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Thermodynamics of oxygen defective TiO 2-x : The Magneli phases.

Thermodynamics of oxygen defective TiO 2-x : The Magneli phases. Leandro Liborio Giuseppe Mallia Nicholas Harrison Computational Materials Science Group. (1) K. Kobayashi et al ., Europhysics Lett., Vol. 59, pp. 868-874, 2002.

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Thermodynamics of oxygen defective TiO 2-x : The Magneli phases.

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  1. Thermodynamics of oxygen defective TiO2-x : The Magneli phases. Leandro Liborio Giuseppe Mallia Nicholas Harrison Computational Materials Science Group

  2. (1) K. Kobayashi et al., Europhysics Lett., Vol. 59, pp. 868-874, 2002. ( 2) W. Masayuki et al., J. of Luminiscence, Vol. 122-123, pp. 393-395, 2007. (3) P. Waldner and G. Eriksson, Calphad Vol. 23, No. 2, pp. 189-218, 1999. Magneli Phases Figure 1b Figure 1a TnO2n-1 composition, .Oxygen defects in {121} planes. Ti4O7 at T<154K insulator with 0.29eV band gap(1). T4O7 Metal-insulator transition at 154K, with sharp decrease of the magnetic susceptibility.

  3. View along the a lattice parameter View of Hexagonal oxygen arrangement Rutile unit cell View of Hexagonal oxygen network Magneli Phases: T4O7 crystalline structure Figure 3c Figure 3b Figure 3a Figure 3e Figure 3d Metal nets in antiphase. (121)r Cristallographic shear plane.

  4. Technical details of the calculations CASTEP CRYSTAL Local density functional: LDA Ultrasoft pseudopotentials replacing core electrons Plane waves code Supercell approach Simulated systems: Oxygen point-defective supercell, Magneli phases supercells, Titanium bulk metal. Hybrid density functional: B3LYP, GGA Exchange GGA Correlation 20% Exact Exchange All electron code. No pseudopotentials Local basis functions: atom centred Gaussian type functions. Ti: 27 atomic orbitals, O: 18 atomic orbitals Supercell approach Simulated systems: Oxygen point-defective supercell, Magneli phases supercells, Oxygen molecule.

  5. Final state Initial state T, pO2 T, pO2 TiO2-x or TinO2n-1 TiO2 bulk + nDef oxygen atoms Phonon contribution pV contribution Defect Formation Energies: Thermodynamical Formalism Figure 5a

  6. Oxygen molecule’s standard chemical potential at T=298K and pO2=1atm Oxygen molecule’s total energy at 0K Defect Formation Energies: Oxygen chemical potential Limits for the oxygen chemical potential: Hard limit Soft limit Assuming the oxygen behaves as an ideal gas: Expression (5) allows the calculation of 0O2(T,pO2) at any T and pO2

  7. Oxygen chemical potential CASTEP CRYSTAL E0 and the 0K total energy of the oxygen atom are calculated with CRYSTAL. MxOy: ZnO, Anatase, Rutile, Ti4O7, Ti3O5 0O2(T0, p0O2)=mean +/-  Now 0O2has to be calculated Now E0 has to be calculated T>298K and pO2=1atm T>0K and any pO2 (4) W. Li et al., PRB, Vol. 65, pp. 075407-075419, 2002.

  8. Results for the Magneli phases Figure 8a Isolated defects Magneli phases Figure 8b

  9. Equilibrium point 1: 1 2 Equilibrium point 2: Relationship between pO2 and T in the phase equilibrium. Results for the Magneli phases

  10. 1 2 3 Ti3O5 Ti4O7 Ti5O9 Figure 10b 3 2 1 Results for the Magneli phases Figure 10a Forbidden region (1) P. Waldner and G. Eriksson, Calphad Vol. 23, No. 2, pp. 189-218, 1999.

  11. CASTEP Results for the Magneli phases Figure 10a Figure 10b Figure 10c Figure 10d Forbidden region Forbidden region (1) P. Waldner and G. Eriksson, Calphad Vol. 23, No. 2, pp. 189-218, 1999.

  12. Figure 12a Figure 12c Figure 12b CRYSTAL Results for the Magneli phases P. Waldner and G. Eriksson, Calphad Vol. 23, No. 2, pp. 189-218, 1999.

  13. Cation + anion (100) layer Ti Formation mechanism for an oxygen-defective plane L. Bursill and B. Hyde, Prog. Sol. State Chem. Vol. 7, pp. 177, 1972. S. Andersson and A. D. Waldsey, Nature Vol. 211, pp. 581, 1966.

  14. a) b) e) f) d) c) Formation mechanism for an oxygen-defective plane Final stages • Antiphase boundaries (dislocation) acts as high conductivity paths for titanium. • Dislocations are needed • No long-range diffusion • Formation of Ti interstitials.

  15. Conclusions • The thermodynamics of rutile’s higher oxides has been investigated by first principles calculations. • First principles thermodynamics reproduce the experimental observations reasonably well. • Spin does not affect the thermodynamics. • At a high concentration of oxygen defects and low oxygen chemical potential, oxygen defects prefer to form Magneli phases. • But, at low concentration of oxygen defects and low oxygen chemical potential, titanium interstitials proved to be the stable point defects. • These results support the mechanism proposed by Andersson and Waldsey for the production the crystalline shear planes in rutile.

  16. Acknowledgements • Prof. Nic Harrison • Dr. Giuseppe Mallia • Dr. Barbara Montanari • Dr Keith Refson

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