鈣鈦礦氧化物，其通式為ABO3，是結構特殊且穩定的氧化物材料。由於結構特殊，使它具備了許多獨特的性質，包含：多鐵性效應、催化活性、電化學性質及其相關的傳輸性質等，使它們成為當今炙手可熱的明星材料。而在其中的稀土－過渡金屬鈣鈦礦氧化物，可藉由調整A-site（稀土）或B-site（過渡金屬）的元素，調整或改變其結構，進而得到不同的材料特性及功能。
　　本研究利用第一原理計算來探討稀土－過渡金屬鈣鈦礦氧化物RE-TM-O3，包含Gd(Fe0.8Ni0.2)O3、LaMnO3、LaCoO3、LaCrO3、LaFeO3、LaNiO3、La(Mn0.5Co0.125Cr0.125Fe0.125Ni0.125)O3、La(Mn0.125Co0.5Cr0.125Fe0.125Ni0.125)O3、La(Mn0.125Co0.125Cr0.5Fe0.125Ni0.125)O3、La(Mn0.125Co0.125Cr0.125Fe0.5Ni0.125)O3、La(Mn0.125Co0.125Cr0.125Fe0.125Ni0.5)O3及La(Mn0.2Co0.2Cr0.2Fe0.2Ni0.2)O3，其中La(Mn, Co, Cr, Fe, Ni)O3系統又為高熵氧化物，針對其優化後的幾何結構與電子特性進行討論。分析不同的A-site或B-site佔據元素如何影響鈣鈦礦氧化物的幾何結構、能隙及態密度。
　　計算結果說明正交晶系鈣鈦礦氧化物La (Mn, Co, Cr, Fe, Ni)O3系統在結構優化後，是熱力穩定的。其中，當佔據B-site的Ni超過一定比例時，能隙會消失，系統由絕緣體/半導體特性轉變為金屬性。藉由分析部分態密度圖，在此系統中，主要是由B-site的過渡金屬d軌域與O的p軌域之間有混成，其中Mn-d及Ni-d與O-p的軌域混成作用更明顯。在Bader電荷分析中，此系統中各個元素的Bader電荷值大小與原始鈣鈦礦氧化物中各元素的Bader電荷值相比，幾乎不變，顯示對於多元陽離子化合物，每個陽離子晶格點可以視為等效的。
在正交晶系扭曲鈣鈦礦GdFeO3的計算結果顯示，在B-site參雜Ni後系統會由半導體變成導體。另外，藉由分析Gd(Fe0.8Ni0.2)O3部分態密度圖，推論Gd(Fe0.8Ni0.2)O3系統有一定程度的自旋極化現象及磁性，且磁性的貢獻主要來自於Gd的f軌域。

The perovskite oxides, the general formula of ABO3, have many excellent physical properties including multiferroic effects, catalytic activity, electrochemical properties and related transport properties, making them popular materials for engineering applications. In this work, we investigate the geometric and electronic structures of rare-earth and transition-metal perovskite oxides, La(Mn, Co, Cr, Fe, Ni)O3 and Gd(Fe0.8Ni0.2)O3 based on first-principles calculations. La (Mn, Co, Cr, Fe, Ni)O3, known as “high entropy oxides”, contain 5 elements on the b-site sublattice of the perovskite structure, which are thermodynamically stable after structure relaxation. Upon substitution of Ni at the b-site to certain concentrations in La(Mn, Co, Cr, Fe, Ni)O3, no band gap exists in the system. From PDOS analysis, we observe hybridization between d orbitals of transition metals, especially from Mn and Ni, and p orbitals of oxygens. From Bader-charge analysis, charges of each element in La(Mn, Co, Cr, Fe, Ni)O3 are similar as charges of elements in the parent perovskites, LaMnO3, LaCoO3, LaCrO3, LaFeO3 and LaNiO3. It shows that each b-site in perovskite high-entropy oxides is nearly equivalent. For Gd(Fe0.8Ni0.2)O3, the calculated results show that substituting Ni for Fe in the b-site of GdFeO3, band gap 1.97~2.08 eV, makes the system conducts with spin polarization and magnetism. Besides, the magnetism mostly comes from f orbitals of Gd.

[1]J. W. Yeh, S. K. Chen, S. J. Lin, J. Y. Gan, T. S. Chin, T. T. Shun, C. H. Tsau & S. Y. Chang (2004), “Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes”, Advanced Engineering Materials, 6 (5) pp.299~303.
[2]B. Cantor, I. Chang, P. Knight & A. Vincent (2004), “Microstructural development in equiatomic multicomponent alloys”, Materials Science and Engineering A, 375~377 pp.213~218.
[3]C. M. Rost, E. Sachet, T. Borman, A. Moballegh, E. C. Dickey, D. Hou, J. L. Jones, S. Curtarolo & J. P. Maria (2015), “Entropy-stabilized oxides”, Nature Communications, 6 (1) pp.1~8.
[4]J. Zhou, J. Zhang, F. Zhang, B. Niu, L. Lei & W. Wang (2018), “High-entropy carbide: A novel class of multicomponent ceramics”, Ceramics International, 44 pp.22014~22018.
[5]T. J. Harrington, J. Gild, P. Sarker, C. Toher, C. M. Rost, O. F. Dippo, C. McElfresh, K. Kaufmann, E. Marin, L. Borowski, P. E. Hopkins, J. Luo, S. Curtarolo, D. W. Brenner & K. S. Vecchio (2019), “Phase stability and mechanical properties of novel high entropy transition metal carbides”, Acta Materialia, 166 pp.271~280.
[6]J. Gild, Y. Zhang, T. Harrington, S. Jiang, T. Hu, M. C. Quinn, W. M. Mellor, N. Zhou, K. Vecchio & J. Luo (2016), “High-entropy metal diborides: A new class of high-entropy materials and a new type of ultrahigh temperature ceramics”, Scientific Reports, 6 pp.37946.
[7]T. Jin, X. Sang, R. R. Unocic, R. T. Kinch, X. Liu, J. Hu, H. Liu ＆ S. Dai (2018), “Mechanochemical-assisted synthesis of high-entropy metal nitride via a soft urea strategy”, Advanced Materials, 30 (23) pp.1707512.
[8]J. Gild, J. Braun, K. Kaufmann, E. Marin, T. Harrington, P. Hopkins, K. Vecchio & J. Luo (2019), “A high-entropy silicide: (Mo0.2Nb0.2Ta0.2Ti0.2W0.2)Si2”, Journal of Materiomics (in press).
[9]R. Z. Zhang, F. Gucci, H. Zhu, K. Chen & M. J. Reece (2018), “Data-driven design of ecofriendly thermoelectric high-entropy sulfides”, Inorganic Chemistry, 57 (20) pp.13027~13033.
[10]D. Bérardan, S. Franger, D. Dragoe, A. K. Meena & N. Dragoe (2016), “Colossal dielectric constant in high entropy oxides”, Physica Status Solidi-Rapid Research Letters, 10 (4) pp.328~333.
[11]D. Bérardan, S. Franger, A. K. Meena & N. Dragoe (2016), “Room temperature lithium superionic conductivity in high entropy oxides”, Journal of Materials Chemistry A, 4 pp.9536~9541.
[12]M. P. Jimenez-Segura, T. Takayama, D. Bérardan, A. Hoser, M. Reehuis, H. Takagi, & N. Dragoe (2019), “Long-range magnetic ordering in rocksalt-type high-entropy oxides”, Applied Physics Letters, 114 pp.122401.
[13]N. Osenciat, D. Bérardan, D. Dragoe, B. Léridon, S. Holé, A. K. Meena, S. Franger & N. Dragoe (2019), “Charge compensation mechanisms in Li‐substituted high‐entropy oxides and influence on Li superionic conductivity”, American Ceramic Society, 00 pp.1~7.
[14]A. Sarkar, R. Djenadic, N. J. Usharani, K. P. Sanghvi, V. S. K. Chakravadhanula, A. S. Gandhi, H. Hahn & S. S. Bhattacharya (2016), “Nanocrystalline multicomponent entropy stabilised transition metal oxides”, Journal of the European Ceramic Society, 37 (2) pp.747~754.
[15]R. Djenadic, A. Sarkar, O. Clemens, C. Loho, M. Botros, V. S. K. Chakravadhanula, C. Kübel, S. S. Bhattacharya, A. S. Gandhi & H. Hahn (2017), “Multicomponent equiatomic rare earth oxides”, Materials Research Letters, 5 (2) pp.102~109.
[16]A. Sarkar, C. Loho, L. Velasco, T. Thomas, S. S. Bhattacharya, H. Hahn & R. Djenadic (2017), “Multicomponent equiatomic rare earth oxides with a narrow band gap and associated praseodymium multivalency”, Dalton Transactions, 46 pp.12167~12176.
[17]A. Sarkar, R. Djenadic, D. Wang, C. Hein, R. Kautenburger, O. Clemens & H. Hahn (2018), “Rare earth and transition metal based entropy stabilised perovskite type oxides”, Journal of the European Ceramic Society, 38 (5) pp.2318~2327.
[18]J. Dabrowa, M. Stygar, A. Mikuła, A. Knapik, K. Mroczka, W. Tejchman, M. Danielewski & M. Martin (2018), “Synthesis and microstructure of the (Co,Cr,Fe,Mn,Ni)3O4 high entropy oxide characterized by spinel structure”, Materials Letters, 216 (1) pp.32~36.
[19]S. Jiang, T. Hu, J. Gild, N. Zhou, J. Nie, M. Qin, T. Harrington, K. Vecchio & J. Luo (2018), “A new class of high-entropy perovskite oxides”, Scripta Materialia, 142 (1) pp.116~120.
[20]Y. Sharma, B. L. Musico, X. Gao, C. Hua, A. F. May, A. Herklotz, A. Rastogi, D. Mandrus, J. Yan, H. N. Lee, M. F. Chisholm, V. Keppens & T. Z. Ward (2018), “Single-crystal high entropy perovskite oxide epitaxial films”, Physical Review Materials, 2 (6) pp.060404.
[21]J. W. Yeh (2006), “Recent progress in high-entropy alloys”, European Journal of Control, 31 (6) pp.633~648.
[22]H. Chen, J. Fu, P. Zhang, H. Peng, C. W. Abney, K. Jie, X. Liu, M. Chid & S. Dai (2018), “Entropy-stabilized metal oxide solid solutions as CO oxidation catalysts with high-temperature stability”, Journal of Materials Chemistry A, 6 pp.11129~11133.
[23]A. Sarkar, L. Velasco, D. Wang, Q. Wang, G. Talasila, L. de Biasi, C. Kübel, T. Brezesinski, S. S. Bhattacharya, H. Hahn & B. Breitung (2018), “High entropy oxides for reversible energy storage”, Nature Communications, 9 pp.3400.
[24]P. Hohenberg & W. Kohn (1964), “Inhomogeneous electron gas”, Physical Review B, 136 (3B) pp.864~871.
[25]E. J. Pickering & N. G. Jones (2016) “High-entropy alloys: A critical assessment of their founding principles and future prospects”, International Materials Reviews, 61 (3) pp.183~202.
[26]D. B. Miracle & O. N. Senkov (2016), “A critical review of high entropy alloys and related concepts”, Acta Materialia, 122 (1) pp.448~511.
[27]V. M. Goldschmidt (1926), “Die gesetze der krystallochemie”, Naturwissenschaften, 14 (21) pp.477~485.
[28]N. Ramadass (1978), “ABO3-type oxides - Their structure and properties - A bird's eye view”, Materials Science and Engineering, 36 pp.231~239.
[29]P. Linus (1929), “The principles determining the structure of complex ionic crystals”, Journal of the American Chemical Society, 51 (4) pp.1010~1026.
[30]R. Witte, A. Sarkar, R. Kruk, B. Eggert, R. A. Brand, H. Wende & H. Hahn (2019), “High-entropy oxides: An emerging prospect for magnetic rare-earth transition metal perovskites”, Physical Review Materials, 3 (3) pp.034406.
[31]Z. Rák, J. P. Maria, D. W. Brenner (2018), “Evidence for Jahn-Teller compression in the (Mg, Co, Ni, Cu, Zn)O entropy-stabilized oxide: A DFT study”, Materials Letters, 217 (15) pp.300~303.
[32]G. Kresse & J. Furthmüller (1996), “Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set”, Computational Materails Science, 6 (1) pp.15~50.
[33]G. Kresse & J. Furthmüller (1996), “Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set”, Physical Review B, 54 (16) pp.11169~11186.
[34]P. E. Blöchl (1994), “Projector augmented-wave method”, Physical Review B, 50 (24) pp.17953~17979.
[35]G. Kresse & J. Furthmüller (1996), “Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set”, Computational Materials Science, 6 (1) pp.15~50.
[36]J. Perdew, K. Burke & M. Ernzerhof (1997), “Generalized gradient approximation made simple”, Physical Review Letters, 77 (18) pp.3865~3868.
[37]L. Vegard (1921), “Die konstitution der mischkristalle und die raumfüllung der atome”, Zeitschrift für Physik, 5 (1) pp.17~26.
[38]X. Yang & Y. Zhang (2012), “Prediction of high-entropy stabilized solid-solution in multi-component alloys”, Materials Chemistry and Physics, 132 (2~3) pp.233~238.
[39]M. Yu & D. R. Trinkle (2011), “Accurate and efficient algorithm for Bader charge integration”, Journal of Chemical Physics, 134 pp.064111
[40]B. Richard (1994), Atoms in molecules: A quantum theory, USA: Oxford University Press.
[41]W. Setyawan & S. Curtarolo (2010), “High-throughput electronic band structure calculations: Challenges and tools”, Computational Materials Science, 49 (2) pp.299~312.
[42]S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys & A. P. Sutton (1998), “Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA + U study”, Physical Review B, 57 (3) pp.1505~1509.
[43]Z. Yang, Z. Huang, L. Ye & X. Xie (1999), “Influence of parameters U and J in the LSDA+U method on electronic structure of the perovskites LaMO3 (M = Cr, Mn, Fe, Co, Ni)”, Physical Review B, 60 (23) pp.15674~15682.
[44]C. E. Calderon, J. J. Plata, C. Toher, C. Oses, O. Levy, M. Fornari, A. Natan, M. J. Mehl, G. Hart, M. B. Nardelli & S. Curtarolo (2015), “The AFLOW standard for high-throughput materials science calculations”, Computational Materials Science, 108 pp.233~238.
[45]T. Arima, Y. Tokura & J. B. Torrance (1993), “Variation of optical gaps in perovskite-type 3d transition-metal oxides”, Physical Review B, 48 (23) pp.17006~17009.
[46]Y. Nohara, A. Yamasaki, S. Kobayashi & T. Fujiwara (2006), “Electronic structure of antiferromagnetic LaMnO3 and the effects of charge polarization”, Physical Review B, 74 (6) pp.064417.
[47]M. D. Scafetta, A. M. Cordi, J. M. Rondinelli & S. J. May (2014), “Band structure and optical transitions in LaFeO3: theory and experiment”, Journal of Physics: Condensed Matter, 26 (50) pp.505502.
[48]S. Dabaghmanesh, N. Sarmadian, E. C. Neytsb & B. Partoens (2017), “A first principles study of p-type defects in LaCrO3”, Physical Chemistry Chemical Physics, 19 (34) pp.22870.
[49]A. L. Gavin & G. W. Watson (2017), “Modelling the electronic structure of orthorhombic LaMnO3”, Solid State Ionics journal, 299 pp.13~17.
[50]J. H. Jung, K. H. Kim, D. J. Eom & T. W. Noh (1997), “Determination of electronic band structures of CaMnO3 and LaMnO3 using optical-conductivity analyses”, Physical Review B, 55 (23) pp.15489.
[51]R. Kumar & R. J. Choudhary (2005), “Structural, electrical transport and x-ray absorption spectroscopy studies of LaFe1−xNixO3 (x ≤ 0.6)”, Journal of Applied Physics, 97 (9) pp.093526.
[52]F. Arfat (2009), “Structural and electrical resistivity study of Ni doped orthoferrites GdFe1-xNixO3 (x ≤ 0.5)”, African Physical Review, 3 pp.0006.
[53]K. K. Sharma, R. Kumar & R. Pandit (2013), “Effect of Ni doping on structural and dielectric properties of GdFeO3”, International Journal of Modern Physics: Conference Series, 22 pp.179~183.
[54]P. Kaur, K. K. Sharma, R. Pandit, R. Kumar, R. K. Kotnala & J. Shah (2014), “Temperature dependent dielectric and magnetic properties of GdFe1-xNixO3 (0.0 ≤ x ≤ 0.3) orthoferrites”, Journal of Applied Physics, 115 pp.224102.
[55]X. Li & Z. Q. Duan (2012), “Synthesis of GdFeO3 microspheres assembled by nanoparticles as magnetically recoverable and visible-light-driven photocatalysts”, Materials Letters, 89 (15) pp.262~265.