The Wulff Shape of Alumina: II, Experimental Measurements of Pore Shape Evolution Rates

The rate at which a facetted tetragonal cavity of nonequilibrium shape approaches a cubic equilibrium (Wulff) shape via surface diffusion was modeled. The shape relaxation rate of a facetted stretched cylinder was also modeled. For the first geometry, only an approximate solution based on linearizing the mean potential difference between the source and sink facets was obtained. For the stretched cylinder, both an approximate and an exact solution can be obtained; the approximate solution underestimates the evolution rate by a factor of ∼2. To assess the applicability of the models, nonequilibrium shape pores of identical initial geometry (∼20 μm × 20 μm × 0.5 μm) were introduced into (0001), {10[Onemacr]2}, {1120}, and {100} surfaces of sapphire single crystals using microfabrication techniques, ion-beam etching, and hot pressing. The large (∼20 μm × 20 μm) faces of the pore are low-index surfaces whose nature is dictated by the wafer orientation. A series of anneals was performed at 1900°C, and the approach of the pore shape to an equilibrium shape was monitored. The kinetics of shape evolution are highly sensitive to the crystallographic orientation and stability of the low-index surface that dominates the initial pore shape. The measured variations of the pore aspect ratio were compared to those predicted by the kinetic model. The observations suggest that when the initial bounding surface is unstable, shape relaxation may be controlled by diffusion. However, surface-attachment-limited kinetics (SALK) appears to play a major role in determining the pore shape evolution rate in cases where the initial bounding surfaces have orientations that are part of the Wulff shape.     

The Wulff Shape of Alumina: III, Undoped Alumina

Controlled-geometry cavities were introduced into the m{10     0} plane of undoped sapphire substrates using photolithographic methods, and subsequently internalized by diffusion bonding the etched sapphire to an undoped high-purity polycrystalline alumina. Pore-boundary separation during growth of the sapphire seed into the polycrystal entrapped the pores within the single crystal. Pores with an equivalent spherical radius of ≈1 μm reached a quasi-equilibrium shape after prolonged anneals at 1600° and 1800°C. The introduction of mechanically induced surface defects accelerated pore shape equilibration. The Wulff shape of undoped alumina was determined by characterizing the shape and facet structure of these equilibrated internal pores using optical microscopy, scanning electron microscopy, and atomic force microscopy. The observed planes in the Wulff shape of undoped alumina, c(0001), r{     012}, s{1     01}, a{11     0}, and p{11     3} planes, were consistent with those reported by Choi et al .; however, a different energy sequence is inferred. The absence of the m-plane in the Wulff shape is consistent with other experimental studies, but inconsistent with those lattice simulations that predict the m-plane to be one of the lowest energy planes in pure alumina. A comparison of Wulff shapes at 1600° and 1800°C suggests that the surface energy of undoped alumina becomes more isotropic as temperature increases.     

低温烧结氧化铝陶瓷的动力学研究

用CaO-MgO-SiO2玻璃(CMS-G)和TiO2为烧结助剂,在1450℃下实现了氧化铝陶瓷的致密烧结.探讨了CMS-G和TiO2质量百分含量对氧化铝陶瓷烧结性能、显微结构以及其烧结动力学的影响.结果表明:CMS-G和TiO2可有效促进氧化铝陶瓷的致密化,当CMS-G含量为3%、TiO2含量为1%时,氧化铝陶瓷的相对密度达到98.25%;液相烧结激活能为113.4kJ/mol,表明扩散控制了烧结过程.     

Kinetics of Phase Change in Explosively Shock-Treated Alumina

The effect of shock treatment on the kinetics of transformation of transition-phase alumina has been examined. Alumina powder, consisting of spherical particles produced by melting and quenching, was shock-treated at 13- to 26-GPa maximum pressure and subsequently heat-treated at 1000° and 1050°C for various times. At 1050°C, the transformation of unshocked powder was typical of other aluminas with an incubation period of 60 min before significant conversion occurred. In contrast, in the shock-treated material, no incubation period was observed and the α-phase content increased exponentially with time. The growth kinetics of the shocked powder corresponded to a linear growth process with an activation energy of 482 kJ/mol. TEM examination revealed α-phase morphologies consistent with linear growth.     

氧化铝上乙醇脱水制乙烯的动力学

为开发多段绝热床生物质乙醇脱水制乙烯反应工艺,在Φ10 mm等温积分反应器中以自研发的氧化铝为催化剂研究了生物乙醇脱水制乙烯反应动力学。实验在排除内外扩散的影响的条件下,考察了反应温度、反应空速和水醇比对反应的影响,建立了生物质乙醇脱水制乙烯的半理论半经验的幂函数本征动力学模型。模型方程具有统计意义上的可靠性,并与实验结果吻合良好。     

The Wulff Shape of Alumina: IV. Ti4+-Doped Alumina

Controlled-geometry cavities, initially ≈20 μm × 20 μm × 0.5 μm, were introduced into     -plane titanium-doped (≈210 ppma;≈500 wt. ppm) sapphire substrates using photolithographic methods, and subsequently internalized by diffusion bonding. The samples were annealed in air for prolonged periods at 1600° and 1800°C to convert the titanium to the 4+ state and to allow the pore shapes to adjust. Pores with an equivalent spherical radius of ≈3.6 μm reached a quasi-equilibrium shape within 160 h at 1600°C and within 48 h at 1800°C. The Wulff shape was determined using optical microscopy, scanning electron microscopy, and atomic force microscopy. The Wulff shape of Ti⁴⁺-doped alumina includes well-defined c(0001),     , and     facets and smoothly curved sections. The     and a     facets, which are components of the Wulff shape of undoped sapphire, are not discernable. In contrast to undoped alumina, for which the r-plane has the lowest energy, the c-plane is the lowest energy plane in Ti⁴⁺-doped alumina. The surface energy sequence of the stable c, r, and p surfaces differs from that in undoped alumina. The Wulff shape varies with temperature. Samples equilibrated at 1800°C were re-annealed at 1600°C. Pore shape changes were reversible, indicating that the observed pore shapes were close to the equilibrium (Wulff) shape.     

酸浸提取煤矸石中氧化铝工艺优化及其动力学

以贵州盘县煤矸石为原料,采用单因素实验和正交实验方法,以浓硫酸为酸浸介质酸浸提取煤矸石中氧化铝,考察了酸浸反应主要影响因素,研究了浸出动力学. 结果表明,最佳酸浸提取条件为：酸矸质量比1.4,反应时间4 h,反应温度170℃. 该条件下氧化铝的浸取率达98.47%. 该酸浸反应过程符合收缩未反应核模型的粒径不变缩核模型,反应受界面化学反应控制,反应动力学方程为1-(1-x)1/3=kt,反应活化能为61.32 kJ/mol.     

氧化铝蒸发的动态过程建模与仿真

基于物料平衡原理和热量平衡原理,分析蒸发器出口料液浓度与进口料液和蒸汽之间的动态变化,建立了四效逆流降膜蒸发加三级闪蒸的氧化铝蒸发过程时滞动态数学模型和蒸发单元状态空间模型.通过模型计算和仿真验证了模型的有效性,与氧化铝蒸发过程实际测量值相比较,证明了模型能够很好地反映氧化铝蒸发的动态生产过程,为优化控制系统设计奠定了...     

Mathematical Modeling of Two-Stage Extraction Kinetics using the Single Drop Technique

This paper focuses on the mathematical modeling of the two-stage extraction using the single drop technique. Two stages of extraction are being considered: the drop formation step, where dimensions of the drop are highly dependent on time, and the drop travel step, during which the drops size and dimensions are assumed constant. Models for both extraction steps are derived and the combined model is proposed. Two-stage and one-stage models of extraction are compared. Errors occuring when considering only the travel stage of the single drop extraction have been calculated and their dependencies on various extraction parameters have been determined. The analysis of the combined two-stage model has proven that the travel-stage-only model generates significant errors during the determination of reaction rate constants when the drop formation time is significant in relation to the whole extraction time. Thus, the two-stage model should be used to reduce originating errors.     

Microstructure of 96% Alumina Ceramics: I, Characterization of the As-Sintered Materials

Characterization of the microstructure and microchemistry of a group of commercial 96% Al₂O₃ ceramics, using analytical and conventional electron microscopy techniques, was conducted. A continuous glassy grain-boundary phase was found in all samples, in addition to a number of intragranular and intergranular crystalline second phases; the phases present depended on the original boundary-glass composition. The faceted nature of many of the Al₂O₃-glass interfaces was studied and is thought to be an equilibrium structure.     

发酵动力学建模的新方法

提出一种基于径向基函数网络(RBFN)和偏最小二乘回归(PLSR)技术的发酵动力学建模新方法.通过对谷氨酸发酵过程中菌体生长模型为例进行研究,研究结果证明了该方法的有效性.     

Alumina–Aluminide Alloys (3A) Technology: I, Model Development

The general reaction behavior of the 3A process under the thermal explosion mode of synthesis has been investigated via a continuum model. The continuum model uses mass and energy balances to predict temperature difference ( T _s,avg− T _f) curves, as well as profile curves of the reactant conversions and sample temperature. In particular, the effect of the dimensionless parameters associated with the rate of local heat generation (β, the thermicity factor), the activation energy (γ, the Arrhenius number), the rate of heat redistribution (α, the modified thermal diffusivity), the rate of heat transfer by convection (Bi, the Biot number or convective heat transfer parameter), and the rate of heat transfer by radiation (Ω, the radiative heat transfer parameter) were investigated. Conditions to control the reaction process, which should produce high-density final products, were determined. It was found that the overall maximum temperature may be reduced for high γ, low β, high α, and high Bi and Ω. In terms of processing conditions, this may be obtained by reducing the initial reactant concentrations, optimizing the particle size, using small sample sizes and high compaction pressure, and increasing the heat loss by using a high thermal conductivity inert gas.     

Kinetic Analysis of Solution-Precipitation During Liquid-Phase Sintering of Alumina

Densification controlled by solution-precipitation during liquid-phase sintering was analyzed for the aluminamagnesium aluminosilicate glass system. As a model system for liquid-phase sintering, narrowly sized alumina powders and up to 20 vol% magnesium aluminosilicate glass samples were isothermally sintered at 1550° to 1650°C. Densification rate increases with increasing liquid content and sintering temperature but decreases with increasing density. For samples with >15% grain growth, the densification rate during the solution-precipitation stage of sintering was proportional to (particle size)⁻² and thus interface reaction-controlled. Activation energies ranged from 270 to 500 kJ/mol over the relative density range of 66% to 96%, respectively. The low activation energy is attributed to densification by particle rearrangement, whereas the higher activation energy is due to densification controlled by interface-reaction-controlled solution-precipitation. Intermediate activation energies are attributed to simultaneous densification by the two mechanisms.     

Applying Reaction Kinetics to Pseudohomogeneous Methanation Modeling in Fixed-Bed Reactors

Reactor simulations can reduce the effort when designing fixed-bed reactors for methanation processes. Several microkinetic models were developed under a variety of operating conditions. However, most production-scale fixed-bed methanation processes exceed the temperature range in which these kinetic models were obtained. In addition, heat and mass transport limitations strongly influence the reaction kinetics. In this work, microkinetic rate equations for CO and CO₂ methanation were analyzed with respect to their suitability for high-temperature, pseudohomogeneous reactor modeling. The best-suited kinetic model was fitted to the operating conditions and validated by means of CFD simulations. It is shown that the simulations match the experimental data for various operating conditions.     

Morphological Changes in Process-Related Large Pores of Granular Compacted and Sintered Alumina

Large pore defects clearly develop in Al₂O₃ ceramics during sintering. These large pores originate from voids caused by the incomplete deformation and adhesion of powder particles in collapsed dimples at the centers and boundaries of granules in the green compacts. The coalescence of pores, with limited shrinkage, during densification and grain growth in the late intermediate to final stages of sintering, is considered responsible for the development of the large pores. The mechanism of pore coalescence is explained by thermodynamic arguments, which demonstrate that the largest pores result in a stable system.     

Effect of the Liquid-Forming Additive Content on the Kinetics of Abnormal Grain Growth in Alumina

Alumina specimens with various amounts of CaO and SiO₂ (1:2 ratio) were prepared, and their abnormal grain growth (AGG) kinetics were investigated. A plot of the area fraction covered by abnormal grains versus log (sintering time) had a sigmoidal shape with an apparent incubation period before the onset of AGG. The overall kinetics of AGG was similar to that of a phase transformation controlled by nucleation and growth. The incubation time and the end point of AGG were strongly dependent on the amount of liquid-forming additives. Correspondingly, the final microstructure was affected by the liquid content: a large grain size and a high aspect ratio at low liquid content and a small grain size and a low aspect ratio at high liquid content.     

Transparent Alumina: A Light-Scattering Model

A model based on Rayleigh–Gans–Debye light-scattering theory has been developed to describe the light transmission properties of fine-grained, fully dense, polycrystalline ceramics consisting of birefringent crystals. This model extends light transmission models based on geometrical optics, which are valid only for coarse-grained microstructures, to smaller crystal sizes. We verify our model by measuring the light transmission properties of fully dense (>99.99%), polycrystalline α-Al₂O₃ (PCA) with mean crystal sizes ranging from 60 to 0.3 μm. The remarkable transparency exhibited by PCA samples with small crystal sizes (<2 μm) is well explained by this model.     

Dihedral Angles in Magnesia and Alumina: Distributions from Surface Thermal Grooves

Dihedral angles, Ψ_s, from surface thermal grooves were measured using a metal reference line technique for polycrystalline MgO, undoped Al₂O₃, and MgO-doped Al₂O₃. The values of Ψ_s span the following ranges: 89° to 116° for MgO at 1520 K, 76° to 166° for undoped Al₂O₃ at 1870 K, and 90° to 139° for MgO-doped Al₂O₃ at 1870 K. For all three systems, the median Ψ_s values are 105° to 113°, implying that the median γ_gb/γ_s is 1.1 to 1.2, in contrast to metals where γ_gb/γ_s ranges typically from 1/4 to 1/2. The widths in Ψ_s distributions were different for the three materials with the width increasing in the following order: MgO, MgO-doped Al₂O₃, undoped Al₂O₃. For all three materials, the grainboundary grooves and their corresponding Ψ_s were not symmetrical with respect to the surface normal. The asymmetry for MgO was due to the pinning of the grain boundaries by the surface thermal grooves. The range of inclination angles of the grain boundary to the surface was a function of Ψ_s, with the maximum inclination angles of ∼13°, in quantitative agreement with theory.