Effect of Pore Distribution on Microstructure Development: III, Model Experiments

Model experiments have been conducted on a series of alumina samples in which the microstructures have been tailored to conform to the classical configuratins depicted in the models of final-stage sintering. Simultaneous measurements of sintered density, grain size, pore number density, and pore size distribution were made as a function of sintering time at constant temperature (1850°C). The data supported a model of grain-boundary-diffusion-controlled densification and surface-diffusion-controlled grain growth. An atom flux equation for grain-boundary diffusion transport was deduced from the data. The kinetics analysis highlights the importance of incorporating the number of pores per grain as an independent variable in mechanistic studies of final-stage sintering. The number of pores per unit volume was identified as a critical factor influencing densification kinetics. The effect of pore distribution on microstructure development was simulated for comparison with the data obtained from the model experiments.     

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.     

Influence of Atmosphere on the Final-Stage Sintering Kinetics of Ultra-High-Purity Alumina

The influence of sintering atmosphere on the final-stage sintering of ultra-high-purity alumina has been investigated. Model final-stage microstructures were tailored via a latex sphere impregnation and burnout technique. Critical experiments have been conducted to quantitatively examine the influence of the oxygen partial pressure on the final-stage sintering kinetics. Samples were sintered at 1850°C in either dry hydrogen ( P o₂∼ 3 × 10⁻¹⁷ atm) or wet hydrogen P o₂∼ 5 × 10⁻¹⁰ to 2 × 10⁻¹¹ atm), and their microstructures were characterized as a function of sintering time, Sintering in dry hydrogen decreased the susceptibility of the final-stage microstructure to pore/boundary breakaway. In the kinetic analysis, the variation in the number of pores per grain, N _g, was taken into account. It was found that in both atmospheres, the densification rate was controlled by grain boundary diffusion, and that sintering in dry hydrogen increased the densification rate by a factor of 2.25. In addition, it was determined that the grain growth rate in both atmospheres was controlled by the rate of surface diffusion of matter around the pores and that sintering in dry hydrogen enhanced the grain growth rate by a factor of 5.6. The overall effect of the dry hydrogen atmosphere was that it enhanced the coarsening rate relative to the densification rate by a factor of 2.5, and consequently shifted the grain size-density trajectory to much lower densities for a given grain size.     

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.     

Effect of Pore Distribution on Microstructure Development: II, First- and Second-Generation Pores

A sintering model has been developed to predict the consequences of independently varying the grain growth rate in alumina during final-stage sintering of a microstructure containing both small (first-generation) and large (inter-agglomerate second-generation) pores. The model shows that although it may be thermodynamically favorable to increase the grain growth rate, the kinetics of densification are such that it almost always pays to inhibit grain growth. This conclusion was verified by experiments on undoped, MgO-doped, and ZrO₂-doped alumina impregnated with model spherical large pores produced by the burnt-out latex sphere method. A new type of ceramic processing map has also been developed to aid in the selection of the optimum processing conditions for the sintering of ceramics containing large pores.     

固相烧结—Ⅰ气孔显微结构模型及其热力学稳定性,致密化方程

讨论了二维及三维闭口气孔的稳定性，发现二维状态时气孔的稳定性问题可以用数学方法根据气孔的颗粒配位数和二面角的大小解析；而三维状态时气孔则可借助球形气孔模型近似地确定。在这一模型的基础上，建立了烧结中期和后期的气孔显微结构模型，并由此推导了因相烧结中，后期作用于气孔的烧结应力和固相烧结中斯和后期的致密化方程。     

An Experimental Measurement of Effective Diffusion Distance for the Sintering of Ceramics

The traditional models of sintering predict a pronounced dependence of densification rate on the scale of the microstructure as measured by the grain size. This study evaluates the grain size exponent for densification during isothermal sintering of an aggregated nanocrystalline zirconia powder, and for a submicrometer alumina powder. The results gave grain size exponents that are much higher than those anticipated for the expected sintering mechanisms. Furthermore, microstructural analysis showed that this overestimate of the exponent could be due to the spatial heterogeneity in the microstructure on the scale of the diffusion distance. To assess this issue, pore boundary tessellation was used to determine a new measurement of effective diffusion distance that takes into account the local spatial arrangement of pores. This measurement gives exponents much closer to those expected for the sintering of tetragonal zirconia by volume diffusion, and for the sintering of the alumina by grain-boundary diffusion.     

Model for the Effect of Powder Packing on the Driving Force for Liquid-Phase Sintering

A model for liquid-phase sintering is presented that explicitly considers the effect that the pore size distribution of the sintering compact has on the capillary forces that drive densification. In particular, the effect that liquid redistribution in the pore structure has on the driving force for sintering is considered under the assumption that the liquid can easily move to find a low-energy configuration in the pore structure. It is shown that, for a powder compact that has a narrow pore size distribution, densification exhibits approximately the same time dependencies as those predicted by the Kingery model for liquid-phase sintering. However, systematic changes in the absolute densification rate with the volume fraction of liquid, and the mean and breadth of the pore size distribution, are predicted. With more extreme pore size distributions, such as a bimodal distribution, behavior significantly different from that predicted by Kingery is found. In particular, it is predicted that, without there being a change in sintering mechanism, abrupt changes in densification rate may occur if the peaks in the bimodal distribution are well separated. The model provides a rational basis for interpreting how powder packing and processing steps can influence densification by liquid-phase sintering.     

Densification and Shrinkage During Liquid-Phase Sintering

The process of densification and shrinkage during the final stage of liquid-phase sintering is described. The densification occurs by the liquid filling of pores during grain growth. The pore filling results in an instantaneous drop of liquid pressure in the compact and causes gradual accommodation of grain shape. The grain shape accommodation by the growth causes the specimen shrinkage. At the same time, the grains tend to restore their spherical shape, resulting in microstructure homogenization around filled pores. The process of densification and shrinkage appears to be determined by the growth of grains during sintering.     

Densification of Powder Compact Containing Large and Small Pores

A classical sintering theory predicts that a pore with high coordination number grows instead of shrinking during sintering. This has led to the proposition that grain growth may be beneficial to densification. Pan and colleagues argue against this theory using computer simulations, while Flinn and colleagues have provided direct experimental evidence showing that very large pores shrink despite their high coordination number. The current paper brings the analytical and experimental work together. In particular, further computer simulation evidence is provided to support the argument and an analytical model is developed to predict the densification rate of powder compacts containing large and small pores. The analytical model shows that there is a sudden reduction in the shrinking rate of the large pores when the small pores are eliminated.     

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.     

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.     

Sintering kinetics window: an approach to the densification process during the preparation of transparent alumina

In this work, sintering kinetics window combined with microstructure development is adopted to understand the densification process of transparent alumina ceramic using submicrometre alumina powder. Alumina powder was densified via pressureless sintering and spark plasma sintering to explore the sintering behaviours of submicrometre alumina powder respectively. Sintering process could be divided into three typical stages, the criterion of which is based on whether the dominant mechanism is independent particle rearrangement or independent atomic diffusion. Through the investigation of sintering mechanisms of both sintering methods in the same way, it is found that it is necessary to remove the large pores (>100 nm) before grain growth is activated for complete densification. It suggests that at the temperature when the grain growth is activated, the corresponding pore structure proves to be the crucial factor influencing the complete densification of transparent alumina ceramic.     

Effect of MgO Solute on Microstructure Development in Al2O3

The effect of MgO as a solid-solution additive in the sintering of Al₂O₃ was studied. The separate effects of the additive on densification and grain growth were assessed. Magnesia was found to increase the densification rate during sintering by a factor of 3 through a raising of the diffusion rate. The grain-size dependence of the densification rate indicated control primarily by grain-boundary diffusion. Magnesia also increased the grain growth rate during sintering by a factor of 2.5. The dependence of the grain growth rate on density and grain size suggested a mechanism of surface-diffusion-controlled pore drag. It was argued, therefore, that MgO enhanced grain growth by raising the surface diffusion coefficient. The effect of MgO on the densification rate/grain growth rate ratio was, therefore, found to be minimal and, consequently, MgO did not have a significant effect on the grain size/density trajectory during sintering. The role of MgO in the sintering of alumina was attributed mainly to its ability to lower the grain-boundary mobility.     

Theory of the Dependence of Densification on Grain Growth During Intermediate-Stage Sintering

A semiempirical model for intermediate-stage sintering is developed based on simultaneously occurring volume and grain-boundary diffusion mechanisms of mass transport and explicitly incorporating the effects of grain growth. The sintering equation derived depends strongly on the reduction of pore number density associated with grain growth and is independent of the mechanism of grain growth. The time and temperature dependencies of densification predicted by the equation, which are tested using data for metal and ceramic powders, agree well with observations. The data indicate that grain-boundary diffusion contributes negligibly to densification.     

The microstructural origin of rapid densification in 3YSZ during ultra-fast firing with or without an electric field

Recent research has shown that very rapid heating of 3YSZ powder compacts (ultra-fast firing), whether by passing an electric current through the sample (flash sintering) or by using external heat sources, causes a great acceleration of densification rate for a given relative density and temperature. Here, the microstructural evolution of 3YSZ is studied using four sintering methods with widely differing heating rates, produced with or without electric fields. The microstructural development depended greatly on thermal history. Most significantly, slow, conventional heating resulted in pores much larger than the grain size, whereas most pores were smaller than the grain size with the rapid heating methods, whether the heating involved an electric field or not. The smaller pore size clearly provides a major contribution to the acceleration of densification following rapid heating. In contrast, grain growth was not suppressed by rapid heating but was suppressed by an electric field.     

Novel model for the sintering of ceramics with bimodal pore size distributions: Application to the sintering of lime

A mathematical model for the sintering of ceramics with bimodal pore size distributions at intermediate and final stages is developed. It considers the simultaneous effects of coarsening by surface diffusion, and densification by grain boundary diffusion and lattice diffusion. This model involves population balances for the pores in different zones determined by each porosimetry peak, and is able to predict the evolution of pore size distribution function, surface area, and porosity over time. The model is experimentally validated for the sintering of lime and it is reliable in predicting the so called “initial induction period” in sintering, which is due to a decrease in intra‐aggregate porosity offset by an increase inter‐aggregate porosity. In addition, a novel methodology for determination of mechanisms based on the analysis of the pore size distribution function is proposed, and with this, it was demonstrated that lattice diffusion is the controlling mechanism in the CaO sintering. © 2016 American Institute of Chemical Engineers AIChE J, 63: 893–902, 2017     

Constrained Film Sintering of Nanocrystalline TiO2

The sintering of thin, nanocrystalline TiO₂ films either 140 or 65 nm thick is characterized and compared with the sintering of bulk material. Grain size, pore size distribution, and density data are obtained. Observation of the microstructural evolution during sintering suggests that grain growth, as well as pore growth, at low density can be attributed to differential sintering. A continuum mechanical model for the intermediate stage is useful until the grain size becomes one-half the film thickness. From then on, the ratio of grain size to film thickness affects the degree by which both densification and grain growth decrease, as compared with the continuum computation results.     

Useful Extensions of the statistical theory of sintering

The statistical theory of sintering is modified to account for the new concept of pore coordination number (after Lange) as well as other refinements of the original assumptions (after Kuczynski). When pores are located in the grain boundaries, the theory postulates that for a given dihedral angle, a critical pore coordination number, n_crmc, exists such that when n < n_c, pores shrink, whereas when n > n_c pores grow. A general morphological kinetic equation is developed for uniform microstructures with pores located at the grain boundaries. This equation provides for contributions of grain boundary and volume diffusion to densification and is unrestricted with respect to the type of firing schedule imposed. Using this modified model, one may evaluate the significant parameter x, a measure of ‘the path of microstructural evolution’. For reasonably uniform compacts, the equation also provides a quantitative estimate of the relative width of the pore size distribution, y, during the later stages of sintering.