Mechanics of shape evolution of particle aggregates in viscous sintering

Sintering of glass/amorphous particles takes place by viscous flow driven by surface tension. While the viscous sintering of two particles is described by the growth of contact area, the shape evolution of aggregates of particles is very complicated and requires analytical methods for the characterization. Here, we analyzed the viscous sintering of linear chains of particles by finite element simulation. Consider a plane which cuts the chain perpendicular to its axis. We show that the growth rate of cross-sectional area is driven by the difference between the integral of pressure on the cross-section and the surface tension acting along its circumference, i.e., the sintering force. The cross-sectional area increases when the sintering force is positive, and decreases when it is negative. This relationship is generalized to particles aggregate of any shape, so that its shape evolution is characterized by the distribution function of growth rate of cross-sectional area.     

Modelling of elimination of strength-limiting defects by pressure-assisted sintering at low stress levels

The structural reliability of sintered products depends on large defects introduced during powder processing, which cannot be removed by pressureless sintering. Here, we present a model how a large single ellipsoidal void is deformed, and finally disappears by pressure-assisted sintering. Taya-Seidel’s model is applied to predict the shrinkage of a large void in a compressible linear viscous material by using bulk viscosity, shear viscosity, and sintering stress that are determined experimentally for sintering of alumina powder at low stress levels. The application of mechanical stress promotes the densification rate. Its effect is maximum for hot isostatic pressing (HIP) and minimum for sinter forging. The effect is intermediate for hot pressing (HP) and spark plasma sintering (SPS), because the hydrostatic component of stress varies with densification. While a crack-like defect can be removed during densification, a spherical void must be eliminated by shear deformation in the final stage during dwell time.     

Effect of pore orientation on anisotropic shrinkage in tape-cast products

During tape casting, an anisotropic shrinkage can be observed, which is attributed to particle alignment during the casting process. The understanding of the relationship between green body microstructure and shrinkage anisotropy is of great importance for further miniaturization of multilayer ceramics. In the current study, four alumina powders with different particle shape (spherical, standard, plate-like and extreme plate-like) were used to cast green tapes. The sintering shrinkage behavior and the microstructure were analyzed. In particular, the pore orientation was determined quantitatively by using a modified linear intercept method. The relationship between pore alignment and anisotropic sintering shrinkage of cast green tapes is discussed in all three spatial directions. The shrinkage anisotropy could be correlated quantitatively with the pore anisotropy. Furthermore, this correlation was verified by mathematical modeling based on elongated particles and pores.     

The sintering behavior of ellipsoidal particles

The sintering behavior of ellipsoidally shaped particles, particularly spheroids, was studied using a numerical kinetic Monte Carlo model for solid-state sintering. Compact packings of spheroids with five different aspect ratios from 0.5 to 2.0, thus comprising oblate, spherical, and prolate particles, were generated by simulating the pouring of such particles into a cubic container. For each spheroid particle aspect ratio, five different packings were generated to provide statistics on the sintering properties. The sintering behavior was quantified by the densification rate, relative density, anisotropic strain, grain size, and grain coordination number, as determined from the kinetic Monte Carlo model. The spherical particles were found to sinter to a relative density of 0.87 before grain growth occurs, whereas the oblate and prolate particles reach a relative density of 0.91 before grain growth sets in, with the prolate particles sintering slightly better compared to oblate particles. The more extreme the particle aspect ratio, the more anisotropic the strain is. Finally, the oblate and prolate spheroids have a slightly higher mean grain coordination number and a slightly higher initial relative density compared to the spherical particles.     

Evolution of the fractal dimension for simultaneous coagulation and sintering

Simulation results on the evolution of aggregate structure in aerosol processes with coagulation and sintering as the dominant mechanisms are presented. A model for simulation of the three-dimensional morphology of nano-structured aggregates formed by concurrent coagulation and sintering is applied. The model is based on a stochastic diffusion controlled cluster-cluster aggregation algorithm and sintering is modeled as a successive overlapping of spherical primary particles, which are allowed to grow in order to maintain mass conservation. This leads to computer simulated structured aggregates which are then subject to evaluation. Two different methods to determine the fractal dimension are presented which give comparable results. It is shown that even very small particles show the same fractal behavior. Furthermore, equilibrium structures assuming a constant ratio of the characteristic collision time to the characteristic fusion time are considered as well as the kinetics of structural changes due to a change in the ambient conditions.     

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.     

Domain coarsening in viscous sintering as a result of topological pore evolution

The microstructure evolution in 3D was studied by X-ray microtomography to reveal the relation between topology of pore networks and characteristic length in viscous sintering. The mean intercept length was defined from solid/pore interface for characterizing the length of solid phase and pore phase. The increase of the characteristic length with densification was termed as domain coarsening. The topological pore evolution was analyzed by using genus. The characteristic length increased with decreasing genus in the intermediate stage. The domain coarsening takes place as a natural consequence of pore evolution in viscous sintering, i.e., the decrease of total surface area concurrent with the topological transformations.     

Correlations among sintering temperature,shrinkage, and open porosity of 3.5 YSZ/Al2O3 composites

Slip-cast ceramic samples of the system (100−x) (ZrO₂–3.5 mol% Y₂O₃)–xAl₂O₃ (abridged as (100−x) 3.5 YSZ/xAl₂O₃ composite, where x is expressed in wt%) were examined using dilatometry, isothermal sintering and electron microscopy methods. The shrinkage in the range 1100–1300 °C was found to be higher for the (100−x) 3.5 YSZ/xAl₂O₃ samples with prevailing fraction of PSZ than for the composites with a corundum matrix. When the weight fraction of corundum was increased, the relative shrinkage of the (100−x) 3.5 YSZ/xAl₂O₃ samples decreased and the open porosity of the ceramic materials grew. The effect of <gamma>-Al₂O₃ impurity on the sintering process and linear dimensions of ceramics is shown. Heat treatment of (50–40) 3.5 YSZ/(50–60) Al₂O₃ composites at 1300 °C are proposed as the optimum conditions for porous diaphragm formation.     

A model for initial-stage sintering thermodynamics of an alumina powder

A model was proposed to calculate several thermodynamic parameters for the initial-stage sintering of an alumina powder obtained after calcinations at 900 °C for 2 h of a precursor. The precursor was synthesized by an alumina sulphate-excess urea reaction in boiling aqueous solution. The cylindrical compacts of the powder with a diameter of 14 mm were prepared under 32 MPa by uniaxial pressing using oleic acid (12% by mass) as binder. The compacts were fired at various temperatures between 900 and 1400 °C for 2 h. The diameter (D) of the compacts before and after firing was measured by a micrometer. The D value after firing was taken as a sintering equilibrium parameter. An arbitrary sintering equilibrium constant (K_a) was calculated for each firing temperature by assuming K_a = (D_i − D) / (D − D_f), where D_i is the largest value before sintering and D_f is the smallest value after firing at 1400 °C. Also, an arbitrary change in Gibbs energy (ΔG _a°) was calculated for each temperature using the K_a value. The graphs of ln K_avs. 1 / T and ΔG _a° vs. T were plotted, and the real change in enthalpy (ΔH°) and the real change in entropy (ΔS°) were calculated from the slopes of the obtained straight lines, respectively. Inversely, real ΔG° and K values were calculated using the real ΔH° and ΔS° values in the ΔG° = − RT ln K = ΔH° − TΔS° relation. The best fitting ΔH° and ΔS° values satisfying this relation were found to be 157,301 J mol^− 1 and 107.6 J K^− 1 mol^− 1, respectively.     

Effects of sintering temperature and holding time on porosity and shrinkage of glass tubes

The influences of sintering temperature and holding time on porosity and shrinkage of glass tubes have been studied by optical microscope. It is evident that there exists three stages for the sintering process of glass. At the first stage, both increasing temperature and prolonging the holding time contribute to lowering the porosity and to intensifying the shrinkage greatly. At the second stage, the glass further densifies and the voids among particles become smaller and less. Finally, at the third stage the shrinkage rate almost keeps unchanged to sintering temperature and holding time.     

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.     

助烧剂和造孔剂对真空烧结SiC多孔陶瓷性能的影响

以粒度≤0.063mm的SiC为主要原料,分别加入30%(质量分数)的Al2O3-Y2O3与10%的Al2O3-高岭土复合助烧剂,并外加不同量(分别为12.8%、26.3%、30.0%和36.4%)的造孔剂羧甲基纤维素钠(CMC),制样后首先在空气炉中经过300℃2h或1100℃4h的预烧,然后在真空炉中于1550℃4h真空烧结而制备成SiC多孔陶瓷,并研究了助烧剂种类以及造孔剂CMC外加量对SiC多孔陶瓷显微组织、显气孔率及抗折强度的影响。结果显示:采用Al2O3-Y2O3作为助烧剂的SiC多孔陶瓷比Al2O3-高岭土作助烧剂的具有较高的抗折强度,显气孔率稍有减小;随着羧甲基纤维素钠量的增加,加入两种助烧剂的SiC多孔陶瓷均表现为显气孔率增加,抗折强度降低。     

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     

Effect of pore geometry on the sintering of Ca-based sorbents during calcination at high temperatures

In this article, we present a mathematical model that describes the calcination and sintering of calcium-based sorbents in furnace sorbent injection (FSI) conditions. We assumed that the sorbent decomposition follows a shrinking core model with a changing pore size distribution in every layer and we used a comprehensive mathematical model for sintering. Cylindrical and plate-like or slit pore geometries, usually associated with carbonate- and hydroxide-derived sorbents, respectively, were adopted and compared. It was concluded that sorbents with cylindrical pores sinter to a greater extent than those with slit pores. The decomposition and sintering kinetics were determined for three calcium sorbents with different pore geometries in FSI conditions. The study revealed that the presence of CO₂ and H₂O in the reaction atmosphere affects the sintering parameters whereas the calcination parameters remain constant. The model effectively correlated the experimental data and adequately predicted not only the evolution of the specific surface area but also the evolution of the pore size distribution of the sorbent over time. The most striking aspect of the research was that although our model calculated the total area by adding together the pore sizes in all the layers of the sorbent, the results were very similar to those of other sintering models.     

Dilatometric study of anisotropic sintering of alumina/zirconia laminates with controlled fracture behaviour

Al₂O₃ and ZrO₂ monoliths as well as layered Al₂O₃/ZrO₂ composites with a varying layer thickness ratio were prepared by electrophoretic deposition. The sintering shrinkage of these materials in the transversal (perpendicular to the layers, i.e. in the direction of deposition) as well as in the longitudinal (parallel with layers interfaces) direction were monitored using high-temperature dilatometry. The sintering of layered composites exhibited anisotropic behaviour. The detailed study revealed that sintering shrinkage in the longitudinal direction was governed by alumina (material with a higher sintering temperature), whilst in the transversal direction it was accelerated by the directional sintering of zirconia layers. For interpretation of such anisotropic sintering kinetics, the Master Shrinkage Curve model was developed and applied. Crack propagation through laminates with a different alumina/zirconia thickness ratio was described with the help of scanning electron microscopy and confocal laser microscopy.     

Computation of sintering stress and bulk viscosity from microtomographic images in viscous sintering of glass particles

Sintering stress and bulk viscosity were derived as functions of relative density from microtomographic images in viscous sintering of glass particles. Three methods were proposed to estimate the sintering stress from relative density, specific surface area, and average of curvature on pore surface, which were directly measured by X‐ray microtomography. The surface energy method gave valid value in the final stage of sintering, while the mixed method gave better estimation in the intermediate stage. For the initial stage of sintering, the sintering stress was calculated from the average contact radius and the average coordination number observed by X‐ray microtomography. The sintering stress at the final stage increased in free sintering, but it decreased in constrained sintering due to pore coarsening. The bulk viscosity was calculated from the shrinkage rate and the sintering stress.     

Rapid microwave sintering of alumina ceramics with an addition of carbon nanotubes

Compacted alumina samples with an addition of 1.0 and 2.5 wt % carbon nanotubes (CNT) have been microwave sintered at heating rates 50 and 100°С/min to a maximum temperature of 1550–1600°С with zero hold time. The densification kinetics has been studied using optical dilatometry. No noticeable influence of CNT on the development of thermal instability during rapid microwave sintering of alumina has been detected. The relative densities of the samples containing 1.0 and 2.5 wt % CNT sintered at a maximum temperature of 1550 °C and zero hold time were 93.8 and 87.5%, respectively. Microwave sintering with a repeated development of thermal instability has resulted in an increase in the final density to 95.0%.     

Thermal sintering studies of an autothermal reforming catalyst

This paper describes a novel approach to life studies on catalysts used in non-isothermal reactors, using a single long-term experiment. Temperature dependence of catalyst aging is determined by comparing the activity reduction of portions of the catalyst from different sections of the reactor, subjected to different temperatures. Time dependence is determined by fitting the drift in catalyst temperatures to a time-dependent reaction rate via a thermodynamic reactor model. Experimentally, a monolithic autothermal reforming catalyst was subjected to thermally accelerated aging under reforming conditions in an adiabatic laboratory mini-flow reactor for 1000 h. Methane was used as the fuel. The axial temperature profile of the catalyst was monitored using thermocouples placed at various locations along the catalyst. A gradual change in temperature profile, with increasing temperatures due to decreasing steam-reforming activity, was observed. The aged monolith was cut up into short pieces centered on the thermocouple locations. The pieces, each aged at a different temperature due to its location, were tested individually for activity. The reduced activities were correlated with the aging temperature to obtain the temperature dependence of thermal sintering rates. A generalized power-law equation (GPLE) model for sintering was fit to the activity data. A plug flow reactor (PFR) model describing the reaction was built and the sintering kinetics were incorporated. The PFR model was used to predict changes in catalyst performance due to sintering under normal operating conditions. Thermal sintering deactivation for this catalyst was found to be within acceptable limits for commercial applications.     

热压烧结金刚石工具用石墨模具抗氧化研究

采用氧化失重实验,对热压烧结金刚石工具用石墨模具的氧化腐蚀性能进行了研究。着重讨论了抗氧化剂组分、总磷酸盐浓度和抗氧化浸渍工艺等因素对石墨模具抗氧化性能的影响。结果表明:以复合磷酸盐为主体,添加金属氟化物和氮化物制备出的抗氧化剂,对石墨模具的抗氧化性和抗压强度有明显提高。当抗氧化剂总磷酸盐浓度大于25%,采用真空加压抗氧化浸渍工艺,对石墨模具的抗氧化效果最好。