Fracture Toughness of TiB2 and B4C Using the Single-Edge Precracked Beam, Indentation Strength, Chevron Notched Beam, and Indentation Strength Methods

The mode I fracture toughness ( K _Ic) of boron carbide (B₄C) and titanium diboride (TiB₂) was determined using four competing techniques. The indentation strength (IS), chevron notched beam (CNB), and indentation fracture (IF) methods are common techniques that were compared to the recently standardized single-edge precrack beam (SEPB) method. The SEPB method was more difficult to apply, but it represents the most rigorous method for K _Ic determination, because it uses few assumptions and requires a direct measurement of crack length. The IS method was an expeditious and economical alternative when low indentation loads were used. CNB K _Ic values were virtually rate-independent when displacement rates less than or equal to 0.5 mm/min were used. The IF method was the least satisfactory technique, because of high variability in K _c values and because of the low differentiation between the two materials studied.     

Fractographic Criteria for Subcritical Crack Growth Boundaries in 96% Al2O3

The percent intergranular fracture (PIF) was measured along radii extending from fracture origins in 96% A1₂O₃ specimens, fractured at various loading rates and temperatures, and plotted vs estimates of stress intensity factors ( K ₁) at the corresponding crack lengths. Two types of curves were observed. The first was similar to curves previously observed for hot-pressed alumina. In this case the subcritical crack-growth boundary was located approximately where the minimum in the PIF occurred near K ₁=4MPa·m^½, as was also the case for hotpressed alumina. Therefore, the location of this minimum or the projecting grams formed by intergranular fracture as the crack velocity increased can be used as criteria for locating the subcritical crack-growth boundary. The second type of curve lacks the minima in PIF characteristic of the first type and is characterized by a gradual trend toward higher PIF beginning at K ₁=3MPa·m^½. This type of curve may be caused by acceleration of the crack to high crack velocities at values of K ₁ approximately equal to or slightly greater than those necessary to cause critical crack growth on the lower fracture-energy planes in sapphire. Assuming that this is the case, the K ₁ at which the trend toward higher PIF begins can be used to calculate the radius to the critical flaw boundary for this type of fracture.     

Phase Relations in the System Bi2O3-WO3

Phase relations in the system Bi₂O₃-WO₃ were studied from 500° to 1100°C. Four intermediate phases, 7Bi₂O₃· WO₃, 7Bi₂O₃· 2WO₃, Bi₂O₃· WO₃, and Bi₂O₃· 2WO₃, were found. The 7B₂O · WO₃ phase is tetragonal with a ₀= 5.52 Å and c ₀= 17.39 Å and transforms to the fcc structure at 784°C; 7Bi₂O₃· 2WO₃ has the fcc structure and forms an extensive range of solid solutions in the system. Both Bi₂O₃· WO₃ and Bi₂O₃· 2WO₃ are orthorhombic with (in Å) a ₀= 5.45, b ₀=5.46, c ₀= 16.42 and a ₀= 5.42, b ₀= 5.41, c ₀= 23.7, respectively. Two eutectic points and one peritectic exist in the system at, respectively, 905°± 3°C and 64 mol% WO₃, 907°± 3°C and 70 mol% WO₃, and 965°± 5°C and 10 mol% WO₃.     

Transformation Enthalpies of the TiO2 Polymorphs

The enthalpies of transformation of pure, well-characterized samples of brookite and anatase to rutile were determined by solution calorimetry in a 3Na₂O·4MoO₃ melt at 971 ±2 K. The experiments gave the following results: brookite→rutile, ΔH°₉₇₁= -0.17±0.09 kcal mol⁻¹; anatase → rutile, ΔH°₉₇₁= -0.78±0.20 kcal mol⁻¹.     

Fracture Toughness and Spalling Behavior of High-Al2O3 Refractories

The fracture energies and spalling resistance of high-Al₂O₃ refractories were studied. The fracture energies, γ _WOF and γ _NBT , were measured by the work-of-fracture and the notched-beam-test methods, respectively. Spalling resistance, as measured by the relative strength retained in a water quench, correlated well with the thermal-stress resistance parameter applicable to stable crack propagation under conditions of thermal shock, (γ _WOF /α² E ₀). Many of the refractories exhibited high ratios of γ_WOF to γ_NBT; such high ratios were shown analytically to maximize the parameter ( R ¹¹¹¹= E _0γWOF/S₁²) which describes the resistance to catastrophic spalling. The increase of crack length with increasing quenching temperature difference (Δ T ) was somewhat less than that predicted theoretically; the discrepancy was attributed to an increase of crack density with Δ T . In general, the results show that fracture energy is important in establishing the spalling resistance of high-Al₂O₃ refractories.     

Studies in Lithium Oxide Systems: XII, Li2O-B2O3-Al2O3

Tentative phase relations in the binary system BnOa-A1₂O₃ are presented as a prerequisite to the understanding of the system Li₂O-B₂O₃-Al₂O₃. Two binary compounds, 2A1₂O₃.B₂O₃ and 9A1₂O₃.-2B₂O₃, melted incongruently at 1030° f 7°C and about 144°C, respectively. Two ternary compounds were isolated, 2Li₂O.A1₂O₃.B₂O₃ and 2Li₂O. 2AI₂O₃. 3B₂0₃. The 2:1:1 compound gave a melting reaction by differential thermal analysis at 870°± 20° C, but the exact nature of the melting behavior was not determined. The 2:2:-3 compound melted at 790°± 20° C to Li_zO.-5Al₂O₃ and liquid. X-ray diffraction data for the compounds are presented and compatibility triangles are shown.     

Mullite Crystallization from SiO2-Al2O3 Melts

SiO₂-Al₂O₃ melts containing 42 and 60 wt% A1₂O₃ were homogenized at 2090°C (∼10°) and crystallized by various heat treatment schedules in sealed molybdenum crucibles. Mullite containing ∼78 wt% A1₂O₃ precipitated from the 60 wt% A1₂O₃ melts at ∼1325°± 20°C, which is the boundary of a previously calculated liquid miscibility gap. When the homogenized melts were heat-treated within this gap, the A1₂O₃ in the mullite decreased with a corresponding increase in the Al₂O₃ content of the glass. A similar decrease of Al₂O₃ in mullite was observed when crystallized melts were reheated at 1725°± 10°C; the lowest A1₂O₃ content (∼73.5 wt%) was in melts that were reheated for 110 h. All melts indicated that the composition of the precipitating mullite was sensitive to the heat treatment of the melts.     

Internal Friction, Dielectric Loss, and Ionic Conductivity of Tetragonal ZrO2-3% Y2O3 (Y-TZP)

The defect structure in 3 mol% Y-TZP was studied by correlated internal friction, dielectric loss, and ionic conductivity experiments. A prominent mechanical and dielectric loss peak occurs in the temperature range between 380 and 550 K that depends on the frequency of measurement. The relaxation parameters were determined as H_m = 90 ± 3 kJ·mol⁻¹, τ_∞= (1.0_+1.5^−0.6) × 10₋₁₄ s for the mechanical relaxation and H_d = 84 ± 3 kJ·mol⁻¹, τ_∞= (1.6_+1.7^−0.9) × 10^–13 s for the dielectric relaxation. The ionic conductivity below 790 K is controlled by an activation enthalpy of H _σ= 89 ± 3 kJ·mol⁻¹; at higher temperatures H _σ= 60 ± 3 kJ·mol^–1. An atomistic model is presented which assumes that oxygen vacancies are trapped by yttrium ions forming anisotropic complexes which—by reorientation—cause anelastic and dielectric relaxation. At higher temperatures (>790 K) these complexes are dissociated, which leads to the reduced activation enthalpy for ionic conductivity.     

Investigation of the Phase Diagram for the Pseudobinary System Li2SO4–La2(SO4)3 and Its Ionic Conductivity

The phase diagram of the pseudobinary system Li₂SO₄–La₂(SO₄)₃ has been investigated by means of X-ray diffraction and differential thermal analysis. LiLa(SO₄)₂ is formed by a peritectic reaction in this system; the peritectic temperature is 653±3°C. The eutectic reaction of Li₂SO₄ and LiLa(SO₄)₂ occurs at 553±3°C; the composition at the eutectic point is 17 mol% La₂(SO₄)₃. LiLa(SO₄)₂ is monoclinic with a=1.375 nm, b=0.6744 nm, c=0.7068 nm, and β=105.4°. The ionic conductivity of LiLa(SO₄)₂ has been studied from room temperature to 350°C and is found to be relatively low at room temperature or at lower temperatures. Its activation energy is 0.66 eV. Thus it is not suitable as a fast ion conductor.     

Phase Diagram of the Pseudobinary System Ga2O3-Bi2-x3+Bix5+O3+x2-

The pseudobinary system Ga₂O₃-Bi_{2- x} ³⁺Bi _x ⁵⁺O_{3+ x} ^2- was studied in view of its importance for growth of SrGa₁₂O₁₉ crystals from a bismuth oxide flux. A subsolidus transition of γ*-Bi₂O₃ to a β'-phase and a strictly stoichiometric 1:2 phase with 33.3 mol% bismuth oxide were found. The single-crystal data for the compound indicated space group P2₁2₁2, with lattice constants a=0.79180±0.0003 nm, b =0.8288±0.0003 nm, and c =0.5889±0.0003 nm; the measured density was 7.1±0.3 g/cm³ and the cell content (Z) 2.     

Fracture Toughness of Al2O3 with an Unstabilized ZrO2Dispersed Phase

The fracture toughness of Al₂O₃ is considerably increased by the incorporation of fine monoclinic ZrO₂ particles. Hot-pressed composites containing 15 vol % ZrO₂ yield K_lcvalues of ∼ 10 MN/m^3/2, twice that of the A1₂O₃ matrix. It is hypothesized that this increase results from a high density of small matrix microcracks absorbing energy by slow propagation. The microcracks are formed by the expansion of ZrO₂during the tetragonal → monoclinic transformation. Since extremely high tensile stresses develop in the matrix, very small ZrO2 particles can act as crack formers, thus limiting the critical flaw size to small values.     

Grain Growth in Sintered ZnO and ZnO-Bi2O3 Ceramics

Grain growth in a high-purity ZnO and for the same ZnO with Bi₂O₃ additions from 0.5 to 4 wt% was studied for sintering from 900° to 1400°C in air. The results are discussed and compared with previous studies in terms of the phenomenological kinetic grain growth expression: G ⁿ— G ⁿ₀= K ₀ t exp(— Q/RT ). For the pure ZnO, the grain growth exponent or n value was observed to be 3 while the apparent activation energy was 224 ± 16 kJ/mol. These parameters substantiate the Gupta and Coble conclusion of a Zn²⁺ lattice diffusion mechanism. Additions of Bi₂O₃ to promote liquidphase sintering increased the ZnO grain size and the grain growth exponent to about 5, but reduced the apparent activation energy to about 150 kJ/mol, independent of Bi₂O₃ content. The preexponential term K ₀ was also independent of Bi₂O₃ content. It is concluded that the grain growth of ZnO in liquid-phase-sintered ZnO-Bi₂O₃ ceramics is controlled by the phase boundary reaction of the solid ZnO grains and the Bi₂O₃-rich liquid phase.     

Studies in Lithium Oxide Systems: II, Li2O Al2O3–Al2 O 3

Solid-state reactions between Li₂O and Al₂ O₃ were studied in the region between Li₂O.Al₂ O ₃ and Al₂ O ₃. The compound Li₂ O Al₂ O ₃ melts at 1610°± 15°C. and undergoes a rapid reversible inversion between 1200° and 1300°C. Vaporization of Li₂ O from compositions in the system proceeds at an appreciable rate at 1400°C, as shown by fluorescence. Lithium spinel, Li₂ O -5Al₂O₃, was the only other compound observed. The effect of Li₂ O on the sintering of alumina was investigated.     

Effect of High-Temperature, High-Oxygen-Fugacity Annealing on the Stability of the (Bi,Pb)2Sr2Ca2Cu3O10 ±δ-type Compound

The stability of the (Bi,Pb)₂Sr₂Ca₂Cu₃O_10±δ-type compound has been evaluated under conditions of elevated temperature (500°-860°C) and elevated oxygen fugacity (i.e., in O₂/Ar gas mixtures containing ≤120% O₂, at total pressures of 5207 MPa). At sufficiently high oxygen fugacities and temperatures, the (Bi,Pb)₂Sr₂Ca₂Cu₃O_10±δ-type compound transformed into a mixture of a strontium-rich (Bi,Pb)₁-(Sr,Ca,Cu)₂O_y-type compound, a calcium-rich (Bi,Pb)₂-(Sr,Ca,Cu)₂O_y-type compound, CuO, and a small amount of (Sr,Ca)O. The decomposition of the (Bi,Pb)₂Sr₂Ca₂-Cu₃O_10±δ-type compound was accompanied by a 2%-3% weight gain, which was consistent with an oxidation reaction. The conditions of oxygen fugacity and temperature leading to decomposition, and the resulting decomposition products, are compared for the (Bi,Pb)₂Sr₂Ca₂Cu₂O_10±δ-type and Bi₂Sr₂Ca₁Cu₂O_8±Ψ-type compounds.     

Preparation of BaTi4O9 from Oxalates

A barium titanate precursor with a barium:titanium ratio of 1:4 was prepared by controlled coprecipitation of mixed barium and titanium species with an ammonium oxalate aqueous solution at pH 7. The results of thermal analysis and IR measurement show that the obtained precursor is a mixture of BaC₂O₄·0.5H₂O and TiO(OH)₂·1.5H₂O in a molar ratio of 1:4. Crystallized BaTi₄O₉ was obtained by the thermal decomposition of a precipitate precursor at 1300°C for 2 h in air. The dimensions of the powder calcined at 1000°C are between 100 and 300 nm. The grain dimensions of the sintered sample for 2 h at 1300°C are of the order of 10 to 30 μm. Dielectric properties of disk-shaped sintered specimens in the microwave frequency region were measured using the TE₀₁₁ mode. Excellent microwave characteristics for BaTi₄O₉—ɛ= 38 ± 0.5, Q = 3800–4000 at 6–7 GHz and τ _f = 11 ± 0.7 ppm/°C—were found.     

High-Pressure Sintering of Nanocrystalline γAl2O3

High-pressure sintering of nanocrystalline γ-A1₂O₃ has been studied over a temperature range of 923-1323 K and at a pressure of 1 GPa. The γ-Al₂O₃ to α-Al₂O₃ transformation temperature changed from 1473 K without pressure to ∼1023 K at 1 GPa. Full density was obtained at 1273 and 1323 K in 10 min. The microhardness value of fully dense α-alumina with a grain size of 142 nm was found to be 25.3 ± 0.8 GPa. The Hall-Petch slope for the very fine grain size range is different from that of the coarse-grained alumina.     

Slow Crack Growth Behavior in Transformation-Toughened Al2O3-ZrO2(Y2O3) Ceramics

Significant increases in the critical fracture toughness (K _IC ) over that of alumina are obtained by the stress-induced phase transformation in partially stabilized ZrO₂ particles which are dispersed in alumina. More importantly, improved slow crack growth resistance is observed in the alumina ceramics containing partially stabilized ZrO₂ particles when the stress-induced phase transformation occurs. Thus, increasing the contribution of the ZrO₂ phase transformation by tailoring the Y₂O₃ stabilizer content not only increases the critical fracture toughness (K_IC) but also the K _Ia to initiate slow crack growth. For example, crack velocities ( v )≥10^–9 m/s are obtained only at K _Ia≥5 MPa.m^1/2 in transformation-toughened ( K _IC=8.5 MPa.m^1/2) composites vs K _Ia≥2.7 MPa.m^1/2 for comparable velocities in composites where the transformation does not occur ( K _IC=4.5 MPa.m^1/2). This behavior is a result of crack-tip shielding by the dissipation of strain energy in the transformation zone surrounding the crack. The stress corrosion parameter n is lower and A greater in these fine-grained composite materials than in fine-grained aluminas. This is a result of the residual tensile stresses associated with larger (≥1 μm) monoclinic ZrO₂ particles which reside along the intergranular crack path.     

Indirect Dissolution of (Al, Cr)2O3 in CaO—MgO—Al2O3—SiO2 (CMAS) Melts

The dissolution of (Al, Cr)₂O₃ into CaO—MgO—Al₂O₃—SiO₂ melts, under static and forced-convective conditions was investigated at 1550°C in air. With sufficient MgO in the melt, or sufficient Cr₂O₃ in (Al, Cr)₂O₃, a layer consisting of a spinel solid solution, Mg(Al, Cr)₂O₄, formed at the (Al, Cr)₂O₃/melt interface. The dissolution kinetics of 1.5 and 10 wt% Cr₂O₃ specimens were determined as a function of immersion time, specimen rotation rate, and magnesia content of the melt. Electron microprobe analysis was used to characterize concentration gradients in the (Al, Cr)₂O₃ sample, the Mg(Al, Cr)₂O₄ spinel, or in the melt after immersion of specimens containing 1.5 to 78 mol% Cr₂O₃. The dissolution kinetics and microprobe analyses indicated that a steady-state condition was reached during forced-convective, indirect (Al, Cr)₂O₃ dissolution such that spinel layer formation was rate limited by solid-state diffusion through the spinel layer and/or through the specimen, and spinel layer dissolution was rate limited by liquid-phase diffusion through a boundary layer in the melt. This is consistent with a model previously developed for the indirect dissolution of sapphire in CMAS melts.     

Preparation of Gadolinium Gallium Garnet [Gd3Ga5O12] by Solid-State Reaction of the Oxides

We have prepared dense polycrystalline gadolinium gallium garnet (GGG) by solid-state reaction of the oxides. The oxides were prereacted at 1350°C, ground, pressed, and sintered at 1650°C, yielding 97% dense samples. Ga₂O₃ evaporated from the sample surface leaving Gd₄Ga₂O₉ that could spall off the sample. For the short times needed to sinter samples, the bulk composition of the material remained essentially constant. The microhardness of the GGG was 11.8 ± 1.2 GN · m⁻².     

Constant-K1 Double-Cantilever-Beam Test for Ceramic Materials

A constant- K ₁, double-cantilever-beam (DCB) test is described wherein a computer is used to adjust the load continuously as crack growth occurs. DCB samples of float glass were used to experimentally verify the procedure.