Magnetite reduction kinetics under H2 and CO atmospheres at high temperature

Magnetite reduction kinetics under H2 and CO atmospheres at high temperature | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Magnetite reduction kinetics under H2 and CO atmospheres at high temperature Hao Cheng, Guoqiang Cao, Zhongren Ba, Donghai Hu, Yongbin Wang, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7745848/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 20 Jan, 2026 Read the published version in Korean Journal of Chemical Engineering → Version 1 posted 4 You are reading this latest preprint version Abstract Magnetite reduction using H2-CO-N2 mixtures with varying H2/CO molar ratios (9:1, 5:5, and 1:9) was investigated over a temperature range of 1400-1550 oC by thermogravimetric analysis (TGA). The results show that both increasing the hydrogen content in the reducing gas mixture and elevating the reaction temperature significantly accelerate the reduction process. Analysis of peak distribution characteristics and interruption experiments indicates that the overall reduction proceeds in two distinct steps: Fe3O4 → FeO followed by FeO → Fe. Kinetic modeling demonstrates that these steps are governed by different mechanisms: the Fe3O4 → FeO step is best described by a nucleation and growth model, while the FeO → Fe step follows a phase-boundary controlled (contracting cylinder) model. Using the model-fitting method, the apparent activation energies (Ea) for Fe3O4 → FeO were determined to be 73.65, 81.43, and 108.46 kJ/mol, and for FeO → Fe were 114.35, 118.32, and 130.08 kJ/mol, corresponding to H2/CO ratios of 9:1, 5:5, and 1:9, respectively. In addition, the model-free (iso-conversional) method was applied to evaluate the variation of Ea with conversion. The obtained activation energies for Fe3O4 → FeO were 72.94, 89.62, and 97.27 kJ/mol, while those for FeO → Fe were 115.06, 118.86, and 122.74 kJ/mol under the same H2/CO ratios. The close agreement between values derived from both methods confirms the reliability of the kinetic analysis and provides robust insight into the reduction mechanisms of magnetite under mixed H2–CO atmospheres. magnetite kinetic mechanistic model H2/CO activation energy Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Highlights Both an increase in hydrogen concentration within the reducing gas mixture and an elevation in reaction temperature markedly accelerate the reduction process. The overall reaction proceeds in two sequential steps, beginning with the reduction of Fe 3 O 4 to FeO, followed by the subsequent reduction of FeO to metallic Fe. Kinetic analysis reveals that the Fe 3 O 4 → FeO step is governed by a nucleation-and-growth model, whereas the FeO → Fe step is controlled by a phase-boundary reaction mechanism. 1 Introduction As a backstone industry of the national economy, the steel sector plays a vital role in driving economic development, while paradoxically ranking among the most significant contributors to global carbon emissions [ 1 ]. Currently, approximately 90% of global steel production remains dependent on the conventional blast furnace (BF) route, which requires high-grade coking coal, and accounts for over 70% of the industry's total CO 2 emissions [ 2 ]. In response to escalating climate challenges, researchers are intensifying efforts to develop alternative ironmaking technologies, such as COREX [ 3 ], HIsmelt [ 4 ] and Coal gasification Flash Ironmaking Technology [ 5 ]. These emerging processes, which can directly utilize iron ore particles as feedstock, are gaining increasing attention. Notably, they demonstrate significant potential by employing non-coking coal as the principal energy source and achieving iron oxide reduction at temperatures exceeding 1400 o C [ 6 ]. Therefore, systematic kinetic investigations into the reduction mechanisms of iron oxides at elevated temperatures are essential for elucidating reaction pathways and optimizing industrial metallurgical processes. Carbon, carbon monoxide (CO), and hydrogen (H 2 ) are the predominant reducing agents in the iron oxides reduction, and their roles have been extensively studied under high-temperature conditions [ 7 – 9 ]. Nagasaka et al. investigated experimental data with carbon mass fractions ranging from 3% to saturation, reporting apparent activation energies of approximately 100–200 kJ/mol at 1400–1550 o C [ 10 ]. Sato et al. conducted experiments by immersing iron oxides into a temperature-controlled molten Fe-C alloy bath, and from analysis of the experimental data, an activation energy of approximately 170 kJ/mol was obtained at temperatures above 1400 o C [ 11 ]. Li et al. examined the effect of temperature on iron oxide reduction by H₂. Their results indicated that when the temperature was below the melting point of metallic iron (1538 o C), the reduction degree increased significantly with temperature, rising from 34.83% at 1480 o C to 73.98% at 1520 o C. However, above the melting point, the increase slowed, reaching 92.19% at 1580 o C. Data fitting yielded an average apparent activation energy of approximately 104.74 kJ/mol [ 12 ]. Nagasaka et al. also investigated the reduction of iron oxides by CO using a thermogravimetric analyzer. Their results revealed that, under otherwise identical conditions, higher temperatures led to faster reduction rates. Regression analysis established an empirical rate equation, with an apparent activation energy of about 60.7 kJ/mol [ 10 ]. To date, kinetic models for high-temperature (> 1400 o C) reduction reactions using carbon as the reductant have been extensively studied, with experimental results showing good consistency across research groups. These findings confirm the accuracy and practical applicability of carbon-based reduction kinetics [ 13 ]. By contrast, kinetic investigations of reduction using H 2 and CO gas mixtures remain limited. The reported kinetic parameters have generally been determined under specific laboratory conditions and do not fully meet the requirements for industrial application, primarily due to experimental constraints in previous studies. As a result, the reaction mechanisms and rate-limiting steps in the hydrogen-assisted reduction of iron oxides are still not well understood. Further systematic studies are therefore required to establish reliable kinetic data and theoretical foundations for advancing H 2 -CO reduction technologies in ironmaking. In the present work, thermogravimetric analysis (TGA) was employed to investigate the isothermal reduction of magnetite by CO-H 2 -N 2 mixed gases with varying H 2 /CO ratios at temperatures ranging from 1400 to 1550 o C. Based on the peak distribution characteristics of the derivative thermogravimetric (DTG) curves, combined with interrupted experiments, the overall reduction process was divided into two distinct stages. The corresponding kinetic mechanisms were explored, and the two-step kinetics were further analyzed using both model-fitting and iso-conversional methods. Finally, key kinetic parameters, including the apparent activation energy and pre-exponential factors, were determined to provide a comprehensive understanding of the reduction behavior. 2. Experimental 2.1 Sample preparation Reagent-grade magnetite powder (Fe 3 O 4 , > 99.8%, supplied by Macklin) is used as the experimental sample, with a nominal particle size range of 50–300 nm. For each test, approximately 10 mg of the sample was weighed. High-purity hydrogen, carbon monoxide, and nitrogen (99.999%) were employed as reducing and carrier gases, respectively. Nitrogen was also used as the protective atmosphere throughout the experiments. 2.2 Experimental apparatus and procedure The reduction behavior of magnetite particles was investigated using a thermogravimetric analyzer (NETZSCH STA 449F5) with a measurement precision of ± 1 µg. The heating rate of the instrument was maintained at 20 o C/ min. Temperature control during the reduction process was achieved with an integrated S-type thermocouple in the reactor assembly. Experiments were conducted at atmospheric temperatures ranging from 1400 to 1550 o C. Hydrogen, carbon monoxide, and their mixtures were employed as reducing gases, while nitrogen was used as an inert diluent throughout the reaction system. 2.3 X-ray diffraction analysis The crystalline phases of the samples were analyzed using a smart rotary-target X-ray diffractometer (Rigaku SmartLab, Japan) operating at 45 kV and 200 mA with Cu Kα₁ radiation (λ = 0.15408 nm). Prior to measurement, the samples were ground to below 200 mesh and pressed into pellets. Wide-angle diffraction scans were conducted over a 2θ range of 20°-70° at a scanning rate of 10°/min, and the diffraction patterns were recorded for subsequent analysis. 2.3 Kinetic model 2.3.1 Model fitting method The reduction degree of sample is obtained by Eq. ( 1 ) $$\:a=({m}_{0}-{m}_{t})/{m}_{l}$$ 1 where α is the degree of reduction, \(\:{m}_{0}\) is the sample’s initial mass, \(\:{m}_{t}\) is the mass at the reduction time t, \(\:{m}_{l}\) is theoretical final weight loss. The Johnson-Mehl-Avrami (JMA) model has been extensively utilized to explain the isothermal reduction kinetics of hematite [ 14 , 15 ], which is expressed in Eq. ( 2 ) $$\:\alpha\:=1-\text{e}\text{x}\text{p}[-(kt{)}^{n}]$$ 2 By taking the logarithm and rearranging of Eq. ( 2 ), Eq. ( 3 ) was obtained. $$\:\text{Ln}\left[-\text{ln}\left(1-\:\alpha\:\right)\right]=nlnt+nlnk$$ 3 where α represents the conversion degree, k denotes the reaction rate constant, t is the reaction time, n represents Avrami exponent, Table 1 lists the n values for different mechanism models. By plotting the curve of \(\:\text{ln}\left[-\text{ln}\left(1-\:\alpha\:\right)\right]\) against \(\:lnt\) , the slope of the curve is n [ 16 ]. The optimal kinetic mechanism model can be determined based on the value of n. Table 1 Kinetic models No. Mark Models g(α) n 1 D1 One-dimensional diffusion α 2 0.62 2 D2 Two-dimensional diffusion (1-α) ln(1-α) + α 0.57 3 D3 3D-diffusion (Jander equation) [1-(1-α) 1/3 ] 2 0.54 4 A1 Avrami-Erofeev [-ln(1-α)] 1 5 A1.5 Avrami-Erofeev [-ln(1-α)] 2/3 1.5 6 A2 Avrami-Erofeev [-ln(1-α)] 1/2 2 7 A3 Avrami-Erofeev [-ln(1-α)] 1/3 3 8 R2 Phase-boundary controlled (contracting cylinder) 1-(1-α) 1/2 1.11 9 R3 Phase-boundary controlled (contracting sphere) 1-(1-α) 1/3 1.07 10 F2 Second-order (1-α) 2 1.00 Then, under isothermal conditions, the kinetic equation is expressed as Eq. ( 4 ). $$\:r={d}_{a}/{d}_{t}=k\left(T\right)f\left(a\right)$$ 4 where r is reduction conversion rate; k(T) represents the reaction rate constant; and \(\:f\left(a\right)\) denotes kinetic mechanism model function; T is the reduction reaction temperature; By substituting the Arrhenius equation for k(T), the temperature-dependent rate constant can be introduced, as expressed in Eq. ( 5 ); $$\:\frac{da}{dt}=k\left(T\right)f\left(a\right)=Aexp(-E/(RT)\left)f\right(a)$$ 5 where A denotes the pre-exponential factor, E signifies the apparent activation energy, R is the universal gas constant; Rearranging and integrating Eq. ( 5 ) to obtain Eq. ( 6 ) $$\:{G}_{j}\left(a\right)={\int\:}_{0}^{a}[f\left(a\right){]}^{-1}da={k}_{j}\left(T\right)t$$ 6 where \(\:{G}_{j}\left(a\right)\:\) is the integral form of the kinetic mechanism model function. The subscript j represents a specific mechanism function, and the corresponding rate constant (k) is calculated through the slope of the plot of \(\:{G}_{j}\left(a\right)\) against t. Then, rate constant (k) is substituted into the logarithmic form of the Arrhenius equation together with the corresponding T, as shown in Eq. ( 7 ). The scatter diagram of ln(k) vs. 1/T is plotted, and the regression line is obtained by linear fitting. Apparent activation energy Ea and pre-exponential factor A and are calculated according to the slope and intercept of the regression line. $$\:ln{k}_{j}\left({T}_{i}\right)=ln{A}_{j}-{E}_{j}/{(RT}_{i})$$ 7 2.3.2 Free-model method The iso-conversional method is a widely applied kinetic analysis approach for determining the activation energy ( E a ) of chemical reactions. It evaluates the reaction time (t) required to reach a constant conversion level (α) under different temperatures, thereby eliminating the need to assume a specific reaction mechanism. This avoids errors associated with the selection of mechanism functions and allows for the direct determination of apparent activation energy through systematic analysis of experimental data [ 17 – 19 ]. The method is based on integrating the Arrhenius equation with the rate expression under the assumption of an invariant mechanism function. Accordingly, Eq. ( 8 ) an be derived, in which a linear regression of ln(t) versus 1/T provides the activation energy ( E a ) from the slope of the fitted line. $$\:\text{ln}\left(t\right)={E}_{a}/\left(RT\right)+C$$ 8 where t is the reduction reaction time under a certain reduction degree, and C is a mechanism function, which was seen as a constant. 3. Results and discussion 3.1 Characteristics analysis of hydrogen and carbon monoxide reduction of magnetite Isothermal reduction experiments of magnetite were performed at temperatures between 1400 and 1550 o C under various gas compositions. As shown in Fig. 1 , the reduction degree (α) is plotted as a function of time (t). The results demonstrate that, for a fixed H 2 :CO ratio, the reduction rate increases with temperature. Moreover, an elevated hydrogen fraction markedly enhances the reduction rate and substantially decreases the overall reduction time. These observations are consistent with previous studies [ 20 , 21 ]. For example, He et al. reported that increasing the hydrogen concentration strengthens the thermodynamic driving force at the reaction interface, thereby accelerating the reduction process and improving the overall reduction rate [ 22 ]. Figure 2 presents the derivative thermogravimetric (DTG) curves as a function of reaction time (t). Across the temperature range of 1400–1550 o C, the reaction rate consistently increases with rising temperature. For H 2 /CO ratio of 5:5 and 1:9, the peak distribution characteristics of the DTG–t curves (Fig. 2 b and c) reveal two distinct reduction stages: the Fe 3 O 4 → FeO transition (corresponding to the removal of 25% of the total oxygen) and the FeO → Fe transition (corresponding to the removal of the remaining 75%). At the onset of the reaction, the reduction rate rises sharply and then declines, reaching a minimum at α = 0.25, which coincides with the completion of the Fe 3 O 4 →FeO step. Subsequently, the FeO→Fe stage proceeds at a comparatively lower rate. Notably, the reduction rate from Fe 3 O 4 to FeO is substantially faster than that from FeO to Fe. Additionally, higher temperatures clearly accelerate the overall reduction, as evidenced by higher reaction rates at identical reduction times under the same gas compositions. When the hydrogen proportion is increased to 90%, the DTG curves exhibit a rapid rise to a maximum reduction rate followed by a gradual decline until the reaction is complete. This indicates that both temperature and the H 2 /CO ratio are key parameters influencing the reduction kinetics of magnetite. The observed differences in reduction rates can be attributed to two primary factors. First, increasing temperature enhances the diffusion capacity of both H 2 and CO, thereby increasing the number of gas molecules available for the reduction reactions [ 23 ]. Second, the kinetic conditions for iron oxide reduction by H 2 are more favorable than by CO at high temperatures. This advantage arises because the molecular sizes of H 2 and H 2 O are much smaller than those of CO and CO 2 , enabling reactants and products to diffuse more readily through the pore network of the solid particles. Consequently, H 2 exhibits superior kinetic behavior compared with CO, resulting in higher reduction rates [ 24 ]. To elucidate the sequential nature of the two-step reduction process, controlled-interruption experiments were conducted at 1400 o C under a H 2 /CO ratio of 5:5. The phase evolution was monitored at different reduction extents using XRD patterns (Fig. 3 a) in combination with semi-quantitative phase analysis (Fig. 3 b). At the early stage, corresponding to approximately 5% oxygen mass loss, the sample consisted predominantly of Fe 3 O 4 (88%) and FeO (12%), with no metallic iron detected. This trend persisted at reduction levels of 15% and 20% oxygen mass loss, where progressive Fe 3 O 4 depletion (decreasing from 88% to 43%) was accompanied by FeO enrichment (increasing from 12% to 57%), indicating the dominance of the Fe 3 O 4 → FeO transformation. The onset of metallic iron formation was observed at α = 25%, marking the initiation of the second reduction step (FeO → Fe). Subsequent phase evolution revealed continuous FeO consumption (decreasing from 98% to 57%) concurrent with metallic iron accumulation (increasing from 0% to 43%), thereby confirming sequential reaction kinetics in which the reduction of Fe 3 O 4 to FeO precedes metallic iron formation. This staged mechanism is consistent with the DTG analysis (Fig. 2 ), which demonstrated a distinct temporal separation between the two reduction steps, with the FeO → Fe reaction commencing only after substantial completion of the Fe 3 O 4 → FeO step. These results are consistent with previous studies. Ding et al. reported that hematite reduction exhibits a characteristic triple-peak profile in its rate curve, with minima at reduction degrees of approximately 0.11 and 0.32, corresponding to the theoretical Fe 2 O 3 →Fe 3 O 4 (11%) and Fe 3 O 4 →FeO (33%) transformations, respectively, thereby highlighting the three-step nature of the overall reduction sequence [ 25 ]. Similarly, Kang et al. identified two minima at α = 0.1 and α = 0.27 on DTG curves as stage-division points, which enabled them to decouple the reduction into three independent steps. Kinetic parameter estimation for each stage provided predictive fits to the experimental curves, showing strong agreement with observed behavior [ 15 ]. Likewise, Wagner et al. demonstrated that the onset of FeO → Fe reduction occurs only after the near-completion of Fe 3 O 4 → FeO, in line with the findings of the present work [ 26 ]. 3.2 Reduction kinetics 3.2.1 Model-fitting method According to the analysis in Section 3.1 , the two-step reduction reactions can be regarded as sequential and effectively decoupled. To describe their independent kinetics and determine the associated parameters, the classical Johnson–Mehl–Avrami (JMA) model was employed, which has been widely applied to interpret isothermal reduction processes. Using H 2 as the reducing gas, the kinetic behavior of the two steps was analyzed based on Eq. ( 7 ), with \(\:\text{ln}\left[-\text{ln}\left(1-\alpha\:\right)\right]\) plotted against \(\:lnt\) , as shown in Fig. 4 . (a and b). The calculated average 𝑛 values for the two steps were 2.196 and 1.204, respectively. For the first step, the results indicated that the A2 model provides the best fit. For the second step, possible kinetic models include R2, R3, A1, A1.5, or F2. However, given the relatively close 𝑛 values, it is difficult to unambiguously assign a single optimal model based solely on the JMA analysis. To address this, the root mean square error (RMSE) was introduced as a complementary criterion to evaluate the deviation between experimental data and model predictions, with the optimal kinetic model identified as the one exhibiting the smallest RMSE [ 27 ]. The RMSE values of different kinetic models for the two reduction steps are summarized in Table 2 . According to the principle of minimum RMSE, the optimal kinetic models for the first and second steps are identified as A2 and R2, respectively. This indicates that nucleation governs the first step of the hydrogen reduction process, while the second step is controlled by the phase boundary. Consequently, the kinetic parameters, including the reaction rate constant (𝑘), activation energy (𝐸 𝑎 ), and pre-exponential factor (𝐴), can be determined based on the A2 and R2 models. Table 2 The RSS values for the two steps at different conditions. Gas Models RSME Step 1 Step 2 1400℃ 1450℃ 1500℃ 1550℃ 1400℃ 1450℃ 1500℃ 1550℃ H 2 /CO = 9:1 R2 0.3711 0.3329 0.3148 0.3631 0.0633 0.0558 0.1076 0.2250 R3 0.4674 0.4290 0.4179 0.4600 0.1601 0.1320 0.0878 0.2667 A1 0.7285 0.6901 0.6719 0.7221 0.4258 0.3922 0.3112 0.4738 A1.5 0.2962 0.2576 0.2394 0.0840 0.0659 0.0818 0.1756 0.2395 A2 0.1320 0.0932 0.0759 0.0163 0.2018 0.2318 0.3316 0.3158 F2 1.7216 1.7216 1.7216 1.7216 1.7216 1.7216 1.7216 1.7216 H 2 /CO = 5:5 R2 0.1637 0.2097 0.2948 0.2813 0.1067 0.0785 0.0671 0.0637 R3 0.2397 0.3033 0.3914 0.3796 0.1984 0.1563 0.1322 0.1562 A1 0.4849 0.5631 0.6535 0.6440 0.4612 0.4144 0.3873 0.4208 A1.5 0.0739 0.1310 0.2214 0.2154 0.0825 0.0857 0.0841 0.0666 A2 0.1236 0.0473 0.0673 0.0862 0.1769 0.2181 0.2345 0.2047 F2 1.7216 1.7216 1.7216 1.7216 1.7216 1.7216 1.7216 1.7216 H 2 /CO = 1:9 R2 0.2058 0.2719 0.3174 0.3483 0.1241 0.0891 0.0697 0.0757 R3 0.2798 0.3602 0.4117 0.4442 0.2223 0.1606 0.1503 0.1722 A1 0.5188 0.6122 0.6703 0.7048 0.4885 0.4152 0.4105 0.4379 A1.5 0.1152 0.1870 0.2383 0.2723 0.0866 0.1007 0.0833 0.0613 A2 0.1068 0.0413 0.0702 0.1060 0.1507 0.2266 0.2202 0.1882 F2 1.0328 1.0328 1.0328 1.0328 1.0328 1.0328 1.0328 1.0328 Figure 5 (a) presents the Arrhenius plots for the two-step reduction under pure H 2 conditions, yielding apparent activation energies ( E a ) of 73.65 and 114.35 kJ/mol, with corresponding pre-exponential factors of 588.75 and 3588.54 min − 1 , respectively. The coefficients of determination R 2 of the regression lines all exceeded 0.97, confirming the robustness of the fitting results. The kinetic parameters were further determined under mixed-gas conditions (H 2 /CO ratios of 5:5 and 9:1) using the same analysis approach. As shown in Fig. 4 (c-f) and Table 2 , the optimal kinetic models for the two steps under all reduction conditions were consistently identified as A2 (nucleation and growth of nuclei) and R2 (phase-boundary controlled, contracting cylinder), based on ln[-ln(1-α)] versus ln t plots in combination with RMSE evaluation. These results align with those obtained for the H 2 /CO ratio = 9:1 condition, confirming the consistency of model selection. Figure 5 (b-c) further display the Arrhenius fits under different H 2 /CO ratios. When the ratio was 5:5, the activation energies of the two steps were 81.43 and 118.32 kJ/mol, with corresponding pre-exponential factors of 689.04 and 1173.92 min − 1 . Under the 1:9 ratio, the activation energies increased to 108.46 and 130.08 kJ/mol, with pre-exponential factors of 3095.49 and 1541.44 min − 1 . In all cases, the regression coefficients (R 2 ) exceeded 0.98, demonstrating excellent reliability of the kinetic fitting. Collectively, these findings show that the two-step reduction process under different gas compositions consistently follows an A2 mechanism for the first step and an R2 mechanism for the second, thereby exhibiting strong mechanistic coherence. As aforementioned, the FeO→Fe reduction commences only after Fe 3 O 4 is fully transformed into FeO. To account for this sequential behavior, the JMA model for the FeO→Fe step was modified by introducing a delay time, t 1 , as follows in Eq. ( 9 ): $$\:{\alpha\:}=1-\text{e}\text{x}\text{p}(-(\text{k}\left(\text{t}-{t}_{1}\right){)}^{n})$$ 9 where, t is the all reaction time, t 1 is the delay time of the reaction FeO→Fe. The obtained parameters from the JMA model are listed in Table 3 . For the total conversion process, the integrated reaction rate can be expressed in equations 10 – 16 . Note that then value for each step was the average of the values obtained for different temperatures (see Table 3 ), since the fitting results are relatively insensitive to the variation of n in the tested range. $$\:{\alpha\:}_{1}=1-\text{e}\text{x}\text{p}[-(588.75\times\:\text{exp}\left(-\frac{73.65\times\:1000}{RT}\right)\times\:\text{t}{)}^{2.196}]$$ 10 (H 2 /CO = 9:1 step 1) $$\:{\alpha\:}_{2}=1-\text{e}\text{x}\text{p}[-(3588.54\times\:\text{exp}\left(-\frac{114.35\times\:1000}{RT}\right)\times\:\left(t-{\text{t}}_{1}{\left)\right)}^{1.204}\right]$$ 11 (H 2 /CO = 9:1, step 2) $$\:{\alpha\:}_{1}=1-\text{e}\text{x}\text{p}[-(689.04\times\:\text{exp}\left(-\frac{81.43\times\:1000}{RT}\right)\times\:\text{t}{)}^{2.071}]$$ 12 (H 2 /CO = 5:5 step 1) $$\:{\alpha\:}_{2}=1-\text{e}\text{x}\text{p}[-(1173.92\times\:\text{exp}\left(-\frac{118.32\times\:1000}{RT}\right)\times\:(t-{\text{t}}_{1}){)}^{1.271}]$$ 13 (H 2 /CO = 5:5, step 2) $$\:{\alpha\:}_{1}=1-\text{e}\text{x}\text{p}[-(3095.49\times\:\text{exp}\left(-\frac{108.46\times\:1000}{RT}\right)\times\:\text{t}{)}^{2.210}]$$ 14 (H 2 /CO = 1:9 step 1) $$\:{\alpha\:}_{2}=1-\text{e}\text{x}\text{p}[-(1541.44\times\:\text{exp}\left(-\frac{130.08\times\:1000}{RT}\right)\times\:(t-{\text{t}}_{1}){)}^{1.229}]$$ 15 (H 2 /CO = 1:9 step 2) $$\:\alpha\:={0.25\alpha\:}_{1}{+0.75\alpha\:}_{2}$$ 16 Table 3 The fitting parameters and determination coefficients of JMA model for each reduction step at different temperatures and H 2 /CO ratios. Gas T/℃ Step 1 Step 2 n k R 2 n k t 1 R 2 H 2 /CO = 9:1 1400 2.229 2.917 0.9671 1.195 0.9823 0.514 0.9801 1450 2.126 3.459 0.9831 1.212 1.2312 0.451 0.9843 1500 2.206 4.117 0.9820 1.249 1.4398 0.375 0.9833 1550 2.224 4.459 0.9655 1.161 1.9809 0.327 0.9861 Average 2.196 — — 1.204 — — — H 2 /CO = 5:5 1400 2.140 1.9857 0.9960 1.319 0.2406 0.9335 0.9538 1450 2.103 2.2873 0.9871 1.364 0.3016 0.6982 0.9611 1500 2.068 2.8448 0.9656 1.240 0.3709 0.5803 0.9628 1550 2.061 3.1518 0.9710 1.162 0.4895 0.4925 0.9595 Average 2.071 — — 1.271 — — — H 2 /CO = 1:9 1400 2.037 1.2537 0.9921 1.262 0.1360 1.674 0.9777 1450 2.164 1.6414 0.9958 1.207 0.1767 1.068 0.9718 1500 2.106 1.9566 0.9937 1.223 0.2128 0.900 0.9809 1550 2.172 2.4096 0.9908 1.223 0.3011 0.687 0.9844 Average 2.120 — — 1.229 — — — 3.3 Model-free method To normalize the two-step reduction process under different gas compositions, reduction experiments were conducted with H 2 /CO ratios of 9:1, 5:5, and 1:9, respectively. Figure 6 (a-f) show the iso-conversion plots of ln( t ) versus 1/T at various conversion degrees for both steps. The linear regression analysis demonstrates statistically significant correlations (R 2 > 0.95) between E a and the reduction degree across all gas atmospheres. This high coefficient of determination confirms that the fitting quality is reliable and that the iso-conversional method provides a robust description of the reduction kinetics under different reducing conditions. The variation of the activation energy as a function of conversion for each step is presented in Fig. 7 . The reduction of Fe 3 O 4 exhibits distinct kinetic characteristics under different H 2 /CO ratios. When the H 2 /CO ratio is maintained at 9:1, the first reduction step (Fe 3 O 4 → FeO) shows relatively low activation energies ranging from 68.38 to 82.35 kJ/mol, with an average of 72.94 kJ/mol. In contrast, the subsequent reduction step (FeO → Fe) requires significantly higher activation energies of 94.52–121.30 kJ/mol, yielding an average value of 115.06 kJ/mol. This pronounced disparity indicates that the initial Fe 3 O 4 → FeO transformation is less temperature-sensitive, whereas the formation of metallic iron (FeO → Fe) is considerably more energy-demanding. For the intermediate reducing atmosphere (H 2 /CO = 5:5), the activation energy ranges increase to 78.92–102.19 kJ/mol (average 89.62 kJ/mol) for the Fe 3 O 4 → FeO step and 117.76–134.30 kJ/mol (average 118.86 kJ/mol) for the FeO → Fe step. Under CO-dominated conditions (H 2 /CO = 1:9), the activation energies rise further, reaching 88.28–110.26 kJ/mol (average 97.27 kJ/mol) for the first step and 117.34–125.62 kJ/mol (average 122.74 kJ/mol) for the second step. These systematic increases in activation energy with decreasing hydrogen content underscore the superior reducing capacity of H 2 relative to CO, highlighting its effectiveness in lowering the energetic barrier for both transformation stages. 4. Conclusions In the present study, the reaction mechanisms and reduction kinetics of magnetite powder under isothermal conditions were investigated using thermogravimetric analysis (TGA) at 1400–1500 o C with reducing gases consisting of different H 2 /CO ratios. Based on the distribution characteristics of the DTG–α curves at various temperatures and gas compositions, as well as results from interrupted experiments, the overall reduction was determined to proceed through two sequential steps: Fe 3 O 4 → FeO and FeO → Fe. The main conclusions are summarized as follows. (1) Both an increase in hydrogen content within the reducing gas mixture and an increase in reaction temperature markedly accelerate the reduction reactions. The enhancing effect of hydrogen becomes more pronounced at higher temperatures, as the endothermic nature of hydrogen reduction partially offsets the exothermic reduction by carbon monoxide, thereby intensifying the temperature dependence of the reaction rate. (2) Kinetic model analysis indicates that the two-step reduction of magnetite follows distinct mechanistic pathways depending on the reaction stage. The Fe 3 O 4 → FeO step is governed by the A2 model (nucleation and growth of product phase), while the FeO → Fe step is controlled by the R2 model (phase-boundary reaction, contracting cylinder). Model-fitting analysis further reveals that with increasing H 2 /CO ratios, the apparent activation energies of Fe 3 O 4 → FeO are 73.65, 81.43 as well as 108.46 kJ/mol, while those of FeO → Fe are 114.35, 118.32 and 130.08 kJ/mol, respectively. Based on these parameters, a global kinetic model was established by incorporating a delay time for the FeO → Fe step to account for the sequential nature of the reaction. (3) A model-free iso-conversional analysis was also employed to evaluate the variation of activation energy with conversion for each step. The obtained activation energies were 72.94, 89.62, and 97.27 kJ/mol for Fe 3 O 4 → FeO, and the activation energies of FeO → Fe are 115.06, 118.86 and 122.74 kJ/mol, as H 2 ratios increased. These values are in good agreement with those derived from the model-fitting method, confirming the reliability of the kinetic analysis. Declarations Conflict of Interest All authors have no financial/commercial conflicts of interest. Acknowledgments This work is financially supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDA29050600). 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1","display":"","copyAsset":false,"role":"figure","size":661494,"visible":true,"origin":"","legend":"\u003cp\u003eThe reduction degree under different temperatures and H\u003csub\u003e2\u003c/sub\u003e/CO ratios.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7745848/v1/9f364dc02dec85d9009e94d1.png"},{"id":94027326,"identity":"50783de4-e914-445d-8932-d2ff2115037d","added_by":"auto","created_at":"2025-10-21 13:47:13","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":672664,"visible":true,"origin":"","legend":"\u003cp\u003eThe DTG curves under different temperatures and H\u003csub\u003e2\u003c/sub\u003e/CO ratios\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7745848/v1/d61f00dd14cd5bfbd4d7364d.png"},{"id":94027327,"identity":"e7b09946-4761-4d56-95c2-a185eadfb7eb","added_by":"auto","created_at":"2025-10-21 13:47:13","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":848411,"visible":true,"origin":"","legend":"\u003cp\u003eXRD patterns and semi-quantitative analysis results of the interrupted reduction experiments at 1400 ℃.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-7745848/v1/22de7b2d6ace7ddfd9a97faa.png"},{"id":94028020,"identity":"52f5e3b6-4a7e-4249-8e29-d024e99ad77e","added_by":"auto","created_at":"2025-10-21 13:55:13","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":2386603,"visible":true,"origin":"","legend":"\u003cp\u003eThe plots of ln [-ln (1-a)] vs. lnt for different temperatures and H\u003csub\u003e2\u003c/sub\u003e/CO ratios\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-7745848/v1/123d40498858c7fa6021d09d.png"},{"id":94027334,"identity":"4ffcf8b4-1772-4d45-83b0-b44427d6289b","added_by":"auto","created_at":"2025-10-21 13:47:13","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":698443,"visible":true,"origin":"","legend":"\u003cp\u003eThe Arrhenius plots of the two steps under different temperatures and H\u003csub\u003e2\u003c/sub\u003e/CO ratios\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-7745848/v1/3294e5a72d50a6cf1216e908.png"},{"id":94028024,"identity":"756c8e95-5ac9-4476-a320-e1f76fe278c8","added_by":"auto","created_at":"2025-10-21 13:55:14","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":906080,"visible":true,"origin":"","legend":"\u003cp\u003eThe iso-conversion plot of ln(t) vs.1/T with different conversion rates for two steps\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-7745848/v1/2d5ef0ccd8ea29cfd0b69107.png"},{"id":94027336,"identity":"a04dab08-d0f5-4ce4-b358-ddd78b4ca675","added_by":"auto","created_at":"2025-10-21 13:47:14","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":339553,"visible":true,"origin":"","legend":"\u003cp\u003eVariation of the activation energy with reduction degree obtained from the slop of the ln(\u003cem\u003et\u003c/em\u003e) against 1/T plots for each step under different ratios of H\u003csub\u003e2\u003c/sub\u003e/CO\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-7745848/v1/380eb59a5f2da824d839b377.png"},{"id":101151943,"identity":"3d0710f9-2c4f-4799-a9c9-bb7bbc13cab5","added_by":"auto","created_at":"2026-01-26 16:08:34","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":7526461,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7745848/v1/a1825216-4886-4a54-8a19-10faf7e36f81.pdf"},{"id":94027332,"identity":"14c286f3-537c-4571-ae1c-ea068f09d241","added_by":"auto","created_at":"2025-10-21 13:47:13","extension":"png","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":463556,"visible":true,"origin":"","legend":"\u003cp\u003eGraphical abstract\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7745848/v1/53495dce331111cc4788715f.png"}],"financialInterests":"","formattedTitle":"Magnetite reduction kinetics under H2 and CO atmospheres at high temperature","fulltext":[{"header":"Highlights","content":"\u003cul\u003e\n \u003cli\u003eBoth an increase in hydrogen concentration within the reducing gas mixture and an elevation in reaction temperature markedly accelerate the reduction process.\u003c/li\u003e\n \u003cli\u003eThe overall reaction proceeds in two sequential steps, beginning with the reduction of Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e to FeO, followed by the subsequent reduction of FeO to metallic Fe.\u003c/li\u003e\n \u003cli\u003eKinetic analysis reveals that the Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e \u0026rarr; FeO step is governed by a nucleation-and-growth model, whereas the FeO \u0026rarr; Fe step is controlled by a phase-boundary reaction mechanism.\u003c/li\u003e\n\u003c/ul\u003e"},{"header":"1 Introduction","content":"\u003cp\u003eAs a backstone industry of the national economy, the steel sector plays a vital role in driving economic development, while paradoxically ranking among the most significant contributors to global carbon emissions [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Currently, approximately 90% of global steel production remains dependent on the conventional blast furnace (BF) route, which requires high-grade coking coal, and accounts for over 70% of the industry's total CO\u003csub\u003e2\u003c/sub\u003e emissions [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. In response to escalating climate challenges, researchers are intensifying efforts to develop alternative ironmaking technologies, such as COREX [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], HIsmelt [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] and Coal gasification Flash Ironmaking Technology [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. These emerging processes, which can directly utilize iron ore particles as feedstock, are gaining increasing attention. Notably, they demonstrate significant potential by employing non-coking coal as the principal energy source and achieving iron oxide reduction at temperatures exceeding 1400 \u003csup\u003eo\u003c/sup\u003eC [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Therefore, systematic kinetic investigations into the reduction mechanisms of iron oxides at elevated temperatures are essential for elucidating reaction pathways and optimizing industrial metallurgical processes.\u003c/p\u003e\u003cp\u003eCarbon, carbon monoxide (CO), and hydrogen (H\u003csub\u003e2\u003c/sub\u003e) are the predominant reducing agents in the iron oxides reduction, and their roles have been extensively studied under high-temperature conditions [\u003cspan additionalcitationids=\"CR8\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Nagasaka et al. investigated experimental data with carbon mass fractions ranging from 3% to saturation, reporting apparent activation energies of approximately 100\u0026ndash;200 kJ/mol at 1400\u0026ndash;1550 \u003csup\u003eo\u003c/sup\u003eC [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Sato et al. conducted experiments by immersing iron oxides into a temperature-controlled molten Fe-C alloy bath, and from analysis of the experimental data, an activation energy of approximately 170 kJ/mol was obtained at temperatures above 1400 \u003csup\u003eo\u003c/sup\u003eC [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Li et al. examined the effect of temperature on iron oxide reduction by H₂. Their results indicated that when the temperature was below the melting point of metallic iron (1538 \u003csup\u003eo\u003c/sup\u003eC), the reduction degree increased significantly with temperature, rising from 34.83% at 1480 \u003csup\u003eo\u003c/sup\u003eC to 73.98% at 1520 \u003csup\u003eo\u003c/sup\u003eC. However, above the melting point, the increase slowed, reaching 92.19% at 1580 \u003csup\u003eo\u003c/sup\u003eC. Data fitting yielded an average apparent activation energy of approximately 104.74 kJ/mol [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Nagasaka et al. also investigated the reduction of iron oxides by CO using a thermogravimetric analyzer. Their results revealed that, under otherwise identical conditions, higher temperatures led to faster reduction rates. Regression analysis established an empirical rate equation, with an apparent activation energy of about 60.7 kJ/mol [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eTo date, kinetic models for high-temperature (\u0026gt;\u0026thinsp;1400 \u003csup\u003eo\u003c/sup\u003eC) reduction reactions using carbon as the reductant have been extensively studied, with experimental results showing good consistency across research groups. These findings confirm the accuracy and practical applicability of carbon-based reduction kinetics [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. By contrast, kinetic investigations of reduction using H\u003csub\u003e2\u003c/sub\u003e and CO gas mixtures remain limited. The reported kinetic parameters have generally been determined under specific laboratory conditions and do not fully meet the requirements for industrial application, primarily due to experimental constraints in previous studies. As a result, the reaction mechanisms and rate-limiting steps in the hydrogen-assisted reduction of iron oxides are still not well understood. Further systematic studies are therefore required to establish reliable kinetic data and theoretical foundations for advancing H\u003csub\u003e2\u003c/sub\u003e-CO reduction technologies in ironmaking.\u003c/p\u003e\u003cp\u003eIn the present work, thermogravimetric analysis (TGA) was employed to investigate the isothermal reduction of magnetite by CO-H\u003csub\u003e2\u003c/sub\u003e-N\u003csub\u003e2\u003c/sub\u003e mixed gases with varying H\u003csub\u003e2\u003c/sub\u003e/CO ratios at temperatures ranging from 1400 to 1550 \u003csup\u003eo\u003c/sup\u003eC. Based on the peak distribution characteristics of the derivative thermogravimetric (DTG) curves, combined with interrupted experiments, the overall reduction process was divided into two distinct stages. The corresponding kinetic mechanisms were explored, and the two-step kinetics were further analyzed using both model-fitting and iso-conversional methods. Finally, key kinetic parameters, including the apparent activation energy and pre-exponential factors, were determined to provide a comprehensive understanding of the reduction behavior.\u003c/p\u003e"},{"header":"2. Experimental","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1 Sample preparation\u003c/h2\u003e\u003cp\u003eReagent-grade magnetite powder (Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e, \u0026gt;\u0026thinsp;99.8%, supplied by Macklin) is used as the experimental sample, with a nominal particle size range of 50\u0026ndash;300 nm. For each test, approximately 10 mg of the sample was weighed. High-purity hydrogen, carbon monoxide, and nitrogen (99.999%) were employed as reducing and carrier gases, respectively. Nitrogen was also used as the protective atmosphere throughout the experiments.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2 Experimental apparatus and procedure\u003c/h2\u003e\u003cp\u003eThe reduction behavior of magnetite particles was investigated using a thermogravimetric analyzer (NETZSCH STA 449F5) with a measurement precision of \u0026plusmn;\u0026thinsp;1 \u0026micro;g. The heating rate of the instrument was maintained at 20\u003csup\u003eo\u003c/sup\u003eC/ min. Temperature control during the reduction process was achieved with an integrated S-type thermocouple in the reactor assembly. Experiments were conducted at atmospheric temperatures ranging from 1400 to 1550\u003csup\u003eo\u003c/sup\u003eC. Hydrogen, carbon monoxide, and their mixtures were employed as reducing gases, while nitrogen was used as an inert diluent throughout the reaction system.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e2.3 X-ray diffraction analysis\u003c/h2\u003e\u003cp\u003eThe crystalline phases of the samples were analyzed using a smart rotary-target X-ray diffractometer (Rigaku SmartLab, Japan) operating at 45 kV and 200 mA with Cu Kα₁ radiation (λ\u0026thinsp;=\u0026thinsp;0.15408 nm). Prior to measurement, the samples were ground to below 200 mesh and pressed into pellets. Wide-angle diffraction scans were conducted over a 2θ range of 20\u0026deg;-70\u0026deg; at a scanning rate of 10\u0026deg;/min, and the diffraction patterns were recorded for subsequent analysis.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003e2.3 Kinetic model\u003c/h2\u003e\u003cdiv id=\"Sec7\" class=\"Section3\"\u003e\u003ch2\u003e2.3.1 Model fitting method\u003c/h2\u003e\u003cp\u003eThe reduction degree of sample is obtained by Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e)\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:a=({m}_{0}-{m}_{t})/{m}_{l}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere α is the degree of reduction, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{m}_{0}\\)\u003c/span\u003e\u003c/span\u003e is the sample\u0026rsquo;s initial mass, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{m}_{t}\\)\u003c/span\u003e\u003c/span\u003e is the mass at the reduction time t, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{m}_{l}\\)\u003c/span\u003e\u003c/span\u003e is theoretical final weight loss.\u003c/p\u003e\u003cp\u003eThe Johnson-Mehl-Avrami (JMA) model has been extensively utilized to explain the isothermal reduction kinetics of hematite [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e], which is expressed in Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e)\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\alpha\\:=1-\\text{e}\\text{x}\\text{p}[-(kt{)}^{n}]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eBy taking the logarithm and rearranging of Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), Eq.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) was obtained.\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:\\text{Ln}\\left[-\\text{ln}\\left(1-\\:\\alpha\\:\\right)\\right]=nlnt+nlnk$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere α represents the conversion degree, k denotes the reaction rate constant, t is the reaction time, n represents Avrami exponent, Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e lists the n values for different mechanism models. By plotting the curve of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{ln}\\left[-\\text{ln}\\left(1-\\:\\alpha\\:\\right)\\right]\\)\u003c/span\u003e\u003c/span\u003e against \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:lnt\\)\u003c/span\u003e\u003c/span\u003e, the slope of the curve is n [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. The optimal kinetic mechanism model can be determined based on the value of n.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eKinetic models\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNo.\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMark\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eModels\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eg(α)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003en\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eD1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eOne-dimensional diffusion\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eα\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.62\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eD2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eTwo-dimensional diffusion\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e(1-α) ln(1-α) + α\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.57\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eD3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3D-diffusion (Jander equation)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e[1-(1-α)\u003csup\u003e1/3\u003c/sup\u003e]\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.54\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eA1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eAvrami-Erofeev\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e[-ln(1-α)]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eA1.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eAvrami-Erofeev\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e[-ln(1-α)]\u003csup\u003e2/3\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.5\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eA2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eAvrami-Erofeev\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e[-ln(1-α)]\u003csup\u003e1/2\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eA3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eAvrami-Erofeev\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e[-ln(1-α)]\u003csup\u003e1/3\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eR2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003ePhase-boundary controlled (contracting cylinder)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1-(1-α)\u003csup\u003e1/2\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.11\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eR3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003ePhase-boundary controlled (contracting sphere)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1-(1-α)\u003csup\u003e1/3\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.07\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eF2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eSecond-order\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e(1-α)\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.00\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThen, under isothermal conditions, the kinetic equation is expressed as Eq.\u0026nbsp;(\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:r={d}_{a}/{d}_{t}=k\\left(T\\right)f\\left(a\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere r is reduction conversion rate; k(T) represents the reaction rate constant; and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:f\\left(a\\right)\\)\u003c/span\u003e\u003c/span\u003e denotes kinetic mechanism model function; T is the reduction reaction temperature;\u003c/p\u003e\u003cp\u003eBy substituting the Arrhenius equation for k(T), the temperature-dependent rate constant can be introduced, as expressed in Eq.\u0026nbsp;(\u003cspan refid=\"Equ5\" class=\"InternalRef\"\u003e5\u003c/span\u003e);\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:\\frac{da}{dt}=k\\left(T\\right)f\\left(a\\right)=Aexp(-E/(RT)\\left)f\\right(a)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere A denotes the pre-exponential factor, E signifies the apparent activation energy, R is the universal gas constant;\u003c/p\u003e\u003cp\u003eRearranging and integrating Eq.\u0026nbsp;(\u003cspan refid=\"Equ5\" class=\"InternalRef\"\u003e5\u003c/span\u003e) to obtain Eq.\u0026nbsp;(\u003cspan refid=\"Equ6\" class=\"InternalRef\"\u003e6\u003c/span\u003e)\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:{G}_{j}\\left(a\\right)={\\int\\:}_{0}^{a}[f\\left(a\\right){]}^{-1}da={k}_{j}\\left(T\\right)t$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{G}_{j}\\left(a\\right)\\:\\)\u003c/span\u003e\u003c/span\u003eis the integral form of the kinetic mechanism model function. The subscript j represents a specific mechanism function, and the corresponding rate constant (k) is calculated through the slope of the plot of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{G}_{j}\\left(a\\right)\\)\u003c/span\u003e\u003c/span\u003e against t. Then, rate constant (k) is substituted into the logarithmic form of the Arrhenius equation together with the corresponding T, as shown in Eq.\u0026nbsp;(\u003cspan refid=\"Equ7\" class=\"InternalRef\"\u003e7\u003c/span\u003e). The scatter diagram of ln(k) vs. 1/T is plotted, and the regression line is obtained by linear fitting. Apparent activation energy Ea and pre-exponential factor A and are calculated according to the slope and intercept of the regression line.\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\:ln{k}_{j}\\left({T}_{i}\\right)=ln{A}_{j}-{E}_{j}/{(RT}_{i})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section3\"\u003e\u003ch2\u003e2.3.2 Free-model method\u003c/h2\u003e\u003cp\u003eThe iso-conversional method is a widely applied kinetic analysis approach for determining the activation energy (\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e) of chemical reactions. It evaluates the reaction time (t) required to reach a constant conversion level (α) under different temperatures, thereby eliminating the need to assume a specific reaction mechanism. This avoids errors associated with the selection of mechanism functions and allows for the direct determination of apparent activation energy through systematic analysis of experimental data [\u003cspan additionalcitationids=\"CR18\" citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. The method is based on integrating the Arrhenius equation with the rate expression under the assumption of an invariant mechanism function. Accordingly, Eq.\u0026nbsp;(\u003cspan refid=\"Equ8\" class=\"InternalRef\"\u003e8\u003c/span\u003e) an be derived, in which a linear regression of ln(t) versus 1/T provides the activation energy (\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e) from the slope of the fitted line.\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$$\\:\\text{ln}\\left(t\\right)={E}_{a}/\\left(RT\\right)+C$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere \u003cem\u003et\u003c/em\u003e is the reduction reaction time under a certain reduction degree, and C is a mechanism function, which was seen as a constant.\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e"},{"header":"3. Results and discussion","content":"\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\u003ch2\u003e3.1 Characteristics analysis of hydrogen and carbon monoxide reduction of magnetite\u003c/h2\u003e\u003cp\u003eIsothermal reduction experiments of magnetite were performed at temperatures between 1400 and 1550 \u003csup\u003eo\u003c/sup\u003eC under various gas compositions. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the reduction degree (α) is plotted as a function of time (t). The results demonstrate that, for a fixed H\u003csub\u003e2\u003c/sub\u003e:CO ratio, the reduction rate increases with temperature. Moreover, an elevated hydrogen fraction markedly enhances the reduction rate and substantially decreases the overall reduction time. These observations are consistent with previous studies [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. For example, He et al. reported that increasing the hydrogen concentration strengthens the thermodynamic driving force at the reaction interface, thereby accelerating the reduction process and improving the overall reduction rate [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e presents the derivative thermogravimetric (DTG) curves as a function of reaction time (t). Across the temperature range of 1400\u0026ndash;1550 \u003csup\u003eo\u003c/sup\u003eC, the reaction rate consistently increases with rising temperature. For H\u003csub\u003e2\u003c/sub\u003e/CO ratio of 5:5 and 1:9, the peak distribution characteristics of the DTG\u0026ndash;t curves (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb and c) reveal two distinct reduction stages: the Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e \u0026rarr; FeO transition (corresponding to the removal of 25% of the total oxygen) and the FeO \u0026rarr; Fe transition (corresponding to the removal of the remaining 75%). At the onset of the reaction, the reduction rate rises sharply and then declines, reaching a minimum at α\u0026thinsp;=\u0026thinsp;0.25, which coincides with the completion of the Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e\u0026rarr;FeO step. Subsequently, the FeO\u0026rarr;Fe stage proceeds at a comparatively lower rate. Notably, the reduction rate from Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e to FeO is substantially faster than that from FeO to Fe. Additionally, higher temperatures clearly accelerate the overall reduction, as evidenced by higher reaction rates at identical reduction times under the same gas compositions. When the hydrogen proportion is increased to 90%, the DTG curves exhibit a rapid rise to a maximum reduction rate followed by a gradual decline until the reaction is complete. This indicates that both temperature and the H\u003csub\u003e2\u003c/sub\u003e/CO ratio are key parameters influencing the reduction kinetics of magnetite. The observed differences in reduction rates can be attributed to two primary factors. First, increasing temperature enhances the diffusion capacity of both H\u003csub\u003e2\u003c/sub\u003e and CO, thereby increasing the number of gas molecules available for the reduction reactions [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. Second, the kinetic conditions for iron oxide reduction by H\u003csub\u003e2\u003c/sub\u003e are more favorable than by CO at high temperatures. This advantage arises because the molecular sizes of H\u003csub\u003e2\u003c/sub\u003e and H\u003csub\u003e2\u003c/sub\u003eO are much smaller than those of CO and CO\u003csub\u003e2\u003c/sub\u003e, enabling reactants and products to diffuse more readily through the pore network of the solid particles. Consequently, H\u003csub\u003e2\u003c/sub\u003e exhibits superior kinetic behavior compared with CO, resulting in higher reduction rates [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e].\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eTo elucidate the sequential nature of the two-step reduction process, controlled-interruption experiments were conducted at 1400 \u003csup\u003eo\u003c/sup\u003eC under a H\u003csub\u003e2\u003c/sub\u003e/CO ratio of 5:5. The phase evolution was monitored at different reduction extents using XRD patterns (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea) in combination with semi-quantitative phase analysis (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb). At the early stage, corresponding to approximately 5% oxygen mass loss, the sample consisted predominantly of Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e (88%) and FeO (12%), with no metallic iron detected. This trend persisted at reduction levels of 15% and 20% oxygen mass loss, where progressive Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e depletion (decreasing from 88% to 43%) was accompanied by FeO enrichment (increasing from 12% to 57%), indicating the dominance of the Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e \u0026rarr; FeO transformation. The onset of metallic iron formation was observed at α\u0026thinsp;=\u0026thinsp;25%, marking the initiation of the second reduction step (FeO \u0026rarr; Fe). Subsequent phase evolution revealed continuous FeO consumption (decreasing from 98% to 57%) concurrent with metallic iron accumulation (increasing from 0% to 43%), thereby confirming sequential reaction kinetics in which the reduction of Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e to FeO precedes metallic iron formation. This staged mechanism is consistent with the DTG analysis (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), which demonstrated a distinct temporal separation between the two reduction steps, with the FeO \u0026rarr; Fe reaction commencing only after substantial completion of the Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e \u0026rarr; FeO step.\u003c/p\u003e\u003cp\u003eThese results are consistent with previous studies. Ding et al. reported that hematite reduction exhibits a characteristic triple-peak profile in its rate curve, with minima at reduction degrees of approximately 0.11 and 0.32, corresponding to the theoretical Fe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026rarr;Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e (11%) and Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e\u0026rarr;FeO (33%) transformations, respectively, thereby highlighting the three-step nature of the overall reduction sequence [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Similarly, Kang et al. identified two minima at α\u0026thinsp;=\u0026thinsp;0.1 and α\u0026thinsp;=\u0026thinsp;0.27 on DTG curves as stage-division points, which enabled them to decouple the reduction into three independent steps. Kinetic parameter estimation for each stage provided predictive fits to the experimental curves, showing strong agreement with observed behavior [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Likewise, Wagner et al. demonstrated that the onset of FeO \u0026rarr; Fe reduction occurs only after the near-completion of Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e \u0026rarr; FeO, in line with the findings of the present work [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e].\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003e3.2 Reduction kinetics\u003c/h2\u003e\u003cdiv id=\"Sec12\" class=\"Section3\"\u003e\u003ch2\u003e3.2.1 Model-fitting method\u003c/h2\u003e\u003cp\u003eAccording to the analysis in Section \u003cspan refid=\"Sec10\" class=\"InternalRef\"\u003e3.1\u003c/span\u003e, the two-step reduction reactions can be regarded as sequential and effectively decoupled. To describe their independent kinetics and determine the associated parameters, the classical Johnson\u0026ndash;Mehl\u0026ndash;Avrami (JMA) model was employed, which has been widely applied to interpret isothermal reduction processes. Using H\u003csub\u003e2\u003c/sub\u003e as the reducing gas, the kinetic behavior of the two steps was analyzed based on Eq.\u0026nbsp;(\u003cspan refid=\"Equ7\" class=\"InternalRef\"\u003e7\u003c/span\u003e), with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{ln}\\left[-\\text{ln}\\left(1-\\alpha\\:\\right)\\right]\\)\u003c/span\u003e\u003c/span\u003e plotted against \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:lnt\\)\u003c/span\u003e\u003c/span\u003e, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. (a and b). The calculated average \u0026#119899; values for the two steps were 2.196 and 1.204, respectively. For the first step, the results indicated that the A2 model provides the best fit. For the second step, possible kinetic models include R2, R3, A1, A1.5, or F2. However, given the relatively close \u0026#119899; values, it is difficult to unambiguously assign a single optimal model based solely on the JMA analysis. To address this, the root mean square error (RMSE) was introduced as a complementary criterion to evaluate the deviation between experimental data and model predictions, with the optimal kinetic model identified as the one exhibiting the smallest RMSE [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e].\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe RMSE values of different kinetic models for the two reduction steps are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. According to the principle of minimum RMSE, the optimal kinetic models for the first and second steps are identified as A2 and R2, respectively. This indicates that nucleation governs the first step of the hydrogen reduction process, while the second step is controlled by the phase boundary. Consequently, the kinetic parameters, including the reaction rate constant (\u0026#119896;), activation energy (\u0026#119864;\u003csub\u003e\u0026#119886;\u003c/sub\u003e), and pre-exponential factor (\u0026#119860;), can be determined based on the A2 and R2 models.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eThe RSS values for the two steps at different conditions.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"10\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e\u003cp\u003eGas\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\" morerows=\"2\" rowspan=\"3\"\u003e\u003cp\u003eModels\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"8\" nameend=\"c10\" namest=\"c3\"\u003e\u003cp\u003eRSME\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e\u003cp\u003eStep 1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c10\" namest=\"c7\"\u003e\u003cp\u003eStep 2\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1400℃\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1450℃\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1500℃\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1550℃\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1400℃\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1450℃\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e1500℃\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1550℃\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"5\" rowspan=\"6\"\u003e\u003cp\u003eH\u003csub\u003e2\u003c/sub\u003e/CO\u003c/p\u003e\u003cp\u003e=\u0026thinsp;9:1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eR2\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.3711\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.3329\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.3148\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.3631\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u003cb\u003e0.0633\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e\u003cb\u003e0.0558\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e\u003cb\u003e0.1076\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e\u003cb\u003e0.2250\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eR3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.4674\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.4290\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.4179\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.4600\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.1601\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.1320\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.0878\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e0.2667\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eA1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.7285\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.6901\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.6719\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.7221\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.4258\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.3922\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.3112\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e0.4738\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eA1.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.2962\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.2576\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.2394\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.0840\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.0659\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.0818\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.1756\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e0.2395\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eA2\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cb\u003e0.1320\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cb\u003e0.0932\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cb\u003e0.0759\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cb\u003e0.0163\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.2018\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.2318\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.3316\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e0.3158\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eF2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1.7216\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.7216\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.7216\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.7216\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.7216\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1.7216\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e1.7216\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.7216\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"5\" rowspan=\"6\"\u003e\u003cp\u003eH\u003csub\u003e2\u003c/sub\u003e/CO\u003c/p\u003e\u003cp\u003e=\u0026thinsp;5:5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eR2\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.1637\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.2097\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.2948\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.2813\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u003cb\u003e0.1067\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e\u003cb\u003e0.0785\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" 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colname=\"c3\"\u003e\u003cp\u003e\u003cb\u003e0.1236\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cb\u003e0.0473\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cb\u003e0.0673\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cb\u003e0.0862\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.1769\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.2181\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.2345\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e0.2047\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eF2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1.7216\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.7216\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.7216\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.7216\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.7216\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1.7216\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e1.7216\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.7216\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"5\" rowspan=\"6\"\u003e\u003cp\u003eH\u003csub\u003e2\u003c/sub\u003e/CO\u003c/p\u003e\u003cp\u003e=\u0026thinsp;1:9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eR2\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.2058\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.2719\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.3174\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.3483\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u003cb\u003e0.1241\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e\u003cb\u003e0.0891\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e\u003cb\u003e0.0697\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e\u003cb\u003e0.0757\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eR3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.2798\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.3602\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.4117\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.4442\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.2223\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.1606\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.1503\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e0.1722\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eA1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.5188\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.6122\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.6703\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.7048\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.4885\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.4152\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.4105\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e0.4379\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eA1.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.1152\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.1870\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.2383\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.2723\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.0866\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.1007\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.0833\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e0.0613\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eA2\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cb\u003e0.1068\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cb\u003e0.0413\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cb\u003e0.0702\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cb\u003e0.1060\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.1507\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.2266\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.2202\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e0.1882\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eF2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1.0328\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.0328\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.0328\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.0328\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.0328\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1.0328\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e1.0328\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.0328\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(a) presents the Arrhenius plots for the two-step reduction under pure H\u003csub\u003e2\u003c/sub\u003e conditions, yielding apparent activation energies (\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e) of 73.65 and 114.35 kJ/mol, with corresponding pre-exponential factors of 588.75 and 3588.54 min\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, respectively. The coefficients of determination R\u003csup\u003e2\u003c/sup\u003e of the regression lines all exceeded 0.97, confirming the robustness of the fitting results. The kinetic parameters were further determined under mixed-gas conditions (H\u003csub\u003e2\u003c/sub\u003e/CO ratios of 5:5 and 9:1) using the same analysis approach. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(c-f) and Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the optimal kinetic models for the two steps under all reduction conditions were consistently identified as A2 (nucleation and growth of nuclei) and R2 (phase-boundary controlled, contracting cylinder), based on ln[-ln(1-α)] versus ln\u003cem\u003et\u003c/em\u003e plots in combination with RMSE evaluation. These results align with those obtained for the H\u003csub\u003e2\u003c/sub\u003e/CO ratio\u0026thinsp;=\u0026thinsp;9:1 condition, confirming the consistency of model selection. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(b-c) further display the Arrhenius fits under different H\u003csub\u003e2\u003c/sub\u003e/CO ratios. When the ratio was 5:5, the activation energies of the two steps were 81.43 and 118.32 kJ/mol, with corresponding pre-exponential factors of 689.04 and 1173.92 min\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. Under the 1:9 ratio, the activation energies increased to 108.46 and 130.08 kJ/mol, with pre-exponential factors of 3095.49 and 1541.44 min\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. In all cases, the regression coefficients (R\u003csup\u003e2\u003c/sup\u003e) exceeded 0.98, demonstrating excellent reliability of the kinetic fitting. Collectively, these findings show that the two-step reduction process under different gas compositions consistently follows an A2 mechanism for the first step and an R2 mechanism for the second, thereby exhibiting strong mechanistic coherence.\u003c/p\u003e\u003cp\u003eAs aforementioned, the FeO\u0026rarr;Fe reduction commences only after Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e is fully transformed into FeO. To account for this sequential behavior, the JMA model for the FeO\u0026rarr;Fe step was modified by introducing a delay time, t\u003csub\u003e1\u003c/sub\u003e, as follows in Eq.\u0026nbsp;(\u003cspan refid=\"Equ9\" class=\"InternalRef\"\u003e9\u003c/span\u003e):\u003cdiv id=\"Equ9\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ9\" name=\"EquationSource\"\u003e\n$$\\:{\\alpha\\:}=1-\\text{e}\\text{x}\\text{p}(-(\\text{k}\\left(\\text{t}-{t}_{1}\\right){)}^{n})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere, t is the all reaction time, t\u003csub\u003e1\u003c/sub\u003e is the delay time of the reaction FeO\u0026rarr;Fe. The obtained parameters from the JMA model are listed in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. For the total conversion process, the integrated reaction rate can be expressed in equations \u003cspan refid=\"Equ10\" class=\"InternalRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Equ16\" class=\"InternalRef\"\u003e16\u003c/span\u003e. Note that then value for each step was the average of the values obtained for different temperatures (see Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e), since the fitting results are relatively insensitive to the variation of n in the tested range.\u003cdiv id=\"Equ10\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ10\" name=\"EquationSource\"\u003e\n$$\\:{\\alpha\\:}_{1}=1-\\text{e}\\text{x}\\text{p}[-(588.75\\times\\:\\text{exp}\\left(-\\frac{73.65\\times\\:1000}{RT}\\right)\\times\\:\\text{t}{)}^{2.196}]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e(H\u003csub\u003e2\u003c/sub\u003e/CO\u0026thinsp;=\u0026thinsp;9:1 step 1)\u003cdiv id=\"Equ11\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ11\" name=\"EquationSource\"\u003e\n$$\\:{\\alpha\\:}_{2}=1-\\text{e}\\text{x}\\text{p}[-(3588.54\\times\\:\\text{exp}\\left(-\\frac{114.35\\times\\:1000}{RT}\\right)\\times\\:\\left(t-{\\text{t}}_{1}{\\left)\\right)}^{1.204}\\right]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e11\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e(H\u003csub\u003e2\u003c/sub\u003e/CO\u0026thinsp;=\u0026thinsp;9:1, step 2)\u003cdiv id=\"Equ12\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ12\" name=\"EquationSource\"\u003e\n$$\\:{\\alpha\\:}_{1}=1-\\text{e}\\text{x}\\text{p}[-(689.04\\times\\:\\text{exp}\\left(-\\frac{81.43\\times\\:1000}{RT}\\right)\\times\\:\\text{t}{)}^{2.071}]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e12\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e(H\u003csub\u003e2\u003c/sub\u003e/CO\u0026thinsp;=\u0026thinsp;5:5 step 1)\u003cdiv id=\"Equ13\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ13\" name=\"EquationSource\"\u003e\n$$\\:{\\alpha\\:}_{2}=1-\\text{e}\\text{x}\\text{p}[-(1173.92\\times\\:\\text{exp}\\left(-\\frac{118.32\\times\\:1000}{RT}\\right)\\times\\:(t-{\\text{t}}_{1}){)}^{1.271}]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e13\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e(H\u003csub\u003e2\u003c/sub\u003e/CO\u0026thinsp;=\u0026thinsp;5:5, step 2)\u003cdiv id=\"Equ14\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ14\" name=\"EquationSource\"\u003e\n$$\\:{\\alpha\\:}_{1}=1-\\text{e}\\text{x}\\text{p}[-(3095.49\\times\\:\\text{exp}\\left(-\\frac{108.46\\times\\:1000}{RT}\\right)\\times\\:\\text{t}{)}^{2.210}]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e14\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e(H\u003csub\u003e2\u003c/sub\u003e/CO\u0026thinsp;=\u0026thinsp;1:9 step 1)\u003cdiv id=\"Equ15\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ15\" name=\"EquationSource\"\u003e\n$$\\:{\\alpha\\:}_{2}=1-\\text{e}\\text{x}\\text{p}[-(1541.44\\times\\:\\text{exp}\\left(-\\frac{130.08\\times\\:1000}{RT}\\right)\\times\\:(t-{\\text{t}}_{1}){)}^{1.229}]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e15\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e(H\u003csub\u003e2\u003c/sub\u003e/CO\u0026thinsp;=\u0026thinsp;1:9 step 2)\u003cdiv id=\"Equ16\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ16\" name=\"EquationSource\"\u003e\n$$\\:\\alpha\\:={0.25\\alpha\\:}_{1}{+0.75\\alpha\\:}_{2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e16\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eThe fitting parameters and determination coefficients of JMA model for each reduction step at different temperatures and H\u003csub\u003e2\u003c/sub\u003e/CO ratios.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"9\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eGas\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eT/℃\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e\u003cp\u003eStep 1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c9\" namest=\"c6\"\u003e\u003cp\u003eStep 2\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003en\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003ek\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003en\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003ek\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003et\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"4\" rowspan=\"5\"\u003e\u003cp\u003eH\u003csub\u003e2\u003c/sub\u003e/CO\u003c/p\u003e\u003cp\u003e=\u0026thinsp;9:1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1400\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.229\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2.917\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.9671\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.195\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.9823\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.514\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.9801\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1450\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.126\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e3.459\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.9831\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.212\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.2312\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.451\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.9843\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1500\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.206\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e4.117\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.9820\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.249\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.4398\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.375\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.9833\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1550\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.224\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e4.459\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.9655\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.161\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.9809\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.327\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.9861\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eAverage\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.196\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.204\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"4\" rowspan=\"5\"\u003e\u003cp\u003eH\u003csub\u003e2\u003c/sub\u003e/CO\u003c/p\u003e\u003cp\u003e=\u0026thinsp;5:5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1400\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.140\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.9857\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.9960\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.319\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.2406\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.9335\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.9538\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1450\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.103\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2.2873\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.9871\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.364\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.3016\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.6982\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.9611\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1500\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.068\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2.8448\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.9656\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.240\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.3709\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.5803\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.9628\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1550\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.061\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e3.1518\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.9710\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.162\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.4895\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.4925\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.9595\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eAverage\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.071\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.271\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"4\" rowspan=\"5\"\u003e\u003cp\u003eH\u003csub\u003e2\u003c/sub\u003e/CO\u003c/p\u003e\u003cp\u003e=\u0026thinsp;1:9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1400\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.037\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.2537\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.9921\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.262\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.1360\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1.674\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.9777\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1450\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.164\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.6414\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.9958\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.207\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.1767\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1.068\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.9718\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1500\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.106\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.9566\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.9937\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.223\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.2128\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.900\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.9809\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1550\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.172\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2.4096\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.9908\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.223\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.3011\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.687\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.9844\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eAverage\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.120\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.229\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\u003ch2\u003e3.3 Model-free method\u003c/h2\u003e\u003cp\u003eTo normalize the two-step reduction process under different gas compositions, reduction experiments were conducted with H\u003csub\u003e2\u003c/sub\u003e/CO ratios of 9:1, 5:5, and 1:9, respectively. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (a-f) show the iso-conversion plots of ln(\u003cem\u003et\u003c/em\u003e) versus 1/T at various conversion degrees for both steps. The linear regression analysis demonstrates statistically significant correlations (R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;\u0026gt;\u0026thinsp;0.95) between \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e and the reduction degree across all gas atmospheres. This high coefficient of determination confirms that the fitting quality is reliable and that the iso-conversional method provides a robust description of the reduction kinetics under different reducing conditions.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe variation of the activation energy as a function of conversion for each step is presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. The reduction of Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e exhibits distinct kinetic characteristics under different H\u003csub\u003e2\u003c/sub\u003e/CO ratios. When the H\u003csub\u003e2\u003c/sub\u003e/CO ratio is maintained at 9:1, the first reduction step (Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e \u0026rarr; FeO) shows relatively low activation energies ranging from 68.38 to 82.35 kJ/mol, with an average of 72.94 kJ/mol. In contrast, the subsequent reduction step (FeO \u0026rarr; Fe) requires significantly higher activation energies of 94.52\u0026ndash;121.30 kJ/mol, yielding an average value of 115.06 kJ/mol. This pronounced disparity indicates that the initial Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e \u0026rarr; FeO transformation is less temperature-sensitive, whereas the formation of metallic iron (FeO \u0026rarr; Fe) is considerably more energy-demanding.\u003c/p\u003e\u003cp\u003eFor the intermediate reducing atmosphere (H\u003csub\u003e2\u003c/sub\u003e/CO\u0026thinsp;=\u0026thinsp;5:5), the activation energy ranges increase to 78.92\u0026ndash;102.19 kJ/mol (average 89.62 kJ/mol) for the Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e \u0026rarr; FeO step and 117.76\u0026ndash;134.30 kJ/mol (average 118.86 kJ/mol) for the FeO \u0026rarr; Fe step. Under CO-dominated conditions (H\u003csub\u003e2\u003c/sub\u003e/CO\u0026thinsp;=\u0026thinsp;1:9), the activation energies rise further, reaching 88.28\u0026ndash;110.26 kJ/mol (average 97.27 kJ/mol) for the first step and 117.34\u0026ndash;125.62 kJ/mol (average 122.74 kJ/mol) for the second step. These systematic increases in activation energy with decreasing hydrogen content underscore the superior reducing capacity of H\u003csub\u003e2\u003c/sub\u003e relative to CO, highlighting its effectiveness in lowering the energetic barrier for both transformation stages.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Conclusions","content":"\u003cp\u003eIn the present study, the reaction mechanisms and reduction kinetics of magnetite powder under isothermal conditions were investigated using thermogravimetric analysis (TGA) at 1400\u0026ndash;1500 \u003csup\u003eo\u003c/sup\u003eC with reducing gases consisting of different H\u003csub\u003e2\u003c/sub\u003e/CO ratios. Based on the distribution characteristics of the DTG\u0026ndash;α curves at various temperatures and gas compositions, as well as results from interrupted experiments, the overall reduction was determined to proceed through two sequential steps: Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e \u0026rarr; FeO and FeO \u0026rarr; Fe. The main conclusions are summarized as follows.\u003c/p\u003e\u003cp\u003e(1) Both an increase in hydrogen content within the reducing gas mixture and an increase in reaction temperature markedly accelerate the reduction reactions. The enhancing effect of hydrogen becomes more pronounced at higher temperatures, as the endothermic nature of hydrogen reduction partially offsets the exothermic reduction by carbon monoxide, thereby intensifying the temperature dependence of the reaction rate.\u003c/p\u003e\u003cp\u003e(2) Kinetic model analysis indicates that the two-step reduction of magnetite follows distinct mechanistic pathways depending on the reaction stage. The Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e \u0026rarr; FeO step is governed by the A2 model (nucleation and growth of product phase), while the FeO \u0026rarr; Fe step is controlled by the R2 model (phase-boundary reaction, contracting cylinder). Model-fitting analysis further reveals that with increasing H\u003csub\u003e2\u003c/sub\u003e/CO ratios, the apparent activation energies of Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e \u0026rarr; FeO are 73.65, 81.43 as well as 108.46 kJ/mol, while those of FeO \u0026rarr; Fe are 114.35, 118.32 and 130.08 kJ/mol, respectively. Based on these parameters, a global kinetic model was established by incorporating a delay time for the FeO \u0026rarr; Fe step to account for the sequential nature of the reaction.\u003c/p\u003e\u003cp\u003e(3) A model-free iso-conversional analysis was also employed to evaluate the variation of activation energy with conversion for each step. The obtained activation energies were 72.94, 89.62, and 97.27 kJ/mol for Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e \u0026rarr; FeO, and the activation energies of FeO \u0026rarr; Fe are 115.06, 118.86 and 122.74 kJ/mol, as H\u003csub\u003e2\u003c/sub\u003e ratios increased. These values are in good agreement with those derived from the model-fitting method, confirming the reliability of the kinetic analysis.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003ch2\u003eConflict of Interest\u003c/h2\u003e\u003cp\u003eAll authors have no financial/commercial conflicts of interest.\u003c/p\u003e\u003c/p\u003e\u003ch2\u003eAcknowledgments\u003c/h2\u003e\u003cp\u003eThis work is financially supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDA29050600).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eJ Kim, B K Sovacool, M Bazilian, S Griffiths, J Lee, M Yang and J Lee, Decarbonizing the iron and steel industry: A systematic review of sociotechnical systems, technological innovations, and policy options, \u003cem\u003eEnergy Research \u0026amp; Social Science\u003c/em\u003e, 89(2022)P. 102565.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eH Cheng, G Cao, Z Ba, D Hu, Y Wang, J Baltrusaitis, C Li, J Zhao and Y Fang, Process design and techno-economic analysis of integrated coal gasification-flash ironmaking-methanol synthesis process, \u003cem\u003eSustainability Science and Technology\u003c/em\u003e, 1(2024), No.1,P. 014004.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJ Liu, Y Zhu and H Zhou, Numerical simulation study on combustion characteristics and NOx emission of COREX gas swirl burner and boiler, \u003cem\u003eFuel\u003c/em\u003e, 352(2023)P. 129128.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZ Wang, R Li, Y Zong, P Hu and J Zhang, Simulation of the flow, temperature, and concentration fields in the reactor of the HIsmelt process, \u003cem\u003eIronmak. 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Manage.\u003c/em\u003e, 258(2022)P. 115526.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"korean-journal-of-chemical-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"kjce","sideBox":"Learn more about [Korean Journal of Chemical Engineering](http://link.springer.com/journal/11814)","snPcode":"11814","submissionUrl":"https://www.editorialmanager.com/kjce/default2.aspx","title":"Korean Journal of Chemical Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Subscription","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"magnetite, kinetic mechanistic model, H2/CO, activation energy","lastPublishedDoi":"10.21203/rs.3.rs-7745848/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7745848/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Magnetite reduction using H2-CO-N2 mixtures with varying H2/CO molar ratios (9:1, 5:5, and 1:9) was investigated over a temperature range of 1400-1550 oC by thermogravimetric analysis (TGA). The results show that both increasing the hydrogen content in the reducing gas mixture and elevating the reaction temperature significantly accelerate the reduction process. Analysis of peak distribution characteristics and interruption experiments indicates that the overall reduction proceeds in two distinct steps: Fe3O4 → FeO followed by FeO → Fe. Kinetic modeling demonstrates that these steps are governed by different mechanisms: the Fe3O4 → FeO step is best described by a nucleation and growth model, while the FeO → Fe step follows a phase-boundary controlled (contracting cylinder) model. Using the model-fitting method, the apparent activation energies (Ea) for Fe3O4 → FeO were determined to be 73.65, 81.43, and 108.46 kJ/mol, and for FeO → Fe were 114.35, 118.32, and 130.08 kJ/mol, corresponding to H2/CO ratios of 9:1, 5:5, and 1:9, respectively. In addition, the model-free (iso-conversional) method was applied to evaluate the variation of Ea with conversion. The obtained activation energies for Fe3O4 → FeO were 72.94, 89.62, and 97.27 kJ/mol, while those for FeO → Fe were 115.06, 118.86, and 122.74 kJ/mol under the same H2/CO ratios. The close agreement between values derived from both methods confirms the reliability of the kinetic analysis and provides robust insight into the reduction mechanisms of magnetite under mixed H2–CO atmospheres.","manuscriptTitle":"Magnetite reduction kinetics under H2 and CO atmospheres at high temperature","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-21 13:47:09","doi":"10.21203/rs.3.rs-7745848/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2025-10-08T19:23:02+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-08T14:58:17+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-10-06T06:28:50+00:00","index":"","fulltext":""},{"type":"submitted","content":"Korean Journal of Chemical Engineering","date":"2025-09-29T21:04:25+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"korean-journal-of-chemical-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"kjce","sideBox":"Learn more about [Korean Journal of Chemical Engineering](http://link.springer.com/journal/11814)","snPcode":"11814","submissionUrl":"https://www.editorialmanager.com/kjce/default2.aspx","title":"Korean Journal of Chemical Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Subscription","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"1aabf64b-a637-4a76-8d32-b29acd742213","owner":[],"postedDate":"October 21st, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-01-26T16:05:14+00:00","versionOfRecord":{"articleIdentity":"rs-7745848","link":"https://doi.org/10.1007/s11814-025-00643-6","journal":{"identity":"korean-journal-of-chemical-engineering","isVorOnly":false,"title":"Korean Journal of Chemical Engineering"},"publishedOn":"2026-01-20 15:58:38","publishedOnDateReadable":"January 20th, 2026"},"versionCreatedAt":"2025-10-21 13:47:09","video":"","vorDoi":"10.1007/s11814-025-00643-6","vorDoiUrl":"https://doi.org/10.1007/s11814-025-00643-6","workflowStages":[]},"version":"v1","identity":"rs-7745848","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7745848","identity":"rs-7745848","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}