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1 Supplemental Information: Nanoscale Voltage Enhancement at Cathode Interfaces in Li-ion Batteries Shenzhen Xu 1, Ryan Jacobs 2, Chris Wolverton 4, Thomas Kuech 3 and Dane Morgan 1,2 1 Materials Science Program, University of Wisconsin- Madison, Madison, WI, USA 2 Department of Materials Science and Engineering University of Wisconsin Madison, Madison, WI, USA 3 Department of Chemical and Biological Engineering University of Wisconsin Madison, Madison, WI, USA 4 Department of Materials Science and Engineering Northwestern University, Evanston, IL, USA 1. Interface structure and DFT setup details 1.1 Interface structure For the olivine-structured and layered-structured interfaces, the structure plots and the corresponding Li sites are shown in Table S1 and Figure S1. We make the supercell long enough to avoid the influence of the second interface (due to periodic boundary conditions) on the one being studied. For the olivine-structured interface, all of the (x, y, z) direction lattice constants of (Mn/Co/Ti)PO 4 are fixed to those of fully-lithiated LiFePO 4. Based on previous simulation work 1, the lattice mismatch between LiFePO 4 1

2 and the other olivine-structured (Li(Mn/Co/Ti)PO 4 ) materials is quite small ( 2% for all the three directions). For simplicity we just use the lattice constants of LiFePO 4 for our olivine-structured interface supercell. For the layered-structured interface, the supercell we create has 12 unit cells along the y direction as shown in Figure S1, each unit cell is Li 6 M 6 O 12. We find that the in-plane (x-z plane) lattice constant mismatch between LiNiO 2 and LiTiO 2 is about 6% (LiNiO 2 is smaller), much larger than that in the olivinestructured case. We initially used the LiNiO 2 lattice parameter for the entire LiNiO 2 /TiO 2 supercell, but we found some significant distortion of Ti atoms. To avoid this large inplane lattice mismatch, we relaxed the supercell (ions + volume) to obtain an in-plane lattice parameters (5.25Å 14.85Å), which can be compared to the relaxed values for LiNiO 2 (4.97Å 14.34Å) and LiTiO 2 (5.34Å 14.81Å). The out-plane lattice parameter (y direction) of the LiNiO 2 /TiO 2 supercell is 37.38Å, which can be compared to that of LiNiO 2 (35.1Å) and LiTiO 2 (37.16Å). In our calculations of Li intercalation energetics in olivine-structured and layered-structured cases, the same lattice parameters are used for the supercell both before and after lithiation. The ions are relaxed under fixed volume conditions. Here we discuss the dependence of our calculated single Li intercalation energy profile on the size of the in-plane (x-z plane) cross section of the supercell. It should be noted that when we create the supercell of the interface system, we only duplicate the primitive cell along the direction which is perpendicular to the in-plane (x-z plane) cross sections. The main reason for using such a small cell in the x-z plane is to keep the computations tractable even though we have to make the supercell long enough along the y-direction to avoid the influence of the periodic image of the interface being studied, which is introduced by our use of periodic boundary conditions. We do not believe that the small cross sectional area has any qualitative effect on the results of this study. Table S1. Setup details of olivine-structured interfaces with different Li intercalation sites. The red arrows in each schematic plot indicate the Li intercalation position. Schematic plots of highvoltage/low-voltage interface supercells for olivine structures are shown below as a representative case for all the olivine-structured interface systems. For FePO 4 /CoPO 4 and FePO 4 /MnPO 4, FePO 4 is the low-voltage material. For FePO 4 /TiPO 4, TiPO 4 is the low-voltage material. For Li intercalation positions in the low-voltage material farther from the interface the supercell length increases, as shown below. 2

3 (high-voltage material: ; low-voltage material: ) Schematic plot Atoms/supercell (delithiated state) Supercell size axbxc (Å) x48.56x x60.7x x72.84x4.76 Figure S1. Setup details of layered-structured LiNiO 2 /TiO 2 interface with different Li intercalation sites. The red arrows indicate the Li intercalation positions. The coordinate origin is at the interface, and all Li intercalation site positions are given relative to the interface (i.e. a Li intercalation position of 0 Å is at the interface, positive is to the right, negative is to the left). 3

4 1.2 Hubbard U values setup Hubbard U values for the transition metals Fe, Mn, Co, Ti, Ni are shown in Table S2. All of the choices for the U values are obtained from previous simulation works 1, 2. Table S2. U values for Fe, Co, Mn, Ti and Ni transition metals in olivine-structured and layeredstructured materials. The U values of Fe, Co, Mn, Ni are from Zhou et al. 1 and the U value of Ti is obtained from Morgan et al 2. Transition metal Hubbard U value Fe Co Mn Ti 4.2 Ni Influence of the interfacial dipole on the electrostatic potential across the interface In the main text we have explained that when the low voltage material is lithiated, dipoles will be modified at the interface due to the charge transfer mechanism. We also propose that the interfacial dipole will suppress the charge transfer of the subsequently intercalated Li because it would cost more electrostatic energy for the valence electron of the newly intercalated Li to transfer across the interfacial dipole. In this section, we use the averaged electrostatic potential (the original local potential data is obtained from the DFT calculation, the post-processing method to get the averaged electrostatic potential follows a previous reference 3, 4 ) to show this dipole effect. In Figure S2(a), the averaged electrostatic potential (red curve) in the FePO 4 /CoPO 4 interface system shows that the potential plateau difference between FePO 4 and CoPO 4 is only 0.27eV, resulting from chemical bonding of oxygen atoms at the interface leading to the formation of a small dipole. Figure S2(b) shows the case where one Li is intercalated in FePO 4 ~3Å from the interface, and the difference of the potential plateau increases to about 0.6eV between the two materials. This increase is the result of a larger dipole at the interface, and will lead to an increase of the term E e-dipole in Equation 1 of the main text. The potential plateau 4

5 difference can be related to the dipole by the Helmholtz equation (equivalent to a parallel plate model) 5, and we now use this relationship to assess if the physical charges observed in our cells are consistent with the interfacial dipole that would give rise to the 0.6eV potential plateau difference observed above. Based on the relaxed structure and the charge output file from our DFT calculation, the length and the charge of the interfacial dipole are about 3Å and 0.35q respectively. The static dielectric constant of the FePO 4 /CoPO 4 supercell is about 5 (shown Section in the main text), the in-plane surface area of the interface in the supercell is 49.6Å 2. Based on the calculation of the Helmholtz model, the potential plateau difference would be 0.76eV, which matches qualitatively with the 0.6eV difference shown in Figure S2(b). This increased dipole is the result of the valence electron from the intercalated Li atom in FePO 4 transferring to CoPO 4. If more Li atoms are going to intercalate into the system, their valence electrons have to overcome the increased E e-dipole plus the electrostatic energy E e-chg.sep. cost of being separated from the corresponding Li + ions. This analysis demonstrates how the presence of intercalated Li creates an interfacial dipole screening effect when intercalating multiple Li in the lower voltage material of the interface system. (a) 5

6 (b) Figure S2. Averaged electrostatic potential (red curve) for electron across the interface in (a) fully-delithiated FePO 4 /CoPO 4 and (b) FePO 4 /CoPO 4 with single Li intercalated in FePO 4 (3Å from the interface). Red curves represent the planar averaged electrostatic potential, blue curves represent original local potential data obtained from DFT calculation. The left half of the supercell is CoPO 4, the right half is FePO 4. 6

7 3. Explanations of the single-li intercalation energy profile in LiNiO 2 /TiO 2 system In Section 2.4 of the main text, the calculated single-li intercalation voltage profile in LiNiO 2 /TiO 2 system shows a very small voltage-drop rate in the first few layers (up to ~15 Å). We even observe a small voltage increase from the first layer to the second layer. This behavior is different from what we obtained in the olivine-structured cases. To explain this discrepancy, we follow the previous procedure used for the olivine-structured interface to calculate the charge-separation electrostatic energy E e-chg.sep. (in Equation 1 of the main text) of the intercalated Li valence electron being separated from Li + and transferring across the interface. We used Bader charge analysis 6 to obtain the point charge system of the charge difference between the lithiated and delithiated supercell. Once the point charge system is obtained from Bader charge analysis, the Ewald summation method is used to calculate the electrostatic energy of the point charge system. The averaged static dielectric constant of LiNiO 2 and TiO 2 is ε r =13. The results of the charge-separation electrostatic energy E e-chg.sep. change as a function of intercalation position are shown in Figure S3(a). The E e-chg.sep. result at the first intercalation position (~1.5Å away from the interface) is the reference for the results of E e-chg.sep. at other intercalation positions x Li. It should be noted that we multiply all of our calculated electrostatic energy results by a prefactor (-1/q, where q is the unit charge of the electron) to change the unit to Volt (V) in order to compare with our DFT results. We can see that the electrostatic energy E e-chg.sep. (x Li ) change is very small as a function of Li intercalation position. This charge-transfer induced voltage decrease (corresponding to electrostatic energy increase) is only about 0.1 V when the Li position changes from ~1 Å to ~14 Å (with respect to the interface). The electrostatic energy behavior for the layered-structure case is quantitatively different from that of the olivine-structured case. For example, in FePO 4 /CoPO 4 (averaged ε r =5) the charge-transfer induced electrostatic energy change is about 1 V when the intercalation position moves away from the interface by ~12 Å. We also checked the amount of charge transferred across the interface when a Li atom is intercalated in the lower voltage material. There is about 0.4q-0.5q (q is unit charge of an electron) transferred in both olivine-structured and layered-structured interface cases, therefore the amounts of transferred charge in the two cases are nearly the same. The underlying reason for the differences in the electrostatic 7

8 energy behavior may be related either to the structural difference, which might allow more ionic distortion and screening in the layered structure, or the difference of the intercalated Li valence electron distribution between the layered-structured and olivinestructured interface systems. Figure S3(a) shows that the small change of the chargetransfer induced electrostatic energy with respect to Li intercalation positions is the key factor to account for the long-range interfacial effect on the intercalation voltage behavior in LiNiO 2 /TiO 2 interface system (shown in Figure 6 of the main text). (a) (b) 8

9 (c) Figure S3. Results of charge transfer-induced electrostatic energy and strain energy with respect to Li intercalation positions in LiNiO 2 /TiO 2 interface system. (a) Blue diamonds represent the variation of the charge transfer-induced electrostatic energy (in the unit of V) as a function of intercalation distance from the interface. All data points are referred to the first point as the relevant quantity is the change of the electrostatic energy with respect to intercalation positions, instead of the absolute value. (b) Blue diamonds represent the variation of the strain energy (in the unit of V) caused by the distortion of Ti atoms near the inserted Li as a function of intercalation distance. All data points are also referred to the first point. (c) Blue diamonds represent the combined energy contribution of both the electrostatic energy and the strain energy (summation of these two energies), red squares represent our calculated DFT results. The (electrostatic + strain) energy curve is shifted to align its plateau to that of the DFT data points. Although the charge transfer-induced electrostatic energy provides a qualitative explanation for the Li intercalation voltage profile in LiNiO 2 /TiO 2, there is still some discrepancy between our DFT calculated voltage profile (Figure 6 in the main text) and the electrostatic energy profile (Figure S3(a)). Here we just focus on the change of the profile rather than the absolute energy values. By examining the first two layers near the interface, there is a small voltage increase in the DFT results, which cannot be reproduced from just the electrostatic energy E e-chg.sep. results. We find that there is another important contribution to the change of the Li intercalation energetics with respect to insertion positions, i.e. an intercalation position-dependent E distortion (x Li ) strain energy due to the small distortion of Ti atoms near the intercalated Li. After intercalation of one Li in TiO 2, there is a small distortion of the Ti atoms near the Li to lower the energy during the supercell relaxation. This strain energy depends on the distance from the interface. The key reason for this is the structural difference between the LiNiO 2 9

10 region and TiO 2 region. In LiNiO 2, there are complete Li layers between the transition metal oxide layers. These Li atoms stabilize the positions of the nearby transition metal atoms. By contrast, in TiO 2 the Li layers are completely empty. If one Li is intercalated into TiO 2 infinitely far away from the interface, the relaxation (small distortion) of the surrounding Ti atoms will not be influenced by the interface. If the intercalation position is near the interface, the nearby Ti relaxation (distortion) will be suppressed by the interface because of the stabilization effect of the Li layers in LiNiO 2. Thus, one should expect this distortion-induced strain energy to become lower as the intercalation position proceeds away from the interface. We can approximate this strain energy E distortion (x Li ) separately by creating a new, artificial LiTiO 2 /TiO 2 interface cell by replacing all the Ni atoms of LiNiO 2 by Ti atoms. We assume the LiTiO 2 provides approximately the same mechanical constraints at the interface as LiNiO 2. Then, we perform the Li intercalation energy calculation in this new LiTiO 2 /TiO 2 system by inserting single Li in TiO 2 region at different positions. The variation of the intercalation energy in LiTiO 2 /TiO 2 with respect to intercalation position x Li represents the variation of E distortion (x Li ) because there is no interfacial charge transfer in this LiTiO 2 /TiO 2 system so that E e-redox (x Li ), E e- dipole(x Li ) and E e-chg.sep. (x Li ) are constants with respect to intercalation position x Li. The results of E distortion (x Li ) variation are shown in Figure S3(b). Similarly to Figure S3(a), the result at the first intercalation position (~1.5Å from the interface) is the reference for the results at other intercalation positions x Li and we multiply the strain energy results by a prefactor (-1/q) to transfer the unit to Volt (V). We can see this strain energy-related voltage profile increases as the Li insertion position proceeds away from the interface, which is consistent with our expectation. If we combine the two contributions (the charge transfer-related electrostatic energy and the strain energy) together and compare the voltage change caused by these combined effects with our calculated DFT results, we can see they match quite well, as shown in Figure S3(c). We can reproduce not only the voltage plateau region from 3 Å to 14 Å, but also the small voltage increase at the first two layers near the interface. Overall, the small variation of the charge-transfer-related electrostatic energy with respect to intercalation positions plus the strain energy contribution explains the intercalation voltage behavior in LiNiO 2 /TiO 2. 10

11 Finally, several calculations with longer LiNiO 2 /TiO 2 supercells (444 atoms) were conducted to test whether the intercalation voltage will decrease when a single Li is intercalated farther away from the interface than was previously examined. This longer cell calculation is very computationally expensive, so only three intercalation cases were considered, the results of which are shown in Figure S4. From Figure S4, it is clear that the voltage values of these intercalation sites when the intercalation position is 30 Å from the interface decrease by V compared to Li intercalation closer to the interface. This result makes physical sense because the voltage should decrease and approach to the low voltage plateau (i.e. the bulk Li intercalation voltage of TiO 2 ) when the charge transfer mechanism becomes progressively weaker and it becomes progressively more difficult to utilize the redox states in the higher voltage material (e.g. Ni 4+ Ni 2+ ) as the inserted Li gets progressively farther from the interface. We can make a linear extrapolation of our calculated voltage curve to the bulk intercalation voltage of TiO 2 (~2.4V), fitting the three red solid diamond data points in Figure S4 to get a line V(x) = x , where V(x) is Li intercalation voltage (V) with respect to intercalation position x (Å). From this line we predict that the voltage-enhanced region in TiO 2 is about 9nm in this single Li intercalated LiNiO 2 /TiO 2 case. This number is used in our discussion of the implications of our single Li intercalation results in Section 3.2 of the main text. 11

12 Figure S4. Results of Li intercalation calculations in a longer supercell of LiNiO 2 /TiO 2 to test Li site energetics in TiO 2 region farther away from the interface in addition to the results shown in Figure 6 of the main text. The solid red diamonds represent the new data points of intercalation voltages at longer distance from the interface. The hollow red diamonds are the data shown in Figure 6 of the main text. References 1. Zhou, F.; Cococcioni, M.; Marianetti, C. A.; Morgan, D.; Ceder, G., Firstprinciples prediction of redox potentials in transition-metal compounds with LDA + U. Phys. Rev. B 2004, 70, (23), Morgan, B. J.; Watson, G. W., GGA+U description of lithium intercalation into anatase TiO 2. Phys. Rev. B 2010, 82, (14), Al-Allak, H. M.; Clark, S. J., Valence-band offset of the lattice-matched β FeSi2(100)/Si(001) heterostructure. Phys. Rev. B 2001, 63, Franciosi, A., Van de Walle, C., Heterojunction band offset engineering. Surf. Sci. Rep. 1996, 25, Vlahos, V., Booske, J.H., Morgan D., Ab initio investigation of barium-scandiumoxygen coatings on tungsten for electron emitting cathodes. Phys. Rev. B 2010, 81, Tang, W.; Sanville, E.; Henkelman, G., A grid-based Bader analysis algorithm without lattice bias. J. Phys.-Condens. Mat. 2009, 21, (8),