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Firstly, equation (2) gives: Spark Plasma Sintering of Ultrafine WC Powders: A Combined Kinetic and Microstructural Study 25 ( )= ( ) + (4) Therefore a plot of ln () against ln (t) at constant T is a straight line with slope 1/m. The sintering exponent ‘m’ can vary depending on the mechanism (diffusion path) and geometry of the sintering bodies. Table 1 shows the various values of m available in the literature, modelled for the sintering of a pair of spherical particles. The activation energy for sintering, Q can be determined in many ways: Utilizing the exponential dependence of K on T, and the m value determined earlier, we can write, ( )= ( )− (5) Hence a plot of ln (Tm) against 1/T at constant values of time, t should yield a straight line from which Q can be determined if the sintering exponent, m is known.
6. Our microstructural observation show agglomerates that are co-ordinated by a far larger number of particles (Fig. 22) which clearly explains why the agglomerate sintering rate faces a thermodynamic barrier. This inter-agglomerate pore stability retards the shrinkage rate in the intermediate stage. Following the dip in shrinkage strain rate, there is a passive period over which the system tries to evolve by particle growth within the agglomerates. The massive grain growth leads to a breakup of the agglomerate identity into large grains and the stable inter agglomerate pores now start to sinter.
Porosity and relative densities at different intermediate temperatures. Figure 4. Plots of P-P0 vs. tm according to eqns. (7)-(9) between (a) 1373 – 1473 K and (b) 1573-1873 K. 30 Tungsten Carbide – Processing and Applications Figure 5. Calculation of apparent activation energy by Dorn’s method. For analysing the intermediate stage, the porosity fraction was estimated as P = 1 - , where f is the instantaneous density and f is the final density expressed as a fraction of the theoretical density.
TUNGSTEN CARBIDE – PROCESSING AND APPLICATIONS by Edited by Kui Liu