THERMODYNAMICS OF THE Ti-Ti203 SYSTEM
Nov., 1957
proportion to the cube of the respective crystallographic ionic radii. Euckenlg however, used cesium iodide as th,e reference substance and obtained a volume of 41 A.3 for the chloride ion. Ionic volumes based on both scales are given in Table 11. Eucken considers four terms contribute t o the partial ionic volumes, vi: (a) the volume occupied by the unhydrated ion; (b) the “solvent effect” or the volume change due t o structural changes of the solvent, AVI; (c) “electrostriction” which is the decrease in volume of the solvent molecules attached to the ion; (d) a volume increase due t o the formation of a second diffuse hydration layer around the ions. For ions of relatively large size and small surface charge factors (c) and (d) are negligible. Further, neglecting the “solvent effect” as a first approximation,’l the difference vhyd
- vi
may be considered as the volume of water contained in the hydrodynamic volume of the ion. The approximate hydration number, n‘, calculated in this way is given in Table 11. The ‘(solvent effect” may be taken into account by using the equationsg AB8 = n2.75( D8/55.5) Avl = nl.8( D s / N * )
where n is the number of hydrated water molecules per ion, D Sthe change in mole fraction of the water8-polymer per mole fraction of hydrated water molecules, and substituting these values in nu0 = { 4 0 0 ( B i - A & ) ) / N A
- ( v i - Av,)
where vo is the volume of a water molecule. Then, using the value of n’ obtained by Darmois’ approxi-
1569
mation, a self-consistent method of calculation may be applied to compute a constant value of the hydration number n. The self-consistent hydrodynamic ionic volume is then obtained from the term Bi - ABs. Since Da values are only tabulated between n = 4 -+ 15, the Eucken correction could only be carried out for t,he bipyridine complex, leading to a hydration numbgr n = 11 and a hydrodynamic radius Rg cor. = 6.1 A., the corrected values not being significantly different from those obtained by parmois’ approximation, n’ = 9 and R h y d = 5.9 A. Conclusion The diameter of the 12-tungstosilicic acid anion was found to be 11.2 A. and was of the same magnitude as that obtainedofrom the sedimentation and diffusion studies2(11 A.) and fzom the X-ray analysis of the solid (unit cell 12.1 A.). This would seem to indicate that the Einstein viscosity equation is valid for aqueous solutions where the particle size is of the order 10 A. diameter. The sizes obtained for the hexol, phenanthroline and dipyridylcations 11.8,13.0 and 11.8W.diameter1 respectively, would also seem to support this conclusion, since these were the results expected from a consideration of the individual bond lengths and scale models (Catalin) of the substances, a slight increase in value being attributed to the hydration of the ions. Acknowledgments,-The authors are indebted to Professor D. 0. Jordan for helpful criticism and suggestions. One of the authors (T.K.) wishes to express his gratitude to the Commonwealth Scientific and Industrial Research Organization for a Postgraduate studentship.
THERMODYNAMICS OF THE Ti-Ti20s SYSTEM AND THE DISSOCIATION ENERGY OF Ti0 AND TiOzl BY J. BERKOWITZ, Department of Physics, University of Chicago, Chicago, Ill.
w. A. CHUPKA AND Argonne National Laboratory, Lemont, Ill.
MARKG. INGHRAM Department of Physics, University of Chicago, Chicago, Ill. Received June 86, 1867
The concentration of gaseous species in equilibrium with various compositions of the solid Ti-Ti02 system has been studied employing mass spectrometric analysis of the vapor effusing from a Knudsen cell. The gaseous species observed were Ti, TiO, and TiOz. A thermodynamic treatment of ion intensities yields TiO(s) 4TiO(g), AH&,* = 139 5 kcal./ mole; TiOr(s) 4 TiOz(g)? A H L 7 146 & 5 kcal./mole. Combining these values for the heat of sublimation with other well known thermodynamic data yields 6.8 and 13.5 e.v., respectively, for the atomization energies of T i 0 and TiOz.
Introduction The heats of sublimation of T i 0 a n d “ioz have been determined by Groves, Hoch and Johnston,2 using the Knudsen effusion cell technique. They ( 1 ) Sponsored jointly by t h e Office of Ordnance Research, U.S. Army and the National Science Foundation, (2) W. C. Groves, M. Hoch and H. L. Johnston. THISJOURNAL, 69. 127 (1955).
determined the vapor pressures from the weight loss of the cell after a known period of operation a t a known temperature. The Composition of the Vapor was inferred from X-ray diffraction studies of the condensate. This is a rather indirect method and leaves uncertainty concerning the identity Of the species in the gaseous phase* In order to eliminate this uncertainty, the experiments
1570
J. BERKOWITZ, W. A. CHUPKAAND M. G. INGHRAM
Vol. 61
finally becoming of the same order as that due to TiOz. An increase in the TiO/TiOz ratio with time also was observed. Both of these observations indicate a gradual reduction of Ti02 by the molybdenum containers. The only gaseous species containing titanium atoms observed with solid TiOz in the molybdenum Knudsen cells were T i 0 and TiOz. These identifications were made from measurements of the appearance potential, the mass and the isotopic composition of the ion beams observed. From the ion intensity of Ti02 and its variation with temperature, two independent' determinations of the sublimation energy were obtained. These are summarized in part A of Table I. For the analysis of the temperature variation experiments the following equations were used AFo = -RT In P = -RT In lc.I+.T AH' - TASQ
Hence, introducing the function
where the additive constant, In k, has been dropped. A typical plot of z1 vs. 1/T is shown in Fig. 1. TABLE I SUMMARY OF EXPERIMENTAL RESULTS A. Ti02 Absolute pressure experiments ASQ,,
EXperiment
--
5000
I
I
TiO(s)+ Plot o f
\
1
\
-
1
I1
I
-
TiO(g)
E vs
-
I/T
I
I \ I
_
2 3
II
I
AH,, kcal./ mole
kcal./ mole
OK:
P
1881 1.8 1881 2.0 1881 4.0
x
108,
atm.
66.7 66.2 63.7
39.4 39.4 39.4
140.9 140.3 137.9
149.8 149.4 146.7
AH&
Temperature variation experiments 4 5 6
I
I
deg.mole
Av. 148.6
= 136 kcal/mole
AH,,* 1000
I
I
1
tal./
kcal./ mole
AFQT,
TI
I
146.5 144.7 137
Av. 142.7
B. T i 0
Absolute pressure experiments 7 8
2072 1.04* 10-s 47.3 2027 3.26& 10-r 50.9
37.2 37.4
125.4 128.8
100
136.6 138.9
Av. 137.8
Temperature variation experiments
50
9 10
T
135.7 143.0
Av. 139.4
The thermodynamic properties of solid Ti0 and Ti02 have been reported by Kelley.' I n order to compute the gaseous specific heats, an assignment of vibrational frequencies is necessary. For TiO, Herzbergs gives 1008.4 cm.-l as the ground state ( 3 ~ frequency. ) From this figure we have estimated the frequencies of the TiOz molecule, making use of
U
10
5
I
52
I
I
5.6
I
\
1 6.0
Fig. 1. (3) W. A. Chupka and M. G.Inghram, THIBJOURNAL,59,100 (1955).
(4) K. K. Kelley, U. S. Bur. Mines Bull.476,"Contributions to the Data on Theoretical Metallurgy," 1949. (5) G . Hereberg, "Molecular Spectra End Molecular Structure I. Spectra of Diatomic Molecules," D. Van Nostrand Co., Inc., New York, N. Y., 1950.
THERMODYNAMICS OF THE Ti-Ti20a SYSTEM
Nov., 1957
the valence bond approximation,6 thus
where u = frequency of the corresponding diatomic molecule = symmetric stretch of YXs uz = bending mode VI
US =
asymmetric stretch
M = mass of atom Y m = mass of atom X
ha I= bending force constant IC = stretching force constant
We have estimated V 2 / v 3 by comparison with the linear molecules NzO, CSz and COz. Thus, we obtain for Ti02 the frequencies u1 = 874cm.-" u2 Us
= 305 cm.-l (doubly degenerate) = 1129 cm.-l
I n the computation of specific heats, the errors in these frequencies can be considerable without affecting the heat of sublimation appreciably. For the absolute pressure method, the errors are somewhat more serious, since the standard entropy is affected. The latter is also dependent upon the choice of the electronic configuration for the ground states of T i 0 and TiOz. For the present calculation we have chosen 3~ as the ground state of TiO.7 For Ti02 we have assumed that the ground state is non-degenerate and that there are no other low-lying electronic levels. In the above calculations we have assumed unit activity for the condensed phase. The corrections employed in converting from a particular ion current to the corresponding absolute pressure of the species are summarized in Table 11.
1571
experiment was performed in which TiOs was vaporized from a thoria Knudsen cell, Again equal quantities of Ti+ and TiOf were observed. Appearance potential studies showed that the Ti+ was not coming from dissociative ionization of Ti0 but was being formed directly from Ti(g). C. TizOa.-With the appropriate stoichiometric quantities of Ti and Ti02 added to a molybdenum cell to produce Ti203, the gaseous species observed were Ti, Ti0 and TiOz. No higher polymers could be found, the limit on Ti203 being less than 1/280 of TiO. The results were essentially unaltered when Ti203was inserted into and vaporized from a thoria Knudsen cell, I n the latter experiment, the magnitudes of the three ion beams corresponding to Ti(g), TiO(g) and Ti02(g) were determined at an ionizing electron energy of 15 e.v. This low electron energy was used in order to minimize errors due t o dissociative ionization. At 2194°K. Ti+:TiO+:TiOs+ = 600:146000:17
From these observations, the enthalpy change of the reaction Ti(g)
+ TiOz(g)
-P
2TiO(g)
can be computed. Using the previously outlined assumptions with regard to vibrational frequencies and electronic degeneracies, we obtain 5,21@4 (TiOz) = 84.85 e.u. SKals4 (TiO) = 72.62 e.u. XK2194(Ti)(') = 53.78 e.u.
Using these quantities AH2184 for the reaction denoted above is computed to be -8.8 kcal./mole. Since AC,, is very small for the above reaction this value is also the approximate value of AHOo. The enthalpy change accompanying the above reaction also may be calculated from the determinations of the heats of sublimation of Ti0 and TiOz, together with known values for the corresponding heats of formation,g the sublimation energy of Tilo and the dissociation energy of oxygen." This calculation yields AHoo = -3.5 kcal./mole. The TABLE I1 agreement is within the experimental error of the ESTIMATED VALUESOF RELATIVE IONIZATION current investigation. CROSS-SECTIONS AND MULTIPLIER EFFICIENCIES Discussion of Results Ag Ti0 TiOz TiO2.-Our measured vapor pressures of Ti02 Relative ionization cros~-section~' 1 1.2 1.3 are only one-tenth as large as those of Groves, Relative electron multiplier efficiency 1 1.6 1.8 Hoch and Johnston.2 Since Groves utilized moB. Ti0.-The experiment on the vaporization lybdenum Knudsen cells, volatilization of molybdeof TiO(s) was first performed by inserting equi- num oxides in their experiments could explain the molar quantities of Ti and TiOz into a molybdenum discrepancy. The lower vapor pressure observed in Knudsen cell. Approximately equal quantities of our work should make our computed heat of subTi0 and Ti vapor were observed in this experiment, limation 12 kcal./mole greater than that given by with no detectable TiOz as long as appreciable Groves, e l al. However, the method of calculating quantities of material remained in the cell. An up- the entropy of sublimation we have used is also per limit to a possible (Ti0)z species was found to be different. Groves, el al., obtained the free energy 1/800 at 1840'. The parameters assumed in the function for Ti02 gas by assuming that the addicomputations are indicated in Section A above, and tion of an oxygen t o Ti0 (to form TiO2) would inin Table 11,and the calculated heats of sublimation crease the free energy by an amount which is 75% are given in part B of Table I. To check for possible of the increase due t o the addition of an oxygen to reduction of T i 0 by the molybdenum cell, a second (8) We are indebted to the Titanium Division of the National Lead (6) G. Hersberg, "Infrared and Raman Spectra of Polyatomic Moleculea." D. Van Nostrand Co. Inc., New York, N. Y.,1945,p. 172.
(7) J. G . Phillips, Aslrophys. J.,116,567 (1952). (7s) J. W. Otvos and D. P. Stevenson, J. A m . Chem. Sac.,1 8 , 540 (1956).
Company for providing us with samples of T i 0 and Tit08 powder. (9) G. L. Humphrey, J . Am. Chsm. Soc., 73, 1687 (1951). (10) D. R.Stull and G. C. Sinke, "Thermodynamia Propertiea of the Element%" Advances in Chemistry Series No. 18, American Chemical Society, 1956. (11) P. Brix and G. Hersberg, Can. J. Phya., 8 3 , 110 (1954).
NOTES
1572
Ti to form TiO. This appears to be a rather arbitrary assumption. We propose that the valencebond approximation employed here, which approximates only the vibrational contribution, yields a more reliable estimate of the entropy of sublimation. Ti0.-In our study of the vaporization of Ti0 the measured vapor pressures are within a factor of 2 of those reported by Groves, et al. However, there appears to be an error in their calculated entropy of sublimation. The third law entropy of TiO(g) which we have used, which is the same as that recently tabulated by the National Bureau of Standards,I2is 1.13 e.u. higher at 2000°K. than the value reported by Skinner, Johnston and Becketti2 and subsequently employed by Groves, Hoch and Johnston.2 Hence, their AH of sublimation for T i 0 is very likely too low by 2.3 kcal./mole. Ti20a.-Groves, et al., report that their vaporization and X-ray data indicate that Tiz03vaporizes stoichiometrically within lo%, with the T i 0 to TiOz ratio at 0.9 to 1.1. Our results a t comparable temperatures are Ti:TiO:TiOz = 600: 1460: 17 (12) National Bureau of Standards, Selected Values of Chemical
Thermodynamic Properties, Series 111. (13) G. B. Skinner, H. L. Johnston and C. Beckett, “Titanium and Its Compounda,” Herrick L. Johnston Enterpriaes, Columbus, Ohio, 1954.
Vol. 61
This discrepancy, particularly in the TiO/TiOz ratio, could be explained if the condensate in the experiments of Groves, et al., had absorbed oxygen before it was weighed. An alternative explanation is the possibility that the samples used by Groves, et al., were of a composition different from ours. Conclusions The only gaseous species observed in equilibrium with various solid concentrations in the titaniumoxygen system were Ti, Ti0 and TiOz. The heats of sublimation obtained for the latter molecules (TiO2) AHozes(TiO)= 139 A 5 kcal./mole and AHozss = 146 5 kcal./mole are in approximate agreement with the results of Groves, Hoch and Johnston,2 although some cancellation of errors between experimental observations and computations appear to have occurred. Our results indicate that the mechanism of vaporization of TizOa(s)reported by Groves, et al., is probably in error. The sublimation energy of Ti0 obtained in this study combined with the heat of formation of TiO(s),9 the heat of vaporization of Tiloand the dissociation energy of OZ1’yields 6.8 e.v. as the dissociation energy of TiO. The corresponding atomization energy of Ti02 is 13.5 e.v. Within the precision of the above results (ca. 4%), the addition of a second oxygen to titanium liberates as much energy as the first.
*
NOTES HEATS OF FORMATION OF ALUMINA, MOLYBDENUM TRIOXIDE AND MOLYBDENUM DIOXIDE BYALLAD. MAE Contribution from the Minerals Thermodwaamics Experiment Station h e i o n I I , Bureau of Minae, United State8 Department of the Intarior: Waashington, D . (3. Recrived June 6, 1967
Recent measurements’-* of the heat of formation of alumina (corundum) at 298°K. have given values ranging from -399.0 to -402 kcal./mole. It appeared desirable, therefore, to determine this quanti6y again, to enable the selection of a “best” value. Also, occasion arose to determine the heats of formation of molybdenum trioxide and molybdenum dioxide. The results confirm the recent work of Staskiewicz, Tucker and Snyder,4 who obtained results that differed appreciably from the values selected by Brewer6from older literature. Materials.-A small aluminum bar of 99.998%. purity was furnished for this work by T. H. Hazlett, Division of Mineral Technology, University of California. Fine lathe turnings, cut with a Carboloy tool, were used for the measurements. (1) P. E. Snyder and H. Selts, J . A m . Cham. Soc., 67, 683 (1945). (2) C. E. Holley, Jr., and E. J. Huber, Jr., ibid., 73, 5577 (1951). (3) A. Schneider and G. Gattow, 2. anorg. aZZgem. Chem., 377, 41 (1954). . . (4) B. A. Staskiewios, J. R. Tucker and P. E. Snyder, J . A m . Chem. SOC.,77, 2987 (1955). (5) L. Brewer, Chem. Rsvs., Sa, No. 1 (February, 1953).
The molybdenum metal was Fansteel Metallurgical Corp., type 352, 200-mesh powder. It was heated in a stream of pure hydrogen for 2 hr. at 900’ before use in the measurements. Molybdenum dioxide was prepared from high purity molybdenum trioxide by prolonged treatment with hydrogen at 400’. The oxygen content, determined by hydrogen reduction at goo”, was 25.01%, which is the theoretical amount for pure molybdenum dioxide. The X-ray diffraction pattern agreed with the ASTM catalog. Methods.-The energy-of-combustion measurements were conducted with previously described apparatus.6 All weights were corrected to vacuum and all heat values are in terms of the defined calorie ( 1 cal. = 4.1840 abs. joules). National Bureau of Standards benzoic acid, sample No. 39g, wa8 used for calibration. The mean calibration values were 32,480.6 (f0.02%) cal./ohm for the aluminum combustions and 32,495.3 (f0.02’%)cal./ohm for the molybdenum metal and molybdenum dioxide combustions. All combustions were made under 30 atm. oxygen pressure. The samples were ignited by an electrically heated platinum spiral and a small filter paper fuse. The substances showed no oxidation under bomb conditions before ignition. The bomb gases after combustion contained only negligible amounts of oxides of nitrogen. Alundum disks were used to hold the aluminum samples during comb‘ustion. A small piece of freshly cleaned magnesium, for which roper correction was made, was used a8 a kindler. More tgan 98% of the combustion product stayed on the disk; the remainder appeared as a deposit on the bomb walls. The percentage completion of combustion was determined by weighing the total combustion roduct. Completions varied from 99.14 to 99.66%. %-Ray diffractions of the combustion products from the disks agreed with the pattern for corundum reported by (6)
G. L. Humphrey, J . Am. Chcm. SOC..78,
1587 (1951).
