Lithium Clustering during the Lithiation/Delithiation Process in LiFePO4 Olivine-Structured Materials.

Olivine-structured LiFePO4 is one of the most popular cathode materials in lithium-ion batteries (LIBs) for sustainable applications. Significant attention has been paid to investigating the dynamics of the lithiation/delithiation process in Li x FePO4 (0 ≤ x ≤ 1), which is crucial for the development of high-performance LiFePO4 material. Various macroscopic models based on experimental evidence have been proposed to explain the mechanism of phase transition from LiFePO4 to FePO4, such as the shrinking core (i.e., core-shell) model, Laffont's (i.e., new core-shell) model, domino-cascade model, phase transformation wave, solid solution model, many-particle models, etc. However, these models, unfortunately, contradict each other and their validity is still under debate. An atomistic model is urgently required to depict the lithiation/delithiation process in Li x FePO4. In this article, we reveal the lithiation/delithiation process in LiFePO4 simulated by a computational model using the generalized gradient approximation (GGA + U) method. We find that the clustered configuration is the most energetically favorable, leading to co-operative Jahn-Teller distortion among the inter-polyhedrons that can be observed clearly from the bond patterns. This atomistic model not only offers answers to experimental results obtained at moderate or high rates but also gives the direction to further improve the rate capability of LiFePO4 cathode material for high-power LIBs.

Introduction

Olivine-structured LiFePO4 is fast gaining importance in today’s energy world, especially in high-power energy storage devices..[1−4] LiFePO4, as a promising cathode material for high-power Li-ion batteries, compared with conventional lead–acid, nickel–cadmium, and even nickel–metal hydride batteries, are needed urgently to meet the demands of large-scale applications such as electric vehicles (EVs) and hybrid electric vehicles (HEVs).[5,6] However, the mechanism of the phase transition from FePO4 to LiFePO4 is still under debate, which is believed to be crucial for the future development of high-performance LiFePO4 materials.[7,8] Along with essential demands to incorporate unique features, the understanding of the mechanism still attracts significant attention and leads scientists toward investigating the dynamics of the lithiation/delithiation process of LiFePO4 (0 ≤ x ≤ 1), aiming at understanding the experimental results obtained at moderate or high rates and also giving directions to improve LiFePO4 for high-power LIBs.[9−11]

There are two phases of LiFePO4 structures: the highly anisotropic fully lithiated LiFePO4 (LFPO) and its delithiated counterpart, FePO4 (FPO). The lithiation/delithiation process in LiFePO4 (0 ≤ x ≤ 1) is commonly accepted as a two-phase reaction mechanism, with the movement of Li+ ions confined along the b-axis.[12] The pioneering work was carried out by Goodenough et al.,[1] who showed that the flat charge/discharge profile of LiFePO4 arises from the motion of a two-phase interface. Recently, various macroscopic models based on experimental evidence have been proposed to explain the mechanism of phase transition from FePO4 to LiFePO4, such as the shrinking core (i.e., core–shell) model,[1,13] Laffont’s (i.e., new core–shell) model,[14] domino-cascade model,[15] phase transformation wave,[16,17] solid solution model,[18] many-particle models,[19] etc. All of these models intend to explain the lithiation/delithiation process in LiFePO4 to help understand the experimental results. However, these models lack direct and convincing computational support. In this study, we use an atomistic approach to calculate the energy that it takes to incorporate Li+ ions into the FPO lattice. The method gives us an understanding of the lithiation and delithiation processes, which will be useful for future material development.

Results and Discussion

Here, we use the first-principles density functional theory (DFT) GGA + U method to study the configuration of the lithium atoms because the method gives small error especially for transition metals with active localization of d or f orbitals compared with conventional GGA and linear discriminant analysis (LDA) methods.[20−23] In the GGA + U framework, the onsite Coulomb term U, and the exchange term J can be merged into a single effective parameter (U–J),[24] and thus, we only need to take U as an effective parameter that can be numerically fitted by a self-consistent ab initio calculation.[25] For the olivine FePO4 and LiFePO4 system, the value of U = 4.3 eV for Fe well describes the ground state properties and is widely used in the literature.[26−28] All of the calculations are performed by the Quantum Espresso package,[29] with supercells (2a × b × 4c) of eight-unit cells of LiFePO4. The kinetic energy of 600 eV has been used as the cutoff energy for the plane-wave basis, and reciprocal-space k-point meshes of 1 × 3 × 1 have been used to ensure that the total energies converge within five meV per supercell. Magnetism has also been taken into considerations—both the ferromagnetic (FM) and anti-ferromagnetic (AFM) ordering states have been calculated. Table shows the cell parameter and band gap for FePO4 and LiFePO4 structures, and the optimized lattice parameter agrees well with the previous literature by the linearized augmented plane-wave method[30] and available experimental results.[31,32] The FM and AFM states give similar results, and the system is in a magnetic disorder state at higher temperatures,[33] we thus only take the FM ordering for the total energy calculation for simplicity.

Table 1

Lattice Parameters and Band Gap values for FPO and LFPO with GGA + U (U = 4.3) and Experimental (Exp) Values

FPO	a (Å)	b (Å)	c (Å)	gap (eV)	LFPO	a (Å)	b (Å)	c (Å)	gap (eV)
FM	9.93	5.89	4.87	1.88	FM	10.41	6.07	4.73	3.71
AFM	9.93	5.88	4.86	2.07	AFM	10.40	6.06	4.74	3.71
exp[34]	9.82	5.79	4.79	N/A	exp[34]	10.06	5.89	4.64	N/A

As shown in Figure a, the oxygen atoms in the FePO4 framework are located in a slightly distorted, hexagonal close-packed arrangement.[35] The phosphorus atoms occupy tetrahedral sites forming PO4 tetrahedrons with oxygen atoms. Iron atoms are on corner-sharing octahedral positions forming FeO6 octahedrons, while lithium atoms occupy edge-sharing octahedral positions forming LiO6 octahedrons. Each FeO6 octahedron is linked with another four FeO6 octahedrons through the shared corners in the bc plane, forming inclined planes, parallel to the c-axis (i.e., [001] direction). The LiO6 octahedrons form edge-sharing chains along the b-axis (i.e., [010] direction), creating Li tunnels along this direction. Each FeO6 octahedron shares the edges with two LiO6 octahedrons, while the PO4 tetrahedron shares one edge with one FeO6 octahedron and two edges with LiO6 octahedrons, respectively.[35,36] To study Li+-ion transport in LiFePO4, Morgan et al.[37] first used the first-principles method and demonstrated that the diffusion coefficient (D) along the [010] direction was several orders higher than that along the [001] direction. The result of D (path B[001])/D (path A[010]) ≈ 10–37 showed that path B hardly made a contribution to the Li+-ion motion, and the Li+ ions diffused through one-dimensional (1D) channels along the [010] direction with a high energy barrier to cross between the channels. This large barrier was attributed to the FeO6 octahedral transition state in path B face-sharing with two PO4 tetrahedrons. Islam et al.[35,38] further modeled the structure of LiFePO4 and investigated Li+-ion migration energy in LiFePO4 by the atomistic simulation method and found that Li-ion migration was preferential along [010] channels, following a curved trajectory. Li et al.[39] studied the conductivity of Li+ ions along the three principal directions of LiFePO4 single crystals as a function of temperature (325–525 K) by AC impedance spectroscopy. Their results showed that Li+-ion diffusion in LiFePO4 is, to a large extent, confined to 1D through tunnels along the b-axis. Furthermore, the experimental evidence of Li+-ion diffusion along the [010] direction via PO4 tetrahedral interstitial sites in Li1–FePO4 (x = 0.4) was provided by combining high-temperature (620 K) powder neutron diffraction and the maximum entropy method.[40] However, the mechanism of the phase transition from FePO4 to LiFePO4 is still under debate.[9] When one lithium atom is inserted into the FePO4 framework, the reaction energy is defined as below:

Figure 1

(a) Perspective view of the FePO4 framework with one inserted Li+-ion along the b-axis. The red, blue, and yellow sticks represent the FePO4 units, and the green ball represents the Li+-ion; the light green areas are the optional positions for nesting the second Li+-ion. (b) Side view of the FePO4 framework along the c-axis with two optional configurations marked by light green and pink balls.

Here, ELFPO, EFPO, and ELi represent the total energy for the bulk LFPO, FPO, and bulk Li, respectively. For the second or third lithium inserted into the system, the corresponding Ereac is defined similarly by replacing EFPO with the total energy before the lithium being inserted. This process is shown as step 4 of Path 1 in Figure . To further confirm the energy scale in this process, we compared the total energy gain of Path 2, which is about the direct combination of Li+ and FPO– ions. Path 2 produced an energy difference of −11.7 eV, which is very close to the summation of the energy of −11.67 eV in all of the steps of Path 1.

Figure 2

Two parallel paths for the LFPO products. Path 1 shows an energy gain of 11.7 eV upon Li+ and FPO– ions to the one Li-inserted FPO crystal, while Path 2 shows an energy gain of 3.15 eV upon neutral Li and FPO structures to the one Li-inserted FPO crystals. In Path 2, Li+ and FPO– ions are neutralized first and the Li atoms are crystallized as well. The total energy gain from Li+ and FPO– to LFPO via Path 2 is 11.67 eV, very close to that via Path 1.

As shown in Figure a, the first lithium inserts into a FePO4 framework and is put in the center of the cell along the b-axis. An Ereac value of −3.15 eV was obtained, indicating that there is an energy favor of 3.15 eV after lithiation. The energy map for the third lithium insertion is shown in Figure b, and the optional positions for the second lithium inserting into FePO4 are marked in Figure c. Each optional position for the second lithium has two choices along the c-axis, as shown by light green and light red balls in Figure b. However, we found that the two configurations provide very similar results from the energy map (Supporting Information Figures S1–S3), and so here we only focus on the case as shown by the light green ball in Figure b.

Figure 3

Ereac energy map for (a) the second inserted lithium to the center of the lithium cluster, and (b) the third inserted lithium to the two lithium clusters. (c) Optional lithium insertion positions. The lithium atoms are marked as green balls, and the optional positions for the lithium are marked by small triangles. FePO4 polyhedra is not shown for clarity.

For the second inserted lithium, the value of Ereac generally increases when the distance between the two lithium ions increases. Ereac is around −3.48 eV for the first nearest insertion positions as shown in Figure a (marked by blue triangles, corresponding to positions of a–f in Figure c), then increases above −3.32 eV for the second nearest insertion positions as shown in Figure b (marked by cyan triangles, corresponding to positions of g–j in Figure c), of which the distance is about 1 nm to the center lithium. For the farthest position k from the center (Figure c), the value of Ereac is the highest, about −3.17 eV, which is very close to the Ereac of the first lithium (−3.15 eV). The simulations indicate that the two Li+ ions prefer to form clusters rather than be far apart in the FePO4 framework at low lithium concentration and there is little interaction between the two Li+ ions once the distance is larger than 1 nm.

When the third lithium is inserted, similar to the second lithium insertion case, Ereac increases proportionally with the distance from the third lithium to the center lithium cluster, thus yielding a similar pattern. The favorable energy positions are a, b, and d, which are the nearest positions around the center lithium cluster. The Ereac of position a is about −3.58 eV, which is a bit larger than that in the second lithium insertion case (−3.48 eV). Moreover, Ereac of the clustering configuration (positions i, b, c, g, e, and f in Figure c) is about 200 meV energetic favorite than the far-separated positions (position k in Figure c). These results agree well with the previous two lithium cases, and the inserted third lithium prefers to form cluster states rather than the far-separated form. In 2006, Laffont et al.[14] proposed a “new core–shell” model based on studies with high-resolution electron energy loss spectroscopy (HREELS). According to this model, Li+-ion migration along 1D channels is asynchronous. During charge, Li+-ions in the center of the platelet particles were extracted first and moved outward; whereas, during discharge, Li+-ion insertion started from the periphery. Their study unambiguously supports the view that the nanometer interfacial region consists of FePO4 and LiFePO4, but not solid solution LiFePO4, which changes with the gradient of x ranging from 0 to 1 by moving from FePO4 to LiFePO4. This two-phase mechanism attributed to the nature of the two phases. This Laffont’s new core–shell model accounts well for 1D migration, perpendicular to the platelets. A similar result was also observed by Chen et al.[41] for the electron microscopy study of the LiFePO4 to FePO4 phase transition, indicating that the Li+-ions are extracted from narrow and disordered transition zones on the ac crystal plane as the phase boundary progresses in the direction along the a-axis. In 2008, Delmas et al.[15] presented a “domino-cascade” model based on X-ray diffraction and electron microscopy technologies. This model agrees well with the HREELS study reported by Laffont et al.,[14] which shows that there is no solid solution LixFePO4 in the interfacial region between the two limit compositions. According to this model, when the lithium insertion/extraction starts in a given particle, the particle rapidly becomes either charged or discharged. One essential difference between the new core–shell model and the domino-cascade model is the character of the interface. The former supports the coexistence of LiFePO4 and FePO4 regions inside each particle[14] while the latter proposes the coexistence of LiFePO4 and FePO4 particles that are single-domain,[15] indicating the clustering configurations of the lithium clusters in the FPO/LFPO phases. From Figure , we can see that the insertion energy lowers down with the increase of Li+-ion concentration, indicating that it is more likely for the Li+-ion to fill the FPO. In our simulation, Ereac almost converged to zero when the lithium atoms are separated beyond 2 nm. Recently, some studies proposed that there was a solid solution zone during the charging/discharging process as a metastable process,[18] which only lasts for hundreds of seconds and then turns into FPO/LFPO two phases. Another experiment observed the direct evolution of the phase transformation in individual LFPO nanoparticles during both slow and fast charge/discharge rates.[42] The two experimental results provide solid support for our model, i.e., the clustering procedure leads the system to a clear final co-existing LFPO/FPO two-phase condition rather than a disorder solid solution, where the LFPO and FPO are randomly mixed.

Figure shows the local bond patterns with 1, 2, and 3 Li+-ions inserted into the FPO framework based on the clustered configuration. For FeO6 octahedrons, there are two kinds of Fe–O planar bond lengths, which are 2.16 and 2.07 Å (corresponding to b1 and b3 in Figure a, respectively). Due to symmetry, the values of b1, b2, b5, b6, b9, and b10 are equal, and the values of b3, b4, b7, b8, b11, and b12 are equal as well. Upon the insertion of one Li+-ion (Figure b), the Fe–O polyhedron is distorted and the bond length of b1 to b4 is increased by 0.3 Å due to the valence state change from Fe(III) to Fe(II). The distortion of the FeO6 octahedron also leads to the rotation of the PO4 tetrahedron with the bond lengths of b5 and b6 being reduced. Compared with FPO, the insertion of one Li atom leads to a total volume increase (ΔV1) of about 10 Å3, while the total volume (ΔV2) increases by ca. 17 Å3 after two Li+ ions are inserted. The increased total volume is not in proportion to the number of Li+-ions inserted (ΔV2 < 2ΔV1), indicating that there is a local structural distortion preventing further volume expansion. As shown in Figure c, when the second Li+ ion is inserted, the bond lengths of b9 to b12 increase, but the bond lengths of b7 and b8 decrease by 0.2 Å due to the PO4 tetrahedron rotation, which induces slight reduction of the bond lengths of b1 and b2. This kind of distortion belongs to the typical co-operative Jahn–Teller distortion,[43] which is a local phase transition driven by the localized orbital electronic states. The clustered configuration of the Li+ ions favors the co-operative Jahn–Teller distortion and results in the total energy minimization. For the third Li insertion with a clustered configuration (Figure d), the total volume (ΔV3) increases by 23 Å3. Since ΔV3 < ΔV1 + ΔV2 < 3ΔV1, this again belongs to the co-operative Jahn–Teller distortion. Due to the insertion of more Li+ ions, the fraction of Fe(III) is further reduced, and the Fe–O bond length increases in general. If there are more Li+ ions, as shown by the white color in Figure d, there are more bonds with decreasing lengths, indicating that the co-operative Jahn–Teller distortion dominates this procedure for the clustering of the Li+ ions during the lithiation process.

Figure 4

Local structure of the clustering configuration of the FPO framework with inserted Li numbers of (a) 0, (b) 1, (c) 2, and (d) 3. The black and white bond colors indicate the bond patterns changing after the insertion of Li+ ions. The yellow tetrahedrons correspond to PO4, and the blue arrows represent the rotation of the PO4 polyhedron after the insertion of more than one Li+ ions. The typical bond lengths are labeled from b1 to b12, which correspond to the structures in (a), (b), and (c) only. The black and white colors represent the increased and decreased bond lengths, respectively.

Conclusions

To summarize, by first-principles DFT calculation, we provide a clustering model to explain the lithiation/delithiation process with low lithium concentration in the FePO4/LiFePO4 structure. We find that the amount of volume expansion decreases when more lithium is inserted into the structure. From chemical bond patterns, one can see that the co-operative Jahn–Teller distortion is energetically favorable among the nearby FeO6 octahedrons with the rotation of the PO4 tetrahedrons when the Li+-ions are arranged in a clustered configuration. These results support that Li+-ions prefer to form clusters rather than being far apart. Our result agrees well with the new core–shell model.[44]