Determining the sintering kinetics of Fe and Fe_xO_y-Nanoparticles in a well-defined model flow reactor

Figures & data

Figure 1. Experimental setup for determining the sintering kinetics: (a) the particle synthesis, which provides defined particle structures, (b) the model flow reactor (MFR) to induce structure formation of aerosol particles under well-defined conditions, and c) characterization of the particles with online and offline instrumentation.

Figure 2. (a) Mean temperature-time history $T(t)$ and (b) residence time distribution $\tau$ for a number of trajectories $N$ at three different furnace temperatures. Solid lines indicate the mean calculated from CFD simulation for furnace temperatures of 773 K, 1023 K, and 1273 K. The standard deviation of $T(t)$ in (a) is shown as gray area.

Figure 3. Rietveld refinement of Cu-K$\alpha$ XRD data of a powder sampled from the spark generator housing after several hours of synthesis in pure nitrogen. Diffractograms for the separate phases magnetite Fe₃O₄ (27 wt.%), iron-deficient magnetite Fe₃O₄* (41 wt.%), hematite Fe₂O₃ (31 wt.%), and iron Fe (1 wt.%) as refined together with original data, total refined profile (fit) and residual (difference between data and refinement) are displayed.

Figure 4. LCF fitting of the Fe-K edge XANES spectra of polydisperse FexOy nanoparticles after sintering at 1373 K (black line) in purified nitrogen (N₂) (a) and reducing gas mixture of nitrogen and hydrogen (95 vol% N₂+5 vol% H₂) (b) with corresponding Fe and Fe₃O₄ references.

Figure 5. Electron energy loss spectra (EELS) of spherical Fe_xO_y nanoparticles after sintering at 1373 K with a diameter of 20 nm and 60 nm (a) in purified nitrogen and (b) in 5 vol% hydrogen.

Figure 6. (a) and (c) Effective density ${\rho }_{\mathit{eff}}$ and (b) and (d) primary particle diameter $d_{\mathit{prim}}$ as function of the mobility diameter $d_m$ for different furnace temperatures in (a) and (b) N₂ and (c) and (d) in N₂+5%H₂.

Figure 7. Morphology change due to sintering according to the experimental data (symbols, connected by dashed lines) and results of the sintering model using the best fitting combination of $E_a$ and $A_s,$ assuming $m$=1 (solid lines). Shown are the primary particle diameter $d_{\mathit{prim}}$ (circles) and number of primary particles per agglomerate $N_{\mathit{agglo}}$ (crosses) of different sized agglomerates as function the furnace temperature-time histories in (a) pure nitrogen (N₂) and (b) in nitrogen with 5 vol% hydrogen (N₂+5%H₂).

Table 1. Sintering parameters ${\mathit{E}}_{\mathbf{a}}$ and ${\mathit{A}}_{\mathbf{s}}$ determined using error minimization of the residuals sum of squares ($\mathit{\Sigma }\mathit{S}\mathit{Q}\mathit{R}$), for three different gas atmospheres and four sintering exponents $\mathit{m}$.

Gas N2 (particle density 5.2 g/cm³)
$m$	$E_a$	$A_s$	$\Sigma \mathit{SQR}$
1	55.22 kJ/mol	2.54e + 04 s/m^1	0.52
2	77.22 kJ/mol	1.01e + 11 s/m²	0.59
3	101.68 kJ/mol	2.68e + 17 s/m³	0.66
4	127.24 kJ/mol	5.90e + 23 s/m^4	0.72
Gas N2 + 5%H2 (particle density 7.874 g/cm³)
$m$	$E_a$	$A_s$	$\Sigma \mathit{SQR}$
1	59.15 kJ/mol	1.57e + 04 s/m^1	1.09
2	83.85 kJ/mol	5.08e + 10 s/m²	1.20
3	111.04 kJ/mol	1.10e + 17 s/m³	1.29
4	185.61 kJ/mol	1.12e + 20 s/m^4	1.50
Gas N2+1%H2 (particle density 6.02 g/cm³)
$m$	$E_a$	$A_s$	$\Sigma \mathit{SQR}$
1	57.00 kJ/mol	4.92e + 04 s/m^1	2.49
2	75.43 kJ/mol	5.70e + 11 s/m²	2.93
3	234.89 kJ/mol	2.50e + 11 s/m³	4.00
4	320.12 kJ/mol	8.49e + 14 s/m^4	4.06

Figure 8. Numerical solution as sum of quadratic errors ($\Sigma \mathit{SQR}$) as function of the activation energy $E_a$ and the pre-exponential rate $A_s$ of iron oxide in N₂, assuming $m$=1. The global minimum is numerically calculated by the deviation to experimental primary particles.