Fracture of A12O3 in Combined Tension/Torsion: I, Experiments

Combined tension/torsion tests were performed on solid A1₂O₃ rods at principal stress ratios σ₂/σ₁ of 0 (pure tension), -0.17, -0.38, -0.78, and -1.0 (pure torsion). The tensile principal stress at fracture σ₁ increased with increasing compressive principal stress σ₂, resulting in a higher strength in torsion than uniaxial tension. The ratio σ₁ (torsion)σ₁ (tension) was 1.31 for A1₂O₃, in general agreement with limited torsional data for brittle materials in the literature. Brittle fracture data in the tension-compression quadrant of principal stress space show an interesting dichotomy since strengthening is observed in torsional investigations, whereas weakening is observed for pressurized-tube studies. This difference may be either a pressurized-tube test artifact or a real effect due to the presence of stress gradients.     

Characterization of the Piezoelectric Properties of Pb0.98Ba0.02(Mg1/3Nb2/3)O3–PbTiO3 Epitaxial Thin Films

Pb(Mg_1/3Nb_2/3)O₃–PbTiO₃ (PMN–PT) (70/30) thin films were deposited by pulsed laser deposition using two growth strategies: adsorption controlled deposition from lead-rich targets (∼25–30 mass%) and lower-temperature deposition ( T _d≤600°C) from targets containing a small amount of excess lead oxide (≤3 mass %). The substrates used were (001) SrRuO₃/LaAlO₃. Typical remanent polarization values ranged between 12 and 14 μC/cm² for these films. The longitudinal piezoelectric coefficient ( d _33,f) was measured using in situ four-circle X-ray diffraction, and the transverse coefficient ( d _31,f or e _31,f) was measured using the wafer flexure method. d _33,f and e _31,f coefficients of ∼300–350 pm/V and ∼−11 C/m² were calculated, respectively. In general, the piezoelectric coefficients and aging rates were strongly asymmetric, suggesting the presence of a polarization bias. The large, extremely stable piezoelectric response that results from poling parallel to the preferred polarization direction is attractive for miniaturized sensors and actuators.     

Use of Crack Branching Data for Measuring Near-Surface Residual Stresses in Tempered Glass

An analytical procedure based on fracture mechanics is used to obtain the amount of residual stress in glass from measurements on the fracture surface. The technique utilizes the measurement of microcrack branching distances, known as the mirror — mist boundary, which occur at a critical crack branching stress intensity (K _m ) value. This procedurre shows that σ _A r _m ^1/2 Y _F (θ) =σ _R r ^1/2 _m +Ψ₀, where σ _A is the applied stress, r _m is the microcrack branching radius, σ _R is the residual stress, Y _F ( θ ) is the crack-border correction factor, and Ψ₀ is a material constant based on K _m . Thus, the equation is that of a straight line with the slope equal to the magnitude of the residual stress. Data for tempered glass from the literature are used to demonstrate the applicability of the technique.     

Residual Stress in a Soft-Buffer-Inserted Metal/Ceramic Joint

Residual stresses in a soft buffer layer developing during cooling of a metal/buffer/ceramic joint were analyzed. It is shown that there is a parabolic distribution for normal stress and a cubic parabola for shear stress in the buffer. The maximum shear stress, τ₁₂ or τ₁₃, is approximately proportional to the ratio of length to thickness of the buffer, and it is far more than the normal stress σ₁, σ₂ or σ₃. With increasing thickness of the soft buffer, the maximum shear stress will decrease, but the normal stress will change little. A new physics parameter m is suggested in this paper to describe the beneficial role of the buffer, and the influence factors of m are also discussed.     

Controlled Oxygen Partial Pressure Sintering of (Pb,La)(Zr,Ti)O3 Ceramics

Transparent PLZT(7/60/40) ceramics with large piezoelectric coefficients were obtained using a two-step sintering process with controlled oxygen partial pressure. Specifically, low-oxygen-pressure and low-temperature sintering were used in the first step, followed by a high-oxygen-pressure, high-temperature sintering cycle. High-density ceramics with small grain sizes of about 3 µm were prepared. As a result, k _p= 0.71, k ₃₃= 0.78, d ₃₃= 850 × 10^-12 C/N, and a transparency of 15% (λ= 610 nm, thickness of 1 mm) have been achieved; 20% improvement of d ₃₃ was gained compared to conventional processed PLZT ceramics ( d ₃₃= 710 × 10^-12 C/N).     

Influences of Sintering Temperature on Piezoelectric, Dielectric and Ferroelectric Properties of Li/Ta-Codoped Lead-Free (Na,K)NbO3 Ceramics

Li/Ta-codoped lead-free (Na,K)NbO₃ ceramics with a nominal composition of [(Na_0.535K_0.480)_0.942Li_0.058](Nb_0.90Ta_0.10)O₃ were synthesized normally at 1070°–1100°C. The XRD patterns of all samples show a single pervoskite structure with tetragonal symmetry. Although MPB separating the orthorhombic and tetragonal symmetries was absent, the maximum piezoelectric coefficient ( d ₃₃), electromechanical coupling coefficient ( k _p), Curie temperature ( T _c), and remanent polarization ( P _r) were optimized as 216 pC/N, 38.1%, 445°C, and 8.73 μC/cm², respectively.     

Fracture of Al2O3 in Combined Tension/Torsion: II, Weibull Theory

The Weibull statistical fracture theory for multiaxial stresses has been extended to conditions of combined tension/torsion loading. At fracture, a tensile principal stress ratio σ₁ (tension/torsion) σ₁ (uniaxial tension) greater than one is predicted which is dependent on stress state, Weibull modulus, and fracture location. Comparison to experimental tension/torsion data for Al₂O₃ shows that the Weibull theory, although predicting correct trends, generally underestimates strengthening effects of the compressive principal stress, thus providing a conservative failure prediction. This discrepancy may be related to influences of stress state on crack-tip "process zone" behavior.     

ON THE CONSISTENCY OF LEAST SQUARES ESTIMATORS FOR A THRESHOLD AR(1) MODEL

Abstract. For the SETAR (2; 1,1) model

where {a_t(i)} are i.i.d. random variables with mean 0 and variance σ²(i), i = 1,2, and {a_t(l)} is independent of {a_t(2)}, we consider estimators of φ₁, φ ₂ and r which minimize weighted sums of the sum of squares functions for σ²(1) and σ²(2). These include as a special case the usual least squares estimators. It is shown that the usual least squares estimators of φ₁, φ₂ and r are consistent. If σ²(1) ≠σ²(2) conditions on the weights are found under which the estimators of r and φ₁ or φ₂ are not consistent.     

The Effect of Texture and Microstructure on the Macroscopic Properties of Polycrystalline Piezoelectrics: Application to Barium Titanate and PZN–PT

The effects of crystallographic texture and microstructure are analyzed for polycrystalline tetragonal BaTiO₃, pseudotetragonal PZN–PT, and cubic BaTiO₃. For tetragonal BaTiO₃ and pseudotetragonal PZN–PT, we demonstrate that a high anisotropy of the single-crystal properties induces an apparent enhancement in the macroscopic piezoelectric response. For tetragonal BaTiO₃, the predicted macroscopic piezoelectric constants d ₃₁ and d ₃₃ are enhanced with respect to its single-crystal value at the expense of the spatial contributions from d ₁₅. For samples possessing fiber texture, an optimal response is predicted for samples that are not perfectly textured. Similarly, an apparent enhancement of the macroscopic value of d ₁₅ is predicted for PZN–PT. For cubic BaTiO₃, the low anisotropy of the underlying crystal properties induces a uniform decrease of the macroscopic electrostrictive constant, Q ₁₁, with decreasing texture. A completely random polycrystal provides 0.85±0.05 times its single-crystal response.     

Sintering and Electrical Properties of Lead-Free Na0.5K0.5NbO3 Piezoelectric Ceramics

Lead-free Na_0.5K_0.5NbO₃ (NKN) piezoelectric ceramics were fairly well densified at a relatively low temperature under atmospheric conditions. A relative density of 96%–99% can be achieved by either using high-energy attrition milling or adding 1 mol% oxide additives. It is suggested that ultra-fine starting powders by active milling or oxygen vacancies and even liquid phases from B-site oxide additives mainly lead to improved sintering. Not only were dielectric properties influenced by oxide additives, such as the Curie temperature ( T _c) and dielectric loss ( D ), but also the ferroelectricity was modified. A relatively large remanent polarization was produced, ranging from 16 μC/cm² for pure NKN to 23 μC/cm² for ZnO-added NKN samples. The following dielectric and piezoelectric properties were obtained: relative permittivity ɛ ^T ₃₃/ɛ ₀ =570–650, planar mode electromechanical coupling factor, k _p=32%–44%, and piezoelectric strain constant, d ₃₃=92–117 pC/N.     

Effect of Alkali Elements Content on the Structure and Electrical Properties of (K0.48Na0.48Li0.04)(Nb0.90Ta0.04Sb0.06)O3 Lead-Free Piezoelectric Ceramics

In this communication, we report on the effects of alkaline elements (K, Na, and Li) content on the electrical properties of (K_0.48Na_0.48Li_0.04)(Nb_0.90Sb_0.06Ta_0.04)O₃ ceramics. Because of the high volatility, the alkaline elements evaporate during the high-temperature sintering process, generating vacancy defects in the ceramics. As a result, the ferroelectric and piezoelectric properties of the ceramics become weakened. Our results reveal that the volatilization loss can be effectively compensated by a 1 mol% excess of alkaline elements. The remanent polarization P _r, piezoelectric coefficient d ₃₃, and electromechanical coupling coefficient k _p of the compensated ceramics are improved by 15%, 16%, and 20%, respectively, having a value of 30 μC/cm², 310 pC/N, and 0.6.     

Dielectric and Piezoelectric Properties of the Morphotropic Phase Boundary Composition in the (0.8−x) Pb(Mg1/3Ta2/3)O3−0.2PbZrO3−xPbTiO3 Ternary System

Morphotropic phase boundary (MPB) compositions separating rhombohedral and tetragonal phases in the (1− x − y )Pb(Mg_1/3Ta_2/3)O₃– y PbZrO₃– x PbTiO₃ (PMT–PZ–PT100 x ) ternary solid solution system were characterized using X-ray diffraction and dielectric, piezoelectric properties. This work focused on compositions with a PZ content fixed at y =0.2, with an MPB composition found to be located at x =0.4. Piezoelectric coefficients and dielectric permittivity were found to be on the order of d ₃₃=580 pC/N and 4100, respectively. Acceptor modification using manganese was found to induce a "hardening" effect in 0.4PMT–0.2PZ–0.4PT, with decreased piezoelectric coefficients d ₃₃ and dielectric loss and increased mechanical quality factor Q . Piezoelectric coefficients d ₃₃, Q values, and dielectric loss were found to be 500 pC/N, 2000, and 0.4%, respectively, for 0.4PMT–0.2PZ–0.4PT with MnO₂ dopant levels around 0.5 wt%. The figure of merit (product of Q and d ₃₃) was found to be on the order of 1 × 10⁶, significantly higher when compared with other hard piezoelectric PZT materials. Specifically, the PMT–PZ–PT materials may be attractive candidates for high-power ultrasonic applications, particularly fine-scale components that require relating high permittivities.     

Glass-Ceramic Formation in the ZnO-P2O5 System and the Effect of Silica as a Nucleating Agent

Crystallization of a series of ZnO-P₂O₅ based glasses was investigated. ZnO-P₂O₅-CaO glasses could be converted most readily to glass-ceramics and crystallization of these led to formation of alpha-Zn₂P₂O₇, alpha-CaZn₂(PO₄)₂, and ß-CaZn₂(PO₄)₂ phases. A further phase has been tentatively identified as monoclinic (Zn,Ca)₂P₂O₇. The most promising glass-ceramic composition Z15 (59.4ZnO·33P₂O₅·6.6CaO·1SiO₂) crystallized to alpha-Zn₂P₂O₇ and ß-CaZn₂(PO₄)₂, the latter phase being stabilized by the presence of SiO₂ which also encouraged volume nucleation giving a fine-scale (submicrometer) microstructure.     

Influence of Impurity Particles on the Fracture of UO2

Three types of second-phase precipitates were identified by scanning electron microscopy of helical specimens of nominally pure UO₂, i.e. (1) bonded or weakly bonded complex Si particles precipitated during sintering from impurities in the starting material, (2) more strongly bonded Al₂O₃-UO₂ surface particles that formed on the external surfaces during sintering, and (3) metallic Fe or U phases. The influence of these particles on the room-temperature fracture stress, σ _f , was investigated. Particles of types (1) and (2) were as large as 300 μm and caused up to 100% reduction in σ _f , whereas the metallic phases had no significant effect. The critical-strain-energy-release rate, G_c , determined from the measured flaw sizes and associated fracture stresses, was ∼3600 ergs/cm². Purification procedures that reduced the impurity particle sizes and number density improved the strength significantly.     

Phase Transition and Ferroelectric Characteristics of Pb[(Mg1/3Nb2/3)1-xTix]O3 Ceramics Modified with La(Mg2/3Nb1/3)O3

The effects of 0–5 mol% addition of La(Mg_2/3Nb_1/3)O₃ (LMN) on the phase transition and ferroelectric behaviors of Pb[(Mg_1/3Nb_2/3)_1-xTi_x]O₃ (PMNT) ceramics with compositions near the morphotropic phase boundary (MPB) were studied. An evolution of structure from rhombohedral to tetragonal was found with increasing PbTiO₃ (PT) content across the MPB (at ∼32.5 mol% PT), and a coexistence of both rhombohedral and tetragonal phases was also found at the MPB. The dual-phase field extended toward the lower PT content side of the MPB, and, moreover, the rhombohedrality or tetragonality was reduced, especially for the compositions near the MPB, by the addition of La in PMNT. The ferroelectric transition was found to change from normal to diffuse as the La content increased and the compositions became more rhombohedral. In accordance with the structural evolution, the change of remanent polarization ( P _r) and coercive field ( E _c) also became gradually indistinct, and both P _r and E _c were reduced. For compositions near the MPB, both PMNT and La-modified PMNT had a similar electromechanical factor ( k _p) in a range around 0.55–0.60, but the mechanical quality factor ( Q _m) was significantly reduced for the La-modified PMNT. The piezoelectric coefficient ( d ₃₃), however, was largely improved with increasing La content in PMNT of compositions at MPB. A high value of d ₃₃∼ 815 pC/N was obtained for the 5-mol%-La-modified ceramics, but it was associated with a low value of Q _m.     

BiScO3 Doped (Na0.5K0.5)NbO3 Lead-Free Piezoelectric Ceramics

Lead-free potassium sodium niobate-based piezoelectric ceramics (1− x )(Na_0.5K_0.5)NbO₃– x BiScO₃ (KNN–BS) ( x =0∼0.05) have been prepared by an ordinary sintering process. Single perovskite phase of KNN–BS exhibits an orthorhombic symmetry at x <0.015 and pseudocubic symmetry at x >0.02, separating by a MPB at 0.015≤ x ≤0.02. Piezoelectric and ferroelectric properties are significantly enhanced in the MPB, which are as follows: piezoelectric constant d ₃₃=203 pC/N, planar coupling coefficient k _p=0.36, remnant polarization P _r=24.4 μC/cm². These solid solution ceramics look promising as a potential lead-free candidate materials.     

Modified Lead Calcium Titanate Ceramics with a Relatively Large Dielectric Constant for Hydrophone Applications

Modified lead titanate of the base composition (Pb,Ca)Ti-(Co,W)O₃+ 0.01 mol% MnO was doped with 2 to 6 mol% strontium and barium to increase the dielectric constant, K , while preserving a high piezoelectric anisotropy ( d ₃₃ /d ₃₁). K was increased above 500 and a d ₃₃ /d ₃₁ ratio of 34/1 was achieved when the composition Pb_0.65Ca_0.31Sr_0.04Ti_0.09-(CO_0.5W_0.5)_0.06O₃+ 0.01 mol% MnO was fabricated. The large d ₃₃ /d ₃₁ resulted in an impressive hydrostatic piezoelectric coefficient ( d _h= 81 × 10_—12 m₂/V). The relatively low transition temperature ( T _c= 120°C) did not result in an increased aging rate when samples were tested at 40°C and 99% humidity for 120 h after poling. A small tetragonality ratio (1.008) enabled saturation of ceramic properties at poling fields as low as 30 kV/cm at 100°C.     

Structural and Electrical Properties of Er2O3-Doped Na1/2Bi1/2TiO3 Lead-Free Piezoceramics

Sodium bismuth titanates Na_1/2Bi_1/2TiO₃ (NBT) doped with 0–3 wt% Er₂O₃ were prepared by the conventional solid-state reaction method. The X-ray diffraction results revealed that the sintered Er-doped NBT ceramics exhibited a pure perovskite structure with Er³⁺ concentrations ranging from 0 to 1 wt%. At a low Er₂O₃ concentration, the Er-doped NBT ceramics showed enhanced electrical properties with dielectric constant ɛ₃₃^T/ɛ₀=636, a low dielectric dissipation factor (tan δ=3.3%), a low coercive field ( E _c=4.56 kV/mm), and a high piezoelectric constant ( d ₃₃=75 pC/N). The relationship between the composition and properties of Er-doped NBT ceramics has been discussed.     

Use of Fracture Mirrors to Interpret Impact Fractures in Brittle Materials

The impact resistances and fracture mirror radii ( r_m ) of rods of several ceramic materials were measured. The fracture stresses (σ _f ) were determined from σ _f vs r_m^−1/2 curves obtained from fiexural strength tests. An analysis, based on the assumption that the principal factor contributing to the impact energy absorbed is the energy ( U_e ) required to deflect the specimen to the fracture stress, indicated that the impact energy absorbed ( U ) per unit of specimen cross-sectional area ( A ) increased in proportion to the square of the maximum stress. The analysis also indicated that the slopes of the curves of U/A vs σ _f ² are proportional to the reciprocal of Young's modulus. Experimental data for several materials are consistent with this analysis.     

Phase Relations in the Garnet Region of the System Y2O3–Fe2O3–FeO–Al2O3

Liquidus equilibrium relations for the air isobaric section of the system Y₂O₃–Fe₂O₃–FeO–Al₂O₃ are presented. A Complete solid-solution series is found between yttrium iron garnet and yttrium aluminum garnet as well as extensive solid solutions in the spinel, hematite, orthoferrite, and corundum phases. Minimum melting temperatures are raised progressively with the addition of alumina from 1469°C in the system Y–Fe–O to a quaternary isobaric peritectic at 1547°C and composition Y _0.22 Fe _1.08 Al _0.70 O _2.83* Liquidus temperatures increase rapidly with alumina substitutions beyond this point. The thermal stability of the garnet phase is increased with alumina substitution to the extent that above composition Y _0.75 Fe _0.65 Al _0.60 O ₃ garnet melts directly to oxide liquid without the intrusion of the orthoferrite phase. Garnet solid solutions between Y _0.75 Fe _1.25 O ₃ and Y _0.75 Fe _0.32- Al _0.93 O ₃ can be crystallized from oxide liquids at minimum temperatures ranging from 1469° to 1547°C, respectively. During equilibrium crystallization of the garnet phase, large changes in composition occur through reaction with the liquid. Unless care is taken to minimize temperature fluctuations and unless growth proceeds very slowly, the crystals may show extensive compositional variation from core to exterior.