Potential cathode material naxvopo4 for rechargeable sodium ion batteries dft investigation

VIETNAM NATIONAL UNIVERSITY, HANOI VIETNAM JAPAN UNIVERSITY - LUONG HUU DUC POTENTIAL CATHODE MATERIAL NaxVOPO4 FOR RECHARGEABLE SODIUM ION BATTERIES: DFT INVESTIGATION MASTER'S THESIS Hanoi, 2018 VIETNAM NATIONAL UNIVERSITY, HANOI VIETNAM JAPAN UNIVERSITY LUONG HUU DUC POTENTIAL CATHODE MATERIAL NaxVOPO4 FOR RECHARGEABLE SODIUM ION BATTERIES: DFT INVESTIGATION MAJOR: NANO TECHNOLOGY SUPERVISOR: Dr DINH VAN AN Hanoi, 2018 Acknowledgement First and foremost, to my supervisor, JICA expert, Dr Dinh Van An, for his patient guidance, enthusiastic encouragement and useful critiques of this research during my two-year research Next, I would like to express my great thank to staffs and Master Students in Laboratory of Simulation, Vietnam Japan University, for their helps and discussion on weekly seminars when I did my thesis Finally, I would like to acknowledge the Japanese International Co-operation Agent (JICA) and Vietnam Japan University (VJU) for their great supports i TABLE OF CONTENTS Acknowledgement i LIST OF FIGURES iv LIST OF TABLES vii APPREVIATIONS viii INTRODUCTION CHAPTER LITERATURE REVIEW 1.1 Rechargeable batteries 1.2 Vanadyl phosphate family 1.2.1 Beta Vanadyl Phosphate (β -VOPO4) 12 1.2.2 Beta Sodium Vanadyl Phosphate (β -NaVOPO4) 14 1.3 Purposes 15 CHAPTER 2.1 METHODOLOGY 16 Density Functional Theory 16 2.1.1 Kohn-Sham Equation 16 2.1.2 LDA, GGA and GGA+U Methods 18 2.1.3 Hybrid Functionals Method 19 2.1.4 Pseudopotentials 20 2.1.5 Solving the Kohn-Sham Equation 21 2.2 Nudged Elastic Band (NEB) 22 2.3 Calculation Scheme 23 CHAPTER 3.1 RESULTS AND DISCUSSION 25 Crystal structure 25 3.1.1 Vanadyl phosphate 25 3.1.2 Sodium vanadyl phosphate 27 3.2 Electronic structure 31 3.2.1 Vanadyl Phosphate 31 3.2.2 Sodium vanadyl phosphate 32 3.3 Voltage 32 3.4 Diffusion mechanism 33 3.4.1 Positive small polaron and discharging state 34 ii 3.4.2 3.5 Negative small polaron and charging state 39 Suggestions for further studies 42 CONCLUSION 43 Bibliography 44 List of Publications 49 Appendix 50 iii LIST OF FIGURES Figure 1.1: Operation of Rechargeable batteries Figure 1.2: Crossing and Parallel Diffusion in LiFeMnPO4 The brown, green, blue balls indicates Mn, Fe, Li ions, respectively Arrows present the hoping of polaron 10 Figure 1.3: Total DOS and the contributions of V, P, and O to the DOS of - β VOPO4 13 Figure 1.4: Charge-eischarge profiles of β-VOPO4 and chemically sodiated βNaVOPO4 at C/20 (8 mA/g) between 4.3 and 1.5 V 14 Figure 2.1: Procedure of iterative calculation 21 Figure 2.2: Calculation Procedure 23 Figure 3.1: (a) VOPO4 structure: green and brown octahedron present VO6 group and light tetraheron indicate PO4 group and (b) bond lengths (Å) and bond angles (o) of V-O bonds in VO6 octahedron 25 Figure 3.2: Energy difference between five spin polarization configurations of NaVOPO4 27 Figure 3.3: Crystal structure of NaVOPO4 The brown and green octahedrons indicate the 1NN and 2NN vanadyl groups and grey tetrahedrons present the phosphate groups Blue balls are Na ions 28 Figure 3.4: Bond distances (Å) and bond angles (o) of distorted octahedral VO6 (a) and Na6O (b) in NaVOPO4 The dash blue lines indicates the possibility of Na ion diffusion pathway 30 Figure 3.5: Density of States (DOS) of nonmagnitic VOPO4 (a, b) and ferromagnetic NaVOPO4 (c, d) obtain by GGA+U and HSE06 method The positive (negative) part indicates the up (down) spin 31 Figure 3.6: Deintercalation of one Na ion from NaVOPO4 The empty square indicates a hole formed after removal 33 iv Figure 3.7: The Density of States of the defect structures of NaVOPO obtained by (a) GGA+U and (b) HSE06 methods 36 Figure 3.8: Diffusion directions of Na ion in NaVOPO The red, dark green, black, violet balls indicates trace of the Na ion diffusion along the [010], [111], [100], [101] direction 37 Figure 3.9: Diffusion pathway of Na vacancy – positive polaron complex along the [010] direction in deintercaltion The brown and green octahedra indicate the 1NN and 2NN VO6 groups to the Na vacancy, respectively The red, green and blue balls present the trace o f the crossing, single and parallel diffusion processes, respectively Curved arrows illustrate the migration directions of polaron in each EDP 38 Figure 3.10: Activation energy profile of Na vacancy – positive polaron diffusion along the [010] direction in NaVOPO4 The relative energies of the crossing, single and parallel diffusion processes are illustrated in red, blue and green, respectively 39 Figure 3.11: Intercalation of a Na ion to VOPO4 40 Figure 3.12: The density of states of the intercalated structure of VOPO4 obtained by (a) GGA+U and (b) HSE06 methods 40 Figure 3.13: Activation energy profile of Na ion – negative polaron diffusion along the [010] direction in VOPO4 The relative energies of the crossing, single and parallel diffusion processes are illustrated in red, blue and green, respectively 42 Figure A - 1: Investigate the cut-off energy for calculation 50 Figure A - 2: Find the K-POINT value 51 Figure A - 3: Density of States (DOS) of AFM (a, b) and FM (c, d) of NaVOPO by GGA+U and HSE06 The negative (positive) value of DOS indicates the down (up) spin 51 v Figure A - 4: Activation energy profile of Na vacancy – positve polaron complex in NaVOPO4 The red, blue and green curves coresspond to the crosing, parallel and single diffusion processes, respectively 52 Figure A - 5: Activation energy profile of Na ion – negative polaron complex in VOPO4 Red, blue and green curvers illustrate the crosing, parallel and single diffusion processes, respectively 53 vi LIST OF TABLES Table 1-1: Voltage of some cathode materials Table 1-2: LIBs and NIBs comparison Table 1-3: Activation energy (meV) of Li diffusion in Olivine material Table 1-4: VOPO4 family members 11 Table 3-1: Bond lengths and bond angles of V-O and P-O in VOPO4 26 Table 3-2: Bond length and bond angle of V-O and P-O in NaVOPO4 29 Table 3-3: V-O bond lengths (Å) of the defect Na3(VOPO4)4 structure by GGA+U (HSE06) method V ions marked by 1, 2, has an oxidation number of +4 (magnetic moment of 1.0μB) and V4 has an oxidation number of +5 (magnetic moment of 0μB ) 35 Table 3-4: V-O bond lengths (Å) of the Na inserted structure Na(VOPO 4)4 by GGA+U (HSE06) method V ions marked by 1, 2, has an oxidation number of +5 (magnetic moment of 0μB) and V4 has an oxidation number of +4 (magnetic moment of 1.0μB ) 41 Table A - 1: Investigation Hubbard type potential U values 50 vii APPREVIATIONS 1NN: 1st nearest neighbor 2NN: 2nd nearest neighbor DOS: Density of States DFT: Density Functional Theory GGA: General Gradient Approach LDA: Local Density Approach LIB: Lithium ion battery MEP: Minimum Energy Path NIB: Sodium ion battery NEB: Nudged Elastic Band PP: Pseudo-potential PAW: Projected augmented wave USPP: Ultra-soft Pseudo-potential viii Figure 3.10: Activation energy profile of Na vacancy – positive polaron diffusion along the [010] direction in NaVOPO4 The relative energies of the crossing, single and parallel diffusion processes are illustrated in red, blue and green, respectively The NEB calculated of activation energy profile is illustrated in Figure 3.10 The cost that Na ion must pay for diffusion in each mentioned-above EPDs is 396 meV (c1), 397 meV (s1) and 396 meV (p1) This result implies the fact that these three EPDs can equivalently occur during Na ion diffusion Comparing to the other directions, the activation energy corresponding to the diffusion in the [010] direction is the smallest, therefore, the pathway along the [010] direction would be the most preferable diffusion pathway in this material, and the overall activation energy of deintercalation is 395 meV 3.4.2 Negative small polaron and charging state Now, we investigate the diffusion in the fully discharging structure VOPO as shown in Figure 3.11 When a Na ion is included into VOPO4, a negative polaron would be formed at one of two 1NNV sites The change of bond lengths V – O when such Na ion is intercalated is indicated in Table 3-4 Obviously, the V4 – Oj bond length of V4+O6 octahedron is significantly elongated by a substantial amount Figure 3.3: Activation energy profile of Na vacancy – positive polaron diffusion along the [010] direction in NaVOPO4 The relative energies of the crossing, single and parallel diffusion 39 processes are illustrated in red, blue and green, respectively Figure 3.11: Intercalation of a Na ion to VOPO4 of 0.1 Å in average bond length compared with the pristine structure of VOPO4 Such change in bond lengths indicates that there is a lattice distortion at V4 octahedron of the Na ion – inserted VOPO4 structure Also, it is witnessed that the magnetic moment of V4 ion increases by ΔμB = 0.94μB [GGA+U] (1.06μB [HSE06]) That means this V4 ion is reduced from V5+ to V4+ From DOS as shown in Figure 3.12, a new bound state appearing in the band gap, which is contributed by the occupied dyz orbital of V4+ ion, confirms that the newborn negative charge is self-trapped at V4 site Thus, based on the evidence, it is deduced that the negative small polaron forms at one of 1NN V sites Figure 3.12: The density of states of the intercalated structure of VOPO4 obtained by (a) GGA+U and (b) HSE06 methods 40 Table 3-4: V-O bond lengths (Å) of the Na inserted structure Na(VOPO4)4 by GGA+U (HSE06) method V ions marked by 1, 2, has an oxidation number of +5 (magnetic moment of 0μB) and V4 has an oxidation number of +4 (magnetic moment of 1.0μB ) V1 (2NN) V2 (2NN) V3 (1NN) V4 (1NN) O1 1.64 (1.59) Å 1.64 (1.59) Å 1.62 (1.58) Å 1.65 (1.61) Å O2 1.88 (1.81) Å 1.85 (1.80) Å 1.88 (1.85) Å 1.95 (1.93) Å O3 1.91 (1.83) Å 1.90 (1.81) Å 1.88 (1.87) Å 1.99 (1.94) Å O4 1.93 (1.90) Å 1.93 (1.88) Å 1.91 (1.87) Å 1.99 (1.96) Å O5 1.93 (2.04) Å 1.94 (2.03) Å 1.97 (1.91) Å 2.02 (1.99) Å O6 2.23 (2.29) Å 2.45 (2.63) Å 2.61 (2.78) Å 2.73 (3.04) Å Average 1.92 (1.91) Å 1.95 (1.96) Å 1.98 (1.98) Å 2.06 (2.08) Å Magnetic Moment 0.04 (0.06) μB 0.04 (0.06) μB 0.04 (0.06) μB 1.04 (1.06) μB The arrangement of VO6 groups in the 3D framework of VOPO4 is similar to these in NaVOPO4 Therefore, in this case, the diffusion pathway of the Na ion – negative small polaron complex during the intercalation is analogous to the diffusion of the Na vacancy – positive small polaron complex during the deintercalation Four different directions between possible sites of two adjacent Na sites are considered for VOPO4: the [100], [111], [101] and [010] directions with the distances between two adjacent Na sites of 7.35Å, 6.22Å and 5.34Å, respectively The calculated activation energy for crossing and parallel EPDs in the [100], [111] and [101] directions are 4.146eV; 1.506eV and 1.323eV, respectively [shown in Figure A-5 of Appendix] For the diffusion along the [010] direction, we constructed a 1x2x1 supercell to extend the diffusion path Similar to NaVOPO 4, three EDPs c2, p2 and s2 of the Na ion – negative polaron complex were identified Having a 10% smaller volume and no Na ion surrounded, the energy required for diffusion of the Na ion in the 41 Figure 3.13: Activation energy profile of Na ion – negative polaron diffusion along the [010] direction in VOPO4 The relative energies of the crossing, single and parallel diffusion processes are illustrated in red, blue and green, respectively discharging process is significantly higher than for charging process, as shown in Figure 3.13 The activation energy is almost the same for s2 and c2 processes (627 meV), whereas it is higher for p2 (832meV) Because the higher activation energy, process p2 is not preferable to occur in the whole diffusion process of the Na ion in VOPO4 Unlike the NaVOPO4, the hoping of negative polaron in VOPO4 affects much to the diffusion of the Na ion The overall activation energy required for diffusion of the Na ion in intercalation is 627 meV 3.5 Suggestions for further studies For further studies, we suggest some directions to design newmaterials: ❖ Study the doping effect on transition site by the other transition metals ❖ Extend study to the similar materials NaMPO (M=Fe, Mn) 42 CONCLUSION To sum up, we have investigated the geometrical and electronic structures, voltage and diffusion mechanism for the promising cathode materials NaxVOPO4 (x= 0,1) by using GGA+U and HSE06 methods The calculated voltage obtained from both methods is in good agreement with the experiment In principle, the d yz orbital of V sites plays the decisive role to the electronic properties of material during the intercalation/deintercalation As a Na vacancy is introduced, a positive small polaron would form at one of two first nearest neighbour V sites to Na vacancy, then the Na vacancy diffusion is accompanied spontaneously by the migration of a positive small polaron The feasible possibilities of diffusion of the positive small polaron – Na vacancy complexes were explored in three directions With the lowest activation energy of 395 eV required, diffusion along the [010] direction, 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Islam, C A J Fisher (2014), "Lithium and sodium battery cathode materials: computational insights into voltage, diffusion and nanostructural properties", Chem Soc Rev., Vol 43, pp 185-204 [71] Whittingham M S (1976), "Electrical energy storage and intercalation chemistry", Science, Vol 192, pp 1126 48 List of Publications H D Luong, T D Pham, Y Morikawa, Y Shibutani and V A Dinh, “Diffusion mechanism of Na ion – polaron complex in potential cathode materials NaVOPO4 and VOPO4 of rechargeable sodium-ion batteries” Submitted to PCCP (2018) H D Luong, Y Morikawa, Y Shibutani, V A Dinh, “Potential cathode material NaxVOPO4 for rechargeable Sodium – ion batteries: DFT investigation” The 9th Inter Conf on Multiscale Mater Modeling Oct 28 ~ Nov 02, 2018 Osaka, Japan (Accepted) H D Luong, T L Tran, Y Morikawa, Y Shibutani and V A Dinh “NaVOPO and Na2M3(SO4)4 as promising cathode materials for Rechargeable Sodium ion based batteries: DFT investigation” ACCMS-Theme Meeting on “Multiscale Modelling of Materials for Sustainable Development” Sept ~ 9, 2018, Hanoi (Accepted) Lương Hữu Đức, Phạm Thị Dung, Ngô Thị Thu Dinh, Đinh Văn An, “Nghiên cứu chế khuếch tán vật liệu làm điện cực cho pin ion cacbon hợp kim sắt”, VJU Scientific Conference, 02/2018, Hanoi 49 Appendix Table A - 1: Investigation of Hubbard type potential U values TYPES U J Band gap (eV) 4.2 0.7 2.179 4.5 1.0 2.120 5.6 0.7 2.120 3.1 0.0 1.940 Dudarev 3.5 0.0 2.028 approach 3.8 0.0 2.066 4.0 0.0 2.023 Liechtenstein approach Energy per atom of using 3x3x3 k points as a function of the energy cutoff -216.0000 -216.5000 200 400 600 800 -217.0000 E/atom (eV) -217.5000 -218.0000 -218.5000 -219.0000 -219.5000 -220.0000 -220.5000 -221.0000 Figure A - 1: Investigate the cut-off energy for calculation A I Liechtenstein, V I Anisimov and J Zaane, Phys Rev B, 1995, 52, R5467 S L Dudarev, G A Botton, S Y Savrasov, C J Humphreys and A P Sutton, Phys Rev B, 1998, 57, 1505 50 1000 Total energies (E/atom) over M for calculations using MxMxM kpoint M -215.00000 -215.50000 Energy (eV) -216.00000 -216.50000 -217.00000 -217.50000 -218.00000 Figure A - 2: Find the K-POINT value Figure A - 3: Density of States (DOS) of AFM (a, b) and FM (c, d) of NaVOPO by GGA+U and HSE06 The negative (positive) value of DOS indicates the down (up) spin 51 a) Diffusion along the [100] direction b) Diffusion along the [111] direction c) Diffusion along the [101] direction d) Diffusion along the [111] direction Figure A - 4: Activation energy profile of Na vacancy – positve polaron complex in NaVOPO4 The red, blue and green curves coresspond to the crosing, parallel and single diffusion processes, respectively 52 a) Diffusion along the [100] direction b) Diffusion along the [111] direction a) Diffusion along the [101] direction b) Diffusion along the [010] direction Figure A - 5: Activation energy profile of Na ion – negative polaron complex in VOPO4 Red, blue and green curvers illustrate the crosing, parallel and single diffusion processes, respectively 53 ...VIETNAM NATIONAL UNIVERSITY, HANOI VIETNAM JAPAN UNIVERSITY LUONG HUU DUC POTENTIAL CATHODE MATERIAL NaxVOPO4 FOR RECHARGEABLE SODIUM ION BATTERIES: DFT INVESTIGATION MAJOR:... Therefore, the formation of polaron and its effect on the diffusion mechanism would be an essential issue in the full exploration of performance of the cathode materials for rechargeable batteries. .. evaluate fully the operation of materials In principle, in the transition metal-based cathode, the operation of ion batteries is accompanied by the oxidation/reduction of transition metal redox couple