An Experimental Measurement of Effective Diffusion Distance for the Sintering of Ceramics

Abstract

The traditional models of sintering predict a pronounced dependence of densification rate on the scale of the microstructure as measured by the grain size. This study evaluates the grain size exponent for densification during isothermal sintering of an aggregated nanocrystalline zirconia powder, and for a submicrometer alumina powder. The results gave grain size exponents that are much higher than those anticipated for the expected sintering mechanisms. Furthermore, microstructural analysis showed that this overestimate of the exponent could be due to the spatial heterogeneity in the microstructure on the scale of the diffusion distance. To assess this issue, pore boundary tessellation was used to determine a new measurement of effective diffusion distance that takes into account the local spatial arrangement of pores. This measurement gives exponents much closer to those expected for the sintering of tetragonal zirconia by volume diffusion, and for the sintering of the alumina by grain‐boundary diffusion.

Microstructural Characterization of Alumina Films During Constrained Sintering

“…Figure 4 shows that the grain size and the densification rate are highly correlated ( R 2 =0.977) but the exponent is 7, which is far too high to be consistent with model assumptions and suggests that the deceleration in densification rate in the film cannot be accounted for by the increase in average grain intercept. While the value is high, it is comparable with the value of 8 measured previously for free sintering of alumina 17 Figure 4. shows the average pore separation is also highly correlated with densification rate ( R 2 =0.963), giving an exponent of 2.8, very similar to the exponent of 2.9 measured for the free sintering of alumina 17 .…”

“…While the value is high, it is comparable with the value of 8 measured previously for free sintering of alumina 17 Figure 4. shows the average pore separation is also highly correlated with densification rate ( R 2 =0.963), giving an exponent of 2.8, very similar to the exponent of 2.9 measured for the free sintering of alumina 17 . One can conclude that the values of the exponent for pore separation suggest that this is a more reasonable measure of the average diffusion distance than average grain intercept.…”

Effective diffusion distance for isothermal sintering of hydroxyapatite

“…8 In response, a flux weighted effective diffusion distance has been defined that takes into consideration the spatial arrangement of the pores, resulting in more reasonable values for the exponent on the effective diffusion distance. 9 Previous studies have shown that surface area reduction for HAp powders in the temperature range 500-700uC did not lead to shrinkage and the surface area exponents were consistent with surface diffusion for a range of different Ca/P ratios. Densification occurred above 700uC but the mechanism was not identified.…”

“…High grain size exponents were also obtained for zirconia and alumina ceramics in a previous study and this was attributed to the extent of aggregation in the powder and the green compacts. 9 Indeed, Fig. 1b show that the powder particles used here are irregular aggregates that result in low green density.…”

“…20 More recently, pore boundary tessellation has been used to define a flux weighted effective diffusion length l deff , that takes into account the spatial arrangement of pores by biasing the result towards the more closely spaced pores that are expected to make a greater contribution to the flux. 9 The advantage of the flux weighted effective 2 a effect of solid volume fraction on average grain size and average pore size and b on average pore separation 3 Plot of log volume strain rate against log 1/lengthscale using grain size and pore separation diffusion length is that it better approximates the basic assumptions that are used to develop the sintering models and thereby avoids the need to develop more sophisticated sintering models that accommodate different and yet undefined spatial arrangements of pores. Figure 4 shows the relevant plot involving volume strain rate and effective diffusion distance for HAp that resulted in an exponent of 3?4.…”