Fig. 4: Microstructural analyses at different conversion rates and kinetic mechanism explorations.

a, Observations of sintering neck development at different synthesis stages (corresponds to Fig. 2f). b, Schematic of the critical mass transport process. c, EDS analyses of Fe and Ni distribution across a neck at a global conversion rate of around 0.5. d, EDS line profile of Fe and Ni distribution across a neck at a complete reduction. e, Representative secondary electron micrographs of two specimens synthesized using slow and fast heating rates. f, Schematic of the temperature dependency of the two main competing fluxes. Here, J and β denote the flux magnitude of individual mass transport mechanism and the heating rate, respectively. Assuming a constant concentration gradient, the magnitude of the interdiffusion flux facilitating densification, scales with temperature following the Arrhenius law^43,44, that is, J₂ ∝ exp(−1/T). The flux magnitude for FeO_x reduction, takes the form J₁ ∝ exp(−E_a/T)[1 − exp(−ΔG_r/T)]), as suggested by transition state theory^44,45,46, where E_a and ΔG_r are the activation energy and the thermodynamic driving force, respectively. The reduction of FeO_x in H₂ gas exhibits the smallest thermodynamic driving force (ΔG_r ≈ 0, with notable backward reaction^38,39,47; see also the Ellingham–Richardson diagram in Fig. 2b), allowing us to linearize its temperature dependency to J₁ ∝ 1/T exp(−1/T). g, Trade-off between porosity and residual oxide content observed in the specimens obtained using different heating rates. Here the error bars represent the standard deviations. Scale bars, 1 μm (a, for α ≈ 0.00); 200 nm (a, for α ≈ 0.50, α ≈ 0.85 and α > 0.99); 150 nm (c); 200 nm (d); 2 μm (e).