Constrained Sintering of Silver Circuit Paste

Densification kinetics and stress development during constrained sintering of a silver film on a rigid silicon substrate have been studied. Compared with free sintering, the sintering of constrained silver film exhibits a much lower densification and slower densification kinetics. The densification-controlled mechanism changes from fast grain-boundary diffusion kinetics for free sintering to slow lattice diffusion kinetics for constrained sintering. The in-plane tensile stress developed during constrained sintering of silver film, measured using a noncontact laser-scanning optical system, increases rapidly to a maximum level of 1.0–1.5 MPa initially, gradually decreases, and then becomes constant at 0.8–1.0 MPa. The maximum stress observed increases with increasing sintering temperature as a result of the faster densification rate. It is believed that the retardation of densification kinetics of constrained silver film is caused by a change in densification mechanism and the existence of in-plane tensile stress.     

Constrained Densification Kinetics of Alumina/Borosilicate Glass + Alumina/Alumina Sandwich Structure

The densification kinetics and mechanism of a low-temperature cofirable borosilicate glass (BSG) + alumina during the constrained sintering of a sandwich structure of alumina/(BSG + alumina)/alumina has been studied. The densification kinetics becomes slower when the BSG + alumina tape is constrained during firing. However, a viscous flow-controlling mechanism of the BSG also is still operative during free and constrained sintering. The densification behavior of constrained sintering can be mathematically described by free sintering, using the viscous analogy for the constitutive equations of a porous sintering glass.     

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.     

Effect of Mismatched Sintering Kinetics on Camber in a Low-Temperature Cofired Ceramic Package

Linear shrinkage profiles of an unconstrained gold thick film material and a low -tempearture cofireable glass-ceramic (LTCC) green tape were measured using a noncontact optical technique. A laser beam scans across a sample, at various times during the sintering process. The unconstrained sintering kinetics of the gold film were found to differ significantly from those of the LTCC tape. The densification of the gold film was nearly completed before the LTCC began to densify. The development of camber (warpage) during consintering of a gold/LTCC composite structure was monitored and recorded with a video camera. This camber development is analysed based on the viscous constitutive relations for porous based on the viscous constitutive relations for porous sintering bodies. The mismatched sintering kinetics of the two materials lead to the development of in-plane stresses in the two constituents of the composite structure as one material being constrained from composite structure as one material being constrained of the composite structure as one material being constrained from sintering by the other. The resulting camber during the consintering process is explained by the development of these stresses.     

Viscous Sintering of a Bimodal Pore-Size Distribution

The cylinder model, used previously to analyze the viscous sintering of flame hydrolysis preforms and gels, is shown to be consistent with other models of early- and late-stage sintering. The model is then applied to a bimodal pore-size distribution in which the different shrinkage rates of small and large pores produce local stresses. The effect of these stresses on the sintering rate is determined and shown to be substantial. Initially, the small pores accelerate the densification of the large pores; later, shrinkage of the isolated large pores is resisted by the sintered remains of the small pores. Consequently, the time to reach full density is nearly independent of the initial volume fraction of small pores.     

Stresses Induced by Differential Sintering in Powder Compacts

Stresses created by differential sintering, due to differences in initial bulk density, were determined, to an order of magnitude, by an experiment which estimated the differential sintering phenomenon on a macroscopic level. The experiments entailed determining the shrinkage rates of a powder isostatically pressed to two bulk densities. Using this information, stresses were determined by forcing the slower-densifying compact to shrink at the same rate as the faster-densifying compact and measuring the resulting forces with a load cell. Maximum stresses (between 1 and 3 MPa) were observed to occur in the intermediate stage of densification. Despite larger differential strains at higher temperatures, stresses decreased to zero at the latter stage of densification. Viscoelastic experiments, of the stress-relaxation type, were performed. Results showed that the sintering specimen was more rigid at lower temperatures and more fluidlike at higher temperatures. This explains the development of maximum stresses at intermediate temperatures.     

Liquid Phase Sintering of Alumina, I. Microstructure Evolution and Densification

The microstructure evolution and densification of alumina containing 10 vol% calcium aluminosilicate glass and 0.5 wt% magnesium oxide sintered at 1600°C were quantified by measuring the evolution of pore-size distribution, the redistribution of liquid phase, and the fraction of closed and open pores. The densification stopped at a limiting relative density during the final stage of sintering, and the small and large pores were filled simultaneously by glass during sintering. In addition, the results indicate that the pressure build-up of the trapped gases in pores causes a significantly negative contribution to the driving force, and consequently the observed reduction in densification during the final stage of liquid phase sintering.     

Constrained sintering kinetics of 3YSZ films

3YSZ green layers approximately 10 μm thick were screen-printed onto 3YSZ substrates and their constrained sintering kinetics were measured at 1100-1350 °C using an optical dilatometer. The densification rates of the same powder in the form of pellets and free-standing films were also measured. The constrained densification rate was greatly retarded compared with the free densification rate at a given temperature and density. The retardation increased with increasing density and temperature and could not be properly accounted for by existing theories of constrained sintering. As a result the apparent activation energy is much lower for constrained sintering (135 ± 20 kJ mol⁻¹) than for free sintering (660 ± 30 kJ mol⁻¹). It is proposed that this is because the constrained microstructure exhibits larger and more widely separated pores at the higher temperatures.     

Sintering Behavior of Ceramic Films Constrained by a Rigid Substrate

A model is presented in which the sintering behavior of a ceramic film which is constrained by a rigid substrate is contrasted with the sintering behavior of a free film. The problem is made simple by the assumption that the stress field developed in the film is uniform. This simplification allows several closed form solutions to be obtained. The solutions give new insights into the sintering behavior of films supported on a substrate. It is found (1) that the shear rate of the film is more important in the sintering process than its densification rate when the film is constrained by a substrate, (2) that the incompatibility stress is time dependent and reaches its maximum value during the initial stages of sintering, (3) that the magnitude of that maximum stress may be tensile or it may be compressive depending on the shear response of the material, and (4) that if the incompatibility stress is tensile it can lead to the formation of cracks or defects in the ceramic film.     

Effect of sintering temperature on functional properties of alumina membranes

Supported membranes were prepared from different submicron alumina powders. The evolution of pore size, hardness and permeability were monitored after sintering the films at temperatures ranging from 1000 to 1400 °C. These functional properties and the microstructure of the films were compared with the free-standing membranes. Sintering at temperature range from 1000 to 1200 °C maintained the narrow, monomodal pore size distribution of the supported membranes. The effect of sintering temperature on the hardness of the membranes was weak. The permeability was also independent on the sintering temperature. When sintering temperature was raised up to 1300 and 1400 °C, the pore size increased significantly and distribution was changed to bimodal containing fraction of large pores. The hardness of the membranes increased while significant densification was not observed. Permeability increased due to the large pore size and the high porosity. In sintering of the free-standing membranes pore size remained almost unchanged, density increased when sintering temperature was raised, hardness was dependent on the density and permeability decreased continuously. The substrate did not have effect on the grain growth, which was dependent on the sintering temperature. Evolution of the properties of the free-standing membranes suggests local densification. The rigid substrate restricts the sintering shrinkage leading to densification of small areas. This local densification opens large flow channels between agglomerates. This increases the pore size, broadens the pore size distribution and increases the permeability. The macroscopic densification of the film is small.     

Influence of thickness on the constrained sintering of alumina films

Alumina films prepared by tape casting were sintered freely and under geometrical constraint at 1350 °C. The effect of film thickness on sintering kinetics and microstructure development was investigated. A decrease in film thickness in the constrained case leads to enhanced retardation of densification and increased orientation of anisometric pores.     

Creep-Sintering and Microstructure Development of Heterogeneous MgO Compacts

Simultaneous creep and densification and the microstructure development of magnesium oxide powder compacts were studied at 125°C and for applied stresses of up to 0.25 MPa. Die-pressing the powder into compacts with a relative green density of ∼0.40 led to an approximately bimodal distribution of pores, with one fraction having sizes of the order of 10 times the (initial) particle size and the other fraction having pore sizes of the order of the particle size. The presence of the large pores in turn gave rise to rather unusual sintering effects. After first decreasing with relative density (ρ), the densification rate (dρ/dt) and the creep rate (dɛ/dt) then increased dramatically for 0.6 < ρ < 0.75. This range of ρ corresponded to the stage of microstructure development when grain growth and coalescence of the smaller pores have created a more uniform pore distribution. Above ρ∼ 0.75, both dρ/dt and dɛ/dt again decreased with ρ. These trends in the densification behavior are discussed in terms of material parameters such as the equilibrium dihedral angle and the pore coordination number.     

Simulation of densification behavior of nano-powder in final sintering stage: Effect of pore-size distribution

In the final sintering stage, nano-sized powder frequently forms a pore structure where most pores are surrounded by more than 5 grains. The pore structure is different from that of coarse powder. In this study, the densification behavior of nano-sized powder is modelled and simulated in the final sintering stage. The porous body has the initial size distribution of pores, represented as a Weibull function. The mechanical interaction between pores is analyzed to simulate the evolution of porosity characteristics as well as densification kinetics. The densification rate for the size-distributed pores is lower than that for single-sized ones. The experimental relationship between the densification rate and the porosity could well be reproduced by choosing appropriate pore-size distributions. The simulation also shows that the sintering stress with densification may increase or decrease depending on the size distribution, but is remarkably lower than that for single-sized pores.     

Hot-Pressing Alumina—Mechanisms of Material Transport

The effect of load on initial neck growth between alumina single-crystal spheres has been measured at 1530°C. The neck areas are larger than those observed in pressureless sintering and constant for all times between 10 and 480 minutes. The neck areas are proportional to the loads; i.e. they equilibrate at equal stresses (50,000 psi). It is shown quantitatively that the initial enhanced neck growth observed cannot be attributed to enhanced sintering by diffusion under the influence of stress. The plastic flow contribution to densification during hot-pressing is calculated from the stress inferred from the foregoing measurements, from the applied load in hot-pressing, and from geometric relations between particles. It is shown that for aluminum oxide the contribution of plastic flow to densification at the pressures normally used in hot-pressing is small. It is concluded that the final stage of densification of alumina during hot-pressing occurs by enhanced diffusion under the influence of stress.     

Stress Required to Densify a Low-Fire NiCuZn Ferrite Under Constrained Sintering

The effect of uniaxial stress on the densification behavior of a low-fire NiCuZn ferrite during constrained sintering of a multilayer structure of a ferrite tape and a pure alumina tape has been investigated. Compared with free sintering, the densification of ferrite becomes significantly reduced and slowed down under pressure-less constrained sintering. To enhance the constrained densification of ferrite in the temperature range required for free sintering, uniaxial stress applied in the thickness direction is needed. The required uniaxial stress to densify ferrite under constrained sintering to reach a relative sintered density of >95% decreases from 1100–1300 kPa at 900°C to 250–450 kPa at 1000°C. Moreover, no significant grain growth is found when the ferrite is densified under pressure-assisted constrained sintering.     

3D model for powder compact densification in rotational molding

During rotational molding, a loosely packed, low‐density powder compact transforms into a fully densified polymer part. This transformation is a consequence of particles sintering. Powder compact density evolution of the polymer powder is measured experimentally. Obtained results show that the powder densification process consists of two stages, and its mechanism during these two stages is not the same. During the first stage, densification occurs by grains coalescence, and air between the grains escape by open pores between particles. These open pores close in time by particles coalescence progress, and remaining air entrapped in polymer melt becomes air bubbles. Surface tension, viscosity, grains size, and temperature are the controlling parameters during first stage. A three‐dimensional model is proposed for the densification of polymer powder during first stage. Second stage starts after bubble forming. Diffusion is the controlling phenomena during this stage. A diffusion‐based model is used for the second stage of densification. By comparing with the other models, proposed model exhibits several advantages: it is proposed in three‐dimensional and takes into account the nature of layer‐by‐layer powder densification. Model verification by experimental data obtained for densification of two different polymers shows a close agreement between model prediction and experiments. POLYM. ENG. SCI., 52:2033–2040, 2012. © 2012 Society of Plastics Engineers     

Microstructural Development during Sintering of Lithium Fluoride

Measurements are reported of the influences of temperature, green density, and pore network breakup on the densification, grain growth, and pore volume distribution in LiF compacts. As long as most of the pore volume remained open to the compact perimeter, the ratio of the rate of densification to the rate of grain growth was higher than that sometimes reported for copper or typical oxides. Plots of the logarithm of densification rates versus sintered density for LiF are approximately linear during intermediate-stage sintering, like those for some oxides. But the plots for LiF are unlike those of the oxides in that, for LiF, densification rates measured at different temperatures converge near the density at which half the pore volume is isolated from Hg intrusion. Calculations suggest that further densification of the LiF compacts is blocked because air trapped in isolated pores becomes sufficiently compressed to balance the sintering stress.     

Kinetics and mechanisms for the densification and grain growth of the α-alumina fibers isothermally sintered at elevated temperatures

Understanding the densification and grain growth processes is essential for preparing dense alumina fibers with nanograins. In this study, the alumina fibers were prepared via isothermal sintering at 1200, 1300, 1400, and 1500 °C for 1–30 min. The phase, microstructure, and density of the sintered fibers were investigated using XRD, SEM, and Archimedes methods. It was found that the phase transformation during the isothermal sintering enhances the densification of Al₂O₃ fibers in the initial stage, while the pores generated during the phase transformation retard the densification in the later period. The kinetics and mechanisms for the densification and grain growth of the fibers were discussed based on the sintering and grain growth models. It was revealed that the densification process of the fibers sintered at 1500 °C is dominated by the lattice diffusion mechanism, while the samples sintered at 1200–1400 °C are dominated by the grain boundary diffusion mechanism. The grain growth of the Al₂O₃ fibers sintered at 1200–1300 °C is governed by surface-diffusion-controlled pore drag, and that sintered at 1400 °C is dominated by lattice-diffusion-controlled pore drag.     

Enhanced Densification of In2O3 Ceramics by Presintering with Low Pressure (5 MPa)

Sintering of In₂O₃ has been carried out in air to full density. Because of the difference in densification between the agglomerates and the matrix, large interagglomerate pores were observed to form at the initial stage of sintering. Such pore formation could be prevented by applying a small external pressure which resulted in the beneficial rearrangement of agglomerates.     

Constrained Sintering of a Low‐Fire,Polycrystalline Bi2(Zn1/3Nb2/3)2O7 Dielectric

The densification behavior of a low‐fire, polycrystalline Bi₂(Zn_1/3Nb_2/3)₂O₇ (BZN) dielectric under constrained sintering at 800°C–900°C is investigated. Although the constrained densification is retarded in relative to free sintering, a high sintered density of >95% is obtained at 900°C. No significant anisotropy with similar grain sizes is developed under free and constrained sintering. The densification behavior and stress development during constrained sintering of BZN is thus analyzed by using the well‐known isotropic constitutive laws.