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Scaling reducibility of metal oxides

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Abstract

The reducibility of bulk metal oxides in which the cation is in its highest oxidation state (MgO, Sc2O3, Y2O3, TiO2, m-ZrO2, m-HfO2, CeO2, V2O5, Nb2O5, Ta2O5, WO3, CrO3, Al2O3, β-Ga2O3, SiO2, SnO2 and ZnO) has been studied by standard periodic density functional theory. We have defined and calculated descriptors able to describe and quantify semi-quantitatively the extent of reduction: electronic band gap, oxygen vacancy formation energy and electronic localization. We find that there is no single criterion for characterizing the reducibility. We discuss the advantages and limitations of each method, and we apply them to classify the materials with the PBE+U and B3LYP functionals. Typical irreducible oxides such as MgO show a large band gap, high oxygen vacancy formation energy and electronic localization of the reduction electrons forming and F-center, with a diamagnetic singlet electronic state. Reducible oxides such as TiO2 present small band gaps, small oxygen vacancy formation energy and electron localization of the reduction electrons in the cations, decreasing their oxidation state and presenting open-shell electronic states. Intermediate or ambivalent behavior is found for ZrO2, HfO2, β-Ga2O3, ZnO and SnO2.

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References

  1. Helali Z, Markovits A, Minot C, Abderrabba M (2012) First row transition metal atoms adsorption on rutile TiO2(110) surface. Struct Chem 23:1309

    Article  CAS  Google Scholar 

  2. Helali Z, Markovits A, Minot C, Abderrabba M (2014) Metal atom adsorption on a defective TiO2−x support. Chem Phys Lett 594:23–29

    Article  CAS  Google Scholar 

  3. Bond GC, Tahir SF (1991) Vanadium oxide monolayer catalysts preparation, characterization and catalytic activity. Appl Catal 71(1):1–31

    Article  CAS  Google Scholar 

  4. Deo G, Wachs IE, Haber J (1994) Supported vanadium oxide catalysts:’molecular structural characterization and reactivity properties. Crit Rev Surf Chem 4:141

    CAS  Google Scholar 

  5. Weckhuysen BM, Keller DE (2003) Chemistry, spectroscopy and the role of supported vanadium oxides in heterogeneous catalysis. Catal Today 78(1):25–46

    Article  CAS  Google Scholar 

  6. Summers JC, Ausen SA (1979) Interaction of cerium oxide with noble metals. J Catal 58(1):131–143

    Article  CAS  Google Scholar 

  7. Tauster SJ, Fung SC, Baker RTK, Horsley JA (1981) Strong interactions in supported metal catalysts. Science 211(4487):1121–1125

    Article  CAS  Google Scholar 

  8. Tauster SJ, Fung SC, Garten RL (1978) Strong metal-support interactions—group 8 noble-metals supported on TiO2. J Am Chem Soc 100(1):170–175

    Article  CAS  Google Scholar 

  9. Sousa C, Illas F (1994) Ionic-covalent transition in titanium oxides. Phys Rev B Condens Matter 50:13974–13980

    Article  CAS  Google Scholar 

  10. Sanderson RT (1983) Electronegativity and bond energy. J Am Chem Soc 105(8):2259–2261. doi:10.1021/ja00346a026

    Article  CAS  Google Scholar 

  11. Hill YD, Huang Y, Ast T, Freiser BS (1997) Study of the gas-phase chemistry of Y2+ with small alkanes. Rapid Commun Mass Spectrom 11(1):148–154. doi:10.1002/(SICI)1097-0231(19970115)11:1<148:AID-RCM819>3.0.CO;2-5

    Article  CAS  Google Scholar 

  12. Sharma TC, Sharma SC, Bhandari KS (1984) Polarographic behaviour of yttrium. Analyst 109(12):1615–1616. doi:10.1039/an9840901615

    Article  CAS  Google Scholar 

  13. Beltrán A, Andrés J, Calatayud M, Martins JBL (2001) Theoretical study of ZnO (1 0 1 0) and Cu/ZnO (1 0 1 0) surfaces. Chem Phys Lett 338(4–6):224–230

    Article  Google Scholar 

  14. Calatayud M, Markovits A, Menetrey M, Mguig B, Minot C (2003) Adsorption on perfect and reduced surfaces of metal oxides. Catal Today 85(2–4):125–143

    Article  CAS  Google Scholar 

  15. Calatayud M, Markovits A, Minot C (2004) Electron-count control on adsorption upon reducible and irreducible clean metal-oxide surfaces. Catal Today 89(3):269–278

    Article  CAS  Google Scholar 

  16. Calatayud M, Markovits A, Minot C (2008) Periodic DFT studies on adsorption and reactivity on metal and metal oxide surfaces. In: Basiuk VA, Ugliengo P (eds) Quantum chemical calculations of surfaces and interfaces of materials, Chapter 11. American Scientific Publisher, Cambridge, pp 183–210

    Google Scholar 

  17. Ganduglia-Pirovano MV, Hofmann A, Sauer J (2007) Oxygen vacancies in transition metal and rare earth oxides: current state of understanding and remaining challenges. Surf Sci Rep 62(6):219–270

    Article  CAS  Google Scholar 

  18. Menetrey M, Markovits A, Minot C (2003) Reactivity of a reduced metal oxide surface: hydrogen, water and carbon monoxide adsorption on oxygen defective rutile TiO2(1 1 0). Surf Sci 524(1–3):49–62

    Article  CAS  Google Scholar 

  19. Calatayud M, Minot C (2006) Reactivity of the V2O5–TiO2-anatase catalyst: role of the oxygen sites. Top Catal 41(1–4):17–26. doi:10.1007/s11244-006-0090-x

    Article  CAS  Google Scholar 

  20. Calatayud M, Minot C (2009) Is there a nanosize for the activity of TiO2 compounds? J Phys Chem C 113(28):12186–12194. doi:10.1021/jp901465q

    Article  CAS  Google Scholar 

  21. Calatayud M, Tielens F, De Proft F (2008) Reactivity of gas-phase, crystal and supported V2O5 systems studied using density functional theory based reactivity indices. Chem Phys Lett 456(1–3):59–63. doi:10.1016/j.cplett.2008.03.007

    Article  CAS  Google Scholar 

  22. Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77(18):3865–3868

    Article  CAS  Google Scholar 

  23. Blöchl PE (1994) Projector augmented-wave method. Phys Rev B 50(24):17953–17979

    Article  Google Scholar 

  24. Kresse G, Joubert D (1999) From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B 59(3):1758–1775

    Article  CAS  Google Scholar 

  25. Calatayud M (2017). https://sites.google.com/site/calatayudantonino/k/oxides

  26. Kresse G, Furthmüller J (1996) Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 54(16):11169–11186

    Article  CAS  Google Scholar 

  27. Kresse G, Furthmüller J (1996) Efficiency of ab initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput Mater Sci 6(1):15–50

    Article  CAS  Google Scholar 

  28. Kresse G, Hafner J (1993) Ab initio molecular dynamics for open-shell transition metals. Phys Rev B 48(17):13115–13118

    Article  CAS  Google Scholar 

  29. Kresse G, Hafner J (1994) Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements. J Phys Condens Matter 6(40):8245

    Article  CAS  Google Scholar 

  30. Momma K, Izumi F (2008) VESTA: a three-dimensional visualization system for electronic and structural analysis. J Appl Crystallogr 41(3):653–658. doi:10.1107/S0021889808012016

    Article  CAS  Google Scholar 

  31. Morgan BJ, Watson GW (2007) A DFT+U description of oxygen vacancies at the TiO2 rutile (110) surface. Surf Sci 601(21):5034–5041

    Article  CAS  Google Scholar 

  32. Morgan BJ, Watson GW (2009) A density functional theory+ U study of oxygen vacancy formation at the (110), (100), (101), and (001) surfaces of rutile TiO2. J Phys Chem C 113(17):7322–7328. doi:10.1021/jp811288n

    Article  CAS  Google Scholar 

  33. Jedidi A, Markovits A, Minot C, Bouzriba S, Abderraba M (2010) Modeling localized photoinduced electrons in rutile-TiO2 using periodic DFT+U methodology. Langmuir 26(21):16232–16238. doi:10.1021/la101359m

    Article  CAS  Google Scholar 

  34. Morgan BJ, Watson GW (2010) Intrinsic n-type defect formation in TiO2: a comparison of rutile and anatase from GGA plus U calculations. J Phys Chem C 114(5):2321–2328. doi:10.1021/jp9088047

    Article  CAS  Google Scholar 

  35. Scanlon DO, Walsh A, Morgan BJ, Watson GW (2008) An ab initio study of reduction of V2O5 through the formation of oxygen vacancies and Li intercalation. J Phys Chem C 112(26):9903–9911. doi:10.1021/jp711334f

    Article  CAS  Google Scholar 

  36. Laubach S, Schmidt PC, Thissen A, Fernandez-Madrigal FJ, Wu QH, Jaegermann W, Klemm M, Horn S (2007) Theoretical and experimental determination of the electronic structure of V2O5, reduced V2O5−x and sodium intercalated NaV2O5. Phys Chem Chem Phys 9(20):2564–2576. doi:10.1039/b612489e

    Article  CAS  Google Scholar 

  37. Fabris S, de Gironcoli S, Baroni S, Vicario G, Balducci G (2005) Taming multiple valency with density functionals: a case study of defective ceria. Phys Rev B 71(4):041102

    Article  Google Scholar 

  38. Cococcioni M, de Gironcoli S (2005) Linear response approach to the calculation of the effective interaction parameters in the LDA+U method. Phys Rev B 71(3):035105

    Article  Google Scholar 

  39. Fabris S, de Gironcoli S, Baroni S, Vicario G, Balducci G (2005) Reply to Comment on ‘Taming multiple valency with density functionals: A case study of defective ceria’. Phys Rev B 72(23):237102

    Article  Google Scholar 

  40. Kresse G, Blaha P, Da Silva JLF, Ganduglia-Pirovano MV (2005) Comment on “Taming multiple valency with density functionals: A case study of defective ceria”. Phys Rev B 72(23):237101

    Article  Google Scholar 

  41. Fabris S, Vicario G, Balducci G, de Gironcoli S, Baroni S (2005) Electronic and atomistic structures of clean and reduced ceria surfaces. J Phys Chem B 109(48):22860–22867. doi:10.1021/jp0511698

    Article  CAS  Google Scholar 

  42. Nolan M, Grigoleit S, Sayle DC, Parker SC, Watson GW (2005) Density functional theory studies of the structure and electronic structure of pure and defective low index surfaces of ceria. Surf Sci 576:217–229

    Article  CAS  Google Scholar 

  43. Jiang Y, Adams JB, van Schilfgaarde M (2005) Density-functional calculation of CeO2 surfaces and prediction of effects of oxygen partial pressure and temperature on stabilities. J Chem Phys 123(6):064701–064709

    Article  Google Scholar 

  44. Jiang Y, Adams JB, van Schilfgaarde M, Sharma R, Crozier PA (2005) Theoretical study of environmental dependence of oxygen vacancy formation in CeO2. Appl Phys Lett 87(14):141917. doi:10.1063/1.2084324

    Article  Google Scholar 

  45. Loschen C, Carrasco J, Neyman KM, Illas F (2007) First-principles LDA+U and GGA+U study of cerium oxides: dependence on the effective U parameter. Phys Rev B 75(3):035115

    Article  Google Scholar 

  46. Ivanov MV, Perevalov TV, Aliev VS, Gritsenko VA, Kaichev VV (2011) Electronic structure of Δ-Ta2O5 with oxygen vacancy: ab initio calculations and comparison with experiment. J Appl Phys 110(2):024115

    Article  Google Scholar 

  47. Kaczkowski J (2012) Electronic structure of some wurtzite semiconductors: hybrid functionals versus ab initio many body calculations. Acta Phys Pol A 121:1142

    Article  CAS  Google Scholar 

  48. Lany S (2008) Semiconductor thermochemistry in density functional calculations. Phys Rev B 78(24):245207

    Article  Google Scholar 

  49. Erhart P, Albe K, Klein A (2006) First-principles study of intrinsic point defects in ZnO: role of band structure, volume relaxation, and finite-size effects. Phys Rev B 73(20):205203

    Article  Google Scholar 

  50. Garza AJ, Scuseria GE (2016) Predicting band gaps with hybrid density functionals. J Phys Chem Lett 7(20):4165–4170. doi:10.1021/acs.jpclett.6b01807

    Article  CAS  Google Scholar 

  51. Heyd J, Scuseria GE, Ernzerhof M (2003) Hybrid functionals based on a screened Coulomb potential. J Chem Phys 118(18):8207–8215

    Article  CAS  Google Scholar 

  52. Heyd J, Scuseria GE, Ernzerhof M (2006) Erratum: “Hybrid functionals based on a screened Coulomb potential” [J. Chem. Phys. 118, 8207 (2003)]. J Chem Phys 124(21):219906

    Article  Google Scholar 

  53. Henderson TM, Paier J, Scuseria GE (2011) Accurate treatment of solids with the HSE screened hybrid. Phys Status Solidi (b) 248(4):767–774. doi:10.1002/pssb.201046303

    Article  CAS  Google Scholar 

  54. Lucero MJ, Henderson TM, Scuseria GE (2012) Improved semiconductor lattice parameters and band gaps from a middle-range screened hybrid exchange functional. J Phys Condens Matter 24(14):145504

    Article  CAS  Google Scholar 

  55. Brix P, Herzberg G (1953) The dissociation energy of oxygen. J Chem Phys 21(12):2240

    Article  CAS  Google Scholar 

  56. Gray HB (1994) Chemical bonds: an introduction to atomic and molecular structure. University Science Books, Mill Valley, California

    Google Scholar 

  57. Hammer B, Hansen LB, Norskov JK (1999) Improved adsorption energetics within density-functional theory using revised Perdew–Burke–Ernzerhof functionals. Phys Rev B 59(11):7413–7421

    Article  Google Scholar 

  58. Wang L, Maxisch T, Ceder G (2006) Oxidation energies of transition metal oxides within the GGA+U framework. Phys Rev B 73(19):195107

    Article  Google Scholar 

  59. Scienomics (2004–2015) Introduction to MAPS. Paris

  60. Finazzi E, Di Valentin C, Pacchioni G, Selloni A (2008) Excess electron states in reduced bulk anatase TiO2: comparison of standard GGA, GGA plus U, and hybrid DFT calculations. J Chem Phys 129(15):154113. doi:10.1063/1.2996362

    Article  Google Scholar 

  61. Janotti A, Varley JB, Rinke P, Umezawa N, Kresse G, Van de Walle CG (2010) Hybrid functional studies of the oxygen vacancy in TiO2. Phys Rev B 81(8):085212. doi:10.1103/PhysRevB.81.085212

    Article  Google Scholar 

  62. Angenault J (2001) Symetrie et structure. Vuibert, Paris

    Google Scholar 

  63. Hannic F, Hartmanova M (1984) Real structure of undopped Y2O3 single cristal. Acta Cryst B 40:76–82

    Article  Google Scholar 

  64. http://en.wikipedia.org/wiki/Rutile

  65. http://www.mindat.org/min-213.html

  66. Garcia JC, Scolfaro LMR, Lino AT, Freire VN, Farias GA, Silva CC, Alves HWL, Rodrigues SCP, da Silva Jr EF (2006) Structural, electronic, and optical properties of ZrO2 from ab initio calculations. J Appl Phys 100(10):104103

    Article  Google Scholar 

  67. Hann RE, Suitch PR, Pentecost JL (1985) Monoclinic crystal structures of ZrO2 and HfO2 refined from X-ray powder diffraction data. J Am Ceram Soc 68(10):C-285–C-286. doi:10.1111/j.1151-2916.1985.tb11534.x

    Article  Google Scholar 

  68. Gerward L, Olsen JS, Petit L, Vaitheeswaran G, Svane KVA (2005) Bulk modulus of CeO2 and PrO2—an experimental and theoretical study. J Alloys Compd 400:56

    Article  CAS  Google Scholar 

  69. Enjalbert R, Galy J (1986) A refinement of the structure of V2O5. Acta Cryst C 42:1467

    Article  Google Scholar 

  70. Kato K (1976) Structure refinement of H-Nb2O5. Acta Cryst B32:764–767

    Article  CAS  Google Scholar 

  71. Fukumoto A, Miwa K (1997) Prediction of hexagonal Ta2O5 structure by first-principles calculations. Phys Rev B Condens Matter 55:11155–11160

    Article  CAS  Google Scholar 

  72. Jalili H (2008) Materials physics of half-metallic magnetic oxide films by pulsed laser deposition: controlling the crystal structure and near-surface properties of Sr2FeMoO6 and CrO2 films. University of Waterloo, Waterloo

    Google Scholar 

  73. Sawai Y, Hazu K, Chichibu SF (2010) Surface stoichiometry and activity control for atomically smooth low dislocation density ZnO and pseudomorphic MgZnO epitaxy on a Zn-polar ZnO substrate by the helicon-wave-excited-plasma sputtering epitaxy method. J Appl Phys 108(6):063541. doi:10.1063/1.3485600

    Article  Google Scholar 

  74. Madelung O, Rössler U, Schulz M (2000) WO3: transport properties, monoclinic phase. In: Madelung O, Rössler U, Schulz M (eds) Non-tetrahedrally bonded binary compounds II. Springer, Berlin, pp 1–8. doi:10.1007/b71139

    Chapter  Google Scholar 

  75. Lassner EW-DS (1999) Tungsten: properties, chemistry, technology of the element, alloys, and chemical compounds. Kluwer Academic, New York

    Book  Google Scholar 

  76. Saki K, Kenji T, Nobuo I (2008) Structural evolution of corundum at high temperatures. Jpn J Appl Phys 47(1S):616

    Google Scholar 

  77. Geller S (1960) Crystal Structure of β-Ga2O3. J Chem Phys 33(3):676–684. doi:10.1063/1.1731237

    Article  CAS  Google Scholar 

  78. Haiying He RO, Blanco Miguel A, Pandey Ravindra (2006) First-principles study of the structural, electronic, and optical properties of Ga2O3 in its monoclinic and hexagonal phases. Phys Rev B 74:195123. doi:10.1103/PhysRevB.74.195123

    Article  Google Scholar 

  79. Lager GA, Jorgensen JD, Rotella FJ (1982) Crystal structure and thermal expansion of α-quartz SiO2 at low temperatures. J Appl Phys 53(10):6751–6756. doi:10.1063/1.330062

    Article  CAS  Google Scholar 

  80. Haines J, Léger JM (1997) X-ray diffraction study of the phase transitions and structural evolution of tin dioxide at high pressure: ffRelationships between structure types and implications for other rutile-type dioxides. Phys Rev B 55(17):11144–11154

    Article  CAS  Google Scholar 

  81. Postnikov AV, Entel P, Ordejon P (2002) SnO2: bulk and surface simulations by an ab initio numerical local orbitals method. Phase Transit Multinatl J 75(1–2):143–149

    Article  CAS  Google Scholar 

  82. Kisi EH, Elcombe MM (1989) U parameters for the Wurtzite structure of ZnS and ZnO using powder neutron diffraction. Acta Cristallogr C 45:1867

    Article  Google Scholar 

  83. Orita M, Ohta H, Hirano M, Hosono H (2000) Deep-ultraviolet transparent conductive beta-Ga2O3 thin films. Appl Phys Lett 77(25):4166–4168

    Article  CAS  Google Scholar 

  84. Deml AM, Holder AM, O’Hayre RP, Musgrave CB, Stevanović V (2015) Intrinsic material properties dictating oxygen vacancy formation energetics in metal oxides. J Phys Chem Lett 6(10):1948–1953. doi:10.1021/acs.jpclett.5b00710

    Article  CAS  Google Scholar 

  85. Di Valentin C, Pacchioni G (2014) Spectroscopic properties of doped and defective semiconducting oxides from hybrid density functional calculations. Acc Chem Res 47(11):3233–3241. doi:10.1021/ar4002944

    Article  Google Scholar 

  86. Jun C, Lin L, Lu T, Yong L (1999) Electronic structure of F, F+-center in MgO. Eur Phys J B 9(4):593–598

    Article  CAS  Google Scholar 

  87. Zhukovskii YF, Kotomin EA, Evarestov RA, Ellis DE (2007) Periodic models in quantum chemical simulations of F centers in crystalline metal oxides. Int J Quantum Chem 107(14):2956–2985. doi:10.1002/qua.21483

    Article  CAS  Google Scholar 

  88. Kantorovich LN, Holender JM, Gillan MJ (1995) The energetics and electronic structure of defective and irregular surfaces on MgO. Surf Sci 343(3):221–239

    Article  CAS  Google Scholar 

  89. Klein BM, Pickett WE, Boyer LL (1987) Theory of F-centers in the alkaline earth oxides MgO and CaO. Phys Rev B 35(11):5802–5815

    Article  CAS  Google Scholar 

  90. Kasap SO, Capper P (2006) Springer handbook of electronic and photonic materials. Springer, Berlin. doi:10.1007/978-0-387-29185-7

    Google Scholar 

  91. Morkoç H, Özgür Ü (2009) Zinc oxide: fundamentals, materials and device technology. Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

    Book  Google Scholar 

  92. Leiter F, Alves H, Pfisterer D, Romanov NG, Hofmann DM, Meyer BK (2003) Oxygen vacancies in ZnO. Physica B 340–342:201–204

    Article  Google Scholar 

  93. Smith JM, Vehse WE (1970) ESR of electron irradiated ZnO confirmation of the F+ center. Phys Lett A 31(3):147–148

    Article  CAS  Google Scholar 

  94. Soriano V, Galland D (1976) Photosensitivity of the EPR spectrum of the F+ center in ZnO. Phys Status Solidi (b) 77(2):739–743

    Article  CAS  Google Scholar 

  95. van Craeynest F, Maenhout-Van Der Vorst W, Dekeyser W (1965) Interpretation of the yellow colour of heat treated ZnO powder. Phys Status Solidi (b) 8(3):841–846

    Article  Google Scholar 

  96. Wei WF (1977) F+ center in ZnO. Phys Rev B 15(4):2250–2253

    Article  CAS  Google Scholar 

  97. Himmel H-J, Manceron L, Downs AJ, Pullumbi P (2002) Formation and characterization of the gallium and indium subhydride molecules Ga2H2 and In2H2: a matrix isolation study. J Am Chem Soc 124(16):4448–4457

    Article  CAS  Google Scholar 

  98. Jegier JA, Gladfelter WL (2000) The use of aluminum and gallium hydrides in materials science. Coord Chem Rev 206–207:631–650

    Article  Google Scholar 

Download references

Acknowledgements

Authors acknowledge B. Diawara for the Modelview program and Scienomics for the MAPS courtesy license. This work was performed using HPC resources from GENCI- CINES/IDRIS (Grants 2013- x2013082131, 2014- x2014082131, 2015- x2015082131, 2016- x2016082131, 2017- x2012082131), the CCRE-DSI of Université P. M. Curie and KAUST HPC supercomputer Shaheen under project k1087. This work has been carried out in the frame of the COST action CM1104 Reducible metal oxides.

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Published as part of the special collection of articles derived from the 10th Congress on Electronic Structure: Principles and Applications (ESPA-2016).

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Helali, Z., Jedidi, A., Syzgantseva, O.A. et al. Scaling reducibility of metal oxides. Theor Chem Acc 136, 100 (2017). https://doi.org/10.1007/s00214-017-2130-y

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