Janusz Nowotny

SEMICONDUCTING PROPERTIES OF UNDOPED TiO2

Abstract Both electrical conductivity and thermopower were studied for undoped [001] oriented TiO 2 single crystals within the temperature ranges 985–1387 K and oxygen partial pressure 10 −15 − 10 5 Pa. Using a Jonker-type analysis the energy gap in TiO 2 was determined ( E g = 3.09 − 1.33 × 10 −3 T/eV). It was shown that the transport of both electrons and electron holes occurs according to the small polaron model. The electrical properties determined in this work indicate that below and above 1300 K, respectively, the predominant defects in TiO 2 are doubly ionised oxygen vacancies and interstitial Ti 4+ ions.

Defect chemistry of BaTiO3

Abstract Possible defect disorders are considered for BaTiO 3 within both n -type and p -type regimes. Basic for defect structure considerations is the model which is build up on a general lattice electroneutrality conditions. Simplified electroneutrality conditions are discussed in terms of several defect models within both n -type and p -type regimes. Limitations of various models are discussed in more detail. It was shown that in the p -type regime the Schottky-type disorder should be considered rather than the extrinsic model. A T - P (O 2 ) diagram illustrating validity limitations of various models was derived. The diagram also illustrates the effect of acceptor-type impurities on validity limitations of the models. It has been concluded that the available experimental material, which has been accumulated so far, does not permit to rule out any of the existing defect models. Further progress in better understanding of defect disorders requires an accumulation of experimental data for either very pure or well defined speciments regarding the concentration of aliovalent ions and intrinsic nonstoichiometry. A new defect model was proposed for BaTiO 3 . This model, which is essentially based on a general lattice electroneutrality condition, is considered within certain thermodynamic ranges. The model assumes that the concentration of both extrinsic defects and the Schottky-type defects are present at comparable level. The paper gives a short survey on the diffusion data for BaTiO 3 . Their impact on the equilibration kinetics for the BaTiO 3 / O 2 system is considered.

Defect structure, electrical properties and transport in Barium Titanate. VII. Chemical diffusion in Nb-doped BaTiO3

The reequilibration kinetics of polycrystalline Nb-doped BaTiO3 were monitored by measuring electrical conductivity as a function of temperature and oxygen partial pressure over the ranges 1150 < T (K) < 1425 and 220 < p(O2) (Pa) < 105. Application of parabolic and logarithmic equation to the kinetic data gave the same values of the chemical diffusion coefficient for both oxidation and reduction runs as well as for both isothermal and isobaric experiments. The mobility of Ti vacancies (rather than that of Ba vacancies) is interpreted to be the major factor controlling gas/solid diffusion kinetics. The following relation between chemical diffusion coefficient and temperature was obtained: Dchem = 8·83 x 10−5 exp {-2·47[eV]/kT} (cm2s−1) This value is two orders of magnitude lower than that reported by Wernicke for La-doped BaTiO3. The difference is analysed using all the available data for each experiment. n nThe p(O2) exponent of electrical conductivity was determined as 1/4. This value is in agreement with a compensation mechanism involving cation vacancies rather than electrons.

Positive temperature coefficient of resistivity for BaTiO3-based materials

Abstract In this paper electrical properties of BaTiO 3 and its solid solutions are reported at room and moderate temperatures in the range 300–500 K. The electrical properties are mainly analyzed in terms of the positive temperature coefficient of resistivity (the PTC effect). Experimental data on the PTC effect have been reviewed and analyzed against several theoretical models. The Heywang-Jonker model and its further modifications are discussed in more detail. The models involve different explanations of the nature of the potential barrier which is formed across grain boundaries of polycrystalline BaTiO 3 . The grain boundary chemistry of BaTiO 3 is considered, involving phenomena such as segregation, oxygen chemisorption, oxygen incorporation into the grain boundary layer and the formation of surface states. The effects of these process on the temperature characteristics of resistivity are considered, with particular emphasis on the preparative procedure and post-preparative treatments such as annealing under gaseous atmospheres of controlled composition and cooling at different rates.

Electronic and ionic conductivity of TiO2 single crystal within the n-p transition range

Abstract The electrical conductivity of TiO2 single crystal (rutile) was determined within the n–p transition regime in the temperature range 985–1387xa0K and p(O2) 1–105xa0Pa. The determined values of the p(O2) exponent differ from those predicted by defect disorder models (in both n- and p-type regimes), which were derived assuming validity of ionic charge compensation. This difference allows the evaluation of the ionic conductivity. The ionic component thus determined within the n–p transition regime exhibits an activation energy of Ea=158xa0kJxa0mol−1. It was found that the ionic transfer number for undoped TiO2 at the n–p transition is approximately 0.5. The electronic conductivity component was used to determine the width of the forbidden gap of TiO2 (Eg=2.86xa0eV).

Defect structure, electrical properties and transport in barium titanate. III: Electrical conductivity, thermopower and transport in single crystalline BaTiO3

Abstract Both electrical conductivity and thermopower were studied for undoped BaTiO 3 single crystal in the temperature range 1090–1310 K under controlled gas atmosphere corresponding to the n-p type transition range. Reciprocals of the exponent of p (O 2 ) determined from electrical conductivity ( n δ ) and thermopower ( n s ) were determined. The parameters n δ and n s assume about −4 and −4·1 for the n-type regime. Both n δ and n s assume about 5·3 in the p-type regime. These values were interpreted in terms of the defect models involving oxygen vacancies as pre-dominant defects in the n-type regime and Schottky-type defects in the p-type regime. The mobility ratio of electronic carriers was determined. Experimental data indicate that the small polaron (hopping mechanism) model rather than the band model is valid in the n-type regime. Present experimental data do not allow a conclusion on the transport mechanism in the p-type regime. It was shown that the width of the forbidden gap for undoped BaTiO 3 is the following function of temperature: E g (T) = E 0 −βT where E 0 = 2·9 eV. The parameters β assumes 3·2 × 10 −5 and 2·47 × 10 −4 for the hopping and the band models, respectively.

Lattice and grain boundary diffusion of Ca in polycrystalline yttria-stabilized ZrO2 determined by employing SIMS technique

Abstract Diffusion profiles of Ca in highly densified polycrystalline yttria-stabilized (10 mol %) ZrO 2 were investigated by secondary ion mass spectroscopy (SIMS). Lattice diffusion coefficient in temperature range of 1073 to 1273 K was determined: D Lattice =0.458 exp[−393.3 (kJ/mol)/ RT ] (cm 2 /sec). Grain boundary diffusion was estimated based on the Whipples analysis. As a result, values of D Boundary δ s can be represented by D Boundary δ s =4.85×10 −13 exp[−185.8 (kJ/mol)/ RT ] (cm 3 /sec), where D Boundary is the grain boundary diffusion coefficient, δ the grain boundary width and s the segregation factor.

Defect structure, electrical properties and transport in barium titanate. VI: General defect model

Abstract Electrical conductivity data are analysed in terms of defect equilibria for undoped BaTiO 3 within a wide range of temperatures and oxygen partial pressures. Based on the Hall effect data reported by Seuter the equilibrium constants of the formation of (1) oxygen vacancies ( K 1 ), (2) Schottly disorder and (3) intrinsic disorder ( K i ) were determined. The defect diagram of BaTiO 3 thus derived involves four regimes of different charge neutrality. The effect of doping with aliovalent ions on the concentration of intrinsic defects was also determined. It was shown that the validity of the extrinsic disorder is limited to the n-type regime. It has been argued that any model constructed in the p-type regime cannot ignore the formation of cation vacancies. A defect model based on a general charge neutrality was derived. The model is valid within a wide range of compositions involving both n- and p-type regimes, except extremely reducing conditions. The resulting defect diagrams indicate that Schottky-type defect structure predominates in undoped BaTiO 3 in the p-type regime.

Defect structure, electrical properties and transport in barium titanate. II. Consistency requirements between defect models and crystal properties

Abstract The defect disorder of nonstoichiometric compounds is considered in terms of several crystal properties such as electrical conductivity, thermo-power, work function and deviation from stoichiometry. Quantitative interrelationships between the properties are considered in terms of their consistency with a particular defect model. The consistency is analysed in terms of a p (O 2 ) exponent of crystal properties such as electrical conductivity, thermopower, Fermi energy and nonstoichiometry as well as the concentration of electron charge carriers. The analysis is performed for a ternary oxide such as undoped BaTiO 3 . It has been concluded that construction of a defect structure model, especially for a compound of such complication as BaTiO 3 , should be based on several properties rather than on an individual property. It is argued that defect models based solely on electrical conductivity, which combines both concentration and mobility terms, require a verification by other properties such as thermopower.

Grain boundary diffusion in CoO

Abstract The diffusion of 60 Co, 63 Ni, and 45 Ca at 953 °C and 51 Cr at 953 and 1109 °C was measured in polycrystalline CoO scales by means of the radioactive tracer sectioning technique. High density scales were obtained by the oxidation of high purity Co plates at 1000 and 1200 °C in air. The diffusion penetration profiles exhibit two well distinguishable slopes which correspond to different diffusion regimes. The bulk diffusion coefficient, D , determined from the diffusion profile of the higher slope, is in a good agreement with the bulk diffusion data reported elsewhere. The product corresponding to the grain boundary diffusion, D ′ δα , where D ′ is the grain boundary diffusion coefficient, δ is the grain boundary thickness, and α is the segregation enrichment factor, was determined from the diffusion profile of the lower slope. It was found that the grain boundary diffusion enhancement factor, f = D ′ δα / D , for 60 Co and 63 Ni assumes similar values, which are one order of magnitude larger than those for 45 Ca and 51 Cr. The presence of Ca within the grain boundaries of CoO was confirmed using both autoradiography and SIMS methods. It has been revealed that the diffusion coefficient for both Ni and Ca in CoO, determined at 953 °C, exhibits the same value for specimens prepared at 1000 and 1200 °C, in spite of their different porosity and different grain size.