Crystal Structure, Energetics, And Electrochemistry of Li2FeSiO4

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Crystal Structure, Energetics, And Electrochemistry of Li2FeSiO4 Polymorphs from First Principles Calculations A. Saracibar,†,‡ A. Van der Ven,§ and M. E. Arroyo-de Dompablo∥,* †

Departamento de Química Inorgánica, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040 Madrid, Spain CIC Energigune, Albert Einstein 48, 01510 Miñano, Á lava, Spain § Department of Materials Science and Engineering, University of Michigan, 2300 Hayward Street, Ann Arbor, Michigan 48109, United States ∥ MALTA-Consolider Team, Universidad Complutense de Madrid, 28040 Madrid, Spain ‡

S Supporting Information *

ABSTRACT: The influence of crystal structure and relative stability on the electrochemical properties of Li2FeSiO4 polymorphs as cathode materials for Li-ion batteries is investigated. Six Li2FeSiO4 forms related to the crystal structure of Li3PO4 have been considered: three known polymorphs crystallizing in layered structures (with space groups P21, Pmnb, and Pmn21) and three forms reported for other LiMSiO4 materials crystallizing in three-dimensional (3D) frameworks (with space groups Pmn21, Pbn21, and P21/n). While Li2FeSiO4 polymorphs are very close in energy, their energies begin to differ substantially upon removal of Li, rendering those with lower electrostatic energy more stable. The change in relative stability of polymorphs upon delithiation results in a driving force for a phase transformation of the exiting two-dimensional (2D)-Li2FeSiO4 polymorphs to a more stable structure having a 3D network of [SiO4] and [FeO4] tetrahedra. The resulting phase exhibits a voltage plateau that is predicted to be 0.3 V below that of the original phase for the first electron process (Li2FeSiO4/LiFeSiO4 couple). The calculated voltage−capacity curves for the first and second cycles of Li2FeSiO4 at room temperature, assuming transformation to the new polymorph occurs after the first cycle, are in excellent agreement with experiments. Independently of the polymorphs, removal of the second lithium ion occurs at too high of a voltage (above 4.7 V) and is accompanied by major structural rearrangements, precluding the utilization of any of the unmodified Li2FeSiO4 polymorph derived from Li3PO4 as high specific capacity material. KEYWORDS: silicates, lithium batteries, electrode materials, DFT, Li2FeSiO4

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INTRODUCTION The Li2MSiO4 (M = Fe, Mn, Co, Ni) family has attracted much attention as potential high specific energy cathode materials for lithium batteries. In spite of initial expectations, to date, the reversible de-intercalation of the two lithium ions per formula unit has not been achieved for any transition metal ion (M) or their alloys (see ref 1 and the references therein). One complexity in this family is the wide variety of existing Li2MSiO4 polymorphs. Advances have been achieved to successfully control the synthesis conditions for the different polymorphs.2−5 However, a comprehensive investigation of the relative energetic stability of the polymorphs and its electrochemical implications is missing to date. This knowledge is important to enable the discovery of related Li2MSiO4 materials, where compositional or structural modifications could lead to improved electrochemical characteristics. The crystal structure of Li2MSiO4 consists of a distorted hexagonal packing of oxygen ions with half of the tetrahedral sites occupied by Li, M, and Si.6 A large number of Li2MSiO4 polymorphs is possible by assuming a different pattern of occupancy of the tetrahedral voids in the distorted hexagonally packed anion framework, similar to the enumeration of dipolar tetrahedral structures in wurtzite-BeO.7 Any known Li2MSiO4 © 2012 American Chemical Society

polymorph is related to either the low temperature form or the high temperature form of Li3PO4, denoted as β-Li3PO4 and γ-Li3PO4, respectively.8 The γ polymophs are built up by both corner and edge sharing tetrahedra with half of the tetrahedra pointing along one direction of the c-axis and the other half point in the opposite direction along c.9 Three Li2MSiO4 γ-polymorphs have been reported in the literature, crystallizing in space groups P21,10 Pn21,11 and Pmnb.5 Parts a−d of Figure 1 show these structures. A detailed description of the arrangement of edge-sharing tetrahedra in these crystal structures can be found in refs 1 and 5. In the β-Li3PO4 derivatives, there are only corner-sharing tetrahedra, with all the tetrahedra pointing in the same orientation parallel to the c axis.12 One variant crystallizing in the Pmn21 space group is common in the Li2MSiO4 family (see Figure 1e). It can be described as built up of infinite corrugated layers having the composition [SiMO4]∞, lying on the ac plane, and linked along the b-axis by LiO4 tetrahedra. Intersite exchange of M (initially in 2a sites) and Li (initially in 4a sites) ions in this structure has been observed in Received: September 19, 2011 Revised: December 23, 2011 Published: January 3, 2012 495

dx.doi.org/10.1021/cm202818u | Chem. Mater. 2012, 24, 495−503

Chemistry of Materials

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Figure 1. Optimized crystal structures of Li2FeSiO4 polymorphs. View along the [100] axis: P21 (a), Pmnb (b), P21/n (c), Pmn21 (e), Pmn21-mod (f), and Pbn21 (h). A view along the [001] axis is shown for the polymorphs in which the [MO4] and [SiO4] tetrahedra form a 3D network: Pmnb (d), Pmn21-mod, (g) and Pbn21 (i). Color code: Li, green; Fe, brown; and Si, gray.

Li2CoSiO4.2 This cation exchange was identified as the most favorable intrinsic defect by atomistic simulations in Li2MnSiO4.13 Figure 1f, g shows the structure of this Pmn21modification, denoted as Pmn21-mod thereafter. Another β-variety (Pbn21 space group) consists of parallel chains of alternating LiO4 and MO4 tetrahedra along the a axis (Figure 1h−i). Note that while such chains exist also in the Pmn21-mod structure (Figure 1f, g) their connectivity along the b-axis is different. The differences within the Pmn21-mod and Pbn21 structures become evident when looking at the xy plane. As illustrated in Figure 1, the polymorphs can be grouped in two categories: polymorphs consisting of a layered M−Si−O skeleton (crystallizing in space groups Pmn21, P21, and Pmnb) and polymorphs based on a three-dimensional (3D) network of [SiO4] and [MO4] tetrahedra (crystallizing in space groups Pmn21-mod, Pbn21, and P21/n). We will show that this distinction is more appropriate, when dealing with electrochemical properties, than the classical classification of Li2MSiO4 structures into β and γ polymorphs. Computational and experimental efforts have been made to evaluate the influence of the crystal structure and chemistry on the electrochemical performance of Li2MSiO4 materials.3,5,14 It has been found that the various polymorphs display similar electrochemical properties as a positive electrode in Li cells, as predicted by density functional theory (DFT) methods for Li 2 MnSiO 4 , 3 and as experimentally demonstrated for Li2CoSiO414 and Li2FeSiO4.5 For Li2FeSiO4, three polymorphs have been prepared, all of them crystallizing in a layered structure: the Pmn21 (hydrothermal synthesis at 200 °C), the P21 (obtained at 700 °C), and the Pmnb (obtained at 900 °C). Experiments performed by several groups5,15,16 agree that the removal of the first Li ion occurs at ∼3.1 V during the first

charge of the cell, independent of the polymorph (Pmn21, P21, Pmnb).5 Interestingly, the voltage plateau shifts to 2.8 V in subsequent cycling of the Li cells. The voltage shift is observed for all the existing polymorphs (Pmn21, P21, Pmnb). Based on the structural characterization of the Pmn21-delithitated materials, Thomas and co-workers suggested that the voltage shift is due to a structural transformation of the host compound.15 A phase transformation from the P21 polymorph to the Pmn21mod form has been confirmed by a neutron diffraction investigation of cycled Li2FeSiO4.17 However, little is known about the origin of such a transformation. The good performance of Li2FeSiO4 for the one electron process (Fe3+/Fe2+ couple) makes this material a promising candidate as a Li-ion battery cathode for large scale applications, and efforts should be devoted to understanding the electrochemistry of the Li2FeSiO4 polymorphs. In this work, we present a density functional theory (DFT) study of Li2MSiO4 polymorphs. We will first show that the relative stability of the Li2MSiO4 polymorphs depends on the nature of the transition metal, M. A more detailed study is performed for the Li2xFeSiO4 (x = 0, 0.5, 1) polymorphs in order to investigate the relation of energetic stability to electrochemical properties and, in particular, to elucidate the origin of the structural transformation observed upon cycling. We have focused on the experimentally observed forms for Li2FeSiO4 (Pmn21, P21, Pmnb), but have also considered models for related polymorphs: P21/n (observed for Li2MnSiO4), Pbn21, and a second Pmn21 polymorph (observed for Li2CoSiO4). The electrochemistry of the polymorphs is further discussed on the basis of calculated lithium intercalation voltages, structural variations, and electronic structure details. The origin of the phase transformation is finally investigated utilizing a combination of 496



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the Li2MSiO4 family. A previous DFT investigation found that this is indeed a very stable polymorph for Li2MnSiO4.3 To determine if this applies to every TM cation, we investigated the relative stability of selected polymorphs (Pbn21, Pmn21, and P21/n) for Li2MSiO4 (M = Mn, Fe, Co, Ni, Zn, and Mg). Figure 2 shows the relative energies as a function of the M radii.

cluster expansion and Monte Carlo simulations to simulate the voltage−composition curve at room temperature.

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METHODOLOGY

The total energy of Li2xMSiO4 (M = Mg, Mn, Fe, Co, Ni, Zn) was calculated using ab initio methods implemented in the Vienna Ab Initio simulation package (VASP).18−20 The projector augmented wave (PAW) potential set21 was used with the exchange and correlation energies approximated in the generalized gradient approximation with the Hubbard parameter correction (GGA + U), following the rotationally invariant form.18,22 An effective U value of 4 eV (J = 1 eV) was used for the d states of TM ions. The energy cut off for the plane wave basis set was kept fixed at a constant value of 600 eV throughout the calculations. The integration in the Brillouin zone is done on a set of k-points determined by the Monkhorst−Pack scheme: 6 × 6 × 6 for Pmn21 and P21, and 6 × 4 × 6 for Pmnb, Pbn21, and P21/n. A convergence of the total energy close to 5 meV/fu (fu = formula unit) is achieved with such parameters. The structures were fully relaxed (cell parameters, volume cells, and atomic positions); the final energies of the optimized geometries were recalculated so as to correct for the changes in the basis set of the wave functions during relaxation. A ferromagnetic configuration is considered for all crystal structures, and no magnetic constraints were imposed during the relaxation. The electrostatic energy of the relaxed compounds was computed using a simple Ewald summation of the formal charges (O = −2, Li = +1, Si = +4). For the transition metals, the formal charges are assumed to be +2, +3, and +4 for Li2xFeSiO4 with x = 1, 0.5, and 0, respectively. The initial atomic positions for Li2FeSiO4 were taken from ref 12 (Pmn21), ref 11 (P21/n), ref 10 (P21), ref 23 (Pbn21), and ref 5 (Pmnb). The two Li ions were removed from the Li2FeSiO4 optimized polymorphs leading to FeSiO4. For the intermediate LiFeSiO4, one should consider many Li-vacancy arrangements in differently sized unit cell. We enumerated a variety of lithium-vacancy arrangements within the different polymorphs of Li2FeSiO4 using the CASM software package.24,25 We calculated the energies of up to 26 LiFeSiO4 configurations in the Pmn21 host, using supercells having up to 6 formula units (Li12Fe6Si6O24). We also calculated the total energy of the different possible Li-vacancy configurations within the unit cells of the Pbmn21 and the P21 hosts (24 for Pbmn21 and 38 for P21) (Li8Fe4Si4O16). The total energies of the four possible configurations within the Pmn21-modified unit cell (Li4Fe2Si2O8) were calculated. The phase stability of Pmn21 and Pmn21-mod Li2xFeSiO4 has been further investigated as a function of lithium concentration and temperature. A detailed description of the methodology can be found in refs 24 and 26. The total energy of 80 configurations for each Pmn21 and Pmn21-mod were calculated at various concentrations (Li2xFeSiO4 with x = 1, 0.875, 0.75, 0.625, 0.5, 0.375, 0.25, 0.125, and 0). A cluster expansion for the two host structures Pmn21 and Pmn21-mod was parametrized to the first-principles energies of the various Li-vacancy arrangements described above. The cluster expansion was then implemented in Monte Carlo simulations in the grand canonical ensemble. To study the thermodynamics of Li and vacancy ordering in Li2xFeSiO4, we used a Monte Carlo cell containing 216 Li2FeSiO4 unit cells. At each temperature and chemical potential, at least 2000 equilibration Monte Carlo steps per lattice site were performed, after which over a minimum of 6000 Monte Carlo passes were sampled. The thermodynamic stability of Li2FeSiO4 polymorphs was investigated as a function of pressure. Starting from the optimized structures of Li2FeSiO4 polymorphs, we performed relaxed structure calculations at various constant volumes. The energy (E) as a function of the volume (V) was fitted to a second order Birch−Murnaghan equation of state 27,28 between 0 and 20 GPa utilizing the Gibbs program. 29

Figure 2. Calculated energy difference for Pmn21 (set as zero), Pn21 (squares), and Pbn21 (circles) polymorphs of Li2MSiO4 (M = Mg, Mn, Fe, Co, Ni, and Zn).

Energies are relative to that of the Pmn21 polymorph, which is therefore set as the zero of energy. The Pmn21 structure is the most stable for M = Mn, Fe, and Ni, whereas the Pbn21 gains in stability for M = Co, Zn, and Mg. From Figure 2, a clear relation of the energy to the M2+ ionic radii can not be extracted, though the general trend is that smaller cations prefer the Pbn21 (3D) structure and larger ones prefer the Pmn21 (2D). We expect that the electrostatic repulsion between M and Si will largely control the energetics of these polymorphs. Therefore, in the delithiated LiMSiO4 forms, as a result of the smaller and more oxidized M cations, a different relative stability of polymorphs could occur. b. Crystal Structure and Energetics of Li2xFeSiO4 Polymorphs (x = 0, 0.5, 1). Table I summarizes the calculated lattice parameters for the fully relaxed structures of the investigated Li2xFeSiO4 polymorphs, together with a comparison to experimental data available in the literature. So far, the known polymorphs are the Pmn21 (hydrothermal synthesis at 200 °C), the P21 (obtained at 700 °C), and the Pmnb (obtained at 900 °C). Note that in all these polymorphs the [MO]4 and [SiO]4 tetrahedra form a layered structure. It may be concluded that the calculation method allows a correct prediction of the cell parameters and volume, with differences below 3%. Figure 3a−c shows the calculated total energy as a function of volume obtained for the Li2xFeSiO4 polymorphs (Figure 3a, x = 1; Figure 3b, x = 0.5; and Figure 3c, x = 0). Parts d−f of Figure 3 show the electrostatic energy, obtained by a Ewald summation, as a function of volume (Figure 3d, x = 1; Figure 3e, x = 0.5; and Figure 3f, x = 0). Energy differences are referred to the Pmn21 polymorph. In parts a and d of Figure 3, the known Li2FeSiO4 polymorphs (Pmn21, Pmnb, and P21) are labeled in blue. It can be seen in Figure 3a that the Pmn21 and the P21 polymorphs are the most stable structures, with their total energy difference (2 meV) within computational error.

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RESULTS AND DISCUSSION a. Relative Stability of Li2MSiO4 Polymorphs for Various M. The Pmn2 1 is the polymorph most frequently observed in 497



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Table I. Calculated Lattice Parameters (in Å) and Volume (in Å3) for Li2xFeSiO4 (x = 0, 0.5, 1) Polymorphs Compared to Available Experimental Values x 1 0.5 0 1 0.5 0 1 0.5 0 1 0.5 0 1 0 1 0 1a 0.5a 1a a

space group Pmn21 expt5

Pmn21-mod

Pbn21

P21 expt10

Pmnb expt5 P21/n initial, Pmn21 1st charge 1st discharge

a (Å

b (Å)

c (Å)

6.320 6.2695(5) 6.080 6.078 6.271 6.722 7.347 6.276 6.718 8.300 8.313 8.22898(18) 8.245 8.194 6.341 6.2853(5) 6.00 6.260 8.238 6.267(1) 6.508(3) 6.272(2)

5.384 5.3454(6) 5.648 5.649 5.485 5.204 5.302 10.973 10.389 9.888 5.084 5.02002(4) 5.135 5.394 10.747 10.6592(8) 11.488 10.971 10.061 5.330(1) 5.216(2) 5.373(2)

4.998 4.9624(4) 5.031 5.338 5.017 5.060 5.328 5.016 5.079 5.394 8.282 8.23335(18) 8.254 8.338 5.100 5.0367(4) 5.380 5.131 5.297 5.015(1) 5.002(2) 5.009(2)

β

89.33 90.11 90.5 89.77 90.09

99.15 99.20 93.812 93.51

91.27 91.90

V (Å3/fu) 85.05 83.15 86.39 91.60 86.31 88.53 103.77 86.38 88.61 110.69 86.41 83.93 87.16 91.97 86.89 84.36 92.80 88.08 109.71 83.75 84.90 84.40

In situ X-ray diffraction experiments from Nyten et al.15

Figure 3. Calculated total energy difference of Li2xFeSiO4 polymorphs (upper row); Li2FeSiO4 (a), LiFeSiO4 (b), and FeSiO4 (c). The known polymorphs are labeled in blue. The bottom row shows the electrostatic energy difference for Li 2FeSiO4 (d), LiFeSiO 4 (e), and FeSiO4 (f).

Energy differences among Li2FeSiO4 polymorphs are small, reaching a maximum value of 0.065 eV/fu. The trend is that the most stable polymorph (lower total energy) has the lowest volume. There is no correlation between the electrostatic energy (Figure 3f) and the total energy.

Figure 3c shows the calculated energy and volume obtained for the delithiated FeSiO4 polymorphs (referred to the Pmn21). The relative stability of the polymorphs differs substantially from that of the lithiated phases; the Pmn21 is now the least stable polymorph. The energy differences between polymorphs 498



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Figure 4. Optimized structure of (a) Pbn21-LiFeSiO4 and (b) Pmn21-mod LiFeSiO4. View along the b-axis. Color code: Li, green; Fe, brown; and Si, gray.

synthesis of Li2FeSiO4 easily results in a mixture of polymorphs. Interestingly, to date, any reported Li2FeSiO4 polymorph crystallizes in structures based on [FeOSi]∞ layers. Because the layered structures transform upon delithiation, a legitimate question is whether it is possible to prepare a 3D-Li2FeSiO4 host. Some insight into possible synthesis strategies (i.e., by varying pressure, P, and temperature, T) can be gained by means of calculated equations of state of the polymorphs. Figure 5 shows the equation of state for Li2FeSiO4 polymorphs fit to the energy−volume data at 0 K. The parameters

span a wider range of energies (0.3 eV/fu) than for the lithiated forms. In Figure 3c, the trend is that the larger volume structures are more stable, contrary to what is observed for Li2FeSiO4. However, the delithiated structures should be compared with caution. Delithiation from Pmn21, P21, and Pmnb results in a layered structure, as inferred from their structures shown in Figure 1. On the contrary, delithiated P21/n, Pmn21-mod, and Pbn21 have 3D frameworks. Their structures consist of rings of alternating FeO4 and SiO4 tetrahedra on the (001) plane (see Figure 1). Upon delithiation, the rings expand, opening the Si−O−Fe angle. In the delithiated phases, the minimum Si−O−Fe angles are 130° and 135° for Pbn21 and Pmn21-modified, respectively. Such connectivity confers a better energetic stability, because an open Si−O−Fe angle allows larger Si−Fe distances, which minimize cationic repulsions. In the less stable FeSiO4 polymorphs (Pmn21, Pmnb, and P21), there are Fe− O−Si angles of 122°. While the cationic repulsion seems not so relevant in the Li2Fe2+Si4+O4 polymorphs (Figure 3a, d), it drives the energetic stability of the delithiated FeSiO4 phases. Figure 3f shows how the electrostatic energy correlates to the total energy, underlying the relevancy of the Coulombic repulsions in the stability of FeSiO4 polymorphs. The relative stability of the intermediate LiFeSiO4 polymorphs is shown in Figure 3b. The Pmn21 form is the least stable one, with a maximum energy difference of 0.25 eV/fu relative to the most stable Pmn2 1-modified polymorph. Comparing parts b and e of Figure 3, it can be inferred that electrostatic interactions play a role in the stability of LiFeSiO4 polymorphs. The smaller cation size and higher oxidation state in LiFeSiO4 result in important cationic electrostatic repulsion when compared to the fully lithiated compound. This causes the structures having a 3D framework (Pbn21 and Pmn21-mod) to be more stable. Figure 4 shows the most stable crystal structures found for the LiFeSiO4 Pbn21 (Figure 4a) and Pmn21mod (Figure 4b). In both cases, the lithium vacancies order along the a-axis forming chains of SiO4 tetrahedra alternating with vacant sites. Along the b-axis, there are clear differences: in the Pmn21-mod, the Li and Fe alternate in rows, while the Pbn21 polymorph consists of chains of alternating LiO4 and FeO4 tetrahedra. Lattice parameters and atomic coordinates have been included in Table I and in the Supporting Information, respectively. The minimum Si−O−Fe angles are 116° and 119° for Pbn21 and Pmn21-mod, respectively, which are again larger than for the less stable Pmn21 (115°) and P21 (112°). c. Thermodynamics of Li2FeSiO4. Total energy differences among Li2FeSiO4 polymorphs at 0 K are only a few meV/fu (Figure 3a). This small energy range explains why

Figure 5. Fitting of the energy−volume data of Li2FeSiO4 polymorphs to the Birch−Murnagham EOS. The arrow indicates the volume at which the P21 polymorph is desetabilized in favor of a less dense crystal structure.

of the fits are given in the Supporting Information. To isolate a single polymorph, the “general rule” to follow is that pressure favors the low volume phases and temperature favors the larger volume forms. In view of Figure 5, the densest form (Pmn21) can be isolated by pressure; the variation of enthalpy with pressure (at 0 K) predicts that a small pressure of 0.3 GPa already stabilizes the Pmn21 form (see Supporting Information). This is consistent with the reported preparation of this polymorph by hydrothermal means.5 In addition, it has been shown that the Pmn21 form is isolated under high-pressure conditions for the Li2MSiO4 (M = Co, Fe, Mn) family.3−5 In principle, some of the less dense polymorphs might be accessible by quenching the samples from sufficiently high temperature. The EOS in Figure 5 are consistent with the fact that the Pmnb polymorph is obtained at higher temperature than the P21 (900 °C vs 700 °C in ref 5). Preliminary calculations suggest that free 499



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diffraction investigation that found that the initial P21-Li2FeSiO4 transforms to the Pmn21-mod structure following 10 charge− discharge cycles (limited to the Li2FeSiO4/LiFeSiO4 couple), although the intermediate LiFeSiO4 was not characterized.17 More insights about the layered to 3D transformation can be obtained utilizing a cluster expansion model approach to investigate phase stability. To compute phase stability above 0K, one has to account for entropy, the most important of which is configurational entropy due to Li-vacancy disorder. We have investigated phase stability as a function of temperature for the Pmn21 and the Pmn21-mod polymorphs (Figure 1e, g), which are the most stable at the Li2FeSiO4 and LiFeSiO4 stoichiometries, respectively. The energies of a total of 80 configurations within each host was computed from first principles at several lithium compositions. Figure 6 shows the formation energies defined as

energy differences remain small at room temperature (of the order of 5 kJ/mol), and they barely change as the temperature increases (see the Supporting Information). With such small free energy differences, from solely thermodynamic arguments, one can not eliminate the possibility that other related-Li3PO4 polymorphs not prepared yet could be synthesizable. d. Electrochemistry of Li2FeSiO4 Polymorphs. Calculated average voltages for the two-lithium de-intercalation process are listed in Table II (Fe4+/Fe2+ redox couple). Polymorphism Table II. Calculated Average Voltages (in V) for Li2FeSiO4 Polymorphsa dimensionality

space group

Fe4+/Fe2+

Fe3+/Fe2+

Fe4+/Fe3+

2D

Pmn21 expt P21 expt Pmnb expt Pmn21-mod expt Pbn21 P21/n

3.99

3.12 3.135,37 3.09 3.105

4.86

2D 2D 3D 3D 3D

3.96

4.83

3.93 3.83 3.84 3.83

3.06 2.83 2.855,37 2.85

4.82 4.716 4.83

a

From left to right the redox couples correspond to the reactions: Li2Fe2+SiO4 → Fe4+SiO4 + 2Li; Li2Fe2+SiO4 → LiFe3+SiO4 + Li; and LiFe3+SiO4 → Fe4+SiO4 + Li.

produces a maximum variation of 0.16 V in the two electron process; the maximum average voltage is 3.99 V (Pmn21) and the minimum is 3.83 V (Pmn21-mod). As inferred from Figure 3, in all polymorphs, the intermediate LiFeSiO4 is very stable toward decomposition into Li2FeSiO4 and FeSiO4, producing a two voltage plateau structure and a large voltage step at x = 1. The redox couples Fe2+/Fe 3+ and Fe 3+/Fe 4+ are therefore independently investigated. d.1. One Electron Process, Li2FeSiO4/LiFeSiO4. Sirisopanaporn et al. reported that the voltage for the first lithium extraction (Fe2+/Fe3+ redox couple) differs only around 0.1 V for the distinct polymorphs5 (3.13 V for Pmn21, 3.10 V for P21, and 3.06 V for Pbmn). A voltage shift down to 2.84 V during the first discharge of the Li cell was observed for all the polymorphs. Thereafter, intercalation occurs reversibly at 2.85 V. Table II summarizes the calculated average voltage (Fe3+/Fe2+ couple) for Pmn21, Pmn21-mod, Pbn21, and P21; there is an excellent agreement with experimental values. The computational results point out that there is a difference of about 0.29 V between the layered and the 3D-hosts, which is consistent with the experimentally observed voltage down-shift of Pn21, Pmnb, or Pmn21 polymorphs (all layered forms). As previously discussed, the 3D-hosts become energetically more stable than the 2D variants upon delithiation (Figure 3b, c), thereby providing a driving force for the layered to 3D-phase transformation. Experimental evidence of such a transformation has been reported. Nyten el al.15 determined the lattice parameters upon delithiation from Pmn21-Li2FeSiO4 using in situ Xray diffraction (XRD). The results can be compared with our calculated lattice parameters in Table I. The a and b lattice parameters respectively increase and decrease upon delithiation, which is consistent with a transformation of Pmn21 to either the Pbn21 or Pmn21-mod and the subsequent cycling of the latter. Therefore, the transformation seems to occur at the end (x = 1) of the first charge cycle. This is consistent with a neutron

Figure 6. Formation energies of the different configurations calculated from first principles and the predicted ones from the cluster expansions (CEs). Green circles correspond to calculated energies for configurations within the Pmn21-mod structure, and blue diamonds correspond to the Pmn21 one. The red stars represent the energies predicted by the corresponding CE fit, and the black line is the constructed convex hull.

Δf E = E − (x /2)E Li2FeSiO4 − (1 − x /2)E FeSiO4

(2)

where E is the total energy of the configuration per Li2xFeSiO4 formula unit, ELi2FeSiO4 is the energy of Li2FeSiO4 in the Pmn21 host, and EFeSiO4 is the energy of FeSiO4 in the Pmn21 host. Negative energies indicate that Li2xFeSiO4 is stable with respect to a two-phase mixture of Li2FeSiO4 and FeSiO4 at low temperatures. The convex hull, which is drawn in Figure 6, is the line that connects all the lowest energy phases in a formation energy vs composition plot. To be able to directly compare the stability of the Pmn21 polymorph relative to the host Pmn21-mod derived host with Li−Fe mixing, the convex hull of the latter was constructed using Li2FeSiO4 and FeSiO4 in the Pmn21 structure as reference states. Figure 6 clearly shows that Li-vacancy arrangements over the Pmn21-mod host have more negative formation energies than the Pmn21 host at all Li concentrations, and that the difference in energy between the two hosts increases as the lithium content decreases. This reinforces our previous discussion about the layered-Pmn21mod framework becoming stable upon lithium removal, and 500



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initiating the phase transformation of the Pmn21 structure. The vertices of the convex hull correspond to the most stable Livacancy ordered structures. These result in steps in the voltagecomposition profile if Li-ordering persists at finite temperature or a sloping voltage profile if thermal excitations result in Livacancy disorder to form a solid solution. No other single phase than that at x = 0.5 is predicted. The energy dependence of the Li-vacancy configurational disorder was parametrized with a cluster expansion by fitting to 26 energies for the Pmn21 polymorph and to 33 energies for the Pmn21-mod one. The coefficients of this expansion, describing the energy dependence of the crystal as a function of the Livacancy ordering, are the effective cluster interactions (ECIs). Figure 6 illustrates how the energies predicted by the corresponding cluster expansions (red stars for Pmn21 and plus symbols for Pmn21-mod) compare with the original DFT + U values (green circles for the Pmn21-mod polymorph and blue diamonds for the Pmn21). The ECIs for these cluster expansions are given in Supporting Information. The overall root-mean square (rms) error was 0.03 eV/fu, and the cross-validation (CV) score was 0.07 eV/fu, for Pmn21. For the Pmn21-mod, values were 0.01 eV/fu (rms) and 0.03 eV/fu (CV). We performed Monte Carlo simulations to calculate the voltage−composition profile of Li2FeSiO4 at different temperatures. Figure 7 compares the calculated voltage−composition

Figure 8. Calculated phase diagram for the Pmn21-mod polymorph.

Together with voltage, cyclability and rate capability are other important electrode characteristics. Extraction of the first lithium ion from Pmn21-mod Li2FeSiO4 is accompanied by a small volume expansion of 2.3% (see Figure 3), which is consistent with the observed reversible cycling of the first lithium ion following the first charge process. All the Li2FeSiO4 and LiFeSiO4 polymorphs are insulating materials with calculated band gaps of the order of 3.1 and 2.7 eV, respectively. For Li2FeSiO4, calculated band gaps range from 3.16 eV (Pmn21) to 3.0 eV (P21/n). For the intermediate LiFeSiO4, calculated band gap values are 2.4 eV (Pmn21), 2.7 eV (Pmn21mod), 2.6 eV (Pbn21), and 2.6 eV (P21). The mechanism for electronic conductivity in these materials has not been investigated yet. It is unlikely, however, that these materials exhibit intrinsic semiconductor-like conductivity. Indeed, for most insulating intercalation materials, the carrier concentration (electrons or holes) is determined extrinsically, mainly by Li deficiency.30 If this were also the case for the silicates, the band gap will not play a dominant role in the concentration of carriers and nothing about the electrode conductivity can be said from the present calculations. Regarding the lithium mobility, previous DFT investigations found minimum Li migration barriers of 0.75 eV for Pmn2131 and 0.9 eV for Pmn21-mod.17 As pointed out by Liivat et al.31 these barriers are significantly higher than those found in other cathode materials (LiCoO2 0.27 eV,32 LiFePO4 0.23 eV33). Lithium mobility seems to be particularly low in the Pmn21-mod; further investigations could elucidate whether a low lithium diffusivity is common to all 3DLi2MSiO4 compounds. d.2. Second Electron Process, LiFeSiO4/FeSiO4. For all the polymorphs the oxidation of Fe3+ to Fe4+ occurs at a very high voltage (Table II). As seen in Figure 3 the extraction of the second lithium ion from Li2FeSiO4 produces a moderate volume expansion of the order of 7% for the layered Li2FeSiO4: 7.7% (Pmn21), 6.4% (P21), and 6.8% (Pbmn). This is of the same order as occurs in olivine-LiFePO4. However, these layered hosts transform during the first lithium extraction to the most stable polymorphs consisting of a 3D network. For the 3D hosts, the calculated volume expansion as predicted by GGA + U is of the order of 20% (20% for Pmn21-modified, 28% for Pbn21, and 24% for P21/n). As discussed above, this severe structural rearrangement is driven by the need for longer Fe− Fe and Fe−Si distances to minimize stronger cationic repulsions. Because of this large volume variation, continued cycling of the two lithium ions from the Li2FeSiO4 3D-materials is highly improbable. In addition, the creation of holes in the O-2p band,34 has been identified as another difficulty for the

Figure 7. Calculated voltage−composition curves at 300 K (black) and 700 K (red) for Pmn21 and Pmn21-mod (squares and triangles, respectively). Assuming the occurrence of a transformation from Pmn21 to Pmn21-mod, these curves should resemble the first and second cycle voltage curves, respectively, measured experimentally.

curves at T = 300 K (black) and T = 700 K (red) for Pmn21 and Pmn21-mod (squares and triangles, respectively). Assuming the occurrence of a transformation from Pmn21 to Pmn21-mod, these curves should resemble the first and second cycle voltage curves, respectively, measured experimentally. Both voltage curves exhibit two plateaus, separated by an abrupt voltage step at x = 0.5 (half delithiation). The voltage curves vary little with temperature, indicating that Li-disorder is of little importance in these polymorphs. The first plateau for Pmn21 (to be observed on the first cycle) occurs at ca. 3.0 V and the second one at ca. 4.8 V. After a structural transformation to Pmn21mod (in the second cycle and subsequent cycles), the first voltage plateau shifts down by 0.3 V, in agreement with the experimental results. Because of the high stability of the intermediate LiFeSiO4, the voltage step will only vanish at very high temperature (see Figure 8). 501



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structural stability of highly delithiated FeSiO4 phases. The calculated DOS of any of the delithiated FeSiO4 polymorphs show holes in the O-2p band, making these materials unsafe. The structural instability, together with the high voltage needed to extract the second lithium, limits the studied Li2FeSiO4 polymorphs to “medium” capacity materials.

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Article

ASSOCIATED CONTENT

S Supporting Information *

Crystal structures, paramaters of energy−volume fitting for the Birch−Murnagham EOS, and numerical values in (eV) for the ECIs of the Monte Carlo simulated polymorphs of Li2FeSiO4. This material is available free of charge via the Internet at http://pubs.acs.org.

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CONCLUSIONS

The energetics, and thereby the electrochemistry, of six Li2FeSiO4 polymorphs related to the Li3PO4 structure have been investigated from first principles. We found that the starting Li2FeSiO4 polymorphs all have similar energies, with free energy differences on the order of 5 kJ/mol at room temperature. This explains the difficulties encountered in preparing single phase samples of Li2FeSiO4 polymorphs. We can not rule out the possibility that other polymorphs based on the Li3PO4 structures could be synthesizable. Nevertheless, the present DFT investigation indicates that all the polymorphs have very similar electrode characteristics in terms of voltage, volume variation, and electronic structure; one can expect that the electrochemical properties of any new Li3PO4-related form will be similar to those of the already known polymorphs. We found that the stability of the delithiated Li2xFeSiO4 polymorphs is controlled by the strong columbic repulsions between Fe3+ (or Fe4+) and Si4+ cations. The most stable Li2FeSiO4 polymorphs consist of layers of [SiO4] and [FeO4] tetrahedra. We have shown that, for LiFeSiO4 and FeSiO4, the minimization of the electrostatic energy stabilizes the polymorphs consisting of a 3D-[Fe−O−Si] framework. This results in a thermodynamic driving force for the 2D-Li2FeSiO4 polymorphs to transform to a 3D framework during delithiation. This 2D → 3D transformation is accompanied by a voltage down-shift of ca. 0.3 V for the first electron reaction. The simulated voltage−composition curves for the first and second charge of Li2FeSiO4, assuming a transformation from the starting Pmn21 to Pmn21-mod polymorph, which is more stable upon Li removal, are in excellent agreement with experiments. The extraction of the second lithium ion from the 3DLi2FeSiO4 polymorphs causes a severe structural distortion associated with the large electrostatic repulsion between the highly oxidized and small cations. This, together with the high voltage for the Fe3+/Fe4+ redox couple, prevents the reversible cycling of the second lithium ion. Therefore, the unmodified studied silicates will remain as medium capacity materials, exploiting only half of their theoretical capacity, unless novel substitutions improve the electrochemical behavior. The severe structural stress upon cycling of the 3D-polymorphs could be ameliorated in mixing transition metal silicates Li2Fe1−yMySiO4, which could retain the layered structure upon lithium removal. The results presented here suggest that the smaller transition metal cations (Co, Mg, and Zn) would stabilize the 3D hosts. The larger Mn cations could help stabilize the layered structures in addition to lowering the Li insertion voltage. Yet, the trend of Mn4+ (d3 configuration) to adopt octahedral coordination is a handicap for the practical utilization of the whole theoretical specific capacity.16,35,36 In this sense, compositional modifications affecting the polyoxoanionic groups are an interesting alternative, a possible strategy being the substitution of N for O;34 while promising, this route needs to be experimentally tested.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

ACKNOWLEDGMENTS Financial resources for this research were provided by the Spanish Ministry of Science (MAT2007-62929, MAT201122753, and CSD2007-00045). E. Arroyo thanks E. Francisco for fruitful discussions and assistance with the GIBBS program. This work has been possible thanks to the support of the computing infrastructure of the i2BASQUE, CESGA and MALTAconsolider networks.

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Crystal Structure, Energetics, And Electrochemistry of Li2FeSiO4

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