Computational and Experimental Study of Thermodynamics of the

Article pubs.acs.org/JPCA

Computational and Experimental Study of Thermodynamics of the Reaction of Titania and Water at High Temperatures Q. N. Nguyen,† C. W. Bauschlicher, Jr.,‡ D. L. Myers,†,§ N. S. Jacobson,*,† and E. J. Opila†,∥ †

NASA Glenn Research Center, Cleveland, Ohio 44135, United States NASA Ames Research Center, Moffett Field, California 94035, United States

‡

S Supporting Information *

ABSTRACT: Gaseous titanium hydroxide and oxyhydroxide species were studied with quantum chemical methods. The results are used in conjunction with an experimental transpiration study of titanium dioxide (TiO2) in water vapor-containing environments at elevated temperatures to provide a thermodynamic description of the Ti(OH)4(g) and TiO(OH)2(g) species. The geometry and harmonic vibrational frequencies of these species were computed using the coupled-cluster singles and doubles method with a perturbative correction for connected triple substitutions [CCSD(T)]. For the OH bending and rotation, the B3LYP density functional theory was used to compute corrections to the harmonic approximations. These results were combined to determine the enthalpy of formation. Experimentally, the transpiration method was used with water contents from 0 to 76 mol % in oxygen or argon carrier gases for 20−250 h exposure times at 1473−1673 K. Results indicate that oxygen is not a key contributor to volatilization, and the primary reaction for volatilization in this temperature range is TiO2(s) + H2O(g) = TiO(OH)2(g). Data were analyzed with both the second and third law methods using the thermal functions derived from the theoretical calculations. The third law enthalpy of formation at 298.15 K for TiO(OH)2(g) at 298 K was −838.9 ± 6.5 kJ/mol, which compares favorably to the theoretical calculation of −838.7 ± 25 kJ/mol. We recommend the experimentally derived third law enthalpy of formation at 298.15 K for TiO(OH)2, the computed entropy of 320.67 J/mol·K, and the computed heat capacity [149.192 + (−0.02539)T + (8.28697 × 10−6) T2 + (−15614.05)/T + (−5.2182 × 10−11)/T2] J/mol-K, where T is the temperature in K. interaction of Ti metal atoms with H2O. Kauffman et al.9 see evidence for HxTi(OH)2 and Ti(OH)x. Zhou et al.10 suggest H2Ti(OH)2. Wang and Andrews11 see evidence of Ti(OH)2 and Ti(OH)4. Shao et al.12 examined TiO2 interactions with H2O and report on the structure and vibrational frequencies of OTi(OH)2. At high temperatures, Ueno and colleagues reported evidence of an attack of rutile in a 30 mass percent H2O/air environment at 1773 K13 in the form of weightloss and etch pits. A geological study discusses the reaction of TiO2 with hot water, which is attributed to the formation of Ti(OH)4(g).14 Golden and Opila report the recession of singlecrystal TiO2 in high velocity steam15 attributed to gaseous hydroxide formation, although the identity of the vapor species is unknown. Thus, questions remain on the identity of the principal vapor species and the thermodynamic functions for these species. On the basis of previous work on Cr hydroxides and oxyhydroxides and the prevalent +4 oxidation state of Ti, the most likely species are Ti(OH)4(g) or TiO(OH)2(g). In this article, we first present a computational study of these two species, which

1. INTRODUCTION Many common oxides react with water vapor at high temperatures to form hydroxide and oxyhydroxide species.1,2 Precise thermodynamic data are available for some of these species such as the Group I and Group II hydroxides,3,4 Si(OH)4(g)5−7 and CrO2(OH)2(g).8 However, data are unavailable for many important hydroxides and oxyhydroxides. In particular, questions remain about transition metal hydroxides and oxyhydroxides. Titania-forming and titania-containing materials are of great interest for applications in high-temperature environments due to their temperature capabilities, light weight, good strength-toweight ratio, and corrosion resistance. Examples include Ti(Pt) Ni nitinol, Ti−Al alloys, TiB2, TiN, TiC, and refractory coatings containing TiO2. Since high-temperature combustion environments contain water vapor, the interaction of water vapor and titania is important. In addition, such processes are important in geological phenomena. However, we could find no thermodynamic data for titanium hydroxides or oxyhydroxides. Further, the exact stoichiometry of the titanium hydroxide or oxyhydroxide species is not known. There is laboratory evidence that TiO2 does indeed react with water vapor. Several groups have conducted matrix isolation experiments and obtained infrared spectra of species condensed on an Ar matrix. Most of the studies examine the This article not subject to U.S. Copyright. Published 2017 by the American Chemical Society

Received: August 29, 2017 Revised: November 8, 2017 Published: November 13, 2017 9508

DOI: 10.1021/acs.jpca.7b08614 J. Phys. Chem. A 2017, 121, 9508−9517

The Journal of Physical Chemistry A

Article

summarized in Table 1. Note that the values of all species are in the gas phase and the values for Ti(g) and H2O(g) are the same, whereas the values for TiO2(g) differ. Reaction 6 is used to obtain the relative energies of our two target molecules. For the molecules studied in this work, it is possible to optimize all of the geometries and compute the vibrational frequencies using the CCSD(T)/TZ approach. However, this is very timeconsuming and finding a less expensive alternative is desirable. Therefore, the first step was to optimize the geometries of TiO2 and TiO(OH)2 at the CCSD(T)/TZ level. Using the TZ basis set and correlating the same electrons, the geometries were optimized at the MP2 level. For TiO2 the O−Ti−O angle at the MP2 level is 6° smaller than at the CCSD(T) level. The geometries computed at the B3LYP/TZ′ level are in better agreement with CCSD(T)/TZ than are the MP2/TZ. The B3LYP/TZ′ O−Ti−O angle differs by less than 0.1° from the CCSD(T)/TZ. For TiO(OH)2 the O−Ti−O(H) angle at the B3LYP/TZ′ is in better agreement with the CCSD(T)/TZ than is the MP2 result, but for this molecule, the MP2 only differs by 1.3° from the CCSD(T) value. We should note that we also optimized the geometries using the M06/TZ′ and BPW91/TZ′ approaches. These two functionals yield a nonplanar structure for TiO(OH)2, where the Ti atom is above the plane of the three O atoms. This is in contrast with the CCSD(T)/TZ and B3LYP/TZ′ approaches, which yield a planar structure. On this basis, we conclude that B3LYP/TZ′ is the best alternative to the CCSD(T). We should note that the zero-point energy contributions to reaction 2 using the CCSD(T) and B3LYP approaches are in good agreement, 6.2 vs 6.4 kJ. However, to be fair, the values only vary from 5.9 (MP2) to 6.5 kJ (BPW91) when all of the method tests are considered. In addition to the geometry tests, we also tested the effect of inner shell correlation for reaction 2. The O 1s and Ti 2s and 2p electrons were correlated in addition to the valence electrons. The O and Ti basis sets were made more flexible to describe this inner shell correlation. The oxygen basis set was switched to the aug-cc-pCVTZ set, and the Ti TZ basis was more flexibly contracted and tight polarization functions added. The heat of reaction was increased by 0.2 kJ when inner shell correlation was added. Considering the very small effect and the significant increase in computational cost, only the valence electrons are correlated in the reported calculations. Our calculated structures are shown in Figure 1. The calculated vibrational frequencies are given in Table 2. We first study the heat for formation of TiO2(g) at 0 K using reaction 1. The results are summarized in Table 3. Our best value for the reaction energy is determined as follows, the CBS(QZ,5Z) limit value is corrected for inclusion of zero-point energy and for the Ti spin orbit effect (computed as the difference between the weighted average of the J levels and the lowest Ti 3F2 level). It is very difficult to rigorously assign error bars to our calculations. The three largest sources of error are expected to be the basis set incompleteness, higher levels of correlation not included in the CCSD(T), and anharmonic contributions to

yields their structures and thermodynamics. Then we present an experimental transpiration study to determine the principal species and thermodynamics via the second and third law methods.

2. COMPUTATIONAL STUDIES 2.1. Methods. We use the B3LYP hybrid16,17 functional and the coupled cluster singles and doubles approach,18 including the effect of connected triples determined using perturbation theory,19 CCSD(T), to study the species of interest. For openshell calculations the partially spin restricted RCCSD(T) approach20 is used. Some calculations using other functionals and Møller−Plesset second-order perturbation were performed and noted below as appropriate. The CCSD(T) calculations use the cc-pVnZ sets20 for H, the aug-cc-pVnZ sets21,22 for O, and the core−valence cc-pwCVnZDK sets23 for Ti, where n takes the values, T, Q, and 5. The Ti basis sets allow the inclusion of Ti 3s and 3p correlation and the inclusion of scalar relativistic effects using the Douglas−Kroll approach. We denote these basis sets as TZ, QZ, and 5Z. The CCSD(T) calculations are extrapolated to the complete basis set limit (CBS) using the X−3 approach of Helgaker et al.24 Unless otherwise noted, the O 1s and Ti 1s, 2s, and 2p electrons are not correlated. The B3LYP calculations are performed using augmented correlation consistent triple-ζ (aug-cc-pVTZ) sets,21−23 which we denote as TZ′. All of the DFT calculations were performed using Gaussian09,25 while MOLPRO26 was used to perform the CCSD(T) calculations. The interactive molecular graphics tool Jmol27 was used for the visualization of the molecular structures and the vibrational modes. The OH groups have a low rotational barrier and therefore need to be treated as hindered rotors for the calculation of thermodynamic properties.8,28 The hindered rotor option25 in Gaussian09 is used to compute this effect using the Pitzer− Gwinn29 option. The OH bending potential is very anharmonic, and we account for this by solving for the vibrational levels of the bending potential and computing the thermodynamic properties using these computed levels. 2.2. Results. We compute the heat of formation of a target molecule by computing a reaction energy for a case where the heats of formation of the reactants are known. The reactions we study in this work are Ti + O2 → TiO2 (1) TiO2 + H 2O → TiO(OH)2

(2)

Ti + O2 + H 2O → TiO(OH)2

(3)

Ti + O2 + 2H 2O → Ti(OH)4

(4)

TiO2 + 2H 2O → Ti(OH)4

(5)

TiO(OH)2 + H 2O → Ti(OH)4

(6)

For reactions 1 to 5, the heats of formation of the starting materials from both the JANAF3 and Gurvich et al.4 tables are Table 1. Reference Compound Heats of Formation, in kJ/mol Ti(g) TiO2(g) H2O(g) O2(g)

ΔfH(0 K) (JANAF)3

ΔfH(298 K) (JANAF)3

ΔfH(0 K) (Gurvich et al.)4

ΔfH(298 K) (Gurvich et al.)4

470.92 ± 16.7 −303.28 ± 12.6 −238.921 ± 0.042 0

473.63 ± 16.7 −305.43 ± 12.6 −241.826 ± 0.042 0

471 ± 2 −320 ± 20 −238.923 ± 0.040 0

474 ± 2 −323 ± 20 −241.826 ± 0.040 0

9509



Article

however, the difference between the CBS(TZ,QZ) and CBS(QZ,5Z) values is 2.8 kJ, suggesting that some uncertainty remains. All of the species considered in this work are well described by a single reference, and therefore, the neglect of higher excitations is expected to be smaller than the basis set incompleteness. For water, the anharmonic contribution to the zero-point energy is 5% of the harmonic value. The assumption that the anharmonic contribution to the reaction energy is similar to that for water yields a maximum anharmonic correction to the reaction energies of 0.5 kJ, which is significantly smaller than the basis set incompleteness error. On this basis, we estimate the uncertainty in our best values as twice the difference between the 5Z and CBS(QZ,5Z) values or ±10 kJ. The combination of our best estimate with the heats of formation for Ti and O2 yields the heats of formation given in Table 3. We deduce the uncertainty by combining our uncertainty for the reaction energy with that for the Ti atom. Our value is in good agreement with that recommended by the JANAF tables3 (ΔfH°(0) = −303.28 ± 12.6 kJ/mol), but does not rule out the Gurvich et al. value4 (ΔfH°(0) = −320 ± 20 kJ/mol) value. The heat of formation of TiO(OH)2 is computed using reactions 2 and 3. The difference between the 5Z and the CBS(QZ,5Z) and between the two CBS values is smaller for reaction 2, as expected from its smaller exothermicity. Using twice the difference between the 5Z and CBS values gives uncertainties of ±4 and ±8 kJ for reactions 2 and 3, respectively. Adding these uncertainties to those for TiO2 and Ti yields our final uncertainties of ±21 and ±25 kJ/mol. The two values differ by the difference between our computed ΔfH for TiO2 and that recommended by JANAF.3 The preferred values of the enthalpy of formation of TiO(OH)2(g) and Ti(OH)4(g) are from reactions 3 and 4, which do not require the TiO2(g) enthalpy of formation. This avoids the small disagreement between the JANAF3 and Gurvich et al.4 tables. The heat of formation of Ti(OH)4 was determined using reactions 4 and 5. The heats of formation from these two reactions differ by the expected 8.7 kJ, the difference between our computed heat of formation of TiO2 and that recommended by JANAF.3 If the Gurvich et al.4 value is used, the ΔH value would be an additional 16.7 kJ lower. Reaction 6 shows that the reaction of TiO(OH)2 with H2O to form Ti(OH)4 is exothermic by 187.9 kJ. We note that this reaction is actually a two-step process, where a TiO(OH)2·H2O complex forms. At the CCSD(T)/TZ level, this complex is 124 kJ below the reactants.

Figure 1. Calculated structures of the reactants and products for reactions 1−6. From left to right: O2, H2O, TiO2, TiO(OH)2, Ti(OH)4. Angles are in degrees, and bond lengths are in angstroms.

Table 2. Computed CCSD(T)/TZ Harmonic Frequencies, in cm−1 O2 3∑− 1574.0 H2O 1A1 1648.0 TiO2 1A1 330.2 TiO(OH)2 1A1 70.6 461.2 521.4 1029.8 Ti(OH)4 1A 92.9 181.6 234.3 419.3 457.6 783.6 3878.0

3810.4

3920.8

955.3

989.8

187.7 465.8 683.1 3890.6

219.4 480.2 794.4 3891.0

140.2 209.8 252.4 423.21 708.3 786.7 3881.0

153.0 219.6 295.5 454.4 765.1 3878.0 3884.6

the zero-point energy. In principle, the extrapolation complete basis limit should remove any basis set incompleteness error;

Table 3. Summary of Calculation of the Enthalpy of Formation for Listed Molecules reaction energy (kJ/mol)a TZ QZ 5Z CBS(TZ, QZ) CBS(QZ, 5Z) ZPE Ti spin orbit best

ΔfH(0 K) ΔfH(298 K) a

rxn 1

rxn 2

−753.4 −762.8 −767.5 −769.7 −772.5 4.2 2.8 −765.5

−310.3 −309.7 −308.7 −309.2 −307.8 6.2 0.0 −301.5

rxn 3 −1063.6 −1072.4 −1076.3 −1078.9 −1080.3 10.4 2.8 −1067.0 enthalpy of formation (kJ/mol)

rxn 4

rxn 5

rxn 6

−1252.4 −1261.3 −1264.7 −1267.8 −1268.3 10.6 2.8 −1254.9

−499.1 −498.5 −497.2 −498.1 −495.8 6.4 0.0 −489.4

−188.8 −188.9 −188.4 −188.9 −188.1 0.1 0.0 −187.9

TiO2(g)

TiO(OH)2(g)

TiO(OH)2(g)

Ti(OH)4(g)

Ti(OH)4(g)

−294.6 ± 27 −295.6 ± 27

−843.7 ± 21 −847.5 ± 21

−835.0 ± 25 −838.7 ± 25

−1261.9 ± 25 −1274.2 ± 25

−1270.6 ± 21 −1283.0 ± 21

Without zero-point energy in rows 1−5. Best adds ZPE and Ti spin orbit to CBS(QZ,5Z). 9510



Article

Cp contributions, and we use these values instead of the harmonic ones. The details of each contribution to the entropy, enthalpy, heat capacity, and Gibbs free energy are given in Supporting Information Table 2. The key thermochemical information is summarized in Table 4 for the two gaseous species TiO(OH)2(g) and Ti(OH)4(g). This is typically the data required by the common computational thermodynamics databanks (e.g., FactSage30) and from these data all relevant thermodynamic functions can be derived. As discussed, we have selected the data from reactions 3 and 4 to derive the enthalpies of formation of TiO(OH)2(g) and Ti(OH)4(g). These reactions do not involve TiO2(g) as a reactant, only using the elements and H2O, which have more reliable data. Figure 4 is a plot from the computed data of the vapor pressure of TiO(OH)2(g) and Ti(OH)4(g) over TiO2 + 50% H2O/Ar at 1 bar total pressure. Note the TiO(OH)2(g) dominates.

There is a barrier of 69 kJ between this complex and the transition state. However, the transition state is 55 kJ below the reactants; so in spite of the barrier, we suspect that the reaction will occur easily. Up to this point we have computed all thermodynamic properties at 0 K. It is known from CrO2(OH)2 that OH rotation has a low barrier8 and must be treated using a hindered rotor approximation. In Figure 2, we show the OH rotational barrier

3. EXPERIMENTAL PROCEDURES A generalized reaction for TiO2(s) with oxygen and water vapor is TiO2 (s) + xO2 (g) + y H 2O(g) = TiO(2 + 2x + y)H(2y)(g) (7)

Thus, P(TiO(2+2x+y)H(2y)) varies with [P(O2)]x and [P(H2O)]y. In our laboratories and others, the transpiration method has been found to be particularly useful for the study of this type of reaction at elevated temperatures.5,6,8,31,32 The transpiration method as reviewed by Merton and Bell33 involves flowing reactant gases over a condensed sample at a suitable rate in order for solid−gas equilibrium to be established. The product gas flows downstream and is condensed in a cooler portion of the gas train, collected and analyzed to quantitatively determine the amount of sample transported. By independently varying the reactant gas partial pressures and determining the dependence of volatile product formation on reactant gas concentration, the identity of volatile species can be determined. The partial pressure of the volatile species, TiO(2+2x+y)H(2y)(g), can then be determined over a range of temperatures, which allows the extraction of an enthalpy and entropy of reaction. 3.1. TiO2 Pellets. Acros Organics, 99.999% pure titanium oxide, predominately rutile, powder was cold-pressed in a 1/4″ O.D. stainless steel die to a pressure of 141 kg/cm2 (2000 psig). These pellets were dried overnight in a 100 °C drying oven and were sintered in air at 1200 °C for 24 h. The TiO2 pellets were weighed, and the density was calculated to be 3.75 g/cm3, corresponding to 88% of the theoretical density. After the transpiration runs were complete, the reaction chamber was opened and the pellets were examined with X-ray diffraction and scanning electron microscopy. No significant changes in composition were noted. Typical surface morphologies of the pellets before and after exposure are shown in Figure 5. The grains were still rutile, as confirmed by X-ray diffraction, but significant grain growth occurred. 3.2. Transpiration System. The transpiration system is shown schematically in Figure 6. The cell is made out of platinum−20% rhodium (Pt/20Rh) and laser-welded with the sintered TiO2 pellets packed inside. A type R thermocouple is inserted through the bottom of the cell to monitor the reaction temperature. A carrier gas composed of argon and/or oxygen flowed through the reaction cell and was controlled and monitored with a calibrated electronic flowmeter (Tylan FC-260).

Figure 2. OH rotational potential for TiO(OH)2 and Ti(OH)4.

for TiO(OH)2 and Ti(OH)4. We first note that the CCSD(T)/ TZ and B3LYP/TZ′ barriers are very similar; therefore, the larger Ti(OH)4 is only studied at the B3LYP/TZ′ level. The numerical values are given in Supporting Information Table 1. Using the computed barriers and the Pitzer−Gwinn approach, the OH hindered rotation contributions to ΔS, ΔH, and Cp are accounted for. In addition to the OH rotation, we have found that the Ti−O−H bending potential is very flat. In Figure 3

Figure 3. B3LYP OH bending potential for one OH group in Ti(OH)4.

we show the B3LYP/TZ′ bending potential for one OH in Ti(OH)4. Using this potential, it is possible to solve for the vibrational levels, which are also shown in the figure. The double well shape results in level spacings that are significantly different from that expected for a harmonic oscillator. Using the computed levels it is possible to compute the ΔS, ΔH, and 9511



Article

Table 4. Enthalpy of Formation, Entropy, and Heat Capacity for TiO(OH)2(g) and Ti(OH)4(g) ΔfH0(0) ΔfH0(298) S0(298) Cp (298−1600 K)

TiO(OH)2

Ti(OH)4

−835.0 ± 25 kJ/mol −838.7 ± 25 kJ/mol 320.67 J/mol·K 149.192 + (−0.02539)T + (8.28697 × 10−6)T2 + (−15614.05)/T + (−5.2182 × 10−11)/T2 J/mol·K

−1270.6 ± 21 kJ/mol −1274.2 ± 21 kJ/mol 373.7 J/mol·K 169.25 + (−7.1896 × 10−3)T + (7.5164 × 10−6)T2 + (−10818.0308)/T + (−4.8145 × 10−11)/T2 J/mol·K

carrier gas via a peristaltic pump. The liquid water flow rate ranged from 0.5 to 9.3 mL/h and was calibrated before and after each test to verify the flow consistency. A quartz wool plug, located at the junction of the water inlet with the gas train, was used to ensure that liquid to vapor disbursement occurred. The gases (Ar, O2, and water vapor) were introduced through the bottom of the transpiration gas train and then flowed into the transpiration cell. The flow rates of the gases (argon/ oxygen) ranged from 60 to 275 cc/min. Whenever the furnace was above room temperature, the blanket Ar gas that flows on the exterior of the transpiration cell was flowing at rates of 90 cc/min or higher. The gas lines and water line were heated with heating tape (260 °C) prior to introduction into the furnace. This prevented condensation and provided some preheating of the gas. The gas stream traveled up through the sealed reaction chamber, located in the hot zone of the furnace, and then exited through a series of three fused quartz (99.995% purity) condensation (collection) tubes, as shown in red in Figure 6. From our previous studies on the Cr−O−H system,8 it was found to be critical to analyze all the deposits in the entire gas train after the reaction chamber. The series of three fused quartz condensation tubes was held together by polyfluoroethylene fittings. The first condensation tube (#1), as mentioned above, was located in the hot zone at the exit of the transpiration cell in the center of the furnace. This condensation tube was the location of the primary condensate. The end that sat in the hot zone of the furnace had an internal beveled edge that fit snuggly over the transpiration cell exit, thus allowing for a tight seal and maintaining pressure as the gases exited. This straight condensation tube was replaced after each experiment due to the devitrification and resultant damage that occurs during cooling from the high temperature exposures. An image of this tube is shown in the inset in Figure 6. The second fused quartz condensation tube (#2) was a bent one located at the top of the furnace tube. This second fused quartz condensation tube was wrapped with heating tape to ensure the water vapor did not condense prior to reaching the third condensation tube (#3). The third tube was at room temperature, thus allowing the water vapor to condense, collect in a buret, and be measured. Both the second and third fused quartz condensation tubes were reused after the Ti-deposits had been extracted by an analytical method explained in the next section. All the fused quartz tubes and polyfluoroethylene fittings were kept in a clean drying oven held at 100 °C to eliminate any moisture when not in use for an experiment. The experiments were conducted at ambient pressure. The transpiration cell pressure was recorded with a capacitance manometer (Leybold Inficon) that varied between 0.96 and 1.00 atm (730−763 Torr) during the two years of testing. This capacitance manometer was verified by a separate barometric standard (NASA Glenn Aircraft Hanger Barometer). To verify that there were no leaks in the system, the pressure was checked for each experiment by closing the exhaust and watching the back pressure increase as measured by the capacitance manometer.

Figure 4. Plot of vapor pressures of Ti(OH)4(g) and TiO(OH)2(g) above TiO2 and 50% H2O(g)/Ar at 1 bar total pressure as a function of temperature.

Figure 5. View of starting pellet (a) before the transpiration experiments and (b) after the transpiration experiments, showing the extensive grain growth.

Figure 6. Transpiration furnace and transpiration cell (Pt/Rh reaction chamber). The insets show the details of the reaction chamber and condensate on the quartz collection tubes.

The transpiration system used a furnace with molydisilicide heating elements (Applied Test Systems, Inc.) and a 99.8% pure alumina furnace tube. Deionized water was introduced through the bottom of the transpiration gas train into the 9512



Article

3.3. Chemical Analyses. The amount of Ti condensate in the three fused quartz condensation tubes along with the polyfluoroethylene fittings and water that was collected through the exhaust were quantitatively analyzed using inductively coupled plasma atomic emission spectroscopy (ICP-AES) (Varian Vista-Pro, Axial configuration). Although the fittings and exhaust water contained no visible deposits, they were all analyzed. The fittings were digested in a 5% (by volume) hydrochloric acid (HCl) + 2% hydrofluoric (HF) solution for 2−3 h. This solution and the exhaust water were diluted to a known volume, and ICP-AES was used to measure the Ti concentration. The absence of deposit in the exhaust water was also verified in the first several runs by a filtration step resulting in no weight change on Whatman grade #44 filter paper (nominal particle retention size >3 μm; filtration speed: slow). The inside of the main straight fused quartz condensation tube #1 (which includes the hot zone) contained a film on the internal walls in the form of a brown to black deposit. This main condensation tube acquired the most Ti-deposit relative to the other tubes, although some deposit was also formed in the internal walls of tube #2. The fused quartz tubes were soaked in an aqua regia solution (3 part HCl + 1 part nitric acid (HNO3)) for 2 h followed by a rinse with concentrated HF. The entire solution was analyzed with ICP-AES. All runs that contained oxygen, where PtO2(g) formation from the transpiration cell was possible, went through a second series of analyses in which an acidic flux (fusion) step through the use of potassium hydrogen sulfate and potassium pyrosulfate was used in order to extract the Ti-condensate. This mixture was heated over a Bunsen burner until it liquefied, thus converting any remaining deposited TiO2(s) into a soluble solution that was analyzed in the ICP-AES. Some runs had a black deposit that did not fully dissolve in the solution. The first several runs’ black deposits were filtered and dried after the acidic flux (fusion) extraction and characterized by WDXRF to confirm the absence of Ti. The WDXRF analyses suggested primarily PtO. The typical weight of these black deposits was estimated to be 10−20 mg. Since the WDXRD sensitivity to Ti is typically about 0.1%,34 it is possible that up to 20 μg still remained in this deposit. Several additional methods were tried to dissolve the black deposits. These include successive aqua regia and concentrated HF exposures; a flux of sodium carbonate and sodium tetraborate; and a flux of boric acid and sodium fluoride. The black deposit was not significantly attacked. The resultant solution from the acid dissolution contained only 1 μg of Ti. The potential for trace concentrations of Ti in the black deposit must be considered a possible source of error. The second and third quartz condensation tubes along with all the polyfluorethylene fittings were reused since they were not exposed to high temperatures. The third tube and fittings went through a series of acid soaks, which involved an overnight soak in 50% solution of HCl followed by a deionized water rinse, drying, and storage in a clean drying oven (100 °C) prior to reuse. It is also important to note that the ICP-AES procedure is very sensitive for measuring cations and can detect several micrograms, as found in previous studies.6,8 The amount of Ti in the condensate ranged between 9 and 262 μg. 3.4. Calculations with Experimental Data To Identify the Species and To Extract Thermodynamic Data. The identity of the volatile species was determined by using the

measured data to calculate the coefficients x and y in reaction 7. The same calculation methods were used in previous studies.6,8 The vapor pressure of the volatile Ti−O−H species, PTi−O−H, is given by eq 8. PTi − O − H =

n Ti ̇ RTcell V̇

(8)

Here n Ti ̇ is the molar rate of transport of Ti from the reaction cell, R is the ideal gas constant, Tcell is the measured temperature inside the cell, and V̇ is the total volumetric flow rate through the reaction cell. The molar flow rate of Ti is simply the rate at which Ti is deposited downstream. m n Ti ̇ = Ti M Tit (9) Here mTi is the mass of Ti collected at the end of an experiment, MTi is the atomic weight of Ti, and t is duration of an experiment. The total flow rate through the cell is simply the sum of all the flow rates through the cell. V̇ =

RTcell (nȮ 2 + nAr ̇ + nH ̇ 2O + n Ti ̇ − O − H) Ptot

(10)

Here Ptot is the total pressure. The last quantity in eq 10, n Ti ̇ and is much smaller than the others. ̇ − O − H , is the same as n Ti It can thus be neglected. Note also that these flow rates are all at 298.15 K. Initially a series of experiments was conducted to identify the product of the reaction of TiO2 and O2/H2O. This was done by systematically varying PO2 and PH2O. Once the molecule was identified, vapor pressures were determined. Second and third law methods were then used to derive thermodynamic parameters.35,36 The second law method gives a heat of reaction, ΔrH0Tav, at the average temperature of measurement, Tav, using the van’t Hoff equation.

d(ln K p) d

( T1 )

=−

Δr HT0av R

(11)

Here Kp is the equilibrium constant for reaction 7 with known x and y and R is the gas constant. In order to obtain a heat of reaction at 298.15 K, the following expression is used: 0 Δr HT0 = Δr H298 +

T

∫298 ΔCpdT

(12)

Here ΔCp is the change in heat capacity of the reaction and uses the heat capacity of the product in Table 4. The Gibbs energy function (gef) is given by eq 13. 0 gef298.15 = (GT0 − H298.15 )/T

(13)

The Gibbs energy functions were calculated from the quantities derived in the computational part of this study. Then the third law method35 can be used to derive the enthalpy at 298.15 K, using eq 14 for each data point. T {Δ{−(gef298.15 )} − R ln(K p)} 0 = Δrxn H298.15 (Ti − O − H)

(14)

Here Kp is the equilibrium constant for the relevant reaction. The Gibbs energy functions were derived from the quantum calculations results. We used Gibbs energies referenced to 9513



Article

298.15 K, and the required Gibbs energy function is given below. ⎛ G − H0 ⎞ ⎛ H298.15 − H0 ⎞ ⎜ ⎟ − ⎜ ⎟ ⎝ T ⎠ ⎝ ⎠ T ⎛ G − H298.15 ⎞ ⎟ =⎜ ⎝ ⎠ T

gef298.15 =

(15)

4. RESULTS 4.1. Identity of the Ti−O−H Species. A total of 51 tests were conducted over a temperature range of 1473−1673 K and are listed in Supporting Information Table 3. This study was conducted for three primary temperatures of interest: 1473, 1573, and 1673 K along with additional measurements at 1498, 1523, and 1548 K. As discussed in the Experimental Procedures, the identity of the major Ti−O−H species is determined by methodically varying the O2 and H2O reactants. First consider the measurements at 1673 K to determine the value of x and y in reaction 7, as shown in Figure 7. At the

Figure 8. Vapor pressure as a function of P(H2O) for 1473, 1573, and 1673 K.

4.2. Experimental Thermodynamic Data. A second law treatment of the data using a van’t Hoff plot leads to an enthalpy and entropy of reaction at the average temperature of measurement (1600 K). This is shown in Figure 9. The heat

Figure 7. Measured partial pressure of Ti−O−H at 1673 K. O2(g) or H2O(g) is held constant at the values indicated. Figure 9. Van’t Hoff plot for the reaction of TiO2 and H2O(g). The computational data is entirely from the calculated enthalpies and entropies.

highest temperature, the amount of Ti collected was the largest, leading to less scatter in the data. At 1673 K, when the O2 content was held constant at 17%, the value of y is 0.92 ± 0.07; when the H2O content is held constant at 33%, the value of x is 0.01 ± 0.07. A similar analysis was applied to the data at 1573 K. At this temperature, when the H2O content was held at 24% and the O2 content was varied, the value of x is 0.07 ± 0.01; when O2 content was held at 34% and the H2O content is varied, the value of y was 0.85 ± 0.09. At constant P(H2O), variation in P(O2) does not change the amount of Ti−O−H(g) formation, suggesting that the coefficient, x in reaction 7, is zero. At constant P(O2), the amount of Ti−O−H(g) formation varies with [P(H2O)]0.85, suggesting that the coefficient, y in reaction 7 is one. Thus, results at 1573 and 1673 K suggest that the primary reaction is reaction 2. Figure 8 is a plot of all the data vs P(H2O). Note the slopes at 1673 and 1573 K are close to one, confirming the stoichiometry of reaction 2. The data obtained at 1473 K show a larger amount of scatter due to the very small amount of downstream deposit collected and the possibility of more Ti(OH)4(g) forming, as suggested by the theoretical calculations.

capacity of TiO(OH)2(g) from the computational study (Table 4) is used to obtain the enthalpy at 298.15 K. Reaction 6 is applied and yields ΔrH0298 = 248.8 ± 20 kJ/mol. Ideally the plot in Figure 9 could be used to extract an entropy, but we felt the scatter of the data was too great for a reliable number. Also, the lower temperatures likely contain more Ti(OH)4(g). In these situations with considerable scatter and a small temperature range,34 the third law method was used to extract an enthalpy of reaction at 298 K, as described in the previous section. The details of this calculation are given in Table 5, and the value obtained from these data was ΔrH0298 = 347.6 ± 6.4 kJ/mol.

5. DISCUSSION The enthalpies of reaction are converted to enthalpies of formation at 298 K and summarized in Table 6. In this study, the third law enthalpy of formation shows very good agreement with the theoretical calculations given in Table 4. The third law enthalpy given in Table 5 shows no systematic trends with 9514



Article

Table 5. Third Law Calculationa

a

T (K)

1/T (K)

Δgef

ln Kp

third law ΔrH298 (J/mol)

1673 1674 1675 1673 1674 1673 1676 1675 1677 1675 1675 1677 1674 1672 1676 1674 1673 1675 1675 1674 1675 1574 1574 1573 1573 1573 1571 1574 1574 1574 1575 1574 1574 1574 1574 1572 1574 1571 1572 1473 1473 1473 1471 1473 1473 1471 1498 1523 1548

0.000598 0.000597 0.000597 0.000598 0.000597 0.000598 0.000597 0.000597 0.000596 0.000597 0.000597 0.000596 0.000597 0.000598 0.000597 0.000597 0.000598 0.000597 0.000597 0.000597 0.000597 0.000635 0.000635 0.000636 0.000636 0.000636 0.000637 0.000635 0.000635 0.000635 0.000635 0.000635 0.000635 0.000635 0.000635 0.000636 0.000635 0.000637 0.000636 0.000679 0.000679 0.000679 0.00068 0.000679 0.000679 0.00068 0.000668 0.000657 0.000646

−81.463 −81.462 −81.460 −81.463 −81.462 −81.463 −81.459 −81.460 −81.458 −81.460 −81.460 −81.458 −81.462 −81.464 −81.459 −81.462 −81.463 −81.460 −81.460 −81.462 −81.460 −81.575 −81.575 −81.576 −81.576 −81.576 −81.578 −81.575 −81.575 −81.575 −81.574 −81.575 −81.575 −81.575 −81.575 −81.577 −81.575 −81.578 −81.577 −81.689 −81.689 −81.689 −81.691 −81.689 −81.689 −81.691 −81.661 −81.632 −81.604

−15.168 −15.227 −16.369 −15.274 −15.361 −15.240 −15.412 −15.526 −15.292 −15.264 −15.182 −15.151 −16.098 −15.399 −15.251 −16.125 −15.289 −15.290 −15.319 −15.669 −15.351 −16.332 −16.676 −16.664 −16.721 −17.027 −17.012 −16.822 −16.718 −16.723 −16.701 −17.210 −16.669 −16.668 −16.807 −16.688 −16.968 −16.668 −16.647 −17.762 −17.488 −17.089 −18.765 −17.884 −17.066 −18.090 −17.339 −18.144 −16.934

347262.514 348297.315 364411.229 348736.584 350163.628 348273.320 351277.986 352666.860 349818.901 349014.083 347873.670 347849.739 360422.441 350276.922 349042.027 360798.756 348946.717 349384.492 349782.851 354447.474 350222.358 342123.612 346624.148 346248.784 346996.408 351001.195 350366.522 348535.017 347176.280 347243.477 347172.566 353619.560 346533.319 346525.964 348343.155 346352.911 350456.060 345869.678 345818.506 337857.508 334498.298 329616.554 349667.946 339348.195 329335.954 341409.788 338275.074 354078.605 344270.978

calculated structural information and the (H298 − H0) enthalpy increment. Hence, the comparison of theory with experiment compares quantities that are not entirely independent. Nonetheless, the agreement of the two approaches and the temperature independence of the experimentally derived enthalpy at 298 K gives added confidence to the data. From this study, we recommend the experimental third law heat of formation at 298.15 K and the entropy and heat capacity for TiO(OH)2(g) given in Table 4. Figure 10 shows a plot of calculated equilibrium constants from both the experimental and theoretical data. We could not

Figure 10. Plot of the equilibrium constant of TiO(OH)2(g) formation from reaction 2 vs inverse temperature at P(H2O) = 1 bar. The experimental and theoretical lines are the same as in Figure 9. The data points are extracted P(TiO(OH)2) from boundary layer limited vaporization studies.

find any vapor pressure measurements of TiO(OH)2(g) in the literature. However, there are two studies of water-enhanced vaporization of TiO2(s).13,15 It is possible to extract an approximate P(TiO(OH)2) and hence equilibrium constant from these studies. If we assume boundary layer limited flow, the following expression relates partial pressure to vapor flux, J, for laminar flow.37 ⎛ ν∞ρ L ⎞0.5⎛ η ⎞ ⎟⎟ J = 0.664⎜ ∞ ⎟ ⎜⎜ ⎝ η ⎠ ⎝ Diρ∞ ⎠

0.33 ⎛ ν∞ρ∞L ⎞0.8⎛ η ⎞ DiPi ⎜ ⎟ J = 0.0365⎜ ⎟ ⎜ ⎟ ⎝ η ⎠ ⎝ Diρ∞ ⎠ RTL

experimental theoretical

second law third law B3LYP DFT CCSD(T)

−937.8 ± 15 −838.9 ± 6.5 −839 ± 25

(16a) 38

(16b)

Table 7 gives the meaning of each of these variables and values for this estimation of vapor pressure from the studies of Ueno39 and Opila and Golden.15 Values for viscosities are taken from Svehla.40 Figure 10 compares the calculated equilibrium constant from this experimental/theoretical thermodynamic study to the two derived vapor pressures from the boundary layer limited vaporization studies. The boundary layer limited vaporization studies cannot be considered thermodynamic studies. Nonetheless, previous work has shown that equilibrium vapor pressures can be achieved in these flow conditions with water vapor and Al2O341 or SiO242 under slow flow rates and also

Table 6. Experimental and Calculated Enthalpies of Formation and Standard Enthalpies Δf H0298 (kJ/mol)

DiPi RTL

For turbulent flow, this expression changes to

Average ΔrH° (298.15) = 347.6 ± 6.4 kJ/mol.

method

0.33

temperature, indicating the Gibbs energy functions are reliable, which supports the selection of this value. The theoretical information to derive these Gibbs energy functions are only 9515


The Journal of Physical Chemistry A Table 7. Values Used To Estimate Vapor Pressure from Vapor Flux Data quantity measured vapor flux, J free stream velocity, ν∞ density of air−H2O mixture, ρ∞ viscosity, η characteristic dimension, L gas phase diffusivity for TiO(OH)2, Di gas constant, R absolute temperature, T

value (Ueno) −9

1.209 × 10−7 g/cm2·s 1.75 × 104 cm/s

1.239 × 10−4 g/cm3

1.451 × 10−4 g/cm3

6.014 × 104 g/cm·s40 2.553 cm

6.014 × 104 g/cm·s40 1 cm

2.046 cm2/s

1.544 cm2/s

82.06 cm3·atm/mol·K 1773 K

82.06 cm3·atm/mol·K 1513 K

6. CONCLUSIONS The gaseous species Ti(OH)4 and TiO(OH)2 have been studied with quantum chemistry methods. The geometry and harmonic vibrational frequencies of TiO(OH)2(g) and Ti(OH)4(g) were computed using the coupled-cluster singles and doubles method with a perturbative correction for connected triple substitutions [CCSD(T)]. The B3LYP density functional theory was used to compute corrections to the harmonic approximations for the OH bending and rotations. These results were combined to determine the enthalpy of formation. Experimentally, the interaction of TiO2 and H2O/O2(g) at temperatures from 1473 to 1673 K has been studied with the transpiration method. Methodical variation of P(H2O) and P(O2) in transpiration studies identified the major product as TiO(OH)2(g). Experimental measurements were analyzed with both the second and third law methods to determine the enthalpy of formation. The third law method was determined to be more reliable and shows very good agreement with the enthalpy of formation calculated via quantum chemistry methods. Entropies and heat capacities are calculated from these methods and reported for TiO(OH)2(g) and Ti(OH)4(g). ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b08614. Bending potentials, results of quantum chemistry calculations, and raw experimental data (PDF)

■

■

REFERENCES

(1) Jacobson, N.; Myers, D.; Opila, E.; Copland, E. Interactions of Water Vapor with Oxides at Elevated Temperatures. J. Phys. Chem. Solids 2005, 66, 471−478. (2) Meschter, P. J.; Opila, E. J.; Jacobson, N. S. Water Vapor Mediated Volatilization of High Temperature Materials. In Annual Review of Materials Research; Lipkin, D.M., Ed.; Annual Reviews, Inc.: Palo Alto, CA, 2013. (3) Chase, M. W. and National Institute of Standards and Technology (U.S.). NIST-JANAF Thermochemical Tables, 4th ed. Journal of physical and chemical reference data monograph; American Chemical Society; American Institute of Physics for the National Institute of Standards and Technology: Washington, D.C., 1998. (4) Gurvich, L. V., Veyts, I. V.; Alcock, C. B. Thermodynamic Properties of Individual Substances Vol 1−4; Nauka: Moscow, 1982. (5) Hashimoto, A. The Effect of H2O Gas on Volatilities of PlanetForming Major Elements: Experimental Determination of Thermodynamic Properties of Ca-, Al-, and Si-hydroxide Gas Molecules and its Application to the Solar Nebula. Geochim. Cosmochim. Acta 1992, 56, 511−532. (6) Jacobson, N. S.; Opila, E. J.; Myers, D.; Copland, E. Thermodynamics of Gas Phase Species in the Si-O-H System. J. Chem. Thermodyn. 2005, 37, 1130−1137. (7) Plyasunov, A. V. Thermodynamic Properties of H4SiO4 in the Ideal Gas State as Evaluated from Experimental Data. Geochim. Cosmochim. Acta 2011, 75, 3853−65. (8) Opila, E. J.; Myers, D. L.; Jacobson, N. S.; Nielsen, I. M. B.; Johnson, D. F.; Olminsky, J. K.; Allendorf, M. D. Theoretical and Experimental Investigation of the Thermochemistry of CrO2(OH)2(g). J. Phys. Chem. A 2007, 111, 1971−1980. (9) Kauffman, J. W.; Hauge, R. H.; Margrave, J. L. Studies of Reactions of Atomic and Diatomic Cr, Mn, Fe, Co, Ni, Cu, and Zn with Molecular Water at 15 K. J. Phys. Chem. 1985, 89, 3541−3547. (10) Zhou, M.; Zhang, L.; Dong, J.; Qin, Q. Reactions of Group IV Metal Atoms with Water Molecules. Matrix Isolation FTIR and Theoretical Studies. J. Am. Chem. Soc. 2000, 122, 10680−10688. (11) Wang, X. F.; Andrews, L. Infrared Spectra and Structures for Group 4 Dihydroxide and Tetrahydroxide Molecules. J. Phys. Chem. A 2005, 109, 10689−10701. (12) Shao, L.; Zhang, L.; Chen, M.; Lu, H.; Zhou, M. Reactions of Titanium Oxides with Water Molecules. A Matrix Isolation FTIR and Density Functional Study. Chem. Phys. Lett. 2001, 343, 178−184. (13) Ueno, S.; Jayaseelan, D. D.; Kondo, N.; Ohji, T.; Kanzaki, S. Anistropic Behavior of Water Vapor Corrosion of Rutile TiO2 at High Temperature. Mater. Trans. 2004, 45, 281−283. (14) Ayers, J. C.; Watson, E. B. Rutile Solubility and Mobility in Supercritical Aqueous Fluids. Contrib. Mineral. Petrol. 1993, 114, 321− 330. (15) Golden, R. A.; Opila, E. J. A Method for Assessing the Volatility of Oxides in High-Temperature High-Velocity Water Vapor. J. Eur. Ceram. Soc. 2016, 36, 1135−1147. (16) Becke, A. D. Becke’s Three Parameter Hybrid Method Using the LYP Correlation Functional. J. Chem. Phys. 1993, 98, 5648−5652. (17) Stephens, P. J.; Devlin, F. J.; Chabalowski, C.; Frisch, M. J. Ab Initio Calculation of Vibrational Absorption and Circular Dichroism

under more rapid flow rates for SiO2.15 There may be other issues in the case of TiO2, which need to be explored.

■

ACKNOWLEDGMENTS

This work represents in part the Ph.D. dissertation (Q.N.N.) in Chemistry from Cleveland State University. Thanks to D. Johnson, from NASA Glenn, for analytical lab analyses and D. Humphrey, from Arctic Slope Regional Corporation (ASRC), for experimental assistance with the furnace setup and maintenance. Advice from Prof. V. Stolyarova on the Gurvich et al. tables is appreciated. This work was supported by the NASA Glenn Independent Research & Development program and the NASA Transformational Tools and Technology program.

value (Golden and Opila)

7.5 × 10 g/cm ·s 0.046 cm/s 2

■

Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

C. W. Bauschlicher Jr.: 0000-0003-2052-332X N. S. Jacobson: 0000-0002-9177-4129 Present Addresses §

Summer Faculty Fellow at NASA Glenn. East Central University, Ada, Oklahoma 74820, United States. ∥ University of Virginia, Charlottesville, Virginia 22904, United States. Notes

The authors declare no competing financial interest. 9516



Article

Spectra Using Density Functional Force Fields. J. Phys. Chem. 1994, 98, 11623−11627. (18) Bartlett, R. J. Many-Body Perturbation Theory and Coupled Cluster Theory for Electron Correlation in Molecules. Annu. Rev. Phys. Chem. 1981, 32, 359−401. (19) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. A Fifth-Order Perturbation Comparison of Electron Correlation Theories. Chem. Phys. Lett. 1989, 157, 479−483. (20) Knowles, P. J.; Hampel, C.; Werner, H. J. Coupled Cluster Theory for High Spin, Open Shell Reference Wave Functions. J. Chem. Phys. 1993, 99, 5219−5227. See also Knowles, P. J.; Hampel, C.; Werner, H. J. Erratum. J. Chem. Phys. 2000, 112, 3106. (21) Dunning, T. H., Jr. Gaussian Basis Sets For Use in Correlated Molecular Calculations. I. The Atoms Boron through Neon and Hydrogen. J. Chem. Phys. 1989, 90, 1007−1023. (22) Kendall, R. A.; Dunning, T. H., Jr; Harrison, R. J. Electron Affinities of the First-Row Atoms Revisited. Systematic Basis Sets and Wave Functions. J. Chem. Phys. 1992, 96, 6796−6806. (23) Balabanov, N. B.; Peterson, K. A. Systematically Convergent Basis Sets for Transition Metals. I. All-Electron Correlation Consistent Basis Sets for the 3d Elements Sc−Zn. J. Chem. Phys. 2005, 123, 064107. (24) Helgaker, T.; Klopper, W.; Koch, H.; Noga, J. Basis-Set Convergence of Correlated Calculations on Water. J. Chem. Phys. 1997, 106, 9639−9646. (25) Frisch, M. J.; Trucks, E. A.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, Revision D.01; Gaussian, Inc.: Wallingford, CT, 2013. (26) Werner, H. J.; Knowles, P. J.; Manby, F. R.; Schutz, M.; Cleani, P.; Knizia, G.; Korona, T.; Lindh, R.; Mitrushenkov, A.; Rauhut, G.; et al. MOLPRO, version 2010.1, A Package of Ab-Initio Programs, http://www.molpro.net/ (accessed June 2017). (27) Jmol: An Open-Source Java Viewer for Chemical Structures in 3D. http://www.jmol.org/ (accessed June 2017). (28) Ayala, P. Y.; Schlegel, H. B. 1998. Identification and Treatment of Internal Rotation in Normal Mode Vibrational Analysis. J. Chem. Phys. 1998, 108, 2314−2325. (29) Pitzer, K. S.; Gwinn, W. D. Energy Levels and Thermodynamic Functions for Molecules with Internal Rotation I. Rigid Frame with Attached Tops. J. Chem. Phys. 1942, 10, 428−440. (30) Bale, C. W.; Chartrand, P.; Degterov, S. A.; Eriksson, G.; Hack, K.; Ben Mahfoud, R.; Melançon, J.; Pelton, A. D.; Petersen, S. FactSage Thermochemical Software and Databases. CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 2002, 26, 189−228. (31) Glemser, O.; Wendlandt, H. G. Gaseous Hydroxides. In Advances in Inorganic Chemistry and Radiochemistry; Emeléus, H. J., Sharpe, A. G., Eds.; Academic Press, 1963; pp 215−258. (32) Belton, G. R.; McCarron, R. L. The Volatilization of Tungsten in the Presence of Water Vapor. J. Phys. Chem. 1964, 68, 1852−1856. (33) Merten, U.; Bell, W. E. The Transpiration Method. In The Characterization of High Temperature Vapors; Margrave, J. L., Ed.; John Wiley & Sons: New York, 1963; pp 91−114. (34) Anzelmo, J. A.; Lindsay, J. R. X-Ray-Fluorescence Spectrometric Analysis of Geologic Materials 2. Applications. J. Chem. Educ. 1987, 64, A200−A204. (35) Drowart, J.; Goldfinger, P. Investigation of Inorganic Systems at High Temperature by Mass Spectrometry. Angew. Chem., Int. Ed. Engl. 1967, 6, 581−648. (36) Lewis, G. N.; Randall, M. Thermodynamics, second ed.; Pitzer, K. S., Brewer, L., Eds.; McGraw-Hill: New York, 1961; pp 419−448. (37) Geiger, G. H.; Poirier, D. R. Transport Phenomena in Metallurgy; Addison-Wesley Publishing Co.: Reading, MA, 1973; p 532. (38) Welty, J.; Wicks, C. E.; Rorrer, G. L.; Wilson, R. E. Fundamentals of Momentum, Heat and Mass Transfer, 5th ed.; Wiley, 2008. (39) Ueno, S.; Jayaseelan, D. D.; Ohji, T. Development of OxideBased EBC for Silicon Nitride. Int. J. Appl. Ceram. Technol. 2004, 1, 362−373.

(40) Svehla, R. A. Estimated Viscosities and Thermal Conductivities of Gases at High Temperatures, NASA TR-R-132, 1962. (41) Opila, E. J.; Myers, D. L. Alumina Volatility at Elevated Temperatures. J. Am. Ceram. Soc. 2004, 87, 1701−1705. (42) Opila, E. J.; Hann, R. E., Jr. Paralinear Oxidation of CVD SiC in Water Vapor. J. Am. Ceram. Soc. 1997, 80, 197−205.

9517


Computational and Experimental Study of Thermodynamics of the

Recommend Documents