Theoretical analysis of experimental densification kinetics in final sintering stage of nano-sized zirconia

The experimental densification kinetics of 7.8 mol% Y₂O₃-stabilized zirconia was analyzed theoretically during isothermal sintering in the final stage. By taking concurrent grain growth into account, a possible value of the grain-size exponent n was examined. The Coble’s corner-pore model recognized widely was found not to be applicable for explaining the densification kinetics. The corner-pore model of n = 4 shows a significant divergence in the kinetics at different temperatures. Microstructural observation shows that most pores are not located at grain corners and have a size comparable to the surrounding grains. The observed pore structure is similar to the diffusive model where single pore is surrounded by dense body. The diffusive model combined with theoretical sintering stress predicts n = 1 or n = 2, which shows a good consistence to the measured densification kinetics. During sintering of nano-sized powder, it is found that the densification kinetics can be explained distinctively by the diffusive single-pore model.     

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.     

Effect of Pore Distribution on Microstructure Development: I, Matrix Pores

A model has been developed to describe the effect of the matrix (first-generation) pore distribution on microstructure development in the final stages of sintering. A model of simultaneous densification and grain growth was used to predict the effects of the number of pores per grain and the pore size distribution on microstructure evolution. Increasing the number of pores per grain was predicted to increase the densification rate, the grain growth rate, and the relative densification rate/grain growth rate ratio. Narrowing the pore size distribution was predicted to inhibit grain growth initially and to increase the densification rate indirectly. Overall, the pore distribution was predicted to have a strong influence on microstructure development and sintering kinetics.     

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。     

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     

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.     

Sintering of Mullite-Containing Materials: II, Effect of Agglomeration

The sintering behavior of mullite powder compacts which contained soft and hard agglomerates was studied, The maximum density achieved depended on the size and packing of the agglomerates. Although the initial % total pore volume was kept constant, the presence of larger pores in the green compact, due to larger agglomerates, resulted in lower final densities after sintering. Densification rates were enhanced by the breakdown of agglomerates by grinding. The particle and agglomerate packing arrangements caused densification substages to occur. A schematic model is presented which agrees well with the observed experimental behavior.     

Pore evolution of microporous magnesia aggregates with the introduction of nano-sized MgO

Microporous refractories applied in the working-lining of metallurgical furnaces have been rapidly developed in recent years owing to the outstanding mechanical properties, thermal insulation performance and slag resistance, the pore structure of which plays a critical role in the variation of service performance. Meanwhile, the microporous magnesia aggregates were prepared in our previous research with the introduction of nano-sized particles to overcome the shortcomings of high thermal conductivity, poor thermal shock resistance and slag penetration resistance, however, the pore evolution during sintering still remains to be investigated. Hence, in this study, the pore evolution of microporous magnesia aggregates is explored specifically and the effect of nano-sized MgO on pore structure and sintering is simultaneously discussed. The sintering model of microporous magnesia was built for analyzing the pore structure evolution process. The results revealed that a micro-nano double-scale sintering model developed by the introduction of nano-sized MgO dramatically promoted the sintering kinetic force and boundary migration velocity. The sintering pressure discrepancy and free energy change per unit mole of specimens were respectively increased by ～43 times and ～48 times, which effectively improved the closed porosity and pore distribution homogeneity, while reduced the pore size. Meanwhile, the high sintering diving force lead to the significant improvement of direct bonding degree and grain size of microporous magnesia. With the addition of 3 wt% nano-sized MgO, the optimal sintering properties with closed porosity of 6.4%, bulk density of 3.23 g/cm³ and median equivalent pores diameters of 4.07 μm were achieved. The exploration of pore evolution in microporous magnesia aggregates contributed to the fabrication and industrialization development of microporous refractories.     

Precoarsening to Improve Microstructure and Sintering of Powder Compacts

MgO and Al₂O₃ were sintered by two types of processes: a conventional isothermal sintering and a two-step sintering consisting of an initial low-temperature precoarsening treatment before conventional isothermal sintering. The final microstructure from two-step sintering can be more uniform and finer than that of compacts sintered conventionally. A narrow-size-distribution alumina powder was sintered under constant-heating-rate conditions, with and without a precoarsening treatment, and the results were compared. The differences between two-step and conventional processing were clarified by experiments on precoarsened and as-received ZnO powders. These compacts were precoarsened at 450°C for 90 h with virtually no increase in the overall density. The resulting grain size was 1.7 times the starting one, but the standard deviation of the precoarsened powder size distribution was smaller than that of the asreceived powder. Precoarsened compacts sintered to nearly full density showed improved homogeneity. The sintering stress of the precoarsened ZnO was approximately 0.8 that of the as-received one. A computational model has been used with two components of coarsening to describe the differences in pore spacing evolution between the precoarsened and the as-received system. The benefit of two-step sintering is attributed to the increase in uniformity resulting from precoarsening. The increased uniformity decreases sintering damage and allows the system to stay in the open porosity state longer, delaying or inhibiting additional coarsening (grain growth) during the final stage of densification. Two-step sintering is especially useful for nonuniform powder systems with a wide size distribution and is a simple and convenient method of making more uniform ceramic bodies without resorting to specialized powders or complicated heat schedules.     

Microstructure Refinement of Sintered Alumina by a Two-Step Sintering Technique

For a few oxide ceramics, the use of an initial precoarsening step prior to densification (referred to as two-step sintering) has been observed to produce an improvement in the microstructural homogeneity during subsequent sintering. In the present work, the effect of a precoarsening step (50 h at 800°C) on the subsequent densification and microstructural evolution of high-quality alumina (Al2O3) powder compacts during constant-heating-rate sintering (4°C/min to 1450°C) was characterized in detail. The data were compared with those for similar compacts that were sintered conventionally (without the heat treatment step) and used to explore the mechanism of microstructural improvement during two-step sintering. After the precoarsening step, the average pore size was larger, but the distribution in pore sizes was narrower, than those for similar compacts that were sintered conventionally to 800°C. In subsequent sintering, the microstructure of the precoarsened compact evolved in a more homogeneous manner and, at the same density, the amount of closed porosity was lower for the compacts that were sintered by the two-step technique, in comparison to the conventional heating schedule. Furthermore, a measurably higher final density, a smaller average grain size, and a narrower distribution in grain sizes were achieved with the two-step technique. The microstructural refinement that was produced by the two-step sintering technique is explained in terms of a reduction in the effects of differential densification and the resulting delay of the pore channel pinch-off to higher density.     

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 green state processes on the sintering behaviour and the subsequent optical properties of spark plasma sintered alumina

The present investigation gives a quantitative correlation between different green microstructures, and their sintering behaviour during spark plasma sintering. The green microstructures were elaborated via various green shaping processes such as direct casting and direct coagulation casting compared to uniaxial compaction of the as-received sub-micron grained corundum powder. Narrowing pore size distribution and reducing pore size (≈40 nm) in the green compact could favour cold densification during initial uniaxial pressing by grain sliding and rearrangement. This is attributed to the soft homogeneous touching network in direct-cast green samples. Consequently, grain growth was impeded and the onset of shrinkage was delayed. Moreover, the small pores and the narrow pore size distribution in the homogeneous green bodies led to higher final densities, with better optical properties compared to the less homogeneous green samples.     

多孔陶瓷分离膜支撑体的制备研究

采用氧化铝为主要原料制备出多孔陶瓷分离膜支撑体,对原料粉体做了TG/DSC曲线分析,研究了支撑体的烧结温度对收缩率的影响及烧结温度、保温时间和原料粉体粒径对孔结构、孔径的影响,造孔剂用量对孔隙率的影响。结果表明：在烧结温度为1200℃,保温时间4h,控制造孔剂用量大于20%时,制备出孔径分布均匀,孔隙率大于50%,符合透水要求的多孔陶瓷分离膜支撑体。     

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.     

Effects of Particle Packing Characteristics on Solid-State Sintering

Alumina compacts fabricated with different green densities and different pore size distributions were characterized and the changes of the pore characteristics during solid-state sintering were studied. A critical ratio of pore size to mean particle size for pore shrinkage was determined. Porosity in the compact could be classified into two classes: the first class contains pores smaller than the critical ratio, and the second class contains pores larger than the critical ratio. Pores belonging to a different class of porosity behaved differently during sintering. Pores larger than the critical ratio were not totally eliminated during sintering. The first class of porosity controlled the ultimate sintering shrinkage, and the second class of porosity controlled the final sintered density.     

Liquid Redistribution during Liquid-Phase Sintering

A simple two-dimensional packing model, consisting of arrays of circular particles, was used to calculate the free energy changes associated with the filling of pores of different coordinations with liquid. The calculations were used to determine the equilibrium distributions of a liquid in different packing arrangements of particles. The effect of both the volume fraction of liquid and shrinkage on liquid distribution was examined. It was found that, when liquid redistribution can easily take place, the volume fraction of liquid phase, the pore size distribution of a powder compact, and the amount of densification that has occurred all influence the homogeneity of the distribution of the liquid phase. In addition, the model predicts that, as shrinkage occurs or as the volume fraction of liquid phase increases, the pores will try to fill sequentially in order of increasing size. A consequence of this sequential filling of the pores is that the radius of curvature of the liquid meniscus, and hence the driving force for liquid-phase sintering, changes systematically as shrinkage occurs. The modeling suggests that the driving force for sintering changes in a way that depends on the initial overall pore size distribution of the particle arrangement and the way the pore size distribution changes during sintering.     

Evolution of the Pore Size Distribution in Final-Stage Sintering of Alumina Measured by Small-Angle X-ray Scattering

Small-angle X-ray scattering was used to follow the evolution of the pore size distribution during final-stage sintering of alumina and of alumina doped with 0.25 wt% magnesia. The volume-weighted (Guinier) results indicate that the effective size of the largest pores increases as the body goes from 97% to more than 99% dense. The surface-area-weighted (Porod) results show that the median size of the smallest pores decreases slightly over the same density range. Taken together, these data indicate that the pore size distribution becomes broader as final-stage densification proceeds. This was confirmed by a maximum entropy analysis, which was used to derive pore size distributions directly from the data. Finally, the evolution of the pore size distributions in alumina, with and without sintering aid, were compared.     

烧成温度对多孔SiC陶瓷管性能的影响

以SiC为骨料,添加低共熔混合物烧结促进剂,煤粉作为造孔剂,在不同的温度下烧成制备多孔陶瓷管.考察了烧成温度对多孔SiC陶瓷管的孔隙率、气体渗透通量、孔径分布以及抗弯强度等性能的影响,并通过SEM对其结构形貌进行了表征.结果表明:随着烧成温度的提高,孔隙率、气体通量及抗弯强度下降,孔径分布变宽.     

Morphological Changes in Process-Related Large Pores of Granular Compacted and Sintered Alumina

Large pore defects clearly develop in Al₂O₃ ceramics during sintering. These large pores originate from voids caused by the incomplete deformation and adhesion of powder particles in collapsed dimples at the centers and boundaries of granules in the green compacts. The coalescence of pores, with limited shrinkage, during densification and grain growth in the late intermediate to final stages of sintering, is considered responsible for the development of the large pores. The mechanism of pore coalescence is explained by thermodynamic arguments, which demonstrate that the largest pores result in a stable system.     

Microstructural analysis of sintering behavior of intra-grain pores

A latticebased Monte Carlo simulation approach has been developed for studying the behavior of intragrain pores during the intermediate and final stages of sintering. The changes of the microstructures and the resulting properties of intragrain pores during sintering are easily examined. The sintering behavior such as pore size distribution, average pore size, etc. is in very good agreement with the experimental observations. In addition, the relationships between the number of pores and the average pore volume agree well with theory.