Article pubs.acs.org/JPCC
Systematic First-Principles Investigation of Mixed Transition Metal Olivine Phosphates LiM1‑yM′yPO4 (M/M′ = Mn, Fe, and Co) as Cathode Materials Alina Osnis,† Monica Kosa,† Doron Aurbach, and Dan Thomas Major* Department of Chemistry and the Lise Meitner-Minerva Center of Computational Quantum Chemistry and the Institute for Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel S Supporting Information *
ABSTRACT: Li based batteries are widely used for powering mobile electronic equipment and are considered as highly promising power sources for electrical propulsion. Recent developments in the area of rechargeable lithium ion batteries for electronic devices and transportation have stimulated extensive studies of cathode materials which are the limiting factor in terms of voltage and energy density. In the current work we present a systematic computational study of the geometry, electronic structure, and electrochemical potential for olivines LixM1‑yM′yPO4 (M/M′ = Mn, Fe, Co; x = 0.00, 1.00, x = y; y = 0.00, 0.25, 0.50, 0.75, and 1.00). We find that changes in cell volume as a function of transition metal composition may largely be ascribed to changes in the atomic volumes of the oxygen atoms, which modulate the electron charge distribution. Moreover, there is considerable charge transfer from lithium to the transition metal ions and oxygen atoms upon lithiation for all systems studied. The calculated cell potentials are in good agreement with experiment for all systems, and show systematic shifts in redox potential with varying transition metal composition. We also correlate between the highest occupied molecular orbital (HOMO) energies of model transition metal complexes and the redox potentials of the pristine LiMPO4 materials. Furthermore, we estimate the delithiation energy of LiCoPO4 and LiFePO4. We find that fully delithiated LiCoPO4 is highly unstable in agreement with the experimental observation that LiCoPO4 cannot be fully delithiated electrochemically.
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INTRODUCTION One of the greatest challenges facing our society today is the dramatic worldwide increase in energy demand. Decreasing fossil reservoirs, rise in cost, resulting pollution, and geopolitical considerations require a move toward alternative energy sources. Such a move, aimed at reducing our dependence on fossil fuels, requires significant scientific and technological advances in the area of renewable, green energy and electrical propulsion (electric vehicles). Therefore the development of efficient alternative energy resources and power sources for electrical propulsion is a major challenge today for the scientific and technological communities and of primary concern for governments around the globe. Among the most important areas of energy research are rechargeable batteries. In particular, Li based batteries have been recognized as highly promising power sources for electrical propulsion in order to bring the world to a clean energy economy.1−4 Recent developments of rechargeable lithium ion batteries for electronic devices and transportation have stimulated extensive studies of cathode materials, as the cathode is a principle component controlling the charge capacity, voltage, energy density, and the power of the electrochemical cells. As a result of intensive research in recent decades, LiCoO2,5,6 LiMn2O4,7,8 and LiFePO49−11 have emerged as highly promising cathode materials and are commonly employed in commercial Li ion batteries. In particular, LiFePO4 has attracted great attention due to its © 2013 American Chemical Society
high stability, improved safety, reasonable specific capacity, low cost, and environmentally benign properties, subsequently leading to its commercialization.9,12−14 Additionally, due to their relatively low surface reactivity with standard Li ion battery electrolyte solutions, LiMPO4 compounds can be used as nanoparticles in composite cathodes. Thereby, despite the poor intrinsic transport properties of LiMPO4 olivine compounds, high rate capabilities can be obtained with LiFePO4, Li[MnFe]PO4, and LiCoPO4 cathodes.15,16 The question of bonding in cathode materials appears to be central for tailoring the voltage of a positive electrode and thus of the complete cell. Goodenough and co-workers suggested replacing simple O2‑ ions by XO4n‑ polyanions in the positive electrode hosts in an attempt to design systems with higher cell voltage.9 The authors suggested that the strength of the X-O bond can influence the M-O covalence and thereby the relative position of the Mn+/M(n‑1)+ redox energy. As such, stronger XO bonding yields weaker M-O bonding, and consequently a lowering of the Mn+/M(n‑1)+ redox energy relative to that in a plain oxide. Changing the nature of polyanions has thus been recognized as a way to tune the relative position of the redox couples and thereby affording higher cell voltages. To address the question of charge distribution in polyanionic cathode Received: March 20, 2013 Revised: July 14, 2013 Published: July 30, 2013 17919
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material, Frayret et al. used topological Bader analysis of the electron density to describe the charge transfer in LiMSO4F (M = Fe, Co, and Ni) upon delithiation.17 Bader charges were used to highlight the changes in electrostatic interactions between the lithiated and delithiated compounds as a function of transition metal composition. These authors also presented Bader atomic volume evolution upon delithiation. Their study showed that Li is fully ionized in the intercalated compounds and its charge transfers mainly to the metal, and, to a lesser extent to the sulfur, fluorine, and oxygen atoms in the early transition metal compounds, LiFeSO4F and LiCoSO4F. In case of late transition metal materials, such as NiSO4F, the charge is transferred to oxygen upon lithium intercalation, due to the reduced oxidation of nickel compared to iron and cobalt. In another work, Rosso and co-workers have shown that for a series of olivine phosphates, MPO4 (M = Mn, Fe, Co, and Ni), and their fully lithiated analogues, LiMPO4, the charge transfer from the intercalating lithium atom occurs mainly to the transition metal ions, for all metals considered and to a lesser extent to the oxygen atoms.18 Upon lithiation, the accumulation of electron density on the metal ion increases in the order: Fe > Co > Mn > Ni. This picture is consistent with the earlier conclusion of Ceder and co-workers, which suggested that late transition metals gain less charge when lithium intercalates than earlier transition metals. Rather, for late transition metals most of the excess lithium charge transfers to oxygen atoms, which are largely responsible for fine-tuning the cell voltage.19 Interestingly, a recent paper by Mishima et al. which used the maximum entropy method combined with the Rietveld method, suggested that charge transfer upon lithiation occurs mainly to the transition metal ions and phosphorus atoms.20 Moreover, this work suggested that there is greater accumulation of electron density on Mn than Fe upon lithiation, contradicting earlier work. Recently, mixed transition-metal systems have attracted considerable interest since such composite materials facilitate fine-tuning of the inherent properties of the pure analogues, such as the voltage and the stability of the cathode upon delithiation. Among these materials, the LiFe1‑yMnyPO415,21−26 solid solution systems have drawn much attention, as these systems exhibit higher energy density and improved redox kinetics due to improved electronic conductivity in comparison to the pure olivines. On the other hand, the LiMn1‑yCoyPO426−28 and LiFe1‑yCoyPO426,29,30 solid solutions are appealing due to their high operating voltage arising from the Co2+/3+ redox couple. A recent comprehensive experimental study by Muraliganth and Manthiram26 showed that the electrochemical performance of the LiM1‑yM′yPO4 solid solutions depend on the nature and amount of cation substitution. A systematic shift in the redox potential, i.e., open-circuit voltage (OCV), of the M2+/3+ couples was observed in the LiM1‑yM′yPO4 solid solutions as compared to the pristine LiMPO4. The potential of the lower-voltage couple increases, while that of the higher voltage couple decreases in the LiM1‑yM′yPO4 solid solutions as a function of the composition, y. Such shifts in the redox potentials have been explained by a modulation of the strength of the M-O covalence. Such M-O covalence tuning is caused by changes in the electronegativity of M as well as by the nearest-neighbor cation, or inductive, effects (M2+−O−M3+ superexchange interactions) where the cations compete for the same valence electrons.9,20,31−35
The aforementioned studies suggest that modulating the electronic structure of the M2+/M3+ cations is a key factor in fine-tuning the cathode voltages of the LiMPO4 olivine phosphates.36,37 Herein we present a systematic computational study of the electrochemical potential, geometry and electronic structure of LixM1‑yM′yPO4 (M/M′ = Mn, Fe, Co; x = 0.00, 0.25, 0.50, 0.75, 1.00; y = 0.00, 0.25, 0.50, 0.75, 1.00). We also correlate between the highest occupied molecular orbital (HOMO) energies of model transition metal complexes and the redox potentials of the pristine LiMPO4 materials. Furthermore, we estimate the delithiation energy of LiCoPO4 and LiFePO4. We find that fully delithiated LiCoPO4 is highly unstable in agreement with the experimental observation that LiCoPO4 cannot be fully delithiated electrochemically.38
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COMPUTATIONAL METHODOLOGY The LixM1‑yM′yPO4 (M/M′ = Mn, Fe, Co; x = 0.00, 1.00, x = y; y = 0.00, 0.25, 0.50, 0.75, 1.00) systems were studied using density functional theory (DFT). The calculations employ the projector augmented wave (PAW) method,39,40 as implemented in the VASP code.41,42 For the exchange-correlation potential, we use the generalized gradient approximated Perdew-Burke-Ernzerhof (PBE) functional modified for solidstate systems with U correction (PBEsol-GGA+U).43−46 We used U values of 5.5, 5.3, and 6.7 for the Mn, Fe, and Co atoms, respectively, while J = 1.0 eV in all cases, based on the work of Zhou et al.47 All calculations were performed with a unit cell containing four formula units. The structures and cell parameters were fully relaxed with antiferromagnetic ordering for each type of calculation. The convergence of the total energy was verified with respect to the plane wave density cutoff, and the energy cutoff was set to 500 eV. The Monkhorst-Pack scheme for kpoint sampling was used for integration in the irreducible Brillouin zone. The calculation of cell potentials was performed according to the suggested method of Ceder and co-workers.48 The average potential was obtained from total energy calculations, approximating the variations in the Gibbs free energy, ΔG, by the electronic energy, ΔE, and the minor variations in entropy, TΔS, and volume, PΔV, among the systems studied, are neglected. V̅ = −
1 ΔE F x 2 − x1
(1)
where F is the Faraday constant, and x is Li ion concentration in LixMPO4. The charge analysis was performed employing the topological partitioning scheme of Bader on the charge densities generated by VASP, corrected for the core densities, using the codes provided by Henkelman et al.49−51 The convergence of the Bader charges was checked with respect to four sets of the fast-Fourier transform (FFT) grids. The discussion in the text is based on the densities obtained using finer FFT grid, although the default values provide similar density values and a converged electron count. A detailed description of the FFT grids and the resulting Bader charges and volumes are given in the SI (Table S3). All-electron densities were employed in the computation of the Bader charges and volumes. To address the relationship between the redox potentials of the pure olivines and orbital energies of the constituent transition metals, we constructed molecular models of the transition metal octahedral environments. The octahedral 17920
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Figure 1. Variations in unit cell volume for LiM1‑yM′yPO4 (M/M′ = Fe, Co, and Mn) olivines as a function of the composition parameter y.
complexes were computed with the Gaussian 09 program.52 The octahedral geometry parameters of each transition metal atom were taken from the periodic calculations and kept fixed, and hydrogen atoms were added to the ligating oxygens. The total charge of each complex was set to +2, to mimic the formal oxidation state of the transition metal within the LiMPO4 materials. The geometries of the added hydrogens were optimized using the X3LYP functional with the all electron 6311++G(d,p) basis set.53
tions to cell volumes and shows the dominant role of oxygen ions in the unit cell volume changes. The average bond lengths for the M2+−O in the MO6 octahedra in LiM1‑yM′yPO4 systems (Figure 2), indicate that
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RESULTS AND DISCUSSION A. Olivine Geometries. Full geometry optimization was performed for LixM1‑yM′yPO4 (M/M′ = Mn, Fe, Co; x = 0.00, 1.00, x = y; y = 0.00, 0.25, 0.50, 0.75, 1.00) mixed olivines and their partly (x = y) and fully delithiated forms assuming antiferromagnetic (AFM) ordering. Initially, the structures of pure LiMPO4 were optimized based on the experimental crystal structures.54−56 Subsequently the cell compositions were modified to generate the desired mixed olivines and the systems were reoptimized. In cases where different cation distributions within the cell were possible, the various possibilities were constructed and optimized, and the lowest energy system was chosen. The calculated and experimental structural parameters such as optimized lattice constants and unit cell volumes are compared in Figures S1−S3 in the Supporting Information and the agreement is excellent.26 For example, the largest deviation for the cell volume from the experimental values is only 0.8% for LiFe0.5Co0.5PO4 (Table S1). Figures S1 and S2 show a linear increase in the lattice parameters and unit cell volume with increasing Mn content in LiFe1‑yMnyPO4 and LiMn1‑yCoyPO4. The same tendency is seen in LiFe1‑yCoyPO4 with increase of Fe content (Figure S3). In the LiFe1‑yCoyPO4 system, the c-direction does not show the linear variation observed in all other systems/axes. Interestingly, this deviation from linearity persists for both computed and experimentally measured values. In Figure 1 we present a concise view of the variation of the unit cell volumes of the LixM1‑yM′yPO4 mixed olivines (M/M′ = Fe, Co, and Mn). The systematic variations in the unit cell parameters and unit cell volumes can be understood in terms of the decreasing nominal M2+ ionic radii, Co2+ = 0.75 Å < Fe2+ = 0.78 Å < Mn2+ = 0.83 Å,57 corresponding to the increasing electronegativity of these first row transition metal ions. However, inspection of computed Bader volumes (vide infra) provides a more indepth description of LiM1‑yM′yPO4 constituent atom contribu-
Figure 2. Calculated Average M−O bond lengths in LiM1‑yM′yPO4 olivines (M/M′ = Fe, Co, and Mn).
the M−O bonds change with varying y. The changes in M−O bond lengths directly reflect the changes in cell volume (Figure 1 and 2). A noticeable increase in M2+−O bond lengths is found as a function of Mn content y in LiM1‑yMnyPO4 (M = Fe and Co), while a more moderate increase is observed in the case of LiCo1‑yFeyPO4 as a function of the Fe-content y. The 17921
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the difference between the computed cell volumes (which agree well with the experimental data) of LiFePO4 and LiCoPO4 is 8.15 Å3. From this trivial analysis it is clear that the changes in the tabulated geometrical radii of Fe2+, Co2+, and Mn2+ cannot explain the observed changes in experimental and computed cell volumes. To tackle this discrepancy, we computed the Bader volumes for the pure lithiated and delithiated olivine systems (Figure 4).
metal oxygen bonds change significantly during the delithiation process M3+/M2+, whereas there is only a slight change in the P−O bonds. Figure 3 presents the average changes in individual
Figure 3. Average M−O bond lengths in LixMPO4 and MPO4 (M = Fe, Co, and Mn) for different types of coordinating oxygen atoms (termed n = 1, 2, 3, and 3′).
M−O bond lengths in the pure olivines LixMPO4 (M = Co, Fe, Mn; x = 0 and 1). The majority of the M-O bonds tighten with oxidation of the metal ion (M−O1, M−O2, and M−O3′), except for the Mn−O3 bond which is elongated due to a Jahn− Teller distortion, as its value increases from 2.26 to 2.31 Å.58 In the mixed LixM1‑yMnyPO4 systems, Mn−O3 is reduced while Mn−O3′ increases, compared to MnPO4, reflecting moderate Jahn−Teller distortions (see Table S2). We also find that partial removal of lithium ions (Lix=yM1‑y3+M′y2+PO4) results in moderate structural distortions (Table S2). The Bader charge analysis (vide infra) reveals that the atomic charges for all atoms change upon Li extraction (see Figure S7), and that all cations become more positive. In case of partly delithiated compounds (i.e., mixed M3+ and M2+ composition), there is a likely increase in the cation−cation repulsive energy, which acts to increase the volume of the unit cell. A similar effect was noted by Eames et al. for Li2FeSiO4 system.59 On the other hand, the decreased ionic radius of M3+ contributes to the shortening of the M3+−O bonds. B. Atomic Volumes and Charge Transfer. In order to gain insight into the origin of the geometrical changes upon metal substitutions in the M1‑yM′yPO4 and LiM1‑yM′yPO4 olivines (M/M′ = Fe, Co, and Mn) we performed a Bader atomic charge and volume analysis. We note that a simple analysis based on changes in standard transition metal atomic radii upon oxidation cannot account for the observed changes in olivine volumes, suggesting that a more in-depth analysis is required. The data for parent olivines LiMPO4 is shown in Table 1. For example, according to the tabulated ionic radii listed in Table 1, the volume of the 4 Fe2+ ions present in the computed unit cell of LiFePO4 should be 7.96 Å3. The volume of the 4 Co2+ ions present in the computed unit cell of LiCoPO4 should be 7.08 Å3. The difference between the volumes of four Fe2+ and four Co2+ ions is only 0.88 Å3 while
Figure 4. Atomic volumes (Å3) of O, M, P, and Li in pure lithiated and delithiated olivines based on Bader population analysis (a) LiMPO4 and (b) MPO4 (M = Co, Fe, and Mn).
The total volumes of the lithiated and delithiated materials decrease in the order Mn > Fe > Co. Interestingly, the majority of this change among the different olivines may be ascribed to differences in the combined volume of the oxygen atoms and to a lesser extent to the transition metal ions. The combined oxygen volumes are 233, 223, and 216 Å3 for LiMnPO4, LiFePO4, and LiCoPO4, respectively (Figure 4a). The corresponding average partial charges for the oxygen atoms are −1.52, −1.50, and −1.48 au, mirroring the volumetric data (Table S3). The transition metal ion volumes are 42, 40, and 39 Å3 for LiMnPO4, LiFePO4, and LiCoPO4, respectively, and reflect the differences in ionic radii. These data imply that the differences in total volume of the pure lithiated compounds are mainly governed by the changes in the atomic volumes of the oxygen atoms and to a somewhat less extent by metal ions. Delithiation results in significant reduction in the volume of the olivines (Figure 4b). In the case of LiFePO4 there is a significant change in the volume of both the transition metal and the oxygen atoms, although the combined decrease in volume upon delithiation is modest. However, in the case of LiMnPO4 and LiCoPO4 the cell volumes decrease considerable more than for LiFePO4 upon delithiation, and this change may
Table 1. Ionic Radii (Å) and Volumes (Å3) of Fe2+, Co2+, and Mn2+ and Computed and Experimental Cell Volumes M2+ Fe2+ Co2+ Mn2+
R (M2+) V (M2+) 0.78 0.75 0.83
1.99 1.77 2.40
computed cell volume
experimental cell volume
289.83 281.68 302.06
290.82 283.67 302.53 17922
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of Aydinol et al.48 For pure LixMPO4 olivines we compute the average OCV, V̅ , for perfectly ordered structures (x = 0, 1) utilizing eq 1. The variation in voltage for each redox couple in mixed olivines with different M1‑yM′y concentration (M/M′ = Mn, Fe, Co; y = 0.25, 0.50, 0.75) was calculated as described in paper of Malik et al.32 In Figure 6 we compare the
be ascribed largely to the transition metal ions. Inspection of the Bader charges in Table S3 reveals that the changes in cell volumes upon lithiation may be ascribed to charge transfer processes involving mainly the oxygen atoms and metal ions. The charge transfer between lithium and the transition metal ions upon lithiation is expected and in agreement with the work of Mishima et al. Surprisingly, Mishima et al. suggested that there is greater accumulation of electron density on Mn than Fe upon lithiation, contradicting earlier work of Ceder et al.19 as well as the current findings. Mishima et al. also suggested a role for the phosphorus atoms;20 this conclusion is not supported by the present data, which suggest a more direct role of the oxygen atoms. We note that the electronic structure from GGA +U calculations may show some deviation compared to more accurate hybrid functionals such as HSE06.4 The change in the total volume of the unit cell and the change in volume of each of the composite atoms in the mixed LiM1‑yM′yPO4 olivines, as a function of the composition parameter y, is depicted in Figure 5 (for total Bader volumes
Figure 6. Comparison of redox potentials (OCV) of the: (a) Fe2+/ Fe3+ and Mn2+/Mn3+ redox couples in LiFe1‑yMnyPO4; (b) Fe2+/Fe3+ and Co2+/Co3+ redox couples in LiFe1‑yCoyPO4; (c) Mn2+/Mn3+ and Co2+/Co3+ redox couples in LiMn1‑yCoyPO4.
experimentally measured cell voltages26 with those calculated in this work. In general, the computed absolute values of the cell voltages show a depreciation of around 0.2 V compared to the measured OCV, within the expected accuracy for GGA DFT methods.60 The magnitudes of the experimentally determined voltages change with variations in the transition metal concentrations, and are accurately reproduced by our calculations. Similarly to the results obtained by Muraliganth et al.,26 our calculations show that LiFe1‑yCoyPO4 and LiFe1‑yMnyPO4 (y = 0.25, 0.50, and 0.75) exhibit higher potentials for the Fe2+/Fe3+ redox couple than those of LiFePO4 and lower potentials for Co2+/ Co3+ and Mn2+/Mn3+ redox couples than those of LiCoPO4 and LiMnPO4, respectively. The LiMn1‑yCoyPO4 system exhibits higher potentials for the Mn2+/Mn3+ redox couple than those of LiMnPO4 and lower potentials for Co2+/ Co3+redox couples than those of LiCoPO4. These shifts in the redox potentials of the M2+/M3+ couples within the mixed LiM1‑yM′yPO4 (M/M′ = Mn, Fe, Co, y = 0.00, 0.25, 0.50, 0.75, 1.00) cathode materials have been discussed in detail by
Figure 5. Variation in the total Bader volumes of LiM1‑yM′yPO4 (M/ M′ = Fe, Co, and Mn) unit cells and of each of the composite atoms (Li, P, O, and M) as a function of the composition parameter y.
population evolution as a function of lithiation, see Figure S4). The trend of the change in volumes is similar to that found for the pure systems and is mainly affected by the variation in oxygen volumes which varies with the metal composition. C. Shifts in Cell Voltages. Total energy calculations can be used to analyze the cathode voltage, according to the procedure 17923
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Muraliganth et al.26 Indeed, these trends are general and have been rationalized as a modulation of the strength of the M-O covalence,25,33 M2+−O−M3+ superexchange or Coulomb interactions9,31,32 or inductive effects.34,35 The cell voltage and the redox potential of the metals are intimately related to the top of the valence band energy.61,62 The computed relative HOMO energies for a series of model octahedral M(H2O)62+ complexes (Figure S5) are 0.00, 0.09, and 1.32 eV for M = Co, Fe, Mn, respectively, in qualitative agreement with the redox potentials in the olivines. The spatial representations of the HOMOs of the 3 complexes are presented in Figure S6. See also Figure S9 and an accompanying discussion of the density of states for selected mixed olivines. D. Stability of the LiCoPO4 Cathode upon Delithiation. The relative stability of the mixed LiFe1‑yCoyPO4 cathode upon delithiation was computed as the ΔE of the following equation:
Article
ASSOCIATED CONTENT
S Supporting Information *
Computed structural parameters, Bader charges and volume analysis, DOS calculations, and spatial representation of HOMO orbitals. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*Phone: 972-3-5317392. E-mail:
[email protected]. Author Contributions †
These authors contributed equally to this work.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work has been supported by the Institute for Nanotechnology and Advanced Materials at Bar-Ilan University and the Israel National Research Center for Electrochemical Propulsion. M.K. thanks the Israeli Ministry of Absorption for financial support. The Cyprus supercomputing center is acknowledged for providing the CPU for this project, Project No. lspro104.
Li + Fe1 − yCoyPO4 → LiFe1 − yCoyPO4
The computed values are 0.0, −7.53, −15.18, −22.92, and −30.76 kcal/mol per formula unit for y = 0.00, 0.25, 0.50, 0.75, and 1.00, respectively, indicating that the stability of the LiFe1‑yCoyPO4 upon delithiation is decreasing with increasing y values, i.e., with the increasing amount of Co. These findings correlate with the experimental evidence of instability of LiCoPO4 cathodes upon delithiation.38 The volume changes linearly for lithiated and delithiated mixed iron−cobalt olivines (Figure S8a,b) as percentage of cobalt increases. The thermodynamic stability and volumetric changes are important parameters for determining the cyclability of the cathode. Yet, additional factors such mechanical stability, grain size, and boundary effects are important as well. The delithiation process of the mixed LiFe1‑yCoyPO4cathode is currently under investigation in our group.
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REFERENCES
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SUMMARY AND CONCLUSIONS In this work we used DFT to provide deeper understanding into the cell voltage changes and related structure−property relationship of a range of LixM1‑yM′yPO4 olivines, which complement the experimental work reported by Muraliganth and Manthiram. The computed geometries and cell voltages correlate well with the experimental data. Computations provide insights into the intrinsic properties of the cathode materials and in particular the changes in the geometries and cell parameters as a function of the transition metal. This study demonstrates that the geometrical parameters depend on the charge transfer from the metal to oxygen as manifested in Bader volume analysis. The changes in cell volumes as a function of transition metal composition are mostly dictated by the changes in the oxygen volumes and less by the metal cation size. Additionally, for all systems studied, there is considerable charge transfer from lithium to the transition metal ions and oxygen atoms upon lithiation. The computed cell voltages are correlated with the measured values and can be attributed to the relative position of the HOMO level, i.e., the level of the redox active electron in LiMPO4. The computed relative stabilities of LiFe1‑yCoyPO4 upon delithiation indicate that these compounds become less stable as the amount of Co increases, supporting the experimental observation that complete delithiation of the LiCoPO4 cathode is arduous. 17924
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