Pore Drag Research Articles

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.

Modeling the grain growth kinetics of doped nearly fully dense nanocrystalline ceramics

A grain growth model to describe dopant effects on nanocrystalline ceramics is proposed by incorporating the dopant-segregation-dependent grain boundary (GB) energy and the GB mobility subjected to intrinsic drag and pore drag (both affected by dopant segregation) into the parabolic growth formula. The model addresses the common case of residual porosity in grain growth behavior. Taking near-fully dense nanocrystalline lanthanum doped Yttria stabilized Zirconia (La doped YSZ) as the system of study, the grain growth behavior was explored using the model. The substantially suppressed grain growth in La doped YSZ as compared to La-free YSZ could be attributed to the combined effect of thermodynamically reduced GB energy and kinetically reduced GB mobility. Contrary to previous assumptions, the model suggests that, relative to the GB energy overall effect, the effect of the dopant on the GB mobility plays a more significant role in reducing coarsening. Furthermore, model calculation shows that both intrinsic drag and pore drag makes certain contribution to the evolution of GB mobility during the grain growth.

Sintering and grain growth in SrTiO<sub>3</sub>: impact of defects on kinetics

The microstructural evolution of undoped and iron doped SrTiO3 is analyzed during sintering at 1280°C in air and reducing atmosphere. The focus is on densification and grain growth during different holding times investigated by dilatometric studies and microstructural analysis. The sintering equations developed by Coble are used to characterize sintering. The influence of point defects on diffusion, densification and grain growth is evaluated using basic defect chemistry equations. A space charge concept at the grain boundaries is added to bulk defect chemistry concepts to understand sintering of perovskites, since the major part of mass transport during sintering occurs in this region. The extension of the defect chemistry concept allows to explain the change in diffusion mechanism during sintering (grain boundary diffusion or bulk diffusion) as well as grain growth stagnation observed in iron doped SrTiO3. The results are used to separate the complex interplay of densification and grain growth. While grain growth decreases with increasing defect concentration, no clear trend is observed for the densification kinetics, since both grain growth and diffusion are relevant. The results show that grain growth during sintering provides comparable results to grain growth experiments in dense SrTiO3 and, thus, pore drag seems not to be important. The calculated diffusion coefficients are in good agreement with literature data and show a strong dependency on the concentration of strontium vacancies.

Phase-field study of pore-grain boundary interaction

During final stage sintering, a complex interplay of densification and grain growth dominates microstructural evolution. Grain growth starts, when pore drag effects become less important due to pore shrinkage. This grain growth then decreases the driving force available for sintering. Accordingly, the interplay of pores and grain boundaries needs to be considered in detail. A phasefield model was extended to treat pore dynamics under consideration of pressure stability. To study pore attachment and detachment at moving interfaces, an idealized hexagonal microstructure with a constant driving force relationship for pore migration is constructed. Additionally, realistic polycrystalline microstructures were used. The model is in good agreement with experiments and analytic equations. Three different cases were observed in the realistic microstructure: pore attachment at the moving interface, partial and total pore detachment. However, in the partial case, the initial location of pores was found to be important: pores tend to migrate from quadruple junctions over triple junctions to grain boundary planes, where they eventually detach. This results in a variation of pore detachment, which is not captured in analytic equations. Therefore large simulation setups are required to reflect the impact of initial pore location on pore drag effects.

Effect of green density on the templated-grain growth in CuO-doped (K,Na)NbO3 ceramics

Templated-grain growth (TGG) behavior was investigated in 1mol% CuO-doped (K0.5Na0.5)NbO3 (KNN) ceramics. Textured green sheets were prepared by a tape casting process using a slurry containing NaNbO3 template crystals and fine KNN matrix powders. Laminated ceramic green sheets with different green densities were annealed at temperature ranging from 1,100 to 1,160°C. Highly textured ceramics were obtained from both low green density (LGD) and high green density (HGD) samples. The TGG and the densification proceeded non-uniformly in the LGD sample. The LGD sample showed high porosity after annealing while the HGD sample displayed high density. Both the HGD and LGD samples displayed similar texture development with increasing sintering time and temperature despite a large difference in the sintered density. These results demonstrate that the pore drag force is not the critical factor for the TGG in CuO-doped KNN textured ceramics, which is contrary to previous reports.

Investigation of final-stage sintering of various microsize structures prepared by micro powder injection molding

Micro powder injection molding (μPIM) has been developed as a potential technique for mass production of microcomponents in microsystems due to its shaping complexity at low cost, in which sintering is a crucial step to dictate the final properties of the microcomponents. In this paper, final-stage sintering behavior of 316L stainless steel microsize structures prepared by μPIM, φ100 μm and φ60 μm, respectively, was studied. The effect of size reduction in the regime of micrometers on the density of various microsize structures was investigated. Sintering kinetics of the microsize structures of φ100 μm and φ60 μm were studied based on particle level sintering models. It is found that the microsize structures of φ60 μm had higher density than the microsize structures of φ100 μm given the same sintering condition. The results indicate that size reduction in the regime of micrometers facilitated densification of microsize structures. The grain growth mechanism of microsize structures varied with size. Whereas the grain growth of the microsize structures of φ100 μm is governed by surface-diffusion-controlled pore drag, the grain growth of the microsize structures of φ60 μm is controlled by boundary diffusion. During densification, the microsize structures, φ100 μm and φ60 μm, are both controlled by lattice diffusion. The corresponding activation energies are reported in the paper.

Densification and grain growth during solid state sintering of LaPO 4

This work is devoted to the kinetic study of densification and grain growth of LaPO 4 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.

Understanding Grain Growth and Pore Elimination in Vacuum-Plasma-Sprayed Titanium Alloy

In the present study, grain growth, pore elimination, and densification of the vacuum-plasmasprayed structure of Ti-6Al-4V alloy were investigated. The near-net-shaped formed components were deposited using a vacuum plasma spraying process. The as-sprayed specimens were heat treated at 1040 � C (50 � C above the b transus temperature) for up to 1440 minutes in an inert gas atmosphere. The apparent density of the as-sprayed and heat-treated samples was determined by the water displacement method. The theoretical density of the heat-treated samples was calculated from lattice parameters and phase compositions determined using X-ray diffraction (XRD). Densification of the heat-treated specimens at a given temperature and time was determined. Results revealed that the density initially increased sharply with isothermal heat treatment time and then reached a plateau. During short heat treatment times, the grains grow quickly within individual splats at a rate consistent with intrinsic boundary mobilities. For longer heat treatment times, the grain boundary mobility was limited by pore drag, and the grain growth rate was reduced. The pore and grain sizes increased with increasing isothermal heat treatment time up to about 17 and 100 lm, respectively.

Densification and grain growth of stainless steel microsize structures fabricated by μMIM

Micro metal injection molding (μMIM) is being developed by some researchers for possible mass production of metallic microcomponents. Knowledge of densification and grain growth of structures in the micrometer regime is important for the design of microcomponents due to their impacts on dimensional tolerance and mechanical properties. In this paper, the effects of sintering temperature and time on densification and grain growth of stainless steel microsize structures fabricated by μMIM were investigated. In particular, the density of the microsize structures was compared with that of the components, dimensions in the millimeter range, on which the microsize structures reside. Models proposed by Kang, Brook, and Zhao and Harmer were used to study the densification and grain growth kinetics of microsize structures of ∅100μmat the final stage of sintering. Dense layers were formed on the microsize structures. Thus, the density of the microsize structures is higher than that of the microstructured components. The thickness of the dense layers increased with either increasing temperature or time. Zhao and Harmer’s model for lattice diffusion controlled densification and Brook’s grain growth model for lattice diffusion controlled pore drag exhibited good fits for the experimental results of microsize structures.

Anisotropic grain growth with pore drag under applied loads

In the final stage of sintering of ceramics, residual pores co-evolve with grain boundaries because of incomplete densification. Their interactions coupled with external loads are critical to the microstructural evolution of structural ceramics. A modified two-dimensional (2D) diffuse-interface phase field model, which differs from the boundary-tracking methods, is utilized to investigate the effects of stochastically distributed pore drag on grain growth kinetics and morphological evolution process of ceramics under applied loads. Contributions from both the boundary energy and elastic strain energy caused by pore drag forces and applied loading are incorporated in the modified phase field model to describe the isotropic or cubically anisotropic behaviors of polycrystalline materials. The temporal evolution of the spatially dependent grain orientation variables is determined by numerically solving non-linear Ginzburg–Landau equations using a semi-implicit Fourier-spectral method. Numerical results show that the anisotropic strain energy dominates the non-self-similar growth manner, leads to ordered grain morphologies and changes the growth rate.

Two-dimensional analysis of pore drag and drop

We consider stationary coupled migration (drag) and conditions for separation (drop) of pores situated on grain boundaries or triple junctions in two-dimensional (2D) geometry. Pore mobility is realized by surface diffusion and boundaries migrate owing to surface tension. A small velocity approximation yields pore mobility and estimates for the velocity at which separation occurs. The estimate is refined by numerical solution. In contrast to previous expectations, separation occurs in 2D and the critical velocity for pores with circular cross section is non-zero. Our numerics are further confirmed by bifurcation analysis. The critical velocities for 2D pores at triple junctions are considerably smaller than for 2D pores on grain boundaries, which in turn are smaller by a factor of two to three compared to critical velocities of three-dimensional lenticular pores on grain boundaries. We also determine the coupled pore-boundary mobility and demonstrate that the boundary mobility is practically always reduced by pores.

Three‐Dimensional Simulation of Grain Growth in the Presence of Mobile Pores

A kinetic, three‐dimensional Monte Carlo model for simulating grain growth in the presence of mobile pores is presented. The model was used to study grain growth and pore migration by surface diffusion in an idealized geometry that ensures constant driving force for grain growth. The driving forces, pore size, and pore mobilities were varied to study their effects on grain‐boundary mobility and grain growth. The simulations captured a variety of complex behaviors, including reduced grain‐boundary velocity due to pore drag that has been predicted by analytical theories. The model is capable of treating far more complex geometries, including polycrystals. We present the capabilities of this model and discuss its limitations.

Influence of vanadium substitution on sintering behaviour of Pb 3(VO 4) 2(1− x) (PO 4) 2 x ceramics

Intermediate-stage sintering has been investigated in lead orthophosphovanadates Pb 3(VO 4) 2(1− x) (PO 4) 2 x . It was found that rich-vanadium compounds such as Pb 3(VO 4) 2 and Pb 3(VO 4) 1.6(PO 4) 0.4 densify rapidly with important grain growth. For these compounds grain growth is controlled by grain boundaries and densification occurs by a mixed mechanism with lattice and grain boundary diffusion. For Pb 3(PO 4) 2, sintering mechanism supports a model of grain-boundary-controlled densification and grain growth is a surface diffusion-controlled pore drag mechanism. Moreover, the presence of phosphorus in compounds' formulae, tends to decrease the grain-boundary mobility, preventing pore-boundary separation. The kinetics analysis highlights the importance of vanadium substitution in modifying the diffusion coefficient of rate-limiting species.

Effect of initial grain size on sintering trajectories

Sintering trajectories were simulated for different initial grain sizes assuming grain-boundary diffusion as densification mechanism and either pore drag or intrinsic grain-boundary mobility as grain growth mechanisms. Computation of comparable sintering trajectories for initial grain sizes between 10 nm and 250 nm necessitated an adjustment of the isothermal sintering temperature. Conditions where one of the two coarsening mechanisms prevails were determined and shown to depend on density, grain size, and the ratio S of the rate constants related to the two coarsening mechanisms, but little on the dihedral angle. All computed sintering trajectories have a common shape, being very flat at low densities and exhibiting most grain growth in the last 5% of densification before reaching their end-point density. Depending on the difference between the activation energies related to the dominant densification and coarsening mechanisms, a reduction in grain size might be beneficial for densification.

Solid-State Sintering of Hydrothermal Powders: Densification and Grain Growth Kinetics of Nickel–Zinc Ferrites

The hydrothermal process was employed to produce single-phase submicrometric NiZn ferrites. The materials were sintered in air at different temperatures and times (1100 to 1400°C, 5 to 240 min). After sintering, highly dense ceramic bodies with different microstructures were obtained. X-ray diffraction, helium pycnometry, nitrogen adsorption technique, and optical and scanning electron microscopy were used to determine the microstructural parameters of the samples. The modeling of the sintering process demonstrates a crossover between the densification mechanisms from grain boundary diffusion to lattice diffusion with increasing sintering temperature. It is also shown that, in the final-stage sintering, the grain growth kinetics is controlled by pore drag.

The normal grain growth behaviour of nominally pure calcitic aggregates

The normal grain growth behaviour of four different, but all nominally pure, calcite powders (99%+ analytic grade calcite, 99.7% chalk, 99.97% crushed Iceland Spar, 99.95%+ chelometric grade calcite) has been investigated as a function of temperature (550, 600, 650, 700 °C) and confining pressure (100, 190 MPa) under both “dry” and hydrostatic (P fluid = P total) conditions. The initial particle size of both the analytic grade and chelometric grade calcite was about 5 μm, and that of the chalk was about 3 μm, while the experiments on the Iceland Spar were conducted on powders of three different initial particle sizes (3.4, 7.5, 38.5 μm). On each material, at each pressure/temperature condition 6 to 15 experiments, equally spaced in log time from 15 minutes to 50 days, were conducted. Under dry conditions all four materials recrystallized to aggregates which contained less than 2% porosity and which had a grain size of between 4 and 20 μm (depending on the initial particle size). Subsequently the aggregates coarsened by normal grain growth, with the kinetics of the growth process being controlled by the rate at which the grain boundaries could drag the residual pores with them as they migrated. Under nominally identical conditions both the mechanism and rates of pore drag differed greatly for the different materials, implying that this process is highly sensitive to trace solute impurity concentrations. This sensitivity renders the task of providing a systematic account of dry calcite grain growth kinetics highly problematic. Under hydrostatic conditions all the powders followed the same normal grain growth kinetics in which the growth process was rate-controlled by diffusion through the pore fluid on the grain boundaries. An activation enthalpy of 162.6 kJ mol−1 and an activation volume of 34.35 cm3 mol−1 was obtained for this process.

Effect of Yttrium and Lanthanum on the Final‐Stage Sintering Behavior of Ultrahigh‐Purity Alumina

Final‐stage sintering has been investigated in ultrahigh‐purity Al2O3 and Al2O3that has been doped individually with 1000 ppm of yttrium and 1000 ppm of lanthanum. In the undoped and doped materials, the dominant densification mechanism is consistent with grain‐boundary diffusion. Doping with yttrium and lanthanum decreases the densification rate by a factor of ˜11 and 21, respectively. It is postulated that these large rare‐earth cations, which segregate strongly to the grain boundaries in Al2O3, block the diffusion of ions along grain boundaries, leading to reduced grain‐boundary diffusivity and decreased densification rate. In addition, doping with yttrium and lanthanum decreases grain growth during sintering. In the undoped Al2O3, surface‐diffusion‐controlled pore drag governs grain growth; in the doped materials, no grain‐growth mechanism could be unambiguously identified. Overall, yttrium and lanthanum decreases the coarsening rate, relative to the densification rate, and, hence, shifted the grain‐size‐density trajectory to higher density for a given grain size. It is believed that the effect of the additives is linked strongly to their segregation to the Al2O3grain boundaries.

A theoretical study of grain growth in porous solids during sintering

The processes of grain boundary migration, pore drag and pore/boundary separation are described on the basis of the phenomenological equations for boundary migration and surface diffusion. Cylindrical pores on triple grain junctions are assumed to represent the open porosity during intermediate-stage sintering. It is found that cylindrical pores can hardly detach from migrating boundaries. Three-dimensional closed pores, however, which predominate during final stage sintering, can separate from migrating grain junctions. The separation process is modelled numerically and the conditions for separation are formulated. Analytical approximations for the pore mobility are shown to describe the numerical results well. They serve to establish effective mobilities of grain boundaries bearing pores in various configurations. Classical theories of grain coarsening are modified by using these effective mobilities. Mechanical constitutive models of sintering contain the grain size as an internal variable. The present analysis leads to an evolution equation for the average grain size, which depends on the volume fraction of the pores and on their configuration.

Pore Drag and Pore‐Boundary Separation in Alumina

Microdesigned interfacial pore structures were used to study pore drag and pore‐boundary separation in Al2O3. This approach allows the creation of pore arrays containing pores of controlled size and spacing at well‐defined singlecrystal seed/polycrystalline matrix interfaces, and enables experimental determination of the peak pore velocity. From the peak pore velocity, values of the surface diffusion coefficient pertinent to sintering can be extracted. At 1600°C, the surface diffusion coefficient is ∼1 × 10−7 cm2/s for undoped Al2O3 and ∼4 × 10−7 cm2/s for MgO‐doped Al2O3. The values appear to be insensitive to the seed orientation for the two seed orientations studied. The results suggest a strong influence of pore spacing on the separation condition in undoped Al2O3, and a diminished influence in MgO‐doped Al2O3. Quantitative agreement between theoretically predicted and experimentally observed separation/attachment conditions was obtained.

High Temperature Oxidation of Nickel at 1373 K in CO ‐ CO 2 ‐ O 2 Atmospheres and Morphology Analysis on Scales

High temperature oxidation of nickel has been studied at 1373 K in atmospheres, at oxygen partial pressures between . The oxidation kinetics have been followed by continuous mass gain measurements using a thermobalance at the oxidation temperature and by measurements of the scale thickness in metallographic cross sections, after cooling. The grain growth of during oxidation has been also investigated. A double‐layered scale is formed near platinum markers, although only a single scale is observed away from the markers. The outer layer is identical in thickness to the scale formed away from markers, and the growth rate is controlled by the outward diffusion of nickel ions. The diffusivity of nickel ions is proportional to at oxygen partial pressures higher than ≈10 Pa. The oxygen pressure dependence of the diffusivity indicates that the predominant defect is a doubly‐charged nickel vacancy. At oxygen partial pressures lower than ≈10 Pa, the oxygen pressure dependence becomes smaller, suggesting extrinsic behavior. The formation of the inner layer is explained, assuming the inward oxygen transport along grain boundaries in the outer layer. The size of the oxide grains, away from markers, is almost the same as that of the nickel substrate, but the oxide near the markers is much smaller. Grains near the markers coarsen, and the cube of the grain size is proportional to time, and the rate constant is also proportional to .These results suggest that grain growth proceeds through the pore drag mechanism, and that the rate is determined by the lattice diffusion of nickel ions.