Origin of low sodium capacity in graphite and generallyweak substrate binding of Na and Mg among alkaliand alkaline earth metalsYuanyue Liua,b,1, Boris V. Merinova, and William A. Goddard IIIa,1

aMaterials and Process Simulation Center, California Institute of Technology, Pasadena, CA 91125; and bThe Resnick Sustainability Institute, CaliforniaInstitute of Technology, Pasadena, CA 91125

Contributed by William A. Goddard III, February 19, 2016 (sent for review January 25, 2016; reviewed by Yi Cui and Michael L. Klein)

It is well known that graphite has a low capacity for Na but a highcapacity for other alkali metals. The growing interest in alternativecation batteries beyond Li makes it particularly important toelucidate the origin of this behavior, which is not well understood.In examining this question, we find a quite general phenomenon:among the alkali and alkaline earth metals, Na and Mg generallyhave the weakest chemical binding to a given substrate, comparedwith the other elements in the same column of the periodic table.We demonstrate this with quantum mechanics calculations for awide range of substrate materials (not limited to C) covering avariety of structures and chemical compositions. The phenomenonarises from the competition between trends in the ionization en-ergy and the ion–substrate coupling, down the columns of theperiodic table. Consequently, the cathodic voltage for Na andMg is expected to be lower than those for other metals in thesame column. This generality provides a basis for analyzing thebinding of alkali and alkaline earth metal atoms over a broadrange of systems.

energy storage | Na-ion battery | Mg-ion battery |quantum-mechanical calculations

Development of alternative cation batteries beyond Li couldsolve issues related with cost, stability, and other perfor-

mance characteristics (1–3). Na is an obvious candidate, but itsstorage in graphite (the commercial anode for Li-ion battery)is rather poor, with an electrochemical capacity of less than∼35 mAh/g (1, 4–7). Surprisingly, other alkali metals have a highcapacity (approximately hundreds) in graphite (8). To form abasis for improving the battery performance, we seek to under-stand the anomalously low capacity for Na.One explanation in the literature for the low Na capacity is as

follows: Na intercalation expands graphite from its favorableinterlayer spacing, by a greater amount than Li, leading to ahigher strain energy for graphite and, therefore, a less favorableformation energy for the Na-graphite compound compared withthe Li analog (9–11). However, this explanation would suggestthat graphite should have a low capacity for K, Rb, and Cs be-cause of their even larger size, which is in stark contrast to theexperimentally observed capacity dramatically higher than thatfor Na. This inconsistency calls for a revisit of the origin of thelow Na capacity in graphite.In this work, we use quantum-mechanical methods to show

that the Na anomaly has its roots in a general phenomenon:among alkali metals (denoted as M) and alkaline earth metals(denoted as EM), Na and Mg generally have the weakest bindingto a given substrate, independent of variations in substratestructure and chemistry. This phenomenon results from thecompetition between the ionization of the metal atom and the ion–substrate coupling, which have opposite trends along the col-umns. The universality of this phenomenon provides the basisfor analyzing trends in binding of alkali and alkaline earthmetals over a broad range of systems, and offers guidance fordesigning improved systems.

Our density functional theory (DFT) calculations used theVienna ab initio simulation package (VASP) (12, 13) with pro-jector augmented wave (PAW) pseudopotentials (14, 15). ThePerdew–Burke–Ernzerhof (PBE) exchange-correlation func-tional (16) including van der Waals corrections (DFT-D3) (17) isused to model the graphite and its compounds, whereas in othercases where the van der Waals interaction is insignificant, we usePBE only. The plane-wave cutoff energy is 400 eV, with suffi-cient Monkhorst–Pack sampled k points (18) (for example, 15 ×15 × 7 for graphite). All structures are fully relaxed until the finalforce on each atom becomes less than 0.01 eV/Å. We used asingle M or EM atom with 6 × 6 unit cells of each substratematerial to model the binding with graphene, its derivatives,MoS2, SnS2, and TiS2, whereas a 4 × 4 cell is applied for V2O5.For Pt(111), we used a slab consisting of 6 × 6 surface cells, andthree layers, with the bottom layer fixed in the same plane.We consider first the case of graphite. Fig. 1 shows the cal-

culated formation energy (Ef) of M-graphite compounds, whereM = Li, Na, K, Rb, and Cs. The Ef is defined as follows:

Ef = ½EðtotÞ− nM   Eðbulk MÞ− nC   EðgraphiteÞ�=ðnM + nCÞ, [1]

where E(tot) is the total energy of compound, E(bulk M) is theenergy per M atom for the bulk metal, E(graphite) is the energyof C in graphite, and nM and nC are the number of M and Catoms in the compound. Here, we focus on MC6 and MC8 be-cause these stoichiometries are commonly found in non-Na com-pounds. We find that the Ef follows the order: Na > Li > K >Rb >Cs, where all Ms except for Na have negative Ef with graphite, aresult consistent with calculations in the literature that usedifferent method (19). Thus, Na-graphite compounds with high

Significance

The growing demand for energy storage urges the develop-ment of alternative cation batteries, which calls for a system-atic understanding of binding energetics. We discover ageneral phenomenon for binding of alkali and alkaline earthmetal atoms with substrates, which is explained in a unifiedpicture of chemical bonding. This allows us to solve the long-standing puzzle of low Na capacity in graphite and predict thetrends of battery voltages, and also forms a basis for analyzingthe binding of alkali and alkaline earth metal atoms over abroad range of systems.

Author contributions: Y.L. and W.A.G. designed research; Y.L., B.V.M., and W.A.G. per-formed research; Y.L., B.V.M., and W.A.G. analyzed data; and Y.L., B.V.M., and W.A.G.wrote the paper.

Reviewers: Y.C., Stanford University; and M.L.K., Temple University.

The authors declare no conflict of interest.1To whom correspondence may be addressed. Email: wag@wag.caltech.edu or yuanyue.liu.microman@gmail.com.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1602473113/-/DCSupplemental.

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Na contents are not thermodynamically stable, in contrast to theother four M-graphite compounds, in agreement with the exper-imentally observed low Na capacity.To understand why the Ef has a maximum at Na, we partition

the formation process for M-graphite compounds into threesteps, as illustrated in Fig. 2A. First, the bulk metal is evaporatedto form isolated atoms, with an energy cost of Ed (i.e., the cohesiveenergy). Second, the graphite crystal is strained to the configura-tion identical to that of the M-intercalated graphite, with an en-ergy cost of Es. This straining includes both interlayer expansionand in-plane stretching. Third, the M atoms are intercalated intothe strained graphite, with an energy drop by Eb (to be consistentwith the other terms, we define E−b = −Eb; a stronger bindingcorresponds to a lower E−b). According to Hess’s law:

Ef =Ed +Es +E−b. [2]

This analysis helps identify the dominating contribution. Al-though some terms are difficult to measure experimentally (suchas Es and Eb), all are calculated easily using DFT.As shown in Fig. 2B, neither Ed, Es, nor their combination has

a trend similar to Ef, which suggests that they do not embody theorigin of the low Na capacity. For both MC8 and MC8, Es in-creases monotonically as M moves down the periodic table dueto the increasing size of M atoms, whereas Ed decreases as aresult of weakened cohesion. The combination of Es and Edshows a monotonic drop, indicating that the change of Edoverwhelms that of Es. Nevertheless, none of them explains themaximum of Ef at Na.On the other hand, E−b exhibits a maximum at Na, similar to

that of Ef. This suggests that the low Na capacity is related di-rectly to E−b. In particular, compared with Li, the Na binding isso weak that it exceeds the decrease of Es + Ed, making Ef higherfor Na.This weaker binding of Na compared with Li has been

reported for other intercalation compounds, which has beenproposed to account for the observed lower cathodic voltage(20). Here we find that, of all of the five alkali metals, Na alwayshas the weakest binding for any given substrate. We first examinedilute M adsorption on graphene (Fig. 3A), which shows amaximum of E−b at Na. Then we modify the adsorption sites byincorporating structural defects or foreign atoms. Remarkably,

Na always shows the weakest binding (Fig. 3A). We continue thetest by considering other 2D non-C materials that have beentested for batteries, namely MoS2, TiS2, SnS2, and V2O5 (Fig.3B). We then extend this test to the surface of a typical bulkmaterials Pt(111) (Fig. 3B; as commonly found in Pt-based ca-talysis in alkaline solution). In all cases, Na has the weakestbinding among all five alkali metals, independent of the detailedsubstrate chemistry/structure. This general phenomenon calls fora unified explanation.E−b is the energy change when an M atom moves from the

vacuum to the binding site of the substrate. We consider thisprocess to first involve ionization of M by transferring its charge

Fig. 1. Calculated formation energies (Eq. 1) of alkali metal (M)-graphitecompounds. Note that, in contrast to other Ms, NaC6 and NaC8 have a pos-itive formation energy.

Fig. 2. (A) Partition of the formation process of M-graphite compound intoseparate steps. C, brown; M, pink. (B) The energetics of each step, relative tothose of Li (see Eq. 2 and the related text). “−Binding” means the reverse ofbinding energy, i.e., E−b in Eq. 2. Note that only E−b shows a trend similarwith Ef.

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to the substrate, with an energy change by Eion. This is followedby the coupling of the cation to the substrate (negatively charged)with an energy decrease of Ecp (which includes the electrostaticand other quantum-mechanical interactions), as illustrated in Fig.4A. Therefore,

E−b =Eion +Ecp. [3]

As M moves down the periodic table, the ionization potentialdecreases: 5.4 (Li), 5.1 (Na), 4.3 (K), 4.2 (Rb), and 3.9 (Cs),which favors the binding and results in a decrease of Eion. Notethat there is an abrupt drop in the ionization potential betweenNa and K. However, at the same time, the distance between thecation and the substrate becomes larger, which weakens theircoupling, leading to an increase of Ecp. To quantify this compe-tition, Fig. 4B shows the Eion and Ecp with respect to those of Lion the same substrate. The relative Eion is approximated by thedifference in the atomic ionization potential (IP), and the rela-tive Ecp is then derived from Eq. 3. Because the Ecp increasessmoothly from Li to Cs while the Eion drops dramatically fromNa to K (in other words, the coupling strength increases smoothlyfrom Cs to Li while the ionization cost drops dramatically from Kto Na), we obtain maximum of E−b for Na.

The Ecp is a general term that includes various kinds of in-teractions that are difficult to separate. However, for the cases ofM adsorption on metals [e.g., graphene and Pt(111)], one couldexpect the difference in Ecp of different Ms is dominated by theelectrostatic contribution, which is approximately −14.38/(2*d),where d is the distance between the cation and the substrateaccording to the image charge method. Therefore, in these cases:

ΔE−b =ΔEion +ΔEcp ∼Δ½−14.38=ð2 p dÞ�+ΔIP. [4]

As shown in Fig. 4C, the trend of E−b, given by the equation issimilar to that calculated by using DFT, which validates that thecompetition between Eion and Ecp is the reason for the maximumof E−b at Na. Indeed, this weak Na binding is also found indiatomic molecules M-X (where X = F, Cl, Br, I, and OH)(21), which can be explained similarly.It is interesting to consider whether the nonmonotonic trend

of the E−b is present in other columns. Based on the above ex-planations, we anticipate that this can be observed in the col-umns where Eion and Ecp have a reverse trend when movingdown the periodic table. The Ecp perhaps always increases as theatomic size gets larger; however, Eion does not always decrease,given the fact that the IP or electron affinity is nonmonotonic for

Fig. 3. E−b (the negative of the binding energy) for alkali metals binding to various substrate materials, relative to that of Li (the absolute values can befound in Supporting Information). (A) Graphene and its derivatives (with defects or substitutional foreign atoms); (B) non-C materials. Note that Na alwayshas the weakest binding among alkali metals.

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most groups. In fact, only the first two groups have a notablydecreasing IP. Therefore, one may expect a similar phenomenonoccurs for the EM group. Indeed, our calculations show that,among the EM elements, Mg generally has the weakest binding(Fig. 5) with a given substrate. This is consistent with the ex-perimental fact that Mg has a low capacity in graphite, similar tothe case of Na (8, 22). Note that Be and Mg are only physisorbedon pristine or nitrogen-doped graphene with the E−b approxi-mately of −30 meV/EM, significantly weaker than other EMs.This is because the work function of pristine or nitrogen-doped

graphene is too low to allow for a charge transfer from Be/Mg, asshown by the band structures in Supporting Information. Thesesystems are perhaps not practically interesting as the physisorbedadatoms could easily detach or cluster. It should also be notedthat, Be tends to have a stronger covalence than other EMs, dueto its high IP and small size. This might be the reason for thesignificantly enhanced binding of Be with the monovacancy ingraphene, in which case the Ecp contributes a large energy drop.For cathode materials, the weak binding with metal atoms

results in a low cathodic voltage. Therefore, we anticipate that

Fig. 4. (A) Schematic illustration of the binding between the alkali metal (M) and the substrate. (B) Evolution of the ionization energy (Eion) and the couplingenergy (Ecp) as M moves down in the periodic table. (C) Comparison of the calculated E−b (relative to that of Li) with that based on the model of Eq. 4.

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Na and Mg have a low cathodic voltage compared with othermetals in the same columns. Indeed, the Na case has been ver-ified by explicitly calculating the cathodic voltage for variousintercalation compounds (20). On the other hand, a weak bindingwith anode is desired to enhance the voltage when connected withcathode. However, this usually sacrifices capacity, as seen in thecase of Na in graphite. To improve the Na capacity, it is necessaryto reduce Ef. This can be achieved by using prestrained graphite (i.e., reducing the Es term in Eq. 2) with expanded interlayer spacingthrough intercalation of some other species, as has been demon-strated experimentally (9). Our calculations show that the opti-mum Ef for Na-graphite is reached when the graphite interlayerdistance is expanded to 4.3 Å, providing a target value for ex-perimental design. Indeed, such an expanded graphite using or-ganic pillars has been shown computationally to provide a verypromising hydrogen storage of 6.5 wt% at room temperature,meeting the Department of Energy requirement (23). Alternatively,the Ef might be reduced by enhancing the binding, which might beachieved through incorporating defects (24, 25).

In summary, we use quantum-mechanical calculations, to find ageneral phenomenon—among alkali and alkaline earth metals,Na and Mg generally have the weakest binding for a given sub-strate. We show that this results from the competition between theionization of the metal atom, and the ion–substrate coupling. Thisfinding elucidates the origin of the low Na capacity in graphite,predicts the voltage trends for alkali and alkaline earth metal ionbatteries, and provides a basis for analyzing the binding of alkaliand alkaline earth metal atoms in a broad range of systems.

ACKNOWLEDGMENTS. Y.L. thanks Drs. Brandon Wood, Suhuai Wei, andJiayu Wan for helpful discussions and Brandon Wood for providing access tothe Lawrence Livermore National Laboratory computational resources,which were used for some of the computations (supported under the Lab-oratory Directed Research and Development Program). Most of the calcula-tions were performed on National Energy Research Scientific ComputingCenter, a Department of Energy (DOE) Office of Science User Facility sup-ported by the Office of Science of the US DOE under Contract DE-AC02-05CH11231. Y.L. acknowledges the support from Resnick Prize PostdoctoralFellowship at Caltech. This research was funded by the Bosch Energy Re-search Network and by NSF (CBET 1512759).

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Fig. 5. E−b (the negative of the binding energy) for alkaline earth metals binding to various substrate materials, relative to that of Be (the absolute valuescan be found in Supporting Information). Note that Mg always has the weakest binding.

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