J. W. DeFord

Diffusion of H and D in TiO2: Suppression of Internal Fields by Isotope Exchange,

Measurements of H and D diffusion in TiO2, using the isotope exchange technique described in the preceding paper, are reported. Use of this technique resulted in diffusion which was accurately described by Fick’s law with a constant diffusion coefficient, as predicted theoretically, in sharp contrast to single ion diffusion, where dramatic departures from classical diffusion theory were observed. The measured diffusion coefficients for H were 1.8×10−3 exp(−0.59eV/kT) and 3.8×10−1 exp(−1.28eV/kT) and 3.8×10−1 exp(−1.28eV/kT) cm2/sec for diffusion ∥ and ⊥ to the c axis, respectively. Ionic conductivity measurements are reported, which agree well with the bulk diffusion measurements, and permitted us to extend the temperature range of the measurements for c−axis diffusion from 125 to 750 °C, corresponding to a range of more than four orders of magnitude in D. The measured diffusion parameters were found to be essentially independent of sample purity, although it was observed that significant concentrations o...

Experimental technique for the precise determination of H and D concentration in rutile (TiO2)

Results of a precise determination of the ir absorption strength of H and D in rutile are presented, which permit determination of H or D concentration to an accuracy of 3%. The integrated absorption per ion was (2.51±0.09)×10−17 and (1.33±0.05)×10−17 cm for H and D, respectively. The procedure for calculating the H or D concentration in a particular sample from the ir absorption peaks is illustrated. Used in conjunction with the results of the theoretical analysis of the preceding paper, this technique makes possible the accurate determination of the energy and density of all electron trapping levels in TiO2 crystals. We also describe results showing that heat treatment in a dry H2 atmosphere at ∼800 °C results in the introduction of Ti intersititials but negligible H in the crystal, as predicted by the preceding paper. A technique for measuring diffusion parameters of H and D under conditions of strict chemical equilibrium, thus avoiding the large departures from Ficks law which usually plague such mea...

Electron transport properties in rutile from 6 to 40 K

Electrical conductivity mechanisms in single crystal rutile (TiO2) between 6 and 40 K have been studied in Nb‐doped and Nb+H‐doped material by means of electrical resistance and Hall effect measurements. In this range, three scattering mechanisms were found to be important: neutral and ionized impurities and acoustic phonons. In the region from approximately 12 to 25 K the electrical conductivity was found to be strictly exponential in 1/T, indicating acoustic phonon limited scattering, and yielding the donor trapping energies for Nb and H (20.0±0.1 and 4.4±0.1 meV, respectively). With the acoustic phonon limited mobility written as μ=μ0/T3/2, μ0 was found to be (1.2±0.1)×104 and (3.9±0.4)×10−4 cm2(K)3/2/V s in the ‘‘a’’ and ‘‘c’’ directions, respectively. Although qualitative agreement with existing theories on neutral and ionized impurity scattering is obtained, quantitative agreement requires an improved theory taking anisotropy into account. It was also found that the ratio of ‘‘c’’ to ‘‘a’’ mobility ...

Defect and impurity thermodynamics in rutilelike systems

An analysis is presented of the thermodynamics of lattice defects and H or D in rutile. It is shown that the solubility of these imperfections depends strongly on electron Fermi level, which in turn depends on the concentration of the imperfections. A method is presented for using hydrogen solubility to determine conduction band parameters and the energies and densities of electron traps in the crystal. The conditions for obtaining large or small concentrations of H,D or lattice defects are discussed. The use of the method presented depends on an accurate calibration of the oscillator strengths of the H‐D ir absorption in rutile. Such a calibration is presented in the following paper.

Dielectric Loss Mechanism in Rutile (TiO2)

A new mechanism to account for the anomalously large dielectric loss and apparent dielectric constant frequently observed in TiO2 is presented, which appears to agree well with experiment. The mechanism involves field‐induced donor migration where the field arises from a difference in work function between the rutile and a metal electrode. This migration results in a large decrease in electronic resistivity in the bulk of the crystal, with relatively thin insulating layers near the electrode surface. Experimental results on a variety of crystals are discussed, and the influence of electrode materials, surface condition, heat treatment, and ambient is analyzed. A method for numerically calculating the resistivity profile of such a crystal from dielectric loss data is described. Results indicative of room‐temperature p‐type conductivity and a voltage‐induced conduction process are presented.

Anomalous diffusion in nonmetals (origin and effects of internal electric fields)

When electrically active impurities or defects diffuse in a material with a band gap ≳ 10kT, the changing concentration of these ions may result in internal electric fields which will significantly alter the diffusion process, and result in gross misinterpretation of diffusion experiments. Equations are derived which describe the diffusion of interstitial impurities in such a system, and which take proper account of compensating immobile impurities. A technique for numerical solution of these equations is described and the results of calculations for the case of H+ in TiO2 are presented. These calculations predict a large enhancement of the over−all diffusion rate and a very distinctive concentration profile. The latter is of critical importance in identifying this effect, since our calculations show that a measurement of total impurity content vs time will appear to agree fairly well with Fick’s law; however, the apparent diffusion coefficient obtained in this way can be in error by a factor of 100 or mo...

Concentration Dependent Diffusion of H+ in TiO2: Analysis of Electronic Effects in Ionic Diffusion

Diffusion of charged impurities or defects in a non-metallic crystal generally results in changes in the electron Fermi level relative to the lattice energy bands and impurity levels, thus producing substantial internal electric fields. These fields in turn exert a force on the diffusing ion, hence modifying the diffusion process. A self-consistent treatment describing such diffusion processes in materials with band gap 1.5 eV will be developed. Our analysis shows that diffusion proceeds locally according to Fick’s laws, but with an effective diffusion coefficient, D(eff), which may be larger than the diffusion coefficient which would be observed in the absence of internal fields by a factor of 104 or more. D(eff) depends on the concentration of diffusing ions, and hence, changes with position and time. The problem of interdiffusion of two similar ions (as in an isotope exchange experiment) is also analyzed; it is shown that such an experiment virtually eliminates the effects of internal fields if the two species are more or less chemically equivalent, making it possible to determine accurately the field-free diffusion parameters. Detailed calculations for both single ion diffusion and interdiffusion of H and D in TiO2 will be presented; the overall rate for single diffusion typically shews an enhancement by a factor of 10 to 30, and a very distinctive concentration profile is predicted. Experiiments leading to accurate determination of the field-free diffusion parameters for H in TiO2, both by the isotope exchange technique and by ionic conductivity measurements, will be reported. In addition, single diffusion measurements have been carried out, which agree in quantitative detail with the calculations described above, both with respect to overall diffusion rate and concentration profile.

Simultaneous diffusion of two or more ions in the presence of internal electric fields

The theory of diffusion in the presence of internal electric fields developed in the preceding paper is generalized to the case of simultaneous diffusion of more than one species. It is shown that for the case of two chemically similar impurities, an experiment can be devised which virtually eliminates the effects of these internal fields, making possible accurate measurement of diffusion parameters. The theory is applied to H−D diffusion in rutile and it is shown that the main effect of the internal fields is to reduce the difference between the two diffusion coefficients while keeping the average nearly constant. Detailed calculations for the system are presented.