Article pubs.acs.org/JPCC
Point Defects in Layer-Structured Cathode Materials for Lithium-Ion Batteries Yongseon Kim* Department of Materials Science and Engineering, Inha University, Incheon 402-751, Republic of Korea S Supporting Information *
ABSTRACT: The structural characteristics related to point defects within layer-structured cathode materials for lithiumion batteries were investigated. Crystal models containing certain types of defects were designed, and phase diagrams of Li−Co−O and Li−Ni−O systems were simulated by assuming these crystal models were independent phases based on firstprinciple methods, enabling the thermodynamic examination of the stability and formation probability of point defects. From the formation energy and mixing entropy of a defect phase in the thermodynamically stable phase, a quantitative calculation equation was designed to predict the concentration of defects. By combining the equation with the simulated phase diagrams, the equilibrium concentrations of every defect in LiCoO2 and LiNiO2 systems were calculated. Point defects in LiCoO2 were predicted to form below 0.1%, whereas the formation of several percent of Li-deficiency and Li−Ni cation mixing appeared to be thermodynamically unavoidable in LiNiO2. The reliability of the theoretical study was confirmed by good agreement with experimental features, and thus this theoretical approach is expected to be utilized to interpret defect formation and related properties in various material systems.
1. INTRODUCTION The lithium-ion battery (LIB) is widely used as a power source for mobile electronic devices owing to its high energy storage density.1,2 The application is diversified for electronic vehicles, power tools, energy storage systems, and so on, and thus the demand for LIBs has increased sharply; however, despite the growth of the industry, the performance of LIBs has not simultaneously improved. In particular, advanced positive electrode materials for high-capacity LIBs are urgently required. The electrode materials’ structural integrity and thermal safety, as well as their suppression of side reactions with the electrolyte liquid, are essential to accommodate the demand for large-scale pouch-type LIBs.3−6 LiCoO2 (LCO) is among the most frequently used electrode materials for LIBs owing to its balanced properties of reasonable capacity, good rate performance, and safety.1,2,7 The material has a high volumetric capacity, suitable for use in small-sized devices. Because LIBs are used for varied purposes, cathode materials specialized to provide capacity, safety, low cost, and other features have been investigated accordingly. For example, a composite of Li2MnO3−LiMO2 (M = Ni, Co, or Mn) possesses high capacity, olivine-structured LiFePO4 and LiMnPO4 provide high safety, and LiMn2O4 is frequently used for its low material cost;7−16 however, these materials are used for only limited portions of the cathode or are mixed with a majority composition of LCO because significant problems remain in their use as primary electrode materials. Thus it seems that the primary positive electrode material for LIBs is still the layer-structured LiMO2. This category may be © XXXX American Chemical Society
divided into the two classes of Co-based and Ni-based materials. LCO clearly belongs to the former, while LiNi 1−x−y Co x Mn y O 2 (LNCM) and LiNi 1−x−y Co x Al y O 2 (LNCA) are examples of the latter.7,8,17,18 With increasing Ni content approaching 100%, the LiMO2 structure becomes difficult to synthesize in an exact composition: Li-deficient Li1−δNi1+δ′O2 is generally obtained as opposed to the stoichiometric LiNiO2 (LNO).19−21 In addition, the thermal and chemical stability of high-Ni LiMO2 remain inferior to those of Co-based LCO.6,22−25 Nonetheless, efforts for commercial use of Ni-based layer-structure cathode material have continued because the available capacity at commercial charging voltages (generally approximately 4.2−4.3 V) increases and the material cost can be reduced. A fundamental scientific understanding of the material property of Ni-based cathodes from the comparative study of structural features of LNO and LCO would be essential to improve the problems. In addition, research on the properties of layer-structured cathode materials is required not only for the improvement of current LIBs but also to provide a foundation for next-generation LIB technology, considering that the available capacity of these materials can be enhanced by operation at higher voltages.6,26 In this study, a thermodynamic approach is used to study point-defect behavior within the layered-structure LiMO2 materials in relation to their synthesis Received: September 23, 2015 Revised: January 8, 2016
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DOI: 10.1021/acs.jpcc.5b09301 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C
obtain proper phase diagrams in advance, which is composed of common experimental variables of temperature, pressure, and chemical components. Taking these considerations into account, the thermodynamic stability of point defects and their concentration are investigated in this study. Phase diagrams of Li−M−O systems are simulated by first-principles methods, and the stability of each single or pair type of point defect is examined. On this basis, a quantitative calculation model of the concentration of each defect is proposed.
conditions. This topic was investigated by some researchers recently and a few reports are available;27−31 however, thermodynamic calculations in these studies were usually performed taking individual elements as the reference state. That is, the formation reaction of LiMO2 compounds or of point defects in them was composed including Li, M, and O as reactants or products. Therefore, the formation energies were calculated as a function of chemical potentials of the elements (i.e., μLi, μM, and μO). Although the calculation result gave excellent physical insight into defect chemistry, this method does not seem to be practical because it does not fully reflect the real experimental situation: The metal state of Li, Co, or Ni is not the most stable under general experimental conditions because more stable forms such as oxides, carbonates, or hydroxides are involved in general synthesis. For example, the formation energy of a Li vacancy in an n × LiCoO2 supercell may be obtained from the following reaction equation with the conventional approach
2. METHODS The phase diagrams of the Li−M−O system were simulated as a function of synthetic condition. On the basis of these diagrams, the thermodynamic stability and concentration of different varieties of point defects were analyzed. In addition to the generally known phases of the Li−M−O system, crystal models of LiMO2 with various point defects were designed and included in the simulation, as if each were an independent phase. This method enabled the comparative analysis of the thermodynamic stabilities of all included defects. The Li−Co− O system, including the most widely used positive electrode material of LCO, and Li−Ni−O system, including LiNiO2, were mainly investigated. Quantitative analysis of the defects was performed thermodynamically based on the simulated phase diagrams. Phase diagrams depict the thermodynamically stable phases present under certain conditions; thus comparing the normalized Gibbs free energy (G̅ ) for specific phases, as shown in eq 1, is required to obtain the phase diagram of the Li−M−O ternary system.32,33
Li nConO2n → Li n − 1ConO2n + Li
However, considering that Li metal easily transforms to carbonate in air, the reaction may have to be modified as follows Li nConO2n → Li n − 1ConO2n + Li Li + 1/4O2 + 1/2CO2 → 1/2Li 2CO3 ⇒ Li nConO2n + 1/4O2 + 1/2CO2 → Li n − 1ConO2n + 1/2Li 2CO3
The formation energy of Li vacancy would be smaller with this consideration than that of the conventional way because the consideration of spontaneous formation of Li2CO3 (i.e., negative ΔG for the reaction of Li2CO3 formation) is included, and thus the equilibrium concentration of Li vacancy would be higher. Hydroxide or oxide may sometimes be the stable form instead of the carbonate depending on the atmospheric condition; therefore, partial pressure of CO2 and H2O, as well as O2, also has to be considered for the calculation of defect formation. Furthermore, we propose the following equations as the exact mechanism of formation of Li vacancy in an ambient atmosphere rather than those above based on our simulation result of phase diagrams (details will be discussed in the Results and Discussion):
G̅ (LiaMbOc ) =
(300−600 K)
(n + 1/3)LiCoO2 + 2/3CO2 → Li n − 1ConO2n + 2/3Li 2CO3 + 1/3Co
(1)
By assigning a coordinate point (x, y, G̅ ) to each phase in 3-D space and taking a convex hull34 in the −G̅ direction, stable phases and their tie-lines were determined. Ternary phase diagrams could be composed from the projection of these phases and tie-lines onto the x−y plane.21,35 However, the phase diagram resulting from this projection may not be accurate, as only metals or metal oxides were included in the simulation. In reality, Li2O easily reacts with CO2 or H2O in air to form Li2CO3, LiOH, or LiOH·H2O, which are thermodynamically more stable than Li2O. Therefore, the changes in Gibbs free energy (ΔG) related to the reactions Li2O + CO2 → Li2CO3, Li2O + H2O → 2LiOH, or Li2O + 3H2O → 2LiOH·H2O must be considered unless the materials are assumed to be handled in a special environment in which CO2 and H2O have been thoroughly removed. Reaction with other gases in the air other than O2, CO2, and H2O were not considered because of low reactivity with Li, Co, or Ni. Thus, eq 1 is replaced by eq 2, which reflects this consideration
(n + 1)LiCoO2 + CO2 → Li n − 1ConO2n + Li 2CO3 + CoO
G(T , P , LiaMbOc ) a+b+c
(700−900 K)
G̅ [LiaMbOc (CO2 )d (H 2O)e ] G[LiaMbOc (CO2 )d (H 2O)e ] − dGCO2 − eG H2O = a+b+c
(n + 1/3)LiCoO2 → Li n − 1ConO2n + 2/3Li 2O + 1/3Co (10 00K ≥ 10 00K)
The formation reaction of a point defect changes as a function of thermodynamic conditions such as temperature, partial pressure of gases (O2, CO2, and H2O, in particular), and chemical composition. Therefore, the exact reaction should be set up on the basis of phase diagrams, and thus it is essential for a quantitative thermodynamic investigation of point defects to
(2)
The Gibbs free energy is approximated by the internal energy of the material, which can be obtained from density functional theory (DFT) calculations. The 0 K energy was used for the simulation of high-temperature states without modification of electronic or phonon excitation with increase in temperature. The error from this approximation is reportedly not significant B
DOI: 10.1021/acs.jpcc.5b09301 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C for solid-state phases.21,36,37 On the contrary, the energy of gaseous phases was determined by combining experimental data with calculations from the DFT method, as gas phases are difficult to characterize solely by DFT, which utilizes periodic boundary conditions.21,35,36 A general reaction equation can be set in the form of eq 3-1 when it includes a metal or a metallic compound (M) and a gas-phase reactant (G); the standard Gibbs free energy of the formation of the product (Goform,DFT(MxG)) may be calculated as eq 3-2 xM + G → MxG
also considered. The energies of the phases whose melting point was in the temperature range of the phase diagram simulation were modified by adding the phases’ heats of melting, as necessary. The partial pressure of CO2 and H2O was set at 3 × 10−5 and 3 × 10−3 MPa, respectively, assuming the atmosphere to be general air. On the basis of the phase diagrams obtained from these simulations, the stability of a phase with a certain defect or combination of defects was assessed. The position of the phase, that is, on which tie-line or in which tie-triangle the phase should be located, and which stable phases the tie-line or tietriangle contains, was determined. Then, the reaction equation of the formation of the phase of interest, from the stable phases under given conditions, was composed, and the formation energy was calculated by DFT methods. A quantitative calculation model for evaluating the concentration of defects was established from a thermodynamic interpretation of the formation energy and mixing entropy of the defect phases. Details of this method are elaborated in the second part of the Results and Discussion. To experimentally support the simulation and subsequent theoretical investigation, we prepared LNO samples using different cooling routes and their properties were examined. LiOH·H2O and NiO were mixed in a 1.03:1 molar ratio and ground in an Al2O3 mortar. The mixture was heated to 730 °C (1000 K) for 10 h. One sample was slow-cooled at 10 °C/h after heating. A second was immediately quenched in a water bath, with special care not to wet the LNO sample. Thus, the slow-cooled sample was cooled to room temperature over 3 days, whereas the quenched sample reached the same temperature in
