On the modeling of the co2‐catalyzed sintering of calcium oxide

A comprehensive mathematical model for the CO₂‐catalyzed sintering of CaO is proposed. It takes into account the mechanisms of surface diffusion and grain boundary diffusion, catalyzed by CO₂ chemisorption and dissolution, respectively. In addition, the model proposed here considers the change in pore size distribution during sintering, grain growth, and the densification by lattice diffusion, which is the intrinsic sintering mechanism of the CaO. Model predictions are validated using experimental data on the sintering of two CaO samples, one of them derived from pure CaCO₃ and the other from limestone. It is found that impurities in limestone‐derived CaO do not significantly affect the CO₂ dissolution or chemisorption processes; however, they strongly increase the rate of sintering by lattice diffusion. It is also established that low temperatures and CO₂ partial pressures promote the coarsening by surface diffusion, whereas high temperatures and CO₂ partial pressures favor densification. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3286–3296, 2017     

Restructuring of aggregates and their primary particle size distribution during sintering

During sintering (coalescence) of aggregates of polydisperse primary particles (PPs), restructuring takes place, the average PP size increases and the PP size distribution (PPSD) narrows affecting particle performance in a number of applications. Here, aggregate sintering by viscous flow, lattice, and grain boundary diffusion is simulated by multiparticle discrete element methods focusing on PP growth dynamics and elucidating the detailed restructuring of aggregates during their coalescence. The effect of initial PPSD and sintering mechanisms on the evolution of PP polydispersity (geometric standard deviation) and surface area mean diameter are presented. Each sintering mechanism results in a distinct evolution of PPSD but quite similar growth in average PP diameter. Grain boundary diffusion has the strongest impact among all sintering mechanisms and rapidly results in the narrowest PPSD, as it has the strongest dependence on PP size. During sintering of aggregates with initially monodisperse PPs, the PPSD goes through a maximum width before narrowing again as PPs coalesce. A power law holds between projected aggregate surface area and number of PPs regardless of sintering mechanism and initial PP polydispersity. This law can be readily used in aerosol reactor design and for characterization of aggregates independent of material composition, initial PP polydispersity, and sintering mechanism. © 2013 American Institute of Chemical Engineers AIChE J, 59: 1118–1126, 2013     

Pore growth during the initial stages of sintering ceramics

Mercury porosimetry was used to measure changes in pore size distribution during initial stage sintering of compacts of submicron size particles of several oxides. Pore growth was observed in MgO and Fe₂O₃, and in Al₂O₃ under certain conditions. Pores can grow by these mechanisms: surface diffusion, particle size distribution effects, particle coalescence, phase transformation, and evaporation/condensation. Surface diffusion may be the mechanism in the case of an alpha alumina. Phase transformation was shown to be the cause when sintering gamma alumina. In the case of magnesia and ferric oxide, particle coalescence appears to be operating. Since pore growth competes with densification for the use of surface energy, it is an important sintering process.     

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.     

Microstructural Evolution During Vacuum Sintering of Yttrium Aluminum Garnet Transparent Ceramics: Toward the Origin of Residual Porosity Affecting the Transparency

Controlling residual amount of defects in transparent ceramics is a major challenge for laser applications. This study was focused on microstructural evolution of Nd:YAG ceramics during their reactive solid‐state sintering which was correlated to their optical transmittance. From microstructural observations, the microstructural maps and grain size‐density and grain size‐pore size sintering trajectories of Nd:YAG ceramics were established as a function of silica content. For densities higher than 99.7%, the occurrence of intragranular porosity was correlated to a critical pore radius of 0.16 μm. Silica appears to favor the formation of intragranular porosity which was attributed to the increasing of the grain growth rate compared with the densification one. An analytical model was established by coupling the analytical laws derived from sintering trajectories and the classical theory of light diffusion, allowing to correlate the microstructural features of transparent Nd:YAG ceramics to their optical properties.     

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.     

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.     

Strain rate dependence of the contribution of surface diffusion to bulk sintering viscosity

Modeling of bulk sintering viscosity usually neglects the contribution of pore surface diffusion with respect to grain-boundary diffusion. This approximation is questionable at the high densification rates used today in advanced fast sintering techniques. A two-dimensional analysis of the problem shows that the influence of surface diffusion on bulk viscosity at high strain rate can be decomposed as the sum of two terms: a term linked to the change in pore surface curvature and a term linked to the change in grain-boundary size. The computational procedure relies on the partition of pore profile evolution into a transient component accounting for non-densifying phenomena and an asymptotic component accounting for strain-rate-controlled phenomena. The largest impact of surface diffusion is found to arise from the change in grain-boundary size. It follows a transition from Newtonian viscosity at low strain rate to non-Newtonian viscosity which, during densification, increases nearly linearly with strain rate. In some conditions, viscosity can then reach more than twice the value estimated when neglecting pore surface diffusion. Reversely, expansion is accompanied by a decrease in grain-boundary size which causes a decrease in viscosity and can lead to grain separation at high strain rate.     

担载膜受限烧结孔结构模型的改进及验证

针对担载膜受限条件下,复杂的堆积方式及垂直膜面方向出现的加速收缩将影响孔径的问题,对前期建立的担载膜孔结构预测模型进行了改进,从两个方面对模型的关键参数进行定量修正。考虑制备过程中颗粒可能形成的软团聚体对初始堆积方式的影响,对模型重要参数——初始孔隙率进行调整;并结合受限烧结应力模型计算担载膜在垂直膜面方向上的收缩速率和收缩率,研究该方向加速收缩对孔径的影响。在此基础上,采用改进的模型对ZrO2担载膜在800～1200℃烧结后,孔径、孔隙率、膜厚等微结构进行了预测。结果表明:与原模型相比,改进模型具有更好的适应性以及更高的计算精度,能更准确地预测不同烧结温度制备的担载膜的孔径和膜厚,为陶瓷膜孔径的预测与定量控制提供了有效的工具。进一步将模型计算值代入Hagen-Poiseuille方程,可以预测膜的纯水渗透通量。     

The Dependence of Pore Size Distribution on Porosity in Hot Isostatically Pressed Porous Alumina

Pore size distributions in porous alumina bodies produced by the capsule-free hot isostatic pressing technique have been determined experimentally. The distribution of pore diameter has been found to be dependent on the size of the pre-sintered powders and the amount of open porosity in the sintered body. An empirical model has been developed to predict the modal pore size as a function of median particle size and open porosity. The pore size distributions were found to widen with reduced porosity. They were also shown to be positively skewed. The skew reduced with decreasing porosity. The pore size variation with porosity for specimens produced with a sintering aid could not be described by the same mathematical functions developed for specimens produced by solid-state sintering.     

High strength porous alumina by spark plasma sintering

High strength porous alumina was fabricated by spark plasma sintering (SPS) at temperatures between 1000 and 1200 °C with nanocrystalline Al(OH)₃ as the starting powder without any seeds, dopants or inclusions. Decomposition of the Al(OH)₃ produced a series of transitional alumina phases depending on sintering temperature and pressure and finally the stable α-alumina phase was obtained. A network of continuous pores with unimodal pore size distribution was estimated by mercury porosimetry and BET surface area measurements, with the porosity ranging between 20% and 60% based on sintering conditions. Predominance of fine grains and extensive necking between them led to better strength in the sintered samples. The bending strength of the sintered compacts rapidly increased with sintering temperature while retaining reasonable porosity suitable for practical applications. The results clearly indicate that in situ phase formation of α-Al₂O₃ and θ-Al₂O₃ provides strength and porosity, respectively. Phase transformation, pore morphology and microstructure evolution were also studied.     

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 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.     

Role of microstructure reactivity and surface diffusion in explaining flash (ultra-rapid) sintering kinetics

The competition between sintering and coarsening is cited by numerous authors as one of the potential factors for explaining the ultra-rapid sintering kinetics of flash sintering. In particular, surface diffusion is a mechanism decreasing the driving force of sintering by changing the initial highly reactive microstructures (particle contact) into poorly reactive porous skeleton structures (spherical porosity). We show by finite element simulations that flash SPS experiments high specimen temperatures close to 2000 °C. These high temperatures are not sufficient to explain the ultra-rapid sintering kinetics if typical spherical pore theoretical moduli are employed. On the contrary, reactive experimentally determined moduli succeed in explaining the ultra-rapid sintering kinetics. Mesoscale simulations evidenced that the origin of such reactive experimental moduli is a porous skeleton geometry with a significant delay in surface diffusion and particle rearrangement. This highlights the important role of the surface diffusion negation (favoring higher stress intensification factor) in flash sintering.     

Effect of sintering temperature on compressive strength of porous yttria-stabilized zirconia ceramics

Porous yttria-stabilized zirconia (YSZ) ceramics were fabricated by tert-butyl alcohol (TBA)-based gel-casting method for potential applications in heat-insulation materials. The effect of sintering temperature on compressive strength of porous YSZ ceramics was investigated on the basis of measurements linear shrinkage, porosity and pore size. As the sintering temperature increased from 1350 to 1550 °C, a decrease of porosity from 77 to 65%, a decrease of average pore size from and an increase of linear shrinkage from 15.4 to 31.8% were observed. The compressive strength increased remarkably from 3 to 27 MPa with increasing sintering temperature from 1350 to 1550 °C, which was related to the corresponding change of linear shrinkage, porosity, pore size and microstructure. A remarkable decrease of compressive strength with increasing porosity was observed. The compressive strength decreased also with increasing pore size.     

Fabrication of double-decker zircon aggregates by granulation and influence of TiO2 on the sintering process

In this study, four zircon granules are prepared by using granulation method and using TiO₂ and sodium carboxymethyl cellulose (CMC) as a sintering additive and binder, respectively. Then, the effects of TiO₂ addition on phase composition, pore size distribution and sintering process are analyzed by X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS). The results reveal that only a small portion of zircon is decomposed into ZrO₂ and SiO₂ after sintered at 1250 °C, however, the zircon granules consist of zircon, ZrTiO₄ and mullite after sintering at 1550 °C. In general, the addition of TiO₂ accelerated the sintering process, promoted the migration rate of grains and transformed the apparent pores into closed pores, resulting in decreased pore size and enhanced compressive strength. The zircon granule, with 2.0 wt% TiO₂, rendered an optimal apparent porosity of 24.0%, a high closed porosity of 8.35%, a high cylinder compressive strength retention rate of 44.9% and a relatively homogeneous pore size distribution after sintering at 1550 °C.     

Study on molding process of UHMWPE microporous filter materials

A method called loose sintering was first introduced to prepare ultrahigh‐molecular weight polyethylene (UHMWPE) microporous materials. The pore size was predicted by the face‐centered cubic structure model while considering the particles' arrangement and melt. The results showed that the experimental pore diameter was close to that calculated by the present model. The effects of UHMWPE molecular weight, particle diameter, packing density, sintering temperature, and sintering time on pore size, compressive strength, pore diameter distribution, and density were presented. The morphology of micropore and the uniformity of pore distribution were analyzed by scanning electron microscopy and fractal geometry. The results showed that average pore diameter and porosity both increased with the UHMWPE particle diameter while decreased with compressive strength and bulk density. Sintering temperature and sintering time determined whether the heat was redundant to melt the particles. They also determined the pore size and the uniformity. UHMWPE microporous materials could be successfully prepared with suitable processing conditions. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Sintering forces acting among particles during sintering by grain-boundary/surface diffusion

The microstructural evolution during sintering involves the formation and pinch-off of pore channels. The sintering of 3 particles in 3 dimensions is a simple model for studying the pinch-off of a pore channel. We simulate the solid-state sintering of 3 particles by using Brakke's Surface Evolver program, which incorporates coupled grain-boundary diffusion and surface diffusion. The pinch-off of pore channel divides the sintering process into 2 stages; the initial stage and the later stage. The contact area has a noncircular shape bounded by both surface triple junction and triple junction in the later stage. A general method is presented to determine the sintering force acting on the noncircular contact. The mechanical approach of densification, where the relative motion of particles is driven by both sintering force and applied force, is applicable not only for the initial stage, but also for the later stage.     

Computer Simulation of Final-Stage Sintering: I, Model Kinetics, and Microstructure

A Monte Carlo model for simulating final-stage sintering has been developed. This model incorporates realistic microstructural features (grains and pores), variable surface difusivity, grain-boundary diffusivity, and grain-boundary mobility. A preliminary study of a periodic array of pores has shown that the simulation procedure accurately reproduces theoretically predicted sintering kinetics under the restricted set of assumptions. Studies on more realistic final-stage sintering microstructure show that the evolution observed in the simulation closely resembles microstructures of real sintered materials over a wide range of diffusivity, initial porosity, and initial pore sizes. Pore shrinkage, grain growth, pore breakaway, and reattachment have all been observed. The porosity decreases monotonically with sintering time and scales with the initial porosity and diffusivity along the grain boundary. Deviations from equilibrium pore shapes under slow surface diffusion or fast grain-boundary diffusion conditions yield slower than expected sintering rates.     

Influence of spark plasma sintering conditions on microstructure,carbon contamination,and transmittance of CaF2 ceramics

Commercial CaF₂ powder was applied to fabricate transparent CaF₂ ceramics by spark plasma sintering under various sintering conditions. The low sintering temperatures and high pressures caused serious carbon contamination, while the soak time had less influence on the carbon concentration in the ceramics. The highest carbon contamination occurred to the CaF₂ ceramics sintered at 800 °C. A low sintering pressure suppressed carbon contamination but led to high porosity and large pore size. A high pre-loading pressure led to relatively high porosity and carbon concentration. Furthermore, the relatively fast densification in the edge region of the plates may cause the non-uniform distribution of porosity, thereby affecting the distribution of carbon concentration. The low pre-loading pressure and the high sintering pressure reduced porosity and carbon concentration to obtain dense transparent ceramic with uniform microstructure and high transmittance.