Piezoresistivity in PTCR Barium Titanate Ceramics: II, Mathematical Modeling

A modified grain boundary potential barrier model for positive temperature coefficient of resistance (PTCR) barium titanate is developed. It is based on Heywang's double Schottky barrier model, together with Devonshire's thermodynamic phenomenology of polarization behavior. Modifications are made to address the nonlinearity of the dielectric response with respect to electric field in the depletion region adjacent to the grain boundary, and the circular dependence of these quantities with the height of the barrier. Piezoresistivities are calculated for various PTCR compositions and sintering conditions, and these are compared to experimental results from the preceding paper.     

Piezoresistivity in PTCR Barium Titanate Ceramics: I, Experimental Findings

Positive temperature coefficient of resistance (PTCR) barium titanate is the active material in a ceramic sensor which employs piezoresistivity to detect changes in applied stress. High-purity, chemically prepared barium titanate is donor-doped with 0.30 at.% lanthanum, and <0.10 at.% of a transition-metal counterdopant may be added to enhance the PTCR effect. Tape-cast sheets of undoped and PTCR BaTiO₃ are laminated to produce a three-layer trilaminate—a sintered structure which has two semiconducting PTCR layers separated by an insulating layer. The trilaminate is stressed in a four-point bend configuration (placing one semiconducting layer completely in tension, the other in compression), and the resistivities for both stress states are measured concurrently as functions of applied stress and temperature. Results are presented for various semiconducting layer compositions and sintering conditions.     

Shift of the Curie Point of Barium Titanate Ceramics with Sintering Temperature

Definite increases in the Curie point (T_C) of undoped and lanthanum- (La-) doped (<0.5 at.%) barium titanate (BaTiO₃) ceramics sintered at elevated temperatures in the range of 1300°-1450°C were observed. Both undoped and 0.3 at.% La-doped BaTiO₃ (chosen as a typical doping concentration to yield semiconducting materials) ceramics showed almost the same T_C behavior; their T_C values increased by ∼3.5°C as the sintering temperature was increased from 1300° to 1450°C. Semiconducting 0.3 at.% La-doped materials increased in room-temperature bulk resistivity and TC with increased sintering temperature. The bulk resistivity of the La-doped materials, which was obtained from complex impedance analysis, increased from ∼2 omega cm for the material sintered at 1350°C to ∼6 ω cm at 1450°C. The phenomenon of bulk resistivity increase with sintering temperature was observed in the materials with a doping concentration of ≥ 0.2 at.% La, but was not observed in those doped with <0.2 at.% La. The mechanisms of TC and the bulk resistivity increase observed in the present materials with increased sintering temperature are discussed based on various models found in the literature, particularly in terms of the defect chemistry in semiconducting BaTiO₃ ceramics and the influence of liquid phases present during sintering.     

Effect of Microstructure on the PTCR Effect in Semiconducting Barium Titanate Ceramics

The microstructural influence on the PTCR effect in semiconducting barium titanate ceramics was studied and a method for preparing the ceramic bodies exhibiting a PTCR effect of more than seven orders of magnitude was established. Commercial barium titanyl oxalate was used as a starting material and Sb₂O₃ was added as a doping substance. The average grain sizes of the ceramic bodies prepared were 2 to 5 μm over a sintering range of 60 to 92%, to examine in detail the microstructural influence on the PTCR effect. No extra element, such as Mn or Cr, was added to develop the PTCR effect in the present PTCR materials.     

Influence of Stoichiometry on the PTCR Effect in Porous Barium Titanate Ceramics

Porous semiconducting barium titan ate ceramics with small grain sizes (2 to 5 tun) exhibit large PTCR effects (>7 orders of magnitude). The magnitude of PTCR in the ceramic bodies is significantly affected by the grain structure. This study shows the influences of Stoichiometry on both the magnitude of PTCR and resultant grain structures in the sintered bodies .     

Grain Boundary Oxidation in PTCR Barium Titanate Thermistors

The phenomenon of grain boundary oxidation in PTCR BaTiO₃ thermistors is discussed. In particular, the energy spectra of the surface states were calculated for different samples, and these were related to the nominal composition, the impurity content of the base BaTiO₃ powder used, and the prevalent atmospheric conditions during cooling and/or annealing. It is proposed that the interaction of manganese with oxygen creates deep-lying traps, and, in general, some proof is offered that the majority of the surface states are due to different oxidizing chemisorbed gases. It is believed that the ability of a particular sample to adsorb such gases in adequate amounts, and thus exhibit an appreciable PTCR effect, is related to the presence of acceptor-type dopants perferentially segregated onto the grain surfaces. Notably, the role of 3 d transition metal cations in this process is discussed in some detail.     

Defect Chemistry of Donor-Doped and Undoped Strontium Titanate Ceramics between 1000° and 1400°C

The electrical conductivity, sigma, of donor-doped and undoped strontium titanate (SrTiO₃) ceramics and, in some cases, single crystals, Sr1-xLaxTiO₃ (0 ≤ to x ≤ 0.1), was investigated in the temperature range of 1000°-1400°C under oxygen partial pressures, PO₂, of 10_-20-1 bar. In conjunction with Hall data and thermopower data from related papers, a set of constants for a defect-chemical model was determined, precisely describing point-defect concentrations and transport properties of these materials. In contrast to former works, temperature-dependent transport parameters and their non-negligible influence on the determination of the constants was considered, as well as the equilibrium restoration phenomena of the cation sublattice, which can be studied only at such high temperatures. It was shown that defects in the cation sublattice completely govern the electrical behavior of donor-doped and undoped SrTiO₃. In the latter case, frozen-in strontium vacancies act as intrinsic acceptors, determining the sigma(PO₂) curves at lower temperatures. This intrinsic acceptor concentration also can be calculated with this model. The very good agreement between calculation and measurement is shown in many examples.     

Piezoelectric Ceramics with Super-High Curie Points

The perovskite-like layer-structured (PLS) Nd₂Ti₂O₇ and La₂Ti₂O₇ have possibly the highest Curie points of any materials. To pole these ceramics, highly textured, dense ceramics with high DC electrical resistivity are required. The ferroelectric and piezoelectric properties of lead-free Nd₂Ti₂O₇ and La₂Ti₂O₇ grain-oriented ceramics prepared by spark plasma sintering using a two-step method are reported. The T _c of Nd₂Ti₂O₇ and La₂Ti₂O₇ are 1482±5° and 1461±5°C, respectively. The measured piezoelectric constant of the textured La₂Ti₂O₇ was d ₃₃=2.6 pC/N. These results now open up the possibility of studying the ferroelectric/piezoelectric properties of the PLS family of ceramics with super-high Curie points.     

Domain Twinning in Barium Titanate Ceramics

The patterns found in metallographically prepared barium titanate ceramics are shown to be due to 90° domains. Sets of domains are bounded by (110) planes. Forsbergh's solution of the "square-net" pattern is confirmed.     

Preparation of Barium Titanate Films at 55°C by an Electrochemical Method

Work by previous investigators has shown that BaTiO₃ films can be synthesized from solution over temperature ranges from 80°C to greater than 200°C. In the present work, electrically insulating crystalline films of BaTiO₃ have been electrochemically deposited on titanium substrates at temperatures as low as 55°C. Auger spectroscopic analyses with depth profiling indicate that a titanium oxide layer whose thickness is governed by current density acts as a precursor to BaTiO₃. Formation of BaTiO₃ is found to be favored only in highly alkaline solutions. This is consistent with the phase stability reported for the Ba─Ti─CO₂─H₂O system at 25°C. Lower processing temperatures (55°C) favor the formation of thick, electrically resistive, and wellcrystallized BaTiO₃ films, apparently due to increased oxygen solubility in the electrolyte solution. Films produced at 100°C are much thinner and are electrically conductive due to fissures and pores in their microstructure. Initial studies on the effect of current density indicate the formation of thinner and porous films with thicker titanium oxide intermediate layers.     

Transformation-Induced Twinning: The 90° and 180° Ferroelectric Domains in Tetragonal Barium Titanate

Ferroelectric twin domains resulting from the cubic ( c ) to tetragonal ( t ) phase transformation at the Curie point T _C≈130°C in pressureless-sintered BaTiO₃ ceramics, using TiO₂-excess powder, have been investigated using scanning and transmission electron microscopy. Both 90° and 180° domains were identified by spot splitting along characteristic crystallographic directions in the selected-area diffraction patterns and/or from the shape of domain boundaries. Lamellar domains were found predominantly with the 90° types. The 180° domain boundaries mostly appeared wavy in shape, while the 90° ones, having sharpened ends, attained a dagger shape. Failure of Friedel's law in the non-centrosymmetric t -BaTiO₃ was adopted to validate the existence of the 180° domains. The 90° domains with boundaries lying in     are reflection–inversion twins, and the 180° domains lying in {100) _t and }220) _t are inversion twins. Convergent-beam electron diffraction was performed to ensure that changing of the polar direction [001] _t across the 90° and the 180° domain boundaries was consistent with the domain type. It was also used to confirm whether the 180°-type walls are inversion domain boundaries produced by the loss of an inversion center when the cubic phase transforms into tetragonal symmetry. The formation of such ferroelectric domains is discussed with reference to the crystal symmetry reduction from     ( c -phase) to P 4 mm ( t -phase) with a loss of mirror plane (m) and roto-inversion axis     upon c → t phase transformation.     

Dielectric Temperature Characteristics of Cerium-Modified Barium Titanate Based Ceramics with Core—Shell Grain Structure

Various particle sizes of starting barium titanate were used to investigate the effect of chemical inhomogeneity on the dielectric temperature characteristics of a dilute solid solution of cerium-modified barium titanate. Transmission electron microscopy and energy dispersive spectroscopy confirmed three distinct areas in the modified barium titanate: a grain core, a grain shell, and gradient regions. The grain size and volume fractions of the grain core were somewhat proportional to the particle size of the starting barium titanate. The dielectric temperature characteristics will be explained in the present paper in terms of the three inhomogeneous regions. Actually, the dielectric temperature characteristics of the large grains (3μm) proved to be a function of variation in the T _c values, whereas those of the small grains (,3μm) were a function of both the T _c values and the internal stress.     

Use of Succinic Acid to Test the Stability of PTCR Barium Titanate Ceramics under Reducing Conditions

On heating positive temperature coefficient of resistance (PTCR) BaTiO₃ ceramics at 350°C in succinic acid powder, a reducing atmosphere is created as the succinic acid pyrolyzes. Grain boundary resistances, which may give a PTCR effect, are reduced by this treatment, whereas surface layer resistances, which may also give a PTCR effect, are much less affected.     

Effect of Soaking Time on the Temperature Coefficient of Resistivity of Semiconducting Barium Titanate PTCR Ceramics

The influence of soaking time at 1200°C on the temperature coefficient of resistivity (TCR) of semiconducting barium titanate ceramics has been investigated. It is found that soaking duration has influence on the room-temperature resistivity, the maximum resistivity, the temperature ( T _max) at which the maximum resistivity appears, and TCR of the positive temperature coefficient of resistivity (PTCR) ceramics. The increased room-temperature resistivity with the increase of soaking time is contributed mainly by the increase of grain boundary resistivity examined by the complex-plane impedance method. The obtained surface acceptor density ( N _s) by capacitance–voltage measurement is found to increase with the soaking duration. The higher N _s contributes to higher built-in potential and results in lower T _max and higher maximum resistivity. Therefore, the increased surface acceptor density from increasing the soaking time at 1200°C increases the temperature coefficient of resistivity of PTCR ceramics.     

Incorporation of Yttrium in Barium Titanate Ceramics

In this work, X-ray diffractometry and scanning electron microscopy techniques were used to study the incorporation of yttrium in BaTiO₃, with the following nominal compositions: (Ba_{1- x} Y _x )TiO₃(0.015 ≤ to x ≤ to 0.08), (Ba_{1- x} Y _x )Ti_{1- x /4}-(□_Ti) _{x /4}O₃(0.005 ≤ to x ≤ to 0.1), and Ba(Ti_{1- y} Y _y )O_3-delta(0.028 ≤ to y ≤ to 0.258). The phase assemblage and the lattice parameters indicated a slight solubility (∼1.5 at.%) of yttrium at the Ba sites at 1440°C but a high solubility (∼12.2 at.%) of yttrium at the Ti sites at 1515°C. When BaTiO₃was heavily doped with yttrium at the Ti sites (a yttrium concentration ( y ) of <0.059), the crystallographic structure was tetragonal, whereas for y greater than equal to 0.059, the crystallographic structure was cubic.     

Hydrothermal Synthesis of Thin Films of Barium Titanate Ceramic Nano-Tubes at 200°C

A novel, low-temperature synthesis method for producing BaTiO₃ thin films patterned in the form of nano-tubes ("honeycomb") on Ti substrates is reported. In this two-step method, the Ti substrate is first anodized to produce a surface layer (∼200–300-nm thickness) of amorphous titanium oxide nano-tube (∼100-nm diameter) arrays. In the second step, the anodized substrate is subjected to hydrothermal treatment in aqueous Ba(OH)₂, where the nano-tube arrays serve as templates for their hydrothermal conversion to polycrystalline BaTiO₃ nano-tubes. This opens the possibility of tailoring the nano-tube arrays and of using various precursor solutions and their combinations in the hydrothermal bath, to produce ordered, patterned thin-film structures of various Ti-containing ceramics. These could find use not only in a variety of electronic device applications but also in biomedical applications, where patterned thin films are also desirable.     

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°.     

Piezoresistance and Piezocapacitance Effects in Barium Strontium Titanate Ceramics

A large piezoresistance response to hydrostatic pressure is reported for a series of ceramic compositions in the system barium strontium lanthanum titanate (Ba, Sr, La)TiO₂. This property appears to be closely associated with the Curie region (cubic-tetragonal phase transition) and the phenomenon of a positive temperature coefficient of resistance for these same compositions. The piezoresistance coefficient, similar to the temperature coefficient of resistance, is positive in the Curie region, and is found to range up to the order of 700 X 10 ⁻¹² sq. cm. per dyne. Consistent with the observed piezoresistance effect, a positive piezocapacitive effect, ranging up to the order of 700 x 10⁻¹² sq. cm. per dyne, is observed in these compositions in the absence of the lanthanum impurity which produces semiconduction. It is suggested that these materials may be of interest in pressure-sensitive devices such as acoustic transducers and pressure-sensing elements and in techniques for measuring force and displacement.     

Semiconducting–Insulating Transition for Highly Donor-Dopod Barium Titanate Ceramics

BaTiO₃ ceramics doped with La (0.01–0.84 at.%) were prepared only with the addition of La and stoichiometric TiO₂. As a result, even when BaTiO₃ was doped with 0.53 at.% La, it could be converted to a semiconductor by sintering at 1540°C for 2 h in air and cooled slowly in the furnace. Differential thermal analysis data clearly demonstrated that the Curie point in the materials shifted toward lower temperatures with increased content of La substituted at the Ba site up to a critical concentration that varied with the sintering temperature. The obtained results suggest that the semiconducting–insulating transition for highly donor-doped BaTiO₃ was closely related to the incorporation of donor into the grains and to the resultant grain size, which were significantly affected by the sinterability of the BaTiO₃ starting powders and sintering conditions used.     

Grain-Boundary Characteristics and Their Influence on the Electrical Resistance of Barium Titanate Ceramics

The integral and spectral cathodoluminescence (CL) properties of grain-boundary zones in positive-temperature-coefficient-type barium titanate ceramics were investigated with respect to typical sintering parameters in the spectral range 300 to 1800 nm at room temperature. Spatially resolved CL micrographs for the wavelength range 300 to 850 nm show dark grain-boundary zones and light grain interiors. Corresponding micrographs for the infrared wavelength range 800 to 1800 nm show just the opposite CL contrast. The CL properties of the grain-boundary zone can be correlated to doubly ionized barium vacancies. Therefore, grain-boundary zones which are visible in integral CL images of both wavelength ranges represent the theoretically predicted grain-boundary zone of high barium vacancy concentrations. The width of these grain-boundary zones varies characteristically with sintering time and cooling rate. Additional measurements of the electrical conductivity of the specimens confirmed the theoretically assumed correlation between grain-boundary-zone width and electrical resistance of the samples.