First-principles Study of Novel Conversion Reactions for High-capacity Li-ion Battery Anodes Tim Mason, E.H. Majzoub Center for Nanoscience, Department of Physics and Astronomy University of Missouri, St. Louis, MO 63121 Advisor: Eric Majzoub Abstract Anodes for Li-ion batteries are primarily carbon-based due to their low cost and long cycle life. However, improvements to the Li capacity of carbon anodes, LiC6 in particular, are necessary to obtain a larger energy density. Stateof-the-art light-metal hydrides for hydrogen storage applications often contain Li and involve reactions requiring Li transport, and light-metal ionic hydrides are candidates for novel conversion materials. Given a set of known solid-state and gas-phase reactants, we have determined the phase diagram in the Li-Mg-B-N-H system in the grand canonical ensemble, as a function of lithium chemical potential. Our model includes vibrational contributions to the total free energy to obtain finite temperature results. We present computational results for four new conversion reactions that are thermodynamically favorable that do not involve gas evolution. Introduction The demand for improved performance of lithium ion batteries for current applications as well as the need for improved kinetics for possible vehicular applications warrants the continued search for potential new battery materials. While current batteries are based on the Li intersertion/de-insertion process in carbon anodes, greater capacity has been shown to be possible through conversion reactions. Specifically, Oumellal et el have demonstrated the potential of an MgH 2 cathode that lithiates into Mg and LiH versus a metal lithium anode offering a capacity of 1,480 mahg -1 with an average voltage of 0.5V. Conversion reaction materials as they exist today have some problematic features. Oumellal s MgH 2 cathode for example experiences dramatically degraded reversibility after less than 20 cycles which is suspected to be due largely in part to fracturing that occurs during the large volume expansion of approximately 85% that accompanies the conversion reaction[1]. Such poor reversibility tends to cast a pessimistic cloud over these types of electrodes. Silicon anodes are another example of an otherwise promising material foiled by large volume expansions (400%) leading to heavy capacity fade from cracking and disintegration of the anode. One attempt to overcome this was the use of silicon compounds containing inactive host matrices such as CaSi 2 which performed for 10 cycles at a capacity of 1500mAhg -1 but then fell to 310mAhg -1. It is thought that this degradation was due to the alloys inability to sustain the large volume changes[4]. This suggests that there may still be hope in searching for novel conversion reaction materials with high theoretical capacities but smaller changes in volume upon conversion. Useful thermodynamic models that utilize first principles total energy calculations performed on the full set of possible compounds have the potential to aid in the effort to understand and predict the reactions that might occur within a system of any given atomic composition. Recent hydrogen storage work has led to intense exploration of compounds and their structures in the Li-Mg-B-N-H system. We leverage the results of that work using a new linear programming based lithium ion battery model to explore the usefulness of the Li-Mg- B-N-H system as an anode material. In the realm of complex compounds, these models can be useful for searching the composition space for possible conversion materials where intuition may fail. We present a simple model for a lithium ion battery based on the linear programming approach recently developed by Akbarzadeh et al[2] that was used to accurately predict hydrogen storage reactions within the Li- Mg-N-H system by minimizing the grand canonical free energy. In this case, phase diagrams were determined
as a function of temperature and H 2 pressure. We use the same Grand canonical scheme but replace the chemical potential of hydrogen gas with the electrochemical potential of the lithium ions as a battery s voltage is varied from a charged to a discharged state. This results in a five dimensional phase space with one axis for the atomic quantities of magnesium, boron, nitrogen, and hydrogen plus one axis for the lithium electrochemical potential (i.e. the voltage). We show that our model reproduces the findings of Oumellal et al[1] from their MgH 2 lithium ion battery cathode experiment and also predicts four noteworthy reactions with very high lithium density by mass. We have also demonstrated that this method may be used for searching any number of complex systems for potential battery materials. Computational methods In order to determine the competing phases present at equilibrium at a given temperature and lithium chemical potential, we follow the method of Akbarzadeh et al[2] in which the canonical Gibbs free energy is minimized while, in our case, the lithium chemical potential varies up to a potential corresponding to plating of metallic Li at the anode. The method described below examines only the thermodynamics of the system and does not address kinetic mechanisms or their influence on reaction rates. We consider a lithium-ion battery in which the anode and cathode are separately modeled as simultaneous systems defined by the quantity of each species of atoms present. The total number of atoms in each electrode is conserved with the exception of lithium, which is permitted to flow between the two electrodes and is thus jointly conserved between anode and cathode. In each electrode, the atoms are distributed among a set of possible phases such that the total Gibbs free energy of the battery (Eq. 1) is minimized. F a and F c are the free energies per formula unit for the anode and cathode phases, x a and x c are the unknown molar fractions of those phases, and n c Lic is the lithium count per formula unit in phase c of the cathode. The first and second terms in Eq. 1 describe the cohesive energies of all existing phases present in the anode and cathode, respectively, and the third term describes the energy due to the chemical potential of lithium ions. The Gibbs free energy is minimized subject to the atomic quantity constraints in Eqs. 2-4. Where A s and C s are the total quantity of non-li species s in the anode and cathode respectively, and L is the total Li count in both the anode and the cathode. Equation 4 conserves the total amount of lithium but allows it to flow between the anode and the cathode. Minimizing the free energy at varying lithium electrochemical potentials subject to the linear constraints constitutes a linear programming problem. The Gnu Linear Programming Kit (GLPK) package in the open source numerical software package Octave was used to solve for
the molar fractions of each phase in the electrodes. For each set of atomic constraints, we raise the electrochemical potential of the anode Li atoms from -5 to 5 ev, representing a voltage swing of -5 to 5 volts. For small voltage steps, changes in molar fractions can be interpreted as a conversion reaction that gains or loses Li. We scan the composition space (the multi-component phase diagram) to search for mass ratios that result in suitable reversible conversion reactions. In this study, anode material in the Li-Mg-B-N-H system was scanned for reversible reactions involving Li insertion/extraction that do not result in the creation of gases (e.g. N 2, H 2, or NH 3 ) as byproducts. The cathode is modeled with only two possible phases, unlithiated FePO 4 and lithiated LiFePO 4. This is a well-understood cathode material, and it simply provides a familiar reference energy. The phase space of the Li-Mg-N-B-H system is explored by determining the molar fractions of competing phases for each point on a grid of atomic quantities A s that samples the quaternary phase space of Mg-N-B-H within predetermined boundaries. It is only necessary to supply enough lithium to saturate the anode materials in a charged state and therefore the quantity L in equation 4 need not be varied. The calculation on each point on the quaternary composition space results in a set of reactions that occur as the electro-chemical potential of lithium is varied. An 8 8 8 8 array was used to sample 8 4 points in the phase space over the range shown in Table 1. Table 1. Boundaries of the explored space of atomic quantities A s Element Minimum Maximum Mg 0 4 B 0 4 N 0 6 H 0 15 First-principles DFT calculations using the VASP package were performed to obtain static free energies for the candidate anode compounds in the Li-Mg-N-B-H system shown in Table 2. The static energies were calculated using the Vienna Ab-initio Simulation Package (VASP) code. [9,10,11,12] The projector augmented wave method was used for the interaction between conduction electrons and the ion cores, [7,8]in combination with the correlation-exchange functional of Perdew and Wang.[13,14] We employed a plane wave energy cutoff of 600 ev and Monkhorst-Pack k-point meshes of 4 4 4 or larger. All structural parameters we relaxed until the forces on the ions were below 5 ev/å and stresses were below 0.1 GPa. Gamma phonons modes were also calculated using VASP s linear response capability in order to calculate vibrational contributions to the free energies at 300K and 1000K. The number of supercells used for each compound is listed in table 2. Table 2. First-principles static DFT energies and enthalpies of formation for the anode and cathode phases Phase Vasp energy (ev/fu) H of formation (kj/mol*fu) Zero_point (kj/mol*fu) 300K vib (kj/mol*fu) Volume/f.u. Unit cells for phonon calculation Li -1.89 0 3.75-0.24 20.40 2 x 2 x 2
H 2-3.40 0 27.30 23.48 N/A 1 x 1 x 1 N 2-8.36 0 14.95 10.54 N/A 1 x 1 x 1 Mg -1.52 0 2.89-1.65 22.87 2 x 2 x 2 B-alpha -6.69 0 12.43 11.37 7.25 1 x 1 x 1 NH 3-19.16-100.84 90.89 84.05 N/A 1 x 1 x 1 LiH -6.18-85.13 19.65 16.81 16.07 1 x 1 x 1 LiNH 2-19.16-202.72 68.61 60.14 32.72 1 x 1 x 1 Li 2 NH -17.68-205.76 45.99 37.42 34.12 1 x 1 x 1 Li 4 NH -21.89-246.58 48.55 34.99 58.53 1 x 1 x 1 Li 4 BN 3 H 10-81.95-828.45 313.52 275.54 149.93 1 x 1 x 1 Li 3 BN 2 H 8-62.69-615.94 242.98 218.73 123.58 1 x 1 x 1 Li 2 BNH 6-43.58-418.54 176.03 157.92 92.15 1 x 1 x 1 Li 3 N -15.72-162.01 27.77 17.34 44.59 2 x 2 x 2 LiN 3-27.53-52.69 36.37 25.56 45.24 1 x 1 x 1 LiBH 4-24.34-207.45 106.16 95.53 56.53 1 x 1 x 1 LiMgH 3-15.11-143.85 59.68 51.15 175.68 1 x 1 x 1 LiMgN -13.51-167.21 18.54 12.34 31.99 1 x 1 x 1 LiMgBN 2-31.82-481.17 44.41 33.91 64.16 1 x 1 x 1 Li 3 BN 2-34.42-514.35 51.55 37.27 56.91 1 x 1 x 1 Li 2 Mg(NH) 2-33.25-425.64 84.41 70.26 64.53 1 x 1 x 1 Li 2 Mg 2 (NH) 3-47.84-551.53 123.59 100.87 91.04 1 x 1 x 1 Mg(NH 2 ) 2-35.75-375.55 131.38 121.45 72.04 1 x 1 x 1 MgB 2 H 8-44.84-263.56 212.40 196.73 114.49 1 x 1 x 1 MgNH -15.08-172.49 36.89 34.05 28.61 1 x 1 x 1 MgH 2-8.98-63.27 36.11 32.73 30.41 1 x 1 x 1 Mg 3 N 2-25.46-400.90 26.46 13.79 62.34 1 x 1 x 1 FePO 4-42.46 N/A N/A N/A N/A N/A LiFePO 4-47.84 N/A N/A N/A N/A N/A. Battery electrodes often operate far from equilibrium, and formation of metastable phases in the Li-Mg-N-B-H system may therefore be possible. Some compounds resulted in unstable phonon modes. In the case of Li3N, there is a single unstable phonon. Yan and Zhang report that the B 2g mode at slightly smaller volumes [6] and the mode in the present work stabilizes with increased volume suggesting that the mode may be a result of the harmonic approximation. Soft modes were also found in Mg 3 N 2, Mg(NH 2 ) 2 and Li 4 BN 3 H 10. In the case of Mg 3 N 2 these modes disappeared when the VASP Mg PAW pseudopotential was replaced with the the Mg_pv in which the P core electrons are treated as valence indicating that some instabilities are due to the frozen core approximation. Results and discussion The results indicate four very interesting reactions as shown in Table 3. All of the anode reactions are theoretically reversible, emit no gas and possess a high mass percentage of lithium with respect to LiC 6.
Reaction 1 and reaction 4 are particularly worthy of note for their simplicity in product end points and their lithium mass content. Changes in volume of up to 400% in silicon-lithium alloy systems after charging are known to cause cracking and disintegration to a silicon anode leading to heavy capacity fade with capacities well below that of LiC 6 after 5 or more charge cycles[4]. This is the primary barrier to usage of the otherwise promising silicon system, and it is worth comparing the theoretical changes in volume of our four reactions listed in Table 3. The largest expansion occurs in reaction 1 where the volume increases by about 100%, which still compares favorably with silicon. Reaction 2 expands by a smaller 75% but is rendered less competitive by its smaller lithium capacity. Reactions 3 and 4 show Table 3. Reactions at 300K Mg=1; B=0; N=2; H=4 Discharged state: Mg(NH 2 ) 2 (50 wt.% Li) µ Li (V) Volume increase Mg(NH 2 ) 2 2 LiH + Li 2 Mg(NH) 2 Li 2 MG(NH) 2 0.67 LiH + 1.33 Li 2 NH + 0.33 Mg 3 N 2 1.33 Li 2 NH 1.33 LiH +1.33 Li 3 N Final lithiated anode: 4 LiH + 1.33 Li 3 N + 0.33 Mg 3 N 2 Mg=1; B=2; N=2; H=4 (38 wt.% Li) Discharged state: 2 B, 1 Mg(NH 2 ) 2 2 B + Mg(NH 2 ) 2 LiBH 4 + LiMgBN 2 LiBH 4 4 LiH + B LiMgBN 2 Mg + Li 3 BN 2 Final lithiated anode: 4 LiH, 1 B, Mg, Li 3 BN 2 Mg=5; B=8; N=2; H=36 (50 wt.% Li) Discharged state: Mg(NH 2 ) 2, 4 MgB 2 H 8 Mg(NH 2 ) 2 + 4 MgB 2 H 8 7 LiBH 4 + LiMgBN 2 +4 MgH 2 7 LiBH 4 + 4 MgH 2 4 Mg + 7 B +36 LiH LiMgBN2 Mg + Li 3 BN 2 Final lithiated anode: 36 LiH + 1 Li 3 BN 2 + 7 B + 5 Mg Mg=1; B=2; H=8 (51 wt.% Li) Discharged state: MgB 2 H 8 MgB 2 H 8 0.5 B + 1.5 LiBH4 + 1 MgH2 0.5B + MgH2 Mg +0.5 LiBH4 2 LiBH 4 8 LiH +2 B Final lithiated anode: 8 LiH, 2 B, Mg 2.9 3.2 3.3 1.8 3.0 3.4 2.5 3.0 3.4 2.7 2.9 3.0 34% 51% 100% 39% 57% 75% 5% 48% 51% -0.5% 13% 45%
comparable performance. While reaction 4 performs better on volume expansion, reaction 3 represents higher energy density due to the 3.4 volt reaction compared with 3.0 volts reaction 4. Remarkably, the first lithiation step in systems 3, and 4, with potentials of 2.6 and 2.9 volts, have very low volume increases of 4% and 13%, respectively. This is significantly lower than the volume expansion in silicon and the MgH 2 anode. In order to reduce tensile stresses upon volume expansion in silicon-based anodes, silicon is dispersed in matrix of hard, low-ductility Si 3 N 4. This greatly enhances reversibility but reduces capacity to 83 mahg -1.[4] If perhaps the loss of capacity is due to the inability of the silicon to expand as required to absorb lithium in the hard matrix, then this technique may work better with the reactions in this paper which require far less expansion. While Silicon nano-wires have successfully been employed to overcome the fracturing problems with Li-Si alloys,[5] one would expect that the empty space between each nano-wire would cause the capacity per unit volume of these batteries to be very poor. If the Si 3 N 4 can be shown to be effective with these novel materials, then they may make for more compact batteries while still delivering a significant improvement on galvanometric energy capacity far beyond what current cathode technologies can support[5]. Deleted: Conclusions In conclusion we have proposed a new method of searching complex conversion materials for reversible lithium ion batteries. Our study identifies four anode materials. The single phase anodes, (1) Mg(NH 2 ) 2 and (2) Mg(BH 4 ) 2, and two anodes consisting of mixtures (3) 4 Mg(BH 4 ) 2 + Mg(NH 2 ) 2, and (4) 2 B + Mg(NH 2 ) 2. All of them have volume expansions of 100% or less on lithium insersion, making them promising versus silicon. Additionally, (2) and (3) show volume increases of only 50%. Acknowledgements The authors would like to thank the Boeing Company for sponsoring the author s (T.H. Mason) tuition for this research. Biography: Tim Mason is a graduate student in physics at University of Missouri St. Louis References 1. Y Oumellal, A Rougier, GA Nazri, JM Tarascon, et al. Nature Materials, Vol. 7:916-921(2008) 2. Alireza R. Akbarzadeh, Vidvuds Ozolins, and Christopher Wolverton. Advanced Materials, 19:3233-3239,( 2007) 3. J.H. Ryu, J.W. Kim, Y.-E. Sung and S.M. Oh, Electrochem. Solid State Lett. 7 (2004), p. A306 4. U. Kasavajjula, C. Wang, A. J. Appleby, Journal of Power Sources, 163, issue 2, Jan (2007), pp 1003 5. Candace K. Chan and Halin Peng et al.. Nature Nanotechnology, 3:31-35, (2007). 6. Y. Yan, J.Y. Zhang et al. The European Physical Journal B Condensed Matter and Complex Systems, 61, Number 4 397-403, (2008) 7. P.E. Blöchl, Phys. Rev. B, 50, 17953 (1994). 8. G. Kresse, and J. Joubert,Phys. Rev. B,59, 1758 (1999). 9. G. Kresse and J. Hafner. Phys. Rev. B, 47:558, (1993). 10. G. Kresse and J. Hafner. Phys. Rev. B, 49:14251, (1994). 11. G. Kresse and J. Furthmüller. Comput. Mat. Sci., 6:15,(1996). 12. G. Kresse and J. Furthmüller. Phys. Rev. B, 54:11169,( 1996). 13. J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, and C. Fiolhais. Phys. Rev. B, 46:6671, (1992). 14. J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, and C. Fiolhais. Erratum:Phys. Rev. B, 48:4978, (1993).