedraledge (E) into a Li/vacancy layer octahedron. Thebarrier illustrated at the top of Figure 3 is thecalculated result when the Li content is XLi ) 0 (i.e.,MO2, M ≡ Mn or Co); the bottom plot corresponds to

Figure 3. Energy of Co/Mn ion along the Oh f Ohtransition path from an octahedral site in the TM layer,through a shared edge, to an octahedral site in the vacancy/Li layer: (top) delithiated XLi ) 0 (M4+), (bottom) half-lithiated XLi ) 1/2 (average M3.5+). (A (on x axis)) Layeredstructure with no transition metal in the empty/lithiumlayer (i.e., no defects). (B) A single TM atom located in theshared edge between neighboring octahedra (i.e., E inFigure 2). (C) A single TM atom defect in an empty/lithiumlayer octahedron.


a Li content of XLi ) 1/2. The TM ion hop in bothcases is along the “constricted” Oh f Oh path shownin Figure 2 and results in the formation of anoctahedral Mn or Co defect in the Li/vacancy layer.

Figure 4 shows the calculated energy barrier forMn and Co hopping through an octahedral face (F)into a nearest neighbor tetrahedron in the Li/vacancylayer at XLi ) 0 and 1/2. This path is the first half(Oh f Td) of the “open” Oh f Td f Oh path picturedin Figure 2.

Figures 3 and 4 catalog the plausible initial stepsin the transformation of the layered structure tospinel. Other Oh f Oh and Oh f Td f Oh cation hopswithin the transition-metal layer have also beencalculated, but they were found to be particularlyhigh in energy due to cationic repulsion and henceare ruled out.24

As expected, the barrier is calculated to be lower(at a given lithium content) for hops from octahedrato n.n. tetrahedra through a shared face (Oh f Td)than hops directly between octahedra through anoctahedral edge (Oh f Oh). This is consistent withexperimental results that indicate Mn migratesthrough tetrahedral sites during the transformationof orthorhombic or layered LixMnO2 into spinel.17,38

Some additional noteworthy features of the calcu-lated results shown in Figures 3 and 4 are as follows.

(i) The barrier for the TM ion to leave its site inthe TM layer is high for both Co and Mn at MO2composition.

(ii) The formation energy of a tetrahedral Mn defectin the layered structure at XLi ) 1/2 is negative, whileit is positive for Co.

(iii) The activation barriers for Mn migration arehigher than those for Co at XLi ) 0, but they are muchlower at XLi ) 1/2.

The relatively low energy for Mn migration out ofthe TM layer and into n.n. tetrahedra in the Li/vacancy layer at XLi ) 1/2 is probably the Achilles

heel of the l-LixMnO2 material. It suggests that Mncan easily move out of the layered configuration intothe Li/vacancy layer at this composition. This shouldfacilitate the rapid transformation of l-Li1/2MnO2 tos-LiMn2O4 since Mn ions need to move from the TMlayer to the Li/vacancy layer during the transforma-tion. The results of additional calculations, for ex-ample, on the second half of the of the Oh f Td f Ohpath, reported elsewhere further attest to the relativeease for Mn to move between octahedral and tetra-hedral sites along the reaction path toward spinel atXLi ) 1/2 in l-LixMnO2.24

Co by contrast is seen in Figures 3 and 4 to havehigh-energy barriers at both delithiated and partiallylithiated compositions along either type of pathway(Oh f Td f Oh or Oh f Oh) into the Li/vacancy layer.Results of TM ion defect calculations at full lithiation,i.e., XLi ) 1, which are not shown,76 indicate that bothCo and Mn are prevented from entering the Li layerby the lack of octahedral lithium vacancies.

The calculated low activation barrier and defectenergy for Mn going Oh f Td at partial lithiation isconsistent with the lack of stability of l-LixMnO2against transformation into spinel observed experi-mentally. Likewise, the high activation barriers forall possible Co hops out of the TM layer are consistentwith the relative stability observed experimentallyfor layered LixCoO2.

Figures 3 and 4 illustrate that TM ion defectenergies and activation barriers to forming defectsappear to be highly sensitive to the Li concentrationin the layered structure. The relative stability of Mnand Co in the TM layer octahedra changes dramati-cally with increasing Li content, with Mn calculatedto be more stable than Co at XLi ) 0 and far lessstable at XLi ) 0.5. The next section will show thatas the average oxidation state of the TM ions changesfrom +4 to +3.5, due to the Li content changing fromXLi ) 0 to 0.5, different charge-transfer reactionsaccompany tetrahedral defect formation for Mn aswell as for Co. This provides an explanation for thequalitative change in Mn behavior compared to Coand highlights the important role that electronicstructure plays in the mobility of these ions.

5. Valence of Co and Mn during MigrationFigures 3 and 4 indicate a significant variation in

the Mn and Co migration barrier along the Oh f Tdf Oh and Oh f Oh paths as the oxidation statechanges.

Using the calculated electron spin density, the ionicvalences can be determined by integrating the elec-tron spin density in a sphere about the ionic centers.Integrating spin density provides the net spin as-sociated with a given TM ion. This captures theformal valence of the cation better than integratingthe charge density because it distinguishes thepartially filled 3d orbitals of the transition-metalcation from the filled p orbitals of the coordinatingoxygens. With this method it is possible to detect thecharge-transfer and/or bonding changes that occurfor a TM ion as it moves along its migration path.39,40

The results of such spin integrations are shown inFigure 5 for Co (top) and Mn (bottom) in various

Figure 4. Energy for a Mn/Co ion along the path from anoctahedral site in the TM ion layer to a tetrahedral site inthe Li/vacancy layer. (top) Delithiated MO2 (M ≡ Mn orCo: (A) layered structure, (B) single TM ion located intriangular face between TM layer and empty layer (i.e.,F in Figure 2), (C) single tetrahedral TM defect in emptylayer. (bottom) Half-lithiated, i.e., Li1/2MO2: (A) layeredstructure, (B) Li disorder to create a trivacancy around atetrahedron in the Li layer (prevents high-energy face-sharing cations for tetrahedral defect), (C) single TM ionlocated in triangular face between TM layer and Li layer,(D) single tetrahedral TM defect in Li layer, (E) both Liand TM ion in tetrahedral sites (tetrahedral site availableto Li due to vacancy created by TM defect).


positions along the Oh f Td f Oh path at tLi ) 1/2.Figure 5 shows the amount of electron spin (in unitsof 1/2 µâ) as a function of integration radius. The totalspin initially rises rapidly with radius as the dorbitals are integrated over. However, then the spinlevels off as the nonpolarized oxygen states arereached. The value at this plateau is used in deter-mining the formal valence of the TM cations. Forexample, the bottom of Figure 5 shows Mn4+ whichplateaus at a total electron spin of 3, reflecting thet2g

3eg0 d-orbital filling of Mn4+.

Even though the average formal valence state ofthe TM is +3.5 at XLi ) 1/2, Figure 5 shows that themigrating Mn (Co) ion in triangular or tetrahedralcoordination takes on quite a different valence fromthe surrounding octahedral Mn (Co) ions. The mi-grating Mn (Co) ion gains d electrons when it passesthrough the triangular octahedron face and keepsthem as it continues into the neighboring tetrahedralsite in the Li/vacancy layer.

The spin integration results of Figure 5 indicatethat when forming a tetrahedral Mn (Co) defect atXLi ) 1/2, the migrating Mn (Co) approaches a +2valence state while a neighboring octahedral Mn (Co)is oxidized toward +4. This constitutes a charge-disproportionation reaction which can be approxi-

mately expressed by the following equation (whereMtet

2+ is the migrating TM ion)

A similar charge disproportionation reaction is re-ported to occur during the degradation of s-LixMn2O4with electrochemical cycling whereby the Mn2+ dis-solves into the electrolyte.2

Using the spin integration method described above,it was also determined that at an average formalvalence of +4 (XLi ) 0) both Mn and Co undergo asimple tetrahedral defect reaction

6. Ligand-Field Effects on the Energetics ofMigrating Co and Mn

Size effects are often an important contribution tothe energy of ionic systems. However, surprisinglycation size appears to have little if any effect on thepropensity of Mn or Co to enter tetrahedral coordina-tion in the LixMO2 ccp oxide system. According toPauling’s first rule, a smaller cation should be moreenergetically favorable in a small interstitial sitethan a larger cation.41 The tetrahedral sites formedby oxygen anions in a ccp structure are smaller thanthe octahedral sites, so by Pauling’s first rule smallercations should have a greater propensity to entertetrahedral coordination than larger cations. How-ever, the behavior of the LixMnO2 and LixCoO2systems is very different than what is expectedaccording to Pauling’s first rule.

On the basis of cationic radii reported in thescientific literature (53 pm for Cooct

4+ and 40 pm forCotet

4+; 53 pm for Mnoct4+ and 39 pm for Mntet

4+),42

one would expect the tetrahedral defect energies andactivation barriers for MnO2 and CoO2 to be roughlythe same. However, as seen previously, the calculatedenergy for the tetrahedral Mn4+ defect is almost twiceas high as that of Co4+. The activation barrier for theoctahedron-tetrahedron hop is also significantlyhigher for Mn4+ (Figure 4 top).

For the composition Li1/2MO2 (M ≡ Co, Mn), therelevant cations to consider are M2+ in tetrahedralcoordination, M3+ in octahedral coordination, and M4+

(given above) in octahedral coordination (58 pm forCotet

2+ and 54.5 pm for Cooct3+; 66 pm for Mntet

2+ and64.5 pm for Mnoct

3+).42

The radius of Co is less than or equal to the radiusof Mn at all oxidation states and coordinationsrelevant to the Li1/2MO2 composition. However, asdiscussed in the previous section, Mn2+ is calculatedto be more energetically favored in tetrahedralcoordination and have a lower activation barrier forthe Oh f Td hop than Co2+, despite being the largercation.

Finally, according to Pauling’s first rule one wouldexpect lower tetrahedral defect and activation barrierenergies in MO2 than in Li1/2MO2 for both Co and Mnsince the +4 cations have smaller radii than the +2cations. Again, site-occupancy predictions based onPauling’s first rule run contrary to the resultscalculated from first principles.

Figure 5. Integrated net spin for Co and Mn cations alongthe Oh f Td path into the Li/vacancy layer at XLi ) 1/2.(top) Li1/2CoO2 layered Oh Co ions (labeled octa w/no Cotet) have an oxidation state of ∼+3.5 (t2g

5.5). The migratingCo in triangular (octa/tetra face) or tetrahedral coordina-tion takes on nearly 3 units of electron spin (1/2µâ), givingan oxidation state approaching +2 (e4t2

3). When one-fourthof the Co are in Td sites with +2 charge, the other three-fourths of the Co in Oh sites (octa w/1/4 Co tet) have araised oxidation state from ∼+3.6 to +3.7. (bottom) Li1/2-MnO2: The migrating Mn (octa/tetra face and tetrahedral)has about 4.5 units of electron spin, giving an oxidationstate of ∼+2.5 (e2t2

2.5). Mn in Jahn-Teller-distorted octa-hedra (octahedral w/JT) are ∼+3 (t2g

3eg1); in non-Jahn-

Teller-distorted octahedra (octahedral w/no JT) they are+4 (t2g

3).

2Moct3+ f Mtet

2+ + Moct4+ (1)

Moct4+ f Mtet

4+ (2)


It appears that for the layered Mn and Co oxidesconsidered, ionic size effects do not play a significantrole in the preference for octahedral or tetrahedralsites nor in the activation barrier to hops betweenthe two. Consequently, size effects probably do notplay a significant role in determining the mobility ofMn or Co through a ccp oxide framework. In contrast,the results indicate that valence and electronicstructure are more decisive factors in the site prefer-ence of Mn or Co and hence in their propensity tomigrate through a ccp oxide framework. This isconsistent with the work of Goodenough that foundvalence to be an important determinant of the sitepreference of 3d TM ions in oxides.43

The role of electronic structure in Mn and Co sitepreference and mobility can to some extent beunderstood through ligand-field theory (LFT).44,45

LFT qualitatively explains how the degeneracy of the3d orbitals is broken when a free TM ion is sur-rounded by coordinating anions. The ligand-fieldsplitting of d orbitals in octahedral and tetrahedralcoordination is pictured in Figure 6.45

In octahedral coordination, the d level splits intothe eg level, which is 2-fold degenerate, and the t2glevel, which is 3-fold degenerate. The energy separa-tion between the t2g and eg levels is called the ligand-field splitting (≡ ∆o). The t2g level, composed of thedyz, dxy, and dxz orbitals modified by the octahedralligand field, is lowered (2/5)∆o relative to the energybarycenter, i.e., “center of energy”, of the d orbitals.The eg level, composed of the dz2 and dx2-y2 orbitals,is raised (3/5)∆o.45

For d orbitals placed in tetrahedral coordination,the t2 level contains the dyz, dxy, and dxz orbitalsmodified by the tetrahedral ligand field and the elevel contains the dz2 and dx2-y2 orbitals. Figure 6illustrates how the energy levels in tetrahedralcoordination are inverted relative to those in octa-hedral coordination (Figure 6).

Using LFT, the change in the ligand-field stabiliza-tion energy (LFSE) for the charge disproportionationreaction (eq 1) can be estimated for Mn and Co asshown in Figure 7.

The change in LFSE for the charge disproportion-ation reaction that produces tetrahedral Mn at XLi) 1/2 is projected to be equal to the energy of theJahn-Teller splitting (R). For Co, on the other hand,the change in LFSE is projected to be more thantwice the energy of the octahedral ligand-field split-ting (34/15∆o), which should be much larger than theMn Jahn-Teller splitting R.47,48 Hence, LFT indicatesthat charge disproportionation is much more costlyin ligand-field stabilization for Co than for Mn at XLi) 1/2. This is consistent with a much lower mobilityfor Co3.5+ than Mn3+ in a ccp oxide and therefore agreater resistance of metastable Co oxides such asl-Li1/2CoO2 against transformation. Experimentalevidence supporting the decisive role LFSE plays inthe differing stability of the layered structures in-corporating Mn, Co, as well as Ni has been reportedby Choi, Manthiram et al.49

It should be kept in mind that while LFSE isimportant, it is one of many contributions to theenergy in the LixMnO2 and LixCoO2 systems. Forexample, the d levels in Figure 7 are drawn with aconstant center of energy, or barycenter (indicatedby the dashed line), but this is not generally the case.Hence, in addition to a change in the splitting of thed levels with changing coordination, there can be ashift in their average energy.

Also, the change in LFSE does not account for theenergy cost of spin pairing (two electrons with op-posing spin occupying the same orbital).50,51 This isnot relevant for Mn in this case, but for Co the changein LFSE of the charge disproportionation reaction isprobably somewhat counteracted by the change inspin pairing energy (SPE), since a high-spin ion isformed from low-spin ions. The products of Co3+

charge disproportionation have four unpaired d elec-

Figure 6. Energy splitting of the d orbitals in octahedraland tetrahedral coordination. The numbers at each levelindicate the energy degeneracy that still remains afterligand-field splitting. Note that the energy barycenter (i.e.,“center of energy”) need not be the same in octahedral andtetrahedral coordination as pictured.

Figure 7. Change in LFSE associated with the chargedisproportionation reaction in both Li1/2MnO2 (high-spinMn3+) and Li1/2CoO2 (low-spin octahedral Co). ∆o and ∆tequal the octahedral and tetrahedral ligand-field energysplittings, respectively. The Jahn-Teller splitting equalsR. The proportionality between ∆o and ∆t is taken fromcrystal-field theory to be -4/9∆o ) ∆t.46 Note that theenergy barycenter (dashed line) is drawn as a constant,but this is not generally the case nor does it affect thechange in LFSE (although it certainly affects the changein total energy).


trons while the reactants have none, making theproducts more favorable in terms of SPE (Figure 7).

7. Summary of Important Factors Influencing Coand Mn Site Preference in ccp Oxides

The association shown in sections 4 and 5 betweenthe +2 oxidation state and a relatively low energyfor tetrahedral Mn defects in the layered structureis found to carry over to the site preference of Mn inperiodic crystalline structures (likewise the highenergy for Co occupancy of tetrahedral sites). Table1 gives the calculated energy difference betweenlayered Li1/2MO2 and other crystal structures withvarying amounts of tetrahedral TM cations. Note thatthe XLi ) 0.5 structures with tetrahedral Mn in Table1 are markedly lower in energy relative to the layeredstructure (l-Li1/2MO2) than are those with tetrahedralCo.

For the partially inverse spinel structure (ps-(LiM)tet(LiM3)octO8) shown in Table 1, one-fourth ofthe Co or Mn in tetrahedral sites are calculated tohave a +2 formal valence while three-quarters inoctahedral sites adopt a +4 formal valence (givingthe overall average valence of +3.5 required bycharge balance). Similar to the tetrahedral defectcalculations for Mn and Co at XLi ) 1/2 (Figure 4,bottom), the ps-(LiMn)tet(LiMn3)octO8 is calculated tobe lower in energy than l-Li1/2MnO2 while ps-(LiCo)tet-(LiCo3)octO8 is calculated higher in energy than l-Li1/2-CoO2. The generally low energy associated with thecharge disproportionation of Mn3+ to produce Mntet

2+

(eq 1) indicated by the calculations of this section,as well as in sections 4 and 5, is consistent with theexperimental observation that Mn3+ in many envi-ronments favors charge disproportionation.52

The importance of electron supply in the energeticsof tetrahedral Mn is demonstrated by the inversespinel (is-(Mn2)tet(Li2Mn2)octO8) result in Table 1. Inis-(Mn2)tet(Li2Mn2)octO8 one-half of all the Mn are intetrahedral coordination but there are not enoughelectrons available for these Mn to take on a +2oxidation state without the other Mn being oxidizedabove +4. Instead, the valences for Mn are calculatedto be +3 in tetrahedral coordination and +4 inoctahedral coordination (giving the required averagevalence of +3.5). The relatively high energy of is-

(Mn2)tet(Li2Mn2)octO8 compared to l-Li1/2MnO2 furtherdemonstrates that only the +2 oxidation state (outof the oxidation states +2 through +4) seems to becorrelated with the low-energy occupation of tetra-hedral sites by Mn.

Hence, the passage of Mn between octahedral sitesvia an intermediate tetrahedral site (i.e., the “open”Oh f Td f Oh path of Figure 2) is expected to begreatly facilitated when the Mn can take on a +2valence in the tetrahedral site. The amount of Mnions that can become +2 is determined by theaverage degree of Mn oxidation which is determinedby the Li content.

The average Li content also determines the numberof available tetrahedral sites that Mn can enterwithout sharing faces with Li ions in n.n. octahedralsites. Therefore, while LiMnO2 has sufficient elec-trons available for one-half of the Mn to take on a+2 valence through charge disproportionation ofMn3+ (eq 1), Mn movement into tetrahedral sites inl-LiMnO2 is still expected to be highly unfavorabledue to electrostatic interactions with Li in face-sharing n.n. octahedra.

This interplay between electron supply and cationrepulsion on the energetics of structures with tetra-hedral Mn or Co is illustrated by Figure 8, whichgives the calculated energies per TM ion for variousstructures over a range of Li contents. The resultsfor the ps-(LixM)tet(LiyM3)octO8 structure (0 e x e 1and 0 e y e 2) are shown for both M ≡ Co and Mn(with increasing lithiation the Li was added to thetetrahedral sites first, then octahedral). These ener-

Table 1. Energy of Mn and Co Oxides with VaryingAmounts of Tetrahedral TM Ions (Comparison of Coand Mn oxides at XLi ) 0.5)a

energy (eV)/M cation

structurefractionof M tet

Li1/2-MnO2

Li1/2-CoO2

l-Li1/2MO2 (layered) 0 0.0 0.0s-LiM2O4 (spinel) 0 -0.2489 -0.1791(LiM)tet(LiM3)octO8

(part. inv. spin.)1/4 -0.0829 0.1448

(M2)tet(Li2M2)octO8(inv. spin.) 1/2 0.2447 0.3627a Energies are relative to the l-Li1/2MO2 structure for M ≡

Mn and M ≡ Co, respectively. The second column lists thefraction of TM cations in tetrahedral coordination for a givenstructure. The structure labeled (LiM)tet(LiM3)octO8 (part. inv.spin.) corresponds to a partially inverse spinel and (M2)tet-(Li2M2)octO8 (inv. spin.) to a fully inverse spinel (i.e., antispinel).

Figure 8. Formation energy versus Li concentration forthree structures of Mn oxide (top) and Co oxide (bottom):(0) s-LixM2O4-labeled spinel, ()) l-LixMnO2-labeled layered,and (+) partially inverse spinel structure with 1/4Mtetrahedral (ps-(LixM)tet(LiyM3)octO8; 0 e x e 1 and 0 e y e2) labeled 1/4 Mn tet. As the Li content is increased, theLi is added to the tetrahedral site first of ps-(LixM)tet-(LiyM3)octO8, and then to the octahedral sites. For Mn, therealso is the energy of (4) a structure with one-sixth of theMn in tetrahedral sites at XLi ) 1/3 labeled 1/6 Mn tet witha triangle data point and (×) a structure with one-eighthof the Mn in tetrahedral sites at XLi ) 1/4 labeled 1/8 Mntet.


gies, labeled 1/4 M tet with + data points in Figure8, are compared with the energies of the l-LixMO2 ands-LiM2O4 structures (labeled layered with diamonddata points and spinel with square data points,respectively). Additionally, for Mn the results areshown for a structure with one-sixth of the Mn intetrahedral sites at XLi ) 1/3 (labeled 1/6 Mn tet witha triangle data point) and a structure with one-eighthof the Mn in tetrahedral sites at XLi ) 1/4 (1/8 Mntet with a × data point). These respective Li contentswere chosen because they allow the Mn to dispro-portionate so that all of the tetrahedral Mn are +2and all of the octahedral Mn are +4.

When the average formal valence is +4, the cal-culated energy difference between ps-(Mn)tet(Mn3)octO8and l-MnO2 is larger than that between ps-(Co)tet-(Co3)octO8 and l-CoO2. This resembles the results ofthe tetrahedral defect calculations in l-MO2 (Figure4, top) where the energy of the tetrahedral Mn4+

defect is calculated to be higher than the energy ofthe Cotet

4+ defect.Figure 8 shows that with the addition of Li the

energy of ps-(LixM)tet(LiyM3)octO8 drops much morerapidly relative to the layered structure for Mn thanfor Co. Around the Li1/2MnO2 composition (i.e., ps-(LiM)tet(LiM3)octO8), when all of the tetrahedral Mnhave a +2 valence and all of the octahedral Mn are+4 (i.e., total charge disproportionation), ps-(Lix-Mn)tet(LiyMn3)octO8 drops below l-Li1/2MnO2 in energy.The particularly steep drop in energy of ps-(LixMn)tet-(LiyMn3)octO8 compared to l-LixMnO2 with increasingLi concentration is due to the increase in electronsupply, making more Mntet

2+ possible.For Co, the energy of ps-(LixCo)tet(LiyCo3)octO8 by

contrast never drops below that of l-LixCoO2. Theresults of Figure 8 for crystalline structures, likethose in Table 1, mimic the results of the tetrahedraldefect calculations (Figure 4). In each case tetrahe-dral Co is found to be unfavorable at all lithiumconcentrations and oxidation states considered, whiletetrahedral Mn is found to be favorable at theLi1/2MnO2 composition when it has a +2 valence.

Further bolstering the association of +2 valencewith low-energy tetrahedral site occupancy by Mn isthe relatively low energy of LixMnO2 structures withone-sixth and one-eighth of the Mn in tetrahedralcoordination (marked with an × and a triangle inFigure 8) at lithium concentrations giving the tetra-hedral Mn a +2 valence and the octahedral Mn a +4valence (Li1/3MnO2 and Li1/4MnO2 compositions, re-spectively).

For Li concentration higher than Li1/2MO2 there isa rapid rise in energy for both ps-(LixMn)tet(Liy-Mn3)octO8 and ps-(LixCo)tet(LiyCo3)octO8 even thoughthe tetrahedral TM ions maintain a +2 valence. Thecause of this energy rise is the strong repulsionbetween Li+

oct and Mntet2+ or Cotet

2+ that share apolyhedral face. Above a Li content of one-half Li perTM ion, the ps-(LixM)tet(LiyM3)octO8 structure can onlyaccommodate Li in sites that share at least one facewith another cation. At the LiMO2 composition bothps-(LiMn)tet(Li3Mn3)octO8 and ps-(LiCo)tet(Li3Co3)octO8are unstable with the tetrahedral Mn and Co beingforced back into the TM layer octahedra by repulsive

interactions with face-sharing Li ions (hence the lackof a + data point at XLi ) 1 in Figure 8).

Figure 8 exemplifies the conflicting requirementsfor low-energy occupancy and passage through tet-rahedral sites by Mn in LixMnO2 with a ccp oxideframework. It requires the coexistence of both Livacancies to provide tetrahedral sites without face-sharing cations and Mn3+ that can form Mntet

2+

through charge disproportionation (eq 1). However,an increase in the concentration of Li vacanciesdecreases the amount of Mn3+ that can undergocharge disproportionation (eq 1) and vice versa. Thissuggests that the bulk of the Mn migration out ofthe transition-metal layer during the transformationof l-LixMnO2 occurs at partial lithiation when Mn3+

and Li vacancies coexist.39

The required coexistence of Mnoct3+ and Li vacan-

cies for the easy migration of Mn between octahedralsites via a tetrahedral intermediate also explains theability of s-LixMn2O4 to withstand electrochemicalcycling over the 0 e XLi e 2 range without significantcation rearrangement, even though the spinel order-ing is thermodynamically unstable near x ) 0 and 2.

When the spinel-like structure becomes metastablenear XLi ) 0, most of the Mn are +4 and there arelittle or no Mn3+ that can charge disproportionate.Hence, Mn passage through tetrahedral sites isprobably very unfavorable energetically. This cuts offthe “open” Oh f Td f Oh path of Figure 2. As a result,the Mn are “trapped” in the metastable spinel-likeconfiguration (λ-MnO2) at high charge. When thespinel structure becomes metastable near XLi ) 2there is a lack of Li vacancies. This also prevents Mnrearrangement even though Mnoct

3+, which can un-dergo charge disproportionation, are in abundance.Consequently, the metastable s-Li2Mn2O4 is pre-served at deep discharge as well. When Mnoct

3+,which can charge disproportionate, and Li vacanciescoexist at one-half lithiation, the spinel structure isthermodynamically stable. Therefore, when the Mnare most prone to migration, there is no thermody-namic driving force to do so and the spinel hoststructure is retained (although Mn can still dissolveinto the electrolyte through charge disproportion-ation).

This discussion has focused on stoichiometric spinelstructure, but nonstoichiometric spinels can exist aswell. In the case of spinels that are oxygen deficientthere could be significant concentrations of Mn3+

remaining at full charge. The results of this studysuggest that such spinels may be susceptible to cationrearrangement if they are energetically metastable.

8. Effect of Chemical Substitutions on Mn SitePreference

In sections 4, 5, and 7 it was shown how low-energyoccupation and passage through tetrahedral sites byMn is associated with the +2 oxidation state. It wasalso shown that Mnoct

3+ can readily produce Mntet2+

through charge disproportionation (eq 1). On theother hand, tetrahedral Mn with a +3 or +4 oxida-tion state was found to be less favorable.

Chemical substitutions that oxidize Mnoct3+, which

might otherwise produce Mntet2+ through charge


disproportionation, are a promising approach forhindering the transformation of metastable hoststructures such as l-LixMnO2. Such chemical substi-tutions would be expected to hinder Mn passagealong Oh f Td f Oh (Figure 2) type paths.

There are two categories of elements that will likelyproduce the desired effect: fixed low-valence cationsand electronegative (relative to Mnoct

3+) multivalentcations. It should be noted that fixed low-valencecations have the drawback of reducing the capacitysince it is extremely difficult to oxidize Mn above +4.Some cations in these categories that have alreadybeen shown experimentally to improve the electro-chemical performance of l-LixMnO2 and/or o-LixMnO2include Al3+,18 Co3+,7 Cr3+,53 Ni2+,54 Li+, and Cr3+.55

A series of first-principles results will now beshown that demonstrate the effect of a variety ofchemical substitutions on the valence of Mn and howthis in turn affects the site preference of Mn.

As discussed previously, a strong preference by Mnfor octahedral over tetrahedral coordination shouldresult in reduced mobility for Mn through a ccpoxygen framework. A reduced mobility for Mn in turncould increase the resistance of metastable chemi-cally substituted Mn oxide structures against struc-tural transformation.

The results of sections 4, 5, and 7 indicate thatthere is a good correlation between the energetics ofa tetrahedral Mn defect in l-LixMnO2 and the energydifference between l-LixMnO2 and a periodic smallunit cell structure with tetrahedral Mn like ps-(Lix-Mn)tet(LiyMn3)octO8 provided the Li contents andtetrahedral Mn oxidation states are the same in boththe periodic structure and the tetrahedral Mn defectcalculation. Specifically, Mntet

4+ is found to be rela-tively unfavorable whether it occurs as a defect inlayered l-MnO2 or within a periodic structure like ps-(Mn)tet(Mn3)octO8. Likewise, Mntet

2+ is found to berelatively favorable whether it occurs as a defect inlayered l-Li1/2MnO2 or within ps-(LiMn)tet(LiMn3)octO8.

To gauge the favorability of Mn entering tetrahe-dral sites in the presence of chemical substitutionsthat alter the Mn oxidation state, the energy differ-ence between structures such as ps-(LiMn)tet(Li-Sub3)octO8 (Sub ≡ Mn and/or substitutional elements)with tetrahedral Mn and l-Li1/2Mn1/4Sub3/4O2 (Sub ≡Mn and/or substitutional elements) without tetrahe-dral Mn have been evaluated over a large range ofchemical substitutions.

It is assumed that as with pure Mn oxides, the sitepreference for Mn at a given valence will be reflectedby the energy difference between the chemicallysubstituted compounds with and without tetrahedralMn. The use of simple structures such as ps-(LiMn)tet-(LiSub3)octO8 with tetrahedral Mn instead of largesupercells with tetrahedral Mn defects, like thoseused in section 4, greatly reduces the calculationtime.

Obviously it is an approximation to use the energydifference between a structure with tetrahedral Mnand a structure with only octahedral Mn as anindication of Mn mobility in a ccp oxide. To preciselydetermine Mn mobility along the “open” Oh f Td fOh path, the activation barrier is the required quan-

tity not the energy in tetrahedral coordination.However, if the energy of tetrahedral site occupancyfor Mn is high, the activation barrier for the Oh fTd f Oh path can only be equal or higher. Therefore,the energetics of Mn in tetrahedral coordination canprovide an upper bound on the mobility of Mn alongthe Oh f Td f Oh path.

Figure 9 shows the energy difference between ps-(LiMn)tet(LiSub3)octO8 (Sub ≡ Mn and/or elementssubstituted for Mn) and l-Li1/2Mn1/4Sub3/4O2, whichis believed to be a particularly good gauge for thestability of the layered structure. The reason for thisis that ps-(LiMn)tet(LiSub3)octO8 is equivalent to atetrahedral Mn and Li defect placed in a smallsupercell of layered structure (four MnO2 units asopposed to the 12 and 32 MnO2 unit supercells usedin section 4). Hence, its energy should be related tothe Mn tetrahedral defect energy in layered at agiven composition. Furthermore, the partially inversespinel (ps-(LiMn)tet(LiSub3)octO8) can be easily formedfrom l-Li1/2Mn1/4Sub3/4O2 by moving one-fourth of theMn into nearest neighbor tetrahedra in the Li layer,which equals the fraction of Mn that move from theTM layer to the Li layer during the transformationof layered to spinel (i.e., one Mn per eight oxygen).78,79

Therefore, ps-(LiMn)tet(LiSub3)octO8 could resembleintermediate structures that arise during the trans-formation.

Consistent with the proposed importance of Mnvalence and LFSE, low fixed valence cations (e.g.,Al3+, Mg2+, Li+) and electronegative multivalent

Figure 9. Energy difference between ps-(LiMn)tet(Li-Sub3)octO8 with tetrahedral Mn and l-Li1/2Mn1/4Sub3/4O2without tetrahedral Mn as a function of the spin on thetetrahedral Mn (Tetra Mn spin dx). Sub ≡ elementssubstituted for Mn and/or Mn. Pure Li1/2MnO2 is labeled“pure”. Each data point (*) has been labeled according tothe element substituted (e.g., Co) and the fraction of Mnin the “pure” structural counterpart they have replaced(e.g., 0.25). The substituted elements occupy only Oh sitesin both ps-(LiMn)tet(LiSub3)octO8 and l-Li1/2Mn1/4Sub3/4O2.Mn occupies Td sites and any available Oh sites in ps-(Li-Mn)tet(LiSub3)octO8 and only Oh sites in l-Li1/2Mn1/4Sub3/4O2.For data points that are clumped together, a single labelcontaining all the chemical substitutions contained in thecluster of points is enclosed in parentheses (e.g., 0.25Cr,0.25Fe). The chemical substitutions listed in these labelsare ordered (going from top to bottom in the label) fromlowest Mntet d spin to highest, i.e., from left-most data pointto right-most in the cluster. The data points for 0.25 Cuand 0.75 Ni cannot be resolved because they have nearlythe same coordinates: (0.25 Cu, 3.517, 0.887 eV); (0.75 Ni,3.519, 0.886 eV).


cations (e.g., Co3+, Ni2+, Cu2+) that oxidize Mn3+ arecalculated to stabilize Mn in the octahedral sites ofl-Li1/2Mn1/4Sub3/4O2. This is indicated in Figure 9 bythe ps-(LiMn)tet(LiSub3)octO8 with these chemicalsubstitutions (i.e., Sub ≡ Al, Mg, Li, Co, Ni, or Cu)being higher in energy than l-Li1/2Mn1/4Sub3/4O2rather than lower as is the case for pure Li1/2MnO2(labeled “pure” in Figure 9).

The correspondence between chemical substitu-tions that have been reported to experimentallystabilize layered l-LixMnO2 material and/or improveits capacity (e.g., Al3+, Co3+, Cr3+, Ni2+, Li+) and thechemical substitutions that are calculated to stabilizeMn in the layered octahedral sites according toFigure 9 is reassuring.7,18,53-55 Another encouragingfeature of Figure 9 is that none of the elements thatare found in compositions calculated to destabilizethe layered structure (e.g., Ti4+, Zr4+, Sn4+, V5+) havebeen reported experimentally to be successful instabilizing l-LixMnO2 material.

Cr substitution provides a particular example thatsupports interpreting the results of Figure 9 as ameasure of the layered structures stability againsttransformation. Experiments have shown that reduc-ing the Mn/Cr ratio in Cr-substituted l-LixMnO2reduces in size or eliminates the spinel-type step inthe voltage curve that arises during electrochemicalcycling of pure l-LixMnO2.53,56 This implies that Crsubstitution can hinder or prevent the transformationof the layered structure to spinel.

Davidson et al. found that replacing one-fourth ofthe Mn in l-LixMnO2 with Cr fails to prevent a stepin the voltage curve from developing with electro-chemical cycling.53 The calculated energy of thepartially inverse spinel (ps-(LiMn)tet(LiCrMn2)octO8)with one-fourth of the Mn substituted with Cr is-0.1494 eV/(Mntet) lower in energy than l-Li1/2(Cr1/4-Mn3/4)O2. Using this result as a gauge of stabilitysuggests that the layered structure with one-fourthCr should still be susceptible to forming tetrahedralMn and hence should still be susceptible to trans-forming into spinel, consistent with experimentalobservation.

A compound with one-half of the Mn ions substi-tuted by Cr was found to have no spinel step in itsvoltage curve.53 The energy of (LiMn)tet(LiCr2Mn)octO8for this case is calculated to be 0.2806 eV/(Mntet)higher in energy than l-Li1/2(Cr1/2Mn1/2)O2.24 Thisresult suggests that forming tetrahedral Mn in thelayered structure with one-half Cr should be unfa-vorable, and hence the structure should resist trans-forming into spinel, again consistent with observa-tion. While Figure 9 may give a measure of thestability of chemically substituted layered compoundsagainst Mn migration into the Li/vacancy layer, itshould be kept in mind that the elements substitutedfor Mn may themselves be prone to migration intothe Li/vacancy layer. However, in the Davidsonexperiment it appears that both the Cr and Mn resistmigrating into the Li/vacancy layer when the Mn issufficiently oxidized.

In addition to revealing which chemical substitu-tions could prevent the transformation of the layerstructure, Figure 9 also illustrates the relation

between the valence of Mn and its energy in tetra-hedral coordination. Starting at Mntet

2+ (i.e., d5

filling), the relative energy of ps-(LiMn)tet(LiSub3)octO8rises roughly linearly with increasing valence (i.e.,decreasing d filling) to a maximum peak at around+4 valence (i.e., d3 filling) for the tetrahedral Mn.

This is consistent with calculations shown in sec-tions 4, 5, and 7 that found the tetrahedral Mn4+

defect (Figure 4) as well as the delithiated ps-(Mn)tet-(Mn3)octO8 (Figure 8) to be particularly high in energy.It is also consistent with experimental results thatshow chemical substitutions which oxidize Mn to +4such as Ni40 increase the stability of the layeredstructure.54 When Mn is oxidized to +4 it becomes,practically speaking, electrochemically inactive inl-LixMO2 materials due to the great difficultly inoxidizing Mn above +4.

Figure 9 indicates that chemical substitutionswhich oxidize Mn stabilize the layered structureagainst transformation only up to a point. At valenceshigher than +4, i.e., tetrahedral Mn orbital fillingsless than d3, the trend abruptly shifts (Figure 9).Although in reality such valences are rare for Mn inccp oxides, Mn is predicted to become less stable inthe layered octahedral sites with valences increasingabove +4.

Figures 10-13 give further confirmation that themaximum energy for Mn occupation of tetrahedralsites in a ccp oxide occurs when the Mn valence is+4 (i.e., d3 filling), independent of cation ordering.Figures

Figure 10. Equivalent plot to Figure 9 except ∆E givesthe energy difference between fully inverse spinel, i.e.,antispinel (is-Mntet(LiSub)octO4; Sub ≡ substitutional ele-ments or Mn) and spinel (s-Litet(MnSub)octO4). Also, the xaxis is now the average spin on the tetrahedral Mn sincethere are two tetrahedral Mn per inverse spinel unit cell.All of the chemical substitutions replace 50% of the Mnions. In the anti-spinel, all of the octahedral Mn arechemically substituted. In the spinel half of the octahedralMn are chemically substituted.

Figure 11. Equivalent plot to Figure 9 at XLi ) 0.25.


10-13 contain energy plots equivalent to Figure 9that were generated from comparisons between fullyinverse spinel (is-(Mn)tet(LiSub)octO4) and spinel(s-Li(MnSub)O4), ps-(LiMn)tet(Sub3)octO8 and l-Li1/4-Mn1/4Sub3/4O2, ps-(Mn)tet(Sub3)octO8 and l-Mn1/4Sub3/4O2,spinel s-(Mn)tet(Sub2)octO4 and cation-deficient rock-salt rs-(MnSub2)octO4. Figure 10 is particularly no-table because it illustrates how chemical substitu-tions which reduce Mntet toward an ideal +2 d-orbitalfilling (e.g., 0.5 Nb), or that oxidize Mntet well above+4 (e.g., 0.5 Mg) are calculated to actually make thefully inverse spinel with tetrahedral Mn more stablethan spinel at one-half lithiation.

8.1. Electronic Structure Model for the Energeticsof Mn Oxides

Figures 9-13 show that the energy differencebetween structures with and without tetrahedral Mnis approximately a linear function of d-orbital fillingon the tetrahedral Mn within certain ranges.

One can intuitively understand the piecewise linearstructure of the plots in Figures 9-13 using a simplemodel based on the change in electronic structurewhen Mn moves from an octahedral to a tetrahedralsite. In this model it is assumed that the slopes ofthe lines in Figures 9-13 are equal to the energydifference between the energetically highest occupiedd orbital (HODO) of the tetrahedral Mn and theHODO of the octahedral Mn. This assumption isconsistent with electrons being transferred betweenoctahedral d levels and tetrahedral d levels that arefixed with respect to each other independent ofoxidation state.

Given the typical d-orbital splitting for tetrahedraland octahedral environments this leads to threedifferent regimes for the energy change when Mn

moves from octahedral to tetrahedral coordination asillustrated in Figure 14 (this model neglects thesplitting of the eg level by Jahn-Teller distortion).Figure 14 schematically pictures how the d orbitalschange for a Mn that moves from octahedral (Oh)coordination (e.g., in the layered structure) to tetra-hedral (Td) coordination (e.g., tetrahedral site in ps-(LiMn)tet(LiSub3)octO8).

The different regimes that occur as a function ofthe tetrahedral Mn d-orbital filling (dx) are as follows.

(1) x e 2. In this regime as Mn moves fromoctahedral to tetrahedral coordination the d electronsmove from t2g (lowered octahedral d) to e (loweredtetrahedral d) orbitals. The energy difference betweentetrahedral and octahedral Mn is given by the energydifference between the filled e and t2g orbitals plus aconstant (∆EMn7+) that accounts for other energycontributions independent of d-orbital filling (∆EMn7+

is the ∆E intercept at d0 of Figures 9-13).

(2) 2 < x e 3. The energy difference in this regimeincludes the contribution from the x e 2 regime plusthe energy difference between the filled t2 (raisedtetrahedral d) and the t2g (lowered octahedral d)orbitals giving

(3) 3 < x e 5. The energy difference in this regimeincludes the contribution from the x e 2 and 2 < x e3 regimes plus the energy difference between thefilled t2 (raised tetrahedral d) and eg (raised octahe-dral d) orbitals giving

This simple model, which gives a piecewise linearrelationship between the energy of tetrahedral Mnand its valence, fits the results of Figures 9-13surprisingly well, considering the wide variety ofsingle and multivalent cation substitutions used ingenerating these plots. This again indicates the

Figure 12. Equivalent plot to Figure 9 at XLi ) 0.

Figure 13. Energy difference between the s-(Mn)tet-(Sub2)octO4 spinel and rs-(MnSub2)octO4 cation-deficientrock-salt structures.

Figure 14. In tetrahedral coordination (Td) the d-orbitalsplitting is opposite and smaller in magnitude than thed-orbital splitting in octahedral coordination (Oh). Conse-quently, the transfer of electrons from d orbitals in an Ohligand field to d orbitals in a Td field as Mn moves from anoctahedral to a tetrahedral site falls into three differentregimes: x e 2, 2 < x e 3, and 3 < x e 5. These regimesare distinguished by the highest occupied d orbital (HODO)in the Oh and Td fields. Only integer fillings of the d shellare pictured, but fractional fillings can occur as well.

∆Eoctftet ) (Ee - Et2g)x + ∆EMn7+ (3)

∆Eoctftet ) (Et2- Et2g

)(x - 2) + 2(Ee - Et2g) +

∆EMn7+ (4)

∆Eoctftet ) (Et2- Eeg

)(x - 3) + (Et2- Et2g

) +

2(Ee - Et2g) + ∆EMn7+ (5)


substantial role Mn valence plays in determining itssite energy.

The model of eqs 3-5 suggests that the energy ofa manganese oxide can be conveniently separatedinto two contributions. One contribution is from theinteractions involving Li cations, O anions, Mn7+ (i.e.,d0) ionic cores, and elements substituting for Mn (d0

ionic cores if the d orbitals of these elements arefilled). The difference in this energy term betweenthe structures with and without tetrahedral Mnequals the y intercept (∆EMn7+) of ∆Eoctftet given byeqs 3-5. The other energy contribution is from theenergy of the filled Mn d orbitals (and in someinstances the substitutional element d orbitals) whichgives the piecewise linear valence dependent termsof ∆Eoctftet in eqs 3-5.

The simple d-level splitting model of eqs 3-5explains well the abrupt change in slope as theorbital filling moves from the 2 < x e 3 regime tothe 3 < x e 5 regime (Figures 9-12). When the fillingof the Mn d orbitals exceeds d3, the HODO of theoctahedral Mn goes from being lower in energy (t2g)to higher in energy (eg) than the HODO of thetetrahedral Mn (t2). Therefore, at d3 the slope of∆Eoctftet as a function of Mntet d filling abruptlychanges sign from positive to negative. The x e 2regime cannot be resolved from the 2 < x e 3 regimein Figures 9-13, which suggests that there is littlesplitting between the Mn d orbitals in tetrahedralcoordination (i.e., t2 and e).

While Figure 14 only illustrates a single Mn7+ ioncore and its associated d electrons moving from Ohto Td coordination, the proposed model of eqs 3-5 canalso be used to account for charge disproportionation(eq 1). When charge disproportionation occurs anadditional electron is transferred to the tetrahedralMn t2 orbital from a Mn eg orbital (or perhaps anothermultivalent cation d orbital) that remains in octahe-dral coordination. The HODOs over the 3 < x e 5d-filling regime (i.e., t2 tetrahedral, eg octahedral)remain the same whether charge disproportionationoccurs or not. Therefore, the presence of chargedisproportionation should not change the slope of theplot over the 3 < x e 5 regime according to eq 5. Thiscan be seen by comparing the 3 < x e 5 regime ofFigure 14 with the disproportionation reaction dia-gramed in Figure 15.

Equations 3-5 can be used to estimate the octa-hedral ligand-field splitting (∆o) from the slopes of

the lines fit to Figures 9-13. The octahedral ligand-field splitting is found to be roughly the same for allof the MnO2 host structures and Li contents consid-ered (i.e., Figures 9-12), ranging from ∆o ) 2.1 to2.3 eV. These values resemble the ligand-field split-ting reported experimentally for MnO2 of 2.5 eV.57

The estimated octahedral ligand-field splitting for theMn3O4 structures on the other hand (Figure 13) isfound to much lower at ∆o ) 1.2 eV. This is close tothe ligand-field splitting reported experimentally forMnO of 1.3 eV.57

In addition to having a lower estimated ∆o, thecalculations on Mn3O4 (Figure 13) differ from theMnO2 host structures in having the y intercept∆EMn7+ shifted to such a negative value that thetetrahedral Mn structure (s-(Mn)tet(Sub2)octO4) isalways lower in energy than the structure with onlyoctahedral Mn (rs-(MnSub2)octO4), although a maxi-mum in energy at Mntet

4+ is maintained.While the piecewise linear regions and energy

maximum around +4 valence of Figures 9-13 areconsistent with ligand-field effects, it is important tobear in mind that LFSE cannot by itself predict theenergy difference between octahedral and tetrahedralMn.

For example, in section 6 the change in LFSEassociated with the charge disproportionation reac-tion creating tetrahedral Mn2+ (eq 1) is projected tobe equal to the Jahn-Teller splitting R, i.e., a positiveenergy (see Figure 7). However, first-principles cal-culations show that the energy of producing tetra-hedral Mn2+ through charge disproportionation (eq1) in l-Li1/2MnO2 is negative (Figures 4, 8, and 9).

The possibility that Mn generally favors tetra-hedral coordination as its valence approaches +2 (i.e.,d5) is unlikely given that MnO has a rock-saltstructure not zinc blende or some other structurewith Mntet

2+. Instead, the driving force for Mn move-ment out of the octahedral sites of l-Li1/2MnO2 intoneighboring Li layer tetrahedral sites appears to bedue to the unique cationic ordering and associatedcationic interactions that are present in l-Li1/2MnO2.

In the case of l-Li1/2MnO2, the positive change inLFSE for charge disproportionation (i.e., R) is insuf-ficient to counter the cationic interactions that favorMn movement into Li layer tetrahedra. Conversely,in chemically substituted compounds such as l-Li1/2-Mn3/4Mg1/4O2, the much higher change in LFSEassociated with Mn4+ movement from octahedral totetrahedral coordination (38/45 ∆o assuming -4/9∆o) ∆t) overwhelms the interactions favoring theformation of tetrahedral Mn4+ so that it becomeshighly unfavorable energetically.

While LFSE can be useful for explaining the trendsof Mn site preference with valence, it does not captureimportant energy contributions that are more sensi-tive to cationic ordering. These energy contributions,for example, make the formation of tetrahedral Mn2+

favorable in l-Li1/2MnO2 but unfavorable in s-LiMn2O4.A more clear picture of these energy contributionscan be gained from the model of eqs 3-5.

One energy contribution that is sensitive to cationicordering given explicitly in eqs 3-5 is the y intercept∆EMn7+. According to the proposed model ∆EMn7+

Figure 15. Schematic of the charge disproportionationreaction which involves two Mn as opposed to the singleMn reactions shown in Figure 14. Charge disproportion-ation can occur over the 3 < x e 5 filling range. The set oforbitals Oh and Td linked by a right arrow (f) correspondto the Mn moving from octahedral to tetrahedral coordina-tion. The other set of orbitals labeled Oh correspond to aMn that remains in octahedral coordination. Integer fillingsof the d shell are pictured, but fractional fillings can occuras well.


accounts for the interactions involving Li cations, Oanions, Mn7+ (i.e., d0) ionic cores, and elementssubstituting for Mn (d0 ionic cores if the d orbitals ofthese elements are filled). It is assumed that theseinteractions are primarily electrostatic. ∆EMn7+ canhave a substantial effect on site energetics as thedifference in y-intercepts of Figures 9-13 show.

The other energy contribution that is sensitive tocationic ordering is implicitly part of d-orbital termssuch as (Et2 - Eeg)(x - 3) in eqs 3-5. A coefficientsuch as (Et2 - Eeg), which gives the energy differencebetween the tetrahedral t2 and octahedral eg orbitals,can be broken down into two parts.

One part depends on the ligand-field splitting in agiven coordination (i.e., ∆o and ∆t). This part is thechange in LFSE is represented in Figure 7 (e.g., Rfor Mn charge disproportionation; eq 1, 38/45 ∆o forMn4+ Oh f Td).

The other part depends on the average energy ofthe d orbitals, i.e., the energy barycenter, in a givensite. The energy barycenter of d orbitals in octahedralcoordination is represented by the level above b inFigure 16.45 In moving Mn between octahedral andtetrahedral sites there is a change in LFSE causedby the change in the splitting of the d orbitals (e.g.,from t2g and eg to e and t2) and a change in energybarycenter caused by the change in the averageinteractions experienced by electrons in the d orbit-als.

Taking into account the change in barycenter ofthe d levels and the interactions involving the Mn7+

ionic cores, a more complete expression for the energychange (∆Ecd) associated with the Mn charge dispro-portionation reaction (eq 1) than that given in Figure7 can be obtained

The change in LFSE of R associated with the chargedisproportionation reaction of Mn (Figure 7) is nowaugmented with two other terms to give a morecomplete expression for the total energy change: ∆Eb,which equals the change in the d barycenter (Etb -Eob), and ∆EMn7+, which equals the change in Mn coreinteraction energies when Mn moves from an octa-hedral to a tetrahedral site (EMntet

7+ - EMnoct7+).

Equation 6 helps clarify why the energy of thecharge disproportionation reaction producing tetra-hedral Mn in l-Li1/2MnO2 is negative. The y interceptof Figure 9 is close to zero, which indicates that∆EMn7+ ≈ 0 when changing from l-Li1/2MnO2 to (ps-(LiMn)tet(LiMn3)octO8). Therefore, in this case theenergy of charge disproportionation is approximately∆Ecd ) 5∆Eb + R. Since R is positive, ∆Eb must benegative for the formation of tetrahedral Mn in l-Li1/2-MnO2 to be energetically favored. In other words, thed-orbital energy barycenter in ps-(LiM)tet(LiM3)octO8is lower than the barycenter in l-Li1/2MnO2 accordingto this model.

Just as values for ∆o can be estimated from Figures9-13 using eqs 3-5, so to can values for ∆Eb and∆EMn7+. Whereas ∆o is estimated to be roughlyconstant (2.1-2.3 eV) for the MnO2 host structures(Figures 9-12), the values of ∆Eb and ∆EMn7+ areestimated to vary much more widely (-0.48 to 0.29eV and -2.1 to 0.36 eV, respectively). This is consis-tent with the d-orbital barycenter and the Mn7+ coreinteractions being more sensitive to cationic orderingthan the ligand-field splitting, as previously sug-gested.

Since the LFSE term is determined by Mn valenceand appears to be relatively insensitive to cationordering in the MnO2 host structures, it would seemto be the easiest energy term to manipulate throughchemical substitutions. This is because the exactplacement of the chemical substitutions in the Mnsublattice would presumably be less important for theLFSE term than for the terms that are more sensitiveto cationic ordering (i.e., ∆Eb and ∆EMn7+).

9. Qualitative Ionization ScaleThe previous sections highlighted the role valence

plays in determining Mn site preference and mobilitythrough a ccp oxide framework and consequently inthe susceptibility of metastable structures such asl-LixMnO2 to structural transformation. Since chemi-cal substitutions are one way of manipulating thevalence of Mn, it is useful to be able to predict theeffect substituted cations will have on the valence ofMn in either tetrahedral or octahedral sites. Thelarge number of calculations used to produce Figures9-13 can be used to provide a qualitative oxidationscale between Mn and other 3d TM ions. The relativeoxidation/reduction strength of the substituted TMions that Mn coexists with in Figures 9-13 can byobtained by determining the valence of each cationusing the spin integration method described in sec-tion 5.

Figure 17 holds in a compact form all of the valenceinformation on crystalline TM oxides produced by thefirst-principles calculations of this study. The positionof a given ion pair (e.g., Nioct

3+f4+) on the chart

Figure 16. Effect of octahedral coordination on the energyof TM 3d orbitals: (a) 3d level of free TM ion. 3d orbitalsare degenerate. (b) Average interactions between anions,neighboring cations, and 3d electrons shift the averageenergy of the 3d orbitals. (c) Splitting of 3d energy levelsin an octahedral ligand field. Note that while the energyof the 3d orbitals may be increasing due to the negativelycharged ligands, the overall energy of the system isdecreasing in going from a free ion to bound one.

∆Ecd ) (5Etb + EMntet7+) + (3Eob - 6

5∆o + EMnoct

7+) -

2(4Eob - 35

∆o - R2

+ EMnoct7+)

∆Ecd ) 5(Etb - Eob) + R + (EMntet7+ - EMnoct

7+)

∆Ecd ) 5∆Eb + R + ∆EMn7+ (6)


indicates the relative energy ranking of that ioniza-tion reaction (e.g., the ionization energy of Nioct

3+ toNioct

4+) compared to the various ionization energiesof Mn in octahedral and tetrahedral coordination.The qualitative ranking of the Mn ionization energiesin octahedral and tetrahedral coordination is labeledprominently along the center of Figure 17.

The purpose of this scale is to aid in qualitativelypredicting the effect of 3d TM ion chemical substitu-tions on the valence of Mn in octahedral or tetrahe-dral sites of a ccp oxide. This scale can be useful forchoosing chemical substitutions that will keep octa-hedral Mn in a relatively immobile valence state (i.e.,near +4) over the range of an electrochemical cyclewhere the coexistence of Mn3+ and Li vacancies wouldallow the rapid transformation of a metastable ccpoxide (e.g., as with l-LixMnO2 or o-LixMnO2).

To illustrate the use of the qualitative ionizationscale given in Figure 17, consider the case of layeredLi(Ni1/2Mn1/2)O2.58 Assuming that the oxidation statesof Li and O are +1 and -2, respectively (calculatedto be true except in extremely electron-deficientcases), Ni and Mn must hold an average valence of+3. Moving up from the bottom of the scale one notesMnoct

3+f4+ is ranked lower than Nioct2+f3+. This

means Mn3+ is favored to be oxidized to +4 over Ni2+

being oxidized to +3. Since one-half Mn4+ and one-

half Ni2+ gives an average valence of +3 required bythe Li content, the predicted valences are Mn4+ andNi2+. This matches calculated40 and experimentalresults.59

Since Figure 17 is constructed only with calcula-tions on Mn oxides substituted with one other 3dmetal, it is not clear whether using Figure 17 topredict the valence of two or more non-Mn 3d TMions coexisting in an oxide would be valid. However,with additional calculations on non-Mn TM oxidecompositions perhaps Figure 17 can be expanded toaddress combinations of non-Mn TM ions.

10. Effect of Valence on Site Preference of Other3d Transition Metals

Since the results of the previous sections indicatethat the site preference and tendency toward migra-tion of Mn or Co is strongly affected by the electronoccupancy of the d levels split by ligand-field effects,it is possible that this may be the case for all of the3d TM ions.

The 3d orbitals of Mn and Co and those of the otherfirst-row transition metals should have a qualita-tively similar ligand-field splitting in octahedral ortetrahedral sites of an oxide.44,45 The magnitude ofthe splitting may vary as it depends on the extent ofoverlap between the TM d and oxygen p states.46,60

However, as a first approximation it is instructiveto neglect this variation in ligand-field splittingacross the 3d series and simply characterize a TMion at a given valence by the number and configu-ration (e.g., high or low spin) of its d electrons. Forexample, Fe3+ would be expected to behave somewhatsimilar to Mn2+ when both have a high-spin d5

configuration (e.g., t2g3eg

2 in octahedral coordination).The relative energetics of tetrahedral and octahe-

dral occupancy for Mn and Co in a ccp oxide withLi1/2MO2 composition was observed to be consistentwith the projected change in LFSE for Mn and Cowhen they are moved from octahedral to tetrahedralcoordination (Figure 7; section 6). To test how wellthis trend holds for other 3d transition metals,calculations equivalent to those done with Mn andCo in section 7 were performed for the transitionmetals Ti through Cu on the ps-(LiM)tet(LiM3)octO8and l-Li1/2MO2 (M ≡ 3d TM) structures as well theirdelithiated counterparts ps-(M)tet(M3)octO8 and l-MO2.

Table 2 gives the calculated energy difference(∆Eoctftet) between ps-(LiM)tet(LiM3)octO8 and l-Li1/2-MO2 for the 3d transition metals from Ti to Cu(ordered lowest ∆Eoctftet to highest). It also lists thechange in valence and d-orbital filling that ac-companies the structural change from l-Li1/2MO2 tops-(LiM)tet(LiM3)octO8. The valence and d-orbital fill-ing have been determined using spin integration asdescribed in section 5. For each respective change ind-orbital filling that accompanies the formation oftetrahedral M, the projected change in LFSE andspin-paining energy (SPE) is given. The SPE isimportant to consider because the splitting from spinpairing (∆s) can be of comparable magnitude to thesplitting from the ligand field in 3d transition metals(hence the existence of high-spin octahedral cationswhen ∆s > ∆o).50,51 ∆s is the additional repulsive

Figure 17. Qualitative ionization energies for 3d ions atvarious valences in an oxide framework. The position of agiven ion pair indicates the energy ranking of that ioniza-tion reaction. Comparisons are relative to Mn ionizationenergies in Oh and Td coordination labeled prominently inthe center of the figure. Solid black arrows indicate well-determined upper and/or lower energy limits for a givenionization energy. Dashed lines with a question markindicate that in that direction the energy limit was notdetermined. For example, the ionization energy Croct

2+f3+

is calculated to be lower in energy than Mnoct2+f3+ but it

is uncertain which Mn ionization energy it lies above. Ifan ionization energy lies at the same level as one of theMn energies and does not have an arrow on either side(e.g., Cooct

3+f4+), that ionization energy and the Mn energywhich it is level with were found to be approximately equalin energy (i.e., Cooct

3+f4+ ≈ Mntet3+f4+). The chart entry

Feoct3+f4+ marked with an asterisk (*) contradicts the result

calculated for anti-spinel (Mn)2(Li2Fe2)O8 but it is consis-tent with all other calculations performed on Lix(MnFe)O2structures.


energy caused by two electrons of opposing spinoccupying the same d orbital. For finding the changein SPE of Tables 2 and 3, ∆s is assumed to be roughlyequal for both octahedrally and tetrahedrally coor-dinated d orbitals. Table 3 contains the results fromcalculations on ps-(M)tet(M3)octO8 and l-MO2 for the3d transition metals from Ti to Cu (ordered lowest∆Eoctftet to highest).

Each 3d metal from Ti to Cu in Table 2 and 3 willnow be discussed.

10.1. TiTi is calculated to have a delocalized d band in

l-Li1/2TiO2. This is reflected by each Ti holding a +3.5charge. In l-TiO2, Ti is calculated to have an emptyd band and a +4 valence. At both Li concentrationsthe tetrahedral Ti is +4 and the projected change inLFSE and SPE for Ti moving from octahedral totetrahedral coordination is zero. This is consistentwith Ti having a relatively low calculated value for∆Eoctftet (fourth lowest in Table 2 and third lowestin Table 3).

However, the that fact ∆Eoctftet for Ti is higher thanMn and Fe in Table 2 and higher than Cr in Table 3runs contrary to expectations based solely on LFSEand SPE since Mn and Fe at XLi ) 1/2 and Cr at XLi) 0 have a projected change in LFSE and SPE thatis greater than zero.

If l-LixTiO2 could be synthesized, the negative valueof ∆Eoctftet for Li1/2TiO2 (-0.12 eV) suggests that Ti

in a layered structure could be susceptible to migra-tion into the Li layer at partial lithiation. Experi-mentally layered LiTiO2 has not been synthesized asthe similar ionic size between Li and Ti leads to adisordered rock-salt structure.61 Layered Li(Ni0.45-Ti0.55)O2 has been synthesized; however, it suffersfrom poor cyclability which is blamed on Ti migrationinto the Li/vacancy layer.62 Additionally, Ti has beenreported to migrate into the Na layer of layeredNaTiO2.63 These experimental observations are con-sistent with the relative ease Ti4+ is expected to havein moving between octahedral and tetrahedral coor-dination due to a lack of ligand-field stabilization.

10.2. VAt XLi ) 1/2, V is calculated to maintain the same

valence (+3.5) in octahedral and tetrahedral coordi-nation, i.e., there is no charge disproportionation informing tetrahedral V at this Li composition (Table2). The projected change in LFSE and SPE at XLi )1/2 is (3/5)∆o - (9/10)∆t, which is positive whetherthe proportionality given by crystal-field theory |4/9∆o| ) |∆t| is assumed46 or if ∆t ≈ 0 is assumed asthe results in section 8 suggest for Mn. The greaterchange in LFSE and SPE for Li1/2VO2 than forLi1/2TiO2 is consistent with a greater value of ∆Eoctftetin Table 2. This suggests that V should be less pronethan Ti to enter tetrahedral sites at this averagevalence, and hence l-Li1/2VO2 should be more resis-tant against transformation than l-Li1/2TiO2. How-

Table 2. Energy Differences between ps-(LiM)tet(LiM3)octO8 and l-Li2M4O8 (M ≡ 3d TM) for Each 3d TM from Ti toCu Listed from Lowest ∆E to Highesta

reaction ∆Eoctftet (eV) d filling ∆ LFSE and SPE

2Mnoct3+ f Mnoct

4+ + Mntet2+ -0.33 2t2g

3eg1 f t2g

3 + e2t23 R

4Feoct3.5+ f Fetet

3+ + 3Feoct3.67+ -0.17 4t2g

41/2 f e2t23 + 3t2g

41/3 2∆o - 2∆sCuoct f Cutet

b -0.15 NA NA4Tioct

3.5+ f Titet4+ + 3Tioct

3.33+ -0.12 4t2g1/2 f e0t2

0 + 3t2g2/3 0

Voct3.5+ f Vtet

3.5+ 0.039 t2g11/2 f e11/2 (3/5)∆o - (9/10)∆t

Croct3.5+ f Crtet

3.5+ 0.30 t2g21/2 f e2t2

1/2 ∆o - ∆t2Nioct

3+ f Nioct4+ + Nitet

2+ 0.43 2t2g6eg

1 f t2g6 + e4t2

4 (6/5)∆o - (4/5)∆t + R4Cooct

3.5+ f 3Cooct4+ + Cotet

2+ 0.58 4t2g51/2 f 3t2g

5 + e4t23 (14/5)∆o - (6/5)∆t - 2∆s

a Column 1 gives the valence states accompanying the movement of the TM ion from octahedral to tetrahedral coordination.Column 2 gives the energy difference between ps-(LiM)tet(LiM3)octO8 and l-Li2M4O8 per tetrahedral M. Column 3 holds the changein d-orbital filling that results from moving the TM ion from octahedral to tetrahedral coordination. The projected change inLFSE and spin pairing energy (SPE) that results from the change in d-orbital filling is listed in column 4. This energy is expressedin terms of the octahedral splitting (∆o), the tetrahedral splitting (∆t), the Jahn-Teller splitting (R), and the spin-pairing splitting(∆s). ∆s is the additional repulsive energy from two electrons of opposing spin occupying the same d orbital. b The change invalence/d filling for Cu could not be determined using the method of section 5.

Table 3. Energy Differences between ps-(M)tet(M3)octO8 and l-M4O8 (M ≡ 3d TM) for Each 3d TM from Ti to CuListed from Lowest ∆E to Highesta

reaction ∆Eoctftet (eV) d filling ∆ LFSE and SPE

Croct4+ f Crtet

4+ 0.54 t2g2 f e2 (4/5)∆o - (6/5)∆t

Voct f Vtetb 0.57 NA NA

Tioct4+ f Titet

4+ 0.64 t2g0 f e0 0

Feoct f Fetetb 0.76 NA NA

Cuoct f Cutetb 1.0 NA NA

Cooct4+ f Cotet

4+ 1.3 t2g5 f e2t2

3 2∆o - 2∆sMnoct

4+ f Mntet4+ 2.1 t2g

3 f e2t21 (6/5)∆o - (4/5)∆t

Nioct4+ f Nitet

4+ 2.6 t2g6 f e3t2

3 (12/5)∆o - (3/5)∆t --2∆s

a Column 1 gives the valence states accompanying the movement of the TM ion from octahedral to tetrahedral coordination.Column 2 gives the energy difference between ps-(M)Tet(M3)octO8 and l-M4O8 per tetrahedral M. Column 3 holds the change ind-orbital filling that results from moving the TM ion from octahedral to tetrahedral coordination. The projected change in LFSEand spin-pairing energy (SPE) that results from the change in d-orbital filling is listed in column 4. This energy is expressed interms of the octahedral splitting (∆o), the tetrahedral splitting (∆t), and the spin-pairing splitting (∆s). b The change in valence/dfilling for Cu, Fe, and V could not be determined using the method of section 5.


ever, ∆Eoctftet is still relatively small (0.039 eV/Vtet),suggesting that V might still easily migrate out ofmetastable octahedral sites at this composition.

The value of ∆Eoctftet for VO2 was calculated to bethe second lowest in Table 3. Unfortunately thevalences of V in ps-(M)tet(M3)octO8 could not be clearlydetermined using the spin integration method ofsection 5 because the net spin on the V did not matcha spin-polarized configuration consistent with theaverage formal oxidation state. Instead, the V tookon a non-spin-polarized state.

10.3. Cr

Like V, Cr is calculated to maintain a +3.5 oxida-tion state in both octahedral and tetrahedral coor-dination at XLi ) 1/2 (Table 2). At this lithiumconcentration the projected change in LFSE and SPEis higher for Cr than for V, which is consistent withthe greater value of ∆Eoctftet calculated for Cr inTable 2. This supports Cr having a stronger prefer-ence for octahedral sites at the +3.5 valence than V.At +4 valence Cr was calculated to have the lowest∆Eoctftet in Table 3. This is consistent with therelatively low projected change in LFSE and SPE forCr4+ moving from octahedral to tetrahedral coordina-tion ((4/5)∆o - (6/5)∆t).

The enhanced stability of l-Lix(Cr1/2Mn1/2)O2 re-ported experimentally can be explained by theseresults.53 As l-Li(Cr1/2Mn1/2)O2 is delithiated, the Mnis oxidized to +4 first according to section 9 andexperiment.55 As already discussed, Mn4+ is highlystable in octahedral coordination. Cr is oxidized to+4 later in the charge, when Li vacancies that canfacilitate TM ion migration are more plentiful. Therelatively high value of ∆Eoctftet calculated for Cr3.5+

in Table 2 probably reflects a strong preference foroctahedral coordination at this valence. One wouldexpect Cr to have an even stronger preference foroctahedral coordination in l-Li1/2(Cr1/2Mn1/2)O2 sinceits valence is +3 which has a t2g

3 orbital fillingsthesame orbital filling as Mn4+.

While Cr4+ has the lowest ∆Eoctftet in Table 3 andrelatively weak ligand-field stabilization, the absolutevalue of ∆Eoctftet (0.54 eV) for CrO2 is still higher thanthat for Li1/2CrO2 (0.3 eV). Furthermore, there prob-ably is no longer a driving force to convert to spinelin highly delithiated l-Lix(Cr1/2Mn1/2)O2. The fact thatthe structural integrity of l-Lix(Cr1/2Mn1/2)O2 is main-tained over delithiation attests to a relatively strongoctahedral site preference exhibited by Cr at partiallithiation.

It has been observed that when Cr6+ is formed indelithiated l-Li(Li1/5Mn2/5Cr2/5)O2, it spontaneouslymoves into tetrahedral coordination.55 This is con-sistent with the lack of d electrons for Cr6+ and hencethe lack of ligand-field stabilization.

10.4. Mn

Mn goes from having the lowest ∆Eoctftet at XLi )0.5 (Table 2) to the second highest ∆Eoctftet at XLi )0 (Table 3). The low value of ∆Eoctftet for Mn at XLi )0.5 is consistent with a relatively small projected

change in LFSE and SPE equal to the Jahn-Tellersplitting (R).47,48

As mentioned before, the fact that ∆Eoctftet is lowerfor Mn than for Ti despite R being greater than zeroruns contrary to expectations based solely on LFSE.According to the simple model of eqs 3-5 in section8.1, the low energy of ps-(LiMn)tet(LiMn3)octO8 com-pared to l-Li1/2MnO2 can be explained by a lower dbarycenter in ps-(LiMn)tet(LiMn3)octO8 (eq 6). The delectrons of the tetrahedral Mn2+ enter d orbitals thatare shifted lower in energy, probably because theyare surrounded by less negative charge in a tetra-hedral site than in an octahedral one. Ti4+, on theother hand does not have any d electrons, so there isno energy reduction resulting from a lower tetra-hedral d barycenter.

Another factor that could make ∆Eoctftet particu-larly low for Mn in Table 2 is the half-full orbitalshells of Mn2+ and Mn4+ (the products of Mn3+ chargedisproportionation). In general, half-full or full orbitalshells have lower energy than other fillings becausethe electron-electron repulsion is decreased64 (thisis why in the chemistry of low atomic numberelements the electrons arrange so often to producefull “octets”). On this basis one expects Mn2+ to havea lower electron-electron repulsion energy due to itshalf-full d shell64 (e2t2

3 in tetrahedral coordination).It is also favorable for the levels that result fromligand-field splitting to be half-full or full.50 There-fore, the half-full t2g level (t2g

3) of Mn4+ is favorablein this regard as well. The energetic favorability ofhalf-filled levels is another reason Mn3+ in manyenvironments is observed to be unstable to bothreduction to Mn2+ and oxidation to Mn4+.52

10.5. FeAt XLi ) 0.5 there is a large positive change in

LFSE (2∆o) for the formation of tetrahedral Fe.However, this is counteracted by a large negativechange in spin-pairing energy (-2∆s). The decreasein spin-pairing energy is caused by one of the low-spin Feoct

2/3+ becoming high-spin Fetet3+. Recalling

that ∆s can be comparable in magnitude to ∆o in 3dmetal oxides,50,51 the net change in LFSE and SPEgiven for Fe in Table 2 is probably small. This isconsistent with the negative value calculated for∆Eoctftet (-0.17 eV/Fe tet). However, the net changein LFSE and SPE should still have a positive valuesince Fe is calculated to be low spin in octahedralcoordination (t2g

4.5 or t2g4.33), indicating that |∆s| < |∆o|.

l-LiFeO2 has been synthesized by ion exchangefrom NaFeO2, but it shows little or no electrochemicalactivity.65 It was not reported whether this is a resultof Fe3+ migration; however, the results of Table 2suggest that Fe should be susceptible to migrationout of the TM layer at partial lithiation in l-LixFeO2

At XLi ) 0 Fe was found to be of intermediatestability in octahedral coordination. Unfortunatelythe valences of the Fe ions could not be clearlydetermined using the spin integration method ofsection 5 because the net spin on the Fe did notmatch a high-spin or low-spin configuration consis-tent with the average formal oxidation state (+4).This suggests that the d-orbital filling takes on an


intermediate spin configuration for Fe and/or theassumed oxygen formal oxidation state of -2 is nolonger justified due to strong covalency between theFe and O.

10.6. CoCo has the highest value of ∆Eoctftet in Table 2. This

is consistent with it having the largest projectedchange in LFSE ((14/5)∆o - (6/5)∆t). However, thechange in LFSE is somewhat counteracted by anegative change in spin-pairing energy (-2∆s). Thespin-pairing energy is reduced in the charge dispro-portionation of Co where four d fillings of t2g

5.5 changeto three t2g

5 and e4t23. This helps explain why ∆Eoctftet

calculated for Co is not as high compared to the other3d metals as one would expect on the basis of LFSEalone.

At XLi ) 0 Co has the third highest ∆Eoctftet. Itschange in LFSE and SPE is 2∆o - 2∆s and the sameas Fe at XLi ) 0.5, which has a low ∆Eoctftet. Apossible explanation for this is that the magnitudeof ∆o is higher and/or the magnitude of ∆s is lowerfor Co4+ than for Fe3.5+.

The remarkable success of LiCoO2 as an electrodematerial is likely related to the strong intrinsicpreference of Co for octahedral sites over the +3 to+4 valences as indicated by the high calculated valueof ∆Eoctftet in Tables 2 and 3. This strong preferenceof Co for octahedral sites clearly suggests that Co willnot easily migrate through an close-packed oxygenframework at these oxidation states.

10.7. NiNi is calculated to have the second highest ∆Eoctftet

at XLi ) 0.5 and the highest ∆Eoctftet at XLi ) 0. AtXLi ) 0.5, Ni is calculated to undergo a chargedisproportionation reaction (eq 1) similar to Mn andCo. The projected change in LFSE and SPE is higherfor Ni than Cr, which is consistent with the highervalue of ∆Eoctftet calculated for Ni than Cr in Table2. On the basis of these calculations, Ni is expectedto be the second most stable in octahedral sites atan average valence of +3.5 of the 3d metals from Tito Cu.

The high value of ∆Eoctftet calculated for Ni at XLi) 0 is consistent with the large projected change inLFSE (12/5∆o - 3/5∆t). However, as with Co3.5+, thechange in LFSE is somewhat counteracted by anegative change in spin-pairing energy (-2∆s), whichhelps explain why ∆Eoctftet calculated for Ni4+ is notas high compared to the other 3d metals as one wouldexpect on the basis of LFSE alone.

The calculated stability of Ni in octahedral coor-dination is consistent with the good electrochemicalperformance observed experimentally for Li(MnNi)-O2 compounds. The Ni2+ oxidizes Mn to +4, whichas already discussed has a strong preference foroctahedral sites. When the average valence of Ni isbetween +3 and +4, there is a high concentration ofLi vacancies that would facilitate ion migration,except for the strong preference of Ni for octahedralsites over this valence range. Ni2+ also most likelyhas a strong preference for octahedral coordination

due to ligand-field effects, although probably not asstrong as Ni3+ since there is an additional electronin the eg level.

10.8. CuAt an average formal valence of +3.5, Cu is

calculated to have the third lowest ∆Eoctftet equal to-0.15 eV per tetrahedral Cu. This suggests that Cuat this average valence does not have a strongpreference for octahedral sites. At an average formalvalence of +4, ∆Eoctftet for Cu (1 eV) is ranked fourthhighest in Table 3. In practice, such high oxidationstates for Cu are probably difficult to achieve. How-ever, if it were to occur, a metastable structure likel-LixCuO2 should be prone to transformation atpartial lithiation according to these results. Unfor-tunately, the valence of Cu in both cases could notbe clearly determined using the spin integrationmethod of section 5.

10.11. Overall Trends for 3d MetalsThe energy of all the 3d metals entering tetrahe-

dral coordination from the l-LixMO2 structure de-creases as XLi goes from 0 to 1/2. This is similar tothe defect calculations on Co and Mn in section 4 thatfound tetrahedral defect energies in the layeredstructure to decrease for both as Li content increasesfrom 0 to 1/2.

At XLi ) 0.5, three of the eight TM ions (Mn, Co,and Ni) were found to undergo a major chargedisproportionation reaction (eq 1) when moved fromoctahedral to tetrahedral coordination. In contrast,at XLi ) 0 none were found to undergo chargedisproportionation.

Table 2 shows a good correlation between therelative energetics of octahedral and tetrahedral siteoccupancy by a 3d metal ion and the projected changein LFSE for moving a 3d metal ion from octahedralto tetrahedral coordination. From rows 4 (Ti) to 8 (Co)in Table 2 the correlation is perfect; the valuecalculated for ∆Eoctftet increases along with theprojected change in LFSE (from 0 for Ti to (14/5)∆o- (6/5)∆t for Co).

The two deviations from this trend are Mn and Fe,which have the two most negative values for ∆Eoctftet.Both of these cases probably have relatively smallnet changes in LFSE and SPE, which is consistentwith a more general association between low valuesof ∆Eoctftet and low projected changes in LFSE andSPE. The case of Fe illustrates that focusing exclu-sively on LFSE can be misleading when spin pairingis present, especially in low-spin cations.

Table 3 also shows a good correlation between∆Eoctftet and the projected change in LFSE, with thelargest changes in LFSE being associated with thehighest values of ∆Eoctftet.

The results given in Tables 2 and 3 support thedecisive role of LFSE in the site preference and mostlikely the mobility of 3d metal ions in a ccp lattice.For Mn, Ni, and Co the results in Table 2 areconsistent with the experimental work of Choi, Man-thiram et al. who found increasing resistance of l-Lix-MO2 against transformation into spinel as M is


changed from Mn to Ni to Co.49 Table 2 shows that∆Eoctftet and the projected change in LFSE and SPEfor Ni fall between those values for Mn and Co; thisagrees with the observed intermediate stability ofl-LixNiO2 compared to l-LixMnO2 and l-LixCoO2.

11. ConclusionsFor phase transformations involving rearrange-

ment of transition-metal cations over octahedral siteswithin a fixed ccp oxide framework, such as thetransformation of layered LixMnO2 to spinel, theresults of this study indicate that the low-energypathway for transition-metal migration betweenoctahedral sites is through a shared nearest neighbortetrahedral site (i.e., Oh f Td f Oh) rather thandirectly between octahedral sites (Oh f Oh). Thissuggests that the smaller the energy change is fortransition-metal ion movement between octahedraland tetrahedral coordination, the more easily the TMions should be able to rearrange in a ccp oxide whentransforming from a metastable structure to a stableone. As a result, the resistance against transforma-tion of metastable transition-metal oxides with a ccpoxygen sublattice (e.g., LixMnO2 with R-NaFeO2structure) will depend on the relative stability of thetransition metal in octahedral coordination comparedto tetrahedral coordination. The availability of emptytetrahedra without any cations occupying nearestneighbor face-sharing octahedra is also an importantfactor in the ability of TM ions to migrate through accp oxide. Such tetrahedra provide a relatively low-energy pathway by avoiding the highly repulsiveinteraction between face-sharing cations.

The energetics of Mn movement between octahe-dral and tetrahedral sites is found to be particularlysensitive to valence. Of the 3d transition metals fromTi to Cu, Mn is calculated to be the second moststable in octahedral coordination at +4 valence andthe least stable at +3 valence. This appears to resultfrom a large difference in ligand-field stabilizationbetween the +4 to +3 states of charge for Mn. Themost unfavorable change in LFSE associated withMn movement from octahedral to tetrahedral coor-dination occurs when Mn is +4 with three spin-polarized d electrons occupying a half-filled t2g shellin octahedral coordination. In contrast, Mnoct

3+ (t2g3eg

1)is calculated to undergo a charge disproportionationreaction (eq 1), forming Mntet

2+ (e2t23) and Mnoct

4+

(t2g3), which allows Mn2+ movement into tetrahedral

coordination with a relatively low change in LFSE.The low-energy passage of Mn through tetrahedral

sites enabled by Mnoct3+ charge disproportionation

appears to underlie the instability of metastable ccpMn oxides such as the layered R-NaFeO2 and orthor-hombic structures with electrochemical cycling. Inboth of these structures Mnoct

3+, which can chargedisproportionate, and Li vacancies, which facilitateMn migration by providing empty tetrahedral siteswithout face-sharing cations, coexist over the Liconcentration range where these structures are notthermodynamically stable.

Spinel-like LixMn2O4, on the other hand, maintainsits structural integrity, even when it is not thermo-dynamically stable at high and low lithium content.

This is probably because significant amounts of Mn3+

and Li vacancies do not coexist over ranges of Liconcentration where the spinel-like structure ismetastable. At low lithium concentrations the Mn areprimarily in the +4 oxidation state and consequentlyhave relatively low mobility. At high Li content (x ≈2 in LixMn2O4) there are insufficient Li vacancies toallow easy Mn rearrangement. When substantialconcentrations of Mn3+ and Li vacancies coexist ins-LiMn2O4, the spinel structure is thermodynamicallystable and hence not adversely effected by theincreased mobility of Mn. However, there still is theproblem of Mn dissolution into the electrolyte throughMn3+ charge disproportionation.

LFSE also appears to be a decisive factor in thesite preference of other 3d TM ions in a ccp oxide.As with Mn, this should impact the resistance ofother metastable 3d TM oxides against transforma-tion. The resistance against transformation impartedby ligand-field effects appears to be epitomized in thecase of layered LixCoO2. Contrary to the case withMn, the change in LFSE associated with Co move-ment from octahedral to tetrahedral coordination ishighly unfavorable in Li1/2CoO2. This provides im-pressive stability for layered LixCoO2 with electro-chemical cycling over Li concentrations where thespinel structure is thermodynamically stable (e.g.,Li1/2CoO2).

The results of this investigation lead to the predic-tion that, in general, metastable Mn oxide structureswith a ccp oxygen sublattice will rapidly transformto stable ccp structures if Mn3+ and/or Mn2+ coexistwith sufficient vacant interstitial sites. This is dueto the lack of ligand-field stabilization for Mnoct

2+ andthe susceptibility of Mnoct

3+ to charge disproportion-ation, which results in low ligand-field stabilization.This in turn makes tetrahedral sites relatively ac-cessible to Mn, which facilitates cationic rearrange-ment.

The energy difference between oxide structureswith and without Mn in tetrahedral coordination canbe fitted reasonably well to a simple model in whichthe energy difference is broken down into two con-tributions. One contribution is independent of Mnd-orbital filling and hence Mn valence. It accountsfor the change in interaction energy between a Mn7+

(i.e., d0) ionic core and the surrounding cations as aMn moves from an octahedral to a tetrahedral site.The other energy contribution is from the changingenergy of the filled d orbitals as Mn is moved fromoctahedral to tetrahedral coordination. The latterenergy contribution varies in a piecewise linearfashion with Mn valence and has a peak at Mn4+,reflecting the ligand-field splitting of octahedrallyand tetrahedrally coordinated d orbitals.

The energy contribution from the changing Mn dorbitals as Mn moves from octahedral to tetrahedralcoordination can in turn be separated into the changeof the Mn d-orbital energy barycenter and the changein ligand-field stabilization energy. While the changein LFSE is determined by the Mn valence, thed-orbital barycenter and the energy of interactionsinvolving the Mn7+ ionic cores are found to be muchmore sensitive to cationic ordering.


Using ionic valences found through a large seriesof calculations on substituted Mn oxides, a qualitativeionization scale between Mn and other 3d metals hasbeen constructed. This scale allows one to predict thevalences for Mn (in octahedral and/or tetrahedralcoordination) coexisting with another 3d TM cation(in octahedral coordination) in a ccp oxide. This couldbe useful for designing TM oxide materials withimproved kinetic stability over the range of Liconcentrations covered by electrochemical cycling.

The findings of this study point to a number ofdifferent strategies for producing lithium manganeseoxide structures, other than spinel, that resist trans-formation with electrochemical cycling. If a meta-stable ccp oxide structure such as l-LixMnO2 oro-LixMnO2 (XLi < 1) is used, high concentrations ofMnoct

3+ and Li vacancies should be prevented fromcoexisting over regions of metastability. This can beaccomplished by chemically substituting for Mn withlow fixed valence and/or electronegative multivalentcations that can oxidize the Mn eg orbital. There aremany different examples of this approach that havehad some success experimentally.7,18,53-55 Anotherway of oxidizing the Mn eg orbital is to introducevacancies into the Mn sublattice.66

Given that Mn4+ is the most stable valence inoctahedral coordination, it might be desirable for Mnto be electrochemically cycled between elevated oxi-dation states centered closer to +4 rather than overthe +3/+4 redox range characteristic of LixMnO2structures. Unfortunately at this time there probablyare not any electrolytes that can withstand theoxidative strength of Mn at valences higher than+4.67 An additional problem with Mn charged above+4 in ccp oxides is the possibility of decompositionreactions producing O2.58,68

Another strategy is to use a structure with anoxygen sublattice that is different from that of spinel(i.e., non-ccp). For such a structure to transform intospinel the oxygen needs to rearrange, which shouldmake the transformation much more difficult.

One way this has been accomplished experimen-tally is by using a close-packed oxide structure thatis not cubic-close packed.69,70 Such structures may bemore resistant against transformation to spinel, butthere still is a network of octahedral and tetrahedralsites that could possibly allow undesirable Mn move-ment during electrochemical cycling. The phospho-olivine structure is an example of a non-ccp oxide thathas shown good reversible capacity with iron (LiFe-PO4) however not with Mn (although Mn combinedwith Fe is reported to perform well).71 Oxides con-taining polyanions such as PO4

-3 offer a rich diversityof structures that might be suitable for use in apositive electrode.72

Another option is to use a non-close-packed struc-ture. A more open structure can constrain Mn byeliminating energetically favorable sites it can mi-grate through (e.g., tetrahedral sites). A layeredstructure can be made less close packed by pillaringopen the Li/vacancy layer with a large cation like K+

or with a cluster of atoms.73 The tunneled Mn oxidesare another example of non-close-packed structures.Good cyclability and resistance against transforma-

tion to spinel has been achieved by Doeff et al. usingsuch a structure.74,75

12. AcknowledgmentsThis research was supported in part by the MRSEC

Program of the National Science Foundation underaward number DMR-02-13282 and by the AssistantSecretary for Energy Efficiency and Renewable En-ergy, Office of Freedom CAR and Vehicle Technolo-gies, of the U.S. Department of Energy under Con-tract No. DE-AC03-76SF00098, Subcontract No.6517748 with the Lawrence Berkeley National Labo-ratory. Methodological developments that made thiswork possible have been supported by the Depart-ment of Energy under contract number DE-FG02-96ER45571. NPACI is acknowledged for providingsubstantial computing resources for this work. G.C.acknowledges a faculty development chair from R.P. Simmons.

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