Grain Orientation Dependence of the PTCR Effect in Niobium-Doped Barium Titanate

The positive temperature coefficient of resistivity (PTCR) effect is directly measured in single grain boundaries in 0.1-mol%-Nb-doped BaTiO₃ with 1 mm coarse grains. The PTCR effect largely depends on grain boundary structure. Random grain boundaries exhibit the PTCR effect as in polycrystalline samples, but the PTCR effect does not appear in highly coherent boundaries such as small-angle boundaries, twin boundaries, and coincidence site lattice (CSL) boundaries with low Σ values. For Σ= 3 boundaries, the resistance increase above the Curie temperature is a function of deviation angle. A small PTCR effect is observed in Σ= 3 boundaries with a deviation angle of about 9° in contrast with ideal Σ= 3 boundaries and boundaries with a deviation of about 4°.     

A New Phenomenon in Barium-Lead Titanate Ceramics with Positive Temperature Coefficients of Resistivity

A curious resistivity anomaly in high-Curie-point barium-lead titanate materials with positive temperature coefficients of resistivity (PTCR) has been observed just below the Curie point (∼420°C), besides the normal PTCR anomaly. The additional resistivity anomaly was observed in the resistivity-temperature characteristics, especially on cooling, and shewed a significant dependence on the cooling rate.     

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.     

Investigation of Resistivity and Permittivity for (Ba,Pb)TiO3 PTCR Ceramics

A scheme to examine quantitatively the interdependence between the measured resistance and permittivity data for semiconducting (Ba,Pb)TiO₃ samples having Curie points above 300°C was developed based on the Schottky-type potential barrier model. Specifically, the nonvanishing spontaneous polarization in the ferroelectric state was considered in terms of a useful parameter to explain the low resistivity below the Curie point. The resistivity derived from the measured permittivity shows a consistent temperature dependence with the dc measured one, i.e., the positive temperature coefficient of resistance (PTCR) characteristics. It is also observed that more satisfactory agreement can be achieved when the acceptor states are assumed to be distributed over a certain energy interval. The values of acceptor-state densities thus obtained are found to be in excellent agreement with those extracted from the slope in the Arrhenius plots of resistivity vs l/( T ε_m), where T is the absolute temperature and ε_m the dielectric constant. The validity of the present methodology is justified by obedience to the Curie–Weiss law for the calculated bulk dielectric constant.     

Instability of the Characteristics of the Positive Temperature Coefficient of Resistivity in High-Curie-Point Barium-Lead Titanate Ceramics and Their Grain Structures

A significant isothermal increase in resistivity with time has been observed in high-Curie-point barium-lead titanate ceramics in the temperature region of the Curie points, giving rise to an instability of the characteristics of the positive temperature coefficient of resistivity (PTCR). The isothermal increase in resistivity (ρ) with time (t) observed at various temperatures can be expressed by the equation log ρ=A+B√t, where A and B are both temperature-dependent constants. The temperature dependence of A gave the usual PTCR characteristics because A is log ρ at t=0, while the temperature dependence of B was found to show a characteristic curve with a peak around the Curie point. Observation by SEM revealed a considerable difference between the grain structure of a sample showing a significant resistivity change and that of a sample showing little resistivity change.     

Engineering grain size and electrical properties of donor-doped barium titanate ceramics

A semiconducting lanthanum-doped barium titanate ceramic has been fabricated for battery safety applications by simple means from nanoparticles prepared at room temperature by kinetically controlled vapor diffusion catalysis. The material, characterized by electron microscopy, X-ray diffraction and electrical measurements, exhibits a difficult to achieve combination of submicron grain size (∼500 nm) and attractive electrical properties of room temperature resistivity below 100 Ω cm and a 12-fold increase in resistivity through the Curie temperature (positive thermal coefficient of resistivity, PTCR). Systematic investigation of sintering conditions revealed that a short period of heating at 1350 °C under air is necessary to suppress abnormal grain growth, while precise control of the cooling rate is needed to achieve the targeted electrical properties. Cooling must be sufficiently fast to avoid complete back-oxidation, yet slow enough to facilitate oxygen adsorption at the grain boundaries to produce the thin oxide layer apparently responsible for the observed PTCR.     

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.     

Differential Negative Resistance and Piezoresistivity in Thin Semiconducting BaTiO3 Ceramic Bars

Thin, semiconducting barium titanate (BaTiO₃) ceramic bars, with a diameter of 10 to 20 μm, consisting of single grains joined together in series have been prepared to investigate the piezoresistivity in the materials, which was evaluated from their current ( I )-voltage ( V ) characteristics under the loading condition of various bending stresses. I-V characteristics of single grain boundaries in some of the materials were found to exhibit distinct differential negative resistance (DNR) at room temperature with its feature changing with stress. The DNR appeared on the I-V curves at an electric field of several volts per one grain, and has been confirmed to be connected with the transition of current between two conduction states in the grain boundary region. The obtained results indicate that this phenomenon cannot be interpreted by a rise in the temperature of the materials up to their positive temperature coefficient of resistivity (PTCR) region above the Curie point by Joule heating due to current flow, that is their self-heating effect. This newly observed DNR phenomenon has thus been tentatively interpreted by the morphological change in the ferroelectric domain structure in the vicinity of grain boundaries under mechanical and electric stresses, on an assumption that different configurations of ferroelectric domains yield different conduction states in the grain boundary due to a difference in the degree of surface acceptor charge compensation or the anisotropic carrier mobilities in the crystal.     

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.     

PTCR anomaly in barium-titanate-based composites

We have identified a PTCR anomaly in undoped BaTiO₃ (BT) ceramics. This anomaly was ascribed to a disconnection of the semiconducting grains, due to dimensional changes of the BT grains at the Curie point, in a composite composed of two constituent BT phases, one with a low electrical resistivity and the other with a high electrical resistivity. The composite exhibits a significant PTCR effect of three orders of magnitude at the Curie temperature.     

PTCR Characteristics in Barium Titanate Ceramics with Curie Points Between 60° and 360°C

PTCR characteristics in porous semiconducting barium titanate ceramics with Curie points from 60° to 360°C were investigated. The magnitude of the PTCR effect in these cerumics decreases self-onsistently with increasing Curie point within this temperature range. A PTCR efSect of more than 4 orders of magnitude was ahserved, for a Ba_0.44Pb_0.6TiO₃ ceramic with a Curie point of 360°C .     

Proposed Phenomenological PTCR Model and Accompanying Phenomenological PTCR Chart

The positive temperature coefficient of resistivity (PTCR) behavior of semiconductive BaTiO₃ is well explained by the Heywang model, which predicts the resistivity behavior above the Curie point based on the acceptor state density at the grain boundaries, the charge carrier density, and the energy gap, E _s, between the conduction band and the acceptor levels. However, the relationship between these parameters and the production parameters (sintering time, composition, and cooling rate) is not well understood. Recently, the present authors have found that E _s can be increased by thorough oxidation. This increase is attributed to a change in the oxidation state of the acceptor. Based on this finding and results from the literature, a phenomenological PTCR model and an accompanying PTCR chart for acceptor–donor-codoped BaTiO₃ are proposed to clarify this relationship. The PTCR chart clarifies that acceptor dopant concentrations, oxidation time, and oxygen partial pressure during oxidation or cooling can be optimized simultaneously to obtain optical PTCR properties.     

Valence Change of Mn Ions in BaTiO3-Based PTCR Materials

The effect of Mn on the PTCR characteristics of La-doped BaTiO₃ ceramics was studied. Acceptor state density was measured from a p-1/ T graph as a function of Mn concentration. The behavior of room-temperature resistivity with Mn concentration was explained by compensation of acceptors at grain boundaries. The valence state of Mn was analyzed by ESR, and it changed near the Curie temperature of BaTiO₃ from 3+ in tetragonal phase to 2+ in cubic phase. Therefore, the number of electron traps increased at the Curie temperature, leading to the great improvement in the PTCR effect. The valence change of Mn ions was explained by vanishing of the Jahn-Teller effect as the phase changes from tetragonal to cubic.     

Direct Observation of the Double Schottky Barrier in Niobium-Doped Barium Titanate by the Charge-Collection Current Method

Charge-collection (CC) current was measured at a single grain boundary, which exhibited positive temperature coefficient of resistivity (PTCR) effects, in 0.1-mol%-Nb-doped BaTiO₃. The CC current systematically reversed across the grain boundary above the Curie point, which indicated the presence of a double Schottky barrier (DSB) at the grain boundary. In contrast, the CC current was constant across the grain boundary below the Curie temperature. The result obtained from the CC current measurement agrees with the classical DSB model in donor-doped BaTiO₃, indicating the PTCR effects.     

Effect of processing on the positive temperature coefficient of resistivity in lead metaplumbate/polyethylene composites

The positive temperature coefficient of resistivity (PTCR) effect of a barium metaplumbate/polyethylene [(BaPbO₃)/PE] composite with 12 vol% of BaPbO₃ was studied. The composite samples were prepared by hot-pressing a mixture of BaPbO₃ ceramic and high-density polyethylene powders around the melting point of polyethylene. The composites exhibit a pronounced PTCR effect of up to a six-decade increase in resistivity within a narrow range of temperature (∼10°C). The dependences of the room temperature resistivity and the magnitude of the resistivity jump on the pressing and annealing temperature, and the electrical behavior after repeated heating-cooling cycles were investigated. The fracture surfaces of the composite samples were examined in a scanning electron microscope in order to correlate the electrical behavior with the microstructure.     

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.     

Synthesis, formation and characterization of ZnTiO3 ceramics

Zinc titanate (ZnTiO₃) powders of perovskite structure were synthesized by conventional solid state reaction using metal oxides. Powders of ZnO and TiO₂ in a molar ratio of 1:1 were mixed in a ball mill and then heated at temperatures from 700 to 1000 °C for various time periods in air. The crystallization temperature of ZnTiO₃ powder was 820 °C, activation energy for crystallization was 327.14 kJ/mol and for grain growth was 48.84 kJ/mol. A transition point was observed when the electrical resistivity was measured versus temperature. Like some ferroelectric materials, a PTCR behavior above the transition temperature was observed with Curie temperature of 5 °C.     

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.     

Fabrication of High-Curie-Point Barium-Lead Titanate PTCR Ceramics

High-Curie-point semiconducting barium-lead titanate positive temperature coefficient of resistivity (PTCR) ceramics of composition Ba_0.897Pb_0.1La_0.003TiO₃ and Ba_0.5Pb_0.5La_0.003TiO₃ were prepared. The starting powders were synthesized by reacting commercial BaTiO₃, PbO, and TiO₂. To avoid the nonstoichiometry due to the volatilization of Pb during the sintering process, a lead atmosphere sintering approach with PbTiO₃ as packing powder was used. The samples being fabricated by this method show a PTCR effect of 3 to 4.5 orders of magnitude above the Curie point. The curie points were about 180°C for Ba_0.897Pb_0.1La_0.003TiO₃ and about 360°C for Ba_0.497Pb_0.5La_0.003TiO₃.     

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.