Modeling and Simulation of Elementary Processes in Ideal Sintering

Three-dimensional numerical simulation of sintering was performed to illustrate the interplay between shapes and forces in particle scale. Elementary rules for topological transition of triple lines were derived from the analysis of micromechanical models of sintering: bond formation, pore channel closure, and pore disappearance. The particle motion was driven by the force acting on a particle, i.e., a vector sum of sintering forces. The non-equilibrium sintering stress was defined to analyze the pore shrinkage. A particle changed its own shape through interaction with neighbor particles; then, the coordination number affected particle motion, pore shrinkage, coarsening, and grain growth.     

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.     

Particle Rearrangement and Pore Space Coarsening During Solid-State Sintering

Coarsening of porosity during sintering has been observed in powder compacts of metallic, ceramic, and amorphous materials. Monitoring and modelling of the growth of individual (closed) pores in the late sintering stages are well established. Porosity is interconnected up to very high densities. Coarsening of the continuous pore space takes place during the initial and intermediate sintering stages. This coarsening is caused by localized transport of atoms or molecules (diffusion or viscous flow) as well as by bulk particle movement (rearrangement). Its quantitative exploration poses problems both experimentally and theoretically. Ways to characterize the geometry of the interconnected pore space and of closed pores are discussed with emphasis on stereological parameters. Recent and classical approaches, experimental findings with 2D model arrangements (as the formation and opening up of particle contacts, pore coarsening, and particle rearrangement) and some advances of computer simulations are discussed together with open questions.     

Sintering Stress of Nonlinear Viscous Materials

An analytical model for the sintering stress of materials characterized by a nonlinear viscous behavior during densification is proposed. The growing applications in the field of nanosized powders processing (in particular, consolidation of high surface area components used in supercapacitors, rechargeable batteries, gas absorbers) have renewed the interest in this fundamental parameter of sintering science, because of the sintering stress’ characteristic inverse proportionality with respect to the powder particles radius. This increase in the magnitude of the sintering stress is also responsible for power‐law creep being the mechanism that underlies densification even without the application of any additional external load, and therefore for a nonlinear viscous behavior of the solid material. The analytical treatment of problems involving nonlinear viscous materials has traditionally involved complex self‐consistent methods and approximations, unless the local case of an isolated pore embedded in a fully dense skeleton was considered. The paper proposes a simple first‐order iterative method that allows the derivation of both bulk modulus and sintering stress of a material containing an arbitrary amount of pores, as functions of porosity and of the material's nonlinearity parameter, namely strain rate sensitivity. An expression for densification kinetics is also obtained and compared with experimental data.     

圆柱状金属泡沫多孔前置体的气动热效应分析

以超声速气流冲击轴线与来流方向相一致的带有金属泡沫多孔前置体的实体圆柱为研究对象,采用连续尺度单区域法数值模拟泡沫多孔前置体内部的流场及气动热效应。多孔域阻力特性基于分布阻力法加入,选用局部非热平衡模型,考虑流体相与固体相的传热温差,并通过Rosseland扩散模型加入固体相的辐射热效应。研究发现,在模拟气流工况下前置有一定长度的柱状泡沫多孔材料可显著降低模型激波阻力和前缘气动热效应,此外相对于气动压缩效应对温度场的影响黏性耗散效应较小。     

The effect of alkaline earth carbonates on the microstructure and mechanical properties of impermeable and lightweight ceramics

Lightweight impermeable ceramic bodies were designed by combining pore templating and controlled viscous sintering through in-situ crystallization. Various amounts of limestone were added to a glass-fluxed low-temperature stoneware tile formulation. Closed porosity was created by decomposition of carbonates prior to sintering, thus leaving voids that were not completely filled by the viscous melt. The resulting oxides chemically modified the liquid phase and promoted the crystallization of β-wollastonite, diopside and anorthite. Hence, viscous sintering was affected. The addition of limestone brought on several advantages: the temperature of maximum sintering rate was decreased (<900?°C); the dimensional stability range was extended; the matrix was reinforced by newly-formed crystals that compensated for the global structure weakening evoked by increased porosity; an increase in whiteness was observed in concomitance to crystallization, reaching values only obtained when using zircon as opacifier (L*=87).     

Specially elaborated thermally induced phase separation to fabricate poly(L‐lactic acid) scaffolds with ultra large pores and good interconnectivity

Poly(L ‐lactic acid) (PLLA) scaffolds with pore diameters from several micrometers to ～300 μm were fabricated by a specially elaborated thermally induced phase separation technique. Two different coarsening protocols, i.e., normal coarsening and multi‐step coarsening were compared in consideration of phase separation and domain growth. A normal coarsening route produced scaffolds with pore size from several micrometers to 150 μm depending on the coarsening time after phase separation, accompanying with the emergence of isolated pores at long time coarsening. Scaffolds with large pores with size up to ～300 μm were fabricated by the two‐step coarsening technique, e.g., the PLLA‐solvent (dioxane/water) system was coarsened at a temperature after phase separation for a period, followed by coarsening at a lower temperature for another period. In parallel with formation of the large pores, the interconnectivity between pores was also improved, which was evidenced by scanning electron microscopy, gelatin solution pervasion, and collagen entrapment. The present technique provides the ability to produce scaffolds with high purity, controllable microstructures, and ease of modification, and hence can be widely used in tissue engineering field. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 3336–3342, 2006     

A new empirical model for quiescent annealing of binary co-continuous polymer blends

The high sensitivity of the morphology and final properties of co-continuous polymer blends to thermal annealing has motivated many researchers to study the evolution of their morphology during thermal annealing process. In this work, phase coarsening of a low interfacial tension polylactic acid/polycaprolactone blend and a medium interfacial tension polylactic acid/polyethylene blend during quiescent annealing was studied in detail. To this aim, characteristic length scale of the microstructure of the polymer blends was determined at different annealing times. It was found that the phase size in both blends increased linearly by time at the early stage of the annealing and then the phase coarsening rate gradually decreased at longer times. Finally, the phase size of the blends approached a finite size. The mechanisms involved in the observed phase coarsening behavior were discussed in detail. Linear and exponential phase coarsening models in the literature could not explain the observed phase coarsening behavior in the studied blends. A new empirical model was presented which showed a very good agreement with both the obtained results in this work and the previous experimental data in the literature. The obtained results indicate the significant potential of the new model in analyzing phase coarsening behavior of co-continuous polymer blends.

     

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     

Cost‐effective porous ceramic tubes fabricated through a phase inversion/casting process using calcined bauxite

Cost‐effective ceramic tubes based on low‐price commercial calcined bauxite for economical separation were fabricated by a new phase‐inversion casting method. The thermal shrinkage and weight loss during heating of the green tubes were characterized by dilatometric analysis and TG, respectively. Three shrinkage stages appear successively, corresponding to the viscous deformation of polymeric binder at 200‐300°C, significant combustion loss of ~5.2 wt% at 500‐620°C and sintering shrinkage over 800°C, respectively. However, due to high enough viscosity of the casting suspension that can guarantee the green tube against collapse or deformation during the phase inversion/casting process, the sintered tubes display nearly uniform microstructure instead of characteristic asymmetrical structure of the phase inversion process. The influence of sintering temperature on the pore property (including pore size and porosity) and mechanical strength was investigated. As the sintering temperature increases from 1200 to 1400°C, the porosity and average pore size decrease from 46.4% to 37.0% and from 0.98 to 0.81 μm, respectively, and the flexural strength increases from 25.8 to 65.1 MPa. The cost‐effective ceramic tube sintering at the range of 1250‐1400°C can be capable of functioning as a microfiltration membrane or an ultrafiltration membrane support.     

Preparation and Sintering of Colloidal Silica-Potassium Silicate Gels

Porous silica gelled from colloidal silica and potassium silicate mixtures as developed by Shoup has been investigated. Various gels exhibit an average pore size from 50 to 250 nm and a porosity up to 85%. Dealkalization by solution leaching is found to depend on the average pore size and is easier for large pore sizes. A domain model has been proposed for the gel networks to account for the observation of both macropores and mesopores as measured by Hg porosimetry and N₂ desorption, respectively. The pore coarsening observed during sintering is explained by the material transport from areas around interdomain pores to those around intradomain pores in order to minimize the total surface energy.     

Ostwald ripening kinetics of angular grains dispersed in a liquid phase by two-dimensional nucleation and abnormal grain growth

Based on the fact that the angular shape of solid grains dispersed in the liquid matrix indicates a singular interface, the coarsening kinetics of angular grains was formulated based on 2-dimensional (2-D) nucleation and solved numerically. For comparison, diffusion-controlled coarsening of grains with a spherical shape was also solved numerically. The solutions showed that coarsening by 2-D nucleation induced abnormal grain growth whilst diffusion-controlled coarsening did not. This result agrees with the general experimental observation that the abnormal grain growth in liquid phase sintering takes place exclusively in the system with angular grains. The ratio of the largest grain size to the average increased monotonously with time in coarsening by 2-D nucleation whilst it decreased in diffusion-controlled coarsening. The artificially-added large grain (10 times larger than the average) became the abnormal grain in 2-D nucleation controlled coarsening but did not in diffusion-controlled coarsening.     

Microstructural Evolution in Liquid-Phase-Sintered SiC: Part III, Effect of Nitrogen-Gas Sintering Atmosphere

Effects of N₂ sintering atmosphere and the starting SiC powder on the microstructural evolution of liquid-phase-sintered (LPS) SiC were studied. It was found that, for the β-SiC starting powder case, there was complete suppression of the β→α phase transformation, which otherwise goes to completion in Ar atmosphere. It was also found that the microstructures were equiaxed and that the coarsening was severely retarded, which was in contrast with the Ar-atmosphere case. Chemical analyses of the specimens sintered in N₂ atmosphere revealed the presence of significant amounts of nitrogen, which was believed to reside mostly in the intergranular phase. It was argued that the presence of nitrogen in the LPS SiC helped stabilize the β-SiC phase, thereby preventing the β→α phase transformation and the attendant formation of elongated grains. To investigate the coarsening retardation, internal friction measurements were performed on LPS SiC specimens sintered in either Ar or N₂ atmosphere. For specimens sintered in N₂ atmosphere, a remarkable shift of the grain-boundary sliding relaxation peak toward higher temperatures and very high activation energy values were observed, possibly due to the incorporation of nitrogen into the structure of the intergranular liquid phase. The highly refractory and viscous nature of the intergranular phase was deemed responsible for retarding the solution–reprecipitation coarsening in these materials. Parallel experiments with specimens sintered using α-SiC starting powders further reinforce these arguments. Thus, processing of LPS SiC in N₂ atmosphere open the possibility of tailoring their microstructures for room-temperature mechanical properties and for making high-temperature materials that are highly resistant to coarsening and creep.     

Investigation on low-temperature reactive viscous flow sintering behavior of lanthanum-borate glass-ceramic with BaTi4O9 ceramic filler

In this paper, the sintering behavior of the lanthanum-borate (B₂O₃-La₂O₃-MgO-TiO₂,BLMT) glass-ceramic with BaTi₄O₉ filler composite was investigated in terms of the wetting behavior, interfacial reaction, sinter-shrinkage process, sintering activation energy, as well as phase and microstructure evolution with change in filler contents and sintering temperature. Our research suggested that the glass is unable to wet the filler material within a temperature up to 1000 °C, indicating that the densification process of composites is dominated by viscous flow of glass matrix. The increase in filler content that performs as a rigid particle in composite causes the rise in the sinter-shrinkage-onset and -end temperature, thereby proving that the viscous-flow densification of the composites with x≤ 30 wt% filler content is accomplished before the crystallization of BLMT glass, whereas the composites with x≥ 40 wt% cannot. After densification, a chemical reaction that almost synchronizes with the glass crystallization occurred between glass and ceramic, which not only imposes significant influence on the crystallization behavior, but eradicates the closed pore formed by the viscous flow and the induced crystallization porosity. The densification process of the BaTi₄O₉ filler-BLMT glass composite was referred to as two-stage reactive assisted viscous flow sintering process which consists of viscous flow of glass, of the crystallization process of glass, and/or of the chemical reaction between glass and filler.     

Numerical Simulation of Solid-State Sintering: I, Sintering of Three Particles

A kinetic, Monte Carlo model, capable of simulating microstructural evolution sintering in a two-dimensional system of three particles, has been presented. The model can simulate several mechanisms simultaneously. It can simulate curvature-driven grain growth, pore migration and coarsening by surface diffusion, and densification by diffusion of vacancies to grain boundaries and annihilation of these vacancies. Morphologic changes and densification kinetics are used to verify the model.     

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.     

Evolution of Average Microstructural Properties in the Final Stage Sintering of Alumina

Models of simultaneous coarsening and densification in final stage sintering commonly assume that the coarsening process results in microstructures that evolve self-similarly from a fixed microstructural geometry, differing only in scale. This assumption is experimentally tested for alumina in the solid volume fraction range of 0.97–1 using nondimensional microstructural parameters. The results clearly show that such models based on assumed geometries often underestimate the pore size relative to the grain size. The largest differences between the model and the experiments occur for lower firing temperatures and higher doping levels. It is concluded that the coarsening reflected in the effect of temperature and dopant level is not a self-similar process from a common microstructural geometry.     

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.     

Towards understanding particle rigid-body motion during solid-state sintering

A quantitative understanding of particle rigid body (RB) motion that inherently accompanies grain boundary (GB) diffusion is highly desirable to understand and control the dynamic interplay between coarsening and densification during solid state sintering. By computer simulation using a multi-phase-field approach, we analyze systematically the roles played by each of these processes at different stages of the shrinkage of the internal pore in a three-particle green body as a function of particle size as well as thermodynamic and kinetic factors of interfaces. We demonstrate that particle RB translation promotes both neck growth, and pore rounding and shrinkage. Moreover, the forces acting at GBs and pulling neighboring particles towards one another dynamically evolve as particles fuse. In contrast, particle RB rotation has no contribution to pore shrinkage. The translational force acting on an individual particle varies with not only its size, but also the number and sizes of its neighboring particles.     

Transport properties of porous media from the microgeometry of a three-dimensional voronoi network

In this work a way of calculating effective transport coefficients from the microgeometry of a porous medium is presented. The model material consists of a random packing of uniform spheres, and by applying the Voronoi—Delaunay tessellation technique the void between the spheres is simulated as a network of cylindrical pores. The tessellation yields all the necessary information for the structural characterization, such as the pore diameter, pore angle and pore length distribution functions and the topological interconnection. The effective transport coefficients of ordinary diffusion, Knudsen flow and viscous flow are calculated numerically by mass balancing at each network node and over all nodes of the system. The results obtained agree very well with the experimental ones, especially for ordinary diffusion. For Knudsen and viscous flow, inaccuracies in the estimation of the pore overlapping volume cause a relative error between the numerical and experimental results of the order of 16%–33%.