Systematic DFT calculations

In the present study, a large set of DFT calculations is systematically made for many different kinds of solute elements that are substituted on three possible cation sites of LFP. Many experimental and theoretical studies on solute atoms in LFP have been reported since the early work of the aliovalent doping in LFP12. There has been controversy on the capability of the aliovalent doping. History of the debate on the doping can be found in reference13. It should be emphasized that they discussed the solubility of single aliovalent dopants and related defect/carrier formation in LFP. The situation is very different from the present study where we treat only co-substitution of elements to maintain the charge neutrality within the compound. Generally speaking, single aliovalent elements and co-substitution of elements behave differently in wide-gap materials. In the present study, the charge neutrality is maintained by assuming that the formal ionic charges are unchanged. For example, when Zr4+ and Si4+ are incorporated and are located, respectively, at Fe2+ and P5+ sites, two Si atoms and one Zr atom are put into the supercell of the DFT calculation. The situation can be expressed as (Zr Fe +2 Si P ). The chemical compositional space investigated in the present study is shown as 630 cubes in Fig. 1a. DFT calculations are thoroughly made for all possible solute arrangements within the unit cell composed of four formula units of LFP (that is, 28 atoms). The lowest energy structure among them is adopted as the one representing the given chemical composition. An example of the dependence of the energy on the solute arrangement is shown in Fig. 1b. A section of the results obtained from the calculations for the relative volume change between lithiated and fully delithiated materials is shown in Fig. 1a. RVC is defined by 100·(V L –V D )/V L (%), where V L and V D denote lattice volumes of lithiated and delithiated material LFP, respectively.

Figure 1: Theoretical results of co-substituted LFP. (a) Variety of the chemical compositional space investigated in the present study. The shaded area corresponds to chemical compositions that are excluded from the present study, since the charge compensation is not possible within the given supercell. Calculated RVC between lithiated and fully delithiated materials on a (A Li , M Fe , Si P ) section is shown together. (b) An example of the dependence of the energy on the solute arrangements for (Li Li , Zr Fe , Si P ), that is, Z2S material. The energy is per four formula units of LFP, and relative to the lowest energy arrangement. Orange and green octahedrons, respectively, denote FeO 6 and ZrO 6 . Violet and blue tetrahedrons denote PO 4 and SiO 4 , respectively. Green and red balls, respectively, show Li and O. Full size image

According to the series of calculations performed, the effective ways of reducing the RVC are found by double substitutions of LFP with either Si4+ or Al3+ at the P site and trivalent or tetravalent cations at the Fe site. Among them, some sets of substitutions show RVC of smaller than 3%: for example, (Y Fe +Si P ), (Zr Fe +2 Si P ) and (Zr Fe +Al P ). We will focus on the (Zr Fe +2 Si P ) system, which will be hereafter called Z2S. Its chemical formula is Li(Fe 1−x Zr x )(P 1−2x Si 2x )O 4 .

DFT calculations for Z2S with supercells composed of 8 and 16 formula units are additionally made, which corresponds to x=0.125 and 0.0625, respectively. Results of the RVC are shown in Fig. 2(a) together with the trends observed in the mismatch of the (100) planes (bc planes) between lithiated and delithiated materials (Fig. 2b). The planar mismatch is defined by 100·(A L –A D )/A L (%), where A L and A D denote areas of bc planes in lithiated and delithiated materials, respectively. According to the domino-cascade model by Delmas et al.10 for the delithiation mechanism of LFP, the interphase boundaries between LFP and FP prefer (100) planes. A smaller planar mismatch between the planes is therefore expected to be beneficial for retarding the degradation during repeated charge/discharge cycles.

Figure 2: Effects of solutes on RVC. (a) RVC between lithiated (δ=0) and delithiated (δ=1−x) materials for Li 1−δ (Fe 1−x Zr x )(P 1−2x Si 2x )O 4 . Blue square and red circle denote DFT results and experimental results, respectively. (b) Planar mismatch of (100) planes (bc planes) between lithiated and fully delithiated materials for Li 1−δ (Fe 1−x Zr x )(P 1−2x Si 2x )O 4 . (c) Correlations between the RVC of FeO 6 , LiO 6 and PO 4 polyhedra with the lattice RVC for many different substituted materials. (d) Explanation of the solute effects on the lattice RVC. Full size image

Both the volume and the planar mismatch decrease linearly with the solute concentration. A possible mechanism for the decrease in the RVC following the substitutions is briefly discussed here. Figure 2c shows correlations between the RVC of FeO 6 , LiO 6 and PO 4 polyhedra with the lattice RVC for many different substituted materials that have been calculated in the present study. A clear trend can be seen between the lattice RVC and the polyhedral RVC for FeO 6 and LiO 6 . On the other hand, the polyhedral RVC for PO 4 is almost unaffected by the lattice RVC. The magnitude of the reduction of the polyhedral RVC is larger in LiO 6 than in FeO 6 , which explains the observed effect with the substituted LFP. As drawn in Fig. 2d, the polyhedral RVC became smaller in FeO 6 and larger in LiO 6 in the substituted LFP, thereby making the lattice RVC smaller.

Synthesis and characterization of targeted materials

On the basis of the results of the computational screening of the substituted LFP, synthesis experiments were performed for Li(Fe 1−x Zr x )(P 1−2x Si 2x )O 4 materials with varying x. Initially, the conventional solid-state reaction method was used. Many different procedures, starting materials, synthesis temperatures, atmospheres and durations were tried; however, the production of a single-phase solid-solution material was unsuccessful. We have chosen to use an epoxide-mediated sol–gel method to obtain more intimate mixing of the starting materials. By optimizing the processing parameters, single-phase solid-solution samples were successfully synthesized. Pictures of the sol–gel products and the final powder sample are shown in Fig. 3a,b. Particle diameters using scanning electron microscopy were ~0.1 μm in both pristine and co-substituted samples.

Figure 3: Synthesis of Z2S co-substituted LFP. (a) Pictures of the gel, dried gel and the final calcined powder for the Li(Fe 1−x Zr x )(P 1−2x Si 2x )O 4 sample with x=0.125. (b) Scanning electron microscopy image of the calcined powder with x=0.125. (c) XRD (Cu-Kα) profile and the result of the Rietveld refinement for the Li(Fe 1−x Zr x )(P 1−2x Si 2x )O 4 sample with x=0.125. Full size image

Structural analysis by the powder X-ray diffraction (XRD) shows that the samples of Li(Fe 1−x Zr x )(P 1−2x Si 2x )O 4 are single-phase up to the value of x=0.125. XRD patterns are shown in Supplementary Fig. 1. Figure 3c shows the result of the Rietveld refinement14 of the XRD profile for the x=0.125 sample. Only 1% of the Li site is found to be occupied by Fe and the Zr content at the Fe site is 13%, which satisfactorily agrees to the intended ratio of cations and the mixed quantities. We can therefore conclude that single-phase solid-solution samples of Z2S are successfully synthesized up to x=0.125. More details of the XRD analyses were described in Supplementary Note 1.

Electrochemical experiments

We first made experiments using a beaker-type cell with a lithium metal anode. Charge and discharge curves with the Z2S (x=0.125) cathode and the rate of 170 mAg−1 (corresponding to 1C for the pristine cathode) are shown in Fig. 4a. First discharge capacity was 128 mAhg−1, which corresponds to 88% of theoretical capacity (145 mAhg−1 for Z2S (x=0.125) cathode). The cells with the pristine and the Z2S (x=0.125) cathodes are compared in Supplementary Fig. 2 of Supplementary Note 2. Both of them exhibit a plateau at the same potential value, 3.4 V, implying that the co-substitution does not affect the redox reaction of Fe ions significantly. Their rate capabilities are found to be almost the same.

Figure 4: Charge/discharge experiments with Z2S cathodes. (a) Charge and discharge curves for a beaker-type cell with Li(Fe 1−x Zr x )(P 1−2x Si 2x )O 4 cathode of x=0.125. (b) Experimental and calculated lattice parameters of Z2S samples as a function of the solute concentration before delithiation and (c) after delithiation. Red circles and blue squares correspond to experimental and calculated results, respectively. Full size image

The experimental and calculated lattice parameters of compounds before and after the delithiation are shown in Fig. 4b,c as a function of solute concentration, x. The lattice parameters for all three axes show small dependence on x before the delithiation. The dependence is much larger in the delithiated compounds especially for a and b axes. In other words, the presence of the solute elements has a much larger impact on the structure of delithiated compounds.

The experimental lattice RVC and the planar mismatch of bc plane are shown in Fig. 2a,b to compare with the computed values. Satisfactory agreements between experiments and computed results can be seen. The experimental lattice RVC decreases linearly with x from 6.3% (x=0) to 3.7% (x=0.125). A similar trend can be observed for the planar mismatch of bc planes. It decreases linearly with x from 1.5% (x=0) to 0.3% (x=0.125) by experiments. We can therefore expect that the strain energy at the interphase boundary of LFP/FP can be significantly decreased by the co-substitution of LFP.

The cycle life performance was examined for the Z2S cathode in an aluminium-laminated pouch cell using a natural graphite anode. A cell with a pristine LFP cathode was prepared for comparison. Charge/discharge cycles of the cells were made between 2.00 and 3.80 V using a 1 C current rate. The specific capacity of two cells with Z2S (x=0.050) cathode (Cell-A) and pristine cathode (Cell-B) are compared in Fig. 5a. Although the initial capacity of Cell-B with pristine LFP cathode (144 mAh g−1) was higher than that of Cell-A (125 mAh g−1), the capacity fades much faster in Cell-B. As a result, the capacity became larger in Cell-A after 2,100 cycles. The cycle life with 80% capacity retention was 10,000 cycles for Cell-A, whereas it was 1,800 cycles for Cell-B. This significant increase in cycle life of Cell-A compared with Cell-B can be ascribed to the difference in the cathodes, since all other components of the cell and cell testing are the same. The capacity retention often shows linear decrease with the square root of the number of cycles. Using this empirical relationship, the cycle life observed for 70% capacity retention can be estimated as 25,000 cycles for Cell-A. This is significantly greater than our target cycle life of 70% capacity retention of 10,000 cycles. It should be noted that the substitution of Fe by Zr inevitably decreases the theoretical capacity because Zr cannot contribute to the redox reaction under the present condition. However, initial capacity of cathode is not the critical parameter for the large-scale battery systems, contrary to the application to portable devices. The capacity after many cycles, as the result of large initial capacity and slow capacity fading, is crucial.