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.     

A critique of master sintering curve analysis

In this work, we explore factors affecting the accuracy of the master sintering curve (MSC) approach for analyzing the complete sintering profile of ceramic powders. We show that the instantaneous anisotropic shrinkage must be accounted for to develop an accurate MSC. The MSC diverges at >90% density because of basic assumptions that oversimplify the analysis of the densification process. We also show that powder chemistry and forming techniques can affect the fitting parameter Q. Q should not be interpreted as the sintering activation energy, or used to interpret mechanistic differences since it is comprised of several mechanisms that influence densification throughout the sintering cycle. Despite these limitations, the MSC is a useful and practical tool for predicting thermal load (i.e. time and temperature) effects on the densification of a ceramic part fabricated from a singular powder that is fabricated by a singular forming process.     

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.     

Prediction and control of microstructure evolution for sub-microscale α-Al2O3 during low-heating-rate sintering based on the master sintering curve theory

The master sintering curve (MSC) can sometimes be used for analyzing the shrinkage behaviour of ceramics. Densification of α-Al₂O₃ with the mean particle size of 350 nm was continuously recorded during heating at 0.5, 2 and 5 °C/min. A MSC was successfully constructed using dilatometry data with the help of combined-stage sintering model. The validity of the MSC has been verified by a few experimental runs. The microstructural evolution with densification during different heating-rate sintering was explored. The sintered microstructure is a function of the time–temperature sintering conditions, and it is verified that there exists a link between sintered density and microstructure. The MSC can be used to predict and control microstructure evolution during sintering of α-Al₂O₃ ceramics.     

Densification behaviour and two stage master sintering curve in lithium sodium niobate ceramics

The Master Sintering Curve (MSC) has received much attention in recent years due to its ability to predict sintering behaviour of a given powder and green body process regardless of its thermal history. In this paper MSC, based on the combined stage sintering model is constructed for one of the most important lead-free piezoelectric viz. lithium sodium niobate, Na_1-xLi_xNbO₃ (x=0.12, LNN-12), ceramic using shrinkage data. The present study has been carried out to understand and control the densification behaviour during pressureless sintering. Two distinct stages of densification have been observed en route to the upper limit to sintering temperature. The activation energies of densification for the two temperature ranges viz. 800–1150 °C and 1150–1300°C were found to be 365 kJ/mol and 2530 kJ/mol, respectively, through the construction of MSC. The MSC should be useful in predicting the densification behaviour and the final density and for designing a reproducible fabrication schedule for the LNN-12 ceramics.     

Construction and validation of master sintering curve for TiO2 for pressureless sintering

Abstract

One of the ultimate objectives for sintering research is to predict densification results under different thermal profiles for a given processing method. This paper studies the construction and validation of the master sintering curve (MSC) for rutile TiO₂ for pressureless sintering. The MSC was constructed using dilatometry data at two heating rates and was then validated using isothermal holds at three different temperatures. The scanning electron microscopy (SEM) observation shows that the partially sintered samples have the same density under different heating procedures, which demonstrates that the assumptions of the model are reliable. The concept of the MSC could be used to predict the sintering shrinkage and final density and calculate the activation energy. A value of 105 kJ mol^-1 for TiO₂ was obtained. The MSC could be applied to predict the sintering profile to prepare ceramics with required density and a minimum of grain growth.     

纳米TiO2陶瓷无压烧结的主烧结曲线

采用纳米金红石相TiO2粉末在空气中进行烧结,用热膨胀仪记录恒定加热速率条件下的烧结过程,测量了烧结体密度,根据烧结3个阶段的全期烧结模型(combined-stage sintering model),建立TiO2主烧结曲线(master sintering curve).纳米TiO2主烧结曲线对烧结路径不敏感,烧结体的相对密度仅是时间和温度的函数,利用主烧结曲线得到的相对密度和Archimedes法实测的密度吻合,证明了主烧结曲线的有效性;根据纳米金红石的主烧结曲线,得到其在空气中的烧结激活能为105 kJ/mol;可以预测烧结收缩量和最终相对密度,准确描述烧结全程的烧结行为.     

Obtainment of porcelain floor tiles added with petroleum oily sludge

This study focuses on the processing of vitrified floor tiles incorporated with a petroleum oily sludge. Floor tile formulations containing up to 5 wt% of the petroleum oily sludge in replacement of kaolin were prepared. The tile formulations were granulated by the dry process, pressed, and fired at temperatures between 1200 and 1250 °C using a fast-firing cycle. The specimens were characterized before and after firing. XRD was used to identify the crystalline phases present during sintering and SEM was used to show how the structure changes during densification. Three parameters were used to describe densification: linear shrinkage, water absorption, and flexural strength. The results showed that the petroleum oily sludge could be used as an alternative raw material in the floor tile formulations. The densification behavior of the floor tile pieces is influenced by the petroleum oily sludge addition and firing temperature. The vitrified floor tiles produced reached the technical characteristics of porcelain floor tiles, depending on petroleum oily sludge content and firing temperature.     

A New Scheme of Finding the Master Sintering Curve

The master sintering curve approach represents densification data in terms of a master variable that combines sintering time and temperature. Recently, a finite-element scheme to predict sintering deformation that requires only the master sintering curve instead of a full constitutive law as the input data has been developed. Here, a modification to the original master sintering curve approach, so that it is more suitable for finite-element analysis, is presented. Finite-element shape functions are used to represent the densification data as well as the master sintering curve. This approach confers extra flexibility to the master sintering curve approach, even when it is not used with finite-element analysis. For example, by using shape functions, a varying activation energy can be used to obtain a master sintering curve for a set of densification data that cannot be fitted using a constant activation energy.     

Colloidal Processing of Zirconium Diboride Ultra‐High Temperature Ceramics

Colloidal processing of the Ultra‐High Temperature Ceramic (UHTC) zirconium diboride (ZrB₂) to develop near?net‐shaping techniques has been investigated. The use of the colloidal processing technique produces higher particle packing that ultimately enables achieving greater densification at lower temperatures and pressures, even pressureless sintering. ZrB₂ suspension formulations have been optimized in terms of rheological behavior. Suspensions were shaped into green bodies (63% relative density) using slip casting. The densification was carried out at 1900°C, 2000°C, and 2100°C, using both hot pressing at 40 MPa and pressureless sintering. The colloidally processed materials were compared with materials prepared by a conventional dry processing route (cold pressed at 50 MPa) and subjected to the same densification procedures. Sintered densities for samples produced by the colloidal route are higher than produced by the dry route (up to 99.5% relative density by hot pressing), even when pressureless sintering is performed (more than 90% relative density). The promising results are considered as a starting point for the fabrication of complex‐shaped components that can be densified at lower sintering temperatures without pressure.     

BN基复合陶瓷致密化的主要障碍

本文对ＢＮ基复合陶瓷进行了热压和无压烧结试验,对烧结体的密度变化和显微结构进行了研究,分析了影响ＢＮ基复合致密化的主要因素,认为卡片房式结构是妨ＢＮ基复合陶瓷致密化的主要原因。热压过程中施加的压力足够大时,可以破坏这种卡片房式结构,使片状ＢＮ定向排列,因而能获得同致密度的ＢＮ基复合陶瓷,热压过程中若有液相出现,有利于片状ＢＮ定向排列,因而能促进ＢＮ基复合陶瓷的致密化。无压烧结因不能消除坯体中的卡片     

Transport mechanisms and densification during sintering: I. Viscous flow versus vacancy diffusion

Different materials transport mechanisms lead to distinctly different morphological evolution during the sintering of ceramic particles. These behaviors are analyzed using meso-scale, finite-element models based on rigorous formulations of coupled equations for continuum transport and interfacial phenomena. While such two-particle models are simplistic with respect to a real powder compact, they nevertheless provide important mechanistic understanding of the sintering behavior of different systems. Calculations clearly show how viscous flow mechanisms for glassy particles produce simultaneous shrinkage and neck growth due to the global nature of materials transport. In contrast, results for crystalline systems without grain boundaries show that the more localized nature of diffusive transport leads to neck growth with very little densification until late stages of sintering. Surprisingly, surface vacancy diffusion leads to system elongation before densification occurs. Changes caused by the presence of a grain boundary are discussed in a companion paper [Djohari, H., Derby, J.J., 2009. Transport mechanisms and densification during sintering: II. Grain boundaries. Chem. Eng. Sci., in press doi:10.1016/j.ces.2009.05.022].     

Constrained Densification Kinetics of Alumina/Borosilicate Glass + Alumina/Alumina Sandwich Structure

The densification kinetics and mechanism of a low-temperature cofirable borosilicate glass (BSG) + alumina during the constrained sintering of a sandwich structure of alumina/(BSG + alumina)/alumina has been studied. The densification kinetics becomes slower when the BSG + alumina tape is constrained during firing. However, a viscous flow-controlling mechanism of the BSG also is still operative during free and constrained sintering. The densification behavior of constrained sintering can be mathematically described by free sintering, using the viscous analogy for the constitutive equations of a porous sintering glass.     

固相烧结—Ⅰ气孔显微结构模型及其热力学稳定性,致密化方程

讨论了二维及三维闭口气孔的稳定性，发现二维状态时气孔的稳定性问题可以用数学方法根据气孔的颗粒配位数和二面角的大小解析；而三维状态时气孔则可借助球形气孔模型近似地确定。在这一模型的基础上，建立了烧结中期和后期的气孔显微结构模型，并由此推导了因相烧结中，后期作用于气孔的烧结应力和固相烧结中斯和后期的致密化方程。     

An Arrhenius-Type Viscosity Function to Model Sintering Using the Skorohod–Olevsky Viscous Sintering Model Within a Finite-Element Code

The ease and ability to predict sintering shrinkage and densification with the Skorohod–Olevsky viscous sintering (SOVS) model within a finite-element (FE) code have been improved with the use of an Arrhenius-type viscosity function. The need for a better viscosity function was identified by evaluating SOVS model predictions made using a previously published polynomial viscosity function. Predictions made using the original, polynomial viscosity function do not accurately reflect experimentally observed sintering behavior. To more easily and better predict sintering behavior using FE simulations, a thermally activated viscosity function based on creep theory was used with the SOVS model. In comparison with the polynomial viscosity function, SOVS model predictions made using the Arrhenius-type viscosity function are more representative of experimentally observed viscosity and sintering behavior. Additionally, the effects of changes in heating rate on densification can easily be predicted with the Arrhenius-type viscosity function. Another attribute of the Arrhenius-type viscosity function is that it provides the potential to link different sintering models. For example, the apparent activation energy, Q , for densification used in the construction of the master sintering curve for a low-temperature cofire ceramic dielectric has been used as the apparent activation energy for material flow in the Arrhenius-type viscosity function to predict heating rate-dependent sintering behavior using the SOVS model.     

Densification behavior and mechanical properties of nano-alumina ceramics prepared by Spark Plasma Sintering with pressure applied at different sintering stages

High densification and fine grain size are the key to achieve excellent mechanical properties of ceramic materials. Pressure-assisted sintering is an effective approach to achieve this goal. However, the pressure at different sintering stages has different effects on the densification behavior of nano-ceramics. In this work, it is found that adjusting the pressure applying regime during Spark Plasma Sintering of nano-alumina ceramics can effectively increase the densification rate and balance the relationship between the densification behaviors of particle coarsening, grain growth and vapor migration. When the pressure is applied at the beginning of the second sintering stage, the high densification and fine grain size microstructures can be both obtained at lower temperatures, leading to the best mechanical properties. This result is of great significance for the preparation of nano-ceramics with excellent mechanical properties.     

Sintering behavior of bimodal iron nanopowder agglomerates

The most important issue in the processing of nanoscale metal powders is whether the metal nanopowder can be fully consolidated into ultra-fine- or nano-grained powder metallurgy parts by pressureless sintering. This paper focuses on the sintering behavior of bimodal iron (Fe) nanopowder agglomerates by considering their microstructure and densification kinetics. During the sintering, bimodal Fe nanopowder compacts underwent discontinuous shrinkage behavior until they neared full density. Three contributions to the sintering mechanisms, asymmetric sintering, densification enhancement, and grain growth inhibition, are presented in relation to the effect of bimodal nanopowder structure. Smaller nanoparticles in the bimodal nanopowders, which are predominantly present at the boundaries and interstitial spaces of larger nanoparticles, are responsible for the three mechanisms stated above. This result is strongly supported by the apparent activation energy values ranging from 48.2 to 90.6 kJ/mol, which correspond to the energy for grain-boundary diffusion in Fe. The experimental results of this study show that bimodal nanopowder agglomerates can be used to produce full density nano-grained powder metallurgical parts by pressureless sintering.     

Microstructural Coarsening During Sintering of Boron Carbide

The sintering behavior of boron carbide was investigated with particular attention given to microstructure development at various stages in the sintering process. Hot-pressing and pressureless sintering techniques were employed and the effects of heating rate, firing atmosphere, and composition were used to characterize the sintering behavior. Pressureless sintering at temperatures up to 2300°C produces only limited densification. Microstructural coarsening is responsible for this since it leads to conditions where densification is slow. Hot-pressing and carbon additions suppressed coarsening and permitted densification to >95% of theoretical density.     

Two-stage master sintering curve applied to two-step sintering of oxide ceramics

Tetragonal (3 mol% Y₂O₃) and two cubic zirconia (8 mol% Y₂O₃) as well as alumina green bodies were used for the construction of the Master Sintering Curve (MSC) created from sets of constant-rate-of-heating (CRH) sintering experiments. The activation energies calculated according to the MSC theory were 770 kJ/mol for Al₂O₃, 1270 kJ/mol for t-ZrO₂, 620 kJ/mol and 750 kJ/mol for c-ZrO₂. These values were verified by an alternative approach based on an analysis of the densification rate in the intermediate sintering stage. The MSCs established from the Two-Step Sintering (TSS) experiments showed at high densities a significant deflection from those constructed from the CRH experiments. This deflection was explained by lower sintering activation energy in the closed porosity stage. A new two-stage MSC model was developed to reflect the change in sintering activation energy and to describe TSS. The efficiency of TSS of four materials under investigation was correlated with their activation energies during the final sintering stage.