A Study on the Heat Effect and Kinetics During Magnesiothermic Reduction of Porous SiO2

doi:10.21203/rs.3.rs-838158/v1

Magnesiothermic reduction reaction (MRR) is an effective method to synthesis Si nanoparticles. In this paper, the heat effect and MRR kinetics were investigated by real-time temperature monitoring and analyzing the DSC curve of the MRR. It was found that the MRR onset temperature is about 465 °C, and the system temperature rose sharply at 535 °C. After the disappearance of the magnesium phase, the system temperature remained consistent with the set value. The exothermic peak lags and the spike decreases when adding NaCl into the system. The MRR was chemical reaction control, corresponding with the apparent activation energy was 193.456 kJ·mol^-1(without NaCl) and 191.434 kJ·mol^-1(with NaCl) in the temperature interval 465 °C −700 °C, respectively. NaCl affects the reaction mechanism by lowering the temperature of the system. Our work successfully prepared the spherical Si nanoparticles, which average grain size increased from 25 nm to 40 nm with the extended reaction duration. The conversion rate of porous SiO₂ precursor was as high as 92%.

Electronic Materials and Devices

Optical Materials and Devices

Si nanocrystalline

heat effect

magnesiothermic reduction kinetics

phase composition

As for the lithium-ion battery negative electrode materials, the graphite has approached the theoretical specific capacity (372 mAh·g^− 1) and cannot be an excellent match for future high energy density power batteries. Amongst the next-generation negative electrode materials, Si has received significant attention due to its high theoretical specific capacity (3579 mAh·g^− 1 for Li₁₅Si₄) [1 − 3]. Unfortunately, the Si electrode suffers from drastic volume change (> 300%) during the charge-discharge cycle, which leads to rapid capacity loss and poor cycling performance [4 − 6]. At present, the regulation of its microstructure remains a viable candidate for reliving volume expansion in order to improve cycle life [7], e.g., nanostructured Si (nanoparticles [8], nanotubes [9 − 11], nanowires [12], and nanoporous [13 − 15]), and shell covering structures of Si-based materials (Si@C [16 − 18], Si@Cu [19], and Si@void@C [20]). In addition, nanostructured Si also is an attractive material for photovoltaics [21], photocatalysis [22], and thermoelectrics [23]. However, it remains a challenge to produce nanostructured Si at a high yield with a low cost.

In 2007, the magnesiothermic reduction reaction was firstly used to fabricate microporous Si replicas from three-dimensional SiO₂ micro-assemblies, which was considered one of the most promising methods to fabricate Si nanoparticles [24]. Other Si-based materials were also synthesized via the MRR [25 − 27], demonstrating a high specific capacity and excellent rate capability. It was found that the additional free spaces were why abundant mesoporous structures could effectively reduce the volume expansion of Si particles. Furthermore, Liu et al. proposed that a single Si nanoparticle (less than 150 nm), i.e., nano effect, could also alleviate the bulk expansion of the Si [28].

Among the numerous paper reported to date, the MRR was a violent exothermic reaction, which caused a large quantity of heat released and accumulated in the system. The heat effect resulted in the local temperature of the system reaching 1941°C, which significantly affected the structure of the reactant and product [29]. Shi et al. prepared the product Si nanoparticles by alleviating the massive local heat via reducing the ramp rate [30]. Si nanoparticles also were successfully fabricated by Meekins et al., directly adding the heat scavenger NaCl into reactants of the MRR [31]. Yang et al. concluded that the quantity of the gasified magnesium decreased as their particle sizes exceed 80 µm, avoiding sintering the solid reactant or product [32]. Another way to mitigate heat accumulation was to improve the reaction apparatus by placing Mg and SiO₂ separately [33]. The above strategies have alleviated the adverse impact caused by the heat effect and have synthesized Si-based materials with excellent electrochemical properties. Nevertheless, it is still noted that the existing studies remain unclear in terms of the role of heat effect on the phase composition and the reaction kinetics of the MRR.

This work revealed the actual temperature change process within the MRR system by real-time temperature monitoring. It also determined the influence of system heat effect on the phase composition and the kinetics of the MRR process. Si nanoparticles with D_(0.5) of 25 nm were successfully prepared. D_(0.5) is the average grain size, which increased to 40 nm with the reaction duration increases, and the conversion rate of SiO₂ to Si reached 92%. It is theoretical guidance for the efficient production of Si nanoparticles via the MRR.

2.1 Si nanoparticles preparation

The amorphous SiO₂ particles with a diameter of about 20 µm used in this study are an aggregate formed by the non-compactly interconnected SiO₂ nanoparticles (D_(0.5) = 25 nm). Firstly, The uniformly mixed amorphous SiO₂ (2 g, 99.5% purity, Ningbo Jinlei Nanomaterials Technology Co., Ltd.) and Mg powder (1.6 g, 99.5% purity, China National Pharmaceutical Group Chemical Reagent Co., Ltd.) were sealed into a stainless steel container (20 mL) then transferred to a horizontal tube furnace under an argon atmosphere. A K-type high-temperature thermocouple connected to a data acquisition unit (Agilent 34970A) was inserted inside the reactant to measure the real-time temperature of the MRR. Determine when to turn off heating power based on the real-time temperature of the system. Then ramped up to a predetermined temperature with a ramp rate of 5°C·min^− 1. Noteworthy, we turned off heating power at the real-time temperature reached the highest point recorded by the data collector (denoted as 0 h) and heated at 650°C for 2 h, 4 h, and 8 h. The comparison experiment was repeated the above experimental steps after adding NaCl into the systems (NaCl : SiO₂ = 5:1 in mole).

When the mixture was cooled naturally to room temperature, the obtained brown products were immersed in ethylene glycol solution, stirred magnetically for 30 minutes to remove heat scavenger NaCl. The samples were then immersed in 2 mol·L^− 1 HCl solution for 12 h to remove the newly formed MgO, Mg₂Si, and Mg₂SiO₄. After being immersed in 1 mol·L^− 1 HF solution for 10 minutes to ensure the removal of unreacted or newly formed SiO₂, the Si nanoparticle aggregate was obtained. Finally, the aggregate was immersed in ethanol and ultrasonically dispersed for 30 minutes to get more uniformly distributed Si nanoparticles. We also calculated the crystallite sizes of Si nanoparticles with Scherrer analysis. The formula is as follows:

$${L_{hkl}}=\frac{{K\lambda }}{{\beta \cos \theta }}$$

1

Where, L_hkl is microcrystals size in the direction perpendicular to the (hkl) crystal plane; λ is X-ray wavelength; θ is Bragg angle; β is peak width (maximum full width at half or integral width); K is Scherrer factor. Subcrystals are essentially absent in the grains of nanomaterials. Therefore, L_hkl can be considered as the grain size of nanoparticles.

2.2 Material characterization

Thermogravimetric (TG) and differential scanning calorimetry (DSC) analysis was conducted from 20°C to 800°C at a ramp rate of 5°C·min^− 1 in argon on a TGA − DSC instrument (SDTQ 600). The X-ray diffraction (XRD) patterns were obtained using a powder diffractometer (D 8 Advance) with Cu Kα radiation (λ = 0.1542 nm) at 40 kV and 30 mA. The morphologies of the materials were observed by scanning electron microscopy (SEM) using a field-emission scanning electron microscope (Quanta 250 FEG) in conjunction with energy dispersive spectrometry (EDS). The microstructure of the samples was characterized by transmission electron microscopy (TEM) at an acceleration voltage of 200 kV (G 20).

The TG − DSC curves of the reaction between the Mg and SiO₂ mixture were displayed in Fig. 1(a). The exothermic peak occurs around 465°C, the slope of the curve at the initial stage of the reaction (465°C − 535°C) is smaller than system temperature reaches 535°C. And the highest temperature was recorded at 575°C. This means that the reaction slowly occurs at the initial stage (465°C − 535°C), the Mg pressure increases with the temperature rise. Thus the reaction is drastic once the Mg vapor pressure is sufficient to diffuse into the SiO₂ particles ( at 535°C). The TG curve in Fig. 1(a) indicates that the mass does not change during the reaction. Figure 1(b) shows the real-time temperature profile of the Mg reduction SiO₂ obtained by turn-off heating power when the system temperature reaches the exothermic spike, i.e. when the real-time temperature of the system reaches 1270°C. It observes that the temperature slowly rises as time passes, until the 86 minutes, i.e., system temperature at 465°C, the profile suddenly over set temperature and appear exothermic peak. And the profile rapidly increases from 535°C to 1270°C in 20 seconds. It suggests that the MRR releases a large amount of heat, causing the rapid rise of the actual temperature around 535°C. The mass of the reactant (~ 20 g) much larger than the DSC experimental amount (~ 5 mg) is why the highest temperature of the real-time temperature profile is higher than 575°C. The heat conduction and radiation do not effectively dissipate the large quantity of heat released from the MRR in this condition.

To alleviate the local heat accumulation of the MRR process, the heat scavenger, i.e., NaCl, was mixed into the reactants. Table 1 summarizes the adiabatic temperature of the system calculated by HSC 6.0 (Thermochemical analysis software). It clarifies the adiabatic temperature of the MRR process reaches 2325°C, and the added NaCl could reduce the heat accumulation of the MRR exothermic process effectively, shown in systems 2 − 4. Brindley et al. [34] proposed that the formation temperature of Mg₂SiO₄ is 1100 − 1400°C, described by solid˗state Eq. (5) of Table 2. Thus, adding NaCl into the reactant proportionally (NaCl : SiO₂ = 5 : 1 in mole) to control system temperature and avoid byproduct Mg₂SiO₄. In comparison, the adiabatic temperature of the system is lower when Mg₂Si reacts with SiO₂, as shown in system 5 of Table 1.

Table 1

The adiabatic temperature at different NaCl addition amounts in the Mg and SiO₂ mixture (systems 1 − 4); Mg₂Si and SiO₂ mixture (system 5)
Systems	SiO₂ / mol	Mg / mol	Mg₂Si / mol	NaCl / mol	Adiabatic temperature / °C
1	1	2	0	0	2325
2	1	2	0	1	1810
3	1	2	0	3	1332
4	1	2	0	5	1017
5	1	0	1	5	812

After adding NaCl to the reactants, the TG − DSC curves of the reaction are displayed in Fig. 2(a). The exothermic peak occurs around 475°C, and the highest temperature is recorded at 533°C. It indicates that the MRR with NaCl onset temperature is about 475°C and much more violent when the system temperature reaches 533°C. Compared with the exothermic peaks in Fig. 1(a), it can be seen that the exothermic peaks lags and the highest temperature decrease. The melting of NaCl causes the sharp heat absorption peak of the DSC curve around 803°C. The TG curve in Fig. 2(a) also indicates that the mass does not change during the reaction. Figure 2(b) shows the real-time temperature profile of the Mg reduction SiO₂ obtained by turn-off heating power when the system temperature reaches the exothermic spike (792°C). As shown in Fig. 2(b), the exothermic peak appears when the system temperature reaches 535°C, with a temperature spike of 792°C. It is clear that adding NaCl can effectively prevent heat accumulation inside the system during the pre-reaction period (475°C − 535°C). What's more, NaCl can destroy the heat accumulation and reduces the temperature (highest temperature from 1270°C decrease to 792°C), but when the MRR is strong, NaCl cannot fully absorb the heat released near 535°C. The NaCl limits the reaction temperature rise over the NaCl melting point. Indeed, the heat released will be used to melt NaCl rather than products.

The temperature profiles in the reactor with different reaction durations (2 h, 4 h, and 8 h) at 650°C are shown in Fig. 3. There are two stages in the MRR actual temperature change process after the system temperature rises to the reaction onset temperature. The first stage shows a significant exothermic peak, which only lasts 30 minutes. Then, the system temperature decreases and remains consistent with the set value at the second stage.

According to the DSC curve in Fig. 1(a) and Fig. 2(a), the magnesiothermic reduction kinetic parameters without and with NaCl in the system were calculated. Assuming β being the ramp rate, starting temperature is T₀, and the temperature at the moment t being T = T₀ + βt, thus, dT = βdt. The reaction kinetics basic formula of the non-isothermal thermal analysis is based as follows [35]:

Where α is conversion rate; k₀ is reaction rate constants; A is the preexponential factor; n is reaction order; E is activation energy; R is the gas constant, 8.314 J·mol^− 1·K^− 1.

The DSC curve in Fig. 1(a) and Fig. 2(a) integrated to obtain H (heat of reaction accumulation value) at the corresponding temperature point. The modified heat conversion rate (α) can be acquired from H and H₀ (total heat effect), as shown in Fig. 4.

The kinetic parameters of the reaction were calculated using the Freeman − Carroll method. The Freeman − Carroll method [36] is widely used without any prior knowledge of the reaction order, the apparent activation energy and order of reaction may be calculated from a single experimental curve. Liu [37] pointed out that the Freeman-Carroll method can only be used to determine the activation energy of a reaction accurately and has a significant error in calculating the reaction order. Therefore, only the apparent activation energy of the reaction was discussed here.

$$\frac{{\Delta \lg ({\text{d}}\alpha /{\text{d}}T)}}{{\Delta \lg (1 - \alpha )}}= - \frac{E}{{19.144}}\frac{{\Delta (1/T)}}{{\Delta \lg (1 - \alpha )}}+n$$

3

This allows obtaining the activation energy E and the reaction order n from the slope and the intercept of a straight line. According to the fitted straight line in Fig. 5, the Freeman − Carroll formula without NaCl in the system can be obtained as:

$$\frac{{\Delta \lg ({\text{d}}\alpha /{\text{d}}T)}}{{\Delta \lg (1 - \alpha )}}= - 10105.3\frac{{\Delta (1/T)}}{{\Delta \lg (1 - \alpha )}}+1.2$$

4

The Freeman − Carroll formula with NaCl in the system can be obtained as:

$$\frac{{\Delta \lg ({\text{d}}\alpha /{\text{d}}T)}}{{\Delta \lg (1 - \alpha )}}= - 9999.7\frac{{\Delta (1/T)}}{{\Delta \lg (1 - \alpha )}}+3.1$$

5

The Freeman − Carroll formula indicates that the apparent activation energy of the reaction was 193.456 kJ·mol^− 1 (without NaCl) and 191.434 kJ·mol^− 1(with NaCl) in the temperature interval 465 − 700°C, respectively. It means that NaCl does not change the apparent activation energy of the reaction, i.e., NaCl is not involved in the reaction. It is known that when the apparent activation energy is between 42 kJ·mol^− 1 and 420 kJ·mol^− 1, the limiting link of the reaction is the chemical reaction process[38]. Therefore, the chemical reaction controls the magnesiothermic reduction, and lowering the temperature will reduce the concentration of activated molecules and further decrease the reaction rate. NaCl is lowering the temperature of the system by heat absorption, thereby reducing the rate at which the reaction occurs.

Table 2 showed that the Gibbs free energy change (△G) and enthalpy changes (△H) of different reactions were calculated by HSC 6.0 software. Obviously, all reactions in Table 2 are negative enthalpies reactions. The △G of four equations at 450°C − 650°C, 101325 Pa indicate that the first four reactions could be more easily achieved in thermodynamic conditions than reaction (5), and the reaction proceeds more completely at chemical equilibrium.

Table 2

The △H and △G of different reactions (450°C ~ 650°C, 101325 Pa)
Equations	Chemical reaction	△H(KJ·mol^− 1)	△G(KJ·mol^− 1)
1	2Mg_(g) + SiO_2(s) = Si_(s) + 2MgO_(S)	− (580 ~ 579)	− (396 ~ 345)
2	4Mg_(g) + SiO_2(s) = Mg₂Si_(s) + 2MgO_(s)	− (944 ~ 940)	− (606 ~ 522)
3	2Mg_(g) + Si_(s) = Mg₂Si_(s)	− (366 ~ 360)	− (200 ~ 150)
4	Mg₂Si_(s) + SiO_2(s) = 2MgO_(s) + 2Si(s)	− (213 ~ 204)	− (192 ~ 190)
5	SiO_2(s) + 2MgO_(s) = Mg₂SiO_4(s)	− (62 ~ 64)	− (58 ~ 62)

Figure 6 presents the XRD patterns of the products obtained by turn-off heating power when the system temperature reaches the exothermic spike (0 h) and different reaction duration under 650°C. As shown in 0 h of Fig. 6(a), the products from MRR contain MgO, Mg₂Si, Si, and Mg₂SiO₄ without indication of Mg, which indicates that the reaction between Mg and SiO₂ is rapid and the Mg is consumed entirely. This observation can be confirmed by the DSC curve of the magnesiothermic reduction SiO₂ in Fig. 1(a) since there is no pronounced peak of Mg melting heat absorption observed at 648°C. The disappearance of the Mg phase indicates that reactions (1), (2), and (3) of Table 2 have been completed. The large quantities of heat released are why the synthesis of Mg₂SiO₄ via Eq. (5), which consumes the residual reactant SiO₂. These four reactions were completed within 20 minutes (the time used for the system temperature to pass from the reaction start temperature (465°C) to 465°C again) shown in Fig. 1(b). The product composition was almost constant with extended durations. XRD patterns at 650°C for 2 h, 4 h and 8 h proved this point.

However, the typical diffraction peaks of Si, MgO, and Mg₂Si can be detected obviously in Fig. 6(b), which means that adding NaCl into the reactant could inhibit the formation of Mg₂SiO₄ effectively. Thus there is no indication of Mg₂SiO₄ in the mixture. Figures 7(a)−(d) shows the SEM micrograph and constituent elemental distributions inside the particles (obtained at 0 h and washed by glycol). The particles with a diameter of approximately 25 µm and internal porous morphology were observed. Furthermore, the non-homogeneous elemental distributions of O, Mg, and Si over the particles are shown in the EDS mapping images (Figs. 7(b) − 7(d)). Mg elemental content decreases from the outer layer to the inside, i.e., forming a concentration gradient along the radial direction, which is confirmed by EDS analysis in Fig. 7(e). It could be deduced that Mg₂Si and MgO in a 1 : 2 mole ratio roughly generated within the outer layer of the precursor SiO₂ particle when forming Si and MgO also at a molar ratio 1 : 2 approximately at grain inside. O elemental of grain outer surface more than the scale value is that the small amount Si has been oxidized. What's more, it also suggests the Mg₂Si and MgO are generated via reaction (2) at the outer layer SiO₂ aggregate. With Mg gas diffusion to the inner reaction interface, the Mg gas concentration decreases, forming Si and MgO via reaction (1) at grain inside the SiO₂ aggregate. The newly generated Si produced near the Mg source will be further converted to form the Mg₂Si, reaction (3). These three reactions were completed within 30 minutes (the time used for the system temperature to pass from the reaction start temperature (475°C) to 475°C again) shown in Fig. 2(b).

With the increase of reaction durations, the content of Si increases while Mg₂Si decreases, as proved by the increase in the sharp diffraction peaks strength of the phase of Si and decrease of the Mg₂Si peak strength, as shown in Fig. 6(b). Only MgO and Si diffraction sharp peaks are present in the reaction product without diffraction peaks of Mg₂Si under 8 h. The conversion rate of SiO₂ to Si with different reaction durations (Table 3) further confirms these results, showing a 58% conversion rate after 0 h, but the value increased to 62% and 75% after 2 h and 4 h, respectively. Note that the conversion rate of SiO₂ is up to 92% when the reaction duration is extended to 8 h at 650°C.

Table 3

The conversion rate of SiO₂ to Si at 0 h and with different reaction durations under 650°C (with NaCl)
Reaction durations (h)	0	2	4	8
Conversion (%)	58	62	75	92

As shown in Fig. 8, the XRD of three mixtures indicates that synthesized products Si demonstrate different levels of sharp and narrow diffraction peaks without apparent amorphous scattering, indicating a high degree of crystallinity, clearly states that amorphous SiO₂ transformed into crystalline Si after the MRR. In addition, it demonstrates that the product Si obtained in 0NaCl − 0 h has sharper peaks compared with that of the Si received in 5NaCl − 0 h and 5NaCl − 8 h, confirming larger crystallite sizes. These results are consistent with the general observation in the literature that added NaCl into reactants could inhibit excessive growth of Si crystalline grains by reducing heat accumulated. Furthermore, compared to the full width at half maximum of the XRD peaks of 5NaCl − 0 h with 5NaCl − 8 h, and we can see that the size of the Si crystal grains grows with increasing reaction duration. This observation is further confirmed by the TEM images of the Si display in Figs. 9(g) and 9(h). We also calculated the fine size of Si crystalline grains by Scherrer analysis based on the XRD patterns of Fig. 8. This yielded an average Si crystallite size of 58.201 nm, 24.835 nm, and 41.034 nm, corresponding to 0NaCl − 0 h, 5NaCl − 0 h, and 5NaCl − 8 h, respectively. In brief, the high temperature would lead to excessive growth of the products Si nanoparticles. Meanwhile, Si crystalline grains would also grow to a specific crystal shape due to the diffusion of Si atoms and the migratory movement of grains with reaction duration increases at a higher reaction temperature (650°C).

Figure 9 displays the SEM and TEM images of reactant SiO₂ and the products Si. It shows that the size of the SiO₂ particle is 20 µm, as indicated in Fig. 9(a), and each particle is composed of many primary SiO₂ nanoparticles (about 25 nm) in Fig. 9(e). As shown in Fig. 9(b), the structure of the obtained product Si changes dramatically compared with that of the precursor SiO₂. The smaller nanopores disappear. In contrast, the inter-adhesive macroporous network with a pore diameter (~ 200 nm) and a wall thickness (~ 50 nm) comes into being, which is further confirmed in Fig. 9(f). The Si particles obtained with NaCl are illustrated in Fig. 9(c), which essentially maintain the morphological structure of the precursor SiO₂ due to its heat scavenger effect. And the Si nanoparticles with a diameter of about 25 nm show in Fig. 9(g), which is consistent with the result calculated from Scherrer analysis, are loosely interlinked to compose the Si particles around 12.5 µm (Fig. 9(c)). Compared to the precursor SiO₂, micron-sized spherical Si particles exhibit volume shrinkage due to the removal of Mg₂Si, MgO, and SiO₂. Figures 9(d) and (h) show that the structure of the Si also maintained the spherical morphological of the precursor SiO₂ after extending the duration to 8 h at 650°C. However, the Si particles diameter increases to around 18 µm, and the primary Si nanoparticles diameter also increases to about 40 nm. It clearly illustrates that crystal grains grow in a specific crystal shape with increasing reaction duration, consistent with the results obtained in Fig. 8.

Magnesiothermic reduction slowly occurs at the initial stage (465°C − 535°C), and the Mg pressure increases with the temperature rise. The reaction is drastic once the Mg vapor pressure is sufficient to diffuse into the SiO₂ particles (at 535°C). The Mg vapor diffusion process will lead to a concentration gradient along the radial direction in SiO₂ aggregate. It caused that Mg₂Si and MgO are generated at the outer layer while Si and MgO formed at grain inside the SiO₂ aggregate. What's more, The newly generated Si produced near the Mg source will be further also converted to form Mg₂Si. The heat released from the reaction will lead to a transient high temperature and the formation of the byproduct Mg₂SiO_4, which consumes SiO₂ and MgO. All reactions without NaCl are completed within approximately 20 minutes after the system temperature reaches onset temperature.

As a heat scavenger, NaCl does not affect the apparent activation energy of the reaction, and it affects the reaction mechanism by lowering the temperature of the system. Mg₂SiO₄ is not generation in system, but the reaction (1), (2), and (3) occurs in the same order as before the addition of NaCl. These three reactions are completed within 30 minutes after the system temperature reaches onset temperature. And the diameter of the initial prepared Si nanoparticles is about D_(0.5) = 25 nm. What's more, the formed Mg₂Si phase could reduce the residue SiO₂ in the next 8 h, which leads to the highest conversion ratio (92%) of SiO₂, and the diameter of Si nanoparticles obtained increases to D_(0.5) = 40 nm.

Acknowledgments

I would like to express my sincere gratitude to my tutor and senior students for their guidance and help in completing this work. Also, I especially thank the Analytical and Testing Center, Northeastern University (China), for the instrumental or data analysis.

Funding

Not applicable

Conflicts of interest/Competing interests

Have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Availability of data and material

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Code availability

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Author contributions

Material preparation, data collection, and analysis were performed by Boxia Zhang, Fei Wang, Jianshe Chen,Binchuan Li, Kuiren Liu, Qing Han.The first draft of the manuscript was written by Boxia Zhang and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Consent to participate

All authors happily agree to participate in this research study.

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All authors permit the permission to the journal to publish this research study.

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A Study on the Heat Effect and Kinetics During Magnesiothermic Reduction of Porous SiO₂

Status:

Version 1

Abstract

Figures

1 Introduction

2 Experimental

2.1 Si nanoparticles preparation

3 Results And Discussion

4 Conclusions

5 Declarations

6 References

Status:

Version 1