Oxidation of Liquid Silicon in Air Atmospheres Containing Water Vapor

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Thermodynamics, Transport, and Fluid Mechanics

Oxidation of liquid silicon in air atmospheres containing water vapor Yan Ma, Bo Jiang, Elmira Moosavi-Khoonsari, Stefan Andersson, Elizabeth J. Opila, and Gabriella M. Tranell Ind. Eng. Chem. Res., Just Accepted Manuscript • Publication Date (Web): 25 Mar 2019 Downloaded from http://pubs.acs.org on April 2, 2019

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Industrial & Engineering Chemistry Research

Oxidation of liquid silicon in air atmospheres containing water vapor Y. Ma1*, B. Jiang1*, E. Moosavi-Khoonsari1,2, S. Andersson3 , E.J. Opila4 and G. M. Tranell1 1. Department of Materials Science and Engineering, Norwegian University of Science and Technology, 7491 Trondheim, Norway 2. Research and Development, TATA steel Europe, 1951MD Velsen-Noord, The Netherlands 3. Department of Metal Production and Processing, SINTEF Industry, 7465 Trondheim Norway 4. Department of Materials Science and Engineering, University of Virginia, VA 22904-4745, Charlottesville, USA E-mail: [email protected]; [email protected]

Abstract The oxidation of silicon (Si) has been extensively investigated over the past 50 years. Yet, an understanding of the mechanism and rate of liquid Si oxidation in atmospheres containing water vapor, is lacking. The effect of water vapor on the oxidation process is of particular importance in the industrial, metallurgical production and processing of liquid silicon, as a significant amount of silica fume is generated under such conditions. The generation of fume is due to active oxidation of liquid metal in the tapping, refining and casting steps – a major occupational health and safety challenge for the Si producers. In this work, the effect of water vapor in the atmosphere on the Si oxidation rate and fume characteristics was investigated experimentally at 1823K in air-H2O atmospheres. Compared with oxidation in dry air, the rate of oxidation in wet air is higher, and increases to the threefold compared to dry air with increasing water vapor content at 7kPa, above which the alloy surface was passivated and the

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oxidation rate stable. To explain the experimental observations, Si oxidation reactions in wet atmosphere were modeled by FactSage 7.1 thermochemical software, by density functional theory (DFT) calculations and by estimates of detailed reaction thermochemistry and kinetics using statistical thermodynamics and statistical mechanics methods. The increased rate of fuming was explained by the formation of Si-O-H species in the system and the more “sticky” nature of the H2O molecule on the Si surface as compared to the O2 molecule, yielding a higher degree of oxygen utilisation towards active Si oxidation, i.e SiO formation. Key words: Silicon, oxidation, water vapor, FactSage, DFT

1. Background The oxidation of silicon is relevant in numerous applications and industries from electronics to metal production. In the production process for metallurgical grade silicon (MG-Si), fugitive emissions originating from active oxidation of the liquid metal in the tapping and refining processes may account for as much as 40-80% of all emissions at the silicon production site1. In order to reduce these industrial emissions, earlier studies have been carried out to better understand the mechanism and rate of liquid silicon oxidation in dry air 2-4. Wagner’s 5 first described the principles of active and passive oxidation of silicon in the 1950´s. Active oxidation of liquid silicon in dry air is a process consisting of three steps: (1) the formation of volatile SiO gas, which is (2) oxidized into liquid SiO2 (due to the exothermic nature of the reaction) and (3) cooled to amorphous fume particles1. Næss and co-workers2-4 have concluded that the gas velocity above the metal surface is rate determining for the mass transport of oxygen through the O2 and SiO boundary layers to the silicon surface, affecting the SiO formation rate and subsequent oxidation to SiO2 particulate matter. The two reactions


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in the oxidation process, with their associated Gibbs energies of reaction (valid from 273 to 2273K) calculated using FactSage 7.1 FactPS and FToxid databases 6, are shown below: Si(l)+1/2O2(g)=SiO(g)

ΔGo(kJ)= -154.31-0.0507T(K)

(1)

SiO(g)+1/2O2(g)=SiO2(l/s6)

ΔGlo(kJ)= -788.46+0.2468T( K)

(2)

ΔGso(kJ)= -798.04+0.2516T(K) where SiO2 (s6) denotes high-temperature cristobalite. Moisture is present in many gases and atmospheres of industrial importance. It is well known that steel oxidises faster in an atmosphere containing water vapor than in dry oxygen7. It is also known that water vapor may change the phase constitution, microstructure and growth rate of the oxidation product during the oxidation process of steel7. Næss and co-authors4 conducted a limited number of oxidation experiments with MG-Si in humid air. In these experiments, the gas humidity (PH2O(g)=3 kPa) brought an increase in the rate of fume formation compared to dry air. However, the mechanism by which water vapor in the gas increases the Si oxidation was not explained. While to our knowledge, no other studies have experimentally investigated the effect of water vapor on the oxidation of liquid silicon, Opila and other authors

8-18

have experimentally investigated the reaction of silica

with water vapor at various water vapor pressures, at high temperature, based on relevance in disciplines such as geochemistry and high temperature corrosion. With this background, the current work attempts to clarify the effect of water vapor on the rate of liquid Si alloy oxidation through experimental work, complemented by FactSage thermodynamic modelling, density functional theory (DFT) modelling and by statistical thermodynamics and statistical mechanics methods.



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2. Experimental and modelling procedures 2.1 Experimental materials and procedure The effect of moisture on the oxidation/fuming of Si alloys was investigated in the experimental set-up shown in Figure 1, as used in our previous studies

4, 19-22,

with the

addition of a humidifier connected to the air supply lance. The gas flow above the melt has been modelled in a previous study [4]. The experiments were carried out at 1823K, using an industrial MG-Si alloy which was composed of 99wt% Si and minor/trace elements such as Fe, Al, Ti, Ca. As a graphite crucible was used for the experiments, the alloy was carbon saturated throughout the trials. This is representative for most industrial Si melts. The water vapor pressures of the gas for the different experiments are listed in Table I.

Figure 1. The experimental set-up used in the current study Table I. Experimental matrix of the current work, dry air experiment data is taken from Næss et al4. Alloy

Gas

Melt Temp (K)

Water

partial

No of exp.

Holding time (min)

2

20

pressure (kPa) Synthetic air

1823

0


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MG-Si

Synthetic air

1823

3.1

2

20

Synthetic air

1823

7.4

2

20

Synthetic air

1823

12.3

2

20

For each Si alloy experiment, the graphite crucible was filled with 1.75kg Si. The crucible was covered by a graphite lid connected to a fume exhaust system. During the experiment, dry synthetic air initially passed through the humidifier with the rate 3 L/min to achieve the desired humidity, before being blown above the metal surface (0.0102m2) through the lance. After the experiments, the fume was collected at three sites: the so-called transition tube, the cooler and the filter. The majority of fume was collected from the filter. The transition tube, cooler and filter fabric together with the collected fume were all weighted directly after each experiment, and reweighed again after being dried for at least 20 mins at 110oC to ensure that no free water remained in the fume. The total amount of fume generated in each experiment was measured and the mass flux, 𝐽𝑚, was calculated as:

𝐽𝑚 =

𝑚 𝐴𝑡

(3)

where 𝑚 is the total mass of fume generated (using the data obtained after drying), 𝐴 is the surface area of the molten metal (assuming no surface oxide/slag coverage) and 𝑡 is the holding time of the experiment. Fume samples from some of the experiments were characterized using a Zeiss Supra 55 PV field emission scanning electron microscope (SEM). Particle size distributions were estimated with the aid of both laser diffraction (LD), assuming an average density model, and visual SEM



image counting for SiO2 protoparticles. All the samples were dispersed in an ultrasonic bath for 10 min before being measured by LD and preparing SEM samples. To obtain representative size distribution data of the fume, at least 1500 protoparticles were measured through particle counting from SEM imaging of each sample. 2.2 System equilibrium thermodynamic modelling As a starting point for describing the system thermodynamically, phase equilibria of reactions were calculated using FactSage 7.1 thermochemical software6. Thermodynamic descriptions of the Si melt and those of oxides were taken from the FTlite and FToxid databases, respectively. Gaseous product species of reactions between the Si melt and water available in the FactSage FactPS database are the oxides SiO and SiO2 and the hydrides SiH, SiH4 and Si2H6. Thermodynamic properties of SiO(OH)2 and Si(OH)4 species reported in literature 9, 12, were taken from the FactSage SGPS database. For the modelling, the oxidation process was simplified to three main reaction zones: the reaction between the metal and gas jet leading to the fume formation (R1), the reaction of fume with the gas phase across the boundary layer from the melt surface to the bulk air interface leading to the fume chemistry alteration (R2), further condensation of fume as a result of cooling (R3). The above mentioned reactions were calculated one by one in the order of reaction number, and the outcomes of the previous reaction were entered as the inputs of the next calculation step in the model, as depicted in Figure 2. It was, for the purpose of obtaining relative ratios of gas species in the output from R1, assumed that 10% of the melt weight was reacted with the gas. While this is an over-estimation, the calculation is aimed at understanding the relative ratio of species in the off-gas .


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Figure 2. Flow of equilibrium calculations for simulation of fuming from oxidation process of Si melt

It was assumed that all chemical reactions reach equilibrium near reaction interfaces. No kinetic factors were considered in the current model. 2.3 Density functional theory (DFT) modelling To further supplement the experimental work, density functional theory (DFT) calculations for both solid-gas and gas-phase interactions and reactions, were carried out. To simplify calculating, the solid-gas interactions at ground state energy (0K) were chosen to approximate the liquid surface to avoid the complex interactions in liquid interfaces. The solid-gas interactions were performed with the Vienna Ab initio Simulation Package (VASP) 23, 24 using the PBEsol functional 25. The standard PBE PAW Si (3s23p2), H (1s1) and O (2s2p4) potentials supplied in VASP were used for all calculations. Electron wave functions were calculated using a cutoff energy of 500 eV. The energy convergence criterion was set to 1×10-6 eV and the forces on the ions were relaxed until they were below 0.001 eV/Å. The Brillouin zone integration was made on a gamma centered k-point grid to assess the energy differences between the gas molecules O2, H2O, H2 and Si(OH)4. A frame of at least 10×10×10 Å was used to avoid long-range interactions due to the periodic boundary conditions. Although the Si(111) surface has the lowest surface energy26, we chose the Si(001) surface in this work due to the Si(001) surface much more reactive than the cleavage Si(111) surface27.The Si(001) slabs were cleaved from the relaxed 2×2×2 Si conventional unit cell structure (a = 5.436 Å). A k-point grid



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of 3×3×1 was applied to the slab surface calculations. All the slabs have eight-layers periodic structure with a 15 Å vacuum. The energy convergence was tested to ensure reasonable results. In order to investigate the water molecule dissociation process on Si(001) surfaces, Ab initio molecular dynamics (AIMD) simulations using the NVT ensemble 28 were carried out via the algorithm of Nosé 29 to control the temperature oscillations during the DFT calculations. Brillouin zone integration was done on a single gamma-centred k-point and the cut off energy was reduced to 400 eV for all AIMD calculations. For all slab models, only ionic positions in the top four layers were optimized, while the volume and symmetry were kept fixed. The formation energy (Ef) for ions or H2O/O2 molecule absorbed on Si(001) slab surface, or reaction with bulk silicon Si(s) is defined as: Ef = Etot - Eslab - Emolecule

(4)

Here Etot is the total energy of final Sislab-molecule system or reaction product, Eslab is the energy of relaxed slab surface, Emolecule are the energy of isolated molecule or radical, respectively. All the formation energies were expressed per Si/Sislab atom. A negative value of Ef indicates that the reaction is exothermic, while it is endothermic for a positive value. The DFT calculations are performed at 0 K, while the AIMD calculation was performed at T = 1500 K to model the solid silicon surface reaction process with water at high temperature. For optimizing molecular structures of a larger set of gas-phase species than included in the VASP calculations discussed above, we have used the M06 density functional 30, 31 using the basis set maug-cc-pVTZ [maug-cc-pV(T+d)Z for Si]

32.

For estimating activation energies of

reactions, first-order saddle points of the energy have been optimized. For all molecular species, a normal mode analysis has been performed to calculate vibrational frequencies. These DFT calculations were performed using the NWChem program package 33.


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The enthalpy of formation and standard entropy of the gas-phase molecules were calculated by standard statistical thermodynamics equations

34,

employing calculated vibrational

frequencies, rigid-rotor rotational constants calculated from the optimized geometries and experimental data on electronic fine-structure states 35. The standard state of Si at 298 K is the solid state, but for practical reasons the Si atom was used as reference species in the DFT calculations. We therefore employed the most accurate estimate of the heat of formation of the Si atom available (452.7 kJ/mol) 36 to adjust the heat of formation to the correct reference value.

3. Results and discussions 3.1 Experimental results The calculated mass flux, based on the measured amount of SiO2 collected, from the Si melt at 1823K is shown in Figure 3. The dry air mass flux data (for the water partial pressure of 0 kPa) were taken from both the current and previous studies carried out by Næss et al4. It is seen that the mass flux from the Si melt increases to almost the threefold compared to that in dry air with increasing water content in the air up to 7.4±0.04kPa and then levels off with further increase in the water vapor pressure to 12 kPa. Above PH2O of 7 kPa there was a glassy slag layer attached to the graphite thermocouple tube, indicative of some degree of surface passivation. While more oxygen enters the system per unit time when air is partly replaced by water vapor, the degree of utilization of this oxygen for fuming also increases. The degree of oxygen utilization was hence calculated and tabulated in Table II. The oxygen utilization defined as the ratio between oxygen exiting the system as SiO2 particulate matter and that entering the system in the gas phase (through both oxygen and water molecules)- increases



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from approximately 4% in dry air to approximately 11% at 7.4 kPa water pressure. No further increase in oxygen utilization was observed with a water pressure of 12.3 kPa.

Figure 3. Mass flux of fume from Si melt at 1823K as a function of water vapor pressure Table II. Oxygen content in- and utilization efficiency of oxygen in the reaction gas Total gas flow rate L/min

Water partial

Mol oxygen/

Average oxygen

pressure/kPa

mol gas

utilization/%

3

0

0.21

4.05

3

3.14

0.22

6.82

3

7.36

0.24

10.99

3

12.33

0.25

10.17


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Figure 4. Typical silica fume morphology generated under the conditions of , (a) wet air experiments and (b) dry air from Næss et al.2 Both at 1823K.

Morphology of fumes which are formed under 1823K in both wet and dry air experiments are shown in Figure 4. It is also shown that the protoparticles (Proto particles are here defined as the smallest visible particle unit, i.e. the amorphous spheres visualized in Figure 4.) are all amorphous and spherical for both conditions. Particle size analysis results from LD and SEM image counting are illustrated in the supplementary information section. It was observed that the size of agglomerates (Agglomerates are clusters of proto-particles joined by bonds not dissolved by immersion of the particulate matter in the solution media used for laser diffraction analysis.) varies with increasing water vapor pressure, with a notable difference in the size range of 0.0-0.2 μm for the highest water vapor pressure. However, the diameter of protoparticles does not show significant differences between dry air and with increasing water vapor pressure, with the bulk of particles in the range 0.01-0.1 m. 3.2 System thermodynamic equilibrium modelling results The FactSage modelled reaction products are shown in Figure 5.



(a)

(b)

(c)


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(d) Figure 5. Simulated fuming from the Si oxidation process under different water vapor pressures, (a) R1 (reaction products of gas jet and Si melt - the melt is not shown), (b) partial pressures of gaseous species in fume generated from R1 (, (c) R2 (reaction products across the boundary layer at the melt / bulk gas interface), and (d) R3 (fume condensation and off-gas formation).

In R1, it was assumed that only 10% of the total volume of melt reacted with the gas jet at the interface. This simulated only one time step (starting from the time gas jet reacts with the melt, until the reaction reaches equilibrium) of the entire process. It should be noted that the equilibrium calculations were aimed at qualitative understanding of the fuming process and the results are reported on the relative basis. It was tested that the reaction of a partial volume of the melt (10%, 20%....) with the gas phase do not change the results. The melts were assumed to be saturated with carbon as a graphite crucible was used during the experiments. Approximately 0.02 wt% C dissolves in the Si melt at 1823K. Since the experimental gas flow rate was low (3L/min), it was determined by thermocouple measurement that the gas reached the melt temperature when exiting the lance at the time of reaction with the melt. Hence, the same gas temperature as the melt temperature 1823K was used for modeling of oxidation reactions. R1 was calculated under adiabatic condition



(ΔH=0), the system temperature decreased with increasing water vapor pressure, i.e. from 2005K at dry air condition to 1988K at water vapor pressure 12kPa. In the reaction between the Si melt and the gas jet, illustrated in Figure 5(a), there are three reaction products from R1, the reacted metal, a liquid or solid “slag” phase, and the gas phase product (so-called ‘fume 1’). The model proposes the formation of a liquid slag phase consisting of mainly SiO2 and less than 0.06 wt% H2O at low water vapor pressures, followed by the formation of solid SiO2 with further increase in the water vapor pressure. The formation of the solid SiO2 slag phase is related to a decrease in the system temperature due to high heat capacity of water vapor. The first solid SiO2 forms at water vapor pressure of 6 kPa at about 1997 K. The calculated system temperature, i.e the temperature generated by reaction between phases as described above was calculated to vary from 2005 to 1979 K for water vapor pressures between 0 (dry air) and 20 kPa. While these temperatures do not reflect real conditions (i.e, the bulk melt was kept at 1823K and 10% of the liquid was in reality not consumed by oxidation), it illustrates the local effect of variations in water contents on the temperature in the reaction zone. While not included in the graphs, modelling indicates the formation of solid SiC and Si3N4 solid species. This is in agreement with typical experimental findings where e.g SiC is found as a layer stopping further reaction between metal and carbon at the metal/crucible interface. The compositions of the ‘fume 1’ generated at R1 from the Si melt is illustrated in Figure 5(b). It is seen that the partial pressures of SiO and SiO2 slightly decrease by less than one order of magnitude, while the partial pressures of SiH and SiH4 increase within a few orders of magnitude up to a water vapor pressure of 10 kPa. The partial pressures of Si(OH)4 and SiO(OH)2 species both increase within 4 and 7 orders of magnitude, respectively. The partial pressures of SiH, SiH4, Si(OH)4 and SiO(OH)2 stabilize above water vapor pressure of 10 kPa.


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The oxidation reaction products from R2 consist of two phases, an oxide liquid solution and the gas phase together called ‘fume 2’, depicted in Figure 5 (c). The temperature gradient was assumed to be negligible across the boundary layer. The oxygen partial pressure across the gas boundary layer was set to vary from 10-13 kPa at the C-saturated metal interface to an oxygen partial pressure of 21.0 kPa, i.e. the bulk air partial pressure. Figure 5(c) may be read as illustrating the reaction product composition throughout the gas boundary layer above the metal from the metal interface at the left of the figure to the bulk gas interface on the far right of the x-axis. As seen, the fume generation is enhanced with increasing water vapor pressure. However, there is a transition between solid and liquid fumes at an oxygen partial pressure of 12kPa. It is can be explained that, the solubility of H2O in SiO2 slag changes with PO2 and the presence of water in SiO2 slag changes the liquidus temperature of slag. Therefore, for 12kPa H2O below 10-6 kPa PO2, SiO2 solid becomes stable relative to liquid slag. When the ‘fume 2’ exits the boundary layer, it cools down resulting in the condensation of part of the fume. This process was simulated as R3. As there are other reactions consuming oxygen, e.g. the formation of CO(g) due to the reaction between oxygen in the air and the carbon from the graphite crucible, the oxygen partial pressure at the bulk air interface was assumed to be about 0.1kPa. Hence, the reaction products generated at oxygen partial pressure of 0.1kPa were quenched using Scheil-Gulliver cooling, and the modelled fume composition from R3 is illustrated in Figure 5(d). The unquenchable part of the fume exited the system as the off-gas, where N2, CO, and H2 are the main constituents. As shown in Figure 5(d), the fume from the Si melt contained mainly an amorphous SiO2 phase, which is a quenched liquid oxide phase from R2. For the dry air experiment, C precipitates out from the fume below 323K. Moreover, for water vapor pressures above 3 kPa, free water condenses



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below 333K. The amount of generated fume clearly changes with increasing water vapor pressure. As illustrated by the first step of calculation (R1) described above, an increasing amount of fume could be partly explained by the formation of SiH, SiH4, Si(OH)4 and SiO(OH)2 from the reaction between Si metal and gas jet. However, these gas species are still several orders of magnitude lower than that predicted for SiO and as such should not be theoretically able to triple the amount of SiO2 particulate matter formed. The liquid/solid SiO2 slag phase is thermodynamically favoured at the Si surface, as seen from the calculation results displayed in Figure 5(a), while this slag phase is only experimentally observed above the water vapor pressure of 7 kPa. 3.3 DFT modelling results To provide an atomistic understanding of the experimental and thermodynamic modelling results, we first study the adsorption energies (ΔEad) for the species (O, H, OH and H2O) adsorbed on a solid Si(001) surface as calculated using the PBEsol functional with periodic boundary conditions, henceforth referred to as solid-state DFT. In this work, the adsorption energies (ΔEad) for the species adsorbed on Si(001) surface were calculated using the ΔEad = Etotal – ESi-slab – Especies

(5)

where, Etotal is the total energy of the Si(001) surface and the adsorbed species, and ESi-slab /Especies are the energies of the Si(001) slab surface and species respectively. For more details, the calculated values of the adsorption energies are shown in Table S1 in the supporting information section, and the top and front views of final geometry optimization structures of the adsorbing Si(001) surface, are shown in Figure 6. We have not performed explicit


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simulations of liquid silicon, but extrapolate the results for solid silicon surfaces with the assumption that the adsorption energies are similar. This obviously increases the uncertainty of the simulation somewhat (see also Section 3.4). However, we can compare the model results to experiments performed on the oxidation of solid silicon to validate our model. Figure 6(a) shows the reconstruction of Si(001) surface

37

with Si dimers, which lowers the

surface energy. In Figure 6(b)-(d) the three most stable sites (top, bridge and backbond) are shown for O adsorbed on the Si(001) surface. Calculations show that the backbond site (d) is the most stable, which is consistent with other studies

38, 39.

For hydrogen adsorption on a

Si(001) surface, a hydrogenated Si-Si dimer is formed with hydrogen preferentially binding to the top Si atoms

40.

Similar type of binding is also observed for OH adsorbed on a Si(001)

surface. Previous theoretical results 41, 42 have shown that water is adsorbed dissociatively at a Si(001) surface with the formed OH and H species adsorbed on the same end of adjacent dimers as seen in Figure 6(i) and (j). The adsorption energy of H2O is -0.87 eV and the dissociative adsorption energy is -2.28 eV as calculated in this study consistent with earlier results of -0.57 eV and -2.37 eV

42.

A weaker adsorption energy of undissociated H2O is

consistent with a precursor state for sticking at a silicon surface, either leading to irreversible dissocation or H2O desorption, that has been inferred from experimental studies

43, 44.

The

adsorption energies of all the adsorbed species are summarized in Table S1 and reaction energies of some key reactions are given in Table S2 in the Supporting Information section.



Figure 6. Top and front view of (a) surface reconstruction model of Si(001) surface, (b)-(d) O adsorbed on a Si(001) surface, (e)-(f) H adsorbed on a Si(001) surface, (g)-(h) OH adsorbed on Si(001) surface, (i) and (j) H2O and dissociated H2O adsorbed on a Si(001) surface respectively. The yellow, red and white spheres are Si, O, H atoms, respectively.

Dissociation of H2O into adsorbed OH and H from water vapor on the Si surface is established from prior experimental and theoretical investigations 27, 41, 42, 45, 46. Experiments have been performed for temperatures below 1000 K and show decreasing degrees of dissociation with increasing temperature

43.

In order to simulate dissociation at temperatures closer to the

current experiments, AIMD simulations were performed of a water molecule impinging on a Si surface at a temperature at 1500 K. Snapshots from one such simulation are shown in Figure 7. At this high temperature, the H2O molecules were found to dissociate at the surface to


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form Si-H and Si-OH groups 41, 42, 46 as given in reaction (18). None of the simulations resulted in re-desorption of H2O molecules. Further oxidation of Si-H and Si-OH species by O2 to Si-OH could subsequently make a contribution to the oxidation of Si

45

and subsequent fume

formation.

Figure 7. Snapshots from AIMD of water dissociation progress on Si(001) surfaces at 1500K.

3.4 Reaction thermochemistry and kinetic considerations For evaluating plausible reaction mechanisms of H2O(g) interacting with liquid Si we have employed a combination of data from thermodynamics databases, and solid-state DFT and gas-phase DFT calculations. It thereby becomes possible to obtain reasonable estimates of free energy differences for elementary reactions as functions of temperatures. For the gas phase species we have employed the enthalpies and entropies calculated by DFT in this study. In the case of the solid-state DFT calculations only binding energies were calculated. In order to include the proper thermodynamics of Si we have used literature data for pure Si to account for silicon being in a liquid state. However, the additional contributions to enthalpy and entropy from the motion of adsorbed O, H and OH were estimated by employing harmonic oscillator partition functions using vibrational frequencies from measured and calculated IR spectra of O, H and OH at solid Si 41, 44, 47-52 (3 vibrational modes for Si-O and Si-



H, 6 for Si-OH)). We assume that although the solid-state DFT calculations have been performed for a solid Si surface, the binding energies of O, OH and H species are similar also at a liquid surface. In a disordered system such as liquid Si it is likely that the distribution of binding energies is much wider than at a crystalline solid, leading to both weaker and stronger binding. The fluctuating nature of the liquid also means that we can only hope to capture the average binding energy reasonably well. The broader energy distribution also applies to any barriers to reaction. In future studies, more realistic Ab Initio MD simulations should be performed also for the liquid phase to clarify how binding energies change from the case of the crystalline solid. Another major uncertainty with the procedure of extrapolating from the solid to the liquid should be that the entropy of the adsorbed species might be somewhat underestimated since we are not explicitly considering their increased mobility in the liquid phase as compared to the solid state. Given the uncertainties in this model, including the quality of the DFT data, the estimated enthalpies and free energies for reactions involving both gas and liquid/solid species could have uncertainties of a few tens of kJ/mol. For reactions involving only gas phase species the uncertainties should be on the order of 10 kJ/mol. Based on the available data a reaction scheme is proposed and shown schematically in Figure 8. Note that this is an idealized illustration of the system. The experimental conditions with a lance delivering the gas to hot liquid Si are probably not nearly as regular as depicted.


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Figure 8. Main reaction mechanisms of liquid silicon in contact with O2 and H2O-containing gas. The silicon melt is in orange and the boundary layer in light blue. Reactions that can occur if there is O2 but no H2O present are indicated by red arrows, reactions that can occur if there is H2O but no O2 by blue arrows, reactions that require both O2 and H2O by green arrows, and reactions that can occur in all these cases are indicated by black arrows. Several arrows in a row indicates a mechanism involving multiple elementary reactions. Thick arrows indicate potentially major reaction routes, thin arrows less important or more uncertain reactions and dashed arrows indicate reactions that are likely to be slow.

In what follows we analyse the thermodynamics and kinetics of the oxidation of liquid Si using the model we have outlined above. Previous experimental results on the oxidation of solid Si surfaces are used to benchmark the model. The extrapolation to the liquid state does, as noted above, suffer from several possible sources of uncertainty. Therefore, the benchmarking of the model against experimental results for solid Si is particularly important, since we thereby are extrapolating from a model that performs well under known conditions, albeit at much lower temperatures. The reaction steps occurring when H2O(g) interacts with a liquid silicon surface may be described as follows: The thermodynamically most plausible products (most negative free energy) of the initial reaction step of H2O(g) + Si(l) at 1823 K are SiO(g) + H2(g) with ∆G = -99 kJ/mol although the reaction is endothermic by 91 kJ/mol. The formation of H2(g) and adsorbed (or dissolved) oxygen (Oads) has a free energy change close to zero, ∆G = +2 kJ/mol,



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and is exothermic by -77 kJ/mol. The initial reaction proceeds through dissociation of H2O at the Si surface into adsorbed H and OH (Hads and OHads) as discussed above. Both experiments and previous calculations indicate that the initial adsorption and dissociation of H2O at a solid Si surface into adsorbed H and OH occur without any activation energy 41, 42, 44, 47, 53, 54. Based on an energy barrier of 244 kJ/mol calculated by Penev et al. 55, which is also consistent with experimental results 43, 56, we estimate a quite short life-time on the order of 10 ns at 1823 K of a pair of adsorbed H atoms before reacting to form H2(g) (the process is endothermic by 120 kJ/mol with ∆G = -96 kJ/mol). The estimate is calculated by using an Arrhenius-type prefactor of 1×1015 s-1 calculated by Transition State Theory with the frequencies for adsorbed H and previously calculated transition state frequencies 57. The Transition State Theory calculations are described in some more detail in the Supporting information. Flowers et al. 43 measured D2 desorption from a heated Si surface occurring between 700 and 1000 K consistent with an activation energy of about 230 kJ/mol and a prefactor of 1×1015 s-1. Our calculated prefactor for this process is 6×1014 s-1 at 850 K, lending credibility to our model. Similarly, the dissociation of OHads into Oads and Hads occurs on a ns – μs time scale based on calculated energy barriers of 200-260 kJ/mol

54, 58.

The reaction is estimated to be exothermic by 48

kJ/mol but to have a ∆G = +10 kJ/mol at 1823 K. There could therefore be significant backreaction of Oads and Hads to reform OHads. It has been found experimentally

59

that OH

adsorbed at solid Si surfaces remained stable at room temperature, but disappeared through dissociation to form Oads and Hads (and subsequently H2(g)) upon heating to 650 K. This is consistent with our model where the barrier to OH dissociation prohibits any reaction at room temperature at any reasonable time scale, whereas the lifetime of OH at 650 K is less than 1


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hour (assuming a typical Arrhenius prefactor of 1013 s-1). That the reaction is irreversible at 650 K is also consistent with our estimated ∆G of -37 kJ/mol. It cannot be ruled out that also some Si-H species, such as silane (SiH4), could be formed from the adsorbed H atoms either at the surface or after diffusion into the bulk. Whether for instance SiH4 could be formed within the bulk liquid is unclear. It is likely that any Si-H species that are formed are rapidly oxidized in contact with oxygen or oxygen-bearing species.The reaction of OHads and Hads to form Oads and H2(g) has a much higher activation energy (369 kJ/mol) 47 and occurs on a time scale of 1 ms. This latter reaction should therefore be of minor importance. Formation of SiO(g) from Oads is endothermic by 300 – 400 kJ/mol depending on the type of binding that Oads experiences. In experiments by Flowers et al. on H2O reacting with a solid Si surface it was found that upon heating the surface, SiO desorbed at 900 – 1000 K with an activation energy of 310 kJ/mol and an unusually large Arrhenius prefactor of 2.5×1017 s-1. Using Transition State Theory with the transition state being a gas-phase SiO molecule restricted to an area equalling the typical area of a surface Si atom, i.e., desorption occurs without an additional energy barrier as was the case for H2, we arrive at a prefactor of 4×1017 s-1 at 900 - 1000 K, consistent with the experiments, and 2×1017 s-1 at 1823 K. Desorption of SiO should therefore occur rapidly, on ns – μs time scales at 1823 K. The DFT data by Kang and Musgrave 47 also suggest that H2O(g) can react with Oads to form 2 OHads with an activation energy of only 16 kJ/mol. Also the reaction with a (newly formed) Hads – OHads pair to form H2(g) + 2 OHads was found to be possible but with a significantly higher activation energy (139 kJ/mol). Considering the above mechanisms and their kinetics it seems likely that at sufficiently high partial pressures of H2O(g) there should therefore always be a significant concentration of adsorbed OH and O at the silicon surface.



There is also the possibility that Si-O-H species may form by reaction of the adsorbed O and OH groups and subsequent reaction. However, this requires a relatively high concentration of OH at the surface. Possible reaction mechanisms have not been investigated in detail. However, the formation of Si(OH)2(g) from 2 OHads is calculated to have a ∆G of -138 kJ/mol but be endothermic by 116 kJ/mol. Similarly, reaction of 2 OHads and 1 Oads to form SiO(OH)2(g) has a ∆G of -139 kJ/mol and is endothermic by 148 kJ/mol. The reaction to form the thermodynamically stable Si(OH)4(g) directly from the Si surface seems unlikely since it requires 4 OH(ads) to be simultaneously in close proximity. However, it might readily form in the gas phase. In the Supporting Information we discuss the subsequent reactions of formed Si-O-H species in the gas phase. Here we only give a brief summary. As discussed the formation of SiO(OH)2(g) is plausible on thermodynamic grounds. The reaction of SiO(OH)2(g) and H2O(g) can readily produce Si(OH)4(g) in a reaction proceeding without activation energy.60 These formed Si-O-H species can react with SiO(g) in fast reactions with no activation energies to form larger species that would eventually grow into silica particles upon further condensation and oxidation reactions. In contrast to these active oxidation mechanisms, the passive oxidation mechanism to form the thermodynamically most stable phase, SiO2, (see section 3.2) is also possible. However, this is a nucleation process requiring a critical concentration of dissolved O atoms at or close to the surface. This is therefore unlikely as long as the dissolved O concentration remains low, i.e., when oxygen is not deposited in Si at a sufficiently high rate to counteract the loss of oxygen through desorption of SiO. That means that the formation of SiO2 is kinetically hindered, even though it is thermodynamically favoured. If SiO2 is formed, the additional mechanism of H2O(g) reacting with (and removing) SiO2 to form Si-O-H species, mainly


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SiO(OH)2(g) and Si(OH)4(g), that has been established by Opila and co-workers 61, 62 can further lower the effective growth rate of SiO2. It has been well established that O2(g) has a low sticking coefficient of about 1% at Si surfaces at temperatures around 300 – 800 K 63. This unexpectedly low sticking has been attributed to non-adiabatic electronic effects related to the special electronic structure of O2 64. Analogous measurements of sticking of H2O(g) at solid Si reveal that the reactive sticking coefficient is near 1 at room temperature and decreases to 0.1 around 800 K 43, 44. The detailed sticking behaviour at liquid Si surfaces is not known, but one could reasonably assume that the sticking coefficient of H2O remains considerably larger than for O2 also at elevated temperatures. This would mean that using H2O provides a more efficient supply of oxygen to the Si surface than by using O2, even though the molar concentration of elemental oxygen is lower. In conclusion, the fact that the reactions of O2 with Si to form SiO and SiO2 are more exothermic than the corresponding reactions involving H2O, does not automatically mean that reactions with O2 are more efficient. As shown in the work of Næss et al2-4 , the rate of active oxidation in the Si-air system is limited by diffusion of oxygen to the Si surface. According to Graham's law65, the rate of diffusion of a gas is inversely proportional to the square root of its molecular weight. If we compare the diffusion rate of O2 and H2O in air by employing Graham’s law, it is obtained that: 𝑅𝑎𝑡𝑒𝑂2

𝑅𝑎𝑡𝑒𝐻2𝑂 =

𝑀𝐻2𝑂 𝑀𝑂2

≈

18 32

= 0.75

(6)

i.e., the diffusion rate of the O2 molecule through the boundary layer is only approximately 75% that of H2O. Thus, it is concluded that both the more effective sticking of the H2O



molecule and its relatively faster diffusion to the metal surface versus that of oxygen will contribute to a higher oxidation rate of the surface.

4. Summary of observations and conclusions The mechanism behind- and effect of water vapor on the oxidation of liquid Si at 1823 K was both experimentally and theoretically investigated using a set of modelling techniques. The results may be summarized as follows: 

The experimental results revealed that the presence of water vapor enhances the rate of fume formation/active oxidation from liquid Si to approximately threefold with increasing water vapor pressure in air from 0 to 7.4 kPa. The utilization of oxygen in the gas also increased from approximately 4 to 11% respectively. Between 7.4 and 12.3 kPa water vapor pressure, the rate of fuming stayed stable, while a a glassy layer on the metal surface indicated partial passivation. The fume proto-particle size distribution was not significantly altered for water-containing atmospheres.



System equilibrium modelling with FactSage7.1 indicated the formation of a liquid or solid SiO2 slag phase already at very low water vapor pressures, which was not consistent with the experimental observations. The experimental increase in fume formation with the introduction of water was confirmed and attributed to an increase in the vapor pressure of Si-H and Si-O-H species. It was also shown that the gaseous Si-species all condensed in the form of amorphous SiO2.



DFT modelling results suggest that the oxidation enhancement in water-containing atmospheres can (mainly) be attributed to increased SiO(g) formation and the formation of Si-H(g) and Si-O-H(g) species. The Si-H2O(g) reaction proceeds through initial dissociation of H2O(g) on the Si surface forming Hads and OHads species, which


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subsequently can dissociate into Oads and Hads. While adsorbed H atoms react to form H2(g), Oads may react to form SiO(g), or together with OHads - Si-O-H species such as Si(OH)2(g) or SiO(OH)2(g). The SiO(OH)2(g) species may also form through direct reaction between SiO2 formed through surface passivation and H2O. The Si-O, Si-H and Si-O-H gas species are all prone to oxidation and/or condensation into solid SiO2-based units. 

Kinetic considerations indicate that while system equilibrium calculations predict the formation of a SiO2 slag surface, the nucleation of SiO2 is slow compared to the desorption of Oads to form SiO, making passivation kinetically hindered at low Oads concentrations. This may explain the lack of observed SiO2 glass on the Si surface at low water vapor pressures predicted by thermodynamic modelling.



The “sticking” of H2O on a liquid Si surface is most likely significantly higher than that of O2, making the “efficiency” of utilization of oxygen contained in the water molecule as an oxidant higher. Combined with the somewhat higher diffusivity of the water molecule than the O2 molecule, this would promote faster formation of SiO2 fume in water-containing air atmospheres than in dry air atmosphere.

5. Acknowledgements Funding from the Norwegian Ferroalloys Research Association (FFF), Saint Gobain, Washington Mills and the Norwegian Research Council through the DeMaskUs project (Contract 245216) is gratefully acknowledged. We thank Uninett Sigma2 AS in Norway for providing computational resources for DFT modelling through the projects NN9264K and NN9353K.



Supporting Information Information about the Si fume particle size distribution and a detailed description of density functional theory modelling results are listed in the supporting information.

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Graphic abstract


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Oxidation of Liquid Silicon in Air Atmospheres Containing Water Vapor

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