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.     

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.     

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.     

Densification and grain growth during solid state sintering of LaPO4

This work is devoted to the kinetic study of densification and grain growth of LaPO₄ ceramics. By sintering at a temperature close to 1500 °C, densification rate can reach up to 98% of the theoretical density and grain growth can be controlled in the range 0.6–4 μm. Isothermal shrinkage measurements carried out by dilatometry revealed that densification occurs by lattice diffusion from the grain boundary to the neck. The activation energy for densification (E_D) is evaluated as 480 ± 4 kJ mol⁻¹. Grain growth is governed by lattice diffusion controlled pore drag and the activation energy (E_G) is found to be 603 ± 2 kJ mol⁻¹. The pore mobility is so low that grain growth only occurs for almost fully dense materials.     

Transport mechanisms and densification during sintering: II. Grain boundaries

Finite element, meso-scale models provide a means to probe the mechanistic driving forces for particle evolution during sintering and were applied in a companion paper [Djohari, H., Martínez-Herrera J., Derby, J.J., 2009. Transport mechanisms and densification during sintering: I. Viscous flow versus vacancy diffusion. Chem. Eng. Sci., in press, doi:10.1016/j.ces.2009.05.018.] to compare different behaviors of the sintering of glassy particles by viscous flow and the sintering of idealized crystalline systems without a grain boundary via vacancy diffusion. Here, the effects of a grain boundary are included in the meso-scale model and resultant behavior is compared to prior cases. A grain boundary acts as a sink for vacancies, drawing a flux toward itself and allowing for their accumulation and collapse. The resultant solid-body motion of the particles leads to significant shrinkage at the onset of sintering; neck growth with little shrinkage was observed in systems without a grain boundary. These effects are scaled by the magnitude of the grain boundary diffusivity and the size of the dihedral angle.     

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.     

Densification of Alumina-Silicon Carbide Powder Composites: II, Microstructural Evolution and Densification

Microstructural evolution adn densification kinetics of Al₂O₃-SiC powder composites were studied using two different SiC powders. Examination of the microstructural evolution of Al₂O₃-fine SiC powder composites showed three well-defined stages of densification: the first was characterized by constant pore size and no grain growth; the second involved rapid pore coarsening and grain growth; the third was characterized by pore shrinkage and slow grain growth. Studies of the densification kinetics of Al₂O₃-coarse SiC powder composites exhibited two stages of densification: in the first stage there were no significant differences in densification rate between pure Al₂O₃ compacts and composites; in the second stage, however, differences in densification behavior between pure Al₂O₃ compacts and composites became pronounced.     

Sintering and densification of nanocrystalline ceramic oxide powders: a review

Abstract

Observation of the unconventional properties and material behaviour expected in the nanometre grain size range necessitates the fabrication of fully dense bulk nanostructured ceramics. This is achieved by the application of ceramic nanoparticles and suitable densification conditions, both for the green and sintered compacts. Various sintering and densification strategies were adopted, including pressureless sintering, hot pressing, hot isostatic pressing, microwave sintering, sinter forging, and spark plasma sintering. The theoretical aspects and characteristics of these processing techniques, in conjunction with densification mechanisms in the nanocrystalline oxides, were discussed. Spherical nanoparticles with narrow size distribution are crucial to obtain homogeneous density and low pore-to-particle-size ratio in the green compacts, and to preserve the nanograin size at full densification. High applied pressure is beneficial via the densification mechanisms of nanoparticle rearrangement and sliding, plastic deformation, and pore shrinkage. Low temperature mass transport by surface diffusion during the spark plasma sintering of nanoparticles can lead to rapid densification kinetics with negligible grain growth.     

Densification of Large Pores: II, Driving Potentials and Kinetics

A kinetic analysis of densification is presented for the case of isolated, identical pores separated by dense, polyerystal-line material where the grain size is a variable (smaller to larger, relative to the pore size). The analysis includes the influence of both grain growth and mass transport rates on the driving potential for mass transport to the pore. For the expected condition where the rate of grain growth is much greater than the rate of pore shrinkage, it is shown that the driving potential is relatively independent of pore surface curvature, and approaches (2γ_s/ R _po) sin (ψ_e/2) during grain growth, where γ_s is the surface energy per unit area of the material, ψ_e is the dihedral angle, and R _po is the initial pore radius. Using this driving potential, an expression is derived for the current densification rate. The proposed mechanism for mass transport is radial diffusion through a spherical polycrystalline unit cell containing a spherical pore, where diffusion is restricted to grain boundaries that intersect the pore. The expression includes the average separation distance between pores and the grain boundary area intersecting each pore. This expression is in qualitative agreement for data reported in Part I for a Zr(3Y)O₂ material where the grain size is always smaller than the pore size, and a Zr(8Y)O₂ material where the grain size is larger than the pore size.     

Kinetics of Constrained-Film Sintering

Results of shrinkage measurements on constrained and corresponding unconstrained films of materials that densify by viscous flow or solid-state diffusion mechanisms have been presented. Constrained-film shrinkage was measured in situ during sintering using laser reflectance; unconstrained-film shrinkage was measured using scanning electron microscopy (SEM). Data for unconstrained films were fitted to densification kinetics expressions for the operative densification mechanism. Constrained-film shrinkage behavior predicted by the Scherer-Garino model,¹ using expressions that fit data for the unconstrained case, was compared to actual data for the constrained films. Data for the viscous sintering case fit the predictions made by the model well, but data for densification by solid-state diffusion deviated from predicted behavior even when grain growth was accounted for, possibly because of pore growth caused by local densification.     

Kinetics and mechanisms for the densification and grain growth of the α-alumina fibers isothermally sintered at elevated temperatures

Understanding the densification and grain growth processes is essential for preparing dense alumina fibers with nanograins. In this study, the alumina fibers were prepared via isothermal sintering at 1200, 1300, 1400, and 1500 °C for 1–30 min. The phase, microstructure, and density of the sintered fibers were investigated using XRD, SEM, and Archimedes methods. It was found that the phase transformation during the isothermal sintering enhances the densification of Al₂O₃ fibers in the initial stage, while the pores generated during the phase transformation retard the densification in the later period. The kinetics and mechanisms for the densification and grain growth of the fibers were discussed based on the sintering and grain growth models. It was revealed that the densification process of the fibers sintered at 1500 °C is dominated by the lattice diffusion mechanism, while the samples sintered at 1200–1400 °C are dominated by the grain boundary diffusion mechanism. The grain growth of the Al₂O₃ fibers sintered at 1200–1300 °C is governed by surface-diffusion-controlled pore drag, and that sintered at 1400 °C is dominated by lattice-diffusion-controlled pore drag.     

Hot‐Pressing Kinetics and Densification Mechanisms of Boron Carbide

The hot‐pressing kinetics of boron carbide at different stages in the hot‐pressing process was investigated. Based general densification equation and pore‐dragged creep model, the densification and grain growth kinetics were analyzed as a function of various parameters such as sintering temperature, sintering pressure and dwell time. Stress exponent of n ≈ 3 at the initial dwell stage suggests the plastic deformation may dominates the densification. The further TEM observations and the calculation based on effective stress and plastic yield stress also indicate that plastic deformation may occur and account for the large increase in density at the initial stage of sintering. Calculated grain size exponent of m ≈ 3 suggests that the grain‐boundary diffusion dominates the densification at the final stage. During the final stage of sintering, grain growth may be determined by evaporation/condensation and grain‐boundary migration.     

固相烧结——Ⅲ 实验：超细氧化锆素坯烧结过程中的 晶粒与气孔生长及致密化行为

研究了超细Y-TZP和YSZ粉料成型体在烧结中期的晶粒生长、气孔生长和致密化行为.根据作者前文     

Sintering kinetics and properties of NiFe2O4-based ceramics inert anodes doped with TiN nanoparticles

Sintering kinetics of NiFe₂O₄-based ceramics inert anodes for aluminum electrolysis doped 7 wt% TiN nanoparticles were conducted to investigate densification and grain growth behaviors. The linear shrinkage increased gradually with the increasing sintering temperature between 1000 and 1450°C, whereas the linear shrinkage rate exhibited a broad peak. The maximum linear shrinkage rate was obtained at 1189.4°C, and the highest densification rate was achieved at the relative density of 75.20%. Based on the pressureless sintering kinetics window, the sintering process was divided into the initial stage, the intermediate stage, and the final stage. The grain growth exponent reduced with increased sintering temperature, whereas the grain growth activation energy decreased by increasing sintering temperature and shortening dwelling time. The grain growth was mainly controlled by atomic diffusion. NiFe₂O₄-based ceramics possessed high-temperature semiconductor essential characteristics. The electrical conductivity of NiFe₂O₄-based ceramics first increased and then decreased with increasing sintering temperature, reached their maximum value (960°C) of 33.45 S/cm under 1300°C, mainly attributed to the relatively dense and uniform microstructure. The thermal shock resistance of NiFe₂O₄-based ceramic was improved by a stronger grain boundary bonding strength and lower coefficient of linear thermal expansion.     

Effect of Pore Distribution on Microstructure Development: III, Model Experiments

Model experiments have been conducted on a series of alumina samples in which the microstructures have been tailored to conform to the classical configuratins depicted in the models of final-stage sintering. Simultaneous measurements of sintered density, grain size, pore number density, and pore size distribution were made as a function of sintering time at constant temperature (1850°C). The data supported a model of grain-boundary-diffusion-controlled densification and surface-diffusion-controlled grain growth. An atom flux equation for grain-boundary diffusion transport was deduced from the data. The kinetics analysis highlights the importance of incorporating the number of pores per grain as an independent variable in mechanistic studies of final-stage sintering. The number of pores per unit volume was identified as a critical factor influencing densification kinetics. The effect of pore distribution on microstructure development was simulated for comparison with the data obtained from the model experiments.     

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.     

The sintering kinetics of ultrafine tungsten carbide powders

The sintering kinetics of nano grained tungsten carbide (n-WC) powders has been analyzed by non isothermal and isothermal sintering. Non isothermal sintering experiments reveal a multi staged sintering process in which at least three major sub-stages can be distinguished. The isothermal shrinkage strain also exhibits an asymptotic behavior with time indicating an end point density phenomenon in most of the temperature ranges. Combined microstructural and kinetic data analyses suggest that differences in the sinterability of inter and intra agglomerate pore phases introduce sub-stages in the sintering process which manifest as stagnant density regions in both the isothermal and non isothermal experiments. Kinetic analysis of the data reveals very low activation energies for sintering suggesting that particle rearrangement and agglomeration at low temperatures may be brought about by surface diffusion leading to neck growth and grain rotation. At higher temperatures rapid grain boundary diffusion by overheating along inter particle boundaries induced by sparking may be a dominant sintering mechanism. Although grain growth and densification in conventional WC powders generally obey an inverse relation to each other, in n-WC powders both can act synergistically to increase the net densification rate. In fact, complete densification cannot be achieved in n-WC powders without grain growth as one abets the other.     

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 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.     

Sintering kinetics window: an approach to the densification process during the preparation of transparent alumina

In this work, sintering kinetics window combined with microstructure development is adopted to understand the densification process of transparent alumina ceramic using submicrometre alumina powder. Alumina powder was densified via pressureless sintering and spark plasma sintering to explore the sintering behaviours of submicrometre alumina powder respectively. Sintering process could be divided into three typical stages, the criterion of which is based on whether the dominant mechanism is independent particle rearrangement or independent atomic diffusion. Through the investigation of sintering mechanisms of both sintering methods in the same way, it is found that it is necessary to remove the large pores (>100 nm) before grain growth is activated for complete densification. It suggests that at the temperature when the grain growth is activated, the corresponding pore structure proves to be the crucial factor influencing the complete densification of transparent alumina ceramic.