## Introduction

Recovering (extracting) valuable metallic elements from industrial wastes is technically important for the efficient recycle of earth unabundant resources. However, the current dry-smelting, hydro-smelting, or combined smelting-electrolytic refining technologies, which are commonly applied for extraction of high purity metals from ores or used oxidized scraps, are not environmentally friendly1,2,3,4,5,6,7,8,9. Because the high quality minable ores deplete first, designing environmentally friendly techniques are necessary to set up ecofriendly recovery processes of used metals.

Although Sn (Tin) is relatively earth unabundant among the industrially demanded metals, Sn and Sn oxides play a key role in several electronic devices and products such as sensor10,11, Pb-free solder12,13, or transparent electrode14,15,16. Despite of the high LME (London Metal Exchange) market price (\$16,450.00/metric ton as of October 4, 2019) of Sn17, which is more than 3 and 1.5 times expansive than Cu and Ni, respectively, 70% of the annually consumed Sn is not appropriately recycled18. Recovery of Sn from used SnO2 or oxidized metal scrap proceeds in a similar process with the ore smelting in the presence of a proper and strong reducer, usually cokes. However, a poor solid-solid contact between SnOx and cokes and a high operation temperature lowers the overall efficiency19.

In our previous report20,21, we have designed a methane reduction (MR) method, an ecofriendly and simple versatile process of Sn recovery from SnOx containing industrial wastes, which also can be potentially applied for Sn ore smelting. A direct facile contact between gas phase methane and SnOx improves the efficiency of the reaction. Moreover, multiple reductants provided by methane (hydrogen and carbon) sequentially reduce SnOx, producing H2O, H2, CO, or CO2 depending on the reduction conditions21. The geometry of a SnO2 bound methane inhibits the initial participation of the carbon of methane to the reduction process21. Rather, the released hydrogen atoms from methane attribute to the initial reduction power of methane21. The extended release of two kinds of reducing agents from methane assures the versatility of the MR of SnOx and the increased economic efficiency21. Another interesting finding was that the H2/CO ratio in the produced gas varies as a function of the CH4/SnO2 ratio. We found that the H2/CO ratio increases if the MR of SnOx proceeds under oxygen depleted conditions because the late released more oxophilic carbon takes up oxygen atoms from SnOx and gas phase H2O21.

Unique chemistry between Sn and CH4 has reported in a recent study by the Metiu and McFarland groups22. They found that molten Sn and other transition metals can directly dissociate CH4 into solid C and H2 and suggested that such direct H2 production from CH4 without CO2 formation as an advanced H2 production method from hydrocarbons22. Based on our previous findings on the CH4 reduction of SnO221, we have reached to a hypothesis that use of alkanes with more carbon and hydrogen contents per mole (CxHy=2x+2, 0 ≤ x ≤ 4) would accelerate the SnO2 reduction and also lower the reaction temperature. Moreover, if molten Sn, which is produced upon SnO2 reduction by alkanes, assists dissociation of alkanes into carbon and hydrogen, the SnO2 reduction would occur under the stronger reduction atmosphere so that the overall SnO2 reduction will be greatly accelerated.

In this letter, we use a combined study of thermodynamic simulations and density functional theory (DFT) calculations to study the effect of the C/H2 ratio in the reducing gas on the efficiency of the reduction of SnO2. To provide a fundamental insight into the mechanism of SnO2 reduction by alkanes with the higher carbon and hydrogen contents per mole and further clarify the reduction potential of the applied alkanes, we introduce commercially available alkanes (CxHy=2x+2, 0 ≤ x ≤ 4) as a reducing agent for SnO2 reduction. The efficiency of the alkane reduction of SnO2 is evaluated by the reduction complete temperature, T100, and compared with the T100 of mole-balanced pure hydrogen. We find that the T100 is an inverse exponential function of the amount of supplied reducing agent (H2 or alkane) and that the addition of carbon as a form of alkane significantly lowers the T100 from that of the H2 reduction of SnO2. Our findings predict that the operation temperature of the alkane reduction of SnO2 can be adjusted by controlling the composition and the x/y ratio of the reducing gas, suggesting an easy and industrially highly accessible recycling process of SnOx containing industrial wastes.

## Results and Discussion

### H2 reduction of SnO2

Figure 1 shows the equilibrium concentrations of the mixture of SnO2 and n∙H2 (n = 2, 4, or 6) at between 0 to 1200 °C. Obviously, H2 reduces SnO2 into Sn through a two-step process. In all cases, SnO2 was first transferred to SnO. SnO was formed at below the melting temperature of Sn (231.9 °C) and further transferred to metallic Sn upon temperature increase. Under the stoichiometric condition (H2/SnO2 = 2, 2 moles of H2 is required to reduce a mole of SnO2 to Sn and 2H2O), the reduction does not complete even at 1200 °C and SnO survives. The T100, at which SnO2 and SnO were completely reduced to Sn, was significantly decreased upon increase of the amount of supplied H2 up to 4 or 6 moles (H2/SnO2 = 4 or 6, respectively, Table 1). Because consistent two moles of H2 were used for SnO2 reduction to Sn, irrespective to the initial H2/SnO2 ratio, the decrease of the T100 is presumably due to the increased chemical potential of gas phase H2 upon increase in the H2/SnO2 ratio.

### Alkane reduction of SnO2: methane and ethane

Figure 2 shows the equilibrium concentrations of the mixture of SnO2 and n∙CH4 (Fig. 2a,b) or n∙C2H6 (Fig. 2c,d) (n = 2 or 4) at between 0 to 1200 °C. Like the cases of the H2 reduction of SnO2, the T100 is equal to the point at which the SnO and SnO2 are completely depleted. Because a mole of CH4 supplies total five units of reducing agents (one C and four H), a mole of SnO2 can be easily reduced to metallic Sn. The increase of H2, C, and H2O above 200 °C shows that CH4 was decomposed into C and H2 and the released H2 from CH4 initially reduces SnO2. The delayed increase of CO2 compared to the increase of C confirms that the reduction by C occurs at the higher temperature than the reduction by H2. In both cases (CH4/SnO2 = 2 or 4) the decrease of H2O, C, and CO2 is coupled with the increase of CO and H2, meaning that C takes up oxygen from SnO2 under C and H2 rich conditions. Despite the active role of hydrogen in the early stage of the reduction, carbon completes the reduction and hydrogen of CH4 was released as gas phase H2. The T100 of CH4 reduction of SnO2 also decreases response to the increase of the CH4/SnO2 ratio (Table 2).

The overall reduction process, initial active reduction of SnO2 by H2 and complete reduction by C, was consistently appeared in the C2H6 reduction of SnO2. C2H6 decomposes rapidly into C and H2 and the overall reduction occurs under highly reducible conditions. However, although the reduction occurs under C and H2 rich conditions, SnO was also appeared as an intermediate, showing that the reduction of SnO2 occurs through a two-step process. The rapidly increased H2 upon C2H6 decomposition gradually decreased as H2 was transformed to H2O. Like the case of CH4 reduction of SnO2, C takes up oxygen, being transformed to CO2 and eventually, to CO. Most of the H2 transformed to H2O was released upon CO formation. When the C2H6/SnO2 increases to 4, the excess C was remained as solid state carbon even after complete reduction of SnO2. The T100 values of C2H6 reduction of SnO2 were generally lower than the values of CH4 reduction of SnO2 (Table 2). The effect of the amount of C and H2 in reducing alkanes on the T100 will be discussed below.

### Alkane reduction of SnO2: propane and butane

C3H8, propane, and C4H10, butane, are commercially widely available alkanes and a component of liquid petroleum gas. No meaningful changes in the reduction behavior was observed in the C3H8 and C4H10 reduction of SnO2 (Fig. 3). Decomposition of C3H8 and C4H10 caused a rapid increase of H2 and C in the initial state of the reduction. Gradual increase of H2O coupled with the increase of reduced Sn and SnO represents the initial reduction of SnO2 by H2 released from alkanes. Because the excess amount of H2 was supplied, even in the presence of solid state carbon, H2 takes up oxygen from SnO2. Subsequent reactions between H2O and solid state carbon produce CO2, CO, and H2. Eventually, all of the oxygen from SnO2 was converted to CO at high temperatures and the excess C and all of H2 from alkanes were released as is. Upon increase of the supplied C3H8 and C4H10, the T100 was also significantly reduced (Table 3). Interestingly, the formation of SnO was suppressed at C3H8/SnO2 = 2 and C4H10/SnO2 = 2. Direct reduction of SnO2 could become available under H2 rich conditions.

### Modelling the reduction trend in alkanes (n·CxHy=2x+2, 0 ≤ x ≤ 4)

The equilibrium concentration diagrams presented in Figs 1 and 2 show that the overall reduction process of SnO2 by H2 and alkanes (CxHy=2x+2, 0 ≤ x ≤ 4) does not differ a lot. Vigorous release of H2 at low temperatures from alkanes generates the similar reducing atmosphere with the reduction by pure H2. Addition of the released C from alkanes induces the gas phase conversion of H2O into H2. Moreover, as the alkane/SnO2 ratio increases from 1 to 2, the T100 decreases. The response of the T100 as a function of the total amount of supplied C, nx, and H, ny, is presented in Tables 2, 3 and Fig. 4a.

Considering that the T100 values are exponentially decreasing upon increase of nx and ny and that the addition of C affects to the T100, we presented the T100 values as a function of nx (Fig. 4b) or ny (Fig. 4c). Figure 4b shows that once the amount of C, nx, is given, the T100 just slightly varies upon change in ny, presenting the quite prominent and dominant effect of C on the T100 of SnO2 reduction by alkanes, as predicted by thermochemical data: the standard formation enthalpy of CO2, $$\Delta {H}_{f}^{0}({{\rm{CO}}}_{2},{\rm{298.15}}\,K)=-{\rm{393.474}}\,\mathrm{kJ}/\mathrm{mol}$$, is greater than that of water, $$\Delta {H}_{f}^{0}({H}_{2}{\rm{O}},{\rm{298.15}}\,K)=-{\rm{285.830}}\,\mathrm{kJ}/\mathrm{mol}$$23. Because single C atom can take over two O atoms from SnO2, whereas two H atoms are required to remove one O atom from SnO2, C of alkanes will naturally more aggressively reduce SnO2.

In Fig. 4c, to more intensively compare the effect of C on the T100 of SnO2, we presented a pair of dataset, the T100 values of H2 or alkane reduction of SnO2 as a function of ny. The control group data, the T100 values acquired from H2 reduction of SnO2, gradually decrease as a function of ny: 615 °C at H2/SnO2 = 8 and 464 °C at H2/SnO2 = 20. The filled square data points in Fig. 4c represent the T100 of SnO2 reduction by CH4, C2H6, C3H8, and C4H10. For the cases where two or more combinations of alkanes are available to match the total amount of supplied hydrogen, ny, we took the case with the higher nx. For example, we took the T100 from 2C2H6 (nx = 4) rather than that from 3CH4 (nx = 3), to compare with the T100 from 6H2 (ny = 12). The T100 values of alkane reduction of SnO2, fitted to an exponential function, show a significantly decrease in T100 (Fig. 4c). Replacing a reducing agent from 4 moles of H2 (ny = 8) to a mole of C3H8 (nx = 3, ny = 8) decreased the T100 of a mole of SnO2 from 615 °C to 494 °C (Fig. 4c). The fitted exponential curves of T100 as a function of nx or ny (solid lines in Fig. 4b,c) show that the T100 of the alkane or H2 reduction can be fit to simple exponential functions (refer to Tables 4 and 5 for fitting constants and R2-values).

Interestingly, we found that the ΔT100 (T100-alkane – T100-hydrogen), an indicator of the effect of carbons from alkanes on the reduction of SnO2 was −121 °C at ny = 3 and rapidly saturated to −101 °C at ny = 4 and beyond (Fig. 4c). The ΔT100 calculated from the two fitted exponential curves predicts the slightly fluctuating ΔT100 centered at −105 °C (Fig. 4d). Because the ΔT100 was estimated comparing the (0, ny) and (nx, ny) data points with the maximum nx value, it naturally represents the maximum effect of C addition to the T100 of SnO2 reduction. The overall increase of nx and ny is beneficial for SnO2 reduction because the lower T100 assures the higher economic efficiency. However, the effect of additional C to the T100 is limited to ΔT100 ≈ −105 °C. The vertically separated three data points in Fig. 4c, (0, 8), (2, 8), and (3, 8), show that the effect of C on the T100 increase as a function of C addition. Because C released from alkanes aggressively attack H2O and liberate hydrogens of H2O, the presence of excess C may increase the chemical potential and the reducing potential of gas phase H221.

### Reaction mechanism of alkane reduction of SnO2

As a prototypical example of alkane reduction of SnO2, DFT-calculated reaction mechanism of CH4 reduction of SnO2 is presented in Fig. 5a. The original DFT-calculated reaction energy values were adopted from our previous publication (Under Creative Commons Attribution 4.0 International License)21. The initial CH4 dissociative adsorption (Process #1, Fig. 5a) initiates the CH4 reduction of SnO2. Because a CH4 molecule was dissociated into a –CH3 methyl group and a hydrogen atom, which are independently bound to surface lattice oxygen atoms of SnO2, the SnO2 surface will be strongly hydrogenated upon exposure to CH4. The sequential combined processes of dehydrogenation of –CH3 to –CH (Processes #2 to #5) and water formation (process #3 and #4) are energetically uphill. This is because two hydrogen atoms produced upon dehydrogenation of single CH4 molecule were used for water formation. As we discussed above, under the CH4 rich reduction conditions, the surface oxygen ions of SnO2 will be eventually hydrogenated and thus the endothermic dehydrogenation of –CH3 and water formation will not hinder the overall reduction of SnO2. The second water formation (Process #6 and #7) and CO2 production (Process #8) are strongly thermodynamically preferred. The overall reduction of SnO2 by CH4 shows that the hydrogen atoms of CH4 participate in the reduction process first and the residual carbon atom finally reduces SnO2. This finding is consistent with the equilibrium concentration diagrams (Figs 2 and 3) showing that H2O always forms first to CO and CO2.

Interestingly, upon initial adsorption of C2H4, C3H8, and C4H10, multiple –OH and –CH3 groups were formed as a result of dissociative adsorption of alkanes (Fig. 5b–d). Later, each –CH3 group was eventually dissociated into –CH2 and –OH, therefore the subsequent –CH2 dissociation, water formation, and CO2 formation processes would saturate into the same processes presented in Fig. 5a. The overall reaction mechanism of SnO2 reduction by alkanes (CxHy=2x+2, 0 ≤ x ≤ 4), therefore, is identical to each other except for the detailed energetics of the initial dissociative binding step. Interestingly, the initial dissociative adsorption of C3H8 and C4H10 are energetically endothermic (Fig. 5c,d). However, considering that the alkane reduction would occur under the high alkane partial pressure conditions20,21, the highly negative entropic contribution to the Gibbs free energy of binding, −TΔS, will definitely compensate the positive ΔE of dissociative adsorption (ΔE1 in Fig. 5c,d)24,25, making the ΔG of dissociative C3H8 and C4H10 binding negative (exothermic). The roughly calculated highly negative −TΔS0 at standard state26 of propane (−0.83 eV) and butane (−0.95 eV) confirm that the ΔG values of dissociative alkane bindings (ΔG = ΔE − TΔS) are negative. The DFT-calculated mechanism of alkane (CxHy=2x+2, 0 ≤ x ≤ 4) reduction of SnO2 shows that the overall reaction mechanism is consistent within the alkanes that we applied (CxHy=2x+2, 0 ≤ x ≤ 4) for SnO2 reduction, irrespective to x and y. This result confirms that the significantly accelerated reduction potential of alkanes upon increase in nx is due to the quantitatively excessive supply of reducing agents by alkanes with the higher nx. As we have noticed in the introducing part, the presence of the already reduced liquid Sn metal may assist the direct reduction of alkanes. If this process occurs, the overall reaction will proceed under the higher H2 partial pressure conditions (under the total pressure greater than 1 atm) with excessive solid state carbon supply. Results on the mechanism of SnO2 reduction by alkanes under the various conditions (partial pressure and carbon content) will be reported in due course.

## Conclusions

We study the mechanism of alkane reduction of SnO2 for efficient low-temperature recovery of Sn from SnO2 using combined study of thermodynamic simulations and DFT calculations. Through a comparative analysis of the reducing power of H2 and commercially available alkanes (CxHy=2x+2, 0 ≤ x ≤ 4) toward SnO2 reduction, we scaled the reducing potential of studied reductants with T100, the temperature at which SnO2 is completely converted to metallic Sn. The alkanes with the higher nx and ny quickly complete the reduction at low T100. Moreover, the positive effect of nx on the T100 was quite prominent in all studied cases of alkane reduction of SnO2. The T100 of the SnO2 reduction by alkanes (n·CxHy) was significantly decreased from the T100 of pure hydrogen with the same amount of hydrogen atoms (n·Hy). The fitted exponential curves of T100 plotted as a function of ny, presents that the effect of C on the T100 being saturated to ΔT100 ≈ −105 °C.

The C and H atoms released from alkanes sequentially reduce SnO2 to Sn and eventually to metallic Sn. The initial stage of SnO2 reduction by alkane is identical to the H2 reduction of SnO2; H2 takes up oxygen from SnO2. However, in the presence of the released C from alkanes, H2 of H2O is released as a gas phase molecule as C takes up oxygen from H2O. Because the gas phase redistribution between H2O, H2, CO, and CO2, caused by solid C occurs at above the T100, the role of the solid C released from alkanes is likely to adjust the chemical potential of hydrogen of H2O and H2, accelerating the reduction of SnO2 by H2. The DFT-calculated atomic scale mechanism of alkane reduction of SnO2 confirmed that the overall reaction mechanism is consistent within applied alkanes (CxHy=2x+2, 0 ≤ x ≤ 4).

Our results show that the alkane reduction of SnO2 is an effective recovery method of metallic Sn from SnO2 or SnO containing industrial wastes or from Sn ores. The low T100 values of alkane reduction and the maximum ΔT100 of −105 °C suggest that the alkane reduction of SnO2 assures high economically efficiency with economic value added that is held by the co-produced H2 and carbons.

## Methods

### Thermodynamic simulation

Thermodynamic simulations were performed with the HSC 6.0 code (Outotec Research, www.hsc-chemistry.com). The relative thermodynamic stability of various Sn, C, O, and H containing chemical compounds was estimated at temperatures between 0 °C and 1,200 °C. The initial equilibrium simulations were performed with 1 kmol of SnO2 balanced with increasing amount of H2 or alkanes. The T100 of several commercially accessible alkanes (CxHy=2x+2, 0 ≤ x ≤ 4), methane (CH4), ethane (C2H6), propane (C3H8), and butane (C4H10), were measured and compared with that of pure H2 to estimate the effect of carbon addition on the reducing power of a gas phase reductant. To generalize the effect of carbon, the measured T100 values were fitted to exponential curves.

### Density functional theory calculation

We performed density functional theory calculations with the Vienna ab-initio simulation package (VASP)27 with the Perdew-Burke-Ernzerhof (PBE)28 exchange-correlation functional to study the reaction pathway and the corresponding energetics of alkane (CxHy=2x+2, 0 ≤ x ≤ 4) reduction of SnO2. The most bottom SnO2 triple layer was fixed during the optimization to ensure the structural robustness of the slab models. The interaction between the ionic cores and the valence electrons was described with the projector augmented-wave method29. The valance-electron wave functions were expanded in the plane-wave basis set up to the energy cutoff of 400 eV. The convergence criteria for the electronic structure and the atomic geometry were 10−4 eV and 0.03 eV/Å, respectively.

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.