Interfacial Processes in Densification of Cubic Zirconia

Abstract

Sintering, a process of forming dense solid bodies from powder compacts remains the most important route for processing of ceramics. The process of sintering involves formation and growth of necks during initial stage, coarsening, relative particle rotation, filling of connected pores in intermediate stage, filling of isolated pores during final stage sintering and rapid grain growth towards the end of densification. The processes involve a combi-nation of grain boundary diffusion, surface diffusion, grain boundary migration and grain boundary sliding. Studies of interfacial processes during sintering are still of interest since modifying interface structure offers a means to tailor low and high temperature mechanical properties of ceramics. Many of the studies in literature on single phase systems are based on geometric changes during sintering. Sintering has been modelled as 1D or 2D array of spheres. The simplest of these consist of a contacting pair of spherical particles. Early models studied changes in size and shape of the necks during initial stage sintering and associated mass transport mechanisms. There have been studies on coarsening that report shrinkage rates of smaller particles is a system of two particles with different radii. In both the cases of neck growth and coarsening, thermodynamic variables as given by dihedral angle (relative grain boundary to surface energy of the system) and kinetic parameters of grain boundary surface diffusivity have been found to influence the size and shape evolution with time. Also, there have been studies comparing self similar geometries at different absolute length scales such as a system of micro and nano sized particles, which show different sintering behaviour depending on the absolute particle size. There have been studies on multi particle arrays both linear and closed. Early studies on linear arrays observed rearrangement of particles and relative rotation due to non spherical shape and bond angle of an array of three particles. Also there was a study that predicted rearrangement due to differential shrinkage in an assembly containing a combi-nation of large and small particles. Similar observations were also made on closed arrays of four or more particles both in 2D and 3D. Formation of high energy local configurations such as six grain boundaries (GBs) meeting at a line were found, followed by the topological transitions such as formation of new GBs or elimination of existing ones, leading to specific features in sintering behaviour. Geometrical evolution during final stage sintering is critical for forming dense final products. While most studies related the shrinkage behaviour to shape of the pore (convex or concave) and the number of grains surrounding a pore, later the absolute size of the pore was observed to be an important parameter. In 2D simulations and experiments large convex pores were found to shrink due to mass transport from surrounding GBs. In 3D simulations, pores with large coordination number as high as 32, pore shrinkage was observed followed by gradual reduction in coordination number and final elimination. Also studied are evolution of pore -GB configuration in case of small pores as separation of these from GB and entrapment into grains will freeze further shrinkage. In addition to the geometry related changes are also crystallography related microstructural changes. Crystallographic arrangement at the atomic scale leads to anisotropy of interfacial energies and diffusivities, that effect microstructural evolution. The presence of positive and negative ions in ionic solids can result in additional features such as charged and neutral planes Crystallography can affect the rotation of powder particles in initial stage sintering to subtle differences in microstructure evolution during grain growth in final stage sintering. Conversely crystallography has to be related to diffusion at interfaces. The rotation of spheres is governed by energetics. The final configuration corresponds to local energy minima in misorientations between the spheres and the single crystal plate. This technique is useful in finding a number of crystallography related aspects such as low energy GBs and equilibrium shapes of metal droplets. Rotation of unconstrained crystal related to neighbouring crystal has also been observed in thin films. Surface energy anisotropy has often been studied using topography of annealed sur-faces studied using atomic force microscopy (AFM). While low energy stable surfaces show perfectly flat surfaces, planes close to a stable plane form terrace and ledge structures whereas unstable planes form hill and valley structures. A method of “inverse Wulff shape” of pores trapped in single crystals has been used to find relative stability of sur-face planes using a combination of electron back scattered diffraction (EBSD) and AFM. Crystallography is very much related to the phenomenon of abnormal grain growth that occurs during later stages of sintering. Similarly, polycrystal assemblies have shown varying GB migration velocities for different crystallographic planes. Most recently, 3D EBSD has been used to study crystallography of GBs in sintered polycrystalline materials. In the present study, we address two specific issues. The first is related to the effect of microstructure of polycrystalline powder particles on initial stage sintering, where we compare sintering between particles with same particle size but different grain sizes. The second is related to the crystallographic aspects of interfaces in sintered materials with specific reference to yttria stabilized cubic zirconia. The present study is mostly confined to pressure less (free) sintering where the only driving force is the reduction in interfacial energy of the system. The effect of polycrystalline nature on initial stage sintering is investigated and com-pared with the behaviour of single crystal particles. We extend the model by Coble on single crystals to polycrystalline particles containing space filling tetrakaidecahedral grains with an identical grain size. The grain boundaries within particles are considered to be additional sources for mass to be plated at the neck and the flux equations are suitably modified. A model was developed to characterize the variation with time in the growth rate (x/R), where x and R are radii of the neck and particle respectively. The model indicated that the neck growth rate for polycrystalline spheres was faster compared to single crystals towards end of initial stage sintering (large value of x/R). There is large scope for extending the model further for complex geometries, diffusion distances and grain size distributions. Sintering experiments were conducted with annealed 2D random arrays of spheres of zirconia with two different grain sizes and a particle size of 40 m. Two different forms of zirconia (8YCZ and 3YTZ) were used as model systems for a few and a large number of grains in a particle respectively. The experimental results were limited, but broadly consistent with the new model. However necks were found to grow to a value f x=R = 0:12 and they did not grow further. In the second part of our study, grain boundaries in yttria stabilized cubic zirconia were studied in the context of macroscopic crystallographic parameters of misorientations of grains on either side of the grain boundary and crystallographic coordinates of grain boundary planes. Our aim was to study the evolution of misorientations and grain bound-ary planes during sintering process, starting from formation of necks during the initial stage to grain boundary migration during later stages. Orientation imaging microscopy based on an EBSD technique in an SEM was carried out on fully dense samples and also on porous samples obtained by interrupting sintering before attaining full density. The fraction of CSL misorientations on nearly dense cubic zirconia with grain sizes varying from submicrocrystalline 0.61 to 10 m was close to a random distribution. The number fraction of necks with CSLs formed in porous cubic zirconia with microcrysatlline particles was slightly higher than a random distribution. However, the present study covers only nearly dense-microcrystalline, nearly dense- submicrocrystalline, porous - microcrystalline regime , but misorientation information could not be obtained experimentally in a low density - submi-crocrystalline regime that is critical for sintering process. We also studied the distribution of grain boundary planes in fully dense 8YCZ with a grain size of 2.8 m by a stereological method using 2D OIM data. The overall distribution of grain boundary planes showed very weak anisotropy with slight maxima with 1.1 multiples of random distribution (MRD) at {100} planes, which is consistent with observations in literature on larger grain sizes. Interestingly, the planes that were abundant were not low energy surface planes (also mentioned in literature), in clear contrast with other ceramics studied in literature. The distribution of grain boundary planes was also plotted for specific misorientations, including those around low index axes of [100], [110], [111] and low misorientations. The grain boundary character distribution (GBCD) shows a high frequency of occurrence in position of pure twists about [100] and symmetric tilts at certain low misorientations . The highest frequency of occurrence was observed for coherent twin 3 on {111} plane and symmetric tilt (higher order twin) 11 on {113} plane, both corresponding to low energy GBs reported in literature in bicrystal experiments. With pure twists on {100} for rotations about [100] axis and pure tilts with {11w} or {1ww} planes for rotations about [110], both the criteria for specialness based on surface planes forming GB or symmetric tilts are found to be valid for specific cases. Notable is the frequency of occurrence of coherent twin 3 on {111} and 11 on {113}, that was 4.8 MRD for microcrystalline 8YCZ and as high as 7.8 MRD for submicrocrystalline 8YCZ samples, which is much higher than frequency of occurrence of any GB plane in any oxide studied in literature.