Scott Kirklin , Bryce Meredig , and Chris Wolverton *
High-Throughput Computational Screening of New Li-Ion Battery Anode Materials
We use density functional theory (DFT) in conjunction with grand canonical linear programming (GCLP), a powerful automated tool for analyzing ground state thermodynamics, to exhaustively enumerate the 515 thermodynamically stable lithiation reactions of transition metal silicides, stannides and phos-phides, and compute cell potential, volume expansion, and capacity for each. These reactions comprise an exhaustive list of all possible thermodynamically stable ternary conversion reactions for these transition metal compounds. The reactions are calculated based on a library DFT energies of 291 com-pounds, including all transition metal silicides, phosphides and stannides found in the Inorganic Crystal Structure Database (ICSD). We screen our computational database for the most appealing anode properties based on gravimetric capacity, volumetric capacity, cell potential, and volume expan-sion when compared with graphitic carbon anodes. This high-throughput computational approach points towards several promising anode composi-tions with properties signifi cantly superior to graphitic carbon, including CoSi 2 , TiP and NiSi 2 .
1. Introduction
Batteries have become indispensable components of portable electronic devices, and are also increasingly used in large-scale applications such as hybrid-electric vehicles, stationary power storage and load leveling. The widespread use of batteries has motivated a global effort to discover and optimize battery mate-rials. For most applications Li-ion batteries represent the cur-rent state of the art. They possess the highest energy and power density of any commercial battery chemistry due to the low mass, high mobility, and high electronegativity of Li ions. [ 1–3 ] For these reasons, lithium batteries have been the subject of extensive research and have seen signifi cant improvement in the last two decades.
As a result, lithium ion battery materials have seen a progres-sion of constantly improving chemistries. The current genera-tion of commercial anode materials has been heavily dominated by graphitic carbon based materials. Carbon has several impor-tant advantages: carbon is easily processed, widely available, has well understood processing, and cycles well. These properties make carbon a convenient choice for lithium-ion batteries, but as demand for compact, long-lasting batteries increases, it is
S. Kirklin, B. Meredig, Prof. C. WolvertonDepartment of Materials Science and EngineeringNorthwestern UniversityEvanston IL, 60208, USA E-mail: [email protected]
DOI: 10.1002/aenm.201200593
Adv. Energy Mater. 2012,DOI: 10.1002/aenm.201200593
necessary to look for higher capacity elec-trode materials. One class of anode mate-rials with signifi cantly superior capacity to carbon, are alloying reaction anodes. [ 4–8 ] This class contains materials such as sil-icon, [ 9 ] phosphorus [ 10 ] and tin. [ 11 ] Carbon has a theoretical capacity of 372 mAh g − 1 and 830 mAh cm − 3 in contrast silicon, phosphorus and tin have very high specifi c capacities: 4007, 2596 and 959 mAh g − 1 and volumetric capacities: 9330, 6982, and 7066 mAh cm − 3 respectively.
Although these materials have very high capacities, they also have exception-ally poor cycle-ability. [ 12 ] In these anodes, failure is attributed to the large volume expansion which occurs during lithia-tion. In order to ameliorate the effects of this volume expansion, using compounds of active elements (which form lithium-containing compounds) with an inactive element(which does not form lithium-con-
taining compounds) has been shown to improve cycle-ability. [ 3 ] In this work we investigate three classes of active-inactive compounds as conversion reaction anode materials: transition metal silicides, phosphides and stannides. These materials were selected for several reasons. First, the active materials were chosen for having very high lithium capacities. Second, the inactive components were chosen because 3d transition metals do not form compounds with lithium. As a result it is generally assumed that on lithiation of the active element, the inactive element will be extruded as a ductile and conducting buffer matrix to reduce stresses and facilitate electrical contact with the current collector. Third, in order to maximize the spe-cifi c capacity, we exclude prohibitively heavy elements from the search space and constrain the search to the fi rst row of transi-tion metals. Finally, these elements are also relatively abundant in the earth’s crust, and therefore relatively inexpensive.
We fi rst defi ne the term ‘conversion reaction’. Conversion reactions as discussed in this work are defi ned as:
TMxAy + zLi → xTM + AyLiz (1)
where TM refers to any 3d transition metal, and A = Si, Sn, or P. A conversion reaction stores lithium by converting the original anode material into a lithium rich compound and a second displaced phase. This is in contrast to an intercalation (or insertion) reaction, in which lithium is inserted into the host structure without disrupting the original lattice, and an alloying reaction, in which lithium insertion causes the forma-tion of one new phase, but does not displace any material into an additional new phase.
The fi rst reported use of silicon as a negative electrode for lithium electrochemical cells was by Sharma and Seefurth. [ 13 ] They established silicon as a very high capacity electrode material for molten lithium cells. At elevated temperatures, silicon reactions to produce a series of lithium-rich com-pounds, including: Li 12 Si 7 , Li 5 Si 2 , Li 13 Si 4 , and Li 21 Si 5 . In con-trast, it is known that at the lower temperature of 300 K the lithiation of silicon self-terminates at a meta-stable phase, Li 15 Si 4 . [ 9 ] The very high capacity of silicides leads to large volume expansion, up to 300\%, which in turn generates large internal stresses. These stresses cause delamination of active material and rapid degradation of capacity. [ 12 ] It has been proposed to address the problem of volume expansion by alloying silicon with an element which does not form com-pounds with lithium. [ 14 ]
Previous studies on transition metal silicides have had con-fl icting results. Fleischauer [ 15 ] et al studied mixtures of iron, manganese and chromium/nickel silicides with excess silicon, forming transition metal silicides and pure silicon. In this case, the TM silicide was found to be electrochemically inactive, with only the excess silicon participating in the lithiation reaction. This study found that ultimate capacity was linearly related to the amount of excess silicon in the anode. In contrast, others have found that on electrochemical lithiation, silicon-rich nickel, titanium and vanadium silicides decompose, producing much higher capacities than can be attributed to excess silicon. [ 16 , 17 ] Here, in addition to determining the theoretical limits to transi-tion metal silicide performance, we weigh in on this discrep-ancy by identifying the thermodynamically preferred reaction pathway.
1.2. Transition Metal Stannides
There have been two commercially successful batteries based on tin conversion reactions. The fi rst commercial battery to use a tin conversion reaction anode was Fujifi lm’s Stalion bat-tery in 1997. It has an amorphous SnM x O y anode, where M is a mixture of elements including B, P and Al. [ 18 ] This lithia-tion reaction proceeds by drawing tin out of the oxide to form a network of lithium stannide particles in a stable inactive matrix. The good cycling ability of this reaction has led to a great deal of interest in discovering other active-inactive com-pounds for use as negative electrodes. [ 19 ] In addition to tin oxide anode materials, transition metal stannides have been found with impressive capacities and are good cycleability. The second tin conversion reaction anode to appear in commer-cial batteries was the Sony Nexelion battery. It is a Co-Sn-C composite, consisting of grains of Co-Sn in a conducting and ductile carbon matrix. [20] Previous studies of transition metal stannides have included Co, [ 21–23 ] Fe, [ 8 , 24 ] Cu, [ 8 ] Ni, [ 8 ] Cr, [ 21 ] and Zn. [ 8 ] It was found that among TM-Sn-C ternary compo-sitions, cobalt stands out as having the best performance. [ 25 ] This high performance is attributed to cobalt not having a stable carbide. In this work we will show that this may not be the only factor contributing to Co-Sn as the best anode material.
Transition metal phosphides were originally anticipated to react with lithium like transition metal oxides, intercalating lithium into a stable host lattice. [ 26 ] Although some transition metal phosphides have been found to exhibit this behavior, e.g. MnP 4 [ 10 ] and VP, [ 27 ] lithiation by intercalation is not the thermo-dynamic ground state; after cycling the material will transform via conversion reaction. Conversion reactions in these materials are appealing due to the formation of Li 3 P, which has one of the highest lithium capacities among all lithium containing com-pounds. [ 26 ] Since this discovery, other transition metal phos-phides including Co, [ 28 ] Fe, [ 29–31 ] Ni, [ 32–35 ] Mn, [ 36 ] Cu, [ 37 , 38 ] Ti, [ 39 ] and V [ 39 ] have been investigated. These compositions are found to form nanocrystallites which, due to their size, do not suffer as much as a result of volume expansion, leading to improved reversibility. [ 6 ]
1.4. High-Throughput Computational Approach
Previous efforts to explore active-inactive compositions have been generally limited to only a few compositions in each system. A more thorough study of conversion reaction thermo-dynamics requires the capability to study thousands of compo-sitions in a completely self-consistent way. In this work we use a robust computational framework to fully explore the range of achievable cell potentials, gravimetric and volumetric capaci-ties, and volume expansions among all possible thermodynami-cally stable reactions involving the transition metal silicides, stannides and phosphides. Density Functional Theory (DFT) is well suited to predicting these properties, [ 40–50 ] so we will use DFT to study the performance of these materials in a system-atic and high-throughput way. In order to authoritatively and exhaustively describe the thermodynamically available reac-tions for each of these anode materials, we adapt a technique developed in the fi eld of hydrogen storage to describe metal hydride decomposition pathways. Just as in lithium conver-sion reactions, in metal hydrides the problem of mapping out ground state thermodynamics and identifying stable decompo-sition pathways is unintuitive and complex. Akbarzadeh [ 51 ] et al presented a method to elegantly solve this problem, the grand canonical linear programming (GCLP) method.
GCLP is a physical model for determining the thermody-namically preferred behavior of a system with very complicated chemistry without relying on chemical intuition or ineffi cient brute force methods. [ 52 ] Subsequently this method has been used for identifying reactions and generating ground state phase diagrams [ 51 , 53–58 ] Here we use GCLP in conjunction with DFT to explore the phase diagrams of transition metal stannides, phos-phides and silicides. We found 291 known compounds from the ICSD, from which there are 24,388,710 possible conversion reactions, but the vast majority of these reactions are thermody-namically unstable. By using GCLP we are able to elucidate the stable reaction paths directly and quickly. Based on the results of this analysis we screen the predicted reactions based on their performance as lithium-ion battery anodes, in terms of capacity, voltage and volumetric expansion. Finally, once we understand what is thermodynamically possible, we can apply simple
Figure 1 . Process of screening all possible reactions in a candidate phase space to fi nd the thermodynamic limits of performance and predicted practical limits. Beginning with all possible reactions, we screen by including only lowest-energy thermodynamically allowed lithiation reac-tions. Next, we apply known kinetic limitations, e.g., block the formation of Si 5 Li 21 . [ 82 ] Finally, we order the remaining reactions based on perform-ance and return those with the highest performance.
Theoretical limits to
performance
Suggestions for experimental investigation
All possible anode reactions
Thermodynamically stable anode reactions
Practically achievable reactions
DFT+GCLP to find stable reactions
Apply known kinetic limitations
Rank by predicted performance metrics
kinetic limitations to these results to further refi ne our search to the most likely candidates for experimental investigation. In this approach, summarized in Figure 1 we generate a list of reactions from a collection of DFT calculated energies of a database of experimentally measured structures. The resulting reaction database can be searched based on simple perform-ance metrics to fi nd reactions which meet any specifi ed set of requirements. We illustrate our approach by screening the data-base for one such set.
2. Methods
2.1. Density Functional Theory
The zero-temperature, zero-pressure enthalpy of each com-pound is determined from density-functional theory calcula-tions [ 59 , 60 ] In this work these calculations were performed using the Vienna Ab-initio Simulation Package (VASP). [ 61–64 ] We generated k-point meshes using the Alloy Theoretic Advanced Toolkit [ 65 ] with a nominal k-point density of 10,000 k-points per reciprocal atom in the Monkhorst-Pack scheme. [ 66 ] Projector augmented wave potentials [ 67 , 68 ] were used in the generalized gradient approximation to the exchange-correlation energy, [ 69 ] with projection operators evaluated in real space. Each structure was optimized with respect to cell shape, volume and internal coordinates to a total energy convergence of 1 meV using the conjugate gradient method [ 70 ] at a plane wave energy cutoff of 520 eV. Electronic occupancies were determined using a
fi nite-temperature Fermi smearing with width 0.05 eV. Given the very large number of materials included in this study, we selected two formation energies, those of FeSi and Li 21 Si 5 , and verifi ed that at our energy cutoff and k-point our values were converged to within 5 meV/atom. The 291 crystal structures in this study consist of all unary and binary compounds in all Li-M-A (M = 3d transition metals, A = Si, Sn, P) systems found in the Inorganic Crystal Structure Database (ICSD). [ 71 ]
2.2. Grand Canonical Linear Programming
Grand canonical linear programming [ 72 ] is a very effi cient approach to determining stable reaction pathways for very large sets of compounds, by utilizing extremely fast linear program-ming routines. This technique was originally developed for predicting hydrogen storage reaction pathways, [ 51 , 56 , 57 , 73 ] ; how-ever, the formalism is completely general and here we apply it to lithiation reaction chemstries. GCLP has been previously used by Mason [ 74 ] et al to do a similar search for lithium battery materials in the Li-Mg-B-N-H system. In this formalism, the grand potential of a collection of phases is most generally expressed by
φ (� �x, T, P ) =
∑ixi Gi (T,, P) −
∑j
μμ j
∑i
xi C̄i, j)( (2)
where �x is a vector containing the relative amount of each compound, i . G i (T,P) is the Gibbs free energy of compound i at a given temperature and pressure, �μ is the chemical poten-tial of each element j , and ̄Ci, j is a composition matrix which contains the elemental composition of element j in each com-pound i . We fi nd the ground state composition by minimizing φ with respect to �x . In order to model battery reactions where only lithium is in contact with a reservoir, we apply a constraint requiring that the amount of every element except lithium be equal to some initial composition, �z0 . The concentration of Li is not fi xed, and is instead dictated by the chemical potential μ Li , which can be adjusted analogously to changing the applied voltage in an electrochemical cell. The constraint is simply given by Equation 3 :
∀ j �= Li : z0
j =∑
iC̄i, j xi (3)
Since the free energy is linear in �x and so is the constraint �z0 we can call on highly effi cient linear programming tech-niques to minimize the free energy. Because existing linear programming algorithms are so fast, it is tractable to use GCLP even for large regions of phase space, containing many com-pounds. This method is dependent on having a large and reli-able database of free energies, G i (T, P) , of compounds. In this work, such a database was constructed using DFT to determine the free energy of formation at 0 K and 0 Pa, i.e., G i (0,0) or simply the formation energies of the compounds.
We illustrate this method in Figure 2 , which shows an imple-mentation of this scheme for FeSi 2 . In the ternary Fe-Si-Li Gibbs triangle for this system, the lithiation reaction for this com-pound will follow a straight line from the initial composition, FeSi 2 , toward the lithium vertex. Along this path, we determine
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Figure 2 . Step-by-step calculation of the potential-capacity curve of FeSi 2 from the fi rst principles phase diagram. On the ternary phase diagram (a), a lithiation reaction corresponds to the bold line drawn from an initial composition, FeSi 2 in this example, straight toward the Li vertex. Along this reaction path, any intersecting tie-line will correspond to a change in the lithiation reaction, and a kink in the convex hull (b). The potential as a function of composition is simply the slope of each segment of the formation energy vs. composition curve; therefore the potential-capacity curve (c) will have a step at each kink in the convex hull.
Si
Fe
Li
Li12Si7SiLi
Li5Si2, Li13Si4,Li21Si5
FeSi2
FeSi
Fe3Si
For
mat
ion
Ene
rgy/
eV
atom
-1C
ell P
oten
tial
vs
Li/
V
x in Lix(FeSi2)(1-x)
a)
b)
c)
the lowest free energy phase composition at every point. Finally, we plot the chemical potential (in eV/Li) of lithium as a func-tion of composition, which is equal to the cell potential because each lithium carries one electron. From these results we can identify a reaction for each two phase region in the formation energy vs. composition curve, or equivalently each plateau in the potential-capacity curve. The formation energy refers to the energy of a compound relative to the composition-weighted average of the pure elemental energies. Steps in voltage coin-cide with kinks in the free energy function, which is due to crossing a tie line in the ternary phase diagram. To enumerate every possible anode reaction for a given region of phase space, we perform this analysis for a mesh of initial compositions and record every unique reaction which occurs. This approach is equivalent to identifying all three phase regions in the ternary
phase diagram, where each region corresponds to a unique lithiation reaction. Further, in consideration of the fact that a single anode material may incorporate several lithiation reactions in sequence, instead of one single reaction, we must also consider every unique combination of lithiation reactions.
In order to use GCLP to accurately predict battery reactions, four assumptions must be valid. First, the thermodynamic data-base of compound formation energies which GCLP uses must contain all of the compounds which can occur at the specifi ed composition. i.e., for FeSi 2 to appear in the result, FeSi 2 must be present and correct in the database. In this work, the database was populated based on a search of the ICSD for every ele-mental, binary or ternary compound with a composition in any Li-A-TM (A = Sn,Si,P) ternary phase diagram. For each com-pound, the formation energy and volume were determined from DFT. After evaluating all 291 compounds, we found that there were 145 thermodynamically stable. A compound is defi ned to be stable if there is no other combination of compounds which is lower in energy than the compound itself. These 145 stable compounds comprise the library used for all GCLP results in this work. Second, GCLP is a purely thermodynamic model, so the results refl ect the predicted equilibrium reaction sequences. As a consequence, no metastable phases will be predicted in any reactions. Furthermore, sluggish reaction kinetics can pre-vent the equilibrium phases from appearing readily, and these kinetic effects are not considered here. Third, we must assume that there is no solid solubility of any element in any phase, i.e., only linear combinations of stoichiometric line compounds are present. This assumption is implicit in the second assump-tion, that only DFT ground state compounds can appear in the predicted reaction. Finally, in applying DFT + GCLP to battery materials at room temperature, we make the additional implicit assumption that entropy does not have a signifi cant contri-bution to free energies. Previous studies have found that the change in free energy between the different lithium silicides varies by less than 20 meV/atom with respect to temperature between 0K and 300K. [ 45 ] The cell potentials presented here are on the order of hundreds of meV/atom, so we expect that the entropic contribution will lead to only small numerical dif-ferences, and no change in qualitative results.
3. Results
3.1. Demonstration of Methodology: Si and FeSi 2
We begin our validation by showing the results of applying DFT + GCLP to the lithiation of pure Si. Figure 3 shows a direct comparison between an experimentally measured silicon lithia-tion potential-capacity curve [ 75 ] with our DFT + GCLP prediction. The experimental data comes from a high temperature lithium titration experiment. Due to the elevated temperature and slow reaction rate, the system is expected to be in true thermody-namic equilibrium at every stage of the reaction. Each partial reaction appears as a single plateau of constant potential, with each plateau separated by steps where the reaction changes. When compared with experiment, DFT is able to reproduce the
Figure 3 . Comparison of DFT + GCLP lithiation curve with an experimen-tally measured curve of silicon with molten lithium at 790 K. [ 75 ]
0
50
100
150
200
250
300
350
400
0 1 2 3 4 5
Po
ten
tial
vs
Li/
V
x in SiLix
Experiment
DFT+GCLP
Figure 4 . Comparison of DFT formation energies with experiment for 3d transition metal silicides. [ 83 ] For each DFT formation energy we compare to the entire range of experimentally measured formation energies.
0
10
20
30
40
50
60
70
0 10 20 30 40 50 60 70
Exp
t. fo
rmat
ion
ener
gy/ k
J m
ol−
1
DFT formation energy kJ mol
Range of expt. ΔH
important features of the lithiation curve very well, indicating that DFT accurately represents the thermodynamic limits to performance for conversion reaction anodes.
Having shown that we are able to accurately reproduce cell voltages for the lithiation of pure silicon, next we dem-onstrate the ability to calculate the cell potential of a conver-sion reaction, as given by Equation 1 . The reaction enthalpy includes the decomposition of an active-inactive compound. In Equation 4 we show the effect of this decomposition term on the cell potential of the complete reaction.
V =μLi
qLi= −
�Gr xn
qLi�NLi= −
�G pr od − �Gr eact
qLi (N pr odLi − Nr eact
Li)
=x�GT M + � GAy Liz
) − �GT Mx Ay − z�GLi
)
qLi z−
(4)
The reaction voltage is given by the chemical potential of lithium divided by the charge carried by each lithium atom, q Li = e . Here the chemical potential of Li, is defi ned to be equal to the negative change in free energy per lithium added. The overall change in free energy, Δ G rxn can be written as the difference between Δ G prod and Δ G react , which are the free energy of forma-tion of the products and reactants respectively. The product and reactant phase terms are further decomposed into the free ener-gies of formation (relative to the pure elements) of each constit-uent phase Δ G phase of the conversion reaction of Equation 1 . The formation energy of lithium and then inactive metal, Δ G TM and Δ G Li , are zero by defi nition. As a result, the voltage of a reaction of the form in Equation 1 is determined from the difference, per lithium atom, between the stability of the lithiated phase, A y Li z , and the active-inactive compound, TM x A y . One consequence of this relation is that for reactions involving only binary com-pounds, the reaction potential is bounded by the potential of the pure active material. Without performing any calculations, this provides a fi rst order approach to selecting active-inactive elec-trode materials. In order to signifi cantly reduce the voltage of a given active material, A, one should use metal-A compounds which are strongly bound and have a large formation energy. However, these compounds might be kinetically limited (due to the high binding energy of the metal-A phase). To essentially preserve the voltage of the active material A, then one should consider weakly bound metal-A compounds.
To validate the formation energies of compounds of this type, TM 1-x A x , we compare the DFT formation energy of 20 transition
metal silicides with the experimentally measured values in Figure 4 . Because there is such a wide range of observed for-mation energies, for each transition metal silicide we show the entire range of formation energies reported in the literature. The DFT formation energy is within the bounds of the max-imum and minimum measured formation energies in nearly all cases, which indicates that DFT + GCLP is able to accurately reproduce the thermodynamics of decomposition and lithiation for the transition metal silicides.
To illustrate the application of DFT + GCLP to predict the cell potential, capacity and volume expansion for a binary anode material, we consider FeSi 2 and refer to Figure 2 . There we show schematically how the lithiation reaction is determined for FeSi 2 . The potential-capacity curve is obtained by following a straight line path through composition space from FeSi 2 toward the lithium vertex of the ternary phase diagram (Figure 2 a). Along this path, the formation energy with respect to FeSi 2 and Li is shown in Figure 2 b. As shown in Equation 4 , the oppo-site of the slope of each segment (Figure 2 c.) is the chemical potential of lithium as a function of lithium content, which is equivalent to a plot of cell potential vs capacity. Because we are confi dent in the lithiation reaction of silicon, as well as the decomposition of FeSi 2 , we are confi dent in the predicted ther-modynamics of the lithiation of FeSi 2 .
The result of this analysis for FeSi 2 is a list of sequential lithiation reactions, Equation 5 through Equation 8 . This set of thermodynamically stable reactions is not necessarily intui-tive, and hence simply guessing the reaction sequence based on chemical intuition is unlikely to yield the correct, low-energy reaction pathway. Below we give a simple example, but with GCLP we have a perfectly general method for determining the low-energy reaction pathway, even in complex cases.
FeSi2 +
5
2Li → FeSi +
1
2Li5 Si2
(5)
+
3
4Li → FeSi +
1
4Li13 Si5
(6)
+
3
4Li → FeSi +
1
5Li21 Si5
(7)
+
14
5Li → 1
3Fe3Si +
1
3Li21Si5
(8)
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Figure 5 . Average cell potential, volumetric lithium capacity and volume expansion for all 515 predicted thermodynamically stable lithiation reac-tions for transition metal silicides, stannides and phosphides.
0 500 1000
1500 2000
2500 3000
3500 4000
4500Reaction Capacity/ mAh cm−3
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Cel
l Pot
enti
al/ V
vs
Li0
2 4 6 8 10 12 14 16 18 20 22
Vol
ume
Exp
ansi
on p
er L
i/ Å
3
Figure 6 . Plot of volume expansion and gravimetric and volumetric capacities for all transition metal stannide, phosphide and silcide lithia-tion reactions.
0 500 1000 1500 2000 2500 3000 3500 4000 4500
Gravimetric Capacity/ mAh g−1
0
1000
2000
3000
4000
5000
6000
Vol
umet
ric
Cap
acit
y/ m
Ah
Å−
3
0
50
100
150
200
250
300
350
% V
olum
e E
xpan
sion
Figure 7 . Comparison of gravimetric and volumetric capacities for all transition metal stannide, phosphide and silcide lithiation reactions.
0
1000
2000
3000
4000
5000
6000
0 500 1000 1500 2000 2500 3000 3500 4000 4500
Vol
umet
ric
Cap
acit
y/ m
Ah
Å−
3
Gravimetric Capacity/ mAh g−1
PhosphidesSilicides
Stannides
3.2. DFT + GCLP Prediction of all 515 Thermodynamically-Allowed Conversion Reactions: TM Silicides, Stannides, and Phosphides
Using our DFT + GCLP approach, we evaluate the lithiation reactions for all transition metal silicides, stannides and phos-phides, and are able to reduce from 24,388,710 to 515 stable lithiation reactions. Figure 5 shows the cell potential, volu-metric capacity and volume expansion for all lithiation reaction sequences for all 515 transition metal silicides stannides and phosphides. This plot represents a comprehensive database of lithiation reaction attributes for this class of materials, which can then be easily searched for reactions which meet any speci-fi ed criteria. In the following sections we outline one choice of desirable parameters, and report the reactions that are selected from these criteria.
3.3. Reaction Screening Approach
We next show how we can screen our database of reaction attributes to accelerate the search for improved anode materials. The screen will involve comparison between several character-istic quantities for each lithiation reaction. These quantities are defi ned in terms of four fundamental properties: N Li , v , m and μ Li . N Li is the number of lithium atoms stored per formula unit of reactants, v is the volume of a phase or sum over phases in equilibrium, m is the mass of a phase or sum over phases in equilibrium, and μ Li is the chemical potential of lithium in a reaction. To avoid confusion between volume and voltage, we will refer to volume as v in the following equations. For each quantity, the anode state is indicated by a supscript ‘L’ or ‘D’ for the lithiated and delithiated states respectively. The perform-ance indicators we derive from these basic properties are the average cell potential, gravimetric capacity, volumetric capacity, volume expansion, and volume expansion per lithium. These properties are defi ned below, where F is Faraday’s constant.
From these equations we also note that the volume expan-sion per lithium is related to the ratio of the volumetric capacity and volume expansion by a factor of F . This relationship and its consequences can be understood by considering Figure 6 and Figure 7 . Figure 6 shows the relationship between gravimetric and volumetric capacity and to percent volume expansion. From Figure 6 the trend between volumetric capacity and percent volume expansion is obvious. Furthermore, Figure 6 shows that for a given volumetric capacity, a wide range of volume expansions and volumetric capacities is possible. This dynamic relationship is critical to establishing reasonable criteria for screening for anode reactions. Figure 7 shows a plot of gravi-metric and volumetric capacities for every transition metal stannide, silicide and phosphide lithiation reaction sequence.
Figure 8 . Average cell potential, lithium capacity and volume expansion for every lithiation sequence from the transition metal silicides.
0 500 1000
1500 2000
2500 3000
3500 4000
4500Reaction Capacity/ mAh cm−3
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Cel
l Pot
enti
al v
s L
i/L
i0 / V
2 4 6 8 10 12 14 16 18 20
Vol
ume
per
Li/
Å−
3
In Figure 6 the silicides and phosphides can be clearly distinguished from the much heavier stannides. Although the stannides have signifi cantly lower gravimetric capacities than the silicides and phosphides, they are very competitive in terms of volumetric capacity. The point which lie at the highest gravi-metric capacities correspond to the lithiation reactions of pure silicon and pure phosphorus, and represent an upper bound on possible capacities.
We use these metrics to evaluate the performance of every lithiation reaction of TM silicides, stannides, and phosphides. In the following sections we describe the search criteria applied in this work. Note that while we believe these to be reasonable search criteria, they only represent one example of a search scheme and it is trivially easy to impose a different suite of con-straints on voltage, capacity (gravimetric and volumetric), and volume expansion.
3.2.1. Cell Potential > 0.25 V vs Li and Cell Potential < 0.75 V vs Li
For anodes at low potentials vs lithium metal, dendrite forma-tion can be a safety concern. Graphitic carbon anodes operate at ∼ 0.1 V, so to offer improved safety and reliability we will set a minimum cell potential at 0.25 V. On the other hand, at very high cell potentials the battery loses voltage, and as a result energy density, because the total battery cell potential is given by the difference between the cathode potential vs lithium and the anode potential vs lithium. Therefore to maximize the bat-tery’s operating potential the anode potential vs lithium metal should be minimized. Due to the inability to satisfy both of these objectives (safety vs. energy density), we set a target window as an acceptable compromise. We fi lter out materials with average potentials outside a prescribed range: 0.25–0.75 V. This restriction will confi ne our results to materials which are safe and high energy density.
3.2.2. Gravimetric Capacity > 372 mAh g − 1 and < 1200 mAh g − 1
The maximum theoretical capacity of a graphite anode, which can only store up to one Li per six carbon atom, is 372 mAh g − 1 . As a minimum, we insist that any new material at least have a capacity which matches that of graphite. Therefore, in our reaction screening scheme, we fi rst remove all reactions which have a gravimetric capacity below that of graphite. Next, understanding that very high capacity reactions inevitably lead to large volume expansions, we look for an upper limit to capacity, beyond which overall battery capacity will not signifi -cantly improve. Kasavajjula [ 76 ] et al showed that, due to the very poor gravimetric capacity of current cathode materials relative to anode materials, gains to total capacity for anodes in excess of 1200 mAh g − 1 are very modest. We also note that materials with very high capacity will also have greater volume expan-sions. In order to avoid materials with high volume expansion, we include an additional constraint that the gravimetric capacity must be below 1200 mAh g − 1 .
3.2.3. Volumetric Capacity > 830 mAh cm − 3
After screening for materials with tailored voltage and gravi-metric capacity, we next screen for materials with a volumetric
capacity greater than graphite, which has a volumetric capacity of ∼ 830 mAh cm − 3 . As shown in Equation 13 volumetric capacity and volume expansion per lithium are related. For this reason, we fi rst screen for suffi ciently large volumetric capacity, and separately minimize the volume expansion.
3.2.4. Minimize Volume Expansion
In attempting to simultaneously optimize capacity and volume expansion, we fi nd that the problem is inherently frustrated - high volumetric and gravimetric capacity are generally accom-panied by large volume expansion. In Figure 6 we summarize all three related quantities - volume expansion, gravimetric capacity, and volumetric capacity - in a single plot. As shown in the defi nition of volume expansion per lithium atom, we observe that the volume expansion per lithium inserted is pro-portional to the ratio of the volume expansion to the volumetric capacity. Because these properties are frustrated, we attempt to fi nd the optimum compromise between high volumetric capacity, and low volume expansion. To this end, for the fi nal fi lter we will sort all of the remaining materials according to volume expansion per lithium inserted (which is the ratio of volume expansion to volumetric capacity). This fi lter is distinct from the previous search constraints, which are pass-fail fi lters, in that orders the results.
3.4. TM-Silicides
We fi nd that among transition metal silicides there are 93 unique lithiation reaction sequences. Figure 8 shows the gravimetric capacity, voltage and volume expansion per lithium for all reactions. In addition to the thermodynamic fi lters pre-viously established, we apply an additional fi lter based on the experimentally observed kinetic limitation to the formation of Si 5 Li 21 and LiSi at room temperature and ambient pres-sure. [ 77–79 ] By removing reactions involving Si 5 Li 21 and LiSi we reduce the number of silicide reactions to 4. For the reactions which meet our thermodynamic and kinetic requirements, we summarize the most salient attributes in Table 1 .
Among transition metal silicides we predict properties of two systems which warrant further experimental investiga-tion. 1) The nickel silicides are found to have the only stable
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Table 1. Tabulated results of the 4 reactions which meet all of the constraints on anode performance. For each reaction we show the products and reactants, gravimetric and volumetric capacities, percent volume expansion, and cell potential.
Products → Reactants Gravimetric Capacity/ mAh g − 1 Volumetric Capacity/ mAh cm − 3 Volume Expansion per Li/ Å 3 Cell Potential/ V
CoSi 2 + 0.57 Li → 0.33 CoSi + 0.048 Li 12 Si 7 426 1280 15.29 0.29
NiSi + 0.68 Li → 0.036 Li 12 Si 7 + LiNi 2 Si 447 1599 13.33 0.26
NiSi 2 + 0.57 Li → 0.33 NiSi + 0.048 Li 12 Si 7 427 1219 15.63 0.36
Si 2 Ti + 0.57 Li → 0.33 SiTi + 0.048 Li 12 Si 7 471 1156 17.54 0.31
Figure 9 . Average cell potential, lithium capacity and volume expansion for every lithiation sequence from the transition metal stannides.
0 500 1000
1500 2000
2500 3000
3500 4000
4500Reaction Capacity/ mAh cm−3
0
0.2
0.4
0.6
0.8
1
1.2
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l Pot
enti
al v
s L
i/L
i0 / V
2 4 6 8 10 12 14 16 18 20 22
Vol
ume
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Li/
Å−
3
ternary silicide, LiNi 2 Si. The presence of a ternary compound introduces a wider range of cell potentials and capacities which is appealing from the perspective of increasing tunability of performance. As previously noted, for binary conversion reac-tions the reaction potential, as defi ned in Equation 2 , the cell potential of an active-inactive electrode material is bounded by the pure active material. This limit is removed by the presence of a stable ternary compound, because the reaction potential is no longer equal to difference per lithium atom of the TM-A and Li-A product phases. In addition to thermodynamic considera-tions, the presence of a ternary phase presents the possibility of diminished mass transport during conversion reactions, because the active and inactive components no longer need to be completely separated.
We found other ternary transition metal-silicon-lithium com-pounds in the ICSD but these were not found to be stable in DFT, so we believe NiSi 2 presents uniquely interesting pros-pects as an anode material. 2) The other binary system of interest are the cobalt silicides. In addition to good thermody-namics, because cobalt does not have a stable carbide, cobalt silicides may have greater cycleability, due to similarity to other Co-P and Co-Sn compounds which have been shown to have good cycle-ability. Among transition metal phosphides, [ 25 ] cobalt phosphides were found to have the best cycleability, which was attributed to this property of cobalt. Furthermore, this mate-rial is an analogue to the commercially successful Co-Sn anode in the Sony Nexelion battery. Due to the similarity to the Sony Nexelion battery, and the fact that cobalt was the best transi-tion metal found among TM-P in carbon, [ 25 ] we believe Co-Si to be an anode system well worth further investigation. Although thin fi lm cobalt-silicon anodes have been studied, [ 80 ] we are unaware of any investigation of Co-Si powder.
3.5. TM-Stannides
We fi nd that among transition metal stannides there are 104 unique lithiation reaction sequences. The most salient prop-erties of these reactions are shown in Figure 9 and listed in Table 2 . After applying the screening criteria previously described, only one reaction remains. The data shows that many stannide reactions have signifi cantly lower gravimetric capacities, due to the much greater mass of tin atoms relative to
Table 2. Tabulated results of the 4 reactions which meet all of the constrareactants, gravimetric and volumetric capacities, percent volume expansion
Products → Reactants Gravimetric Capacity/ mAh g − 1 V
CoSn + 1.3 Li → 0.5 Co + 0.1 Li 13 Sn 5 419
silicon and phosphorus. After applying the previously described fi lters to the stannides we fi nd that only one reaction would be predicted. The predicted composition is a 1:1 ratio of cobalt to tin. This is the same composition as the Sony Nexelion battery, which has already been demonstrated as a commercial suc-cess. [ 20 ] This result illustrates the power of DFT + GCLP, and suggests that any reactions predicted by this method should be carefully studied.
3.6. TM-Phosphides
We fi nd that among transition metal phosphides there are 266 unique lithiation reaction sequences. After applying the screening criteria described above, 39 reactions remain. The most salient properties of these reactions are shown in Figure 10 and listed in Table 3 . The phosphides present a wide range of candidate electrode reactions, due to the high capaci-ties achievable in reactions which form Li 3 P. Beyond this, the phosphides exhibit a more diverse range of compositions, i.e., values of x in P x TM. The broad range of compositions in transi-tion metal phosphides produces a larger number of reactions, with a greater variety of reaction attributes to select from.
Among these transition metal phosphide reactions, we note the reaction with the smallest volume expansion per lithium
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ints on anode performance. For each reaction we show the products and , and cell potential.
olumetric Capacity/ mAh cm − 3 Volume Expansion per Li/ Å 3 Cell Potential/ V
2181 14.72 0.47
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Figure 10 . Average cell potential, lithium capacity and volume expansion for every lithiation sequence from the transition metal phosphides.
0 500 1000
1500 2000
2500 3000
3500 4000
4500Reaction Capacity/ mAh cm−3
0
0.2
0.4
0.6
0.8
1
1.2
1.4
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l Pot
enti
al v
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i/L
i0 / V
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Vol
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atom. The smallest volume expansion per lithium, 12.43 A/Li occurs in:
PTi + 0.6 Li → 0.2 Li3P + 0.1 P3Ti5 (14)
Previous works have shown that for alloying reactions with tin and silicon, the volume expansion per lithium added does not vary much from 14 or 15 Å per Li. We show that this limi-tation can be overcome by conversion reactions, because of the additional fl exibility introduced by the creation and destruc-tion of one or more additional phases during lithiation or delithiation. In the case of the lithiation of PTi, the product phase P 3 Ti 5 has a smaller volume per Ti atom than PTi, which reduces the total volume change relative to PTi. Among reac-tions which meet the specifi ed requirements for cell potential, gravimetric and volumetric capacities, this reaction has the lowest volume expansion per lithium inserted. For the specifi c set of fi lters chosen in this work, we fi nd that this reaction has the best combination of all properties. Unfortunately, PTi has been studied previously and found to be unreactive. [ 81 ] Since our calculations reveal that PTi should be thermodynamically active for lithiation, the experimental reports are likely due to poor kinetics of the lithiation of this material. Given the
Table 3. Tabulated results of the 4 reactions which meet all of the constrainreactants, gravimetric and volumetric capacities, percent volume expansion,
Products → Reactants Gravimetric Capacity/ mAh g − 1 V
Co 2 P + 1.0 Li → 0.667 Co + 0.333 Li 3 P 576
CoP + 0.75 Li → Li 3 P 0.25 Co 2 P 477
Cr 3 P + 0.75 Li → Li 3 P 0.75 Cr 459
CrP + 1.0 Li → 0.333 Li 3 P + 0.1667 Cr 3 P 689
FeLiP + 0.667 Li → 0.333 Li 3 P + 0.333 Fe 610
Li 3 P 0.25 Co2P + 0.75 Li → 0.5 Co + 0.5 Li 3 P 428
Mn 2 P + 1.0 Li → 0.667 Mn + 0.333 Li 3 P 609
MnP + 0.75 Li → 0.25 Mn 2 P + Li 3 P 499
Ni 3 P + 0.75 Li → 0.75 Ni + Li 3 P 414
PTi + 0.6 Li → 0.2 Li 3 P + 0.1 P 3 Ti 5 435
0.25 Mn 2 P + Li 3 P + 0.75 Li → 0.5 Mn + 0.5 Li 3 P 445
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predicted outstanding thermodynamic properties of this mate-rial as an anode, we suggest that this material warrants further experimental study to try and overcome this kinetic barrier to activity.
4. Conclusions
In this study we used a powerful combination of high-throughput DFT with the automated GCLP method to identify an exhaustive list of every possible thermodynamically stable reaction among all transition metal silicides, phosphides and stannides from a database of DFT formation energies. We are able to directly predict several key metrics of performance: the cell potential, volume change per lithium incorporated, and gravimetric and volumetric capacity. The fi lters described in this work were designed to reduce the exhaustive list of lithia-tion reactions to only the reactions which are most promising. After removing all reactions which fail to meet the criteria for viability - gravimetric capacity greater than 372 and less than 1200 mAh/g, average cell potential between than 0.25 and 0.75 V vs Li - what remains is a pool of 16 candidate reactions from anode materials including: Co 2 P, CoP, Cr 3 P, CrP, FeLiP, Co2P, Mn 2 P, MnP, Ni 3 P, PTi, Mn 2 P, CoSi 2 , NiSi, NiSi 2 , Si 2 Ti, and CoSn. Of these we fi nd that PTi, LiSiNi 2 and CoSi 2 are the most appealing candidates for replacing graphitic carbon among transition metal silicides, stannides and phosphides. This con-clusion is based on this particular choice of screening criteria, but having enumerated all reactions it is trivial to defi ne new screening criteria to obtain a new set of reactions to investigate. The data presented here will be made available via an interac-tive search tool online.
The reactions predicted in this work are driven purely by thermodynamics, so any phases which are kinetically blocked from forming may not appear. Furthermore, if mass transport is suffi ciently slow, the reaction kinetics may be too slow for practical implementation. However, in spite of these limitations, the application of high-throughput computational methods to anode reaction discovery is a step toward more effi cient battery development.
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ts on anode performance. For each reaction we show the products and and cell potential.
olumetric Capacity/ mAh cm − 3 Volume Expansion per Li/ Å 3 Cell Potential/ V
2693 15.11 0.4
1868 13.93 0.67
1857 14.51 0.46
2362 14.21 0.62
1467 14.01 0.4
978 15.11 0.4
2493 14.24 0.41
1814 14.32 0.62
1976 14.86 0.33
1109 12.43 0.47
950 14.24 0.41
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In addition to the reactions discovered in this study, we have also developed of a very general implementation GCLP, which can be extended easily to determine the ground state reactions of any given composition. We will further describe the develop-ment of this suite of tools in a future publication. The method is highly fl exible and can be used to explore the energetic land-scape of very large domains of phase space, which it would be prohibitively expensive to investigate using brute force enumer-ation. To extend this analysis to an arbitrary battery chemistry, the only additional input required is a database of enthalpies of all compounds in that system.
Acknowledgements This work was supported by the Center for Electrical Energy Storage: Tailored Interfaces, an Energy Frontier Research Center funded by the U.S. Department of Energy, Offi ce of Science, Offi ce of Basic Energy Sciences. BWM was supported by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program.
Received: August 2, 2012Published online:
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