Apparent Activation Energy For Densification Research Articles

Densification kinetics of nano-hematite using microwave assisted dilatometry

The aim of this paper was to study the densification kinetics of nano-hematite using a microwave assisted dilatometry at 2.45 GHz and kinetics models as an approximation to understand the sintering behavior using microwave heating. A horizontal dilatometer coupled to a multimodal microwave oven and conventional horizontal dilatometer were used to compare the results. The hematite was synthesized by the modified sol-gel method in order to ensure the purity, nanometric scale and intermediate particle size distribution in the starting powder. Novel values of apparent activation energy for densification of nano-hematite were obtained for the initial and intermediate stages of sintering using microwave heating at 2.45 GHz. The results showed that the microwave heating needs 10% less energy to start the initial sintering stage and 56% less energy for densification in the intermediate stage both compared with conventional heating sintering. After the final stage of sintering, smaller grain growth was obtained in microwave heating, as well as a reduction in the final grain size considering the increase in the heating rate.

Densification mechanisms of UO2 consolidated by spark plasma sintering

Despite the growing interest in the spark plasma sintering (SPS) of uranium dioxide, its sintering mechanisms have yet to be studied in great detail. Herein we propose a direct method to calculate the apparent activation energy for densification, Qact, and the stress exponent, n, for SPS of nearly stoichiometric UO2. A set of experiments performed at different heating rates (CHR) and different pressures levels allowed us to calculate Qact and n, respectively, though we were limited to a theoretical density between 50% to 75 %. The master sintering curve was employed as a complementary method to compare Qact. The average values were Qact =96 kJ/mol (CHR), Qact = 100 kJ/mol (MSC) and n = 1.4. We have therefore proposed grain boundary diffusion coupled with grain boundary sliding as the densification mechanism. The activation energy in SPS tends to be lower compared with that in other processes like conventional sintering (250−450 kJ/mol), creep (350−550 kJ/mol) and hot pressing (222 kJ/mol and 480 kJ/mol).This decrease could be due to the effect of the electric field combined with the higher heating rates, typical of SPS.

Sintering and grain growth kinetics in La0.85Sr0.15MnO3–Ce0.9Gd0.1O1.95 (LSM–CGO) porous composite

Abstract The sintering kinetics in La 0.85 Sr 0.15 MnO 3 –Ce 0.9 Gd 0.1 O 1.95 (LSM–CGO) porous composite was studied by applying a two-stage master sintering curve (MSC) approach and comparing with LSM and CGO single-phase materials. In the two-stage MSC, sintering mechanisms occurring at different stages were separated with respect of density, giving a typical apparent activation energy values for each sintering stage of the LSM–CGO system. Compared with the single-phase materials, retardant effect of the different phases on mass diffusion leads to much higher apparent activation energy for densification of the composite. Similarly, constrain effect was also observed in grain growth in the composite. Particularly, in the investigated temperature range (1100–1250 °C), the determined grain boundary mobility of CGO in the LSM–CGO composite (10 −18 –10 −16 m 3 N −1 s −1 ) is comparable with the single-phase CGO, while the grain boundary mobility of LSM in the composite (10 −17 –10 −16 m 3 N −1 s −1 ) is around 1 order of magnitude smaller than the single-phase LSM.

Sintering kinetics of YAG ceramics

Solid state reactive (SSR) sintering kinetics was observed for YAG ceramics. There were two densification stages in sintering process due to its reaction. After the first stage, samples began to expand, then, the second densification stage began. At a heating rate of 10 °C/min, the sample warped down and warped back to straight. The apparent activation energy of the first densification process was about 522 kJ/mol for the initial shrinkage of Al2O3 and Y2O3 mixed powder green-body, which increased in the following process due to the solid state reaction. In the second densification stage, synthesis reaction of YAG still worked. Green-bodies processed with higher heating rate got more shrinkage at the same temperature than lower heating rate green bodies. And its kinetic field diagram was abnormal, compared with that of other reported ceramics, such as Al2O3. It was found that the reaction of YAG provided positive effect to the sintering driving force. The apparent activation energy for densification of SSR YAG sintered in ArH5 atmosphere was 855 kJ/mol at temperature holding sintering. And the apparent activation energy for grain growth was 1053 kJ/mol.

Microwave versus conventional sintering: Estimate of the apparent activation energy for densification of α-alumina and zinc oxide

Abstract A comparative study between the conventional and 2.45 GHz microwave multimode sintering behavior of insulator (α-Al2O3) and semi-conductive ceramic (ZnO) was systematically investigated. The apparent activation energy of nonisothermal sintering was determined by way of the Arrhenius plot of densification data at constant heating rates (CHR) and the concepts of Master Sintering Curves (MSCs), respectively. During microwave densification process, the apparent activation energy was about 90 kJ/mol less than the value for conventional sintering of Al2O3 applying these two estimation methods. However, an opposite result was obtained in the case of ZnO, although its densification process had been also accelerated by microwave as well as Al2O3. The significant differences in activation energy give a good proof of the difference in diffusion mechanism induced by the electromagnetic field underlying microwave sintering.

Influence of La Doping on the Apparent Activation Energy of α-Al<sub>2</sub>O<sub>3</sub> during the Densification Process at Constant Heating-Rate

The apparent activation energy for densification is a characteristic quantity that elucidates the fundamental diffusion mechanisms during the sintering process. Based on the Arrhenius theory, the activation energy for densification of the pure and La doped α-Al2O3at constant heating-rates sintering has been estimated. Sintering of α-Al2O3and La doped powder has been executed by the way of a push rod type dilatometer. It was shown that the shrinkage and the relative density of the samples decreased with increasing heating rates. At the same sintering condition, the shrinkage of the pure α-Al2O3was higher than that of the La doped. According to the calculation, it was found that the apparent activation energy had a single value and did not depend on the relative density for both samples. The apparent activation energy of the pure α-Al2O3was 374.3kJ/mol, which was lower than that of La doped (966.5kJ/mol). So the densification process for α-Al2O3was retarded due to La doping, which was consistent with experimental results of the shrinkage.

Sintering behavior and mechanisms of NiO-doped 8 mol% yttria stabilized zirconia

Sintering behavior and densification mechanisms of NiO-doped YSZ were investigated by using a dilatometer, combined with XRD, SEM and HRTEM characterization. The solubility of NiO in YSZ is found to be 0.5–1 mol% at 1500 °C by XRD, and TEM reveals that, beyond solubility limit, the undissolved NiO exists in the form of nano and/or micro-sized crystals depending on the doping amount. The sintering model was used to address the enhanced sintering of YSZ as a result of small additions of NiO. Lattice diffusion is examined to be the rate-determining mechanism for the intermediate-stage sintering of both undoped and NiO-doped YSZ. However, the apparent activation energy for densification of YSZ is reduced by ∼70 kJ/mol upon NiO doping. It is concluded that the dissolved NiO contributes to the lowering of the activation energy and therefore the enhanced lattice diffusivity.

Linearization of Master Sintering Curve

The master sintering curve (MSC) is a simple and functional sinter model that is used to describe the densification of a particulate material during sintering when one sintering mechanism is dominant. Usually the MSC is expressed mathematically by a sigmoid relationship between the natural logarithm of the work of sintering and the relative density. The work of sintering is an integral term that includes the time and temperature path followed by the material during sintering as well as the apparent activation energy for densification of the material. In this work, the sigmoid form of the MSC is linearized by relating the natural logarithm of the work of sintering to the densification parameter. Linearization of the MSC simplifies the characterization of the model parameters. This is illustrated by example of different powder metal systems, showing how the linearized MSC model parameters can be easily determined directly from the plotted experimental data.

Apparent activation energy for densification of α-Al2O3 powder at constant heating-rate sintering

The apparent activation energy for densification is a characteristic quantity that elucidates the fundamental diffusion mechanisms during the sintering process. Based on the Arrhenius theory, the activation energy for densification of α-Al2O3 at constant heating-rates sintering has been estimated. Sintering of α-Al2O3 powder has been executed by the way of a push rod type dilatometer. It is shown that the apparent activation energy does not have a single value but depends directly on the relative density. The apparent activation energy corresponding to lower relative density was higher than that corresponding to higher relative density. In addition, the value of the evaluated activation energy is different at the same density level when the Arrhenius plot involves different heating rates.

Analysis of Nanocrystalline and Microcrystalline ZnO Sintering Using Master Sintering Curves

Master sintering curves were constructed for dry‐pressed compacts composed of either a nanocrystalline or a microcrystalline ZnO powder using constant heating rate dilatometry data and an experimentally determined apparent activation energy for densification of 268±25 and 296±21 kJ/mol, respectively. The calculated activation energies for densification are consistent with one another, and with values reported in the literature for ZnO densification by grain boundary diffusion. Grain boundary diffusion appears to be the single dominant mechanism controlling intermediate‐stage densification in both the nanocrystalline and the microcrystalline ZnO during sintering from 65% to 90% of the theoretical density (TD). Based on both the consistency of the calculated activation energy as a function of density and the narrow dispersion of the sintering data about the master sintering curve (MSC) for the nanocrystalline ZnO, there is no evidence of either significantly enhanced surface diffusion or grain growth during sintering relative to the microcrystalline ZnO. The MSC constructed for the nanocrystalline ZnO was used to design time–temperature profiles to successfully achieve four different target sintered densities on the MSC, demonstrating the applicability of the MSC theory to nanocrystalline ceramic sintering. The most significant difference in sintering behavior between the two ZnO powders is the enhanced densification in the nanocrystalline ZnO powder at shorter times and lower temperatures. This difference is attributed to a scaling (i.e., particle size) effect.

Densification behavior during hot pressing of BiPbSrCaCuO superconductors

Bi 1.84Pb 0.34Sr 2.03Ca 1.9Cu 3.06O y bulk superconductors with various relative densities were prepared by hot pressing in the temperature range 780°C–840°C and the pressure range of 4.9 MPa–24.5 MPa in air for 2 h. The relationship between porosity, p, and hot pressing conditions was formulated using the following equation: 1n( p) = − a 0 exp( − E/ RT) P + 1n( p 0), where P was the hot-pressing pressure, p 0 the porosity of the compact body, E an apparent activation energy for densification, T the temperature, R the gas constant, and a 0 a constant. The apparent activation energies were 184 kJ/mol and 526 kJ/mol in the lower- and higher-temperature ranges in comparison to 820°C, respectively. The densification mechanisms in the lower and higher temperature ranges are discussed in terms of plastic flow, particle rearrangement and the formation of liquid phase.

Porosity and permeability evolution during hot isostatic pressing of calcite aggregates

Porosity, permeability, and storativity were measured during isostatic hot‐pressing of fine‐grained calcite aggregates at temperatures of 633 to 833 K, confining pressures of 200 to 300 MPa, and argon pore pressures of 100 to 250 MPa. The progressive changes in total porosity were measured in situ by monitoring the sample length changes. The connected porosity and the permeability and storativity were measured in situ by incrementing and oscillating pore pressure techniques, respectively. In a given test, there was a decrease with time in the rate of reduction of porosity, the rates being higher at higher temperature and effective pressure. The permeability k was nonlinearly related to the total porosity ϕ in the form k ∝ ϕn. The exponent n was approximately equal to 3 and thus consistent with the prediction of the “equivalent channel” model, in the range of porosity from 0.18 down to 0.07. Below 0.07, n became much larger (around 14), an effect that can be attributed to loss of connectivity and which is qualitatively similar to that observed by Bernabé et al. [1982] in post‐hot‐pressing measurements. However, a cube law continues to apply below 0.07 total porosity if the permeability is related to the connected porosity itself. The storativity is also nonlinearly related to the porosity. Model analyses of the permeability and storativity results indicate both that the pore apertures decrease and that the pore shapes become more equant as the porosity decreases. The marked downturn in the permeability‐porosity relationship at total porosities below 0.07 appears from microscopical observation to correspond to a change in pore geometry from largely connected, irregular pores between grains to isolated, tubular pores at junctions of several grains. Application of the “Swiss‐cheese” continuum percolation model indicates a percolation threshold of about 0.04 porosity. Microstructural evidence, the apparent activation energy for densification, and the stress dependence of densification rate suggest that porosity reduction has occurred mainly by dislocation creep.

Densification kinetics of vacuum hot-pressed sodium beta-aluminas

Abstract Hot pressing of two sodium beta-alumina powders of nominal composition Na 2 O · 6.9Al 2 O 3 and Na 2 O · 8.5Al 2 O 3 at 1100 – 1600°C and 150 – 350 kg/cm 2 in inductively heated graphite dies under vacuum, proved an easy method for obtaining fully dense materials in very short pressing times. Densification rates and microstructures developed are strongly dependent on the characteristics of the starting powders. The microstructure of the materials obtained from the first powder consisted of approx. equiaxed grains of the β and β″ phases; the intermediate and final stages of densification (ϱ > ∼ 85%) obeyed first-order kinetics and showed stress exponents in the steady state creep equation ( e ∼ σ n ) from 0.74 to 1.76. The apparent volume diffusion coefficients at 90% relative density for which n values close to unity were found, calculated on the assumption of the Nabarro-Herring diffusional creep model were of the order of 10 −9 cm 2 /sec. The apparent activation energy for densification was 55 kcal/mole. A duplex microstructure was observed in the materials hot-pressed from the second powder consisting of nearly equiaxed grains and strongly anisotropic elongated crystals grown perpendicularly to the hot-pressing direction. First-order densification kinetics were observed also for this powder but with much lower densification rates. The apparent activation energy for densification was 130 kcal/mole. A strong texture was observed in the materials hot-pressed from both powders with most of the c axes oriented parallel to the hot-pressing direction.

Densification and α-β transformation mechanisms during hot pressing of Si 3N 4 — Y 2O 3 — SiO 2 composition

Densification of Si 3N 4-Y 2O 3 — SiO 2 mixtures under hot pressing occurs by a complex multicomponent mechanism including as main material transport processes particle rearrangement by rheologic flow and solution/diffusion/reprecipitation. Grain boundary sliding, Ostwald ripening and dislocation flow are also suggested to take place, especially in the final stage of densification. Stress and time analyses of densification and shrinkage rate according to the known models for liquid phase sintering and stationary creep have been used to identify the possible rate-governing mechanisms at the various sintering stages. The apparent activation energy for densification was found to depend on the actual density of the material being hot pressed. The apparent activation energy for the α-β transformation ( E a = −544 KJmol −1 is similar to the apparent activation energy for densification in the intermediate stage where the solution/precipitation process is most active. Overall, the sintering behaviour is largely dominated by the flow properties of the liquid viscous grain boundary phase.

Densification kinetics of vacuum hot-pressed sodium beta-aluminas

Hot pressing of two sodium beta-alumina powders of nominal composition Na 2O · 6.9Al 2O 3 and Na 2O · 8.5Al 2O 3 at 1100 – 1600°C and 150 – 350 kg/cm 2 in inductively heated graphite dies under vacuum, proved an easy method for obtaining fully dense materials in very short pressing times. Densification rates and microstructures developed are strongly dependent on the characteristics of the starting powders. The microstructure of the materials obtained from the first powder consisted of approx. equiaxed grains of the β and β″ phases; the intermediate and final stages of densification (ϱ > ∼ 85%) obeyed first-order kinetics and showed stress exponents in the steady state creep equation ( ε ∼ σ n) from 0.74 to 1.76. The apparent volume diffusion coefficients at 90% relative density for which n values close to unity were found, calculated on the assumption of the Nabarro-Herring diffusional creep model were of the order of 10 −9 cm 2/sec. The apparent activation energy for densification was 55 kcal/mole. A duplex microstructure was observed in the materials hot-pressed from the second powder consisting of nearly equiaxed grains and strongly anisotropic elongated crystals grown perpendicularly to the hot-pressing direction. First-order densification kinetics were observed also for this powder but with much lower densification rates. The apparent activation energy for densification was 130 kcal/mole. A strong texture was observed in the materials hot-pressed from both powders with most of the c axes oriented parallel to the hot-pressing direction.