Sintering of Multilayered Porous Structures: Part I‐Constitutive Models

Theoretical analyses of shrinkage and distortion kinetics during sintering of bilayered porous structures are carried out. The developed modeling framework is based on the continuum theory of sintering; it enables the direct assessment of the cofiring process outcomes and of the impact of process controlling parameters. The derived “master sintering curve”‐type solutions are capable of describing and optimizing the generic sintering shrinkage and distortion kinetics for various material systems. The approach utilizes the material‐specific parameters, which define the relative kinetics of layer shrinkages such as the relative intensity of sintering, and employs the conversion between real and specific times of sintering. A novel methodology is also developed for the determination of the ratio of the shear viscosities of the layer's fully dense materials. This new technique enables the determination of all input parameters necessary for modeling sintering of bilayers using experimental techniques similar to optical dilatometry applied to each individual layer and to a symmetric trilayered porous structure based on the two‐layer materials utilized in the bilayered system. Examples of sintering different porous bilayered systems are presented to justify the capability of the model in predicting and optimizing sintering kinetics.     

Anisotropic kinetic of the kaolinite to mullite reaction sequence in multilayer ceramics

Multilayer ceramics with a composite and organized microstructure were realized from kaolin and alumina fibers to improve strength and fracture toughness. Dilatometry experiments along 3 directions reveal anisotropic shrinkages, which are in correlation with different activation energy for sintering. Mullite growth is strongly anisotropic, inducing the formation of an organized microstructure, where larger mullite crystals are mainly oriented in plane of layer and perpendicular to alumina fibers. Kinetic data from thermal transformations show that the starting reaction mechanism is mullite nucleation, and it is continued by a strongly anisotropic grain growth. It is explained by topotactic transformations at phyllosilicate faces and along alumina arrangements. Mullite growth kinetics is also favored perpendicularly to fiber main dimension by the anisotropy of alumina diffusion coefficient. It shows the limited importance of mullite crystallization in microstructural transformation, but it also shows that controlled mullite growth is central in microstructural arrangement.     

Multi-Scale Study of Sintering: A Review

An integrated approach, combining the continuum theory of sintering with a kinetic Monte-Carlo (KMC) model-based mesostructure evolution simulation is reviewed. The effective sintering stress and the normalized bulk viscosity are derived from mesoscale simulations. A KMC model is presented to simulate microstructural evolution during sintering of complex microstructures taking into consideration grain growth, pore migration, and densification. The results of these simulations are used to generate sintering stress and normalized bulk viscosity for use in continuum level simulation of sintering. The advantage of these simulations is that they can be employed to generate more accurate constitutive parameters based on most general assumptions regarding mesostructure geometry and transport mechanisms of sintering. These constitutive parameters are used as input data for the continuum simulation of the sintering of powder bilayers. Two types of bilayered structures are considered: layers of the same particle material but with different initial porosity, and layers of two different materials. The simulation results are verified by comparing them with shrinkage and warping during the sintering of bilayer ZnO powder compacts.     

Constrained Film Sintering of Nanocrystalline TiO2

The sintering of thin, nanocrystalline TiO₂ films either 140 or 65 nm thick is characterized and compared with the sintering of bulk material. Grain size, pore size distribution, and density data are obtained. Observation of the microstructural evolution during sintering suggests that grain growth, as well as pore growth, at low density can be attributed to differential sintering. A continuum mechanical model for the intermediate stage is useful until the grain size becomes one-half the film thickness. From then on, the ratio of grain size to film thickness affects the degree by which both densification and grain growth decrease, as compared with the continuum computation results.     

Microstructure and mechanical properties of silicon nitride with tri-laminate structures

Silicon nitride ceramics with tri-laminate structures were prepared using two kinds of layers; layer with the aligned silicon nitride whisker seeds (named as “S” layer) and layer without the seed (“N” layer). The fracture toughness values on the casting surface of N layer of sample with a tri-laminate structure (N–S–N structure) showed an anisotropy, and this is contrary to the isotropic fracture toughness observed from the casting surface of sample consisting of only N layers. The fracture toughness anisotropy observed from N layer of the former sample is explained in terms of the microstructural anisotropy induced by the sintering shrinkage anisotropy within the casting plane.     

Modeling kinetics of distortion in porous bi-layered structures

Shape distortions during constrained sintering experiment of bi-layer porous and dense cerium gadolinium oxide (CGO) structures have been modeled. Technologies like solid oxide fuel cells require co-firing thin layers with different green densities, which often exhibit differential shrinkage because of different sintering rates of the materials resulting in undesired distortions of the component. An analytical model based on the continuum theory of sintering has been developed to describe the kinetics of densification and distortion in the sintering processes. A new approach is used to extract the material parameters controlling shape distortion through optimizing the model to experimental data of free shrinkage strains. The significant influence of weight of the sample (gravity) on the kinetics of distortion is taken in to consideration. The modeling predictions indicate good agreement with the results of sintering of a bi-layered CGO system in terms of evolutions of bow, porosities and also layer thickness.     

Sintering characteristics of plasma-sprayed TBCs: Experimental analysis and an overall modelling

In this study, sintering behaviour of plasma-sprayed thermal barrier coatings (PS-TBCs) was investigated experimentally and theoretically. Results show that the sintering kinetics of PS-TBCs is highly stage-sensitive. The sintering proceeds significantly faster at initial short thermal exposure (<20 h), while it slows down dramatically at following long thermal exposure. A detailed examination on microstructural evolution of the PS-TBCs was carried out to understand their sintering behaviour. Results show that, different from the conventional sintering theory, the healing of 2D pores was dominantly responsible for the stage-sensitive sintering kinetics during thermal exposure. In brief, the sintering characteristics of the PS-TBCs are highly structure specific. In addition, a structural model was developed based on the structural characteristics of the PS-TBCs; and the model predicts a well consistent sintering behaviour with experiments. Finally, an outlook towards TBCs with higher performance was put forward.     

Numerical Simulation of Solid-State Sintering: I, Sintering of Three Particles

A kinetic, Monte Carlo model, capable of simulating microstructural evolution sintering in a two-dimensional system of three particles, has been presented. The model can simulate several mechanisms simultaneously. It can simulate curvature-driven grain growth, pore migration and coarsening by surface diffusion, and densification by diffusion of vacancies to grain boundaries and annihilation of these vacancies. Morphologic changes and densification kinetics are used to verify the model.     

Fabrication of thin-film gadolinia-doped ceria (GDC) interdiffusion barrier layers for intermediate-temperature solid oxide fuel cells (IT-SOFCs) by chemical solution deposition (CSD)

A dense gadolinia-doped ceria (GDC) interdiffusion barrier layer as thin as 300 nm was successfully fabricated on a rigid anode/electrolyte bilayer substrate using the chemical solution deposition (CSD) process for intermediate temperature solid oxide fuel cells (SOFCs). Drying-related macro-defects were removed by employing drying control chemical additives (DCCA), which effectively relieved drying stresses. The major process flaws caused by the constraining effects of the rigid substrate were completely eliminated by the addition of GDC nanoparticles into the chemical solution, which suppressed the generation of microstructural anisotropy by mitigating the predominant bi-axial substrate constraints. As a consequence, a thin film GDC interlayer was successfully deposited with a high volumetric density, effectively preventing the chemical interaction between the electrolyte and cathode during the fabrication process and subsequent operation. The cell test and microstructural analysis confirmed excellent electrochemical performance and structural and chemical stability. The CSD process presented in this paper is considered to be a promising technology for the practical preparation of GDC thin film barrier layers for intermediate temperature SOFCs based on the film quality, processing costs and potential for large-scale production.     

Constrained-Film Sintering of a Borosilicate Glass: In Situ Measurement of Film Stresses

We have measured in-plane stresses developed in a borosilicate glass (BSG) film during its constrained sintering on a rigid substrate. Samples were prepared by casting BSG slurries on a silicon substrate and sintered inside a hot stage at 715°C just above the glass-softening temperature. Inplane stresses from the constrained-film sintering were determined by wafer-curvature measurements using an optical system. The measured stresses were tensile and rose rapidly from zero to a maximum level of 20 kPa during the initial stage of sintering and gradually decreased to zero at the final stage; these stresses were considerably smaller than those calculated from available microstructural models. We also measured the densification profiles of the free and constrained films. The stresses had no apparent effect on the densification profile of the constrained film up to 90% relative density; but beyond that, the densification kinetics were reduced in the constrained film. We believe that the stresses could have prevented a few large pores from shrinking during the initial stage of sintering, which then leads to an overall lower density and larger pores in the constrained film.     

Use of heating microscopy to assess sintering anisotropy in layered glass metal powder compacts

Abstract

The objective of the present study was to demonstrate that heating microscopy can be used to investigate the deformation of layered materials during sintering. Three composite systems with layered microstructure were prepared using borosilicate glass matrix and vanadium particles as the inclusion phase. The sintering shrinkage of cylindrical compacts was recorded in axial and radial directions. As expected, sintering was impaired with increasing concentration of vanadium particles. A shrinkage anisotropy factor was determined based on experimental measurements and its evolution during sintering for each sample was discussed. In samples containing three layers with different volume fractions of vanadium inclusions, similar densification was observed in the bottom layer with maximum concentration of inclusions (30 vol.-%) and in the top layer with minimum concentration (2 vol.-%). This indicates that sintering anisotropy of the samples is dependent not only on the composition, but also on the position arrangement of the layers in the sintering part. The results show that heating microscopy is a simple technique which can be used to support the design and fabrication of layered (and by extension functionally graded) materials. Smart choice of composition, dimension and position of the sample in the furnace during sintering should lead to adequate control or prediction of the final sintered shape.     

Properties of Lead Zirconate Titanate Thick-Film Piezoelectric Actuators on Ceramic Substrates

Lead zirconate titanate (PZT) is a piezoelectric material that can sense or respond to mechanical deformations and can be used in ceramic electro-mechanical systems (C-MEMS). The microstructural, electrical, and piezoelectric characteristics of thick PZT films on low-temperature cofired ceramics (LTCC) and alumina substrates were studied. The PZT composition was prepared with low-melting-point additives in order to decrease the sintering temperature and to be compatible with thick-film technology. The integration of the PZT thick-film materials on ceramic substrates could lead to degradation of the PZT's characteristics due to the interactions between an active PZT layer and a substrate, particularly with glassy LTCC material. To minimize the interactions with LTCC substrates, an intermediate PZT barrier layer was integrated. The value of the piezoelectric coefficient d ₃₃ was found to be up to 120 pC/N on an alumina substrate and approximately 50 on an LTCC substrate. Based on these results, a cantilever-type actuator was designed and fabricated on alumina substrates. Under an applied voltage of 200 V, the maximum tip deflection was about 5 μm.     

Constrained Sintering of Silver Circuit Paste

Densification kinetics and stress development during constrained sintering of a silver film on a rigid silicon substrate have been studied. Compared with free sintering, the sintering of constrained silver film exhibits a much lower densification and slower densification kinetics. The densification-controlled mechanism changes from fast grain-boundary diffusion kinetics for free sintering to slow lattice diffusion kinetics for constrained sintering. The in-plane tensile stress developed during constrained sintering of silver film, measured using a noncontact laser-scanning optical system, increases rapidly to a maximum level of 1.0–1.5 MPa initially, gradually decreases, and then becomes constant at 0.8–1.0 MPa. The maximum stress observed increases with increasing sintering temperature as a result of the faster densification rate. It is believed that the retardation of densification kinetics of constrained silver film is caused by a change in densification mechanism and the existence of in-plane tensile stress.     

Densification and Sintering Kinetics in Sintered Silicon Nitride

The sintering sequence of Y₂O₃-Al₂O₃-doped Si₃N₄ was investigated with respect to the relationship between densification, α→β transformation, and microstructural development. Quenching studies were performed to reveal these interactions during a complete sintering cycle. Isothermal studies were conducted to examine the sintering kinetics and compared to Kingery's liquid-phase sintering model. The bulk density increased to ≥90% of theoretical density with only minor transformation taking place. Major transformation occurred in a late sintering stage and was accompanied by the development of elongated grains. The kinetic order of the densification process, taking into account an appropriate correction, was larger than any of the rate exponents predicted by the Kingery model, indicating that other single or mixed mechanisms were active.     

Gas Pressure Sintering of Silicon Nitride Powder Coated with Al2O3 and TiO2

Gas pressure sintering kinetics of silicon nitride powder coated with 10 wt% (9:1) Al₂O₃ and TiO₂ have been studied at 1850°C with a pressure schedule of 0.3 MPa in the first stage and 1 MPa in the second stage. The rates have been analyzed with a liquid-phase sintering model. Diffusion-controlled intermediate-stage kinetics have been observed. The role of second-step pressurization with nitrogen and argon has been determined by monitoring the kinetics. Pressurization at an earlier stage (∼90% relative density) reduces the densification rate but produces a denser material at the final stage. Although final density is greater, a porous surface layer forms on samples sintered with argon pressurization at the second stage. No such porous layer is formed in the case of pressurization with nitrogen. The mechanism of the intermediate-stage kinetics has been discussed with respect to the nature of the product analyzed by XRD after sintering.     

Feasibility of in situ de-agglomeration during powder consolidation

Consolidation of nano-sized powders is a growing area in manufacturing of advanced materials, thanks to the reduced processing times, enhanced mechanical properties and high potential for the introduction of multi-functionality enabled by such reduced particle sizes. Nanopowders, however, are particularly prone to the agglomeration phenomena, and thus to the formation of hierarchical porous structures. The presence of pores differing up to several orders of magnitude in size leads to undesired differential shrinkage and localized grain growth. In order to avoid such issues, strategies for in situ de-agglomeration are proposed here. These optimization strategies are based on the development of an analytical model for shrinkage kinetics and mechanical properties of a hierarchical porous structure, containing both small-size intra-agglomerate pores and large-size inter-agglomerate ones. The modeling approach is an expansion of the continuum theory of sintering to the case of biporous materials presenting nonlinear viscous rheology, as expected for nano-sized crystalline powders. Considering the nonlinear viscous constitutive behavior of the solid phase also allows assessing the influence of the temperature on the microstructural evolution during processing, due to the dependence of the creep characteristic parameter, strain-rate sensitivity, on the thermal history. Material structure optimization strategies, aimed at de-agglomeration or at the design of tailored porous structures, become then possible and are here explored.     

Effect of Anisotropic Microstructure on the Viscous Properties of an LTCC Material

The sintering behavior of a glass–ceramic (commercial material Ceramtape GC) was characterized using the discontinuous sinter-forging technique. The uniaxial viscosity E ^p and the viscous Poisson's ratio n^p of the composite body were determined as a function of density. Particular attention was paid to microstructural changes in order to quantify the anisotropy induced by load application. Pores and alumina particles were found to be both oriented perpendicular to the applied load direction. Finally, the experimental results were used to predict the value of the hydrostatic sintering stress.     

A comprehensive sintering mechanism for TBCs‐Part I: An overall evolution with two‐stage kinetics

A comprehensive sintering mechanism for lamellar thermal barrier coatings was reported experimentally and theoretically in this study. To begin with, an overall property evolution with two‐stage kinetics was presented during thermal exposure. The increase in mechanical property at initial thermal exposure duration (stage‐I) was much faster with respect to that in the following longer duration (stage‐II). At the stage‐I, the in situ pore healing behavior revealed that the significant faster sintering kinetics was attributed to the rapid healing induced by multipoint connection at the intersplat pore tips, as well as a small quantity of the narrow intrasplat cracks. At the following stage‐II, the residual wide intersplat pore parts and the wide intrasplat cracks decreased the possibility of multiconnection at their counter‐surfaces, resulting in a much lower sintering kinetic. Moreover, a structural model based on the microstructure of plasma sprayed YSZ coatings was developed to correlate the microstructural evolution with mechanical property. Consequently, the model predicted a two‐stage evolutionary trend of mechanical property, which is well consistent with experiments. In brief, by revealing the pore healing behavior, this comprehensive sintering mechanism shed light to the structure tailoring toward the advanced TBCs with both higher thermal‐insulating effect and longer life time.     

Computer Simulation of Final-Stage Sintering: I, Model Kinetics, and Microstructure

A Monte Carlo model for simulating final-stage sintering has been developed. This model incorporates realistic microstructural features (grains and pores), variable surface difusivity, grain-boundary diffusivity, and grain-boundary mobility. A preliminary study of a periodic array of pores has shown that the simulation procedure accurately reproduces theoretically predicted sintering kinetics under the restricted set of assumptions. Studies on more realistic final-stage sintering microstructure show that the evolution observed in the simulation closely resembles microstructures of real sintered materials over a wide range of diffusivity, initial porosity, and initial pore sizes. Pore shrinkage, grain growth, pore breakaway, and reattachment have all been observed. The porosity decreases monotonically with sintering time and scales with the initial porosity and diffusivity along the grain boundary. Deviations from equilibrium pore shapes under slow surface diffusion or fast grain-boundary diffusion conditions yield slower than expected sintering rates.