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Thermodynamics of oxygen defective TiO 2-x : The Magneli phases. Leandro Liborio Giuseppe Mallia Nicholas Harrison Computational Materials Science Group.

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Presentation on theme: "Thermodynamics of oxygen defective TiO 2-x : The Magneli phases. Leandro Liborio Giuseppe Mallia Nicholas Harrison Computational Materials Science Group."— Presentation transcript:

1 Thermodynamics of oxygen defective TiO 2-x : The Magneli phases. Leandro Liborio Giuseppe Mallia Nicholas Harrison Computational Materials Science Group

2 Magneli Phases T n O 2n-1 composition,.Oxygen defects in {121} planes. Ti 4 O 7 at T<154K insulator with 0.29eV band gap (1). T 4 O 7 Metal-insulator transition at 154K, with sharp decrease of the magnetic susceptibility. (3) P. Waldner and G. Eriksson, Calphad Vol. 23, No. 2, pp , ( 2) W. Masayuki et al., J. of Luminiscence, Vol , pp , (1) K. Kobayashi et al., Europhysics Lett., Vol. 59, pp , Figure 1a Figure 1b

3 Magneli Phases: T 4 O 7 crystalline structure Rutile unit cell View along the a lattice parameter View of Hexagonal oxygen arrangement View of Hexagonal oxygen network Metal nets in antiphase. (121) r Cristallographic shear plane. Figure 3a Figure 3b Figure 3c Figure 3d Figure 3e

4 Technical details of the calculations CASTEPCRYSTAL 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. 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.

5 Defect Formation Energies: Thermodynamical Formalism TiO 2 bulk T, p O2 Initial state n Def oxygen atoms TiO 2-x or Ti n O 2n- 1 T, p O2 + Final state Phonon contribution pV contribution Figure 5a

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

7 Oxygen chemical potential CASTEPCRYSTAL M x O y : ZnO, Anatase, Rutile, Ti 4 O 7, Ti 3 O 5  0 O2 (T 0, p 0 O2 )=  mean +/-  E 0 and the 0K total energy of the oxygen atom are calculated with CRYSTAL. Exp.PW-GGA (4)CRYSTAL Binding energy [eV] Bond length [ang] Now E 0 has to be calculated Now  0 O2 has to be calculated T>298K and p O2 =1atm T>0K and any p O2 (4) W. Li et al., PRB, Vol. 65, pp , 2002.

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

9 Results for the Magneli phases 1 2 Equilibrium point 1: Equilibrium point 2: Relationship between p O2 and T in the phase equilibrium.

10 Results for the Magneli phases Forbidden region Ti 3 O 5 Ti 4 O 7 Ti 5 O 9 (1) P. Waldner and G. Eriksson, Calphad Vol. 23, No. 2, pp , Figure 10a Figure 10b

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

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

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

14 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. a) d) c) b) e)f)

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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