Co-sintering of Integrated Ceramics: Fundamentals, Observations and Design Guidelines
Open Access
- Author:
- Mohanram, Aravind
- Graduate Program:
- Materials Science and Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- May 02, 2005
- Committee Members:
- Gary Lynn Messing, Committee Chair/Co-Chair
David John Green, Committee Chair/Co-Chair
Carlo G Pantano, Committee Member
Cliva A Randall, Committee Member
Mike T Lanagan, Committee Member - Keywords:
- LTCC
Cosintering
Viscosity - Abstract:
- ABSTRACT There is considerable interest in developing a comprehensive and robust model for simulating sintering behavior of co-fired systems. The development of a reliable modeling tool entails knowledge of measured thermo-mechanical properties such as viscosity and viscous Poisson¡¦s ratio. To measure the viscosity of densifying materials as a function of both porosity and temperature, isothermal cyclic loading dilatometry (ICLD) is proposed as a convenient technique. We demonstrate its merit relative to constant load techniques in minimizing the stress history effects (changes in shrinkage anisotropy and sample microstructure) that arise due to the application of an external load. A constant load test overestimates the viscosity by an order of magnitude compared to a cyclic load test. To obtain accurate viscosity data, maximum loading rates and longer unloading periods are desirable as they reduce effects of shrinkage anisotropy on viscosity values. A novel technique, based on the concept of pressureless constrained sintering and the viscous analogy, for determining the viscous Poisson¡¦s ratio of sintering materials is proposed. The method involves measuring the sintering rate of a free-sintered specimen, and a specimen constrained by two non-sintering layers. The viscous Poisson¡¦s ratio varied from 0.25 at ~ 74% density to about 0.45 at ~ 93%, which agreed well with model predictions. The method applies only during the intermediate stage of densification, because the material is viscous during this period of sintering. The uniaxial viscosity data of three commercial LTCC systems i.e. DuPont 951Tape (DU), Heraeus CT2000 (CT), and Ferro A6 (FE) were measured by cyclic loading dilatometry. The viscosity initially decreases with temperature, changes little during the intermediate stage and increases towards the end of densification. The viscosity increased sharply beyond the onset of crystallization. At slower heating rates, the viscosity increased at lower temperature, because of densification and crystallization. The isothermal viscosity data range from 0.1 to 100 GPa.s between 73% and 95% density. Ceramic particle-filled glasses, DU and CT systems showed a higher isothermal viscosity compared to pure glass system i.e FE. From master viscosity curves based on isothermal data, the activation energies for viscous flow were ~375 „b 30 kJ/mol, 450 „b 10 kJ/mol for DU and FE, respectively. These energies were comparable to values obtained from the master sintering curve approach. Predicting the sintering viscosity accurately is key to developing reliable sintering models. A theoretical understanding for the observed viscosity of LTCC materials, and a framework for predicting the evolution of their viscous behavior during sintering was developed. The complex viscosity of these materials is affected by a host of interdependent factors such as the base glass composition, temperature, porosity, particle size and distribution, contact area, volume fraction of filler particles, phase separation, crystallization and heating rate. A model based on the simplifying assumption that these variables are mutually exclusive is presented. The model predictions were in reasonable agreement with measured data. The concept of constrained sintering has attracted a lot of attention as it offers the advantages of tight dimensional tolerances and minimal distortion. The effect of an external constraint (uniaxial compression and pressure-less constraint) on the microstructure, density and shrinkage anisotropy during the sintering of CT and DU were studied. The difference in the viscous behavior of the two materials led to significantly different microstructures, density and shrinkage anisotropy. The shrinkage anisotropy constant of DU was significantly higher than that of CT and non-linear under uniaxial compression. A combination of higher viscosity, lower viscous Poisson¡¦s ratio, and higher constraining stresses led to lower densities for CT compared to DU. The maximum tensile stress due to a pressure-less constraint, assuming the viscous model, was in the range of ƒî10-100 kPa. The calculated uniaxial compressive stress required for zero radial shrinkage in the perpendicular plane was in the range of ƒî10 ¡V 180 kPa. To evaluate the shrinkage compatibility of different components and validate the measured thermo-mechanical properties, we used in-situ observations of curvature during co-sintering of bilayers of materials including LTCC, silver and alumina, and the bilayer strip model. There was good agreement between the measured viscosity data and model predictions. The rate of curvature follows the differential sintering kinetics between the two layers and is modulated by changes in their viscosity. The viscosities were used to calculate viscous stresses in the bilayers. For silver-LTCC bilayer, the maximum tensile stress in the silver and LTCC layers are ƒî100 kPa and 25 kPa, respectively. The bilayer strip model provides useful guidelines for designing co-fired systems. For a given differential sintering rate, the model predicts maximum warpage for m2n=1, where m and n are the relative thickness and viscosity, respectively.