Thermodynamics and Oxidation Behaviour of Crystalline Silicon Carbide (3C) with Atomic Oxygen and Ozone

Abstract

Thermodynamics of oxidation of crystalline silicon carbide (cubic form) by atomic oxygen (O) and ozone (O₃) was derived to understand the thermodynamic stability of SiC in the upper atmosphere. Equilibrium constants and equilibrium partial pressures were computed for each of eight possible reactions of SiC with O and O₃. Equilibrium activity diagrams were derived, showing the most stable oxidation products of SiC, represented in temperature-oxygen pressure (𝑇-𝑃_O/O3) 2D diagrams. Programs were developed in Mathematica. The diagrams provide an understanding of the oxidation routes of SiC under changing levels of O/O₃ and temperature, as encountered during reentry of space vehicles. At high levels of the volatiles, CO₂, CO, and SiO and temperatures between 1000 and 1500 K, oxidation by atomic oxygen or ozone first produced SiO₂ + C followed by SiO₂ + CO and finally SiO₂ + CO₂. When volatiles were at very low pressures, the sequence of oxidation was SiO + CO followed by either SiO₂ + CO or SiO + CO₂ and finally SiO₂ + CO₂. Stability of SiC in ozone was much lower than in atomic oxygen. With both oxidants, the oxidation of the Si in SiC occurred prior to the oxidation of C. Implications for mechanisms of thermal protection are discussed.

1. Introduction

Silicon carbide is an important material for space applications. It is a particularly useful thermal protection system for very high temperature zones like nose-cones in reentry vehicles. Since temperatures may reach 1700^∘C or higher, oxidation is a major problem and limits the temperatures to which SiC can be used. Several experimental studies on the oxidation of SiC with O₂ have been reported. It was observed [1] that oxidation of SiC between 900–1600^∘C resulted in a surface layer of SiO₂ that formed a protective film. The oxidation of C-SiC heat shield materials under reentry conditions (50–3500 Pa and 1300–1700^∘C) showed that a protective SiO₂ layer was formed [2], and oxidation was insignificant as long as this silica layer was present. Others [3] observed etching of the surface and surface segregation of carbon. From photoemission studies on the SiC surface [4], it was concluded that oxygen is incorporated into the Si surface even at the smallest exposures to O₂, but there was no discernible change on the C-terminated surface. Studies have confirmed that the rate controlling process is the diffusion of O₂ through the solid SiO₂ on the surface [5]. Mogilevsky and Zangvil [6] modelled the oxidation of SiC-reinforced mullite–zirconia matrix composites and evaluated oxygen permeabilities of the matrix as well as the silica layer. Oxidation kinetics in the temperature range of 1200–1350°C showed [7] a parabolic behaviour, which indicated a diffusion-controlled mechanism. In high vacuum, the surface composition of 𝛼-SiC (0001) changed as a function of temperature due to oxide formation, yielding graphitic surface carbon [8]. Thermodynamic modelling of the reactions of oxygen with SiC has also been reported [3, 9]. Phase diagrams of Si-C-O (oxygen) system are available in the literature [10, 11] as either triangular diagrams (Si-C-O) or biaxial diagrams (T-SiC/SiO₂).

Three layers of the atmosphere are involved in the oxidation reactions that occur during re-entry, namely, the troposphere, stratosphere, and mesosphere-lower thermosphere. The troposphere extends to about 18 km at the equator and 8 km at the poles. Tropospheric chemistry would be dominated by oxidation with molecular oxygen whose partial pressures vary from about 0.2 bar to 10⁻³ bar at the tropopause [12, 13]. The stratosphere extends from 15–50 km above the Earth. Atmospheric chemistry of the stratosphere is dominated by ozone, with highest concentrations at 15–30 kilometres above the Earth’s surface. Partial pressures of ozone here vary from about 5−30×10⁻⁹ bar [13]. The mesosphere is located about 50–85 km above Earth’s surface, and the lower thermosphere is located between 80 and 180 km. Within this layer, temperature decreases with increasing altitude. Two strong photodissociation continua, the Schumann-Runge continuum, and the weaker Herzberg continuum produce atomic oxygen (O) by breakdown of O₂ [12].

To obtain an understanding of the chemical behaviour of SiC in the upper atmosphere, knowledge of the nature of reactions with atomic oxygen and ozone is important. The objective here was a theoretical investigation of the thermodynamics of oxidation of SiC by O and O₃. Equilibrium constants were computed for all possible reaction pathways. Equilibrium activity diagrams were derived to show the effects of temperature and pressures of O and O₃ on the oxidation of SiC. The resulting diagrams showed the thermodynamically stable oxidation products under variable temperatures and partial pressures of oxidants. Possible pathways of oxidation were proposed. The studies would be useful for modelling chemical transformations of SiC in the stratosphere and mesosphere-lower thermosphere.

2. Theory and Methods

Oxidation of SiC with O/O₃ can occur in eight different ways. These reactions are stoichiometrically represented in Table 1.

Table 1 

Reactions of SiC with O and O₃.

Standard free energy change of these reactions at temperature 𝑇, (ΔG⁰_𝑟,𝑇) was obtained from the standard free energy of formation (ΔG⁰_𝑓,𝑇) as: ΔG⁰_𝑟,𝑇=ΔG⁰_𝑓,𝑇products−ΔG⁰_𝑓,𝑇(reactants), (1) which is related to equilibrium constant 𝐾 as ΔG⁰_𝑟,𝑇=−𝑅𝑇ln𝑘=−𝑅𝑇lnΠ𝑎^𝜈_𝑝Π𝑎^𝜅_𝑟, (2) where 𝑎_𝑝 and 𝑎_𝑟 are activities of products and reactants, respectively, and the power terms refer to the stoichiometric amounts of the compounds participating in the reaction. Total free energy change under nonstandard conditions was obtained from the relation: ΔG_𝑟,𝑇=ΔG⁰_𝑟,𝑇+𝑅𝑇lnΠ𝑎^𝜈_𝑝Π𝑎^𝜅_𝑟. (3) Equilibrium activity diagrams were derived from net Gibbs free energy changes (ΔG_𝑟,𝑇). This allows us to include the effect of variables (such as partial pressures of CO, CO₂, and SiO) that have important contributions to oxidation. The dominant reaction will be the one with the most negative total free energy change (ΔG_𝑟,𝑇).

The process involved (i) computation of free energy changes for all possible reactions in a system, (ii) comparison to obtain the reaction showing greatest reduction in free energy, and (iii) derivation of the limiting conditions for the reaction to have largest free energy reduction compared to all other reactions. Thus, the values of ΔG_𝑟,𝑇 for all equations in Table 1 were derived at small intervals of the variables (𝑇-log𝑃_O/O3). These values were compared at each value of the variables, and subsequently boundary conditions were obtained.

Thermodynamic data for the computations were obtained from the literature [14]. Equilibrium activity diagrams showing partial pressure-temperature relations were then computed. For derivation of equilibrium activity diagrams, a program OXID2D was developed in Mathematica (see Supplementary Materials available online at doi:10.542/2012/108781). The main program has 2 subroutines (SubOXID_1 and SubOXID_2), which derive the standard free energy change of the oxidation reaction (ΔG⁰_𝑟,𝑇) and equilibrium ozone (O₃) pressures at lower and higher temperatures 𝑇 (flow chart in Figure 1). The first sub-routine (SubOXID_1) is for reactions in the lower temperature range (298.15–1900 K), where SiO₂ is in the solid phase; the other sub-routine (SubOXID_2) is for reactions at temperatures above the melting point of SiO₂ (2000–3200 K). Inputs required are the gas constant 𝑅 (in kJ/mole) and values of log𝑃_CO2, log𝑃_CO, and log𝑃_SiO (Figure 1). Other input data are temperatures and the corresponding standard free energy of formation (ΔG⁰_𝑓,𝑇) of all compounds in the reactants and products. Then, for each temperature T, ΔG⁰_𝑟,𝑇 is derived by (1). The list of temperature-ΔG⁰_𝑟,𝑇 is exported for the main program. Additionally, equilibrium ozone (O₃) pressures are computed for constant values of log𝑃_CO2, log𝑃_CO, and log𝑃_SiO and plotted as 𝑇 versus log𝑃_O3. The subroutines are available as supplementary information.

Figure 1 

Flowchart for subroutine program SubOXID to compute equilibrium ozone/atomic oxygen activity and standard free energy change of reaction with temperature.

The main program OXID2D (supplemental file) then derives the equilibrium boundaries from total free energy change of reaction (ΔG_𝑟,𝑇 ) using (3). To compute the values of ΔG_𝑟,𝑇, activities of CO₂, CO, and SiO have to be defined. Here, these were assigned constant values representing four different conditions, namely, 𝑃_CO2/CO/SiO=10⁰, 10⁻³, 10⁻⁷, and 10⁻¹⁰. The next step of the program (flow diagram in Figure 2) defines minimum and maximum temperatures and ozone (O₃) partial pressures (log𝑃_O3) and the respective increment intervals. A list of the variables, T-𝑃_O3, is then generated. The data from SubOXID_1 & 2 are imported, and the relation between T-ΔG⁰_𝑟,T is fitted into a linear regression equation. From this equation, ΔG⁰_𝑟,𝑇 values are derived for every value of temperature increment. Subsequently, using (3), ΔG_𝑟,𝑇 values are computed from the values of ΔG⁰_𝑟,𝑇 using 𝑃_CO2, 𝑃_CO, and 𝑃_SiO as constants, 𝑇 and 𝑃_O3 as variables, temperature range 𝑇=500 to 3200 K, ozone levels log𝑃_O3=1 to −50, and increment intervals of 𝑇=5K and log𝑃_O3=1. Only negative values of ΔG_𝑟,𝑇 are retained. Derived ΔG_𝑟,𝑇 values for all the reactions are combined into separate lists for each T-log𝑃_O3. In each list, the ΔG_𝑟,𝑇 values are compared, and the reaction showing the most negative value is assigned to that T-log𝑃_O3 as the most favourable (stable) reaction. The reaction is identified and represented by a coloured box at that particular value of T-log𝑃_O3. The process is repeated over all values of T-log𝑃_O3, and all points are combined in a single plot. A similar method was earlier used to derive equilibrium diagrams for nonstoichiometric clay minerals in aqueous environments [15] and also to derive fuzzy phase diagrams representing 464 metastable minerals [16].

Figure 2 

Flowchart for the program OXID2D to derive oxidation phase diagram.

Equilibrium diagrams in the atomic oxygen system were derived with the same program after substituting the ΔG⁰_𝑓,𝑇 values for O and changing the reaction stoichiometries according to those shown in Table 1.

3. Results and Discussion

3.1. Equilibrium Constants and Equilibrium Gas Pressure

Equilibrium constant (log𝑘)-temperature relationships for 8 types of oxidations of cubic (3C) SiC (Table 1) are presented in Figure 3. log𝑘 values were highly positive and suggested that all oxidations were thermodynamically favourable. The oxidation reaction producing SiO₂ + CO₂ had highest values of log𝑘 for both the oxidants O and O₃. This was followed by SiO₂ + CO and then SiO₂ + C. At higher temperatures, there was a crossover, with SiO + CO₂ having higher log𝑘 than SiO₂ + C. In general, reactions producing SiO₂ or CO₂ were energetically more favourable than reactions producing SiO or CO. The value of 𝑘 reduced sharply with temperature for all reactions except (6) and (8).

(a)

(b)

Figure 3 

Equilibrium constant (𝐾)-temperature (𝑇) relations for reactions of (a) SiC with O and (b) SiC with O3.

Equilibrium constants for reactions with O₃ were generally smaller than with O. Thus, at 1000 K, log 𝑘 values for the formation of SiO₂ + CO₂ from O and O₃ were 94.6 and 70.2, respectively; at 2000 K, these values were 36.2 and 33.2. Oxidation to SiO + CO₂ at 1000 K showed a similar trend with equilibrium constants of 56.3 and 38.0 for reactions with O and O₃, respectively.

Equilibrium partial pressures of O and O₃ for oxidation of SiC (under standard pressures of CO₂, CO and SiO) are presented in Table 2. Oxidation was thermodynamically favourable at 1000 K with log𝑃_O levels as low as −29; reactions forming SiO₂ occurred at lower O pressures than those forming SiO. At 3000 K, equilibrium log𝑃_O levels were about −6 for SiO formation, and unlike trends at 1000 K, SiO₂ was formed at higher O levels compared to SiO. Oxidations with O₃ (Table 2) followed a similar trend. However, equilibrium activities for oxidation with ozone were substantially lower than for atomic oxygen.

Table 2 

Equilibrium O, O₃ pressures for oxidation of SiC, Si, and C.

Partial pressures of the volatiles, CO₂, CO, and SiO had a significant impact in lowering the pressures of O/O₃ at which oxidation began. Reactions forming SiO (Figure 4) were particularly affected by increasing levels of the volatiles, as observed by the steep slopes. Oxidation to SiO₂ was comparatively less affected by the levels of volatile products. This was true for both oxidants, O and O₃. Reactivity of SiC towards ozone was particularly remarkable. Even in the presence of substantial levels of the oxidation inhibitors, oxidation to SiO could occur at O₃ pressures as low as 10⁻³⁰ atm, which is about 10¹⁷ times lower than the level of atomic oxygen required for the same oxidation.

(a)

(b)

Figure 4 

Relationship between equilibrium partial pressures of (a) O and (b) O3 and partial pressures of CO2/CO/SiO in oxidation of SiC.

3.2. Oxidation Equilibrium Diagrams

Reaction equilibrium diagrams of thermodynamically stable products formed, when SiC (cubic) was exposed to various O pressures at different temperatures and different levels of CO₂, CO, and SiO, are presented in Figures 5(a)–5(d). Figure 5(a) shows the nature of products under standard (unit) pressures of gaseous products CO₂, CO, and SiO. At temperatures below 1500 K, as O pressure increased, SiO₂ and C were the first reaction products. On further increase in O pressure, SiO₂ and CO₂ were formed (at log𝑃_O≳ −18). At temperatures above 1500 K, the initial products were SiO₂ + CO followed by SiO₂ + CO₂ at higher O pressures. In the region beyond ~2300 K, oxidation proceeded from SiO + CO to SiO₂ + CO and then to SiO₂ + CO₂. Significantly, the sequence of oxidation also suggested that oxidation of the Si in SiC occurred prior to the oxidation of C.

(a)

(b)

(c)

(d)

Figure 5 

Equilibrium diagram of SiC oxidation with atomic oxygen (O) at (a) log𝑃CO2=0, log𝑃CO=0, and log𝑃SiO=0, (b) log𝑃CO2=−3, log𝑃CO=−3, and log𝑃SiO=−3, (c) log𝑃CO2=−7, log𝑃CO=−7, and log𝑃SiO=−7, and (d) log𝑃CO2=−10, log𝑃CO=−10, and log𝑃SiO=−10.

As levels of CO, CO₂, and SiO were reduced to 10⁻³ atm (Figure 5(b)), the stability zone of SiC was reduced from an upper 𝑃_O limit of 10⁻¹² to 10⁻¹⁸. Above temperatures of ~1800 K, SiO was the first oxidation product. Further oxidation produced either SiO₂ + CO or SiO + CO₂ depending on whether temperature was above or below 2350 K. Temperature for formation of SiO was greatly lowered as levels of CO, CO₂, and SiO were further reduced (Figures 5(c) and 5(d)). Thus, SiO was formed at ~1100 K when pressures of CO, CO₂, and SiO were at 10⁻¹⁰ atm (Figure 5(d)); equilibrium pressure for stability of SiC also dropped sharply to about 10⁻²⁰ atm.

Briefly, at lower temperatures and higher levels of volatiles (Figures 5(a) and 5(b)), oxidation with atomic oxygen first produced SiO₂ + C followed by SiO₂ + CO₂. Increasing temperature and reducing pressures of volatiles (Figures 5(c) and 5(d)) resulted in the oxidation sequence SiO + CO then SiO + CO₂ and finally SiO₂ + CO₂. Lower temperatures favoured the formation of SiO₂ (passive oxidation), whereas SiO was formed at higher temperatures (active oxidation).

Stability of SiC in ozone was severely reduced compared to atomic oxygen. Even at log𝑃_CO2/CO/SiO of −3, SiC oxidised to SiO and CO at 10⁻³⁴ atm O₃ and at 1600 K (Figure 6(b)). There was no observable stability field of SiC (down to log𝑃_O3=−50) when pressures of volatiles were very low (10⁻¹⁰ atm, Figure 6(d)). Oxidation products were similar to those observed with molecular and atomic oxygen. However, the stability field of SiO₂ + CO increased significantly. At lower temperatures, oxidation proceeded with the formation of SiO₂ + CO followed by SiO₂ + CO₂. At higher temperatures, SiO + CO formed first; this oxidised to SiO + CO₂ and finally to SiO₂ + CO₂.

(a)

(b)

(c)

(d)

Figure 6 

Equilibrium diagram of SiC oxidation with ozone (O3) at (a) log𝑃CO2=0, log𝑃CO=0, and log𝑃SiO=0, (b) log𝑃CO2=−3, log𝑃CO=−3, and log𝑃SiO=−3, (c) log𝑃CO2=−7, log𝑃CO=−7, and log𝑃SiO=−7, and (d) log𝑃CO2=−10, log𝑃CO=−10, and log𝑃SiO=−10.

With regard to reactions at the surface of reentry vehicles, the diagrams suggest that at the initial phase (in the upper mesosphere, where temperatures fall as low as 200 K, and the main oxidant is atomic oxygen) oxidation would mainly produce SiO₂ and CO₂. On entry into the stratosphere, under the conditions of temperature and ozone pressures encountered, SiO₂ and CO₂ would form. Since tropospheric oxygen levels are in the range of 0.2 bar to 10⁻³ bar at the tropopause [4], the implications are that SiO₂ and CO₂ would be the major oxidation products (provided CO/CO₂ levels are high, as in the presence of ablatives). The initial formation of SiO₂ would result in a protective layer that would retard diffusion and further oxidation of SiC. Although in the absence of CO/CO₂ producing ablatives the oxidation product would be SiO, the initial coating of SiO₂ would protect the bulk SiC from complete oxidation. Such a protective mechanism would be effective only below the melting point of SiO₂, that is, 1996 K. Above this temperature, complete oxidation can occur (since wind speeds would be sufficient to blow away the liquid SiO₂ coating).

Experimental data on the oxidation of silicon carbide with ozone showed that oxidation rates in ozone-containing atmosphere were much higher than those in a pure oxygen atmosphere [17]. In other experimental observations on oxidations with molecular oxygen, SiO₂ has been observed to form a protective film on the surface of SiC between 900 and 1600^∘C [1]; this has been verified under reentry conditions [5]. Protective action reduces when SiO₂ begins to bubble at 3500 Pa and 1580^∘C [5]. Cracks form and become oxidation channels leading to rapid weight loss [13]. The oxidation behavior of the SiC indicated a two-step parabolic oxidation kinetics with formation of crystalline SiO₂ film. Diffusion of oxygen through the SiO₂ film becomes the rate-controlling step of reaction [18]. Charpentier et al. [19] observed with massive 𝛼-SiC samples that the transition between passive and active oxidation occurred at 1300 K for an oxygen partial pressure of 0.2 Pa and at 1600 K for 100 Pa. Our observation that the Si in SiC is more readily oxidized than the C is also corroborated by experimental studies [12] which show that even very small exposures to oxygen lead to an oxygenated Si terminated surface but without any change in the C-terminated surface.

4. Conclusions

Thermodynamics of oxidation reactions of SiC were studied by constructing a reaction equilibrium diagram of SiC with atomic oxygen and ozone. Equilibrium constant (𝑘)-temperature relations were derived for all the eight possible ways in which oxidation could occur. In all reactions, 𝑘 values were observed to be highly positive and to decrease with temperature. The reaction forming SiO₂ + CO₂ was thermodynamically the most favourable. Partial pressure-temperature relations suggest that equilibrium pressures are extremely low.

Derived oxidation equilibrium diagrams showed the thermodynamically most favoured oxidation products and the sequence of oxidation under various conditions. As SiC was exposed to increasing levels of O or O₃, the first products were SiO₂ + C, followed by SiO₂ + CO/SiO + CO₂. High temperature and lower pressures of volatiles (CO, CO₂, and SiO) in the zone of oxidation favoured the formation of SiO over SiO₂. Moreover, in the SiC crystal, it is the Si atom which is more susceptible to oxidation than the C atom, and it is the Si which is first oxidized forming SiO₂.

Oxidation equilibrium diagrams could help to understand reactions during reentry of space vehicles. Since surface heating becomes significant at about 120 km from the Earth’s surface, three layers of the atmosphere are involved, namely, the troposphere, stratosphere, and mesosphere-lower thermosphere. The SiO₂ layer (probably formed in the initial phase of re-entry) protects the bulk SiC from further catastrophic oxidation to SiO which could occur at higher temperatures at the later stages. Protective action towards oxidation would be effective till below the melting point of SiO₂ (1996 K), where upon SiO₂ liquid would be blown off the surface.

Acknowledgments

Financial support from ER & IPR, DRDO, and Government of India is gratefully acknowledged.

Supplementary Materials

This program illustrates the derivation of equilibrium diagrams for oxidation of SiC with ozone. The main program OXID2D derives the equilibrium activity diagrams i.e., the equilibrium boundaries. The main program has 2 sub-routines (SubOXID_1 and SubOXID_2), which derive the standard free energy change of the oxidation reaction and equilibrium ozone pressures at temperatures below and above the melting point of SiO₂. The sub-routine SubOXID_1 is for reactions in the lower temperature range (298.15-1900 K) where SiO₂ is in the solid phase; the sub-routine SubOXID_2 is for reactions at temperatures above the melting point of SiO₂ (2000-3200 K). The data from SubOXID_1 & 2 are imported into OXID2D and must be run prior to the main program.

1. Supplementary Material