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.     

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.     

Microstructural Evolution During Sintering with Control of the Interface Structure

This paper reports recent theoretical perspectives and experimental results on microstructural evolution during sintering in terms of the interface structure, which is either rough (atomically disordered) or faceted (atomically ordered). The paper presents theoretical predictions and calculations of grain growth during liquid-phase sintering based on crystal growth theories. It is shown that various types of grain growth behavior, which may be normal, abnormal, or stagnant, can appear as a result of the coupling effects of the maximum driving force for growth and the critical driving force for appreciable growth. The predictions are also shown to be valid in the case of solid-state sintering. A number of experimental observations showing the effect of some critical processing parameters have been found to be in excellent agreement with the predictions. Principles of microstructure development (grain growth control) during sintering are suggested. In addition, the effect of the interface structure on densification is briefly described and discussed.     

Shape Dependence of the Coarsening Behavior of Niobium Carbide Grains Dispersed in a Liquid Iron Matrix

In niobium carbide–iron (NbC-Fe) specimens where the grains were faceted, abnormally large grains appeared during coarsening. Normal and uniform grain growth occurred when the grain shape was changed to a spherical morphology by the addition of a small amount of boron. The results have been discussed, in terms of a coarsening mechanism, depending on the atomic structure of the interface. For faceted grains with an atomically smooth interface structure, the coarsening was suggested to occur via two-dimensional nucleation and a lateral-growth mechanism. For spherical grains with an atomically rough interfacial structure, diffusion was suggested to control the coarsening process.     

Varistor Performance of ZnO-Based Ceramics Related to Their Densification and Structural Development

Electrical potential barriers are often observed in ZnO-based ceramics. Earlier studies on ZnO photoconduction have shown that the narrow regions, where the sintered grains have grown together, control the resistance of the entire sample. In those regions, the surface/volume ratio is sufficiently high for the acceptor concentration (which occurs because of adsorbed oxygen) to exceed the donor concentration inside the ZnO grains. More recent works have shown that Schottky barriers result from interface states because of the chemisorbed oxygen ion at the ZnO-ceramic grain boundaries. The work reported in this paper involves the relationship between the densification of the microstructure and the varistor performance of ZnO ceramics. The emphasis of densification percentage as an indicator of the degree of sintering shows the desirability of continuity across ZnO grain boundaries, without the presence of voids or films of second phases, in optimizing varistor behavior. The effect of oxygen partial pressure on the development of varistor microstructure and electrical properties, as well the kinetics of grain growth, during the sintering process have been determined and are discussed.     

The Effect of Particle Size Distributions on the Microstructural Evolution During Sintering

Microstructural evolution and sintering behavior of powder compacts composed of spherical particles with different particle size distributions (PSDs) were simulated using a kinetic Monte Carlo model of solid‐state sintering. Compacts of monosized particles, normal PSDs with fixed mean particle radii and a range of standard deviations, and log‐normal PSDs with fixed mode and a range of skewness values were studied. Densification rate and final relative density were found to be inversely proportional to initial PSD width. Grain growth was faster during the early stages of sintering for broad PSDs, but the final grain sizes were smaller. These behaviors are explained by the smallest grains in the broader PSDs being consumed very quickly by larger neighboring grains. The elimination of the small grains reduces both the total number of necks and the neck area between particles, which in turn reduces the regions where vacancies can be annihilated, leading to slower densification rates. The loss of neck area causes grain growth by surface diffusion to become the dominant microstructural evolution mechanism, leading to poor densification. Finally, pore size was shown to increase with the width of PSDs, which also contributes to the lower densification rates.     

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.     

Two-Step Sintering of Nanocrystalline ZnO Compacts: Effect of Temperature on Densification and Grain Growth

Two-step sintering (TSS) was applied on nanocrystalline zinc oxide (ZnO) to control the accelerated grain growth occurring during the final stage of sintering. The grain size of a high-density (>98%) ZnO compact produced by the TSS was smaller than 1 μm, while the grain size of those formed by the conventional sintering method was ∼4 μm. The results showed that the temperature of both sintering steps plays a significant role in densification and grain growth of the nanocrystalline ZnO compacts. Several TSS regimes were analyzed. Based on the results obtained, the optimum regime consisted of heating at 800°C (step 1) and 750°C (step 2), resulting in the formation of a structure containing submicrometer grains (0.68 μm). Heating at 850°C (step 1) and then at 750°C (step 2) resulted in densification and grain growth similar to the conventional sintering process. Lower temperatures, e.g., 800°C (step 1) and 700°C (step 2), resulted in exhaustion of the densification at a relative density of 86%, above which the grains continued to grow. Thermogravimetric analysis results were used to propose a mechanism for sintering of the samples with transmission electron micrographs showing the junctions that pin the boundaries of growing grains and the triple-point drags that result in the grain-boundary curvature.     

Spatial Variations in the Sintering Rate of Ordered and Disordered Particle Structures

Local sintering rates were measured in two-dimensional, ordered and disordered structures constructed from glass spheres. In ordered arrays, made from monosized spheres, the local sintering rates varied from 1/2 to 2 times the average sintering rate. In contrast, disordered arrays, made from bimodal particle sizes, sintered more homogeneously, the local sintering rate deviating less than 15% from the average. The total average densification strain was also greater for the disordered structures. As a result, for the same time and temperature cycle, the disordered structures sintered to near full density while the ordered structures did not. Poor densification in the ordered structure was attributed to packing defects such as domain walls and dislocations. Some evidence was obtained for a correlation between densification and the average coordination number of particles.     

Abnormal grain growth in iron-containing SiC fibers

Understanding the role of sintering aids during microstructure evolution is critical to the manufacture of densified SiC fibers. A variety of TEM characterization techniques are combined to investigate grain growth behavior in iron-doped SiC fibers. Ultra-large SiC grains in micron size, as the self-assembly of nano sub-grains into a similar orientation, were consistently discovered at the surface and indicative of abnormal grain growth. The growth front consisted of polycrystalline nanograins wetted by iron-rich particles, where several sub-grains were found to unify their (111) planes with a misorientation angle less than 10°, indicating grain rotation at the growth front. It is proposed that iron-rich particles form a quasi-liquid interfacial phase during sintering, which facilitates coherent attachment of grains and results in fast grain growth using neighboring irregular-shaped nanograins as building blocks. The imperfect ordered coalescence of nanograins introduces structural heterogeneities, including low angle grain boundaries and porosities.     

Designing nanomaterials with desired mechanical properties by constraining the evolution of their grain shapes

Grain shapes are acknowledged to impact nanomaterials' overall properties. Research works on this issue include grain-elongation and grain-strain measurements and their impacts on nanomaterials' mechanical properties. This paper proposes a stochastic model for grain strain undergoing severe plastic deformation. Most models deal with equivalent radii assuming that nanomaterials' grains are spherical. These models neglect true grain shapes. This paper also proposes a theoretical approach of extending existing models by considering grain shape distribution during stochastic design and modelling of nanomaterials' constituent structures and mechanical properties. This is achieved by introducing grain 'form'. Example 'forms' for 2-D and 3-D grains are proposed. From the definitions of form, strain and Hall-Petch-Relationship to Reversed-Hall-Petch-Relationship, data obtained for nanomaterials' grain size and conventional materials' properties are sufficient for analysis. Proposed extended models are solved simultaneously and tested with grain growth data. It is shown that the nature of form evolution depends on form choice and dimensional space. Long-run results reveal that grain boundary migration process causes grains to become spherical, grain rotation coalescence makes them deviate away from becoming spherical and they initially deviate away from becoming spherical before converging into spherical ones due to the TOTAL process. Percentage deviations from spherical grains depend on dimensional space and form: 0% minimum and 100% maximum deviations were observed. It is shown that the plots for grain shape functions lie above the spherical (control) value of 1 in 2-D grains for all considered grain growth mechanisms. Some plots lie above the spherical value, and others approach the spherical value before deviating below it when dealing with 3-D grains. The physical interpretations of these variations are explained from elementary principles about the different grain growth mechanisms. It is observed that materials whose grains deviate further away from the spherical ones have more enhanced properties, while materials with spherical grains have lesser properties. It is observed that there exist critical states beyond which Hall-Petch Relationship changes to Reversed Hall-Petch Relationship. It can be concluded that if grain shapes in nanomaterials are constrained in the way they evolve, then nanomaterials with desired properties can be designed.     

Abnormal Grain Growth of Lead Zirconium Titanate (PZT) Ceramics Induced by the Penetration Twin

Lead zirconium titanate (PZT) ceramic specimens were prepared by liquid phase sintering with excess PbO. By the addition of a small amount of MgO, the grain shape was changed from spherical to angular. When SiO₂ was further added, twin was induced in a few grains, which grew abnormally during heat treatment. Through the electron backscatter diffraction analysis and the observation of three-dimensional grain morphology, the abnormally grown large PZT grains were determined to be penetration twinned. Abnormal grain growth was suggested to be because of reentrant edges formed at the twinned grains.     

Effect of Sintering Atmosphere on Grain Shape and Grain Growth in Liquid-Phase-Sintered Silicon Carbide

We investigated the effects of the sintering atmosphere on the interface structure and grain-growth behavior in 10-vol%-YAG-added SiC. When α-SiC was liquid-phase-sintered in an Ar atmosphere, the grain/matrix interface was faceted, and abnormal grain growth occurred, regardless of the presence of α-seed grains. In contrast, when the same sample was sintered in N₂, the grain interface was defaceted (rough), and no abnormal grain growth occurred, even with an addition of α-seed grains. X-ray diffraction analysis of this sample showed the formation of a 3C (β-SiC) phase, together with a 6H (α-SiC) phase. These results suggest that the nitrogen dissolved in the liquid matrix made the grain interface rough and induced normal grain growth by an α→β reverse phase transformation. Apparently, the growth behavior of SiC grains in a liquid matrix depends on the structure of the grain interface: abnormal growth for a faceted interface and normal growth for a rough interface.     

Influence of Aluminum Titanate Formation on Sintering of Bimodal Size-Distributed Alumina Powder Mixtures

The sintering behavior of green compacts, in which coarse alumina particles formed a skeletal structure and fine alumina and/or fine titania particles filled the voids of the skeletal structure, was investigated. Sinterability of the green compacts changed according to the titania content in the fine powder. The titania content of 33 mol% was the most effective for the densification. The volume expansion due to the aluminum titanate formation occurred in the voids of the skeletal structure, and the densification of the skeletal structure progressed more because the grain growth between the fine and coarse alumina particles did not proceed. As the titania content decreased, the densification did not progress more than that of the compact with 33 mol% titania content because the grain growth proceeded more. As the titania content increased, the expansion of the compacts was larger, and large grains were formed by the reaction between the titania and coarse alumina particles. Therefore, densification became difficult.     

Mechanism of Grain Growth and α-β'Transformation During Liquid-Phase Sintering of β'-Sialon

The rates of grain coarsening and α-β'transformation during the liquid-phase sintering of Si₃N₄-β'₆₀-YAG sialon have been measured at varying liquid fractions and z values in order to determine the rate-controlling mechanism. The average β'-grain size after sintering for 16 h at 1650°C shows no variation with the liquid-matrix fraction if the z value is fixed and a marked increase with the z value if the liquid fraction is fixed. Similarly, the amount of untransformed α-phase after sintering for 2.5 or 3.5 min at 1600°C shows no variation with the liquid-matrix fraction if the z value is fixed and a marked decrease with the z value if the liquid fraction is fixed. These results show that the grain coarsening and the α-β'transformation are controlled by the interface reaction. This conclusion is consistent with the observations in carbide-Co systems and with the theoretical predictions that the growth of faceted grains is controlled by interface reaction and that of spherical grains by diffusion. A general rule between the shape and the growth mechanism of grains in a liquid matrix is thus proposed.     

Coarsening Behavior of Tricalcium Silicate (C3S) and Dicalcium Silicate (C2S) Grains Dispersed in a Clinker Melt

Microstructural evolution during the heat treatment of cement clinker was investigated. Two model specimens, which consisted of faceted tricalcium silicate (C₃S) and spherical dicalcium silicate (C₂S) grains dispersed in a liquid matrix, were prepared with 5 wt% of large seed particles. The seed particles of faceted C₃S grains grew extensively, whereas those of the spherical C₂S grains grew rather slowly, relative to the matrix grains. As a consequence, C₃S grains exhibited a bimodal size distribution that was typical of exaggerated grain growth, whereas C₂S grains retained a uniform and normal size distribution. These results suggest that the growth of faceted C₃S grains was controlled by the interface atomic attachment, such as two-dimensional nucleation, and that of spherical C₂S grains was controlled by diffusion through the liquid matrix. The dependence of growth mechanisms on grain morphology has been explained in terms of the atomistic structure of the solid/liquid interface.     

Temperature Dependence of the Coarsening Behavior of Barium Titanate Grains

The coarsening behavior of large seed particles during the sintering of BaTiO₃ ceramics has been investigated. At 1350°C, the grains are faceted, and the seed particles grow extensively. At 1380°C, however, the grains are spherical, and coarsening of the seed particles is limited. The observed difference is discussed in terms of the growth mechanism and the atomic structure of the interfaces.     

Effect of Grain Shape on Abnormal Grain Growth in Liquid-Phase-Sintered Nb1−xTixC–Co Alloys

The effect of titanium substitution for niobium on the grain shape change, grain growth inhibition, and abnormal grain growth during liquid-phase sintering of Nb_{1− x} Ti_xC–Co alloy was studied. With increased titanium substitution, the shape of the Nb_{1− x} Ti _x C grains in the liquid cobalt matrix was changed from a cube with round corners to a cube with angular corners, which implied increased edge energy. As the grain corners became more angular, the grain growth became markedly inhibited, and abnormal grain growth occurred. The results could be best explained by the increased edge energy of the interface of the Nb_{1− x} Ti _x C grains, which increased the barrier for the growth by two-dimensional nucleation.     

Theoretical analysis of experimental densification kinetics in final sintering stage of nano-sized zirconia

The experimental densification kinetics of 7.8 mol% Y₂O₃-stabilized zirconia was analyzed theoretically during isothermal sintering in the final stage. By taking concurrent grain growth into account, a possible value of the grain-size exponent n was examined. The Coble’s corner-pore model recognized widely was found not to be applicable for explaining the densification kinetics. The corner-pore model of n = 4 shows a significant divergence in the kinetics at different temperatures. Microstructural observation shows that most pores are not located at grain corners and have a size comparable to the surrounding grains. The observed pore structure is similar to the diffusive model where single pore is surrounded by dense body. The diffusive model combined with theoretical sintering stress predicts n = 1 or n = 2, which shows a good consistence to the measured densification kinetics. During sintering of nano-sized powder, it is found that the densification kinetics can be explained distinctively by the diffusive single-pore model.     

Alternative Explanation for the Role of Magnesia in the Sintering of Alumina Containing Small Amounts of a Liquid Phase

The microstructural evolution during sintering of Al₂O₃ was investigated to determine the role of MgO additive, particularly when its concentration is very low (<200 ppm). Compared with specimens without MgO, a few Al₂O₃ grains were observed to grow enormously after the addition of 50 or 100 ppm MgO. When MgO content was increased to 200 ppm, on the other hand, the overall grain growth process was accelerated and many growing grains impinged on each other. In this case, therefore, a fine and unimodal grained microstructure was obtained. Sintering of Al₂O₃ in a MgO atmosphere further supported the promotion of grain growth by MgO. It is proposed that MgO promotes the grain growth of Al₂O₃ either by lowering the edge energy or by roughening the interface structure.