鋰離子電池工業正在快速的擴張，現在已支配了整個電源工業，尤其是可攜帶
式消費類電子產品。當第一顆鋰離子電池被設計出來，便開始有很多研究著手於有
潛力的陽極、陰極與電解液材料，期許可藉此改善其性能。在陰極材料的部分，橄
欖石磷酸結構已經被廣泛的討論，其優點為具有較高的操作電壓、較大的理論重量
容量、低成本及無毒性；但較低的離子與電子傳導度成為此材料使用上最大的限制。
目前有研究指出，當將一個鋰原子插入LiFe(PO4)F 材料中形成Li2Fe(PO4)F，其穩定
的電容約為145 mAh g−1，而Yahia 團隊已經成功研究出新型的材料鋰鎂氟磷酸-
Li9Mg3(PO4)4F3，其具有較高的離子傳導度，並指出鋰離子的擴散路徑。另外一個很
重要影響電池效能的因素，便是在電極形成鈍性膜，截至目前為止，關於鈍性膜生
成機制仍不甚了解。已有許多研究指出碳酸鋰- Li2CO3 是主要的鈍性膜組成，其普
遍存在於所有的過渡金屬氧化物陰極材料的表面，如：錳、鈷、鎳。有理論計算的
研究鋰離子在鈍性膜中的擴散機制及能障，當沿著不同的通道擴散，其能障大約為
0.60 eV 及0.48 eV。
在此研究中，我們利用密度泛函理論(DFT)探討鋰離子如何在塊材鋰鎂氟磷酸中
的擴散路徑及能障，並模擬晶格常數、體積、XRD 圖譜。我們也計算了鋰鎂氟磷酸
在充、放電過程的電壓與體積變化，在完全充電的情況下，其電壓變化從3.2 V 上
升到4.6 V，並伴隨著5.8%的體積變化，此性質比很多現行的陰極材料都來的好。
同時我們也探討鋰離子如何在此塊材中擴散，鋰離子在塊材中沿著五角形與六角形
通道往C 軸的方向擴散，因而支配整個塊材的離子傳導度；由我們計算的結果可以
得知，鋰離子沿著六角形通道往C 軸擴散的最佳路徑能障是0.74 eV，鋰離子沿著五
角形通道往C 軸擴散則是0.81 eV；而鋰離子在五角形通道與六角形通道間的擴散
最低能障是0.8 eV，可見鋰離子的擴散，可能同時發生於六角形通道與五角形通道。
另外我們更進一步的探討，當鈍性膜生成於陰極材料表面後，鋰離子在介面中
擴散。我們使用碳酸鋰- Li2CO3 與鋰鎂氟磷酸- Li9Mg3(PO4)4F3 當作鈍性膜與陰極的
主要材料，並嘗試將XRD 圖譜中得到的較高強度表面做結合，我們發現碳酸鋰的(-
101)面與鋰鎂氟磷酸(100)面具有較好的晶格匹配，其擴散的能障大約為0.21 eV 到
0.91 eV，此結果與鋰離子在塊材的擴散能障相當，甚至更低。我們可以歸納出兩個
主要的原因，當鋰離子擴散路徑的距離越短，其能障便相對的較低，而擴散路徑上
若有氟離子的存在，其因氟離子的陰電性高，則吸引力較大，其能障便相對的較高。
總而言之，當使用碳酸鋰做為主要的鈍性膜材料，並不會影響鋰離子在整個充放電
過程的擴散。

The lithium battery industry is undergoing rapid expansion, now dominating the power source industry for portable consumer electronics. Since the inception of the first lithium-ion battery, extensive researches have been made to identify potential anode, cathode and electrolyte materials in order to attain an improved performance. Among the widely studied cathode materials, olivine-structured phosphate has received much attention since it offers high operating voltages, large theoretical gravimetric capacity as well as low cost and non-toxicity.[1] However, its applicability is limited by its low ionic and electrical conductivity. Recent studies on Li2Fe(PO4)F showed that the intercalation of one Li atom into LiFe(PO4)F is possible with a reversible and stable capacity of 145 mAh g−1.[2] Similarly, Yahia et al., have synthesized and studied Li9Mg3(PO4)4F3 which showed a high ionic conductivity in which a 3D lithium pathway was observed.[3]
Among other factors, the most important one is the solid-electrolyte-interphase (SEI) film formation mechanism. Until now, no single method or technique can answer all the questions concerning the SEI layers on the electrodes. Controlling the electrolyte/electrode interface is a great important to promote new-generation lithium ion batteries. The mainly composed of Li2CO3 already exists on all transition metal oxide cathode materials such as manganese, cobalt and nickel.[4-6] The lithium ion diffuse in the SEI film of Li2CO3 on the anode surface already have more discuss, but the lithium ion diffuse in the SEI film of Li2CO3 on the cathode surface is not unveiled. The theoretical studies lithium ion diffusion mechanisms in the bulk monoclinic of Li2CO3 have been reported.[7-9] The diffusion barrier are about 0.60 eV and 0.48 eV for along the different channels in the Li2CO3.[8]
In this work, with the aid of density functional theory (DFT) calculations, we have identified the possible lithium diffusion channels and calculated the energy barriers for Li-ion diffusion in bulk Li9Mg3(PO4)4F3. The effect of localized electrons, occupied or vacant neighboring Li sites and the change in the channel dimensions on diffusion are also investigated. As expected, the calculated lattice parameters, unit cell volume and XRD patterns for Li9Mg3(PO4)4F3 are in good agreement with experiment value. The calculated voltage was found to be about 4.6 V with the volume change of 5.8%. It was found that, Li+ migration through the pentagonal and hexagonal channels running along the c axis in the bulk plays an important role in determining the overall ionic conductivity of Li9Mg3(PO4)4F3. Moreover, the Li-ion diffusion observed in the system was not a continuous process but through a series of jump from one site to another. Based on our calculation, the migration barrier for the most favorable diffusion path was about 0.74 eV in the hexagonal channel and about 0.81 eV in the pentagonal channel, which is in a good agreement with the reported experimental value.[3] The Li-ion diffusion between pentagonal and hexagonal channel is 0.8 eV. The diffusion behavior happened in the pentagonal and hexagonal channel at the same time.
We then report a theoretically designed SEI film/ cathode coherent interface using density functional theory calculations, where Li2CO3 and Li9Mg3(PO4)4F3 are used an SEI film and a cathode. We try to combined every high intensity surface of the XRD patterns of the Li2CO3 and Li9Mg3(PO4)4F3. Based on our calculations, we have found that, the Li2CO3(-1 0 1) with Li9Mg3(PO4)4F3(1 0 0) has low lattice mismatch effect. The diffusion barriers are in the range of 0.21 eV to 0.91 eV along the Li2CO3(-1 0 1) layer and the cathode interface. Moreover, the diffusion barrier was found to be very closed to the diffusion barrier in the bulk of Li9Mg3(PO4)4F3, suggesting the diffusion phenomenon may also occur in the interface more easily. In the Li2CO3(-1 0 1) layer and cathode interface, lithium ions diffuse along the shortest distance of different lithium position.

1.Islam, M.S. and C.A. Fisher, Lithium and sodium battery cathode materials: computational insights into voltage, diffusion and nanostructural properties. Chem Soc Rev, 2014. 43(1): p. 185-204.
2.Recham, N., et al., Ionothermal Synthesis of Li-Based Fluorophosphates Electrodes†. Chemistry of Materials, 2010. 22(3): p. 1142-1148.
3.Ben Yahia, H., et al., Crystal structures of the new fluorophosphates Li9Mg3[PO4]4F3 and Li2Mg[PO4]F and ionic conductivities of selected compositions. Journal of Materials Chemistry A, 2014. 2(16): p. 5858.
4.Mansour, A.N., Characterization of LiNiO2 by XPS. Surface Science Spectra, 1994. 3(3): p. 279.
5.Aurbach, D., et al., The study of surface phenomena related to electrochemical lithium intercalation into LixMOy host materials (M=Ni, Mn). J. Electrochem. Soc., 2000. 147(4): p. 1322-1331.
6.Dahn, J.R., Rechargeable LiNiO2/carbon cells. J. Electrochem. Soc., 1991. 138: p. 2207-2211.
7.Shi, S., et al., Defect Thermodynamics and Diffusion Mechanisms in Li2CO3and Implications for the Solid Electrolyte Interphase in Li-Ion Batteries. The Journal of Physical Chemistry C, 2013. 117(17): p. 8579-8593.
8.Iddir, H. and L.A. Curtiss, Li Ion Diffusion Mechanisms in Bulk Monoclinic Li2CO3 Crystals from Density Functional Studies. J. Phys. Chem. C, 2010. 114: p. 20903–20906.
9.Chen, Y.C., et al., Electrical and Lithium Ion Dynamics in Three Main Components of Solid Electrolyte Interphase from Density Functional Theory Study. The Journal of Physical Chemistry C, 2011. 115(14): p. 7044-7049.
10.Jansen, A.N., et al., Development of a high-power lithium-ion battery. J. Power Sources, 1999. 81-82: p. 902-905.
11.Scrosati, B., Recent advances in lithium ion battery materials. Electrochim. Acta, 2000. 45: p. 2461-2466.
12.Megahed, S. and W. Ebner, Lithium-ion battery for electronic. J. Power Sources, 1995. 54: p. 155-162.
13.Tollefson, J., CHARGING UP THE FUTURE. Nature, 2008. 456: p. 436-440.
14.Tarascon, J.-M. and M. Armand, Issues and challenges facing rechargeable lithium batteries. Nature 2001. 414: p. 359-367.
15.Armand, M. and J.-M. Tarascon, Building better batteries. nature, 2008. 451: p. 652-657.
16.Shimotake, H., Progress in batteries and solar cells. 1990: JEC Press.
17.LINDEN, D. and T.B. REDDY, HANDBOOK OF BATTERYS, ed. T. EDITION. 2002, New York: McGraw-Hill.
18.Liu, D. and G. Cao, Engineering nanostructured electrodes and fabrication of film electrodes for efficient lithium ion intercalation. Energy & Environmental Science, 2010. 3(9): p. 1218.
19.Xu, K., Nonaqueous Liquid Electrolytes for Lithium-Based Rechargeable Batteries. Chem. Rev., 2004. 104: p. 4303-4417.
20.Paled, E., The electrochemical behavior of alkali and alkaline earth metals in nonaqueous battery systems-the solid electrolyte interphase model. J. Electrochem. Soc., 1979. 126: p. 2047-2051.
21.Xu, B., et al., Recent progress in cathode materials research for advanced lithium ion batteries. Materials Science and Engineering R, 2012. 73(5-6): p. 51-65.
22.Whittingham, M.S., Lithium Batteries and Cathode Materials. Chem. Rev., 2004. 104: p. 4271-4301.
23.Shao-Horn, Y., et al., Atomic resolution of lithium ions in LiCoO2. Nat Mater, 2003. 2(7): p. 464-7.
24.Winter, M., et al., Insertion electrode materials for rechargeable lithium batteries. Adv. Mater., 1998. 10(10): p. 725-763.
25.Mizushima, K., et al., LixCoO 2 (0<x~l): A new cathode material for batteries of high energy density Mater. Res. Bull., 1980. 15: p. 783-789.
26.Arai, H., et al., Reversibility of LiNiO2 cathode Solid State Ionics 1997. 95: p. 275-282.
27.Arai, H., et al., Thermal behavior of Li1-yNiO and the decomposition mechanism. Solid State Ionics, 1998. 109: p. 295-302.
28.Stoyanova, R., Lithium/nickel mixing in the transition metal layers of lithium nickelate: high-pressure synthesis of layered Li[LixNi1−x]O2 oxides as cathode materials for lithium-ion batteries. Solid State Ionics, 2003. 161(3-4): p. 197-204.
29.Guilmard, M., et al., Thermal Stability of Lithium Nickel Oxide Derivatives. Part I: LixNi1.02O2 and LixNi0.89Al0.16O2 (x ) 0.50 and 0.30). Chem. Mater., 2003. 15: p. 4476-4483.
30.Kim, Y., D. Kim, and S. Kang, Experimental and First-Principles Thermodynamic Study of the Formation and Effects of Vacancies in Layered Lithium Nickel Cobalt Oxides. Chemistry of Materials, 2011. 23(24): p. 5388-5397.
31.Armstorng, A.R. and P.G. Bruce, Synthesis of layered LiMnO2 as an electrode for rechargeable lithium batteries. Nature, 1996. 381: p. 499-500.
32.Armstrong, A.R., et al., Combined Neutron Diffraction, NMR, and Electrochemical Investigation of the Layered-to-Spinel Transformation in LiMnO2. Chem. Mater., 2004. 16: p. 3106-3118.
33.Ohzuku, T., M. Kitagawa, and T. Hirai, Electrochemistry of manganese dioxide in lithium nonaqueous cell J. Electrochem. Soc., 1990. 137: p. 769-775.
34.Thackeray, M.M., et al., Lithium insertion into manganese spinels. Mat. Res. Bull., 1983. 18: p. 461-472.
35.Liu, Q., et al., Preparation and Doping Mode of Doped LiMn2O4 for Li-Ion Batteries. Energies, 2013. 6(3): p. 1718-1730.
36.Kanamura, K., et al., Structural change of the LiMn,O, spinel structure induced by extraction of lithium J. Mater. Chem., 1996. 6(1): p. 33-36.
37.Padhi, A.K., K. Nanjundaswamy, and J.B. Goodenough, Phospho-olivines as positive-electrode materials for rechargeable lithium batteries. J. Electrochem. Soc., 1997. 144(4): p. 1188-1194.
38.Wolfenstine, J. and J. Allen, LiNiPO4–LiCoPO4 solid solutions as cathodes. Journal of Power Sources, 2004. 136(1): p. 150-153.
39.Wolfenstine, J. and J. Allen, Ni3+/Ni2+ redox potential in LiNiPO4. Journal of Power Sources, 2005. 142(1-2): p. 389-390.
40.Ravet, N., et al., Electroactivity of natural and synthetic triphylite. J. Power Sources, 2001. 97-98: p. 503-507.
41.Dutreilh, M., et al., Synthesis and crystal structure of a new lithium nickel fluorophosphate Li2[NiF(PO4)] with an ordered mixed anionic framework. J. Solid State Chem., 1999. 142: p. 1-5.
42.Barker, J., M.Y. Saidi, and J.L. Swoyer, Electrochemical Insertion Properties of the Novel Lithium Vanadium Fluorophosphate, LiVPO[sub 4]F. Journal of The Electrochemical Society, 2003. 150(10): p. A1394.
43.Ellis, B.L., et al., Crystal Structure and Electrochemical Properties of A2MPO4F Fluorophosphates (A = Na, Li; M = Fe, Mn, Co, Ni)†. Chemistry of Materials, 2010. 22(3): p. 1059-1070.
44.Okada, S., et al., Fluoride phosphate Li2CoPO4F as a high-voltage cathode in Li-ion batteries. Journal of Power Sources, 2005. 146(1-2): p. 565-569.
45.Ramesh, T.N., et al., Tavorite Lithium Iron Fluorophosphate Cathode Materials: Phase Transition and Electrochemistry of LiFePO[sub 4]F–Li[sub 2]FePO[sub 4]F. Electrochemical and Solid-State Letters, 2010. 13(4): p. A43.
46.Ramzan, M., S. Lebègue, and R. Ahuja, Ab initio study of lithium and sodium iron fluorophosphate cathodes for rechargeable batteries. Applied Physics Letters, 2009. 94(15): p. 151904.
47.Ramzan, M., et al., Structural, magnetic, and energetic properties of Na[sub 2]FePO[sub 4]F, Li[sub 2]FePO[sub 4]F, NaFePO[sub 4]F, and LiFePO[sub 4]F from ab initio calculations. Journal of Applied Physics, 2009. 106(4): p. 043510.
48.YAKtmOVIC, O.V., O.V. KARtMOW, and O.K. MEL'NIKOV, The mixed anionic framework in the structure of Naz{MnF[PO4]}. Acta Crystallogr. Sect. A, 1997. C53: p. 395-397.
49.Recham, N., et al., Ionothermal Synthesis of Sodium-Based Fluorophosphate Cathode Materials. Journal of The Electrochemical Society, 2009. 156(12): p. A993.
50.Ellis, B.L., et al., A multifunctional 3.5 V iron-based phosphate cathode for rechargeable batteries. Nat Mater, 2007. 6(10): p. 749-53.
51.Balomenou, S., et al., Monolithic electrochemically promoted reactors: A step for the practical utilization of electrochemical promotion. Solid State Ionics, 2006. 177(26-32): p. 2201-2204.
52.Winter, M., et al., InsertioneElectrode materials for rechargeable lithium batteries. Adv. Mater, 1998. 10(10): p. 725-763.
53.Li, J., et al., Solid Electrolyte: the Key for High-Voltage Lithium Batteries. Advanced Energy Materials, 2015. 5(4): p. n/a-n/a.
54.Aravindan, V., et al., Lithium-Ion Conducting Electrolyte Salts for Lithium Batteries. Chemistry – A European Journal, 2011. 17(51): p. 14326-14346.
55.Markovsky, B., et al., On the Electrochemical Behavior of Aluminum Electrodes in Nonaqueous Electrolyte Solutions of Lithium Salts. Journal of The Electrochemical Society, 2010. 157(4): p. A423.
56.Zhang, S.S. and T.R. Jow, Aluminum corrosion in electrolyte of Li-ion battery. Journal of Power Sources, 2002. 109: p. 458-464.
57.Hayashi, K., et al., Mixed solvent electrolyte for high voltage lithium metal secondary cells. J. Electrochimica Acta, 1999. 44: p. 2337-2344.
58.Schnell, M., et al., A Linear AC Trap for Polar Molecules in Their Ground State. 2007. 111: p. 7411-7419.
59.Xu, K., et al., Graphite/Electrolyte Interface Formed in LiBOB-Based Electrolytes. Journal of The Electrochemical Society, 2004. 151(12): p. A2106.
60.Zhang, S.S., A review on electrolyte additives for lithium-ion batteries. Journal of Power Sources, 2006. 162(2): p. 1379-1394.
61.Spahr, M.E., et al., Exfoliation of Graphite during Electrochemical Lithium Insertion in Ethylene Carbonate-Containing Electrolytes. Journal of The Electrochemical Society, 2004. 151(9): p. A1383-A1395.
62.Peled, E., D. Golodnitsky, and G. Ardel, Advanced model for solid electrolyte interphase electrodes in liquid and polymer electrolytes. J. Electrochem. Soc., 1997. 144: p. L208-L210.
63.Fong, R.a., U.y. Sacken, and J.R. Dahn, Studies oflLithium intercalation into carbons using nonaqueous electrochemical cells J. Electrochem. Soc., 1990. 137(7): p. 2009-2013.
64.Aurbach, D., et al., Identification of surface films formed on lithium in propylene carbonate solutions J. Electrochem. Soc., 1987. 134(7): p. 1611-1620.
65.Goren, E., O. Chusid, and D. Aurbach, The application of in situ FTIR spectroscopy to the study of surface films formed on Lithium and noble metals at low potentials in Li battery electrolytes J. Electrochem. Soc., 1991. 138(5): p. L6-L9.
66.Aurbach, D., Review of selected electrode–solution interactions which determine the performance of Li and Li ion batteries. J. Power Sources, 2000. 89: p. 206-218.
67.Eriksson, T., et al., Surface Analysis of LiMn2O4 Electrodes in Carbonate-Based Electrolytes. Journal of The Electrochemical Society, 2002. 149(1): p. A69.
68.Andersson, A.M., et al., Surface Characterization of Electrodes from High Power Lithium-Ion Batteries. Journal of The Electrochemical Society, 2002. 149(10): p. A1358.
69.Bruce, M.G.S.R.T.P.G. and J.B. Goodenough, AC impedance analysis of polycrystalline insertion electrodes: application to Li,_xCo02 J. Electrochem. Soc., 1985. 132(7): p. 1521-1528.
70.Aurbach, D., Review of selected electrode–solution interactions which determine the performance of Li and Li ion batteries. Journal of Power Sources, 2000. 89(2): p. 206-218.
71.Xu, K., Nonaqueous liquid electrolytes for lithium-based rechargeable batteries. Chemical reviews, 2004. 104(10): p. 4303-4418.
72.Kresse, G., Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B, 1996-II. 54(16): p. 11169-11186.
73.Kresse, G. and J. Furthmiiller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set Computational Materials Science, 1996. 6: p. 15-50.
74.Blöchl, P.E., Projector augmented-wave method. Physical Review B, 1994. 50(24): p. 17953-17979.
75.Kang, K., et al., Synthesis, Electrochemical Properties, and Phase Stability of Li2NiO2 with the Immm Structure. Chem. Mater., 2004. 16: p. 2685-2690.
76.Kang, K., et al., Electrodes with High Power and High Capacity for Rechargeable Lithium Batteries. Science, 2006. 311: p. 977-980.
77.Zhou, F., et al., First-principles prediction of redox potentials in transition-metal compounds withLDA+U. Physical Review B, 2004. 70(23).
78.Perdew, J.P. and Y. Wang, Pair-distribution function and its coupling-constant average for the spin-polarized electron gas. Phys. Rev. B, 1992. 46(20): p. 12947-12954.
79.Henkelman, G., B.P. Uberuaga, and H. Jónsson, A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J. Chem. Phys, 2000. 113(22): p. 9901.
80.Aydinol, M.K., A.F. Kohan, and G. Ceder, Ab initio study of lithium intercalation in metal oxides and metal dichalcogenides. Phys. Rev. B, 1997. 56(3): p. 1354-1365.
81.Courtney, I.A., et al., Ab initio calculation of the lithium-tin voltage profile. Phys. Rev. B, 1998. 58(23): p. 15583-15588.
82.Wang, B., S. Luo, and D.G. Truhlar, Computational Electrochemistry. Voltages of Lithium-Ion Battery Cathodes. J Phys Chem B, 2015.
83.Maxisch, T., F. Zhou, and G. Ceder, Ab initiostudy of the migration of small polarons in olivineLixFePO4and their association with lithium ions and vacancies. Physical Review B, 2006. 73(10).
84.Yu, J., et al., Ab initio study of lithium transition metal fluorophosphate cathodes for rechargeable batteries. Journal of Materials Chemistry, 2011. 21(32): p. 12054.
85.Islam, M.M., et al., Insights into Li+Migration Pathways in α-Li3VF6: A First-Principles Investigation. The Journal of Physical Chemistry Letters, 2012. 3(21): p. 3120-3124.
86.Li, W., et al., Li+ ion conductivity and diffusion mechanism in α-Li3N and β-Li3N. Energy & Environmental Science, 2010. 3(10): p. 1524.
87.Wang, L., et al., First-principles study of surface properties ofLiFePO4: Surface energy, structure, Wulff shape, and surface redox potential. Physical Review B, 2007. 76(16).
88.Ramamoorthy, M., D. Vanderbilt, and R.D. King-Smith, First-principles calculations of the energetics of stoichiometricTiO2surfaces. Phys. Rev. B, 1994. 49(23): p. 16721-16727.
89.Christensen, A. and E.A. Carter, First-principles study of the surfaces of zirconia. Phys. Rev. B, 1998. 58(12): p. 8050-8064.
90.Batyrev, I., A. Alavi, and M.W. Finnis, Ab initio calculations on the Al2O3 (0001) surface. Farad. Discuss., 1999. 114: p. 33-43.
91.Wang, X.-G., A. Chaka, and M. Scheffler, Effect of the Environment on a-Al2O3 (0001) Surface Structures. Phys. Rev. Lett., 2000. 84(16): p. 3650-3653.
92.Marmier, A. and S.C. Parker, Ab initiomorphology and surface thermodynamics ofα−Al2O3. Physical Review B, 2004. 69(11).
93.Idemoto, Y., et al., CRYSTAL STRUCTURE OF (Li,KI_,)&03 (x = 0, 0.43, 0.5, 0.62, 1) BY NEUTRON POWDER DIFFRACTION ANALYSIS J. Phys. Chem Solids, 1998. 59(3): p. 363-376.
94.Lu, Y., et al., Preparation of Li2CO3Nanoparticles by Carbonation Reaction Using a Microfiltration Membrane Dispersion Microreactor. Industrial & Engineering Chemistry Research, 2014. 53(27): p. 11015-11020.
95.Rojo, L., et al., Li2CO3 thin films fabricated by sputtering techniques: the role of temperature on their properties. CrystEngComm, 2014. 16(27): p. 6033.