VAPOR-SOLID EQUILIBRIA IN THE SYSTEM TITANIUM-OXYGEN
Feb., 1955
127
where (e) refers to crystal, (1) to liquid and the subscripts denote the temperature. Values of d i for mixtures were obtained by interpolation since molar volumes are nearly additive. The dielectric constants for the molten salts are unknown, so we
have used an estimate of D = 3 for I n any case small differences in D will introduce almost negligible differences in AS*. All entropies of activation were negative and had the value -6.1 e.u. for LiCl a t 700" and -6.4, -6.7 and -7.4 e.u. for NaCl, KC1 and KI, respectively, a t 850". The values for mixtures lay close to those of the component pure salts (deviations generally less than 0.5 e.u.) with a tendency to a maximum negative value in the region of minimum equivalent conductance. The entropy of activation is only very slightly temperature dependent, varying perhaps 0.1 e.u. per 100 or 150". We believe that the values of AS* calculated by this method are reasonable and that probably the differences for the pure salts are real. The close similarity of AS* for all salts and mixtures studied bespeaks a similar conduction mechanism for all. A more refined method is desirable for calculating the heat and entropy of activation for conductance in mixtures. When two cations are the major conducting species there must be two rate processes, each with its own characteristic composition-dependent heat of activation, both of which will be of the same order of magnitude. We are in the process of testing equations which we have derived for binary mixtures. They express equivalent conductance as the sum of exponential terms involving heats of activation in which interaction is considered between the two salts. We have in progress in this Laboratory further work including other experimental approaches in attempts to elucidate in greater detail physicalchemical behavior of molten salts and to test more exactly some of the ideas presented in this paper.
(24) 9. Glasstone, K. V. Laidler and H. Eyring, "The Theory of Rate Processes," McGraw-Hill Book Co., Inc., New York, N. Y., 1943.
(25) Bockris, et al.,14 assumed D = 5 for a series of molten silicates which are rather poorer conductors than the molten halide cases.
however, difficult to ascribe any physical significance to the values of these constants. TABLE IV EQUIVALENT CONDUCTANCE EQUATIONS FOR KCl, LiCl, NaCl AND K I log A = A
+(mho B(1000/T) + C'log cm.2. equlv.
A
100% KCl 100% LiCl 100% NaCl 100% KI
3.34204 2.63987 2.42522 3.91176
(lOOO/T)
1)
B
Compn.
-1.35302 -0.37505 -0.33686 -1.93237
C
+1.24340 -0.16694 -0.59108 +2.53113
By making use of absolute reaction rate theory, the following equation can be derived from equation l Ai = 5.18 X 10'8 ( D
+ 2)di2eASi*/R
e-AHi*/RT
(3)
in which D is the dielectric constant and di is the half-migration distance for the conducting ion. This is analogous to the case for hydrogen ion in aqueous solution given by Glasstone, Laidler and E ~ r j n gand ~ ~ is identical with the equation of B ~ c k r i s , 'et~ al., for molten silicates. Entropies of activation for conductance in the three systems have been calculated by equation 3. The values of d i were estimated for the pure salts from the equation d(c)?b = di(1)t
(-)I/*
VAPOR-SOLID EQUILIBRIA I N THE TITANIUM-OXYGEN SYSTEM' BY WARREN 0. GROVES,~ MICHAELHOCH AND HERRICK L. JOHNSTON Contributionfrom The Cryogenic Laboratory and the Department of Chemistry, The Ohio Stale University, Columbus, Ohio Received November 89, 1064
The vaporization of TiO, TizOa,Ti306 and Ti02 has been studied by the Knudsen effusion method, and the solid phases investigated by high temperature X-ray diffraction technique. TiO, Ti02 (rutile) and Ti103 do not undergo any structural change up to their melting oints. Ti304has a low temperature structure and a high temperature structure (above 16OO'K.). TiO(s) vaporizes to TiO(gf AH: = 134.6 kcal./mole, TiOn(s) to TiOn(g), AH: = 138.9 kcal./mole. Tin03 decomposes on vaporization to TiO(g) TiOs(g), the heat of reaction being AH: = 296.0 kcal./mole.
+
Introduction The purpose of this research is to determine the nature of the vaporization processes of the titanium oxides, to measure the equilibria between the solid and the vapor, and to derive the related thermodynamic properties. The compositions and solid-phase equilibria of the titanium oxide system together with the vaporization processes have been discussed briefly by (1) This work was supported in part by the Office of Naval Research under contract with the Ohio State Univeraity Research Foiindation. (2) General Electric Fellow, 1953-1954. Present Address: New Mexico A. and M., State College, N. M.
Brewer3 in his recent review of the thermodynamic properties of the oxides. Skinner, Johnston and Beckett4 reviewed the literature up to 1951. Kubaschewski and Dench6 constructed the partial free energy of oxygen us. composition diagram a t 1000 and _1200'. _ __ .~ ..-
No direct determination of any of the va.por pressures or dissociation pressures have been pub(3) L. Brewer, Chem. Revs., 62, 1 (1953). (4) G. B. Skinner, H. L. Johnston and C. Beckett. "Titanium and I t s Compounds," Herrick L. Johnston Enterprises, Columbus, Ohio, 1954. (5) 0. Kubaschewski and W. A. Dench, J . Inst. Metals, 82, 87 (1953).
128
W. 0. GROVES,MICHAEL HOCHAND H. L. JOHNSTON
lished except that of T i 0 by Gilles and Wheatley, reported by Brewer3 and Skinner.4 Starodubtsev and Timokhina,6 using a mass spectrometer, observed Ti+, TiO+, Ti, T i 0 and TiOz ions and molecules in the vapor of TiOz heated in vucuo. As we have seenJ5the solid phases in the titanium-oxygen system are characterized by wide homogeneity ranges. In vaporization experiments, the solid phase has t o be characterized as to whether or not it can form an invariant system with the gas. In the case of an invariant system, the vapor and solid composition are equal, and the pressure will remain constant a t constant temperature as vaporization proceeds. If no invariant system can be formed the composition of the solid will change continuously as vaporization proceeds, and the vapor pressure will decrease until a two phase system is reached. An intermediate possibility, which is very commonly found, is a pseudo-invariant system. The composition of vapor and solid are not equal, but the difference is so small that the decrease in vapor pressure and change in composition of the solid are imperceptible. Apparatus and Experimental Procedure The high temperature X-ray diffraction patterns were taken in our camera.7~~When the desired temperature had been reached, the temperature was maintained for an hour to allow equilibrium to be attained. Following this equilibration period, the X-ray beam was turned on, and exposures for one hour were taken. The temperature interval in which X-ray diffraction patterns were taken extended from 1600-2100°K. The metal vapor pressure cell was similar to the one described previou~ly.~The power was supplied by a 15 kw. General Electric heater. The temperature was controlled with a motor-driven variometer10 in series with the work coil, the variometer being operated manually. The temperature was measured with a Leeds and Northrup disappearing filament optical pyrometer, the pyrometer being calibrated against a standard hngsten-ribbon lamp which has been calibrated a t the National Bureau of Standards. The Knudsen cells used in the vapor pressure measurements were either drawn from 0.010 inch tantalum or molybdenum sheet or were constructed of seamless tubing the tops and bottoms being drawn. The cells used in the measurement of the vapor pressure of T i 0 were drawn from tantalum 1" in diameter 1/2-a/4" high. For the first series on TizOa,cells, drawn from molybdenum, '/z" high, a/a" diameter were used. For the other series on Tiz08, and for TiOz and Ti306,molybdenum cells, made of molybdenum tubing 1/4-1/z" o.d., were used. These cells were enclosed into tantalum cells, ' / r 3 / 4 " o.d., the top of the molybdenum cells being flush with the top of the tantalum cell. The tantalum cell had a hole 1/2" diameter, concentric with the effusion hole in the molybdenum cell, in the top. By this method, the molybdenum weight loss was reduced t o a minimum, and the path of the effusing molecules was not obstructed by the tantalum cell. The tantalum cells were degassed a t 2000'; for the cells containing molybdenum, blank runs were carried out, to determine the weight loss. The weight losses obtained with the titanium oxides were corrected for the small, less than lo%, molybdenum weight loss. To correct for temperature fluctuations the effective time, (6) S. V. Starodubtsev and Y.I . Timokhina,Zhur. Tekh., F k , 19, 606 (1949); C. A . , 44, 82231 (1950). (7) J. W. Edwards, H. L. Johnston and R. Speiser, Rev. Sei. Inslr., BO, 343 (1949). (8) M. Hoch and W. L. Johnston, J . A m . Chem. Soc., 7 6 , 2560 (1954). (9) M. Hoch and H. L. Johnston, ibid., 76, 4833 (1954). (10) R. Speiser, G. W. Ziegler, Jr., and H. L. Johnston, Rev,. Sei. rnstr., 20, 385 (1949).
Vol. 59
teff, was calculated by the averaging method.11J2 The effective orifice area was obtained by correcting the measured area for thermal expansion and for the effect of the nonideal conditions, finite size and depth. The thermal expansion data for tantalum and molybdenum obtained in this Laboratory18 were used. The correction for the nonidealized effusion conditions was applied according to the equation derived by Whitman .14 I n order t o determine the composition of the effusing vapor and the composition of the solid from which it evaporated, the material was vaporized from an open molybdenum crucible, and a portion of the vapor condensed on a collector disk. A portion of the solid was analyzed for the Ti:O ratio before and after each vaporization and an X-ray diffraction pattern taken of the material collected. The analyses of the oxides were carried out by igniting samples in air at 800 to 900' in a platinum crucible. From the weight gain, due to oxidation to TiOz, the titanium to oxygen ratio could be calculated. Materials.-The titanium dioxide used in this research was "Baker's Analyzed," C.P. grade, the following analysis being given: water soluble salts, 0.04%; arsenic, 0.00000%; iron, 0.003%; lead, 0.01%; zinc, 0.002%. The iodide process titanium had been donated by the New Jersey Zinc Company, Palmerton, Pennsylvania. Its analysis was: manganese, 0.0082%; silicon, 0.007%; aluminum, 0.0066% nitrogen, tellurium, lead and copper, 0.02%. Intermediate oxides of titanium were prepared by heating together equivalent amounts of titanium and titanium dioxide in molybdenum or tantalum crucibles, the reaction being carried out under high vacuum in the vapor pressure apparatus. Weighed amounts of the oxide and metal were intimately mixed, placed in the crucible and heated to 1500' in uucuo for one hour. The solid was then removed, reground in a mortar and replaced in the crucible for a further heating period of several hours at 1500". Following this treatment, the samples appeared homogeneous, but to ensure complete reaction, the regrinding and heating processes were repeated. At this temperature the reaction of any of the oxides with the crucible appeared to be negligible, although the dioxide and the sesquioxide attacked tantalum a t 1700'. If any tantalum or molybdenum oxides had been formed, they should have been volatile. The following materials were prepared and used: Oxide
Ti0 Til08 T i 8 0 6
Batch
1 2 1 2 1
Mole ratio
TiO.
1.075 1.029 1.503 1.491 1.667
Experimental Results and Discussion of the Data X-Ray Diffraction Data.-Ti0 has the same NaC1type structure a t elevated temperatures, as a t room temperatures. Rutile, TiOz, maintains its structure up to its melting point. A series of patterns of oxygen deficient rutile were obtained. A one-phase system, having a distorted rutile structure, was obtained as low as TiOl,azat room temperature. Ti203 does not undergo any structural changes up to 2100°K. The pattern taken a t 2100'K. showed the corundum-type lattice strongly, but also six faint lines, which corresponded to lines found in the high temperature form of Ti306. This may indicate a slight disproportionation of Ti203 into TiO(g) and Ti306(s) near its melting point: but it is not impossible that some oxygen was picked up during the exposure. (11) J. W. Edwards, H. L. Johnston and P. E. Blackburn, J . A m . Chem. Sac., 73, 172 (1951). (12) G. B. Skinner, J. W. Edwards and H. L. Johnston, ibid.,78, 174 (1951). (13) J. W. Edwards, R. Speiser and H. L. Johnston, J . Appl. Phgs., !2B, 343 (1949). (14) G. I. Whitman, J . Chem. P h w , 20, 161 (1952).
VAPORSOLID EQUILIBRIA IN THE SYSTEM TITANIUM-OXYGEN
Feb., 1955
The room temperature patterns of Ti305did not correspond to that described by Rusakov and Zhdanov,16 nor could the lines be indexed into the Ti20a, rutile or anatase pattern. The pattern might be considered a very strongly distorted (much more than the above-mentioned TiOl.s2) rutile structure. At high temperatures, we obtained a new diffraction pattern for Ti306, different from the room temperature form, and from Ti02 and Tj203. The experiments carVapor Pressure Data.-1. ried out to determine the composition of the solid and vapor are given in Table I. TABLE I VAPORIZATIONEXPERIMENTS Vaporization Analysis Aniount Amount WJ. original, vaporized, Amount, gain, Material Ti0 Original Residue TizOa Original Residue TiaOs Original Residue TiOa Original Residue
g.
1.3244
1 ,58643
1 ,2300
0.23805
g.
6.
g.
Coinposition. TiOz
0.25206 .lo632
0.06084 ,02562
1.0290 1.0302
,24634 .I6359
,02792 ,01851
1.4916 1.4924
,19596 ,15406
.01401
1,6668 1.6069
0.04631
.2797
,3412
.01101
.15825 ,29678 ,03612
.00340
.00114
1.9432 1.8472
T o check our vaporization experiments, material was collected during several vapor pressure runs. The amount was too small to be analyzed, and Xray diffraction patterns were taken. For Ti0 and Ti203the collected vapor showed the T i 0 and Ti203 structures, agreeing well with the vaporization measurements. For Ti305the collected vapor showed a rutile structure, similar to the one when TiOs is vaporized. T i 0 will not vaporize stoichiometrically, the vapor containing Ti and TiO, and very small amounts of Ti02. The solid therefore will steadily become richer in oxygen. Our vaporization measurements and X-ray data indicate that the TiO/Ti ratio is larger than 10: 1. The correction for Ti is smaller using TiO1.029as a solid phase, than if TiOl.ooo would have been used. The activity of T i 0 over the homogeneity range is almost conThe Ti0 system is a pseudo-invariant system, and the measured pressures may be taken as the partial pressure of T i 0 in equilibrium with TiOl.ooo, the composition for which thermodynamic data are available. The vaporization and X-ray data on Tiz03indicate that Ti203 vaporizes stoichiometrically within 10%. The T i 0 to TiOz ratio must be between 0.9 and 1.1. The data were treated according to stoichiometric vaporization : the Ti20s system, even with only one solid phase present, is an invariant system. The vaporization and X-ray data on Tia06are contradictory. Vaporization and analysis of the residue indicate stoichiometric vaporization; the X-ray data from the collected vapor show that vapor contained only TiOz. This discrepancy could (15) A. A . Riinakor and G. S. Zlidanor. Dokladfl Abad. Nairlc S.S.S.R., 17, 411 (1951); C. A . , 46, 6462 (1951).
129
be caused by an oxidation of the solid during the single vaporization run, or the Oxidation of the collected vapor, during the vapor pressure runs. The Ti02 pressure above Ti306 must be a t least equal to the TiOz pressure above Ti203. Tnspecting the measured rates of evaporation we see that this is only possible if almost all the material vaporized was TiOp. Our data were therefore treated as Ti306(s)+ Tiz03(s) Ti02(g). Ti02 showed on the first heating a high evaporation rate, until the composition of the solid dropped to TiOl,e4s. At this point the rate of evaporation became constant, and the collected vapor showed the rutile structure. After the vapor pressure measurements the solid analyzed Ti01.84i.The vaporization of TiOz takes place under invariant conditions, the reaction occurring being 1.208 T i 0 1 . ~ ~ + ~ ( s ) 0.208 TiOl.667(6) TiOz(g) ( A ) The reaction Ti01.943(8)+Ti01.687(s) 0.138 Oz(g) (13) will take place simultaneously. To obtain the free energy of formation of Ti01.943, and for all the subsequent calculations we used the data compiled by Skinner, Beckett and Johnston. To obtain the free energy function of TiOz gas, we assumed that the addition of an oxygen to Ti0 to form TiOz will increase the free energy by an amount which is 75% of the increase due to the addition of an oxygen to Ti to form TiO. Thus
+
+
+
The oxygen pressure for reaction B must be smaller than the pressure for TiOz(s) +TiOl 667
+ 0.167 Oz(g)
which a t 2000°K. is 10-s*3atm. The oxygen loss is negligible compared to the Ti02 loss in the two phase region Ti01.943 - Ti305. The oxygen pressure for reaction B must be larger than the pressure for Ti306+1.5 T&Os+ 0.25 Oz(g) which a t 2000°K. is 10-11.5 atm. The oxygen pressure for reaction B must be between and 10-8.a atm., AFo a t 2000°K. for reaction B is between 14.5 and 10.5 kcal. Thus AFO of formation of T ~ O I , ~ ~a ~ t (2000°K. S) is between - 141.7 and - 137.7 kcal., and we can fix it as - 140 f 1 kcal. For the reaction 1.206 Ti01.~3(8) +0.206 Ti01 G ~ , ( S ) TiO2(s) we obtain a t 2000"K., AFo = 2.5 kcal.; that meaiis the activity of Ti02 in the Ti01,943/Ti305 two phase mixture is 10-o.273 or 0.53 a t 2000°K. We assume that this activity does not vary over our experimental temperature range. To obtain the pressure of TiOz(g) above TiOz,o solid, the experimental pressure was multiplied by 1/0.63 = 1.88.5, and this corrected pressure used in connection with the free energy functions to calculate the heat of vaporization of Ti02. The vapor pressures were cdculated from the rate of effusion, using the equation
+
P = mv'22aRT/ilI
(1)
where P is the pressure in atmospheres, R is the molar gas constant, T is the absolute temperature, m is the rate of effusion in g./sq. cm./sec. and M is the molecular weight of the vapor. I n the presence of more than one species in the gas, the measured total rates of effusion were divided according to the ratio of molecular weight of the components, multiplied by the composition of the gas phase, and the pressure calculated for each TABLEI1
VAPORPRESSURE ABOVETiO" Temp., OK.
1847 1880 *1908 1913 1920 1934 "960 1968
VOl. 59
W. 0. GROVES,MICHAELHOCH AND H. L. JOHNSTON
130
Evap. Pressure, Eff. Eff. Wt. rate. atm. X 108 (calcd. g./cm.a/ time, area, loss, sec. cm.2 g. X l o 3 sec. X 105 asTiO) 109080 0.01524 2.79 0.1678 0.2035 57694 ,01709 3.85 .3905 ,4778 36875 ,01710 3.91 ,6201 ,7643 29275 ,01525 3.17 ,7101 ,876 117378 ,01526 13.04 ,7280 ,900 28721 ,01710 5.27 1.073 1.332 28868 ,01709 8.03 1.628 2.034 14382 .01711 5.38 2.186 2.736
Evap. rate, g./cm z/ 2880. x '106 = 80,262 0.154 ,528 ,312 ,320 ,189 .zoo ,337 ,229 .385 ,406 ,682 ,769 1.289 ,689 1.155 ,793 1,327 .498 0,834 ,570 0.953 1.010 1,679 0.973 1.615 ,950 1.573 .731 1,207 ,589 0.970 ,629 1.034 ,911 1.498 3.044 5.003 0.741 1.217 1.507 2.475 1.119 1.835 1 .G53 2.710 1.510 2.743 1.585 2.594 1.225 1.992
2068 2070 2076 2078 2078 2088 2099 2122
Evap. Pressure, Eff. Eff. Wt. rate, a t m . X 106 time, area, Loss, g./cm.z/ (calcd. &a see. cm.2 g. X l o 3 sec. X 105 TiOd 59260 0.01767 6.72 0.642 0.740 ,700 ,608 ,01767 1.54 14340 3.63 ,717 ,826 .01767 28660 2.98 ,581 ,669 ,01767 29020 1.67 ,654 ,753 ,01767 14460 ,985 1.135 ,01768 1.16 6660 ,01768 1.67 .799 0.920 11820 ,01769 4.96 1.947 2.243 14400
-log
P
6.131 6.155 6.083 6.175 6.123 5.945 6.036 5.649
TABLEVI HEATOF SUBLIMATION OF Ti0 F
Temp., OK.
- R In P
1847 1880 1908 1913 1920 1934 1960 1968
30.605 28.912 27.979 27.709 27.655 26.877 26.035 25.445
-A(-?.-?-)
- Ho
42.78 42.69 42.61 42.61 42.59 42.55 42.48 42.45
AH:
73.382 71.600 70.593 70.314 70.240 69.423 68.513 67.898
AH;. kcal./mole
135.54 134.61 134.69 134.51 134.86 134.26 134.28 133.62
Av. = 134.55 3t 0.52 TABLEVI1 HEATOF SUBLIMATION OF Ti02
-log
P
6.403 6.273 5.913 5.866 5.721 5.656 5.509 5.570 5.530 5.452 5.548 5.571 5.463 5.287
TABLEIV VAPORPRESSURE ABOVETi203 Eff. Eff. Wt. Temp., time, area OK. see. cm.; g.loX98i05 1971 14400 0.01749 0.66 1990 25030 ,04351 5.75 1992 21600 ,01750 1.21 2008 13380 1.82 ,04031 2010 37400 ,04031 5.80 2017 29220 ,01751 3.49 2022 10800 ,04384 6.06 7301 2023 ,04354 3.67 2029 7441 ,04354 4.30 2030 28560 ,01751 4.17 2035 15930 ,04355 6.61 2059 7409 ,04357 5.42 2064 19770 13.91 .04357 2076 14760 ,01753 4.07 6998 2085 3.41 ,04038 2097 20040 2.73 ,01404 2101 14400 2.09 ,01404 2102 12600 3.31 ,01754 2106 6545 ,04361 14.28 2106 14400 2.46 ,01404 2108 14400 6.25 ,01754 2113 6959 5 . lG ,04040 2116 13740 6.53 ,01764 2120 14040 G.09 ,01754 2122 41400 18.84 ,01754 .01405 3.04 2151 10860
K.
P
6.691 6.321 6.117 6.058 6.046 5.876 5.692 5.563
TABLEI11 VAPORPRESSURE OVERTi02-z Eff. Eff. Temp., time, area, OK. sec. cm.1 1849 28872 0.01379 1867 28800 ,01379 1916 12960 ,01380 1918 14400 ,01381 1936 14400 ,01353 1943 10800 .01381 1949 28800 .01381 1954 18072 ,01382 1956 14472 .01382 1958 14400 .01382 1966 14400 ,01353 1972 14400 ,01353 1982 14400 ,01354 2010 14400 ,01354
Tpp.,
-1ogi
a For the runs marked with a * the solid had the composition Ti01.076; for all the others TiOl.029.
Evap. Pressure, Wt. rate, a t m . X 10' calcd as g./cm.2/ loss, g. X 103 aec. X 106 ( TiOi) 0.395 0.364 1.45 0.533 0.488 1.94 1.223 1.107 1.98 1.362 1.232 2.45 1.899 1.709 3.33 2.207 1.985 2.96 3.098 2.808 11.06 2.693 2.414 6.03 2.953 2.645 5.29 3.529 3.161 6.29 2.831 2,530 4.93 2.686 2.397 4.67 3.446 3.067 5.98 5.164 4.565 8.90
TABLEV VAPORPRESSURE ABOVE Ti306
Kp 6.812 6.506 6.724 6.699 6.640 6.392 6.114 6.162 6.101 6.303 6.244 5.996 6.012 6.022 6.136 6,230 6.201 6.040 5.516 6.130 5.822 5.951 5.782 5.821 5.800 5.911
Temp., OK.
1849 1867 1916 1918 1936 1943 1949 1954 1956 1958 1966 1972 1982 2010
F Q - Ho
- R In p - A
28.03 27.43 25.79 25.57 24.91 24.61 23.94 24.22 24.03 23.68 24.12 24.22 23.73 22.92
(+)
47.0 46.9 46.8 46.8 46.8 46.8 46.8 46.7 46.7 46.7 46.7 46.7 46.7 46.6
AH:
AH;
kcal./mole
75.0 74.3 72.6 72.4 71.7 71.4 70.7 70.9 70.7 70.4 70.8 70.9 70.4 69.5
138.7 138.7 139.1 138.9 138.8 138.7 137.8 138.5 138.3 137.8 139.2 139.8 139.5 139.7
-
Av. = 138.9 i 0.5 TABLEVI11 HEATSOF REACTION FOR Ti203
Temp., OK.
1971 1990 1992 2008 2010 2017 2022 2023 2029 2030 2035 2059 2064 2076 2085 2097
F Q - €i8 AH' - R In K p -.[-;i--] F"
62.32 59.52 61.51 61.28 60.74 58.47 55.93 56.37 55.81 57.66 57.12 54.85 55.00 55.09 56.13 56.99
87.7 87.6 87.6 87.5 87.5 87.4 87.4 87.4 87.4 87.4 87.3 87.2 87.2 87.1 87.1 87.0
150.0 147.1 149.1 148.8 148.2 145.9 143.3 143.8 143.2 145.1 144.4 142.0 142.2 142.2 143.2 141.0
AH;.
kcal./mole
295.6 292.7 297.0 298.8 297.9 294.3 289.8 290.9 290.6 294.6 293.9 292.4 293.5 295.2 298.6 302.0
Feb ., 1955
case of Tiz03,we assumed that the rate of effusion of Ti0 is equal to that of TiOz: the value for the equilibrium constant K , will be chahged by only 0.47% if it is assumed that the pressures of Ti0 and Ti02 are equal. This difference is much smaller than the experimental error. The calculations of the pressures and equilibrium constants are given in Tables 11-V, whereas the calculations of the heats of sublimation and heats of reaction are given in Tables VI-IX. Table X contains the heats of dissociation of gaseous molecules to gaseous atoms. After expanding the free energy function as a linear function of the temperature, we obtain the equilibrium constants and pressure of T10 and TiOzabove the four oxides investigated. The results are given in Table XI. The values for titanium are given to complete the table. In the last column, the pressures are given at 2O0O0K., for better comparison. The heat of vaporization of TiO, agrees very well with the value found by Gilles and Wheatley and given by Brewer.a The heat of dissociation of T i 0 is in very good agreement with the spectroscopic value of 158.8 kcal./mole quoted by Herzberg.I6 The value obtained for the heat of vaporization of TiOz is in good agreement with AH1900 = 138 kcal./mole, which is obtained from our data using the Clausius-Clapeyron equation. The heat of dissociation of TiOz is 4.6 kcal. or 1.4% smaller than twice the heat of dissociation of TiO, which is about the amount one would expect. To check the data, and to resolve the discrep-
TABLEVI11 (Continued) Temp.,
131
VAPOR-SOLID EQUILIBRIA IN THE SYSTEM TITANIUM-OXYGEN FO - H
OK.
- R In K p
2101 2102 2106 2106 2108 2113 2116 2120 2122 2151
56.73 55.25 50.46 56.08 53.26 54.44 52.89 53.25 53.06 54.07
AH:
AH:
-A[7] kcal./mole 87.0 87.0 86.9 86.9 86.9 85.9 86.9 86.8 86.8 86.7
143.7 142.2 137.4 143.0 140.2 141.3 130.8 140.0 139.9 140.8
301.9 298.9 289.4 301.2 295.5 298.6 295.8 206.8 296.9 302.9
-
Av* = 296.0
TABLE IX HEATSOF REACTION FOR
Ti306
9
Temp., OK.
-RlnKp
2068 2070 2076 2078
28.05 28.16 27.83 28.25
43.6 43.6 43.5 43.5
71.7 71.8 71.3 71.8
148.3 148.6 148.0 149.2
2078 2088 2099 2112
28.01 27.20 27.61 25.84
43.5 43.5
71.5 70.7
148.6 147.6
43.5 43.4
71.1 60.2
149.2 146.2
-A(-)
* 3.6
AH:, kcal./mole
-
A ~ 148.2 .
0.7
TABLE X Heats of dissociation of TiO(g) and TiOz(g) A H ; = 159.9 kcal/mole TiO(g) Ti(g) O(g) TiOz(g)+ Ti(g) 20(g) AH," = 315.2 kcal./mole
-
+ +
TABLE XI EQUILIBRIUM CONSTANTS AND PRESSURES ABOVETiO, TiOz, Ti208A N D TiaOs Solid phase
Eq. oonstant
29421
--0.583 T
Ti0
K P = PTLO
log Kp = log p ~ i o=
TiOl
Kp =
log Kp = log PTQ =
Ti203
Kp
PTi03
= I)TiOPTiOa
log K p = log PTiO
Tia06/TizOa
Kp
Ti
Kp =
= PTiOl
pTi
-log P at
Vapor pressure equation
2000'K.
X lO-ST
- 30361 -- 0.492 X IO-aT T
+ 10.43 f 11.19
5.44 4.97
-64700 - 1.26 X lO-3T + 21.65 T
E
- 32350 -- 0 . 6 3 X 10-*T + 10.83 T
6.61
-32393 - 0 . 4 8 X IO-* T + 10.51 T
6.64
+ 7.796
4.97
log PTiOa =
log Kp = log &io, = log Kp = log p ~ = i
component according to equation 1. The use of the rates of effusion instead of the pressures introduces a small error in the CalcUhtiOnS because the molecular Iveight of T i 0 and TiOz are different. In the
-24644 - 0.227 X T
10-3 T
ancy in the vaporization of Ti305, further experiments are under way a t other compositions. ( 1 6 ) G. &*.berg, "Spectra, of Diatornic hIolecules," Second Edition, D. Van Nostrand Company, Inc.,New York, N. Y.,1950, P. 576.
