Positive Temperature Coefficient of Resistivity Effect in Highly Donor–Doped Barium Titanate

BaTiO₃ ceramics doped with different La concentrations (0–12 mol%) were prepared by sintering under the reducing conditions of a nitrogen atmosphere containing 1% hydrogen. The critical donor concentration that causes blocking of the exaggerated grain growth was observed to be ∼10 mol% La. The samples, which were semiconducting after sintering under reducing conditions, were subsequently reoxidized by annealing in air to induce the positive temperature coefficient of resistivity (PTCR) effect. After reoxidation at 1150°C a noticeable PTCR effect was observed in the samples doped with La concentrations as high as 2.5 mol%. The room-temperature resistivity after reoxidation was found to increase with increasing donor concentration due to an increase in the thickness of the insulating layers at the grain boundaries. TEM analysis showed that reoxidation of the samples caused precipitation of the Ti-rich compound Ba₆Ti₁₇O₄₀ inside the doped BaTiO₃-matrix grains.     

Positive Temperature Coefficient of Resistivity Effect in Undoped, Atmospherically Reduced Barium Titanate

A sharp positive temperature coefficient of resistivity effect for undoped, fluorinated BaTiO_3−x samples was observed. The qualitative agreement between the behavior of BaTiO_3−x and La-doped BaTiO₃, with respect to the trap density at the boundaries, suggests that in the absence of counterdopants such as Mn, the main origin of surface acceptor states is chemisorbed gases. Impedance analysis indicates that, under the conditions of the present work, fluorine seems not to diffuse in significant amounts into the lattice. The treatment of the fluorinated samples in inert/reducing atmospheres did not markedly decrease the resistivity jump, suggesting that fluorine might be chemisorbed more strongly than oxygen. The composition of two different liquid phases, produced by excess titania and silica additions, did not have an important effect on the resulting properties.     

A Novel Method for the Uniform Incorporation of Grain-Boundary Layer Modifiers in Positive Temperature Coefficient of Resistivity Barium Titanate

The presently developed two-stage process involves diping the prefired porous disks of n -BaTiO₃ in nonaqueous solutions containing Al-buty rate, Ti-isopropoxide, and tetraethyl silicate and subsequent sintering. This leads to uniform distribution of the grain-boundary layer (GBL) modifiers (Al₂O₃+ TiO₂+ SiO₂) and better control of the grain size as well as the positive temperature coefficient of resistivity characteristics. The technique is particularly suited for GBL modifiers in low concentrations (< 1%).     

Lead Titanate Ceramics with Positive Temperature Coefficients of Resistivity

Lead titanate ceramics were successfully made into semiconductors exhibiting anomalous positive temperature coefficients of resistivity (PTCR) about 3 orders of magnitude above the Curie point (480° to 490°C). The PTCR characteristics of the materials prepared were found to be unstable and to show a significant degradation in both room-temperature resistivity and magnitude of the PTCR effect with time. The instability of the PTCR characteristics observed in the present materials is considered to be related to the morphologies of their grain structures.     

Positive Temperature Coefficient of Resistance Effect in Heavily Niobium-Doped Barium Titanate by the Growth of the Double-Twinned Seeds

Positive temperature coefficient of resistivity (PTCR) was attained in heavily niobium-doped BaTiO₃ through the addition of BaTiO₃ seed particles. The seed particles containing a double twin grew during heat treatment, and a uniform microstructure composed of large, coarse grains was obtained. The incorporation of niobium into the grain via grain growth probably caused the semiconducting and PTCR character of the niobium-doped BaTiO₃.     

Grain-Boundary Chemistry of Barium Titanate and Strontium Titanate: II, Origin of Electrical Barriers in Positive-Temperature-Coefficient Thermistors

Scanning transmission electron microscopy (STEM) of positive-temperature-coefficient (PTC) BaTiO₃ thermistors shows that the grain-boundary oxygen content in as-received (oxidatively cooled) materials is slightly enriched compared to quenched samples, and the acceptor-rich space-charge present at high temperatures is retained upon cooling. The defect density of the space charge is approximately equal to the acceptor state density at PTC boundaries determined by electrical measurements. Accordingly, it is proposed that the electrical barrier forms when acceptor defects already segregated in the ionic space charge at high temperature become active interface states when compensating donor defects in the grain-boundary core are oxidized. These acceptor defects appear to be primarily barium vacancies, but need not form upon cooling in the manner proposed by Daniels and Wernicke. Acceptor solutes when present can also contribute to barrier formation through space-charge segregation; the increase in interface state density upon addition of Mn is consistent with the magnitude of the expected segregation.     

Formation of Potential Barrier Related to Grain-Boundary Character in Semiconducting Barium Titanate

Resistance–temperature ( R – T ) characteristics were measured directly at single-grain boundaries in 0.1-mol%-niobium-doped barium titanate bicrystals that had been fabricated from polycrystalline sinters, to determine a geometrical grain-boundary character dependence of the positive temperature coefficient of resistivity (PTCR) effect. Both random boundaries and low-Σ boundaries exhibit a similar grain-boundary character dependence of the PTCR effect through a simple geometrical analysis, using the coincidence of reciprocal lattice points. Differences of the R – T characteristics in individual boundaries have been explained in terms of the formation of a potential barrier that is associated with the oxidation of grain boundaries during cooling, after sintering or annealing. The grain-boundary character is likely to affect the diffusivity of O²⁻ ions and, hence, is crucial to the formation of the potential barrier.     

Factors and Mechanisms Affecting the Positive Temperature Coefficient of Resistivity of Barium Titanate

The chemistry of semiconducting lanthanum-doped barium titanate was examined to determine the factors critical to the positive temperature coefficient of resistivity exhibited by this material. This phenomenon was sensitive to oxidation under certain nonequilibrium conditions. Inhomogeneity is thought to result from such conditions and to produce regions of different resistivity throughout the ceramic body. The existence of high resistivity layers was demonstrated by analysis of dispersions in ac resistance at audio frequencies. Association of these layers with crystallite surfaces, i.e. grain boundaries, was demonstrated by resistivity measurements of semiconducting single crystals before and after oxygen treatments.     

Experimental Evaluation of the Acceptor-States Compensation in Positive-Temperature-Coefficient-Type Barium Titanate

Experimental evidence shows that the acceptor-state levels in Sb-doped positive-temperature-coefficient-type BaTiO₃ are compensated up to a critical acceptor-state density. Using the slope of the natural logarithm of the resistivity with respect to 1/ T , instead of maximum resistivity as a measure for the acceptor-state density, it is possible to estimate this critical value. The value obtained (4.2 × 10¹⁷ m⁻²) is believed to be the first reported estimate based on experimental data. It is in good agreement with the estimate of 6 × 10¹⁷ m⁻² (first reported by Jonker) obtained from the spontaneous polarization of BaTiO₃. This shows that the ferroelectric behavior of BaTiO₃ is indeed a feasible explanation for the low resistivity below the Curie point, as proposed by Jonker.     

Charge-Up Scanning Electron Microscopy Images of Intergranular Phases in Semiconducting BaTiO3 Positive Temperature Coefficient of Resistivity Ceramics

A charge-up image was observed in the intergranular phases of semiconducting BaTiO₃ positive temperature coefficient of resistivity (PTCR) ceramics when the ceramic specimens were heated to the Curie temperature in a scanning electron microscope. Experiments showed that this image was caused by intense secondary electron emission localized in the phases. This charge-up state seemed to be closely related to the PTCR mechanism.     

Depletion-layer Dielectric Properties of Positive Temperature Coefficient of Resistance Barium Titanate

For pure and impurity-added positive temperature coefficient of resistance (PTCR) barium titanate ceramic samples, a −11°C shift of the Curie point at the grain-boundary/depletion-layer region was observed. This result is obtained by fitting the PTCR grain-boundary resistance and capacitance data to a theory which combines a double-depletion-layer model with the Devonshire thermodynamic theory of barium titanate. The parameters used in the fitting are obtained from independent experiments. The shift of the Curie point is believed to result from the grain-boundary clamp ing effect near the cubic-tetragonal phase transition point.     

Determination of Inversion Temperature of Sb2O3-Doped BaTiO3 Positive Temperature Coefficient of Resistivity (PTCR) Ceramics by the Finite Difference Method

The effect of the cooling rate on the PTCR (positive temperature coefficient of resistivity) characteristics of 0.1 mol% Sb₂O₃-doped BaTiO₃ ceramics has been investigated. Resistances both below and above the Curie temperature were increased by slow cooling, which indicated that the resistive layer width at the grain boundary increased as the cooling rate decreased. Concentration profiles of the Ba vacancies as a function of distance from the grain boundary have been simulated by the finite difference method. The inversion temperature of the 0.1 mol% Sb₂O₃-doped BaTiO₃ system was determined to be 1160°C from the measured electrical properties and computed concentration profiles.     

Direct-Current Field Dependence of Dielectric Properties in Alumina-Doped Barium Strontium Titanate

The dielectric properties of (Ba_0.6Sr_0.4)TiO₃ and Al₂O₃-doped (Ba_0.6Sr_0.4)TiO₃ have been characterized. The grain size of the specimen is maximum for (Ba_0.6Sr_0.4)TiO₃ that has been doped with 1 wt% Al₂O₃. The density and the real part of the relative dielectric constant each decrease as the Al₂O₃ content increases. The loss factor is minimum for (Ba_0.6Sr_0.4)TiO₃ that has been doped with 2 wt% Al₂O₃. The dielectric constant of the specimens decreases as the applied dc field increases. The influence of the dc field on the loss factor is much less than that on the dielectric constant. The tunability is ∼24% for (Ba_0.6Sr_0.4)TiO₃ that has been doped with 1 wt% Al₂O₃.     

Crystallization of Sol–Gel-Derived Barium Strontium Titanate Thin Films

Microstructural development of thin-film barium strontium titanate (Ba _x Sr_{1– x} TiO₃) as a function of strontium concentration and thermal treatment were studied, using transmission electron microscopy (TEM) and X-ray diffractometry (XRD). Thin films, ∼250 nm thick, were spin-coated onto Pt/Ti/SiO₂/Si substrates, using methoxypropoxide alkoxide precursors, and crystallized by heat-treating at 700°C. All films had the cubic perovskite structure, and their lattice parameters varied linearly with strontium content. Films with higher strontium concentrations had a larger average grain size. In situ TEM heating experiments, combined with differential thermal analysis/thermogravimetric analysis results, suggest that the gel films crystallize as an intermediate carbonate phase, Ba _x Sr_{1– x} TiO₂CO₃ (with a solid solution range from x = 1 to x = 0). Before decomposition at 600°C, this carbonate phase inhibits the formation of the desired perovskite phase.     

Influence of Stoichiometry on the Microstructure and Positive Temperature Coefficient of Resistivity of Semiconducting Barium Titanate Ceramics

The influence of stoichiometry, i.e., Ba/Ti ratio, on the microstructure and positive temperature coefficient of resistivity (PTCR) characteristics of BaTiO₃ was investigated. Fine-grain microstructures are obtained for Ba-rich, stoichiometric, low-temperature-sintered, Ti-rich materials. The room-temperature resistivities ( ρRT ) of the fine-grain Ti-rich samples are large (>10⁸Ω·cm). Excess Ba²⁺ ions can decrease the ρRT , by more than 2 orders of magnitude, because of the compensation of barium vacancies near the grain-boundary regions. Rapid cooling after sintering can also decrease ρRT (⋍100×) and is ascribed to the suppression of reoxidation. Large-grain microstructures and low ρRT , on the other hand, are generally observed for Ti-rich and Al₂O₃-SiO₂-TiO₂-added samples after sintering at a temperature higher than the corresponding eutectic point.     

Effects of Yttrium Doping on the Grain and Grain-Boundary Resistivities of BaTiO3 for Positive Temperature Coefficient Thermistors

Several positive temperature coefficient (PTC) thermistors made of barium titanate with an excess of titania and containing additives such as yttria, and eventually silica, have been prepared following two different routes. The electrical properties of the ceramic samples have been studied at room temperature, i.e., below the transition temperature, using complex impedance spectroscopy. The latter proved to be very useful to measure separately the grain and grain-boundary resistivities which have been followed as a function of the yttrium concentration. They behave very similarly and go through a minimum for the same composition. From both electrical resistivity measurements and local chemical analysis, it is inferred that the average dopant concentration in the grains is lower than the nominal content in the starting powders. An overall interpretation is given, emphasizing the importance of liquid-phase sintering.     

The effects of Barium Strontium Titanate (BST) on the soft magnetic properties and loss performance of MnZn ferrites

With the increasing power density of the switched mode power supply (SMPS) developed nowadays, higher efficiency is required from the magnetic core, where the MnZn ferrites are often adopted. However, the relatively high operating temperature of the SMPS often results in reduced resistivity of the MnZn, which increases the eddy current loss. To enhance the resistivity of MnZn ferrite at high temperature range (>100 °C), donor-doped barium strontium titanate (BST) with a positive temperature coefficient of resistivity (PTCR) is prepared and dopped in the MnZn ferrite. The influence of BST addition from 0.000 wt% to 0.020 wt% on the MnZn ferrite is investigated over a wide temperature range from 25 °C to 140 °C. The XRD result suggests ionic exchange between the spinel phase and perovskite phase. The SEM result shows a refined and more uniform microstructure of MnZn ferrite brought about by the BST addition. At the maximum of 0.020 wt%, the BST addition shows almost no influence on density and the saturation magnetic induction. However, the initial permeability is slightly reduced by the BST addition, due to the microstructural change. Moreover, the BST concentrating at the grain boundaries improves the DC-resistivity across the temperature range from 25 °C to 140 °C. Due to the addition of BST, the reduction in eddy current loss at 300kHz/100 mT is around 35% at 25 °C, and ∼20% reduction at 140 °C.     

Transient Thermal Gradients in Barium Titanate Positive Temperature Coefficient (PTC) Thermistors

Barium titanate positive temperature coefficient (PTC) ceramic disk thermistors can suffer major mechanical damage if inhomogeneous heating occurs under voltage. The steady-state and transient temperature distributions for thin disk samples (radius of 5 mm, thickness of 2 mm) have been studied with an infrared microscope, using a spatial resolution of 35 µm. The transient temperature distribution is observed to be particularly sensitive to the electrical boundary conditions during the initial heating period after application of a voltage. Small variations in electrode symmetry can lead to axial asymmetric thermal gradients up to 25 K/mm across the entire rim when an ac voltage of 100 V is applied. A finite-difference model in two dimensions, based on solution of the heat equation with a local-temperature-dependent Joule heating-source term, has been developed to describe the axial and radial transient temperature distributions in the cylindrical geometry. The predictions reveal current concentration at the edge of an electrode when the metal layer coverage is slightly smaller than that of the opposite face. This phenomenon results in stronger localized heating in a ring that initiates the thermal gradient.