QuynhGiao N. Nguyen

Glenn Research Center, Cleveland, Ohio

Dwight L. Myers

East Central University, Ada, Oklahoma

Nathan S. Jacobson

Glenn Research Center, Cleveland, Ohio

Elizabeth J. Opila

University of Virginia, Charlottesville, Virginia

Experimental and Theoretical Study of

Thermodynamics of the Reaction of

Titania and Water at High Temperatures

NASA/TM—2014-218372

October 2014
NASA STI Program . . . in Profi le

Since its founding, NASA has been dedicated to the 

advancement of aeronautics and space science. The 

NASA Scientifi c and Technical Information (STI) 

program plays a key part in helping NASA maintain 

this important role.

The NASA STI Program operates under the auspices 

of the Agency Chief Information Offi cer. It collects, 

organizes, provides for archiving, and disseminates 

NASA’s STI. The NASA STI program provides access 

to the NASA Aeronautics and Space Database and 

its public interface, the NASA Technical Reports 

Server, thus providing one of the largest collections 

of aeronautical and space science STI in the world. 

Results are published in both non-NASA channels 

and by NASA in the NASA STI Report Series, which 

includes the following report types:

• TECHNICAL PUBLICATION. Reports of 

completed research or a major signifi cant phase 

of research that present the results of NASA 

programs and include extensive data or theoretical 

analysis. Includes compilations of signifi cant 

scientifi c and technical data and information 

deemed to be of continuing reference value. 

NASA counterpart of peer-reviewed formal 

professional papers but has less stringent 

limitations on manuscript length and extent of 

graphic presentations.

• TECHNICAL MEMORANDUM. Scientifi c 

and technical fi ndings that are preliminary or 

of specialized interest, e.g., quick release 

reports, working papers, and bibliographies that 

contain minimal annotation. Does not contain 

extensive analysis.

• CONTRACTOR REPORT. Scientifi c and 

technical fi ndings by NASA-sponsored 

contractors and grantees.

• CONFERENCE PUBLICATION. Collected 

papers from scientifi c and technical 

conferences, symposia, seminars, or other 

meetings sponsored or cosponsored by NASA.

• SPECIAL PUBLICATION. Scientifi c, 

technical, or historical information from 

NASA programs, projects, and missions, often 

concerned with subjects having substantial 

public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientifi c and 

technical material pertinent to NASA’s mission.

Specialized services also include creating custom 

thesauri, building customized databases, organizing 

and publishing research results.

For more information about the NASA STI 

program, see the following:

• Access the NASA STI program home page at 

http://www.sti.nasa.gov

• E-mail your question to help@sti.nasa.gov

• Fax your question to the NASA STI 

Information Desk at 443–757–5803

• Phone the NASA STI Information Desk at

 443–757–5802

• Write to:

 STI Information Desk

NASA Center for AeroSpace Information

 7115 Standard Drive

 Hanover, MD 21076–1320
QuynhGiao N. Nguyen

Glenn Research Center, Cleveland, Ohio

Dwight L. Myers

East Central University, Ada, Oklahoma

Nathan S. Jacobson

Glenn Research Center, Cleveland, Ohio

Elizabeth J. Opila

University of Virginia, Charlottesville, Virginia

Experimental and Theoretical Study of

Thermodynamics of the Reaction of

Titania and Water at High Temperatures

NASA/TM—2014-218372

October 2014

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Acknowledgments

This work represents in part the Ph.D. dissertation (Q. Nguyen) in Chemistry from Cleveland State University. Thanks to

D. Johnson, from NASA Glenn Research Center (GRC), for analytical lab analyses and D. Humphrey from ZIN Technologies, Inc., 

for experimental assistance with the furnace set-up and maintenance. This work was supported by the NASA Glenn Independent 

Research & Development program. Much of the computing for this project was performed at the Oklahoma Supercomputing 

Center for Education and Research (OSCER) at the University of Oklahoma (OU). OSCER Director Henry Neeman, David Akin, 

Senior System Administrator, and Joshua Alexander, HPC Application Software Specialist all provided valuable technical advice. 

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

Available electronically at http://www.sti.nasa.gov

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2014-218372 1 

Experimental and Theoretical Study of Thermodynamics of the 

Reaction of Titania and Water at High Temperatures 

QuynhGiao N. Nguyen 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Dwight L. Myers 

East Central University 

Ada, Oklahoma 74820 

Nathan S. Jacobson 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Elizabeth J. Opila 

University of Virginia 

Charlottesville, Virginia 22904 

Abstract 

The transpiration method was used to determine the volatility of titanium dioxide (TiO2) in water 

vapor-containing environments at temperatures between 1473 and 1673 K. Water contents ranged from 

0 to 76 mole % in oxygen or argon carrier gases for 20 to 250 hr exposure times. 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 to extract an enthalpy and entropy of formation. The geometry and vibrational 

frequencies of TiO(OH)2(g) were computed using B3LYP density functional theory, and the enthalpy of 

formation was computed using the coupled-cluster singles and doubles method with a perturbative 

correction for connected triple substitutions [CCSD(T)]. Thermal functions are calculated using both a 

structure with bent and linear hydroxyl groups. Calculated second and third heats show closer agreement 

with the linear hydroxyl group, suggesting more experimental and computational spectroscopic and 

structural work is needed on this system. 

Introduction 

Many common oxides react with water vapor at high temperatures to form hydroxide and 

oxyhydroxide species (Refs. 1 and 2). Precise thermodynamic data are available for some of these species 

such as the Group I and Group II hydroxides (Ref. 3), Si(OH)4(g) (Refs. 4 to 6) and CrO2(OH)2(g) 

(Ref. 7). However, data are unavailable for many important 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-to-weight 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 
NASA/TM—2014-218372 2 

matrix. Most of the studies examine the interaction of Ti metal atoms with H2O. Kauffman et al. (Ref. 8) 

see evidence for HxTi(OH)2 and Ti(OH)x. Zhou et al. (Ref. 9) suggest H2Ti(OH)2. Wang and Andrews 

(Ref. 10) see evidence of Ti(OH)2 and Ti(OH)4. Shao et al. (Ref. 11) 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 attack of rutile in a 30 mass percent H2O/Air environment at 1773 K 

(Ref. 12) in the form of weight loss and etch pits. They also discuss the reaction of TiO2 in hot water, 

which is attributed to the formation of Ti(OH)4 (Ref. 13). 

A generalized reaction for TiO2(s) with oxygen and water vapor is: 

 TiO2(s) + xO2(g) + yH2O(g) = TiO(2+2x+y)H(2y) (g) (1) 

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 (Refs. 5, 7, 14, and 15). The transpiration method as reviewed by Merton and Bell 

(Ref. 16), 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. 

In this study we supplement these experimental measurements with computational studies. The goal 

of this study is to utilize both approaches to determine the thermodynamics of the TiO2 and H2O 

interactions at elevated temperatures. 

Experimental Procedure 

TiO2 Pellets 

Acros Organics, 99.999 percent pure titanium oxide, predominately rutile, powder was cold-pressed in a 

1/4 in. 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 hr. The TiO2 pellets were weighed and the 

density was calculated to be 3.75 g/cc, corresponding to 88 percent 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 1. 

The grains were still rutile, as confirmed by x-ray diffraction, but significant grain growth occurred. 

 

Figure 1.—View of starting pellet. (a) Before the transpiration experiments. (b) After the transpiration 

experiments, showing the extensive grain growth. 
NASA/TM—2014-218372 3 

Transpiration System 

The transpiration system is shown schematically in Figure 2. The cell is made out of platinum-20 

percent 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). 

Furnace Set-Up 

The transpiration system used a furnace with molydisilicide heating elements (Applied Test Systems, 

Inc.) and a 99.8 percent pure alumina furnace tube. Deionized water was introduced through the bottom of 

the transpiration gas train into the carrier gas via a peristaltic pump. The liquid water flow rate ranged from 

0.5 to 9.3 ml/hr 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 pre-heating 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 percent purity) condensation (collection) tubes, as shown in red on Figure 2. 

Figure 2.—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. 

 

 

Titanium 

Dioxide

Hot Zone

temperature

Before After

#1

#2

#3
NASA/TM—2014-218372 4 

From our previous studies on the Cr-O-H system (Ref. 7), 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 will be referred to as the main straight condensation tube where the primary condensate 

was collected. The end that sat in the hot zone of the furnace had an internal beveled edge that snuggly fit 

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 2. 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 to 1.00 atm (730 to 

763 Torr) during the two years of testing. This capacitance monitor was verified by a separate barometric 

standard (NASA Glenn Aircraft Hanger Barometer, http://barometer.grc.nasa.gov/cgi-bin/barometer.cgi). 

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. 

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 was quantitatively analyzed 

using inductively coupled plasma atomic emission spectroscopy (ICP-AES) (Varian Vista-Pro, Axial 

configuration). The fittings and exhaust waters contained no visible deposits. The fittings were digested in 

a 5 percent (by volume) hydrochloric acid (HCl) + 2 percent hydrofluoric acid (HF) solution for 2 to 3 hr. 

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 m, 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 parts HCl + 

1 part nitric acid (HNO3)) for 2 hr followed by a rinse with concentrated HF. Based on the analysis of the 

first several runs that contained only Ar(g) and H2O(g), the black deposits collected from the aqua regia 

soak were filtered and discarded, since they contained no Ti deposits. This was confirmed with 

wavelength dispersive x-ray fluorescence (WDXRF). The runs exposed to oxygen formed reaction 

products from the TiO2 pellets but also from the Pt/Rh reaction chamber. The latter was a black deposit, 

likely platinum oxide (PtO) as indicated by WDXRF, that was strongly bonded to the Ti-condensate. All 

runs that contained oxygen went through a second series of analysis in which an acidic flux (fusion) step 

through the use of potassium hydrogen sulfate (pyrosulfate) was used in order to extract the Ticondensate. This mixture was heated over a Bunsen burner until it liquefied, thus converting any 

remaining TiO2(s) into a soluble solution that can be analyzed in the ICP-AES. 

The presence of a black deposit was a concern. The first several runs’ black deposits (PtO) were 

filtered and dried after the acidic flux (fusion) extraction and characterized by WDXRF to confirm the 

absence of Ti. The typical weight of these black deposits was estimated to be 10 to 20 mg. Since the 
NASA/TM—2014-218372 5 

WDXRD sensitivity to Ti is typically about 0.1 percent (Ref. 17), it is possible that up to 20 g 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 g Ti. The potential for trace 

concentrations of Ti in the black deposit must be considered a possible source of error. However, black 

deposits were not formed in experiments run with only argon gas and hence more confidence is given to 

data from these runs. 

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 percent solution of HCl followed by a deionized 

water rinse, drying and were stored 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 to several micrograms, as found in previous studies (Refs. 5 and 7). The amount of Ti in the 

condensate ranged between 9 and 262 μg. 

Calculations With Experimental Data to Identify the Species and 

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 (1). The same calculation methods were used in previous studies 

(Refs. 5 and 7). The vapor pressure of the volatile Ti-O-H species, PTi-O-H, is given by: 

V

n



Ti cell

Ti O H

RT P    (2) 

Here 

 is the molar rate of Ti from the reaction cell, R is the ideal gas constant, Tcell is the measured 

temperature inside the cell, and  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 t

m

n

Ti

Ti Ti  (3) 

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: 

  O H O Ti O H

tot

cell

2 2

RT  	 	 	   n n n n

P

V Ar (4) 

Here Ptot is the total pressure. The last quantity in Equation (4), 

	, is the same as
  and is much 

smaller than the others. 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 and 	. Once the molecule was identified, vapor 

pressures were determined. Second and third law methods were then used to derive thermodynamic 

parameters (Ref. 18). The second law method gives a heat of reaction, 


 , at the average temperature 

of measurement, Tav, using the van’t Hoff equation. 
NASA/TM—2014-218372 6 

 

R

H

1

lnK o p r T av

T

d

d 
  






 



 (5) 

Here Kp is the equilibrium constant for reaction (1) 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: 

  	

T

298

p o r 298 o rHT H C dT (6) 

The Gibbs energy function (gef) is given by 

gef GT H /T o

298.15 o 298.15   (7) 

The standard entropy, heat capacity, and Gibbs energy function were all calculated from the statistical 

mechanics methods, using calculated vibrational frequencies (Ref. 19). If good Gibbs energy functions 

are determined, the third law method (Ref. 18) can be used to derive the enthalpy at 298.15 K, using 

Equation (8) for each data point. 

         Rln P H Ti O H o T 
  gef298.15  TiOH  rxn 298.15   (8) 

Results 

Identity of the Ti-O-H Species 

A total of 51 tests were conducted over a temperature range of 1473 to 1673 K and are listed in 

Appendix A. 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 

section, 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 Equation (1), as 

shown in Figure 3. At the highest temperature, the amount of Ti collected was the largest, leading to less 

scatter in the data. 

A similar analysis was applied to the data at 1573 K. At this temperature, when the H2O content was 

held at 24 percent and the O2 content was varied the value of x is 0.070.01; when O2 content was held at 

34 percent and the H2O content is varied the value of y was 0.850.09. At constant P(H2O), variation in 

P(O2) does not change the amount of Ti-O-H(g) formation suggesting the coefficient, x in reaction (1) is 

zero. At constant P(O2), the amount of Ti-O-H(g) formation varies with [P(H2O)]1

, suggesting the 

coefficient, y in reaction (1) is one. Thus results at 1573 and 1673 K suggest the primary reaction is: 

 TiO2(s) + H2O(g) = TiO(OH)2(g) (9) 

Figure 4 is a plot of all the data versus P(H2O). Note the slopes are all close to one, confirming the 

stoichiometry of reaction (9). The data obtained at 1473 K show a larger amount of scatter due to the very 

small amount of downstream deposit collected. 
NASA/TM—2014-218372 7 

Figure 3.—Measured partial pressure of Ti-O-H at 1673 K. O2(g) or H2O(g) is held 

constant at the values indicated. 

Figure 4.—Vapor pressure as a function of P(H2O) for 1473, 1573, and 1673 K. 

-7.8

-7.6

-7.4

-7.2

-7

-6.8

-1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0

log (P(Ti-O-H)/bar)

log(P(O2)/bar or P(H2O)/bar)

1400C Dependence on P(O2) and P(H2O)

x = 0.01  0.07

33% H2O

y = 0.92  0.07

17% O2
NASA/TM—2014-218372 8 

Derivation of the Gibbs Energy Function for TiO(OH)2(g) 

Shao et al. (Ref. 11) have conducted infrared (IR) matrix isolation spectroscopy on the products of 

TiO2(s) + H2O and observed TiO(OH)2. They also conducted density-functional theory (DFT) 

calculations, which are in good agreement with their experimental results. This study by Shao et al. 

provides the necessary molecular parameters to calculate the Gibbs energy function. Figure 5 is their 

derived structure with angles, bond lengths and C2v symmetry. Table I lists their calculated vibrational 

frequencies. In addition, we conducted an optimization and frequency calculation using the Gaussian 09 

program, revision B.01 (Ref. 20), and the B3LYP density functional with the cc-pVTZ+d basis set. Our 

results are also listed in Table I. As can be seen, our calculated frequencies are close to those of Shao et al. 

We also consider the alternate structure in Figure 5(b). We use the 0.9610–9 cm bond length for the 

O-H bond. We assume the calculated vibrational frequencies are the same for both structures and 

calculate the thermal functions for both structures. 

The standard equations from statistical mechanics were used to calculate the entropy (So

(298)) and 

the Gibbs energy function (gef) (Ref. 19). Using the geometry in Figure 5, the moment of inertia was 

calculated to be 4.834610–114 cm6

/g3 and the symmetry number is 2. The molecule is a singlet, so there is 

no electronic contribution. The structure in Figure 5(a) is expected to have hindered internal rotations and 

the structure in Figure 5(b) is not expected to have any internal rotations. First consider the structure in 

Figure 5(a). The partition function of each internal rotation is given by: 

 

1/ 2 38 10 2.7934 I T

n

Qf  r (10) 

Figure 5.—(a) Structure of TiO(OH)2 from (Ref. 11). (b) Alternate structure with linear –OH groups.

TABLE I.—VIBRATIONAL FREQUENCIES 

Vibrational 

mode 

Calculated frequency by DFT 

(Ref. 11), cm–1 

Calculated frequency 

(this study), cm–1 

a1 3907.5 3885.2 

b2 3904.3 3882.1 

a1 1055.2 1082.7 

b2 784.3 805.3 

a1 678.6 700.2 

b1 537.8 529.1 

a2 515.1 511.7 

b2 474.0 510.3 

a1 460.1 509.0 

b2 225.0 234.9 

a1 192.8 201.0 

b1 53.3 49.1 
NASA/TM—2014-218372 9 

Here Ir is the reduced moment of inertia for the –OH group, n is the symmetry number, and T is the 

absolute temperature. The reduced moment of inertia is defined by: 
















   



3

1

2

1

i i

i r I

A I A (11) 

Here A is the moment of inertia of the –OH groups,  is the direct cosine of between the internal axis of 

rotation and the particular axis, and Ii is the moment about that axis. For this planar molecule there are 

only two direction cosines. The reduced moment of inertia is thus calculated to be 1.36810–40 gm-cm2

. 

As in the case of CrO2(OH)2(g), two hindered internal rotors were assumed (Ref. 7). It is difficult to 

estimate the potential barrier to internal rotation, but we assume 12.6 kJ/mol (3 kcal/mol) here. Using the 

Tables of Pitzer and Gwinn (Ref. 21), the corrections for hindered rotations were determined. Given the 

predicted low potential barrier, the contribution from hindered internal rotations is not too much different 

than that for free internal rotations. Table II gives the contributions from the calculation for So

(298) for 

both structures. 

The heat capacity can be determined from the standard statistical mechanics calculations (Ref. 20). 

These are listed in Table III(a) for the structure in Figure 5(a) and Table III(b) for the structure in 

Figure 5(b). 

Table III(a) Heat capacities for TiO(OH)2(g) structure 5(a). The total is obtained by summing the 

translational (2.5R) and rotational (1.5R), where R is the gas constant and the vibrational and hindered 

internal rotational contributions. Table III(b) Heat capacities for TiO(OH)2(g) structure 5(b). The total is 

obtained by summing the translational (2.5R) and rotational (1.5R), where R is the gas constant and the 

vibrational and hindered internal rotational contributions. 

TABLE II.—CALCULATION OF SO(298) FOR TIO(OH)2(G) 

Contribution So(298) J/mol-K 

Structure 5(a) 

So(298) J/mol-K 

Structure 5(b) 

Translation 165.945 165.945 

Rotation 100.42 100.589 

Vibration 49.713 49.713 

Hindered internal rotations (2) 27.872 ------------ 

Total 343.95 316.247 

TABLE III(a).—HEAT CAPACITIES FOR TIO(OH)2(g) STRUCTURE 5(a) 

Temperature, 

K 

Vibrational Two hindered rotations Total Cp (J/mol-K) 

300 51.428 37.579 122.263 

400 61.290 36.582 131.127 

500 67.530 36.582 137.367 

600 71.656 35.750 140.663 

700 74.595 34.919 142.769 

800 76.872 34.919 145.047 

900 78.773 34.919 146.948 

1000 80.443 34.586 148.285 

1100 81.952 34.420 149.628 

1200 83.334 34.420 151.010 

1300 84.603 34.254 152.112 

1400 85.768 34.254 153.278 

1500 86.836 34.087 154.179 

1600 87.812 34.087 155.156 

 
NASA/TM—2014-218372 10 

TABLE III(b).—HEAT CAPACITIES FOR 

TIO(OH)2(g) STRUCTURE 5(b) 

Temperature, 

K 

Vibrational Total Cp (J/mol-K) 

300 51.428 84.684 

400 61.290 94.546 

500 67.530 100.786 

600 71.656 104.912 

700 74.595 107.851 

800 76.872 110.128 

900 78.773 112.029 

1000 80.443 113.699 

1100 81.952 115.208 

1200 83.334 116.590 

1300 84.603 117.859 

1400 85.768 119.024 

1500 86.835 120.092 

1600 87.812 121.068 

The calculated Gibbs energy functions (gef) are similarly calculated, using the standard equation from 

statistical mechanics (Ref. 19). We converted the gef functions referenced to 0 K (gef0) to ones referenced 

to 298 K (gef298). In order to account for the hindered internal rotations, the tables in Pitzer and Gwinn 

(Ref. 21) were again used. In this case, we applied the following relations to the internal rotations: 

T

T o T T o T o S

T

H H

T

H TS H

T

G H 0  




 



   




 



    




 



  gef  (12) 

Each of the quantities on the right side of Equation (10) is available in the tables of Pitzer and Gwinn 

(Ref. 21). Finally the correction to 298 K is given by: 






 



   




 



   T

H H

T

G H 298 T o 298 o gef (13) 

Table IV(a) and (b) gives the calculated Gibbs energy functions for the structures in Figure 5(a) and (b), 

respectively. 

TABLE IV(a).—CALCULATED GIBBS ENERGY FUNCTIONS FOR THE STRUCTURE IN FIGURE 5(a) 

T (K) gef298 

(translation) 

gef298 (external 

rotation) 

gef298 (vibrations) gef298 (two internal rotations) gef298 (total) 

1400 –181.691 –109.891 –100.901 –38.636 –431.119 

1500 –182.830 –110.575 –105.06 –39.576 –438.041 

1600 –183.913 –111.225 –109.062 –40.417 –444.616 

1700 –184.946 –111.844 –112.916 –41.244 –450.949 

TABLE IV(b).—CALCULATED GIBBS ENERGY FUNCTIONS FOR 

THE STRUCTURE IN FIGURE 5(b) 

T (K) gef298 

(translation) 

gef298 (external 

rotation) 

gef298 (vibrations) gef298 (total) 

1400 –181.691 –110.691 –100.901 –392.652 

1500 –182.830 –110.744 –105.06 –398.634 

1600 –183.913 –111.394 –109.062 –404.37 

1700 –184.875 –112.013 –112.916 –409.875 

Data for TiO2(s) and H2O(g) were taken from the IVTAN tables (Ref. 22) to calculate the gef needed for 

the third law calculations in the next section. 
NASA/TM—2014-218372 11 

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 6. 

Heat capacities are needed in order to obtain an enthalpy of reaction at 298.15 K. Equation (6) is 

applied for this and yields H 233.3 20 o 
r 298   kJ/mol with thermal functions for the structure in 

Figure 5(a) and H 251 20 o 
r 298   kJ/mol with thermal functions for the structure in Figure 5(b). Ideally 

the plot in Figure 6 could be used to extract an entropy, but we felt the scatter of the data was too great for 

a reliable number. Instead we take the calculated value in Table IV of S 343.95J/mol K o

298   with 

thermal functions for the structure in Figure 5(a) and S 316.247J/mol K o

298   with thermal functions for 

the structure in Figure 5(b). Finally the third law method was used to extract an enthalpy of reaction at 

298 K, as described in the previous section. The value was H 403 13 o r 298   kJ/mol with thermal 

functions for the structure in Figure 5(a) and H 339 9 o 
r 298   kJ/mol with thermal functions for the 

structure in Figure 5(b). Clearly there is a large disparity regardless of which thermal functions are used, 

although the thermal functions for the structure in Figure 5(b) give somewhat closer results between the 

second and third law methods. The data are summarized in Table V. A similar disparity was found in our 

CrO2(OH)2(g) studies. These suggest that additional work is needed to determine the structure and 

develop the Gibbs energy functions for transition metal hydroxides. 

Figure 6.—Van’t Hoff plot for the reaction of TiO2(s) and H2O(g). 

TABLE V.—SUMMARY OF EXPERIMENTAL 

ENTALPIES OF REACTION 

Method 


 (kJ/mol) 

 Thermal functions 

from Fig. 5(a) 

Thermal 

functions from 

Fig. 5(b) 

Second law 20520 25120 

Third law 40313 3399 
NASA/TM—2014-218372 12 

Computational Studies 

In order to strengthen the experimental aspect of this study, some computational studies were 

conducted on the TiO(OH)2 species. The Gaussian 09 program, revision B.01, was used for all 

calculations reported here (Ref. 21). A calculation of the enthalpy of formation of TiO(OH)2(g) was 

performed using a computational scheme which closely followed the technique employed previously by 

Opila et al. in computing the enthalpy of formation of CrO2(OH)2(g) (Ref. 7). Geometries and harmonic 

vibrational frequencies for the participating species were computed using the B3LYP density functional 

method with the 6-311++G(d,p) basis set, which is of triple- quality and includes diffuse and 

polarization functions on all atoms. The B3LYP/6-311++G(d,p) geometries and frequencies obtained 

were used for all subsequent energy calculations. In the reaction energy computations, electron 

correlation was accounted for by using a configuration interaction scheme with successive steps 

incorporating first coupled-cluster singles and doubles [CCSD], followed by a coupled-cluster singles and 

doubles method with a perturbative correction for connected triple substitutions [CCSD(T)]. For the 

coupled-cluster computations, the Bauschlicher Atomic Natural Orbital basis set (Ref. 23) was used for 

Ti, and for H and O the cc-pVTZ basis set was employed. Basis sets not available in the Gaussian 

Package were obtained from the Basis Set Exchange at the Environmental Molecular Science Laboratory 

at Pacific Northwest National Laboratory (Refs. 24 and 25). 

The effect of inclusion of the titanium 3s and 3p core orbitals in the correlation procedure was 

computed using second-order Møller-Plesset perturbation (MP2) theory in conjunction with the cc-pVTZ 

basis for H and O and a modified Bauschlicher ANO set for Ti. The Bauschlicher ANO basis set was 

modified by decontracting the outermost six s, seven p, and seven d functions. A correction for basis-set 

incompleteness was estimated by computation of large-basis-set MP2 energies using a completely 

decontracted Bauschlicher ANO basis set on Ti and and the aug-cc-pVQZ set on H and O. Scalar 

relativistic effects were accounted for at the MP2 level using the Douglas-Kroll-Hess second-order 

relativistic correction. For Ti, the Bauschlicher ANO set, modified by decontracting the entire s and 

p spaces, was employed, and the cc-pVTZ_DK set was used for H and O. Temperature corrections 

H°298.15 - H°0 for TiO(OH)2(g) were computed using the B3LYP/6-311++G(d,p) harmonic vibrational 

frequencies, employing standard formulas from statistical mechanics, and employing a free rotor 

treatment of the internal rotation of the hydroxide groups. These calculations were all done for the 

structure with the bent –OH group in Figure 5(b). However, the heat of formation should be similar, 

regardless of which structure these calculations are based on as the Ti-O skeleton dominates. Temperature 

corrections for TiO2(g) and H2O(g) were taken from the JANAF Tables. All computations for this method 

were performed at the OU Supercomputing Center for Education & Research (OSCER) at the University 

of Oklahoma (OU). 

The heat of formation for TiO(OH)2(g) was computed using this scheme from the isogyric reaction: 

 TiO(OH)2(g)TiO2(g)+H2O(g) (14) 

The reaction energy was first computed at 0 K and then converted to a reaction energy at 298.15 K by 

application of temperature corrections: 

H H H (TiO ) H (H O) H (TiO(OH) ) 2 o 2 Thermal o 2 Thermal o

Thermal o r 0 o r 298.15  	 	  (15) 

where o

0 o298.15 o HThermal  H  H . The heat of formation was then obtained from the expression: 

o 2 r T o 2 f T o 2 f T o f HT(TiO(OH) )  H (TiO ) 	 H (H O) H (16) 

 
NASA/TM—2014-218372 13 

TABLE VI.—COMPUTATION OF fH°0 AND fH°298 FOR TiO(OH)2 FROM REACTION (14) 

 Computational Increments E/kJ mole–1

 Ee[HF]/kJ mol–1 358.101 

 [MP2]/kJ mol–1 –115.812 

 [CCSD]/kJ mol–1 –264.317 

 [CCSD(T) ]/kJ mol–1 224.920 

 [core]/kJ mol–1 +38.089 

 [basis]/kJ mol–1 +10.920 

 [rel]/kJ mol–1 –18.892 

 [ZVPE]/kJ mol–1 –5.177 

 

 rH0 = 257.221 kJ mol–1 

 

 rH298 = 259.700 kJ mol–1 

 

Data source IVTAN [22] IVTAN [22] 

T/K 298.15 0 

fH° [H2O]= –241.826 kJ mol–1 –238.921 kJ mol–1 

fH° [TiO2]= –322.856 kJ mol–1 –320.000 kJ mol–1 

 

fH°[ TiO(OH)2]= –819.424 ± 49.856 kJ mol–1 –816.142±49.856 kJ mol–1 

for T = 0 K and T = 298.15 K, using the literature values for the heats of formation of TiO2(g) and H2O(g) 

found in the literature (Ref. 23). The increments in the reaction energy are the changes in the computed 

energy in going from HF  MP2, MP2CCSD, and CCSDCCSD(T), and are designated as e.g., 

[MP2], etc. In addition, the corrections for frozen core electrons, incompleteness of basis sets, and the 

relativistic correction were computed in subsequent steps. A correction for the zero-point vibrational 

energy was also computed. The energy increments, the calculated enthalpies of reaction, and the enthalpy 

of formation for TiO(OH)2(g) as calculated using the composite method are given in Table VI. Errors are 

estimated for each correction and taken from the IVTAN reported tolerances for H2O(g) and TiO2(s) 

(Ref. 22). The deltas for the steps arriving at the final enthalpy of reaction were larger than for the same 

procedure as used by Opila, et al. (Ref. 7) in the computation of the enthalpy of formation of 

CrO2(OH)2(g). Therefore the error for this result is estimated as the square root of the squares of the 

normal expected precision in the method (Ref. 7) with the differences for the core, basis, and relativistic 

steps in the method added to the uncertainty, and including of course the published uncertainties in the 

enthalpies of formation for TiO2(g) and H2O(g). 

Discussion 

Clearly the determination of thermochemical data for TiO(OH)2(g) is challenging both experimentally 

and theoretically. Experimentally the amount of material collected was very small and the insoluble black 

deposit could contain some Ti, resulting in uncertainty whether all the Ti was collected. Theoretically, 

composite quantum chemical methods are still developing for the transition metals. 

Table VII compares the experimental and calculated enthalpies of formation and standard entropies. 

These quantities span a range of values and at this point we can only report a range of the enthalpy of 

formation. The thermal functions calculated for the structure in Figure 5(b) seem to give more consistent 

data. 

Figure 7 shows a plot of experimental equilibrium constants as reported in Figure 6. We could not 

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) (Refs. 12 and 26). 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 (Ref. 27): 
NASA/TM—2014-218372 14 

L

D P

D

L J i i

i RT

0.664

0.5 0.33









































  



  (17a) 

For turbulent flow this expression only changes slightly to (Ref. 28): 

L

D P

D

L J i i

i RT

0.0365

0.8 0.33









































  



  (17b) 

Table VII gives the meaning of each of these variables and values for this estimation of vapor pressure 

from the studies of Ueno (Ref. 12) and Opila and Golden (Ref. 27). 

Figure 7 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; 

however previous work has shown that equilibrium vapor pressures describe these processes (Refs. 31 

and 32). 

TABLE VII.—EXPERIMENTAL AND CALCULATED ENTHALPIES OF FORMATION AND STANDARD ENTHALPIES 

 Method 


 (kJ/mol) So

(298) (J/mol-K) 

 Thermal functions 

from Fig. 5(a) 

Thermal 

functions from 

Fig. 5(b) 

Thermal functions 

from Fig. 5(a) 

Thermal 

functions from 

Fig. 5(b) 

Experimental Second law –98555 –93455 

 Third law –78320 –84720 

Theoretical B3LYP DFT 353.95 316.247 

 CCSD(T) –82050 

TABLE VIII.—VALUES TO ESTIMATE VAPOR PRESSURE FROM VAPOR FLUX DATA 

Quantity Value (Ueno) Value (Opila and Golden) 

Measured vapor flux, J 7.510–9 g/cm2

-s 1.20910–7 g/cm2-s 

Free stream velocity,  0.046 cm/s (Ref. 30) 1.75104 cm/s 

Density of air: H2O mixture,  1.23910–4 g/cm3 1.45110–4 g/cm3 

Viscosity,  6.01410–4 g/cm-s (Ref. 30) 5.24610–4 g/cm-s (Ref. 30) 

Characteristic dimension, L 2.553 cm 1 cm 

Gas phase diffusivity for TiO(OH)2, Di 2.046 cm2/sec 1.544 cm2/sec 

Gas constant, R 82.06 cm3-atm/mole-K 82.06 cm3-atm/mole-K 

Absolute temperature, T 1773 K 1513 K 
NASA/TM—2014-218372 15 

Figure 7.—Plot of pressure of TiO(OH)2(g) versus inverse temperature at P(H2O) = 1 

bar, calculated using theoretically derived Gibbs energy functions and the third law 

experimental enthalpy above. The datapoints are extracted P(TiO(OH)2) from 

boundary layer limited vaporization studies. 

Conclusions 

The interaction of TiO2 and H2O(g)/O2(g) at temperatures from 1473 to 1673 K has been studied 

experimentally with the transpiration method and theoretically with quantum chemistry composite 

methods. 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. 

The geometry and vibrational frequencies of TiO(OH)2(g) were also computed using B3LYP density 

functional theory, and the enthalpy of formation was computed using the coupled-cluster singles and 

doubles method with a perturbative correction for connected triple substitutions [CCSD(T)]. Considerable 

spread was found between the second and third law enthalpy values. There appears to be some difficulty 

determining reliable Gibbs energy functions for this system, indicating a strong need for experimental and 

computational structure and spectroscopic studies. A comparison of the equilibrium constants from this 

experimental study to equilibrium constants extracted from studies of boundary layer limited vaporization 

showed some disparity. More studies are also needed to understand this. 

 

NASA/TM—2014-218372 17 

Appendix A.—Raw Data 

Run Temp Temp Time Ar gas flow rate Room 

Ptotal

[Ti] Condensate

Cell 

Flow 

rate

PTi-O-H log PTi-O-H log PO2 log PH2O

 (°C) (K) (hr) (mole/sec) % (mole/sec) % (moles/sec) % Torr (μg Ti) (mole/sec) (mL/sec) atm

Ti016 1400 1673 20 1.86E-04 100% --- 0% --- 0% 754 3.5 1.01E-12 25.7313 5.41E-09 -8.27 --- ---

Ti034 1400 1673 89.4 1.67E-05 17% 7.37E-05 76% 7.08E-06 7% 747 29.2 1.89E-12 13.6201 1.91E-08 -7.72 -0.77 -1.14

Ti032 1401 1674 91 6.69E-05 68% 2.34E-05 24% 7.38E-06 8% 746 29.3 1.87E-12 13.6727 1.88E-08 -7.73 -0.16 -1.12

Ti050 1402 1675 95 --- 0% 1.36E-04 86% 2.31E-05 14% 760 29.4 1.79E-12 21.9078 1.13E-08 -7.95 --- -0.84

Ti033 1400 1673 45 1.68E-05 17% 6.72E-05 67% 1.63E-05 16% 749 30.3 3.90E-12 13.9676 3.84E-08 -7.42 -0.78 -0.79

Ti026 1401 1674 20 1.68E-04 80% --- 0% 4.11E-05 20% 750 31.0 8.99E-12 29.1236 4.24E-08 -7.37 -0.09 -0.71

Ti046 1400 1673 114 2.69E-05 20% 7.40E-05 55% 3.25E-05 24% 750 157.6 8.02E-12 18.5509 5.93E-08 -7.23 -0.70 -0.61

Ti030 1403 1676 42.7 1.68E-05 17% 5.04E-05 51% 3.20E-05 32% 750 49.0 6.66E-12 13.8331 6.62E-08 -7.18 -0.77 -0.49

Ti031 1402 1675 45 4.99E-05 51% 1.66E-05 17% 3.20E-05 32% 742 47.1 6.07E-12 13.8729 6.01E-08 -7.22 -0.30 -0.49

Ti038 1404 1677 43 1.02E-05 6% 1.02E-04 61% 5.54E-05 33% 755 95.1 1.28E-11 23.1474 7.62E-08 -7.12 -1.22 -0.48

Ti047 1402 1675 41 3.70E-05 35% 3.36E-05 32% 3.45E-05 33% 750 58.8 8.31E-12 14.6360 7.81E-08 -7.11 -0.45 -0.48

Ti045 1402 1675 90 3.66E-05 41% 2.33E-05 26% 2.92E-05 33% 742 121.4 7.82E-12 12.5462 8.57E-08 -7.07 -0.39 -0.48

Ti043 1404 1677 68 8.07E-05 62% 6.73E-06 5% 4.23E-05 33% 750 134.0 1.14E-11 18.0924 8.69E-08 -7.06 -0.21 -0.49

Ti022 1401 1674 20 --- 0% 1.35E-04 65% 7.26E-05 35% 752 26.1 7.57E-12 28.8054 3.61E-08 -7.44 --- -0.46

Ti015 1399 1672 20 1.36E-04 65% --- 0% 7.38E-05 35% 756 52.8 1.53E-11 28.8875 7.27E-08 -7.14 -0.19 -0.45

Ti039 1403 1676 24 2.71E-05 17% 5.42E-05 34% 7.69E-05 49% 755 76.8 1.86E-11 21.8972 1.17E-07 -6.93 -0.77 -0.31

Ti051 1401 1674 43 --- 0% 3.98E-05 45% 4.89E-05 55% 739 38.1 5.14E-12 12.5285 5.63E-08 -7.25 --- -0.26

Ti052 1400 1673 52.7 1.99E-05 22% 1.99E-05 22% 4.89E-05 55% 740 107.4 1.18E-11 12.5117 1.30E-07 -6.89 -0.65 -0.26

Ti042 1402 1675 23 --- 0% 6.08E-05 30% 1.42E-04 70% 753 130.8 3.30E-11 28.0655 1.62E-07 -6.79 --- -0.16

Ti041 1402 1675 47 5.39E-05 28% --- 0% 1.42E-04 72% 751 261.8 3.23E-11 27.2237 1.63E-07 -6.79 -0.56 -0.14

Ti023 1401 1674 20 --- 0% 5.38E-05 27% 1.43E-04 73% 750 79.2 2.30E-11 27.3623 1.15E-07 -6.94 --- -0.14

Ti044 1402 1675 43 3.32E-05 20% 6.64E-06 4% 1.23E-04 76% 740 207.3 2.80E-11 22.9940 1.67E-07 -6.78 -0.69 -0.12

O2 gas flow rate H2O flow rate

Run Temp Temp Time Ar gas flow rate Room 

Ptotal

[Ti] Condensate

Cell 

Flow 

rate

PTi-O-H log PTi-O-H log PO2 log PH2O

 (°C) (K) (hr) (mole/sec) % (mole/sec) % (moles/sec) % Torr (μg Ti) (mole/sec) (mL/sec) atm

Ti074 1301 1574 91 5.78E-05 34% 9.52E-05 57% 1.54E-05 9% 758 19.6 1.25E-12 21.7993 7.40E-09 -8.13 -0.46 -1.04

Ti077 1301 1574 114 --- 0% 1.42E-04 90% 1.63E-05 10% 755 18.6 9.46E-13 20.6067 5.93E-09 -8.23 --- -0.99

Ti079 1300 1573 116 5.74E-05 34% 8.44E-05 50% 2.77E-05 16% 753 32.7 1.63E-12 22.0824 9.56E-09 -8.02 -0.47 -0.79

Ti001 1300 1573 168 1.53E-04 81% --- 0% 3.54E-05 19% 754 57.0 1.97E-12 24.486 1.04E-08 -7.98 -0.09 -0.73

Ti004 1300 1573 24 --- 0% 1.48E-04 76% 4.62E-05 24% 757 13.8 3.33E-12 25.1155 9.63E-09 -8.02 --- -0.62

Ti017 1298 1571 115 --- 0% 1.55E-04 76% 4.77E-05 24% 752 39.5 1.99E-12 26.422 9.72E-09 -8.01 --- -0.63

Ti003 1301 1574 114.5 1.52E-04 76% --- 0% 4.77E-05 24% 748 48.1 2.44E-12 26.1536 1.20E-08 -7.92 -0.12 -0.62

Ti062 1301 1574 94 5.08E-05 25% 1.02E-04 51% 4.77E-05 24% 755 43.0 2.65E-12 26.0075 1.32E-08 -7.88 -0.60 -0.62

Ti063 1301 1574 64 3.37E-05 21% 8.77E-05 55% 3.88E-05 24% 752 23.9 2.16E-12 20.9061 1.34E-08 -7.87 -0.68 -0.62

Ti064 1302 1575 66 1.68E-05 10% 1.08E-04 66% 3.98E-05 24% 750 26.0 2.28E-12 21.5144 1.37E-08 -7.86 -0.99 -0.62

Ti058 1301 1574 71 --- 0% 1.35E-04 67% 6.77E-05 33% 752 28.4 2.32E-12 26.4421 1.13E-08 -7.95 --- -0.48

Ti072 1301 1574 46 5.78E-05 34% 5.52E-05 32% 5.88E-05 34% 750 27.6 3.48E-12 22.4808 2.00E-08 -7.70 -0.47 -0.47

Ti073 1301 1574 48 1.69E-05 10% 9.83E-05 56% 6.09E-05 35% 756 29.4 3.55E-12 22.8755 2.01E-08 -7.70 -1.02 -0.46

Ti071 1301 1574 49 1.05E-04 65% --- 0% 5.54E-05 35% 752 24.0 2.84E-12 20.8742 1.76E-08 -7.76 -0.18 -0.46

Ti080 1299 1572 29 8.74E-05 50% 2.69E-05 15% 6.20E-05 35% 750 18.0 3.60E-12 23.0504 2.01E-08 -7.70 -0.30 -0.45

Ti013 1301 1574 20 --- 0% 1.18E-04 61% 7.66E-05 39% 753 11.5 3.33E-12 25.3927 1.70E-08 -7.77 --- -0.41

Ti070 1298 1571 49 6.77E-05 35% --- 0% 1.28E-04 65% 755 63.5 7.51E-12 25.4558 3.80E-08 -7.42 -0.46 -0.18

Ti076 1299 1572 43 --- 0% 5.19E-05 30% 1.23E-04 70% 752 54.9 7.40E-12 22.8145 4.19E-08 -7.38 --- -0.15

O2 gas flow rate H2O flow rate

Run Temp Temp Time Ar gas flow rate Room 

Ptotal

[Ti] Condensate

Cell 

Flow 

rate

PTi-O-H log PTi-O-H log PO2 log PH2O

 (°C) (K) (hr) (mole/sec) % (mole/sec) % (moles/sec) % Torr (μg Ti) (mole/sec) (mL/sec) atm

Ti010 1200 1473 50 --- 0% 1.35E-04 100% --- 0% 750 1.2 1.39E-13 16.4765 1.02E-09 -8.99 --- ---

Ti075 1200 1473 216 1.15E-04 65% 4.73E-05 27% 1.54E-05 9% 754 9.2 3.14E-13 21.6461 1.75E-09 -8.76 -0.19 -1.06

Ti083 1200 1473 250 6.73E-05 34% 1.01E-04 51% 3.00E-05 15% 750 13.5 7.83E-13 24.2700 3.90E-09 -8.41 -0.47 -0.82

Ti084 1200 1473 240 5.04E-05 32% 5.38E-05 34% 5.23E-05 33% 750 26.3 2.03E-12 19.1759 1.28E-08 -7.89 -0.49 -0.48

Ti055 1198 1471 140 --- 0% 1.35E-04 66% 6.92E-05 34% 755 12.0 4.97E-13 24.8659 2.41E-09 -8.62 --- -0.47

Ti068 1200 1473 94 5.89E-05 34% 2.37E-05 14% 9.08E-05 52% 755 23.6 1.57E-12 21.0944 9.01E-09 -8.05 -0.47 -0.28

Ti066 1200 1473 115 2.69E-05 16% 5.38E-05 31% 9.18E-05 53% 750 25.2 3.65E-12 21.1351 2.09E-08 -7.68 -0.81 -0.27

Ti067 1198 1471 118 --- 0% 6.75E-05 35% 1.23E-04 65% 753 35.6 1.75E-12 23.2584 9.08E-09 -8.04 --- -0.19

O2 gas flow rate H2O flow rate

Run Temp Temp Time Ar gas flow rate Room 

Ptotal

[Ti] Condensate

Cell 

Flow 

rate

PTi-O-H log PTi-O-H log PO2 log PH2O

 (°C) (K) (hr) (mole/sec) % (mole/sec) % (moles/sec) % Torr (μg Ti) (mole/sec) (mL/sec) atm

Ti082 1225 1498 138 6.36E-05 34% 6.09E-05 33% 6.09E-05 33% 754 29.6 1.83E-12 22.9638 9.77E-09 -8.01 -0.46 -0.48

Ti057 1250 1523 144 --- 0% 1.35E-04 67% 6.62E-05 33% 754 22.0 8.86E-13 25.3688 4.36E-09 -8.36 --- -0.48

Ti081 1275 1548 119 6.42E-05 34% 6.09E-05 33% 6.17E-05 33% 754 45.4 2.77E-12 23.9154 1.47E-08 -7.83 -0.46 -0.48

O2 gas flow rate H2O flow rate

NASA/TM—2014-218372 19

Appendix B.—Data for Third Law Method 

Temperature 1/T(K)

Delta gef 

Bent OH ln Keq Third Law DH298

Delta gef 

Linear OH Third Law DH298

1673 0.000598 -116.792 -15.1676 406369.1228 -75.93136 338008.6359

1674 0.000597 -116.8 -15.2272 407453.6275 -75.93016 339037.7809

1675 0.000597 -116.807 -16.3695 423617.2617 -75.92895 355146.038

1673 0.000598 -116.792 -15.2736 407843.1928 -75.93136 339482.7058

1674 0.000597 -116.8 -15.3613 409319.9401 -75.93016 340904.0934

1673 0.000598 -116.792 -15.2403 407379.9287 -75.93136 339019.4418

1676 0.000597 -116.815 -15.4115 410533.756 -75.92774 342007.138

1675 0.000597 -116.807 -15.5262 411872.8927 -75.92895 343401.669

1677 0.000596 -116.822 -15.292 409124.4252 -75.92654 340542.3955

1675 0.000597 -116.807 -15.2639 408220.1153 -75.92895 339748.8916

1675 0.000597 -116.807 -15.182 407079.7021 -75.92895 338608.4784

1677 0.000596 -116.822 -15.1507 407155.2632 -75.92654 338573.2335

1674 0.000597 -116.8 -16.0984 419578.7535 -75.93016 351162.9069

1672 0.000598 -116.785 -15.3993 409333.8455 -75.93257 341028.7009

1676 0.000597 -116.815 -15.2511 408297.7968 -75.92774 339771.1787

1674 0.000597 -116.8 -16.1254 419955.0686 -75.93016 351539.2219

1673 0.000598 -116.792 -15.2887 408053.3257 -75.93136 339692.8387

1675 0.000597 -116.807 -15.2905 408590.5246 -75.92895 340119.3009

1675 0.000597 -116.807 -15.3191 408988.8831 -75.92895 340517.6594

1674 0.000597 -116.8 -15.6691 413603.7866 -75.93016 345187.9399

1675 0.000597 -116.807 -15.3506 409428.3905 -75.92895 340957.1668

1574 0.000635 -116.054 -16.3317 396394.6267 -76.05076 333429.0053

1574 0.000635 -116.054 -16.6756 400895.1623 -76.05076 337929.5409

1573 0.000636 -116.047 -16.6636 400471.8127 -76.05196 337559.8188

1573 0.000636 -116.047 -16.7208 401219.4366 -76.05196 338307.4427

1573 0.000636 -116.047 -17.027 405224.2235 -76.05196 342312.2296

1571 0.000637 -116.032 -17.0123 404493.631 -76.05437 341688.8401

1574 0.000635 -116.054 -16.8217 402806.0317 -76.05076 339840.4103

1574 0.000635 -116.054 -16.7178 401447.2943 -76.05076 338481.6729

1574 0.000635 -116.054 -16.723 401514.4916 -76.05076 338548.8702

1575 0.000635 -116.062 -16.7008 401491.5834 -76.04955 338472.3172

1574 0.000635 -116.054 -17.2102 407890.5743 -76.05076 344924.9529

1574 0.000635 -116.054 -16.6687 400804.3337 -76.05076 337838.7123

1574 0.000635 -116.054 -16.6681 400796.9787 -76.05076 337831.3574

1574 0.000635 -116.054 -16.807 402614.169 -76.05076 339648.5476

1572 0.000636 -116.039 -16.6883 400527.971 -76.05317 337669.5873

1574 0.000635 -116.054 -16.9685 404727.0739 -76.05076 341761.4525

1571 0.000637 -116.032 -16.6681 399996.7865 -76.05437 337191.9956

1572 0.000636 -116.039 -16.6474 399993.5658 -76.05317 337135.1821

1473 0.000679 -115.301 -17.7622 387368.6802 -76.17256 329731.9574

1473 0.000679 -115.301 -17.4879 384009.4705 -76.17256 326372.7477

1473 0.000679 -115.301 -17.0893 379127.7265 -76.17256 321491.0037

1471 0.00068 -115.286 -18.7652 399086.633 -76.17497 341553.6487

1473 0.000679 -115.301 -17.884 388859.3672 -76.17256 331222.6444

1473 0.000679 -115.301 -17.0664 378847.1262 -76.17256 321210.4033

1471 0.00068 -115.286 -18.0899 390828.475 -76.17497 333295.4907

1498 0.000668 -115.488 -17.3388 388948.1109 -76.14241 330008.8099

1523 0.000657 -115.674 -18.1444 405924.2396 -76.11226 345671.534

1548 0.000646 -115.86 -16.9341 397299.9433 -76.08211 335723.0067
NASA/TM—2014-218372 20 

References 

1. Jacobson, N., et al., Interactions of water vapor with oxides at elevated temperatures. Journal of 

Physics and Chemistry of Solids, 2005. 66(2-4): p. 471-478. 

2. Meschter, P.J., E.J. Opila, and N.S. Jacobson, Water Vapor Mediated Volatilization of High 

Temperature Materials, in Annual Reviews of Materials Research, D.M. Lipkin, Editor. 2013, 

Annual Reviews, Inc. 

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. 1998, 

Washington, D.C. Woodbury, N.Y.: American Chemical Society; American Institute of Physics for 

the National Institute of Standards and Technology. 

4. Hashimoto, A., The effect of H2O gas on volatilities of planet-forming major elements: I. 

Experimental determination of thermodynamic properties of Ca-, Al-, and Si-hydroxide gas 

molecules and its application to the solar nebula. Geochimica et Cosmochemica Acta, 1992. 56, 

511-532. 

5. Jacobson, N.S., et al., Thermodynamics of gas phase species in the Si-O-H system. Journal of 

Chemical Thermodynamics, 2005. 37(10): p. 1130-1137. 

6. Plyasunov, A.V., Thermodynamic properties of H4SiO4 in the ideal gas state as evaluated from 

experimental data. Geochimica et Cosmochemica Acta, 2011. 75(12): p. 3853-65. 

7. Opila, E.J., et al., Theoretical and experimental investigation of the thermochemistry of 

CrO2(OH)2(g). Journal of Physical Chemistry A, 2007. 111(10): p. 1971-1980. 

8. Kauffman, J.W., R.H. Hauge, and J.L. Margrave, Studies of Reactions of Atomic and Diatomic Cr, 

Mn, Fe, Co, Ni, Cu, and Zn with Molecular Water at 15-K. Journal of Physical Chemistry, 1985. 

89(16): p. 3541-3547. 

9. Zhou, M.F., et al., Reactions of group IV metal atoms with water molecules. Matrix isolation FTIR 

and theoretical studies. Journal of the American Chemical Society, 2000. 122(43): p. 10680-10688. 

10. Wang, X.F. and L. Andrews, Infrared spectra and structures for group 4 dihydroxide and 

tetrahydroxide molecules. Journal of Physical Chemistry A, 2005. 109(47): p. 10689-10701. 

11. Shao, L.M., et al., Reactions of titanium oxides with water molecules. A matrix isolation FTIR and 

density functional study. Chemical Physics Letters, 2001. 343(1-2): p. 178-184. 

12. Ueno, S., et al., Anistropic Behavior of Water Vapor Corrosion of Rutile TiO2 at High Temperature. 

Materials Transactions--JIM, 2004. 45(2): p. 281-283. 

13. Ayers, J.C. and E.B. Watson, Rutile Solubility and Mobility in Supercritical Aqueous Fluids. 

Contributions to Mineralogy and Petrology, 1993. 114(3): p. 321-330. 

14. Glemser, O. and H.G. Wendlandt, Gaseous Hydroxides, in Advances in Inorganic Chemistry and 

Radiochemistry, H.J. Emeléus and A.G. Sharpe, Editors. 1963, Academic Press. p. 215-258. 

15. Belton, G.R. and R.L. McCarron, The Volatilization of Tungsten in the Presence of Water Vapor. 

The Journal of Physical Chemistry, 1964. 68(7): p. 1852-1856. 

16. Merten, U. and W.E. Bell, The Transpiration Method, in The Characterization of High Temperature 

Vapors, J.L. Margrave, Editor. 1963, John Wiley & Sons: New York. p. 91-114. 

17. Anzelmo, J.A. and J.R. Lindsay, X-Ray-Fluorescence Spectrometric Analysis of Geologic Materials. 

Part 2. Applications. Journal of Chemical Education, 1987. 64(9): p. A200-A204. 

18. Drowart, J. and P. Goldfinger, Investigation of Inorganic Systems at High Temperature by Mass 

Spectrometry. Angewandte Chemie-International Edition, 1967. 6(7): p. 581-648. 

19. Lewis, G.N. and M. Randall, Thermodynamics, Revised by K.S. Pitzer and L. Brewer, Second 

Edition, McGraw-Hill, New York, 1961, pp. 419-448. 

20. Frisch, M.J., et al., Gaussian 09, Revision B. 01. 2010, Wallingford, CT: Gaussian, Inc. 

21. Pitzer, K.S. and W.D. Gwinn, Energy Levels and Thermodynamic Functions for Molecules with 

Internal Rotation I. Rigid Frame with Attached Tops. Journal of Chemical Physics 1942. 10, 

pp. 428-440. 
NASA/TM—2014-218372 21 

22. Chekhovskoi, D.V., et al., IVTANTHERMO database on thermodynamic properties of individual 

substances, in NIST special database 5. 1993, CRC Press: Boca Raton. 

23. Bauschlicher, C. Theoretical Studies of the First Transition Row Oxides and Sulfides. Theoretica 

Chimica Acta (1995) 92: 183-198. 

24. Feller, D., The role of databases in support of computational chemistry calculations. Journal of 

Computational Chemistry, 1996. 17(13): p. 1571-1586. 

25. Schuchardt, K.L., et al., Basis set exchange: A community database for computational sciences. 

Journal of Chemical Information and Modeling, 2007. 47(3): p. 1045-1052. 

26. Opila, E.J. and R.A. Golden, unpublished work. 

27. Geiger, G.H. and D.R. Poirier, Transport Phenomena in Metallurgy, Addison-Wesley Publishing 

Co., Reading, MA, 1973, p. 532. 

28. Welty, J., C.E. Wicks, G.L. Rorrer, R.E. Wilson, Fundamentals of Momentum, Heat and Mass 

Transfer, 5th Edition, Wiley, 2008. 

29. Ueno, S., et al., Development of Oxide-Based EBC for Silicon Nitride. Int. J. Appl. Ceram. Tech., 

2004, 1 [4], 362-373. 

30. Svehla, R.A., Estimated Viscosities and Thermal Conductivities of Gases at High Temperatures, 

NASA TR-R-132, 1962. 

31. Opila, E.J. and D.L. Myers, Alumina Volatility at Elevated Temperatures. J. Am. Ceram. Soc. 2004, 

87 [9], 1701-1705. 

32. Opila, E.J. and R.E. Hann, Jr., Paralinear Oxidation of CVD SiC in Water Vapor. J. Am. Ceram. 

Soc. 1997, 80 [1], 197-205.