High-temperature combustion calorimetry III. Enthalpies of formation of titanium oxides

J. Chem. Thermodynamics1974,6,1065-1074

High-temperature III. Enthalpies oxides T. V. CHARLU,

combustion calorimetry of formation of titanium

0. J. KLEPPA,

and T. B. REED

a

Departmentof Chemistryand The JamesFranck Institute, The University of Chicago,Chicago,Illinois 60637, U.S.A. (Received5 February 1974) The enthalpies of formation of TiO,, with x varying from 0.81 through 1.26, and of the oxides Tiz03 and Ti305 have been determined by oxidation to TiO&utile) at 1108 K in a high-temperature microcalorimeter. The results for TiaOB and T&O5 are in excellent agreement with values in the literature, while those for TiO, are significantly more negative than previous data. It is suggested that this difference may be attributed to the enthalpy change in the phase transformation: TiO(u) = TiO(8).

1. Introduction The titanium + oxygen system has been the subject of numerous thermodynamic and structural investigations in recent years. It exhibits a large number of intermediate phases, some of which are highly non-stoichiometric in character.‘1-4) Deviation from stoichiometry is particularly pronounced for the high-temperature modification of TiO, TiO@), which has a homogeneous range which extends from about Ti0,,64 to Ti01.2,. (I, 33‘, 6, These phases have very high concentrations of cation and anion vacancies. When non-stoichiometric TiO@) is annealed below 1170 K, it disproportionates and gives rise to the formation of new phases: for TiO,@) with x c 1.00, the phases formed are Ti,O+TiO(a); for x > 1.00, the phases are TiO(ol) + TiO,(@ with y > x.(‘* 5S7-g) In contrast to TiO@), TiO(a) has a rather narrow range of homogeneity, as have the phases Ti203 and Ti,O,. Ariya et al. (lo) determined the enthalpies of formation of several titanium + oxygen phases with compositions ranging from TiO,.,,, to Ti01.676 by means of bomb calorimetry. They prepared the samples by fusing together carefully ground mixtures of TiH and Ti02, in vacuum, in Carborundum capsules at 1470 to 1570 K. However, it is not clear whether they quenched their samples. Prior to this, Humphrey (11) had similarly determined the enthalpies of formation of the stoichiometric compounds TiO, T&O,, Ti,O,, and TiOz by bomb calorimetry, while Mah et aZ.(12) had obtained an improved and more precise value of AH,“(298.15 K) for TiO,(rutile) by the same method. In these earlier calorimetric studies the combustion products always had compositions which ranged from a Lincoln Laboratory,

M.I.T., Lexington, Mass. 02173, U.S.A.

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T. V. CHARLU,

0. J. KLEPPA,

AND T. B. REED

Ti0ieg4 to Ti01.96. As complete combustion to TiOZ never was achieved, suitable corrections were applied to refer the results to the fully oxidized state. Although there is excellent agreement between the standard enthalpies of formation for solid Ti,O, and Ti,O, reported by Humphrey and by Ariya et al., the agreement is less satisfactory for TiO for which Humphrey gives -(123.9rf:O.3) kcal,, mol-’ and Ariya et al. -(125.4&0.4) kcal, mol-‘.T The difference between these two values is 1.5 kcal,, mol-‘, which is more than twice the sum of the uncertainties quoted in the two separate investigations. In view of results obtained in the present work, it seems quite possible that this difference may be due to a real difference between the two TiO samples used (see below). Recently, the high-temperature thermodynamic properties of solid TiO were discussed in some detail by Gilles, (13) who noted certain discrepancies in the data. While one of the discrepencies discussed by Gilles now appears to have been resolved,(14) there remains a disagreement between the standard Gibbs energies for TiO given by Kubaschewski and Dench,(i5) and the more recent and more extensive results of Komarek and Silver. (16) We hoped that the present investigation might contribute towards a further elucidation of this problem. The authors have recently reported the development of high-temperature combustion calorimetry, and have applied this new technique in thermochemical studies of stoichiometric and non-stoichiometric oxides in the W + 0 and V + 0 systems.(17. ’ *) In the present study we have extended this work to parts of the Ti+O system. In the course of the present investigations we found that titanium oxides with compositions between TiOO.sl and TiO,.,O are readily oxidized to TiO(rutile) when powdered oxide samples are exposed to an atmosphere of pure oxygen at 1070 to 1120 K. The reaction proceeds rapidly and can conveniently be carried out in a high-temperature microcalorimeter under conditions of constant temperature and pressure. The results of these experiments are reported below.

2. Experimental MATERIALS All oxide samples were prepared by arc-melting mixtures of TiOZ and Ti in the appropriate proportions in an argon atmosphere. TiOz was a granular high-purity product from Johnson Matthey, while Ti was crystal bar titanium purchased from Ventron, Inc. To achieve homogeneity, these samples were annealed in argon for 3 h at 1570 to 1770 K in a Centor tantalum-element furnace. They were found to be single phase by X-ray and metallographic examination. Prior to each calorimetric run, the oxide samples were annealed further during the thermal equilibration of the calorimeter for at least 3 h at 1108 K. As a result the samples of TiO(P) disproportionated to give a mixture of new stable phases characteristic of this lower temperature. Earlier metallographic work by Pearson indicates that the disproportionation reaction of TiO(& goes essentially to completion t Throughout

this paper c&, = 4.184 J; atm = 101.325 kPa.

HIGH-TEMPERATURE

COMBUSTION

CALORIMETRY

1067

in about 3 h at 1100 K.(‘) In the course of the present work we attempted to confirm this observation by X-ray diffraction. However, the similarity between the diffractograms of TiO(B) and TiO(ol) interfered with this objective. Exploratory calorimetric experiments on titanium + oxygen samples with compositions between Ti00.05 and TiOO,J gave rather incomplete combustions under the conditions of our experiments. Hence, no further work was carried out on these samples. PROCEDURES A single unit microcalorimeter, designed for operation at temperatures up to about 1270 K, was used in the present work. This unit was previously used by us in our work on V + 0.(18) Preliminary experiments with TiO,.,, samples at 908 K, the temperature used in our earlier work, showed that oxidation at this temperature is very slow. Therefore, the experiments were carried out at about 1100 K. Sintering of the oxide samples during oxidation was prevented by mixing the titanium oxides with about 500 mg (about 10 times the mass of sample) of powdered quartz (about 250 mesh). Under our experimental conditions we found quartz to be inert towards the titantium oxides. This was checked by microscopic inspection after annealing the mixture in vacuum at the operating temperature of the calorimeter. The titanium oxide + quartz samples were weighed into a small fused silica crucible which had a snugly fitting ground stopper. The stoppered crucible was in turn contained in a slightly larger platinum capsule with a closely fitting cap. This capsule was placed in a fused silica break-off tube which was evacuated, sealed, and manipulated as described previously.(17, I*) On the basis of the mass gain we found that the initial oxidation of most of the samples was about 99 per cent complete. Complete oxidation to TiOZ was assured by removing the oxide mixture from the capsule, regrinding it in an agate mortar, and repeating the calorimetric combustion experiment. In the case of Ti,O, (Ti01.67) the primary oxidation was only about (90)2) per cent complete, and oxidation did not go to completion in the second run. For this oxide the enthalpy of reaction for complete conversion of Ti,Os to TiO, was calculated by linear extrapolation of the enthalpy change determined in the primary run, Calibration of the calorimeter was based on the enthalpy of oxidation of metallic tungsten to WO, :

W(s)+ W,(g) = W%(s). According to the JANAF Tables, (I’) the enthalpy change for this reaction at 1100 K and 1 atm is -(197.68&0.20) kcalth mol-I. In the calibration experiments we used pure tungsten powder from Sylvania, Inc., with an oxygen content of less than 200 p.p.m. and with principal impurities: Fe, 10; K, 15; MO, 11; Na, 14; Ni, 7; and Si, 8 p.p.m. by mass. The calorimeter temperature was measured with a Pt-to-(Pt+ 13 mass per cent of Rh) thermocouple which had been checked against an N.B.S. calibrated couple.

T. V. CHARLU, 0. J. KLEPPA, AND T. B. REED 1068 ANALYSIS The extent of oxidation of the titanium + oxygen samples was checked by the mass gain of the platinum capsule after the calorimetric run. For oxides with compositions TiO,.,, to TiO,., the observed mass gains (sum of first and second oxidation) were equal to the theoretical mass gains within experimental error. The final oxidation product was confirmed to be the rutile form of TiOZ by X-ray diffraction.

3. Results and discussion The results of the calibration of the calorimeter based on combustion of metallic tungsten are given in table 1. The last column of this table gives the area under the curve of potential against time associated with an enthalpy change of 1 kcalth. The oxidation of tungsten to WO, was always virtually complete in the first run. TABLE 1. Calibration reaction :

of the calorimeter,

at 1100 K, with metallic tungsten according

to the

W(s) + %02(g) = WOds); for which AH(llOO K) = -(197.65 i 0.2) kca&, mol-1 o and M(W) = 183.85 g mol-I; and where m is the mass of tungsten used, A/A0 is the area measured on the e.m.f. against time plot, A0 being a standard area, and E is the calibration constant, the area per unit enthalpy change (calth = 4.184 J) Expt.

m/m2

A/A0 b

1 2 3 4

45.32 46.60 55.52 54.60

4.353 4.505 5.304 5.210

s/kcal- 1

Expt.

88.93 89.52 88.53 88.42 mean: 89.16 &

5 6 7 8 0.65 c

m/w

A/Ae *

e/k& - l

55.14 51.07 45.37 52.84

5.371 4.903 4.403 5.068

90.27 88.94 89.86 88.86

(1 AH(1100 K) calculated from the data in JANAF tables.(19) b Includes break-off tip correction of 0.02 (pertaining to two runs). c Standard deviation.

In table 2 are listed the results obtained in the oxidation (to TiO,) of the titanium oxides of compositions TiOO.sl, Ti00.s9, TiO1.OO, TiO,.,,, TiO,.,,, Ti01.20, In evaluating these enthalpy changes we always TiO 1.26~ Ti%50y and TiR6,. deducted the small exothermic effect associated with crushing the break-off tip (0.01 units per run). The average enthalpies of reaction at 1100 K were referred to 298 K by correcting for the enthalpy differences of products and reactants. The enthalpies of the oxides at 1100 K were calculated by interpolating the available enthalpies for the oxides TiO ,,.eC2, Ti00.334, TiO, Ti01.50, and Ti01.67, as reported by Mah et aZ..(12’20) The standard deviations given in table 2 include the errors in the calibration of the calorimeter. The standard enthalpies of formation of the various oxide compositions are summarized in table 3. They have been calculated from the results in table 2 and the

HIGH-TEMPERATURE TABLE 2. Results of oxidation area measured on the potential

m G

A. 26.53 37.17 27.63 26.92

4.568 6.443 4.769 4.692

-AH,(llOO

secondary oxidation

kcalth

Oxidation

5.493 5.128 5.628

of TiOO,B1;

40.26 38.73

7.139 6.488 6.722

4.951 4.722

of Ti0Q.89;

of TiO:

73

4.311 4.243

M(Ti0)

0.095 0.103 0.058

M(TiOI.aJ

of Ti01.17;

0.061 0.046 0.047
M(TiOl.17)

+ (0.83/2)0&)

83.19 81.00 82.56 K)> =-(82.43 K) =-82.19 of TiOI.zO;

0.208 0.137

108.66 110.13

0.069 0.062 0.094

96.19 94.27 95.15

mol-l

= 63.90 g mol-1

= 64.70 g mol-l 0.072 0.039

91.18 89.51

= 66.62 g mol-l

= TiOz(s) 43.98 4.875 53.48 5.844

f 1.06) kca& kcal, mol-l M(TiOl.20)

118.64 119.40 120.42

= 62.14 g mol-1

TiOl.ds) + @.95/2)0&d = TiO&) 0,067 90.09 49.78 6.203 0.054 89.11 47.44 5.833 = -(89.97 It 1.03) kcal,, mol-1 A&(298.15 K) = -90.11 kcal,, mol-l

0.054 0.045

83.40 82.00

mol-1

= 67.15 g mol-1

TiOI.&s) + 0.400,(g) = TiO,(s) 0.049 75.31 46.73 4.679 0.081 75.73 55.42 5.578 =-(75.75 + 0.63) kcal,, mol-1 A&(298.15 K) = -75.43 kcal,, mol-1

0.045 0.054

for

the

-AH~(llOO K) b kca.l, mol-1

mol-l

of TiOI.oS;

Oxidation

A/A9 the

change

= 60.86 g mol-l

D.

F. Oxidation 43.37 42.77

M(TiOO.sS)

secondary oxidation

0.065 0.062 0.059
TiOlds) 5.716 4.823 4.700

M(T.i00.81)

A/A0 =

TiO(s) + +0,(g) = TiO,(s) 96.20 54.80 7.306 96.57 48.45 6.331 96.54 48.98 6.429 K)) = -(95.82 f 1.09) kcal,, mol-1 K) = -95.94 kcal,, mol-’

E. Oxidation 51.71 44.73 42.78

mg

K) the enthalpy

primary oxidation

Ti00ds) + (1.11/2)0&z) = TiO&) 0.259 107.36 32.48 4.876 0.181 108.10 42.67 6.626 0.124 106.99
53.52 48.46 50.19

mol-’

m is the mass of sample,

TQds) + (1.19/2)Oz(g) = X0,(s) 0.102 119.64 30.55 5.235 0.127 120.28 38.09 6.580 0.088 119.50 23.28 4.069 0.067 120.16 = -(119.72 i 1.05) kcal, mJ298.15 K) = -120.20 kcal,, mol-l B. Oxidation

37.21 34.10 37.34

m

K) *

1069

CALORIMETRY

experiments at 1100 K; where against time curve, and AH,(ilOO reaction shown (cab = 4.184 J)

A/A9 a primary oxidation

COMBUSTION

75.76 76.20

1070

T. V. CHARLU,

0. J. KLEPPA, TABLE

m G

A/A0 a primary secondary oxidation oxidation

AND T. B. REED

2-continued

-A&(1100 K) b kcalth mole r

m mg -

A/A@ = primary secondary oxidation oxidation

-A.H,(llOO K) b kcal, mol - 1

G. 47.98 47.24 53.76

56.19 56.86 74.89

Oxidation of TiO1,as; M,Ti01.26) = 68.06 g mol-f TiO1.&s) + 0.3702(g) = TiOz(s) 0.068 72.10 56.84 5.362 0.026 0.076 71.15 38.66 3.496 0.055 0.051 71.66 = -(71.34 & 1.03) kcalth mol-l AH,(298.15 K) = -70.82 kcah, mol-l

4.484 4.347 5.016

72.09 69.72

H. Oxidation of TiOl.S; M(TiO,J = 71.90 g mol-l TiOl.s(s) + 0.250z(g) = TiO&) 0.057 46.17 88.22 4.885 0.034 0.043 45.19 76.63 4.338 0.054 0.044 45.14 73.93 4.125 0.046
3.180 3.163 4.168

m G 51.89 68.61 97.32

A/A0 PC primary oxidation 1.711 89.8 2.370 92.3 3.352 91.2
44.78 46.01 45.28

-AH,(llOO K) d kcalth mol-l 30.70 31.30 31.58

a Include break-off tip correction of 0.01 to be subtracted. b Based on the calibration constant given in table 1. Uncertainties quoted are standard deviations. c p is the percentage completion of the reaction calculated from the mass gain. d The enthalpy change is calculated for 100 per cent reaction. Due to low mass gains there could be an additional uncertainty in AHr of f2 per cent. TABLE

TiO0.81 riO0.89

DO(u) riOl.05

riO1.17 TiOl.zO TiOl.2e

3. Enthalpies of formation at 298.15 K for the titanium oxides (al%, = 4.184 J)

-AF(298.15 This work

K)/kcal, mol-l Literature

105.60 117.21 129.86

104.0 113.4 125.4 123.9 130.8 144.5 147.5 154.5

135.69 143.61 150.37 154.98

o Ariya et aI.@)

a a f 0.4 =; & 0.3’=’ a cl 4 a

-AHr9(298.15 This work TiO1.r&)

181.64

TiOl.e7(4

195.44

TiO.&utile)

-

K)/kcal, mol-l Literature 181.4 & 0.3 a; 181 45 & 0 2F’ 195.7 i 0.33 =; 195.63 & 0.23’11’ 225.8 f O.l;‘=) 225 5 f 0.2’11’ 22419 f 0.4 a

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standard enthalpy of formation of TiO,(rutile), which, according to Mah et aZ.(12) is -(225.8+0.1) kcal, mol-l at 298.15 K. Figure 1 shows a plot of the standard enthalpies of formation of the various titanium oxides as a function of the mole ratio n(O)/n(Ti). The graph gives our own results as well as corresponding data from Ariya et al. The values attributed to them at the compositions studied by us were in some cases obtained by graphical interpolation. 0.89 1.00 1.17 I.05 1.26

0.75

1.0

1.50

1.25

1.50

2.00

1.b7

1.75

2.0

x FIGURE 1. Standard enthalpies of formation of TiO, phases at 298.15 K; 0, this work; Ariya et al. ;(l*) 0, Mah ef aZ.‘la)

A,

It is apparent that there is a distinct difference between our results and those of Ariya et al. for compositions in the stability range of TiO@). This difference is very pronounced for oxides between TiOo.sl and Ti01.05, but becomes less for higher mole ratios n(O)/n(Ti); it is entirely absent for the two “stoichiometric” phases, Ti%so and Ti01.67, for which our results, those of Ariya et al., and those of Humphrey are in excellent agreement (see table 3). This agreement strongly suggests that the difference between our results and those of Ariya et al. for the TiO phases has a real significance. At the stoichiometric composition our enthalpy of formation is about 4.5 kcal* mol-l more negative than that of Ariya et al.? We propose that this difference may be interpreted as follows. In view of the sluggish character of the fi=cl transformation, (‘) there is good reason to believe that the TiO samples used by Ariya et al. and by Humphrey consisted, in large measure, of the high-temperature phase TiO@). In view of the less negative enthalpy f It is conceivable that the systematic difference between our results and those of Ariya et al. for lower oxygen contents might be due to differences in composition. However, this possibility does not seem plausible to us in view of the ease with which the mole ratios can be determined by the mass-gain method.

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T. V. CHARLU,

0. J. KLEPPA,

AND

T. B. REED

of formation, it is possible that Humphrey’s sample contained somewhat more TiO@) than Ariya et aZ.‘ssample. Our own samples, on the other hand, presumably represented the equilibrium phase assembly characteristic of the operating temperature of the calorimeter, 1108 K. If this interpretation is correct, we may equate the difference between our enthalpy of formation and that of Ariya et al. at the stoichiometric composition with the enthalpy of the transformation: TiO(a) = TiO(@; AH = 4.5 kcal,, mol-‘. If we use Humphrey’s enthalpy of formation, we get AH = 6.0 kcal,, mol-l. The experimental scatter in our values of AH, is about f 1 kcalth mol-’ (table 2), while the quoted errors in the earlier data are about 50.4 kcal,, mol-‘. Therefore the estimated maximum uncertainty in our calculated enthalpies of transformation is about + 1.5 kcal,, mol-’ or 25 to 30 per cent. The phase diagram for titanium + oxygen given by Wahlbeck and Gilles(4’ indicates that at about 1200 K, TiO(a) is in (peritectic) equilibrium with TiO,&3) and Ti,O. Since the two TiO phases have very nearly the same composition, we can accordingly get approximate values for the entropy of the TiO(cz) = TiO@) transformation. From our result combined with Humphrey’s results, we get Combination

AS z 6000 Cal,, mol-l/1200 K = 5.0 Cal,, K-l mol-I. with Ariya et al.‘s value yields AS zz 4500 Cal, mol-1/1200 K = 3.75 Cal,, K-’ mol-‘.

The estimated maximum uncertainty in these entropies of transformation should be 1.0 to 1.25 Cal,, K-l mol-‘. Structural investigations have shown that TiO(ol) has a very complex X-ray diffraction pattern. The recent work by Watanabe et al. (21) indicates that the structure is a monoclinically distorted rock-salt structure with half of the titanium and half of the oxygen atoms missing alternately in every third (110) plane of the original NaCl-type cell. TiO@), on the other hand, has a simple rock-salt structure, in which the lattice vacancies are randomly or near-randomly distributed. From the large difference between the pycnometric molar volume and the X-ray diffraction volume, Ehrlicho) estimated that stoichiometric TiO@) contains about 15 per cent lattice vacancies both on the cation and anion sublattices. If these cation vacancies are distributed randomly over the available cation sites, and the anions over the anion sites, there will be a disordering entropy in TiO@) of approximately -(l/0.85) 2R(0.15 In 0.15+0.85 In 0.85) = 2.0 Cal,, K-l mol- 1.(22) This estimate presupposes no disordering of cations on to anion sites and vice versa. In the event that it is possible for Ti atoms and 0 atoms to disorder on to all vacancies, there would be an additional disordering entropy of 2R In 2 = 2.75 Cal,,, K-l mol-‘. If TiO@) is a largely ionic compound, this latter possibility can be ruled out. Even SO, it is apparent that the entropy change associated with the disordering of the lattice vacancies in TiO represents a very substantial fraction of our value of the entropy of the 01= l3 transformation. The low-temperature heat capacities of TiO(ol) down to about 50 K were measured by Shomate,(23) and the high-temperature enthalpies of both TiO(ol) and TiO(@) by

HIGH-TEMPERATURE

COMBUSTION

CALORIMETRY

1073

drop calorimetry by Naylor. cz4) Naylor found that the entropy change associated with the a= p transformation is about 0.6 Cal,, K-’ mol-‘. Several reasons can be advanced to explain why this very low value was obtained, the most plausible being that in view of the relatively sluggish character of the p=a transformation it seems unlikely that complete conversion can ever be obtained under the conditions of drop calorimetry. One of the referees of the present paper drew our attention to the recent attempt by O’Keeffe and Valigi’25’ to calculate the lattice energies of ordered and disordered TiO. On the basis of what would seem to be reasonable models these authors estimate this difference to be about 200 kcal,, mol-l. This difference is so great that it suggests that at least one of the models must be completely unrealistic. We referred in the introduction to the disagreement between the standard Gibbs energies for TiO of Kubaschewski and Dench,(15) and the more recent and more comprehensive results of Komarek and Silver. (16) A Gibbs-Duhem integration of the standard chemical potentials of oxygen reported in the former work yields a value of -95 kcal,, mol-’ for AG,“(TiO, l3, 1273 K). A corresponding integration of the data in the latter work yields a value of - 104 kcal,, mol-I. If the former result is compared with the enthalpies of formation of Humphrey”‘) and of Ariya et aZ.,(“) corrected to 1273 K, it yields values of S”(Ti0, /3, 1273 K) of 26.9 and 25.7 calti K-i mol- I. However, if the latter result is adopted the calculated values of S”(Ti0, l3, 1273 K) are 33.9 and 32.7 cal, K-l mol-‘, respectively. The former values are much lower than the 1967 JANAF value (30.7 Cal,, K-l mol’l); the latter values are significantly higher. Note, however, that the JANAF values for the standard entropy of TiO are subject to serious question. While the JANAF compilers recognized some of the complications which arise from the lattice disorder in TiO, they attempted to allow for this by incorrectly postulating a residual entropy of 1.7 Cal,, K-l mole1 in TiO(a) at T + 0. (If this entropy term is subtracted from the JANAF values of S”(a), and the correct term’**) applied in S”(p), we arrive at an estimate of the entropy of transformation a= l3 of about 2.6 ca& K-i mol-l.) Apart from this the 1967 JANAF compilers, acting on a suggestion of Goodenough (26) that TiO may undergo a low-temperature antiferromagnetic transition below 50 K, also postulated the existence of this transformation, and assumed that it is associated with an entropy change of R In 3 = 2.2 Cal,, K-l mol-I. There is as yet no experimental evidence for this transformation. If the analysis of the thermodynamic data for solid TiO presented above is correct, it seems reasonable to predict that the melting of TiO@) should be associated with an anomalously low entropy. Typical values of the entropy of fusion for nearly ideal solids with the NaCl structure are about 6 Cal, K-i mol-1.(27) The extensive cation and anion disorder in TiO@) could easily reduce the entropy of fusion for this solid to about 4 Cal,, K-’ mol- ‘. Unfortunately, we are not aware of any experimental enthalpy or entropy of fusion of TiO@). In conclusion, the present work has again drawn attention to the fact that the available thermophysical data for solid TiO are very unsatisfactory. A complete reinvestigation is overdue both of the low-temperature heat capacities of TiO(a) (down into the helium range), and of the high-temperature data both for TiO(u)

1074

T. V. CHARLU,

0. J. KLEPPA,

AND T. B. REED

and for TiO(p). It also would be highly desirable to obtain an improved the enthalpy of the a= p transformation.

value for

We are indebted to Professor Paul Gilles for comments on the manuscript. This work has been supported by the Army Research Office-Durham. It has also benefited from the general support of Materials Research provided by the NSF-MRL. REFERENCES 1. Ehrlich, P. Z. Electrochem. 1939,45, 362. 2. Bumps, E. S.; Kessler, H. D.; Hansen, M. Truns. Amer. Sot. Metals 1953,45(S), 1008. 3. Schofield, T. H.; Bacon, A. E. J. Inst. Metals 195~56,84(2), 47. 4. Wahlbeck, P. G.; Gilles, P. W. J. Amer. Ceram. Sot. 1966, 49, 180. 5. Andersson, S.; Cohen, B.; Kuylenstierna, V.; Magneli, A. Acta Chem. Stand. 1957, 11, 1641. 6. Straumanis, M. E.: Li, H. W. Z. Anorn. All,. Chem. 1960, 305. 143. I. Pearson, Ai D. J. bhyi. Chem. Solids 1958, s(4), 316. I 8. Wang, C. C.; Grant, N. J. J. Met& 1956, 8(2), 184. 9. Kuylenstierna, V.; Magneli, A. Actu Chem. Scund. 1956, 10(7), 1195. 10. Ariya, S. M.; Morozova, M. P.; Volf, E. Russ. J. Znorg. Chem. 1957, 2, 16. 11. Humphrey, G. L. J. Amer. Chem. Sot. 1951,73, 1587. 12. Mah, A. D.; Kelley, K. K.; Gellert, N. L.; King, E. G.; O’Brien, C. J. Bur. Mines, Rept of Investigations 1957, 53 16. 13. Gilles, P. W. J. Chem. Phys. 1967, 46(12), 4987. 14. Gilles, P. W.; Hampson, P. J. J. Chem. Phys. 1971, 55(8), 3712. 1,5. Kubaschewski. 0.: Dench. W. A. J. Inst. Metals 1953. 82, 87. 16. Komarek, K. L.; Silver, Ik Thermodynamics sf Nuclear Materials. International Atomic Energy _. Agency, Vienna. 1962, pp. 749-774. 17. Charlu. T. V.: Klevva. 0. J. J. Chem. Thermodvnamics 1973. 5.325. 18. Charlu; T. V.; Kleppai 0. J. J. High Temp. Sci 1973, 5,260: ’ 19. JANAF TIzermochemical Tables, Dow Chemical Company: Midland, Michigan. 1967. 20. Kelley, K. K.; Mah, A. D. Bar. Mines, Rept of Investigations 1959, 5940. 21. Watanabe, W.; Terasaki, 0.; Jostsons, A.; Castles, J. R. The Chemistry of Extended Defects in Non-Metallic Solids. North-Holland Publishing Company: Amsterdam. 1970, pp. 238-258. 22. Jostons, A.; Jenkins, A. E. J. Phys. Chem. 1969, 73, 749. 23, Shomate, C. H. J. Amer. Chem. Sot. 1946, 68, 310. 24. Naylor, B. F. J. Amer. Chem. Sot. 1946,68, 1077. 25. O’Keeffe, M.; Valigi, M. J. Chem. Phys. 1969, 50, 1490. 26. Goodenough, J. B. Phys. Rev. 1960,117,1442. 27. Dworkin, A. S.; Bredig, M. A. J. Phys. Chem. 1960,64,269.