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.     

Thermodynamics of Densification: I, Sintering of Simple Particle Arrays, Equilibrium Configurations, Pore Stability, and Shrinkage

Equilibrium configurations for linear and closed arrays (rings and regular polyhedra containing a single pore) of identical particles (cylinders or spheres) were determined by minimizing the array's surface and grain-boundary energies with the assumption that each particle conserves its mass. The change in free energy between the initial and equilibrium configuration increases with dihedral angle (i.e., the equilibrium angle). More significantly, it is shown that pores will shrink to an equilibrium size if the number ( n ) of coordinating particles is greater than a critical value. The critical pore coordination number ( n _c) increases with the dihedral angle. Only pores with n n _c are thermodynamically unstable during sintering. It is also shown that any mass-transport mechanism can lead to pore shrinkage while a connecting path to the pore surface remains open. The effective sintering "stress" (i.e., driving force) increases with the dihedral angle and decreases to zero as the equilibrium configuration is reached. Sintering stresses increase with decreasing coordination number. It is also shown that the shrinkage strain for closed arrays increases with the pore coordination number. Rearrangement phenomena within a powder compact are discussed with regard to resultant sintering forces on nonsymmetrically coordinated particles.     

Characterization of the compaction and sintering of hydroxyapatite powders by mercury porosimetry

Mercury porosimetry was used to measure the bulk and real densities, pore volumes and pore size distributions of compacts of hydroxyapatite before and after sintering. The hydroxyapatites were prepared by two different methods and had widely different surface areas. The properties were determined as a function of compaction force and sintering temperature. Densities from porosimetry were in good agreement with geometric densities. A linear relation was found between pore volume and log of the applied force. There was also a linear relationship between bulk volume and pore volume of the compacts. A bimodal pore size distribution was observed for the high surface area hydroxyapatite which disappeared with increasing compaction loads. Pressurization and depressurization measurements indicated that the main body of the pores in the compacts attained a more regular “spherical” shape with increasing compaction force than did the “necks”. The pore volume, percent porosity, and bulk density of the compacts remained unchanged up to 600°C; however, the surface area and the average pore diameter changed at 400°C. The distribution of pores became more uniform, narrower in distribution, and larger in size as the sintering temperature increased. The change in pore area with pore volume indicated that two mechanisms were operating during sintering. The pore area proved to be the most sensitive indicator of changes during sintering.     

Effect of fugitive phase addition on porosity evolution and properties of stoneware tiles

Abstract

Abstract

Different percentages of fugitive phase with three different average particles were added to the green porcelain compositions. The fugitive phase was burnt out during the sintering, and the shrinkage of the samples was proportional to the added volume. The lower the particle size of the fugitive phase was, the higher the shrinkage became. The properties of stoneware tiles as apparent density, linear shrinkage, modulus of rupture, porosity, roughness and water absorption were studied as function of the added fugitive phase. A reduction of the porosity was obtained when the added fugitive phase was <5?vol.-%. The modulus of rupture improvement was found in samples with higher density. The surface roughness increased by both the volume and the particle size of fugitive phase. Large added porosity volume was effectively eliminated, and the porosity was equilibrated to a fixed value related to the initial particle size of the fugitive phase. The main mechanism that contributed to the elimination of porosity during liquid assisted sintering was the gas diffusion. Large pores were hindered by the crystalline phases, and thus pore, coalescence was avoided in the porcelain stoneware.     

团聚氧化镁粉料压块的烧结机理与动力学模型

团聚粉料压块具有由高烧结性粉粒所构成的双层堆积结构。在烧结的第一阶段，一级颗粒快速烧结导致二级颗粒的收缩与重排并增加大气孔。在烧结的第二阶段，一级与二级颗粒的烧结同时进行，但压块的烧结是被一级颗粒的烧结所控制。某些中期烧结模型与试验结果吻合。在烧结的第三阶段中，压块的致密和颗粒长大同时进行，其特点是大量的小晶粒晶界存在，气孔有很高的配位数。提出一个方程式，它与团聚氧化镁试块烧结试验结果相一致。     

原位反应合成多孔莫来石质支撑体及其显微结构

采用粉煤灰、烧铝矾七和球黏土为原料,通过原位反应烧结合成球形多孔莫来石质支撑体.考察了烧结温度对多孔莫来石质支撑体相转变、晶粒尺寸、孔径分布和气孔率的影响,并对其莫来石化的机理进行了探讨.研究表明:在1 300℃烧结温度下,二次莫来石在硅铝酸盐液相中通过溶解-沉淀机制开始成核,并于1 400℃烧结发育成针状的晶粒;当烧结温度升至1 500℃时,溶解在液相中的莫来石进行结构调整和生长,并最终在1 550℃发生原位反应并形成刚性交错网络结构的柱状莫来石.在低温(<1 400℃)烧结阶段,二次莫来石的成核和生长引起体积膨胀,导致气孔率随温度的升高而增大;在高温(≥1 500℃)烧结阶段,大量玻璃相的存在使液相烧结占主导,气孔率因体积收缩呈下降趋势.支撑体的平均孔径随烧结温度的升高而增大,其原因是在高温烧结时莫来石生长消耗过多的SiO2使大量微孔联接形成大孔.     

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.     

Numerical Simulation of Viscous Sintering by a Periodic Lattice of a Representative Unit Cell

In this paper numerical simulations of the viscous sintering phenomenon are presented, i.e., of the process that occurs (for example) during the densification of a porous glass heated to such a high temperature that it becomes a viscous fluid. The numerical approach consists of simulating the shrinkage of a two-dimensional unit cell which is in some sense representative for the porous glass. Hence it is assumed that the microstructure of the glass can be described by a periodic continuation in two directions of this unit cell. In this way it is possible to obtain insights into the viscous sintering process with respect to both pore size and pore distribution of the material. In particular this model is able to examine the consequences of microstructures on the evolution of the pore size distribution. The major finding is that the pores vanish in order of size one after another-the smallest pores first, followed by the larger ones. Moreover, it is shown that pores with concave boundary parts may initially grow before they start shrinking at a later stage.     

Micromechanics of formation and shrinkage of a closed pore in sintering by coupled grain boundary/surface diffusion

The microscopic principle of the stress-assisted sintering is that the relative velocity between two adjoining particles is proportional to the sum of the sintering force and the mechanical force transmitted by the contact. Here, we simulated sintering of four particles by coupled grain boundary diffusion and surface diffusion, in order to analyze how the sintering force varies with the evolution of particle shape, i.e., pinch-off of pore channel, formation and shrinkage of a closed pore. The shrinkage rate of the pore volume was proportional to the relative velocity of particles, then, to the sintering force. We discussed the effect of mechanical stress on sintering also.     

Sintering of Low-Density Glasses: III, Effect of a Distribution of Pore Sizes

The sintering model presented in Part I is extended by considering a Gaussian distribution of pore sizes in the body. The effect of the breadth of the distribution on the densification kinetics is demonstrated; this effect is small except for very broad distributions. The greatest change occurs in the last few percents of shrinkage since the largest pores close relatively slowly. The range of pore sizes typically found in flame hydrolysis preforms or silica gel is narrow enough that the sintering kinetics are adequately described in terms of a single pore size. The specific surface area is shown to be independent of the breadth of the distribution.     

Processing of porous yttria-stabilized zirconia tapes: Influence of starch content and sintering temperature

The tape-casting process was used to produce porous yttria-stabilized zirconia (YSZ) substrates with volume fractions of porosity ranging from 28.9 to 53 vol.% by using starch as a fugitive additive. Concentrated aqueous YSZ slips with different amounts of starch and an acrylic latex binder were prepared. The influence of the volume fraction of starch and sintering temperature on the sintering behavior and final microstructure were investigated. The microstructure consisted of large pores created by the starch particles with lengths between 15 and 80 μm and smaller pores in the matrix with lengths between 0.6 and 3.8 μm. The pores in the matrix reduced the sinterability of the YSZ leading to the retention of closed porosity in the sintered tapes. The porosities were above those predicted for each of the starch contents. However, larger deviations from the predicted porosity were found as more starch was added. The open to total porosity ratio in the sintered tapes could be controlled by the volume fraction of added starch as well as by the sintering temperature. As the volume fraction of starch increased from 17.6 to 37.8 vol.% there was a gradual increase in the interconnectivity of the pore structure. The sintering shrinkage of the tapes at a given temperature could be directly related to the YSZ packing density in the matrix.     

Improved Equation of the Continuous Particle Size Distribution for Dense Packing

The Furnas model describes the discrete particle size distribution for densest packing. Using a model that considers a continuous particle size distribution for the densest packing to be a mixture of infinite Furnas discrete particle size groups, an equation for the cumulative particle size distribution providing the densest packing was derived. Monosize particles with different shapes have a different packing pore fraction. One parameter in the equation is the pore fraction of packed monosize particles; the particle size distribution for achieving densest packing is a function of this pore fraction. A reduced form of this equation is also presented as a working equation. The equation derived here is compared to the modified Andreasen equation for dense packing. An equation and the correlated graph for calculating theoretically the geometric mean particle size and an equation for calculating the specific surface area of the particle size distribution of the improved equation are also derived.     

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.     

Sintering Behavior and Electrical Properties of Nanosized Doped-ZnO Powders Produced by Metallorganic Polymeric Processing

Homogeneous and nanosized (28 nm crystallite size) doped-ZnO ceramic powders were obtained by a metallorganic polymeric method. Calcining and granulating resulted in green compacts with uniform powder packing and a narrow pore-size distribution (pore size 19 nm). Dense ceramic bodies (>99% of theoretical) were fabricated by normal liquid-phase sintering at 850° and 940°C for 1–5 h. Apparently, the low pore-coordination number allowed a uniform filling of the small pores by the liquid formed in the early stages of sintering, and, consequently, high shrinkage and rapid densification occurred in a short temperature interval (825°–850°C). At these sintering temperatures, limited grain growth occurred, and the grain size was maintained at <1 μm. Ceramics so-fabricated showed a nonlinear coefficient, α, of ≥70, and a breakdown voltage, V _b (1 mA/cm²), of ≥1500 V/mm. The high electrical performance of the doped-ZnO dense ceramics was attributed to liquid-phase recession on cooling, which enhanced the ZnO-ZnO direct contacts and the potential barrier effect.     

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.     

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.     

Pore filling behavior of YSZ under CMAS attack: Implications for designing corrosion‐resistant thermal barrier coatings

To understand the pore filling behavior in thermal barrier coatings during calcium‐magnesium‐alumino‐silicate (CMAS) infiltration process, porous yttria‐stabilized zirconia pellets with different sizes of spherical pores were prepared to simulate thermal barrier coatings. The pores (D50 ranging from 6 to 77 μm) were introduced to the pellets using poly methyl methacrylate as pore forming agents. Then the pellets were sintered to remove the pore forming agents and to achieve a similar volume fraction of porosity with thermal barrier coatings. After CMAS infiltration, only some small pores in the CMAS‐infiltrated zones were filled by CMAS, whereas all large pores (larger than 13 μm) remained unfilled; besides, the results also show that even open pores can resist filling by CMAS. The reason may relate to pore diameters; if the diameter of a pore is relatively large, the pore surface will not be completely wetted by liquid CMAS, the liquid meniscus will be discontinuous, and therefore the pore cannot be filled. The key insight gained from this study is that introducing “CMAS‐proof” pores into thermal barrier coatings may be a potential way to mitigate CMAS damage.     

Compressive mechanical properties of partially sintered porous alumina of bimodal particle size system

This paper examined theoretically and experimentally packing behavior, sintering behavior and compressive mechanical properties of sintered bodies of the bimodal particle size system of 80 vol% large particles (351 nm diameter)–20 vol% small particles (156 nm diameter). The increased packing density as compared with the mono size system was explained by the packing of small particles in 6-coordinated pore spaces among large particles owing to the similar size relation between 6-coordinated spherical pore and small particle. The sintering between adjacent large particles dominated the whole shrinkage of the powder compact of the bimodal particle size system. However, the bimodal particle size system has a high grain growth rate because of the different curvatures of adjacent small and large particles. The derived theoretical equations for the compressive strengths of both mono size system and bimodal particle size system suggest that the increase in the grain boundary area and relative density by sintering dominate the compressive strength of a sintered porous alumina. The experimental compressive strengths were well explained by the proposed theoretical models. The strength of the bimodal particle size system was high at low sintering temperatures but was low at high sintering temperatures as compared with that of mono size system of large particles. This was explained by mainly the change of grain boundary area with grain growth. The stress–strain relationship of the bimodal particle size system showed an unique pseudo-ductile property. This was well explained by the curved inside stress distribution along the sample height. The inside stress decreases toward the bottom layer. The fracture of one layer of sintered grains over the top surface proceeds continuously with compressive time along the sample height when an applied stress reaches the critical fracture strength.