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Titanium Dioxide

Crystal: TiO₂

Structure: Rutile

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Mechanical and structural properties:

Cohesive energy:	eV.
Lattice parameter:	see table (data: Ref.1)
Tem (K.)	4.2	77.3	150	298
a (Å)	4.5869	4.5875	4.5888	4.5931
b (Å)	2.9536	2.9538	2.9551	2.9586
Density:	4.28 g/cm³

Stiffness constants: in 10¹¹ dynes/cm², at room temperature

c₁₁: 27.143 (Ref.2) or 26.74 (Ref.3)

c₁₂: 17.796 or 18.08

c₄₄: 12.443 or 12.33

c₃₃: 48.395 or 47.90

c₆₆: 19.477 or 18.94

c₁₃: 14.957 or 14.66

Compressibility (in 10¹¹ dynes/cm²): 0.0478 ??

Poisson ratio:

Sound velocity: 6.9*10⁵ cm/sec., also: V(l)= 10.3*10⁵ cm/sec., V(t)= 5.5*10⁵ cm/sec.

Debye temperature: 943 K

Melting temperature: 2110 ° C

Neel temperature: K

Elastic Debye temperatures for rutile, distorted rutile, scheelite oxides:

A.Y. Wu, R.J. Sladek, Phys. Rev. B25, 5230 (1982)

Phonon spectrum discussed by:

J.G. Taylor et al., Lattice dynamics of Rutile,Phys. Rev. B3, 3457 (1971)

Transverse optic phonon T0 (k=0): cm^-1

Longitude optic phonon L0 (k=0): cm^-1

Gruneissen constant:

Ratio e*/e:

Elastic constants and stoichiometry:

W. Minnear, R.C. Bradt, Elastic properties of polycristalline TiO2-x, J. Am. Ceram. Soc. 60, 458 (1977)

Elasto-optic constants, and Brillouin scattering: See Ref.2

Photoelastic constants:

p₁₁:

p₁₂:

p₄₄:

Refraction index and photoelastic constants: See Ref.6

Electronic properties:

Band gap:

direct: 3.75 eV.

indirect: 3.05 eV. (Ref.4)

Gap: eV.

First exciton: 3.57 eV.

Valence band width: 5.5 eV.

See, for review:

S. Kowalczyk et al., The electronic structure of SrTiO3 and some simple related oxides (MgO, Al2O3, SrO, TiO2), Sol. St. Comm. 23, 161 (1977)

Piezospectroscopy of TiO2, valence band, shear deformation:

J. Pascual, J. Camassel, H. Mathieu, Piezospectroscopic investigation of the nature of the subsidiary valence band extrema in TiO2, Sol. St. Comm. 28, 239 (1978)

Band structure discussed by:

N. Daude, C. Gont, C. Jonamin, Electronic band structure of TiO2, Phys. Rev. B15, 3229 (1977)

Optic spectra, etc., see:

K. Vos, H.J. Krusemeyer, Reflectance and electroreflectance of TiO2 single crystals: I. Optical spectra, J. Phys. C10, 3893 (1977)

And: K. Vos, Reflectance and electroreflectance of TiO2 single crystals: II. Assignment to electronic energy levels, J. Phys. C10, 3917 (1977)

X-ray photoelectron spectra:

K.S. Kim, N. Winograd, Charge transfer shake-up satellites in x-ray photoelectron spectra of cations and anions of SrTiO3, TiO2, and Sr2O3, Chem. Phys. Letters 31, 312 (1975)

Ti oxides: electron level (experimental):

K. Ichikawa, O. Tarasaka, T. Sagawa, Soft x-ray emission and x-ray photoelectron spectra of Ti oxides, J. Phys. Soc. Jap. 36, 706 (1974)

Photoemission, etc.:

T. Matsukawa, T. Ishii, Valency band x-ray photoemission of PbI2 and CdI2, J. Phys. Soc. Jap. 41, 1285 (1976)

UV electronic excitation of TiO2 and TiO:

J. Frandon, B. Brousseau, F. Pradal, Excitations electroniques dans TiO2 rutile et TiO. Mesure des pertes d'energie des electrons entre 3 et 60 eV., J.de Phys. 39, 839 (1978)

XPS data:

S.K.Sen, J.Riga, J.Verbist, 2s and 2p x-ray photoelectron spectra of Ti4+ ion in TiO2; Chem. Phys. Letters 39, 560 (1976)

Dielectric constants:

Static dielectric constant: 170 (//), and 86 (^ ) (Ref.5)

Optic dielectric constant: 8.427 (//), and 6.843 (^ )

Remark: strong temperature dependence.

Also: at room temperature: e (¥ )= 8.422 and 6.693 (Ref.6)

Optic modes, temperature dependence, and damping:

F. Gervais, B. Pirian, Temperature dependence of transverse- and Longitude optic phonon -optic modes in TiO2 (rutile), Phys. Rev. B10, 1642 (1974)

Phonons at 143 cm^-1 (IR), 189 cm^-1 (R), and 83 cm^-1 (specific heat)

Cited by: W. N. Lawless, Specific heats of paramagnetics, ferromagnetics , and antiferromagnetics at low temperature, Phys.R ev. B14, 136 (1976)

Optoelectronic properties of rutile: V. Gupia, J. Phys. Chem. Sol. 41, 591 (1980)

Electron mobility:

Hole mobility:

Polaron coupling constant: a = ( for m*=1 )

Effective mass:

conduction band:

valence band:

Electron affinity: (in eV., from bottom of conduction band under vacuum)

Spin-orbit coupling: (valence band)

Cation polarisation: Å^-3

Anion polarisation: Å^-3

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Other information:

Raman tensor/cell ç dç = 22±2 Å²

p(zyzy)/p(yzzy)= 1.16

Ref.: see Ref.2

Model calculation of stress dependence of Raman tensor in TiO2. Rigid ions + axial tensor forces: J. Pascual et al. , Phys. Rev. B21, 2439 (1980)

Rutile Raman data at high pressures: J.F. Mammone, S.K. Sharma, Sol.St.Com. 34, 799 (1980)

Transformation enthalpies for TiO2 polymorphs: T. Mitsuhashi, O.J. Kepplar, J.Am.Ceram.Soc. 62, 356 (1979)

Schlenker et al. , Phys.Rev. B14, 1429 (1976): Ti4O7: normally chains Ti3+ and Ti4+, but Ti3+ pairs covalency bonding at low and intermediaire temperatures.

See also supplementary information on TiO₂, below.

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References:

G.A. Samara, S. Peercy, Pressure and temperature dependence of the static dielectric constant and Raman spectra of TiO2 (rutile), Phys. Rev. B7, 1131 (1973)

Manghani et al., J.Geophys.Res. 74, 4317 (1969), also: J. Reintjes, M.B. Schulz, Photoelastic constants of selected ultrasonic delay-line crystals, J. Appl. Phys. 39, 5254 (1968)

M.H. Grimsditch, A.K. Ramdas, Elastic and elasto-optic constants of rutile from a Brillouin scattering study, Phys. Rev. B14, 1670 (1976)

D.C. Cronemeyer, Electronic and optic properties of rutile single crystals, Phys. Rev. 87, 876 (1952)

R.A. Parker, Static dielectric constant of Rutile (TiO2), 1.6-1060K., Phys. Rev. 124, 1719 (1961)

T.A. Darvis, K. Vedam, Pressure dependence of the refractive indices of the tetraedric crystals: ADP, KDP, CaMoO, CaWO, Rutile, J.Opt.Soc.Am. 58, 1446 (1968)

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Supplementary information on rutile TiO2:

Uniaxial-stress dependence of the first-order Raman spectrum of rutile. I. Experiments.

P.Merle, J.Pascual, J.Camassel, H.Mathieu, Phys.Rev. B21, 1617 (1980)

We report an investigation of the uniaxial stress dependence of the first-order Raman spectrum of rutile (TiO2). We find a normal mode behaviour, characterised by an increase in the phonon frequency versus uniaxial compression, for the two Raman modes G 1 (A1g) and G 5 (E.g.). We deduce two deformation potentials for G 1 (in unit of cm^-1): a1 = -610 cm^-1, b1 = -820 cm^-1 and four deformation potentials for G 5 (doubly degenerate mode): a5 = -1170 cm^-1, b5 = -1840 cm^-1, c5 = +35 cm^-1, and d5=-230 cm^-1. We find many fewer classical results for G 3 (B1g): the phonon frequency increases for uniaxial stress parallel to vector c but decreases for uniaxial stress parallel to vector a ([100] direction) or parallel to vector a’ ([110] direction). The corresponding deformation potentials are a3=+620 cm^-1 and b3=+330 cm^-1. Within experimental error, all phonon energies displace linearly versus deformation.

Uniaxial-stress dependence of the first-order Raman spectrum of rutile. II. Model calculation.

P.Merle, J.Pascual, J.Camassel, H.Mathieu, Phys.Rev. B21 (1980)

We calculate the effect of uniaxial stress on the first-order Raman spectrum of rutile (TiO2). We use a rigid-ion model (RIM) fitted with axially symmetric tensor forces. All interactions are restricted to the first nearest neighbours and the change in the Coulomb part of the potential is neglected. The stress-induced change in the repulsive (short-range) interaction permits us (i) to account for the magnitude and sign of all experimentally determined deformation potentials and (ii) to identify (in terms of the four different bounds which define the rutile structure) the most important interaction which rules the frequency shift of a given Raman mode.

Uniaxial stress dependence of the direct-forbidden and indirect-allowed transitions of TiO2.

H.Mathieu, J.Pascual, J.Camassel. Phys.Rev., B18, 6920 (1978)

We have investigated the effect of uniaxial compression along the [001], [100], and [110] directions on the direct and indirect absorption edges of TiO2. Very-high-stressed conditions (c =24 kbar) have been achieved in this work, enabling us to investigate accurately all linear and nonlinear stress dependence of the corresponding band extrema. Concerning the direct-forbidden edge, we confirm our previous assignment as a G 3v® G 1c transition. We define and measure two independent deformation potentials a(d)=-2.13±0.02 eV and b(d)=-3.74±0.04 eV, which correspond to a hydrostatic pressure coefficient: dBand Gap Egd/dP = =1.17*10exp(-6) eV/bar. Concerning the indirect transition, we find a stress-induced splitting for [100] stress. This correspond to a subsidiary maximum of the valence band along the D direction in the first Brillouin zone. The corresponding shear-deformation potential Cv is deduced. We find | Cv| = 0.758±0.014 eV. The two deformation potentials associated with the indirect transition are ai = -2.04±0.02 eV and bi = -4.34±0.04 eV, which gives a pressure coefficient dBand Gap Egi/dP=1.19*10exp(-6) eV/bar. Finally, we analyse the nonlinear dependence obtained for [100] stress in terms of twofold stress-induced coupling between G 3v and two neighbouring G 1 bands. The corresponding deformation potentials are: | E31| = 7.58±0.14 eV and | E’31| = 5.2±0.5 eV.