A study of the thermal decomposition of BaCO3

A Study of the Thermal Decomposition of BaC03 I. ARVANITIDIS, Du. SICHEN. and S. SEETHARAMAN In the present work, the decomposition reaction, BaCO 3 (solid) = BaO (solid) + CO2 (gas), was investigated by thermogravimetric analysis (TGA) and differential thermal analysis (DTA) methods. Both shallow powder beds and densely compacted spheres of the carbonate were employed. In the case of the shallow powder beds, TGA and DTA were carried out simultaneously. The DTA curves showed that BaCO3 exhibited two phase transformations, the transformation of orthorhombic to hexagonal occurring at 1079 K and that of hexagonal to cubic at 1237 K. The activation energy and the forward reaction rate constant of the decomposition of BaCO3 were evaluated from the ther- mogravimetric results of the powder beds. The activation energy of the decomposition was found to be 305(+ 14) kJ �9 mole -t. The experimental results obtained with the compacted spheres were com- pared with those corresponding to the powder beds. After the initial stages, the formation of liquid due to the eutectic reaction between BaCO3 and BaO appears to play an important role in the reaction kinetics. I. INTRODUCTION THE use of BaO in sulfur/phosphorus refining slags in iron- and steelmaking is getting increased attention due to the higher basicity of BaO compared to CaO. Lower sul- fur/phosphorus contents and faster refining rates could be achieved by adding BaO to the slag along with CaO.tq By adding barium carbonate to hot metal, the stirring effect will be enhanced due to the evolution of CO z gas. It has also been shown that BaO can be used to remove N in industrial processes, t2] Even in the development of a solid- state reaction method for the synthesis of superconducting ceramics, e.g., YBa~Cu3Ox, BaCO3 is decomposed to form the complex oxide phase. [3J A knowledge of the kinetics of the decomposition of BaCO3 would be helpful in under- standing and optimizing these processes. The decomposition of BaCO3 has been studied by several researchers53-~] As early as 1937, Hackspill and Wolfe [71 reported eutectic reaction between BaCO3 and BaO in the BaCO3-BaO system. Lander ~41 found that the eutectic re- action occurred at 1303(_ 3) K. BakertS~ carried out a phase diagram study for this system at different pressures of car- bon dioxide. The phase diagram proposed by Baker is re- produced in Figure 1. According to this phase diagram, the eutectic point is at 1333 K and 0.00661 atm. The formation of the liquid due to the eutectic reaction could complicate the process of decomposition. To the knowledge of the present authors, a systematic study of the kinetics of de- composition of BaCO3 to date has not been carried out. The present investigation seeks to obtain an understanding of the kinetics and mechanism of the decomposition of the BaCO 3 by simultaneous thermogravimetric analysis (TGA) and differential thermal analysis (DTA). I. ARVANITIDIS, Graduate Student, Du. SICHEN, Associate Professor, and S. SEETHARAMAN, Professor, are with the Theoretical Metallurgy Department, Royal Institute of Technology, S-100 44 Stockholm, Sweden. Manuscript submitted September 19, 1994. 1I. EXPERIMENTAL A. Materials BaCO3 powder (99.999 pct pure) was supplied by Al- drich Chemic (Steinheim, Germany). In view of the hygro- scopic nature of BaCO 3, the powder was first calcined at 673 K for 24 hours and preserved in a desiccator. The cal- cined powder was well ground in an agate mortar under Ar atmosphere just before being used in the thermal analysis. In some experiments, dense spheres were used. The spheres were prepared by mixing a small amount of acetone in the BaCO 3 powder and pressing the mixture isostatically in sil- icon-rubber molds. In one of the spheres, a Pt-10 pct Rh/Pt thermocouple was embedded in the center during pressing. These were later sintered in a muffle furnace at 673 K for 24 hours. After sintering, the spheres had a diameter of I. 1 cm and a weight of 2.2 g, which would give a porosity of less than 8 pct. Anhydrous aluminum oxide powder (chlo- ride < 0.02 wt pct, sulfate < 0.05 wt pct, arsenic < 0.0005 wt pct, and iron < 0.02 wt pct) obtained from E. Merck (Darmstadt, Germany) was used as the reference substance in DTA measurements. This was heated up to 1573 K to remove the adsorbates before use. The argon gas (maxi- mum of 2 ppm impurity) and CO2 gas (>99.998 pet pure) used during thermal analysis were supplied by AGA Gas (Stockholm). B. Apparatus and Procedure The TGA and DTA studies were carried out on a SE- TARAM TGA92 (France) unit, which allows simultaneous TGA and DTA. The balance of the unit had a detection limit of 1 /zg. The system was fully controlled by an IBM PC* through a CS92 controller. The assembly of the unit *IBM PC is a trademark of International Business. is shown in Figure 2. The alumina sample holder, which was provided with two tricouple transducers, one for the sample and the other for the reference, was hung from the balance beam. The holder was previously calibrated against the melting point of gold (1337.43 K). In the case of powder samples, the TGA and DTA stud- METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 27B, JUNE 1996--409 Temp. 1873 1673 1473 1273 i I I 40 60 80 100 BaCO 3 ( mole % ) Fig. l--Phase diagram for the eutectic region in the BaO-BaCO3 system: (1) Pco., = 0.035 atm, (m) P~-o: = 0.098 atm, (n) Pco: = 0.208 atm, (p) Pco: = 0.4 atm, (q) Pco: = 1 atm, (r) Pco: = 5 atm, (s) Pco.. = 10 atm, and (t) Pco., = 20 atm. ies were carried out simultaneously under Ar atmosphere. In general, about 10 mg BaCO 3 was kept in the sample crucible made of platinum. The crucible had a dimensions of 5 mm in diameter and 6 mm in height. A crucible of the same type containing 6.55 mg of A1203 powder was used as the reference. The sample and reference crucibles were mounted on the transducers of the DTA fitting and intro- duced carefully into the alumina reaction tube (16-mm i.d.). The length of the alumina sample holder was properly de- signed so that the sample, the reference, and the DTA trans- ducers were in the even temperature zone of the graphite furnace. Two TGA experiments were carried out under pure CO2 atmosphere. In these experiments, the amount of the BaCO 3 powder sample and the type of the platinum crucible were the same as used in the experiments in which Ar at- mosphere was employed. In the case of dense spheres, it was not possible to carry out TGA and DTA measurements simultaneously. For TGA experiments, the dense BaCO3 sphere was kept in a Pt basket which was hung from the balance. Separate experiments were carried out in which the temperature of the sphere was monitored by a Pt-10 pct Rh/Pt thermocouple embedded in the center of the sample. These samples were hung from the balance by means of a platinum wire. Special care was taken to ensure that the sample holder or the suspension wire was not touching the walls of the reaction chamber. Before heating, the chamber was evacuated for 900 seconds down to a vacuum of 10 Pa. The sample was then heated up to 573 K and kept at that temperature for 900 seconds in vacuum. This was to ensure the removal of any residual moisture in the sample, which could be adsorbed as the sample was mounted in the apparatus. The reaction chamber was then filled with argon or CO2 gas through the cartier-gas inlet shown in Figure 2. A constant flow rate of 0.3 L �9 min-~ in the case of argon or 0.05 L �9 min -~ in the case of CO2 was then maintained and the gas was led out through the outlet at the lower end of the reaction tube. After passing the gas for 2400 seconds, Beam Balance I Au~liary-Gas Car~er-Gas Inlet 7 Control ] Graphite Furnace Module Sample Holder I I Computer [ Thermocouple Gas Outlet ~ ~--- To Vacuum Pump DTA Transducev- -~ T ..../Reference Fig. 2--A schematic diagram of the experimental assembly. the sample was heated up at a constant heating rate to a desired temperature. In the experiments using argon gas, the higher temperature limit was chosen as 1673 K, which was found to be high enough for complete decomposition of BaCO 3. On the other hand, the higher temperature limit for the decomposition of BaCO3 under CO2 atmosphere was kept at 1823 K. Four heating rates were employed in the case of powder bed experiments using Ar, namely, 7, 10, 12, and 15 K �9 min -t. In the case of the decomposition of BaCO 3 under CO2 atmosphere, two heating rates, 5 and 10 K �9 min -1, were employed. The heating rate used for the dense spheres was I0 K. min-L The weight changes of the sample and the DTA signals were registered by the com- puter at intervals of 1.2 seconds. The surface area of the ground BaCO3 powder was meas- ured by BET analysis on a FLOWSORB* II 2300 unit. *FLOWSORB is a trademark of Micromeritics Instrument Corp., Norcross, GA. Nitrogen gas was used as the adsorbate. III. RESULTS A. Powder Sample The results of the TGA measurements for the decom- position of BaCO 3 under Ar atmosphere at different heating rates are presented in Figure 3. The dimensionless mass change, X, represents the ratio of the weight loss at time t to the final weight loss. The results could be confirmed by repetition of some selected experiments. It should be men- 410~VOLUME 27B, JUNE 1996 METALLURGICAL AND MATERIALS TRANSACTIONS B 1.0 0.8 0.6 X 0.4 0.2 0.0 0 500 1000 1500 2000 2500 3000 Time (s) Fig. 3- -The results of the TGA measurements in Ar for different heating rates. tioned that the value of X for curve 4 is greater than one at the final stage. This is because of the experimental un- certainties. In order to compare the results of different heat- ing rates, the zero time for each decomposition was taken when the weight of the sample just started to decrease. It is seen that the time required for the complete decompo- sition decreased as the heating rate increased. This would be expected, as the sample would attain higher temperatures quickly at faster heating rates and, consequently, the reac- tion rate would be higher. A discontinuity in slope was observed between X = 0.4 and 0.5 in each decomposition curve, indicating that there was a change in the reaction mechanism. In fact, the reaction rate even became zero at this moment, as shown by the fiat portion in these curves. After this portion, the reaction rate increased again. The DTA value and the normalized weight change ob- tained at the heating rate of 12 K �9 min-' are plotted as functions of temperature in Figure 4. This figure has been divided into four parts, A through D. In region A, there is a strong endothermic peak at 1079 K, which would corre- spond to the orthorhombic-hexagonal transformation of BaCO 3. The X-temperature curve is nearly horizontal, in- dicating negligible decomposition of ]3aCO 3 in this region. In region B, the DTA curve shows a downward trend. The X values show a corresponding upward trend, indicating a weight loss. Even though this weight loss is not significant in the early stages, the loss of CO2 from the system and the formation of BaO are evident. In this region, an endo- thermic peak at 1237 K in the DTA curve is also noticed, which corresponds to the phase transformation, hexagonal- cubic. There is a less intense endothermic peak around 1265 K, which cannot be explained. The deviation from the bas- ' ' f' ' ' ' ' 1 ' 1.o A B C I D ! -2 0.8 -4 -6 ID 0.6 ~, -8 .---, x 0.4 -to 8 o _12 "~ 0.2 -t4 I I )~ -16 o.0! ,,, ----,-I I -18 ; , I ~ , I , I , I , I ~ I 1000 1100 1200 1300 1400 1500 1600 1700 Temp (k') Fig. 4 - -DTA and TGA curves as functions of temperature for a heating rate of 12 K �9 min -t. Table I. The Temperatures Corresponding to the Two Endothermic Peaks Heating Rate (K.min -t) Fi~t Peak (K) Second Peak (K) 7 1078.6 1237.4 10 1079.0 1235.9 12 1079.7 1237.1 15 1080.0 1237.0 eline is maximum around 1350 K. The X-temperature curve has a strong increase in slope corresponding to this region. After this point, the DTA curve starts moving toward the baseline. In region C, there is an arrest of the decomposition reaction at first, as seen in the X-temperature curve. This aspect is elaborated upon in Section IV. After this short arrest in the reaction, the decomposition proceeds again, as shown by the X-temperature curve. But the DTA curve shows a very peculiar trend in which a number of peaks appear close to each other. Since the baseline of the DTA curve shifts due to the change in the specific heat of the sample as the reaction proceeds, the present authors, from a consideration of the endothermicity of the reaction, inter- pret these as a series of endothermic peaks. Region D cor- responds to the completion of the decomposition. The same trend was observed in the thermal analyses carried out at other heating rates. The temperatures corresponding to the two sharp peaks obtained in each analysis are presented in Table I. The results of the TGA measurements for the decom- position of BaCO3 at a pressure of 1 atm CO, are presented in Figure 5. It is seen that while the decomposition started at a temperature around 1615 K at the heating rate of 5 K METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 27B, JUNE 1996--411 0.5 0.0020 0.4 0.3 0.2 0.1 0.0 5 K/min I0 K/min 1600 1650 1700 1750 1800 1850 T (K) Fig. 5- -The results of the TGA measurements in CO, for different heating rates. Table II. The Experimental Conditions and the Results of the BET Measurements Experimental conditions: Pressure: 750 mm Hg Weight of the sample: 1.3875 g Temperature of the sample: 453 K Run I II Adsorption (m 2) 0.91 0.87 Desorption (m 2) 0.83 0.89 Surface area (m:.g) 0.620 0.634 �9 min -t, the onset temperature for the decomposition at the heating rate of 10 K �9 min -1 was found to be about 1630 K. In both cases, the decomposition proceeded very fast before X = 0.23, where a discontinuity in slope was ob- served in each decomposition curve. Thereafter, the weights of the samples decreased at much lower rates, thereby in- dicating a change in the reaction mechanism. The surface area of the BaCO3 was measured by BET analysis. The experimental conditions and the results are presented in Table II. An average value of 0.627 m z �9 g-~ was calculated for the surface area of BaCO 3 powder from two measurements. B. Spheres The normalized weight change of the sphere is plotted as a function of temperature in Figure 6. In order to see the onset temperature of the decomposition, the derivative of X with respect to T is also plotted in the same figure. As shown in this figure, the decomposition started at a tem- perature around 1260 K, which was in accordance with the X 1 I I 0.001! O.O01q 0.0001 0 .000~- - t"q I i I I I 1200 1300 1400 1500 1600 T(I,:) 1.0 0.8 0.6 X 0.4 0.2 0.0 Fig. 6~Fract ion of the decomposition of the dense sphere as a function of temperature. results of the powder samples. The decomposition pro- ceeded until X ~ 0.24, before the reaction was interrupted due to the disintegration of the sample. In Figure 7, the temperatures detected by the thermocouple placed at the center of the sphere and the thermocouple of the furnace are plotted as functions of time. Below 1550 K, the tem- perature curves are parallel, with the sample temperature being 15 K lower than the furnace temperature. At 1550 K, the temperature measured by the thermocouple in the sam- ple showed a sudden increase, reaching the same value as the furnace temperature. Thereafter, the two thermocouples showed almost the same value. The sudden increase in tem- perature may be attributed to the falling off of the sample. IV. DISCUSSION According to Lander, t41 BaCO 3 exhibits two phase trans- formations, one at 1079 K (corresponding to orthorhombic- to-hexagonal transformation) and another at 1241 K (hexagonal BaCO 3 to cubic form). The two endothermic peaks in each DTA curve obtained in the present work cor- respond to these two phase transformations. It is seen in Table I that the transition temperatures obtained at different heating rates show very good agreement (with an uncer- tainty of less than ___ 1 K) in the case of both peaks. From the temperatures listed in Table I, a mean value of 1079 K can be obtained for the orthorhombic-hexagonal transfor- mation. The mean value of the temperatures corresponding to the second peak in the DTA curves has been calculated to be 1237 K, which corresponds to the hexagonal-cubic phase transformation. While the temperature obtained for the orthorhombic-hexagonal transformation is identical to Lander's result, IaJ the temperature of the hexagonal-cubic transformation is 4 K lower than the value reported by the same author. 412--VOLUME 27B, JUNE 1996 METALLURGICAL AND MATERIALS TRANSACTIONS B 1600 1550 down the decomposition process, as shown in part B of Figure 4. After the formation of the liquid layer, the CO,, gas produced by Reaction [1] is likely to dissolve in the liquid, which is basic in nature, forming CO~- ions, thereby increasing the chemical potential of COz in the melt. This increase in chemical potential of CO2 would lead to a low- ering of the reaction rate. When the concentration of dis- solved CO2 reaches the saturation solubility of COz in the liquid, Reaction [1] is arrested, as shown in part C of Figure 3. Since the reaction can not proceed at this point, the heat consumption due to the endothermic decomposition be- comes zero. This explains the fact that the difference in temperature between the reference and the sample is min- imal, as shown in Figure 4. It is seen in part C of the figure that the DTA curve shows a series of peaks just after X = 0.4. A plausible explanation is that when the temperature is increased, the CO2 level in the liquid is less than the saturation solubility at the new temperature. This allows the decomposition to start again. The decomposition of BaCO 3 results in an increase in the concentration of CO j- in the liquid. When the concentration of COj- reaches the new equilibrium value, the decomposition once more is arrested. This process repeats until the reaction is completed, thus resulting in a series of thermal peaks, as shown in Figure 4. Since the weight change corresponding to each thermal peak is very small, the discontinuity in the weight change is not identified in the TGA measurement. In the preceding reasoning, the decomposition of BaCO3 already dissolved in the melt is included in the decompo- sition of the solid BaCO3 in the core. Without knowledge of the thermodynamic activities of the components in the melts, it was not possible to speculate on the decomposition of BaCO3 in the liquid. Under pure CO2 atmosphere, the reaction mechanism seems to be different. According to the phase diagram in Figure 1, the sample passes through phase regions of BaCO3-1iquid, liquid, and liquid-BaO. The reaction curves before X = 0.23 in Figure 5 correspond to the reaction of BaCO3 to liquid. The discontinuity in each X-temperature curve indicates that all BaCO3 became liquid phase. There- after, the reaction proceeded following the isobar shown in the BaCO3-BaO phase diagram. This period corresponded to the X-temperature curves after X = 0.23, as shown in Figure 5. As the reactions were terminated at 1823 K in both experiments, the fractions of decomposition were less than 0.5. Hence, the samples were still in the liquid region before the decompositions were stopped. Examination of the samples after the experiments showed that the samples were completely molten. In the case of the sphere, the decomposition proceeded only up to 24 pct before the sphere fell off. It is seen in Figure 6 that the reaction starts at a temperature around 1260 K, which is the same as observed in the powder bed. However, the decomposition proceeds very slowly as com- pared with the powder sample. At 1500 K, only less than 5 pet decomposition is noticed. This is in conformity with the fact that the reaction is topochemical.tgJ Since the sphere is dense, the reaction takes place only at the surface of BaCO3. The surface area of the sphere is much smaller in comparison with the powder sample. Hence, the reaction rate is slower. Since the eutectic reaction takes place above 1303 to 1333 K, layers of oxide and liquid cover the BaCO3 surface. The amount of liquid increases with time and tem- perature. When the surface tension fails to hold the liquid in the basket, the sample falls off. This explains the inter- ruption of the TGA measurement, as shown by the sudden jump in the weight change in Figure 6. It is seen in Figure 7, where the temperature difference between the sample and the furnace is shown, that the falling off of the sample occurs about 50 K earlier than the one in the TGA study. In the case of the experiments involving the measurement of the sample temperature, the sample was hung by Pt wire, and consequently, the sample could fall off easier when broken. The temperature of the center part of the sphere was always found to be lower than that of the furnace, indicating that there were temperature gradients in the sphere and possibly in the boundary layer with the gas. It was not possible to place the thermocouple at different positions in the sphere to measure the profile of the tem- perature, as the sample crumbled in such cases even at the start of the experiment. Hence, it is very difficult to analyze the effect of heat transfer on the reaction process. However, in the case of powder samples, the results obtained by TGA measurements at initial stages could be used to calculate the activation energy of Reaction [1]. In these cases, only 10 mg BaCO3 was used in the bed. The amount of CO2 gas produced by Reaction [1] was very little. Since the flow rate of the argon gas was high, the resistance to the transport of CO2 gas during the decom- position was negligible. At initial stages, the oxide formed due to the decomposition was very little. Since the molar volume of BaO is only about one-half that of BaCO3, the oxide product layer is likely to be porous. As the particle size of the BaCO 3 powder was very small, of the order of a few micrometers in diameter, the resistance to the diffu- sion of CO2 through the oxide was also negligible. This was true even at the stages when a small amount of liquid was formed due to the eutectic reaction. It can be found from the DTA curve in Figure 4 that the temperature change due to the thermal effect of Reaction [I] was only less than 1 K. Further, if we consider the small particle size of the powder, it is reasonable to expect that the transport of the heat from the surrounding layer through the oxide layer to the BaCO3-BaO interface is not the rate-controlling step at the initial stages. Since the decomposition process is likely to be chemical reaction control, a mathematical analysis can then be made to calculate the activation energy of Reaction [1] at the initial stages using the results of the TGA measurements. The total weight of the sample is m = mBaco 3 + mB~ 9 [5] Since 1 mole BaCO 3 will produce 1 mole BaO, assuming that the weight loss is entirely due to Reaction [1], the following equation is valid: ?h = mBao (MBaco3 -- Msao) [6] MBao where MBao and MB, co~ are the molecular weights of BaO and BaCO3, respectively. Inserting Eq. [6] into Eq. [4], we obtain n'A'Mco,_'kJ Pco_~ f i t - ~ (~_ZT----- I) [7] r~ 414~VOLUME 27B, JUNE 1996 METALLURGICAL AND MATERIALS TRANSACTIONS B x 10 "4 3 0 , , 1200 1250 1300 Temp K 8 x 10"i "0" 1 expefi2K/mental o,n/ 1350 x10 ~ 1400 "o" e~peflmenlal ~50 1300 1350 TempK 110 ~ "o" experimental 1300 13150 1400 1400 Tamp K Temp K Fig. 8--Calculated results for different heating rates:--evaluated function and o experimental. Table I lL The Values of Q Calculated from the Results of Different Runs Heating Rate (K'min-') Q (kJ.mole-') k, (N-m-'.s -~) 7 286 3.235-10 ") 10 313 2.311"10 m 12 319 2.957"10 I~ 15 302 3.267"101~ 12x.. ~ o; experimental ~]ue 1 0.0 ~ 0,6 0.4 0.2 i i ,I i i i i 1280 1300 1320 1340 1360 1380 1400 1420 Temp (k9 Fig. 9-47alculated results for a heating rate of 12 K �9 min -] using the data between X = 0.005 and 0.30:--evaluated function and o experimental. The fraction of the decomposition can be expressed as m o - m i v = - - [8 ] m 0 - m~ with mo and m= being the initial and final weights, respec- tively. Hence, dX rh dt mo - ms {9] The area of the reaction surface in each particle is related to X by the following equation: A = A,,'i 1 - X) ~" [10] where Ao is the initial surface area of the particle and c~ is a geometry factor. In the case of spherical particle, c~ is equal to 2/3. The reaction rate constant k/ can be expressed by the Arrhenius equation: k: = k') exp ( -R~) [11] In Eq. [11], Q is the activation energy and k~! is a constant. Combining Eqs. [7], [9], [10], and [11], the following re- lationship can be obtained: dX n'Ao'( 1 - X)~'Mco2"k~ Pco~ dt - -R-T~'~ 7 ~ (~'co,. - 1) exp ( -~T) [12] When the flow rate of Ar gas is high and the amount of C02 produced is very small, Eq. [12] can be simplified as dX (1 - X) ~ exp (_O)R_T 7t --= 8. [13] with the constant B being B = n'A~176176 R(mo - m=) Equation [13] provides a method to calculate the activation energy of Reaction [1]. For this purpose, the computer pro- gram MATLAB was employed. The data between X = 0.005 and 0.15 obtained in each TGA measurement were fitted in Eq. [13] using the Gauss-Newton method, so that the activation energy Q along with the constant B could be evaluated. The values of Ao were taken from the results of BET measurements. In these calculations, the panicles of the BaCO3 powder were assumed to be spherical, and oe had a value of 2/3. In the calculations, the temperature change of the sample due to the heat of reaction was taken into account. Figure 8 presents the calculated results for different heating rates. The solid lines represent the calcu- lated dX/dt as a function of temperature. The circles rep- resent the values of dX/dt obtained in the TGA measurements. It is seen that the experimental data are very well fitted by the calculated dX/dt functions in the case of all heating rates. The values of Q calculated from the results of different heating rates are listed in Table III. In order to find out that a chemical reaction is rate controlling for the decomposition even after X = 0.15, the experimental data obtained between X = 0.005 and X = 0.30 in the TGA measurement with a heating rate of 12 K �9 min-' were used in a similar calculation. The evaluated function of dX/dt is compared with the experimental points in Figure 9. While the function fits the experimental data reasonably well, the data close to X = 0.30 show some scatter. This calculation gave an activation energy of 321 kJ �9 mole-~, which is quite close to the value 319 kJ �9 mole -1 calculated by using the data prior to X = 0.15. From the values listed in Table III, an average value of 305 kJ �9 mole -1 can be obtained for the activation energy of the decomposition. This value is higher than the value 230 kJ �9 mole -~ reported by Fahim et al.,t61 who determined the activation energy using an iso- METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 27B, JUNE 199(v~415 thermal method in the temperature range of 1323 to 1443 K. The forward reaction rate constant could be calculated from the constant B in Eq. [13] using the value of n �9 Ao evaluated from the measured surface area. In these calcu- lations, the average value of Q, 305 kJ �9 mole -~, was used for all heating rates. The values of ks are also presented in Table III. The value of k s varies from 23.1 �9 109 to 32.7 �9 109 N �9 m- ' �9 s -~. It should be pointed out that due to the likely crack formation toward the center of the particles, the reaction surface area is likely to be different from the value based on BET measurements. The variation of the surface area of the reaction results in scatter in the calcu- lated k I values. V. SUMMARY The decomposition of barium carbonate in argon was investigated in the present work by thermoanalytical tech- nique. The experimental study consisted of two parts. In the first part, the decomposition was studied in shallow powder beds by thermogravimetric technique coupled with DTA analysis. In the second part, densely compacted spheres were employed. The DTA measurements showed two endothermic peaks, one at 1079 K and the other at 1237 K, corresponding to the two phase transformations of BaCO3, orthorhombic-to-hexagonal and hexagonal-to-cu- bic, respectively. In the case of both powder beds and dense spheres, the eutectic reaction between BaCO3 and BaO ap- pears to have a significant effect on the decomposition of BaCO3. The activation energy of the decomposition was evaluated to be 305 kJ �9 mole-' using the gravimetric data obtained at the initial stages of the decomposition in pow- der beds. The value of the forward reaction rate constant, kl, was found to be between 2.31 �9 10 '~ and 3.27 �9 10 '~ N �9 m- ' �9 s -~. ACKNOWLEDGMENTS The authors are thankful to Mr. J.A. Bustnes for his help in the experimental measurements. Financial support from the Swedish Research Council for Engineering Sciences (TFR) for this work is gratefully acknowledged. NOMENCLATURE A surface area (m 2) k s forward chemical reaction rate (N �9 mole-' �9 constant s- ') kb backward chemical reaction rate (m �9 s- ') constant ml weight of species i (kg) m weight flux of species i (kg �9 s- ') m 0 initial weight (kg) m~ weight at complete reaction (kg) Mi molar weight of species i (kg �9 mole -~) n number of particles Pco: partial pressure of CO2 (N �9 m -2) P~co2 equilibrium partial pressure of (N �9 m -2) CO2 Q activation energy (J �9 mole-') R gas constant (J �9 mole-' �9 K -9 T temperature (K) X fraction of decomposition a order of reaction REFERENCES 1. C. Nassaralla, R.J. Fmehan, and D.J. Min: Metall. Trans. B, 1991, vol. 22B, pp. 33-38. 2. B. Ozturk, M. Sasagawa, and R.J. Fruehan: Electr. Furn. Conf. Proc., 1991, vol. 48, pp. 203o10. 3. C.L. Hung: J. Mater. Sci., 1990, vol. 25, pp. 3297-3308. 4. J.J. Lander: Am. Chem. Soc., 1951, vol. 73, p. 5893. 5. B.K. Tushar and A.W. Searcy: J. Chem. Soc. Faraday Trans. 1, 1976, vol. 72, pp. 1889-95. 6. R.B. Fahim, M.I. Zaki, and G.A.M. Hussein: Powder Technol., 1982 vol. 33, pp. 161-65. 7. L. Hackspill and G. Wolfe: Compt. Rend., 1937, vol. 204, pp. 1820- 22. 8. E.H. Baker: J. Chem. Soc., 1964, pp. 699-704. 9. A.W.D. Hills: Heat And Mass Transfer in Process Metallurgy, A.W.D. Hills, ed., Eyre and Spottiswoode, London, 1967, pp. 39-77. 10. Handbook of Chemistry and Physics, 58th ed., R.C. Weast, ed., CRC Press, Boca Raton, FL, 1977. 416--VOLUME 27B, JUNE 1996 METALLURGICAL AND MATERIALS TRANSACTIONS B