Ind. Eng. Chem. Res. 1987,26, 1628-1632
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Bartholomew, R. N.; Casagrande, R. M. Ind. Eng. Chem. 1957,49, 428. Beeckmans, J. M.Fluidization ZV,Kunii, D., Toei, R., Eds.; Plenum: New York, 1984; p 177. Beeckmans, J. M.; Nilsson, J.; Large, J.-F. Znd. Eng. Chem. Fundam. 1985,24 90. Boland, D.; Geldart, D. Powder Technol. 1971,5,289. Brubaker, T. A.; Tracy, R.; Pomernacki, C. L. Anal. Chem. 1978,50, 1017A. Chen, J. L.-P. Chem. Eng. Commun. 1981,9,303. Chen, J. L.-P.; Keairns, D. L. Can. J . Chem. Eng. 1975,53, 395. Christian, G. D. Analytical Chemistry, 2nd ed.; Wiley: New York, 1977. Fan, L. T.; Lee, C. H.; Bailie, R. C. AZChE J . 1962,8,239. Gidaspow, D.;Ettehadieh, B. Znd. Eng. Chem. Fundam. 1983,22, 193. Gidaspow, D.;Ettehadieh, B.; Bouillard, J. AlChE Symp. Ser. 1985, 80(241), 57. Gidaspow, D.; Lin, C.; Seo, Y. C. Ind. Eng. Chem. Fundam. 1983,22, 187. Gidaspow, D.; Syamlal, M.; Seo, Y., “Fluidization V”, Proceedings of the Fifth Engineering Foundation Conference on Fluidization, Engineering Foundation, AIChE, 1986, p 1. Grohse, E. W. AZChE J . 1955,1, 358. Hunt, R. H.; Biles, W. R.; Reed, C. 0. Pet. Refin. 1957,36, 179. Kelly, V. P. Nucl. Sci. Eng. 1961,10, p. 40. Kunii, D.; Levenspiel, 0. Fluidization Engineering; Wiley: New York, 1969.
Naimer, N. S.; Chiba, T.; Nienow, A. W. Chem. Eng. Sci. 1982,37, 1047. Nienow, A. W.; Cheesman, D. J. Fluidization; Grace, J. R., Matsen, J. M., Eds.; Plenum: New York, London, 1980; p 373. Ratziaff, K. L. Anal. Chem. 1980,52,1415. Rowe, P. N.; Nienow, A. W.; Agbim, A. J. Trans. Znst. Chem. Eng. 1972a,50,310. Rowe, P. N.; Nienow, A. W.; Agbim, A. J. Trans. Znst. Chem. Eng. 1972b,50, 324. Rowe, P. N.; Macgillivary, H. J.; Cheesman, D. J. Trans. Znst. Chem. Eng. 1979,57, 194. Seo, Y.-C. Ph.D. Thesis, Illinois Institute of Technology, Chicago, 1985. Shannon, P. T. Ph.D. Thesis, Illinois Institute of Technology, Chicago, 1959. Sustek, J. Anal. Chem. 1974,46, 1676. Syamlal, M. Ph.D. Thesis, Illinois Institute of Technology, Chicago, 1985. Tanimoto, H.; Chiba, S.; Chiba, T.; Kobayashi, H. Fluidization; Grace, J. R., Matsen, J. M., Eds.; Plenum: New York, London, 1980; p 381. Van Duijn, J.; Rietema, K. Chem. Eng. Sci. 1982,37, 727. Yang, W. C.; Keairns, D. L. Znd. Eng. Chem. Fundam. 1982,21,228. Yoshida, K.; Kameyama, H.; Shimizu, F. Fluidization; Grace, J. R., Matsen, J. M., Eds.; Plenum: New York, London, 1980; p 389. Receiued for review February 20, 1986 Accepted May 2, 1987
Solid-state Kinetic Measurements Using Dynamic X-ray Diffraction D. E. Anderson and W.J. Thomson* Department of Chemical Engineering, Washington State University, Pullman, Washington 99164-2710
Dynamic X-ray diffraction (DXRD) is a novel application of powder X-ray diffraction as a kinetic tool that has been developed to obtain phase-specific kinetic data from simultaneous reactions in solids. As such, it is an improvement over the more conventional techniques such as thermogravimetric analysis (TGA) and differential thermal analysis (DTA). Results are presented here to show how the DXRD measurement parameters can be optimized to produce a high rate of data acquisition with minimal error. It is shown that a solid-phase concentration measurement can be obtained every 15 s. Applying the DXRD technique to the decarbonation reaction of calcium carbonate (CaC03 CaO + COz) and to limestone sulfation has demonstrated its precision and applicability to three-phase/two-reactionsystems.
-
Conventional techniques for measuring solid-state kinetic data make use of accompanying changes in either the mass or the enthalpy of the reacting sample. For example, in thermogravimetric analysis (TGA) the change in mass of the reacting sample might be attributed to the evolution of a gaseous product. In the case of competitive reactions, however, it might not be possible to distinguish between the rate of formation of the different products. Similarly, competitive reactions can confuse differential thermal analysis (DTA) because of the difficulty, if not impossibility, of designating the relative contributions of competing reactions to the total enthalpy change. Moreover, because these conventional techniques are limited to bulk property changes, they cannot easily be employed to study surface reactions. Whereas TGA and DTA techniques find ready applications for simple reacting systems (i.e., one reaction), the only method which has been available for studying simultaneous solid reactions is the “Quench and Analyze” method. Here the reactions are allowed to proceed to a point where they are quenched (usually cooled) and then analyzed by X-ray diffraction or wet chemistry. The procedure is repeated many times until the entire reaction path(s) has been covered. Two good examples of
the painstaking nature of this technique are Park et al.’s (1979) studies of oil shale mineral reactions and Kuzel et al.’s (1981) investigation of the preparation of thick film resistors. Obviously, this approach is also limited to relatively slow reactions. We describe here an impyoved tool for kinetic analysis which overcomes these limitations: dynamic X-ray diffraction (DXRD). Since every unique crystal structure generates a unique powder X-ray diffraction pattern, X-ray diffraction can determine which chemical phases are present in a sample at any time. The Joint Committee on Powder Diffraction Standards (JCPDS) has catalogued the diffraction patterns of over 30000 materials (Cullity, 1978), so the use of X-ray diffraction for phase identification is already routine. Modern X-ray diffractometers, however, are also capable of a high degree of quantitative accuracy, precision, and repeatability. In fact, X-ray diffraction is used in the steel industry for quality control to determine the amount of austenite and martensite present in quenched steels (Pask, 1967). This precise quantitative analysis is made possible by employing a set of standards and exploiting the high resolution of modern X-ray diffraction equipment. The availability of hot stages has also
0888-588518712626-16 28$01.50/0 0 1987 American Chemical Society
Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987 1629
4
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Figure 1. Dynamic X-ray diffraction apparatus.
made high-temperature, in situ phase analysis at equilibrium commonplace. See, for example, Iyengar et al. (1985). Furthermore, the interfacing of modern diffractometers with microprocessors and digital data acquisition makes it possible to collect phase-specific data as a function of time and at high temperatures. The remainder of this manuscript describes how DXRD can be used to measure solid-state kinetic data and reports on the optimal system parameters required to collect repeatable data in a minimum time. The technique is then illustrated by discussing the experimental results for two different reacting systems.
Experimental Methods Description of Equipment. Figure 1 shows a schematic of the diffractometer and the associated accessories for operating in the DXRD mode. The DACO microprocessor is essential to DXRD, as it controls goniometer movement and transfers the goniometer position, scintillation counter output, and time to the PDP 11/23+ for storage. The sample is contained in a high-temperature cell. Diffractomer and Accessories. The powder X-ray diffraction for DXRD was performed on a Siemens D500 diffractometer. Cu K a X-rays generated at 40 kV and 30 mA were used for all of the experiments reported here. The sample enclosure is an Anton-PAAR, HTK-10 hightemperature chamber. X-rays penetrate this chamber through a radiation window and gas flows through it to allow control of the gas composition. The platinum sample holder shown in Figure 2 also serves as the heating element. It is controlled by a Micristar 828D programmable temperature controller. Automation and Data Handling. A DACO-MP computer, also a Siemens product, directs the handling of digital data and controls the programmed goniometer movement. Twenty independent peak scans can be programmed to execute without operator intervention, and
up to 1600 scans may be programmed with minimal operator intervention. Twenty to 60 scans are sufficient for typical DXRD applications. A 10-s delay between scans allows the goniometer to set itself for the next scan, and additional delay time may be added as required for slow reactions. Scan data (time, angle, and intensity) are passed from the DACO-MP to a DEC PDP 11/23+ computer. Peak intensities are integrated here using an algorithm developed by Siemens. Alternately, data may be retrieved to be subjected to other integration methods. At the end of a run, the time, integrated intensities, and peak positions are combined with physical data to calculate the mole fractions of each phase at each scan time. The details of this procedure will be described below. Sample Temperature. Early in the developmental stage of DXRD, it was found that sample movement (as the goniometer moved) caused significant problems. Initially this was overcome by using a relatively thick sample bed (1.2 mm was typical) contained within a platinum frame which was cemented to the center of the heating strip. Unfortunately, this resulted in a large temperature difference between the top of the sample and the bottom of the strip. Type-S thermocouples of 0.20-mm-diameter wire were placed both at the center of the underside of the heating strip and directly above this position, as near the top of the sample as possible while keeping the thermocouple covered. This revealed that the bottom of the strip was typically 60-80 K hotter than the upper thermocouple when the bottom thermocouple read 873 K. Because of attenuation, only a thin skin at the top of the sample is visible to X-rays. In the case of CaC03, for instance, 99% of the diffracted X-rays is diffracted from the upper 200 pm of the sample bed, and most species have even thinner effective bed depths. Thus, while it is important to have a measurement of the surface temperature, this is not easily achieved. As will be discussed below, another technique of sample mounting was also developed during the course of this investigation. Whereas this latter method resulted in a very thin sample thickness (about 150 pm), the intensity of the diffracted X-rays was less than with the thicker bed. Consequently, all of the data reported here were obtained with the thicker bed, and temperature control and data logging were all accomplished by using the upper thermocouple. Inaccuracies in this temperature measurement were subsequently corrected by using the results obtained with the thin sample layers. This will be discussed below in more detail. Data Analysis. Scan Parameters. If DXRD is to be a valuable experimental tool for studies of solid-state kinetics, then it is important to reduce the amount of time necessary to scan a peak and obtain a valid intensity. Optimization with respect to time allows manipulation of the two time-related parameters: the number of points in a peak scanned and the count time at each point. The scan time is equal to the number of points scanned mul-
1630 Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987
tiplied by the count time at each point, neglecting the time required to move the goniometer from one point to another. Since we seek to obtain the most accurate and easily integrated peak in a minimum time, we may scan a typical peak over a fixed range, varying the number of points and the count time simultaneously to keep the total scan time constant. In order to evaluate this aspect of DXRD, an arbitrary time of 1min was selected to scan the major peak of calcite from 28 to 30' 28. This range scans the major calcite peak in its entirety at any reasonable temperature. Since it takes the same amount of time to scan the width of the peak in any of these 1-min scans, the optimal step size and count time are those that result in the most accurate and easily integrated peak. The criteria for selecting the optimum scan parameters must reflect two things: peak definition and the statistical deviation of the points in the peak,. Peak definition is related to the number of points used to integrate the peak and the positioning of those points. For example, in the simplest case of approximating integrated intensity by peak height, f20% error can result (JCPDS, 1978) because the broadness of the peak is not taken into account. On the other extreme, if a large number of points define the shape of the peak, the count time per point will need to be very small to be able to scan the peak in a short enough time to be of use to DXRD. The resulting statistical scatter of the points (due to a low signal-to-noise ratio) can result in integration attempts of low integrity. Species Concentration. The quantitative conversion from integrated intensities to concentrations is not trivial. Two basic methods exist for doing this. One method involves the use of an internal standard and reference intensity ratios. This method is described in detail by Chung (1974). It lends itself well to systems in which only a few phases among many are of interest. The concentration of a phase is calculated from the ratio between its intensity and the intensity of the internal standard. The only requirement is to know the concentration of the internal standard throughout the reaction. The other method avoids the need for an internal standard by employing absorption coefficients. I t requires that all significant phases are monitored at least once during reaction. The strength of this method is that it is completely general, requiring no external knowledge of how the concentration of an internal standard changes as the sample reacts. The latter method was the one chosen for this work, and it requires the solution of a set of linear equations. For a mixture of n phases, the equation for the jth row will be
where ui is the volume fraction of component i and pi is the linear absorption coefficient of component i. The latter may be calculated from data tabulated in literature. Ijp is the intensity that phase j would have if the sample were pure phase j . It is sometimes possible to measure the pure phase intensity directly. Usually, however, it is necessary to determine this value from reference intensity ratios. The reference intensity ratio (RIR) used here is defined as the ratio of the integrated intensities of the major peaks of the phase in question and a reference phase (typically corundum) in a 50 wt % mixture. It is related to pure phase intensity according to ~ - = -C- L RIR, Iap
Ipp
CL,
RIRp
where a and (3 are particular phases.
(2)
Although reference intensity ratio measurements are usually straightforward, the JCPDS has published values for very few of them, and those values that have been measured are known to be in error by as much as M O % . This large margin for error arises because integrated intensity was approximated by peak height in the JCPDS measurements. All DXRD results have consequently used reference intensity ratio measurements performed in this laboratory, and they are based upon integrated intensity. It should be noted that the actual magnitudes of the pure phase intensities calculated from eq 2 will not matter as long as the sum of the calculated volume fractions is set equal to one. This approach was developed into a software package compatible with rapid data analysis and is described in detail by Anderson (1985).
Results Scan Parameter Optimization. The first task in the development of DXRD was to optimize the scanning parameters with respect to time. As mentioned earlier, the approach consisted of scanning a calcite peak from 28' to 30' 28 with various numbers of points and count times per point selected such that the total count time over the scan was held constant at 1 min. Visual inspection of these scans indicated that the optimum compromise between the number of points scanned and the count time per point occurred when the count time per point was 1.5 s. This corresponds to a step size between points of 0.05'. The resulting peak definition is excellent. The next step in the optimization task was to determine the error involved by deviating from these parameters in order to shorten the total time spent scanning. To assess this, DXRD was applied to calcite decomposition. Calcite decomposition is known to be first order up to 80% conversion (Beruto and Searcy, 1974), so a rate constant is easily calculated. The scans of the major calcite peak were cycled continuously as the decomposition proceeded at 910 K. Each cycle consisted of a 17-point scan of 0.05' step sizes and 1.5s count times. Data were collected with a receiving slit width of 0.15'. In typical powder X-ray diffraction applications, this slit width is larger than optimum for a 0.05' step size. Although this may cause a mild distortion of peak shape, the statistical significance of the peak intensity measurement is enhanced. Since only intensity measurements are of interest in DXRD, this slit width is desirable. The full set of 17-point samples was taken to be the "best" data set, and the first-order rate constant was determined by numerically integrating the peak intensities to calculate fraction converted vs. time. The rate constant obtained from this data set was then compared to rate constants calculated from the same data set, except with points symmetrically truncated from the leading and trailing edges of the peaks inward to simulate a shortened scan. Data were similarly deleted from the full set to simulate scans of 0.10' step sizes at several different total scan widths. Figure 3 shows the results of this exercise. As can be seen, either a 0.05' or a 0.10' step size gives comparable results (less than 5% error) for scan times greater than 12 s. To achieve the smallest error in the shortest scan time, however, a step size of 0.10' can be safely used to measure an entire peak every 7.5 s. The larger step size is preferable for short scan times because it results in a broader coverage of the entire peak. For example, at a scan time of 7.5 s, the 0.10' step size uses 5 points which cover 60% of the peak width, whereas 5 points at a 0.05' step size only cover 30% of the peak width. Thus, we have concluded that the minimum number of points that must be sampled is 5, and the 5-point scan must cover at least 60% of the peak width. The
Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987 1631 PERCENT ERROR IN RATE CONSTANT VS SCAN TIME
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minimum count time per point is 1.5 s. Including overhead time (e.g., the time for goniometer movement between scans), this corresponds to the acquisition of three data points every 50 s. Accuracy and Repeatability. Since calcite decomposition kinetics are well-studied, they provide a good check on the repeatability and reliability of the DXRD system. Reagent grade calcite with an average particle diameter of 26 pm was decomposed to calcium oxide at temperatures from 800 to 900 K. All decompositions were isothermal and carried out in 35-kPa absolute pressure of Nz flowing at 1.0 L/min to prevent recarbonation. In order to prevent decomposition from taking place prior to reaching the desired temperature, the sample was heated in flowing COz at 35-kPa absolute pressure. Based on published values of the equilibrium constant, this is sufficient to prevent decomposition up to 1120 K. Once the temperature was reached, the flow was switched to N2 and residence time distribution measurements indicated that the atmosphere reached 95% Nz well within 3 min. Consequently, all analyses were conducted by ignoring the first 2 min of the reaction. The calcite peaks were scanned from 28.9 to 29.9' 28 with a step size of 0.05' and a count time of 1.5 s. These 21 points were integrated and converted to mole fraction to provide a mole fraction data point every 40 s. Good first-order rate plots were obtained between 10% and 80% decomposition and the calculated activation energy was 224 kJ/mol. This is consistent with the value of 205 kJ/mol reported by Beruto and Searcy (1974) and also by Borgwardt (1985). It is also consistent with Powell and Searcy's (1980) activation energy of 209 kJ/mol, which was measured under reaction limiting conditions. Our rate constants, however, were typically 3-10 times lower than the literature values. This was attributed to inaccurate surface temperature measurements. The upper thermocouple was placed as near the surface of the sample as possible while remaining covered by the sample, but the diameter of the thermocouple junction was about 0.4 mm, which is one-third of the depth of the actual sample bed. Furthermore, even though the thermocouple wire was only 0.2 mm, calculations indicated that it was acting as a heat sink. As a result, a limited set of experiments were also conducted with a very thin (about 150 pm) sample bed where the heating strip temperature was essentially equal to the sample temperature. While these experiments provided accurate temperature measurements, the very small sample sizes decomposed so fast at the higher temperatures that it was difficult to obtain quality rate data. Nevertheless, it was possible to extrapolate the low temperature data since the calculated activation energy for the thin bed experiments was nearly
\ 1 1.04 '
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Figure 4. Arrhenius plot of calcite decomposition.
identical with the value obtained with the thick bed experiments. The thick bed temperatures were then corrected by comparing those measured rates with the rates extrapolated from the low temperature, thin bed experiments. Figure 4 shows an Arrhenius plot of all of the calcite decomposition rate constants, and as can be seen, the thick bed results are very repeatable while the thin bed results have a larger scatter. It should also be pointed out that these rate constants are now in substantial agreement with the literature values. Application to Limestone Sulfation. DXRD can be applied to virtually any set of solid-state reactions, and we are currently studying oil shale mineral reactions and solid-state reactions in high temperature ceramics processing, as well as the processing of thick films for semiconductor applications. To demonstrate the use of DXRD to measure kinetics in a multiphase system, we have also applied the technique to limestone sulfation. In this application, Vicron, a commercial limestone, was calcined and then exposed to 2000 ppm SOz, 8% C02,and 6% O2in N2 and allowed to react at temperatures between 900 and 1100 K. Depending upon temperature and gas-phase composition, two competing reactions can occur: CaO + l/zOz
+ SO2
-
-
CaSO,
(3)
CaO + COz CaC03 (4) Thus, three phases must be monitored with DXRD. The major peaks for these three phases, CaO, CaSO,, and CaCO,, occur at 28 = 36.9O, 25.6', and 29.2', respectively. The Vicron was calcined at 1000 K for 1 h with a 1.0 L/min N2 flow. At the end of this hour, the sample was heated or cooled to the sulfation temperature in 1min and an 18-min full scan of the sample was performed. When the full scan was complete, the reactant gas replaced the Nz, but at a flow rate of 0.25 L/min. DXRD scanning began after 40 s, starting with the CaO peak. Some of the results of this set of experiments are shown in Figures 5 and 6. Figure 5 shows the mole fractions of the three phases present during the sulfation at 910 K. At the higher temperatures, CaC03 formation (eq 4) is not thermodynamically favored, so only two phases were found to be present during reaction, CaO and CaS04. The higher rate of sulfation at higher temperature is illustrated in Figure 6. CaS0, formation is faster at 1100 K than at 910 K even
1632 Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987
,-
' O f
CaO
w
-I
0 5 20
0
40
60
80
TIME ( m i n )
Figure 5. Limestone sulfation with 2000 ppm SO2 a t 910 K. 10-
I
0
20
I
1
40
60
I
80
TIME (min)
Figure 6. Comparison of CaSO, formation rates during limestone sulfation.
though the competing reaction (eq 4) does not occur at 1100 K.
Discussion and Conclusions DXRD is a general technique for measuring phasespecific kinetic data of a solid. The only restrictions on the sample are that it is crystalline or polycrystalline and that it can exist as a solid at the conditions of interest. DXRD has been performed successfully on a threephase/two-reaction system involving CaC03, CaO, and CaS04. We are currently applying it to even more complex systems. The accuracy of the temperature measurements made with a thick sample bed (on the order of 1 mm) is poor because of the relatively large size of the thermocouple in such an extreme geometry. The sample bed can be made sufficiently thin, however, that the temperature of the sample will essentially match the temperature of the heating strip. While this technique allows accurate temperature measurements without placing a thermocouple directly within the sample, the lower diffraction intensities can lead to scattered data when attempting to monitor fast reactions. Some limiting factors inherent to DXRD are peak crowding and data inaccuracy. Although it has not yet been a problem during DXRD, it is conceivable that a major peak of one phase could be inseparably overlapped
with a significant peak of another phase. In this case, it might be necessary to select a secondary peak of the obscured phase or correct the overlapped intensity by the appropriate fraction of the intensity of the unobscured phase. Although eq 1 is an exact equation, error could arise during calculation because of inaccuracies in absorption data or reference intensity ratios, but these limitations should seldom be troublesome. Reference intensity ratios can easily be measured by the experimenter to whatever degree of accuracy is required. Furthermore, although the absorption data available in the literature are known to be generally 10% inaccurate, the resulting error in concentration is only a few percent because absorption coefficients are usually similar for the products and reactants of a reaction. DXRD combines the quantitative ability of modern X-ray diffractometers with programmable digital data acquisition to follow the kinetics of solid-state reactions. The analysis and procedures have been developed, optimized, and demonstrated and have been found to be in good agreement with kinetic measurements by conventional techniques.
Acknowledgment Funding was provided in part by Environmental Energy Research Corporation Subcontract 8536-22 under prime Contract 68-020-3987 with the Environmental Protection Agency and in part by the National Science Foundation under Grant CBT-8611104. Registry No. CaC03, 471-34-1; CaO, 1305-78-8; COz, 124-38-9.
Literature Cited Anderson, D. E. M.S. Thesis, Washington State University, Pullman, 1985. Beruto, D.; Searcy, A. W. Trans. Faraday SOC.1974, 70,2145-2153. Borgwardt, R. H.AIChE J. 1985, 31(1), 103-111. Chung, F. H. J. Appl. Crystallogr. 1974, 7, 519-525. Cullity, B. D. Elements of X - R a y Diffraction; Addison-Wesley: Reading M A , 1978. Iyengar, S. S.; Engler, P.; Santana, M. W.; Wong, E. R. in Advances i n X - R a y Analysis, Barret, C. S., Predecki, P. K., Leyden, D. E., Eds.; Plenum: New York, 1985; Vol. 28, pp 331-338. Joint Committee on Powder Diffraction Standards (JCPDS) 1978 Alphabetical Index, Swarthmore, PA, 1978. Kuzel, R.; Broukal, J.; Kindl, D. I E E E Trans. Compon., Hybrids, Manuj. Technol. 1981, CHMT-4(3), 245-249. Park, W. C.; Lindermanis, A. E.; Robb, G. A. I n S i t u 1979, 3, 353-381. Pask, J. A,, Ed. A n Atomistic Approach to the Nature and Properties of Materials; Wiley: New York, 1967. Powell, E. K.; Searcy, A. W. Metall. Trans. 1980, l l B , 427-432. Received f o r review J u n e 2, 1986 Accepted April 23, 1987
