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Ind. Eng. Chem. Res. 1998, 37, 3800-3805
KINETICS, CATALYSIS, AND REACTION ENGINEERING Intrinsic Kinetics and Mechanism of Rutile Chlorination by CO + Cl2 Mixtures H. Y. Sohn,* L. Zhou,†,‡ and K. Cho§ Departments of Metallurgical Engineering and Chemical and Fuels Engineering, University of Utah, Salt Lake City, Utah 84112-0114, and Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, Taejon, Korea
The intrinsic kinetics for the chlorination of natural rutile in CO-Cl2 gas mixtures were studied in a shallow fluidized bed. The effects of particle size, temperature, and partial pressures of chlorine and carbon monoxide were determined. The chlorination of rutile was found to follow a topochemical reaction scheme, the rate of which can be expressed as eq 7, in the ranges 950 °C e T e 1150 °C and 0.9 kPa e (pCl2, pCO) e 57 kPa, where T is in K, d is in µm, p is in kPa, and t is in min. A reaction mechanism involving lower-valence titanium oxides produced near the surface during chlorination is proposed. Introduction The excellent properties exhibited by titanium, titanium alloys, and titanium oxides make them prime candidates for many aerospace and commercial applications.1,2 Titanium alloys have a high strength-to-density ratio, good fracture characteristics, and high corrosion and erosion resistance. Titanium dioxide pigment has increasing applications in the paper, plastics, painting, and fabric industries.3 High-quality titanium metal and dioxide are produced from titaniferous raw materials through the common intermediate titanium tetrachloride (TiCl4), which is obtained by chlorinating these titaniferous materials in a fluidized-bed reactor with coke as the reductant. Titanium metal is produced by reducing the titanium tetrachloride by magnesium,4,5 and titanium dioxide pigment is obtained by oxidizing the titanium tetrachloride.3 Rutile is the most favored raw material, followed by titania slag and beneficiated ilmenite. The overall chlorination reaction with carbon as the reductant can be expressed as
TiO2 + 2Cl2 + 2CO ) TiCl4 + 2CO2
(1)
C + CO2 ) 2CO
(2)
linearly on the partial pressures of carbon monoxide and chlorine in the CO-Cl2 system in both fixed and fluidized-bed reactors. The samples contained 74-250µm particles, but the particle-size dependence was notdetermined. The rate expression he obtained is
(
X ) 55pCOpCl2 exp -
)
1.05 × 104 t T
(3)
where X is the fraction of rutile chlorinated, T is in K, p is in atm, and t is in min. Bergholm7 investigated the chlorination of Australian rutile and studied the effects of operating conditions using rutile and carbon mixture tablets. He found that the rate of reaction increased with increasing carbon monoxide concentration but was independent of the chlorine partial pressure in the CO-Cl2 system. He did not provide a rate expression for his study. Morris and Jensen8 studied the fluidized-bed chlorination rates of Australian rutile and developed empirical equations based on the experimental results in the CO-Cl2 system. They used particles of 149-177-µm size and did not obtain the particle-size dependence of the chlorination rate. The rate expression they obtained is
(
)
1.90 × 104 t T (4)
Dunn6 studied the chlorination rates of several titanium-containing materials in CO-Cl2 gas mixtures. He found that the chlorination rate of rutile depended
1 - (1 - X)1/3 ) 6065(pCOpCl2)0.665 exp -
* Corresponding author. Departments of Metallurgical Engineering and Chemical and Fuels Engineering, University of Utah. Telephone: 801-581-5491. Fax: 801-581-4937. E-mail:
[email protected]. † Department of Metallurgical Engineering, University of Utah. ‡ Present address: Millenium Inorganic Chemicals, Baltimore, MD 21226. § Korea Advanced Institute of Science and Technology.
where X is the fraction of rutile chlorinated, pCO and pCl2 are in atm, T is in K, and t is in min. Rao and Chadwick9 studied the rate of chlorination of synthetic rutile in CO-Cl2-He gas mixtures by a thermogravimetric method in the temperature range of 500-1000 °C. The synthetic rutile was prepared by oxidizing a thin titanium metal foil. They found that the exponents for the partial pressures of CO and Cl2
S0888-5885(98)00238-3 CCC: $15.00 © 1998 American Chemical Society Published on Web 09/12/1998
Ind. Eng. Chem. Res., Vol. 37, No. 10, 1998 3801
Figure 1. Schematic diagram of the experimental apparatus. 1, gas cylinders; 2, rotameter; 3, multimeter; 4, furnace; 5, solid reactant; 6, gas distributor; 7, temperature controller; 8, cooling tube; 9, NaOH scrubber; 10, NaOH quench tower; 11, reservoir; 12, pump.
varied with the reaction temperature. There have also been several articles published on the chlorination of rutile using carbon as a reducing agent.10-12 The result of the literature survey presented above indicate that there has been a moderate amount of previous investigation of this reaction system. Furthermore, the only two rate expressions obtained in previous studies contain a large difference in the activation energy, and neither includes the all-important effect of rutile particle size. Additionally, there has been little reported on the mechanism of the chlorination reaction. As part of an overall investigation on the chlorination of various titaniferous materials,13-15 this study had an objective of determining the intrinsic kinetics of rutile chlorination, including the effect of particle size, reactant partial pressures, and temperature as well as examining the mechanism. By systematic measurements of the reaction rates, it was hoped that the conflicting results of the previous investigations on the effects of temperature and reactant partial pressures would be clarified. Experimental Work Materials. The natural rutile particles used in this work were provided by Du Pont. The rutile sample contained 94.4% TiO2, 1.1% Fe2O3, 1.7% Al2O3, and 1.5% SiO2. The minerals were ground and screened into various size fractions from 38 to 250 µm. The chlorine, carbon monoxide, and nitrogen gases were all supplied by Air Product Co. Apparatus and Procedure. The chlorination of rutile was carried out in a fluidized-bed reactor which consisted of a gas inlet system, a quartz reactor, and a product gas cooling system. A schematic diagram of the experimental apparatus is shown in Figure 1. The fluidized-bed reactor consisted of a 95-cm-length quartz tube of 2.5-cm i.d. which had an expansion zone of 5-cm i.d. at the upper part to reduce the carryover of the reactant particles. A coarse fritted disk of 2.5-cm diameter was used as a bed supporter and a gas distributor. The reactor was externally heated in a silicon-carbide furnace. The temperature of the bed was measured by a thermocouple immersed in the bed. The product gas was cooled by passing it through a water-cooled condenser and was absorbed in two vessels containing 10% sodium hydroxide solution. The unabsorbed chlorine was removed in a caustic tower. It was reported9 that phosgene (COCl2) formed when chlorine and carbon monoxide were mixed with each
other under visible light and caused an anomaly to the experimental results below 800 °C. Above this temperature, phosgene decomposes and does not have any effect on the chlorination reaction. In this study, the experimental temperature range was higher than that of phosgene stability. The experimental procedure was to preheat the reactor to the desired temperature, flow nitrogen for 5 min to remove the oxygen in the system, and place the preweighed materials while the flow of nitrogen was maintained at 900 cm3/min at 25 °C and 86.1 kPa. Since the objective was to determine the intrinsic kinetics, a shallow fluidized bed was prepared by using a small 3-g initial amount of rutile to eliminate heatand mass-transfer effects and ensure uniform temperature and gas concentration in the bed. When the temperature was stabilized, the reactant gases were introduced. At the end of each experiment, the reactor was purged with nitrogen while cooling, and the quartz reactor was taken out and cooled to room temperature. The remaining sample was subjected to chemical as well as morphological analysis. The materials balance for titanium was closed by analyzing the titanium tetrachloride in the scrubbers, computing the amount of titanium thus collected, and calculating the amount of titanium dioxide left. Results and Discussion The chlorination kinetics of natural rutile were investigated in the temperature range of 950-1105 °C in mixtures of chlorine, carbon monoxide, and nitrogen gases. The partial pressures of the reactant gases Cl2 or CO varied from 0.9 to 57 kPa, which are comparable with the practical situation in the fluidized-bed chlorination of rutile in industry. The average particle diameter of natural rutile was varied from 41 (-28 to +42 mesh fraction) to 126 µm (-100 to +150 mesh fraction). The experiments were run in a batch mode. The previous examination13 of microstructural changes in rutile during the chlorination reaction indicated that the reaction occurred at the surface of the particle and proceeded toward the center of the particle in a topochemical manner. There was no obvious cracking or internal structural change observed. Thus, the shrinking-core model with no product layer is applicable for this reaction. The characteristics of a fluidized bed ensure intimate contact between the reactant gases and the solid particles and excellent mass transfer. The reaction rate is controlled by the chemical reaction according to the following expression:
1 - (1 - X)1/3 ) kappt
(5)
with
(
kapp ) Ad-1pCOmpCl2n exp -
E RT
)
(6)
in which A, m, and n are constants to be determined from the experiments and E is the activation energy for the chlorination reaction. Effect of Flow Rate. The mass-transfer effects can be removed in a shallow bed using a sufficiently higher flow rate. Rhee and Sohn16 found that the chlorination of iron was independent of the flow rate beyond 600 cm3/
3802 Ind. Eng. Chem. Res., Vol. 37, No. 10, 1998
Figure 2. Effect of particle size on the conversion versus time relationship for rutile chlorination.
Figure 3. Plot of ln kapp versus ln dp from Figure 2.
min at 25 °C and 86.1 kPa in the same fluidized bed. Based on their observation, a flow rate of 900 cm3/min at 25 °C and 86.1 kPa was used for our experiments, which is about 10 times higher than the minimum fluidized velocity. Effect of Particle Size. The effect of the particle size on the chlorination rate was determined at 1050 °C. The partial pressures of chlorine and carbon monoxide were kept at 43 kPa. The average size of rutile particles was varied from 41 (-28 to +42 mesh) to 126 µm (-100 to +150 mesh). An increasing conversion of titanium with decreasing particle size was observed as shown in Figure 2, in which the left-hand side of eq 5 is plotted against time for different particle sizes. The largest difference between the experiment and the calculated conversion is less than 10%. The slopes give the apparent rate constant value, kapp, for different particle sizes. As shown in Figure 3, the slope of the ln kapp versus ln dp plot was essentially -1, according to eq 6. Effect of Chlorine and Carbon Monoxide Partial Pressures. Experiments were conducted to investigate the effect of the partial pressures of the reactant gases on the chlorination kinetics. The flow rates of the
Figure 4. Effect of chlorine partial pressure on rutile chlorination (T ) 1050 °C; particle size ) 106-150 µm; flow rate at 25 °C and 86.1 kPa).
Figure 5. Effect of carbon monoxide partial pressure on rutile chlorination (T ) 1050 °C; particle size ) 106-150 µm; flow rate at 25 °C and 86.1 kPa).
reactant gases were varied to give different partial pressures. The total system pressure was 86.1 kPa (the atmospheric pressure in Salt Lake City, UT), and the total flow rate was 900 cm3/min at 25 °C and 86.1 kPa. Eight different sets of experiments were performed at 1050 °C on the -100 to +150 mesh fraction with an average particle size of 126 µm. In one set of experiments, the partial pressure of chlorine was varied from 0.9 to 57 kPa, with the carbon monoxide partial pressure fixed at 29 kPa; in another set of experiments, the chlorine partial pressure was held at 29 kPa and that of carbon monoxide was varied. The nitrogen partial pressure was adjusted as necessary to keep a total pressure of 86.1 kPa. The results are presented in Figures 4 and 5. It is observed from these figures that there is an increasing amount of titanium chlorinated with the increasing partial pressures of chlorine or carbon monoxide. The m and n values in eq 6 were evaluated from the slopes of the plots, as shown in Figures 6 and 7, to give m ) 0.55 and n ) 0.74. Effect of Temperature. To examine the effect of temperature on the chlorination rate of rutile, experi-
Ind. Eng. Chem. Res., Vol. 37, No. 10, 1998 3803
Figure 8. Effect of temperature on rutile chlorination (particle size ) 106-150 µm; pCO ) pCl2 ) 43.05 kPa).
Figure 6. Plot of ln kapp versus ln pCl2 from Figure 4.
Figure 7. Plot of ln kapp versus ln pCO from Figure 5.
ments were carried out at different temperatures under constant partial pressures of chlorine and carbon monoxide, both at 43.05 kPa. The particle size was 106150 µm. The reaction temperature varied from 950 to 1150 °C. The slopes of the conversion function, 1 - (1 - X)1/3, versus time, as shown in Figure 8, represent the apparent rate constants at different temperatures. Figure 9 shows an Arrhenius plot and best-fit straight line through these data. An apparent activation energy of 175 kJ/mol was obtained. Considering all the effects elucidated above and combining all the parameters obtained, the overall rate expression for the chlorination of rutile is represented by
1 - (1 - X)1/3 ) 2.87 × 104d-1pCO0.55pCl20.74 ×
(
exp -
)
2.10 × 104 t (7) T
in the ranges 950 °C e T e 1150 °C and 0.9 kPa e (pCO, pCl2) e 57 kPa, in which d is in µm, pCO and pCl2 are in kPa, T is in K, and t is in min. On the basis of the microscopic examination and the kinetics study, we believe that the particle-size effect
Figure 9. Arrhenius plot of the rate constants from Figure 8 (E ) 175 kJ/mol).
can be safely extended beyond the range tested in this work. Caution should be exercised, however, when extending the ranges of temperature and, especially, partial pressures in the use of this rate equation. Comparison with Previous Results. The activation energies obtained by Dunn6 and Morris and Jensen8 were 87.3 and 158 kJ/mol, respectively, compared with 175 kJ/mol obtained in this work. A comparison was made of the chlorination rates obtained by Dunn,6 Morris and Jensen,8 and this work, as shown in Figure 10. In this figure, the data of Morris and Jensen,8 who used particles of only one size (geometric mean diameter of 162 µm), and those of Dunn6 (geometric mean diameter of 136 µm) were adjusted to the geometric mean size (126 µm) of one of the size fractions (105149 µm) used in this work, assuming that the rate is inversely proportional to particle size, as in eq 7. The comparison is made at 1050 °C and for pCO ) pCl2 ) 43 kPa ()0.5 atm). Under these conditions, Dunn’s result lies between those of Morris and Jensen and of this work, being closer to the former at lower conversion but to the latter at higher conversion. The relative position of Dunn’s results changes, however, as the temperature
3804 Ind. Eng. Chem. Res., Vol. 37, No. 10, 1998
Figure 10. Comparison of the results by different investigators (T ) 1050 °C; pCO ) pCl2 ) 43.05 kPa; dp ) 126 µm): (---) this work; (-‚-) Dunn;6 (s) Morris and Jensen.8
changes, because of the considerable difference in his activation energy from those of the others. Dunn’s lower activation energy might indicate that his data were somewhat affected by mass-transfer effects. Additionally, the conversion function (X being proportional to time) he found best for his data is not appropriate for single-sized particles reacting topochemically, as found true in the case of rutile.13 The fact that Dunn’s sample had a rather wide size distribution may have contributed to that form of conversion function. Overall, the results of this work are in better agreement with those of Morris and Jensen in terms of the effects of temperature and reactant partial pressure. However, the overall rate found in this work is somewhat faster. Reaction Mechanism In order to investigate the chlorination mechanism, experiments were carried out to examine the changes in the surface of synthetic rutile reacted with only chlorine or carbon monoxide gas at a higher temperature of 1400 °C than the range of 950-1150 °C used in the kinetics study. Figure 11 shows the results of X-ray diffraction analysis of the synthetic rutile under a chlorine or a carbon monoxide atmosphere. It is observed that in carbon monoxide atmosphere, only TiO2 is detected, whereas in the chlorine atmosphere, the major phases are TiO2 and TiO, with Ti2O3 as a minor phase. Although there may be more complicated reactions involved, the reaction mechanism for the chlorination of rutile, suggested by these experimental observations, can be presented as follows:
O0 ) V0•• + 2e′ + 1/2O2
(8)
TiTi + e′ ) TiTi′
(9)
TiTi′ + e′ ) TiTi′′
(10)
where the prime denotes the number of electrons added to the corresponding titanium defects. As described in eq 8, the trapped electrons in the oxygen vacancy may be excited at the high temperature and transferred to the Ti in its normal lattice position. Therefore, the Ti can change from the tetravalent state to the trivalent or divalent state according to eqs 9 and 10. The notations in eqs 8-10 are customarily used for point defects associated with nonstoichiometry, as can
Figure 11. X-ray pattern for rutile reacted with (a) CO and (b) Cl2.
be found in refs 17 and 18. In eqs 9 and 10, TiTi was used instead of Tii because the Ti interstitials (TiTi) are not distributed at random but are placed at regular positions after a small degree of reduction by ordering of the defect. In addition to its change due to nonstoichiometry, the valence of Ti also changes with phase transition from TiO2 to the lower oxides by a series of simultaneous losses of oxygen, which can also be represented by eq 8. With CO gas alone, the liberated oxygen reacts with CO to produce carbon dioxide:
CO + 1/2O2 ) CO2
(11)
However, the extent of the loss of the oxygen is limited, and the final product (or residue) seems to be very slightly reduced nonstoichiometric TiO2 (TiO2-x). Considering the overall reaction
TiO2 + 2CO ) Ti + 2CO2
(12)
the pressure ratio, pCO2/pCO, must be maintained below about 9.7 × 10-7 at 1600 K, for reduction to occur. With Cl2 gas, the loss of the oxygen is significant to produce the lower oxides due to the following thermodynamic reason. Considering the overall reaction of
TiO2 + 2Cl2 ) TiCl4 + O2
(13)
the reduction of TiO2 would be possible if the combination of the partial pressures, pTiCl4(pO2/pCl22), is maintained below about 1.5 × 10-3 at 1600 K. This reaction is possible because the TiCl4 and O2 gases generated during the reaction are carried away from the fluidizedbed chlorinator by the incoming Cl2 gas and the level of O2 in the Cl2 gas is sufficiently low. If the reduction of TiO2 occurs, the lower oxides such as Ti3O5, Ti2O3, and TiO may be present. The composition range of Ti3O5 is rather narrow,19 and it is stable only above
Ind. Eng. Chem. Res., Vol. 37, No. 10, 1998 3805
about 1200 °C.20 The Ti4+, Ti3+, and Ti2+ ions in their normal sites in stoichiometric titanium oxides and the TiTi′ and TiTi′′ as well as Tii defects related to nonstoichiometry may react with chlorine gas to produce TiCl4 because the chlorine gas is an electrophilic reagent and TiCl4 is thermodynamically the most stable form compared with the other lower chlorides such as TiCl3 and TiCl2. This reaction can be given by the following equation:
Ti* + 2Cl2 ) TiCl4
(14)
where Ti* denotes titanium ions for all possible valent states present in titanium oxides, namely,
Ti4+ + 2Cl2 + 4e′ ) TiCl4
(15)
Ti3+ + 3/2Cl2 + 3e′ + 1/2Cl2 ) TiCl4
(16)
Ti2+ + Cl2 + 2e′ + Cl2 ) TiCl4
(17)
The remaining Ti ions on the surface left by the departure of the neighboring oxygen ions and Ti ions located at octahedral interstices near the surface apparently are the sites for the chlorination reaction. When both CO and Cl2 exist, the chlorination takes place according to eqs 8, 11, 13, and 14. In order to further test the existence of low-valence titanium oxide, experiments were conducted with natural rutile under chlorine atmosphere at 1400 °C. This temperature was somewhat higher than that for the reaction with CO-Cl2 mixtures, because the reaction with chlorine alone is too slow at the lower temperatures. The formation of titanium tetrachloride was observed during the experiments. The major phases of the residue in the natural rutile is in part due to the wider homogeneity range of TiO (TiO0.65-1.25) than that of Ti2O3 (TiO1.49-1.51) or Ti3O5.18 It should be noted that Ti2O was not detected by X-ray diffraction for both synthetic rutile and natural rutile. If Ti2O was present at high temperatures, the preferential volatilization of titanium21 would cause a rapid removal of Ti2O by chlorination reaction. Even the existence of the Ti2O phase has not been resolved.20 Conclusions The intrinsic kinetics of rutile chlorination with COCl2 gas mixtures have been investigated. The effect of particle size was determined for the first time, together with those of temperature and CO and Cl2 partial pressures. The rate was found to be inversely proportional to the particle size, as expected in a spherical topochemical reaction system. The disagreement in the previous results in terms of activation energy as well as the effect of conversion has been clarified. Based on the X-ray measurements performed in this work, a reaction mechanism in which the titanium dioxide goes through lower-valenced suboxides before being chlorinated was formulated. Acknowledgment This work was supported in part by Du Pont’s Chemicals and Pigments Department through an unrestricted research grant to the University of Utah.
Special thanks go to Drs. Gary K. Whiting, Peter C. Compo, and Kevin J. Leary of Du Pont for helpful technical discussions and support. L.Z. received during the course of this work a Graduate Fellowship from Utah MMRRI and a University of Utah Graduate Research Fellowship. Literature Cited (1) Hayes, F. H.; Bomberger, H. B.; Froes, F. H.; Kaufman, L.; Burte, H. M. Advances in Titanium Extraction Metallurgy. J. Metals, 1984, 36 (6), 70-75. (2) Orr, N. H. Industrial Application of Titanium in the Metallurgical and Chemical Industries. In Light Metals 1982; Andersen, J. E., Ed.; TM: Warrendale, PA, 1982; pp 1149-1156. (3) Powell, R. Titanium Oxide and Titanium Tetrachloride; Noyes Development Co.: Park Ridge, NJ, 1968; pp 1-6. (4) Turner, P. C.; Hensen, J. F. Progress toward Low-Cost Titanium. Adv. Mater. Process. 1993, 143 (1), 42-43. (5) Nado, T. Recent Progress in Ti Sponge Production in OTC. In Light Metals 1988; Boxall, L. G., Ed.; TMS: Warrendale, PA, 1988; pp 759-768. (6) Dunn, W. E., Jr. High Temperature Chlorination of TiO2 Bearing Minerals. Trans. AIME 1960, 218, 6-12. (7) Bergholm, A. Chlorination of Rutile. Trans. AIME 1961, 221, 1121-1129. (8) Morris, A. J.; Jensen, R. F. Fluidized-Bed Chlorination Rates of Australian Rutile. Metall. Trans. B 1976, 7B, 89-93. (9) Rao, Y. K.; Chadwick, B. K. Chlorination of Rutile (TiO2) with CO-Cl2-He Gas Mixtures. Trans. Inst. Min. Metall., Sect. C 1988, 97, 167-179. (10) Vijay, P. C.; Subramanian, C.; Rao, C. S. Chlorination of Rutile in Fluidized Bed. Trans. Indian Inst. Met. 1976, 29 (5), 355359. (11) Lin, C.-I.; Lee, T.-J. On the Chlorination of Titanium Dioxide-Carbon Pellet. J. Chin. Inst. Chem. Eng. 1985, 16, 4955; 1986, 17, 119-123. (12) Barin, I.; Schuler, W. On the Kinetics of the Chlorination of Titanium Dioxide in the Presence of Solid Carbon. Metall. Trans. B 1980, 11B, 199-207. (13) Zhou, L.; Sohn, H. Y.; Whiting, G. K.; Leary, K. J. Microstructural Changes in Several Titaniferous Materials during Chlorination Reaction. Ind. Eng. Chem. Res. 1996, 35, 954-962. (14) Zhou, L. Fluidized Bed Chlorination of Several Titaniferous MaterialssKinetics, Morphological Changes and Mathematical Modeling. Ph.D. Dissertation, University of Utah, Salt Lake City, 1994. (15) Zhou, L.; Sohn, H. Y. Mathematical Modeling of Fluidized Bed Chlorination of Rutile. AIChE J. 1996, 42, 3102-3112. (16) Rhee, K. I.; Sohn, H. Y. The Selective Chlorination of Iron from Ilmenite Ore by CO-Cl2 Mixtures: Part I. Intrinsic Kinetics. Metall. Trans. B 1990, 21B, 321-330. (17) Kingery, W. D.; Bowen, H. K.; Uhlmann, D. R. Introduction to Ceramics; John Wiley & Sons: New York, 1976. (18) Kofstad, P. Nonstoichiometry, Diffusion, and Electrical Conductivity in Binary Metal Oxides; Robert E. Krieger: Malabar, FL, 1983; pp 6-21. (19) Wahlbeck, P. G.; Gilles, P. W. Reinvestigation of the Phase Diagram for the System Titanium-Oxygen. J. Am. Ceram. Soc. 1966, 49, 180-183. (20) DeVries, R. C.; Roy, R. A Phase Diagram for the System Ti-TiO2 Constructed from the Data in the Literature. Am. Ceram. Soc. Bull. 1954, 33, 370-372. (21) Gilles, P. W.; Carlson, K. D.; Fransen, H. J.; Wahlbeck, P. G. High-Temperature Vaporization and Thermodynamics of the Titanium Oxides. I. Vaporization Characteristics of the Crystalline Phases. J. Chem. Phys. 1967, 4, 2461-2465.
Received for review April 16, 1998 Revised manuscript received August 4, 1998 Accepted August 13, 1998 IE980238K
