Constrained Densification of Alumina/Zirconia Hybrid Laminates, II: Viscoelastic Stress Computation

To analyze the inhibited densification during sintering and differential shrinkage during cooling of Al₂O₃/ZrO₂symmetric and asymmetric laminates, viscoelastic formulations, in which the viscosity and elastic modulus vary with time, have been developed. The viscoelastic mismatch stresses have been numerically computed over the entire processing cycle, including the heating period, the isothermal period, and the cooling period. The viscosity and free sintering rates that are needed for stress computation have been obtained by modifying the parameters that are measured for a normal isotropic densifying compact using cyclic loading dilatometry. The modification is based on the available sintering models to account for the effect of strain history on compact viscosity and sintering rates. The stress calculation shows that, with the exception of the initial heating period, the viscoelastic stress is identical to the viscous stress that is calculated solely from the strain rate mismatch. Sintering damage in the laminates is shown to occur during densification under conditions where the differential sintering stress is smaller than the intrinsic sintering pressure. The magnitude of residual stress in hybrid laminates on cooling is dependent on the cooling rate, and slower cooling rates are capable of almost completely relaxing the expansion mismatch stress at temperatures of >1200°C.     

Viscous Flow as the Driving Force for the Densification of Low-Temperature Co-Fired Ceramics

Filled glass–ceramic composites, like low-temperature co-fired ceramics (LTCC), must densify at temperatures <900°C. The densification mechanism of LTCC is often described by liquid-phase sintering. The results of this paper clearly show that densification of ceramic-filled glass–composites with a glass content above 60 wt% can be attributed to viscous sintering, which is decisively controlled by the viscosity of the glass during the heat treatment. This is demonstrated by the experimental determination of the viscosity of a MgO–Al₂O₃–B₂O₃–SiO₂ glass dependent on temperature, by investigation of the wetting behavior of the glass on the ceramic filler mullite, and of the microstructural development. It was found that the glass does not wet the filler material in a temperature range up to 1000°C. Therefore, liquid-phase sintering can be excluded. Independent of any wetting effect and therefore in the absence of capillary forces, densification starts at a temperature of 750°C, which corresponds to a viscosity of 10^9.5 dPa·s. This densification can be attributed to viscous flow of the glass matrix composite.     

Effect of Rigid Inclusions on the Densification and Constitutive Parameters of Liquid-Phase-Sintered YBa2Cu3O6+x Powder Compacts

The presence of rigid inclusions in a powder compact leads to a reduction in the densification rate of the compact and may also lead to processing defects. In this paper, the densification rate and the constitutive parameters of both homogeneous YBa₂Cu₃O_{6+ x} and composite powder compacts (YBa₂Cu₃O_{6+ x} powder with 10 vol% dense inclusions of YBa₂Cu₃O_{6+ x} ) are reported. A small amount of liquid phase, which formed during sintering, was present in the samples. However, even with the presence of a liquid phase, the addition of inclusions still reduces the densification rate of the composite and increases its viscosity. The results have been compared with a published analysis of the problem using measured values of the constitutive parameters. Both the viscosity and viscous Poisson's ratio of the porous body have been measured.     

Liquid-Phase Sintering of MgO–Bi2O3

Liquid-phase sintering of MgO-5 wt% Bi₂O₃ was studied by loading dilatometry. The ratio of the creep viscosity to the densification viscosity (∼1.8) and the sintering stress remained nearly constant in a wide density interval. These results, together with results on several other systems, indicate that the constancy of the sintering stress during densification may be a general phenomenon, regardless of densification mechanism.     

Effect of Green Density on the Subsequent Densification and Grain Growth of Ultrafine SnO2 Powder during Isochronal Sintering

An ultrafine powder of SnO₂ has been synthesized by a gas flow condensation method. The average particle size of the powder was about 40 nm. The effect of the green density on the subsequent densification and grain growth of the ultrafine SnO₂ during sintering has been studied. A loose green compact consolidated under 500 MPa (green MC) showed rapid densification as well as rapid grain growth at relatively low sintering temperatures. A dense green compact fabricated under 4.5 GPa (green GC) exhibited a slow increase in the density and almost no grain growth even at high sintering temperatures.     

Effect of Crystallization on the Stress Required for Constrained Sintering of CaO–B2O3–SiO2 Glass–Ceramics

The effect of crystallization on the stress required for complete constrained sintering of a low-temperature cofirable CaO–B₂O₃–SiO₂ glass–ceramics has been investigated under uniaxial constant and cyclic loading. As the formation of crystalline phase of wollastonite (CaSiO₃) increases, the uniaxial viscosity of the porous glass–ceramics during firing increases. Moreover, the required uniaxial stress to have complete constrained sintering, i.e., zero strain or strain rate at the perpendicular directions, is in the range of 80–180 kPa, which shows no significant dependence on heating rate and firing temperature. The measured data of required stress are close to those calculated using the viscous analogy for the constitutive relationship of a porous sintering compact.     

The Effect of Applied Stress on the Densification of a Low-Temperature Cofired Ceramic-Filled Glass System Under Constrained Sintering

The effect of uniaxial stress on the mechanical response and densification behavior of a low-fire borosilicate glass (BSG)+alumina system during constrained sintering of a multilayer BSG+alumina/alumina laminate has been investigated. Compared with free sintering, the pressure-less constrained sintering of BSG+alumina exhibits poorer densification, and larger porous bulk viscosity at a given temperature. This is caused by the in-plane tensile stress and anisotropic development generated in the transverse directions of the laminate during constrained sintering. The applied uniaxial stress required in the thickness direction to densify BSG+alumina under constrained sintering varies in the range of 50–400 kPa at 700°–800°C. The above results are in agreement with those calculated using the viscous analogy for the constitutive relationships of a porous sintering compact.     

Sintering Kinetics at Constant Rates of Heating: Effect of Al2O3 on the Initial Sintering Stage of Fine Zirconia Powder

The sinterabilities of fine zirconia powders including 5 mass% Y₂O₃ were investigated, with emphasis on the effect of Al₂O₃ at the initial sintering stage. The shrinkage of powder compact was measured under constant rates of heating (CRH). The powder compact including a small amount of Al₂O₃ increased the densification rate with elevating temperature. The activation energies at the initial stage of sintering were determined by analyzing the densification curves. The activation energy of powder compact including Al₂O₃ was lower than that of a powder compact without Al₂O₃. The diffusion mechanisms at the initial sintering stage were determined using the new analytical equation applied for CRH techniques. This analysis exhibited that Al₂O₃ included in a powder compact changed the diffusion mechanism from grain boundary to volume diffusions (VD). Therefore, it is concluded that the effect of Al₂O₃ enhanced the densification rate because of decrease in the activation energy of VD at the initial sintering stage.     

Reaction Sintering of ZnO-AI2O3

The reaction sintering of equimolar mixtures of ZnO and A1₂O₃ powders was investigated as a function of primary processing parameters such as the temperature, heating rate, green density, and particle size. The powder mixtures were prepared by two different methods. In one method, the ZnO and A1₂O₃ powders were ball-milled. In the other method, the ZnO powder was chemically precipitated onto the A1₂O₃ particles dispersed in a solution of zinc chloride. The sintering characteristics of the compacted powders prepared by each method were compared with those for a prereacted, single-phase powder of zinc aluminate, ZnAl₂O₄. The chemical reaction between ZnO and A1₂O₃ occurred prior to densification of the powder compact and was accompanied by fairly large expansion. The mixing procedure had a significant effect on the densification rate during reaction sintering. The densification rate of the compact formed from the ball-milled powder was strongly inhibited compared to that for the single-phase ZnAl₂O₄ powder. However, the densification rate of the compact formed from the chemically precipitated mixture was almost identical to that for the ZnAl₂O₄ powder. The difference in sintering between the ball-milled mixture and the chemically precipitated mixture is interpreted in terms of differences in the microstructural uniformity of the initial powder compacts resulting from the different preparation procedures.     

Plastic Flow During Hot-Pressing

The contribution of plastic flow to overall densification of a powder compact during hot-pressing was analyzed by incorporating the creep characteristics of materials at high temperatures into an equation applicable to hot-pressing conditions. When the particles are assumed to be spherical and when the effective stress acting at the points of contact under axial loading conditions is taken into consideration, the final form of the equation is: where α₁ and β are geometric constants which can be calculated from the packing geometry, A and n are material constants, D is the relative density of the compact, and R is the radius of the spheres at any stage of deformation in arbitrary units. Computerized plots of D vs t were obtained for several materials. Experimental verification of these plots using hot-pressing data for Pb-2% Sb, Ni, and Al₂O₃ spheres and coarse irregular Al₂O₃ particles showed that the experimental data fitted the theoretical prediction for orthorhombic packing well. A large deviation with respect to the initial packing density was encountered with very fine irregular Al₂O₃ powder, although its densification behavior with time was similar to that of the coarse particles.     

Constitutive modeling of the behaviour of cermet compacts during reaction sintering

This study deals with the identification of a constitutive equation describing the mechanical behaviour of a nickel ferrite based cermet during sintering. This constitutive equation considers the material as a continuum and may enable one to predict the densification behaviour of a powder under different thermal treatments and the impact of compact geometry, external loading on strain and stress generation. A classical viscous equation of the Newtonian type that includes a term describing free sintering densification has been chosen. The method used for the identification of the parameters of this equation is the one proposed Gillia et al., which is based on dilatometry measurement. It includes a stairway thermal cycle for the determination of the free sintering term and intermittent loading for estimating the viscosity. This approach has been successfully applied to nickel ferrite cermet. The model has been found to be adequate to model the densification behaviour up to 1250 °C, but experimental and theoretical efforts must be accomplished to describe the behaviour above this temperature, when the material exhibits swelling.     

Retrograde Densification in Bi2Sr2CaCu2O8 Superconductors

Bi₂Sr₂CaCu₂O₈ was prepared using the mixed oxide-carbonate method and sintered at temperatures ranging from 850° to 911°C. The samples were characterized for density, mechanical strength, phase composition, microstructure, and superconducting transition temperatures. A unique retrograde densification characteristic is demonstrated in the temperature range 850° to 890°C whereby the material first becomes less dense as the sintering temperature is raised, and only in a narrow temperature range from 900° to 905°C does the material densify then with the formation of a liquid phase. The retrograde densification mechanism is shown to be that of the formation of thin platelike crystallites which grow in a randomly oriented fashion, thus pushing the structure apart. This retrograde densification, coupled with a narrow sintering range overlapping the melting temperature, makes this compound a difficult one to process.     

Influence of Low-Temperature Co-Fired Ceramics Green Tape Characteristics on Shrinkage Behavior

To establish a better understanding of the complex densification and shrinkage processes of low-temperature co-fired ceramics (LTCC) and to improve the dimensional control in the manufacture of LTCC multilayer devices, the influence of glass, composite, and microstructural green tape characteristics on the densification and shrinkage behavior of LTCC materials, with special focus on the development of anisotropy, was investigated. To study the influence of these factors, a commercial LTCC system was analyzed regarding chemical and microstructural composition as well as sintering behavior. The results of the analysis showed that the commercial LTCC system is composed of alumina as a ceramic filler and a CaO–SiO₂–B₂O₃–Al₂O₃ glass. Based on these results, a similar glass was produced. To understand the mechanisms of densification, its wetting behavior and viscosity as a function of temperature were investigated. As developed glass was mixed with an alumina powder and milled down to average grain sizes of 1, 2, and 3 μm, respectively. From these composite powders, slurries were prepared and tape cast. The sintering kinetics including onset temperature, development of viscous flow as well as phase development of both commercial and internally developed LTCC tapes LTCC tapes in relation to their modified composition and green tape structures were analyzed in situ by means of optical dilatometry, thermo-mechanical analysis (TMA), and high-temperature-X-ray diffraction. The viscous behavior of the glass-filler composites was determined by means of cyclic dilatometry in a TMA device.     

Synthesis and Sintering of Cerium(II) Monosulfide

Cerium monosulfide (CeS) powder was synthesized by the reduction of Ce₂S₃ powder with metallic Ce, which was obtained from ceria (CeO₂) powder using carbon disulfide (CS₂) gas. To obtain the maximum amount of CeS from a mixture of Ce₂S₃ and Ce, an excess amount of metallic Ce, a stoichiometric composition, was necessary in the synthesis at 1273 K for 10.8 ks. The preliminary sintering experiments also were performed using a synthetic CeS powder containing a small amount of Ce, Ce₂O₂S, and β-Ce₂S₃ as impurities. It was found that the oxygen content in the sintered compact decreases gradually as the sintering temperature increases, because of the removal of the impurities due to the evaporation of the volatile CeO. Single-phase CeS was formed by sintering at 2173 K. To evaluate the activation energy for densification of single-phase CeS, a CeS powder was prepared by milling an initial sintered compact and was used as an ingredient for hot-press experiments. Densification data during hot-press sintering were analyzed using a kinetic equation, showing that boundary diffusion is a rate-limiting process. The results suggest that this boundary diffusion model can explain well the densification data, with an apparent activation energy of 479 kJ·mol^-1.     

Sintering of Nanophase γ-Al2O3 Powder

The sintering of ultrafine γ-Al₂O₃ powder (particle size ∼10–20 nm) prepared by an inert gas condensation technique was investigated in air at a constant heating rate of 10°C/min. Qualitatively, the kinetics followed those of transition aluminas prepared by other methods. Measurable shrinkage commenced at ∼ 1000°C and showed a region of rapid sintering between ∼1125° and 1175°C followed by a transition to a much reduced sintering rate at higher temperatures. Starting from an initial density of ∼0.60 relative to the theoretical value, the powder compact reached a relative density of 0.82 after sintering to 1350°C. Compared to compacts prepared from the as-received powder, dispersion of the powder in water prior to compaction produced a drastic change in the microstructural evolution and a significant reduction in the densification rate during sintering. The incorporation of a step involving the rapid heating of the loose powder to ∼1300°C prior to compaction (which resulted in the transformation to α-Al₂O₃) provided a method for significantly increasing the density during sintering.     

Microstructure and Short-Term Oxidation of Hot-Pressed Si3N4/ZrO2(+Y2O3) Ceramics

Composite ceramic materials based on Si₃N₄ and ZrO₂ stabilized by 3 mol% Y₂O₃ have been formed using aluminum isopropoxide as a precursor for the Al₂O₃ sintering aid. Densification was carred out by hot-pressing at temperatures in the range 1650° to 1800°C, and the resulting micro-structures were related to mechanical properties as well as to oxidation behavior at 1200°C. Densification at the higher temperatures resulted in a fibrous morphology of the Si₃N₄ matrix with consequent high room-temperature toughness and strength. Decomposition of the ZrO₂ grains below the oxidized surface during oxidation introduced radial stresses in the subscalar region, and from the oxidation experiments it is suggested that the ZrO₂ incorporated some N during densification.     

Bending Creep Test to Measure the Viscosity of Porous Materials during Sintering

A bending creep test is proposed for measuring the change in viscosity of a porous material during densification. Equations, based on simple beam deflection theory, were derived to obtain the viscosity from a series of loading experiments using rectangular samples of different densities. By measuring the deflection in the center of the specimen between the spans, the viscosity of a porous material during densification can be measured. Experiments with porous Y₂O₃-stabilized ZrO₂ beams were used to illustrate the bending creep test. Consistent with theory the viscosity increased from 50 to 400 GPa·s as the sample densified from 87% to 98% density. The rapid increase in viscosity was considered to be a result of both densification and grain growth.     

Magnetic Properties of Nickel–Zinc Ferrite Toroids Prepared from Nanoparticles

Toroids comprised of silica-coated 10 nm diameter nickel–zinc (Ni–Fe) ferrite nanoparticles (Ni_0.5Zn_0.5Fe₂O₄) have been fabricated by careful control of both the coating process and subsequent densification by viscous sintering. A narrow processing window is identified between a maximum temperature at which the nanoparticles coarsen, losing their super-paramagnetic properties, and a lower temperature required for viscous flow densification. Key to the successful fabrication was drying and cold isostatic pressing of the silica-coated nanoparticles; other routes invariably led to cracking during either drying or sintering. The super-paramagnetic blocking temperature, the coercive field, and remanent magnetization could all be controlled over a wide range by varying the thickness of the silica coating from 1 to 15 nm. The dipole–dipole coupling distance is estimated to be 4 nm. The high-frequency (1–500 MHz) properties were sensitive to the sintering temperature as well as the thickness of the silica coating. Toroids sintered at 1000°C or less exhibited no high-frequency magnetic losses and their permeability decreased with increasing temperature, suggesting that the permeability was controlled by thermally activated magnetization relaxation.     

Sintering of Spherical Glass Powder under a Uniaxial Stress

The sintering of spherical borosilicate glass powder (particle size 5 to 10 μm) under a uniaxial stress was studied at 800°C. The experiments allowed the measurement of the kinetics of densification and creep, the viscosities for creep and bulk deformation, and the sintering stress which was found to increase with density. The data show excellent qualitative agreement with Scherer's theory of viscous sintering. In addition, the quantitative comparison between theory and experiment shows good agreement; the measured viscosity of the bulk glass was ∽1×10⁹ P (∽1×10⁸ Pa·s) compared to ∽3×10⁹ P (∽3 Pa·s) obtained by fitting the data with Scherer's theory.     

Initial Coarsening and Microstructural Evolution of Fast-Fired and MgO-Doped Al2O3

The effect of an initial coarsening step (50-200 h at 800°C) on the subsequent densification and microstructural evolution of high–quality compacts of undoped and MgO–doped Al₂O₃ has been investigated during fast–firing (5 min at 1750°C) and during constant–heating–rate sintering (4°C/min to 1450°C). In constant–heating–rate sintering of both the undoped and MgO–doped Al₂O₃, a refinement of the microstructure has been achieved for the compact subjected to the coarsening step. A combination of the coarsening step and MgO doping produces the most significant refinement of the microstructure. In fast–firing of the MgO–doped Al₂O₃, the coarsening step produces a measurable increase in the density and a small refinement of the grain size, when compared with similar compacts fast–fired conventionally (i.e., without the coarsening step). This result indicates that the accepted view of the deleterious role of coarsening in the sintering of real powder compacts must be reexamined. Although extensive coarsening after the onset of densification must be reduced for the achievement of high density, limited coarsening prior to densification is beneficial for subsequent sintering.