Defect structure evolution and abnormal grain growth during spark plasma sintering of nano WC–Si powders

Abstract

The microstructural evolution during spark plasma sintering of ultrafine WC–1 wt% Si (n-WC–Si) is presented. At 1323 K (T < T_m^Si), extensive stacking faults on the $\left\{{10\bar 10} \right\}$ prismatic planes are observed. The defect microstructure can be described as a combined shear of $1/6\left\langle {\bar 12\bar 13} \right\rangle$ on the prism planes and simultaneous out-diffusion of carbon through the faults to the interparticle boundaries. At temperatures near T_m^Si (1673 K), a large fraction of abnormally grown platelets is observed. These platelets contain a single planar defect on their basal planes, described by a $1/3\left\langle {10\bar 10} \right\rangle$ translation of the carbon atoms across a Σ1 grain boundary (GB). Three factors contribute to the abnormally high density of platelets: (i) the low-temperature prismatic dislocations interact to form facet-roughening steps/kinks that act as nucleation sites, (ii) a liquid phase triggers an increased growth rate in the vicinity of the Si inclusions, and (c) the basal twin produces a re-entrant edge for 2D nucleation.

APPENDIX A1

The local temperature gradient in the sample was calculated by using the formula developed by Olevsky and Froyen.29 In their model of heat conduction in SPS, the local temperature gradient, without considering heat loss is given by:

$$\nabla T = {1 \over {G + {r_{\rm{p}}}}}\sqrt {{{\Delta t{E^2}{\lambda _{\rm{e}}}{T_0}} \over {2nC}}} \;\;\;\;,$$

(A1)

where G is the grain size, r_p is the pore radius, C is the specific heat capacity, T₀ is the temperature from which sintering is assumed to start (873 K, in this case), E is the electric field (V/m), λ_e is the electrical conductivity, Δt is the total (ON + OFF) pulse sequence duration, and n is the number of pulses required to reach the desired temperature. In our experiments, we used a pulse ON/OFF ratio of 12/2 which corresponds to 39.6 ms ON time and 6.6 ms OFF time. The ON pulse comprises twelve 3.3 ms pulses. Other approximate values were also plugged in: G ≈ 100 nm, r_p ≈ 50 nm, Δt = 46.2 ms, n = 120220, E ≈ 1000 V/m. The values of C and λ_e were obtained from the literature: C_1300K ≈ 0.0175 J/K/m³.30 For a sample with residual porosity P, the heat capacity is given by C = (1 − P)C_1300K.29 Data on the electrical resistivity of WC at high temperatures was largely unavailable. Therefore, with a knowledge of the room temperature resistivity of WC (ρ_300K ≈ 20 μΩ m) and the temperature coefficient of resistivity α ≈ 4500/K,31 a linear approximation was applied from 300 K to the temperature of interest (1300 K) using the relation ρ = ρ_300K (1 + α ΔT). Although strictly, this might be in error, a variation of one order of magnitude in the final result may be expected owing to this approximation. The electrical conductivity (λ_e = 1/ρ) of a sample with residual porosity, P was calculated as λ_e(P,T) = λ_e(0,T) [(1 − P)/(1 + 2P)].29 Using these values, ∇T ≈ 60 × 10⁶ K/m.