Ind. Eng. Chem. Res. 2008, 47, 1409-1415
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Structure and Kinetics of Leaching for the Formation of Skeletal (Raney) Cobalt Catalysts Andrew J. Smith,*,† Leonito O. Garciano II,† Tam Tran,‡ and Mark S. Wainwright† School of Chemical Sciences & Engineering, UniVersity of New South Wales, Sydney 2052, Australia, and DiVision of Engineering, Science and Technology, UNSW Asia, Singapore
The reaction front during leaching of cobalt-aluminum alloys to form skeletal cobalt is sharp and welldefined. In situ milling of a sample by dual-beam electron microscope/focused ion beam provides a highresolution image of the internal catalytic structure, which is similar to that found for skeletal copper but on a finer scale. The leaching kinetics fit the Avrami-Erofe’ev nucleation-and-growth model with an exponent equal to 1. This represents a rate-limiting step involving lineal (one-dimensional) growth of numerous pore nuclei randomly distributed across the reaction interface, but not such that it is covered completely to fit the shrinking unreacted-core (envelope) kinetic model. The coalescing of product cobalt metal around the activated nuclei focuses the pore growth to being mostly lineal. The reaction rate was inversely proportional to the original mean particle size and has an activation energy of 72 ( 4 kJ/mol. A quantitative model is determined. 1. Introduction Skeletal (Raney) catalysts are formed by the leaching of selected aluminum alloys, such as nickel, copper, or cobalt, in caustic solutions. Skeletal cobalt catalysts have been known since the 1930s1 and were the subject of an excellent set of papers by Aller in the 1950s.2-4 Conventional supported and coprecipitated cobalt catalysts have been used by industry for a number of hydrogenation reactions where cobalt offers the right balance between activity and selectivity. This balance is also seen with skeletal cobalt catalysts, making them useful for key industrial reactions. It is well-known that the leaching conditions used in the preparation of skeletal catalysts have a significant impact on their final physical and chemical properties and on their catalytic performance.2,5,6 Since the rate of leaching is critical in determining the catalyst performance and its properties, it is important to have a full knowledge of the leaching kinetics and the mechanism controlling the reaction process. A shrinking unreacted-core kinetic model7 has been claimed to fit the leaching data for copper, either as surface reaction-controlled (small particles)8 or as product layer diffusion-controlled (larger particles),9 and also for rapidly quenched nickel-aluminum alloys.10 However, not all skeletal catalyst systems appear to obey these shrinking-core kinetics. Choudhary and co-workers5 report that formation of skeletal Ni fits well to a Prout-Tompkins style model. Bakker and co-workers11 identified the individual leaching rates of the single phases of the skeletal nickel precursor alloy, with annealed NiAl3 following linear kinetics and Ni2Al3 following parabolic kinetics. Information on the structure or leaching kinetics of skeletal cobalt is scarce in the literature. Very little advance in understanding with respect to the structure and formation of these catalysts has been published since Aller’s work in the 1950s,4 with most of the skeletal catalyst research focusing on nickel and copper. A relatively recent dissertation by Cho12 * Corresponding author. Phone: +61 2 9385 4319. Fax: +61 2 9385 5966. E-mail:
[email protected]. † University of New South Wales. ‡ UNSW Asia.
explored the leaching kinetics for the formation of skeletal cobalt from a range of precursor alloy compositions. The kinetics did not fit the shrinking-core models, and the rate-limiting step remained inconclusive. Cho also presented electron microscope images of the structure of leached skeletal cobalt. There were large cracks on the outer surface and a three-dimensional interconnected network of metal rods internally on a scale of tens of nanometers. Because of magnetic interference by the cobalt itself, the images of the fine porous part of the leached alloy were somewhat indistinct, but both the external and internal structures appeared to be similar to that seen for skeletal copper.13 Extending Aller’s and Cho’s work, this is the first of two papers exploring the structure of skeletal cobalt and the leaching kinetics associated with its preparation. Using the FIB (focused ion beam) miller in a similar fashion to previous work with skeletal copper,13 a more detailed image of the internal structure of skeletal cobalt is presented here. Through consideration of numerous potential models, the leaching kinetics are successfully modeled for the first time. The second paper deals with the effect on the structure and leaching kinetics of promoting the skeletal cobalt with chromia. The refitting of kinetic data from other studies (including skeletal systems other than cobalt) to the model derived in this paper and the inferences that may be drawn from that will be the subject of a later publication. 2. Experimental Section 2.1. Alloy. The precursor cobalt-aluminum alloy used in this study was kindly donated by the Davison Division of W. R. Grace & Co., Baltimore, Maryland. The alloy was crushed using a mortar and pestle and screened to narrow particle size ranges using a series of laboratory test sieves with openings of 50, 160, 211, 245, 300, and 355 microns. 2.2. Particle Characterization. The particle size distribution was determined by a Coulter LS230 and a Malvern Mastersizer. Crystal identification was confirmed by X-ray diffraction on a D5000 diffractometer. A Nikon model Epiphot 200 optical microscope was used for imaging the reaction front of partially leached alloy. Electron microscopy images were obtained on an xT Nova NanoLab 200 that combines a dual-beam highresolution focused ion beam (Ga FIB) and a high-resolution
10.1021/ie070801b CCC: $40.75 © 2008 American Chemical Society Published on Web 02/09/2008
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Table 1. Particle Size Ranges and Mean Particle Size as Determined in This Study particle size range (µm)
mean particle size, s0 (µm)
-125 + 50 -160 + 125 -211 + 160 -300 + 246 -355 - 300
84.6 152.9 257.8 302.4 319.6
scanning electron microscope. The composition of acid-digested catalyst samples was analyzed using a VISTA AX CCD simultaneous inductively coupled plasma-atomic emission spectrometer (ICP-AES). Surface area was determined by a single-point BET (Brunauer, Emmett, and Teller) nitrogen adsorption method, and pore volume was determined by the BJH (Barret, Joyner, Halenda) method on a Micromeritics system. 2.3. Leaching. The leaching experiments were conducted using a 0.6 L round reactor. Stirring was found to have no effect on the measured kinetics. The temperature during leaching was maintained by a Haake (FISONS) k20 refrigeration unit with DC3 circulator. In an experimental run, 5.0 g of the alloy was weighed accurately and added to 0.5 L of sodium hydroxide solution maintained at the test temperature. The volume of hydrogen evolved during leaching ((0.1%) was measured by a precalibrated displacement wet-type gas flow meter (DM3A) from Alexander Wright division. In some experiments, the concentration of dissolved aluminum in the leach liquor was also monitored using ICP-AES and the extraction results derived from both techniques were compared. Liquid samples were taken using an Alitea peristaltic pump.
Figure 1. Electron microscope image of crushed, unreacted Co-Al alloy particles.
3. Results and Discussion 3.1. Structure and Characteristics. The alloy composition was 39.3 wt % Co and consisted primarily of Al13Co4 and Al9Co2 intermetallic phases. This is consistent with the binary equilibrium phase diagram.14 The mean particle sizes and the size ranges for the screened particles used in the experiments are shown in Table 1. The mean particle sizes for the ranges (-211 + 160) and (-300 + 246) µm are outside the specified screen size ranges. This is characteristic of particles that are not spherical but are rather elongated, passing through on their narrow dimensions or being held up across their wide dimensions on a given sieve. The same was experienced by Cho12 and reported in her dissertation. Microscope images of the particles show the irregular and pointed shapes formed during crushing, confirming the nonspherical nature of the particles (Figure 1). Leaching of the alloy in NaOH gives a sharp reaction front (Figure 2), similar to that seen with skeletal copper7 and in agreement with that observed by Cho.12 At higher resolution, the internal structure of the catalytically active leached alloy (Figure 3) is revealed as similar in structure to that seen for skeletal copper13 but on a finer scale. There is some difficulty in obtaining a clear image for the internal cobalt structure in the electron microscope because of the magnetic properties of cobalt. The effects of sodium hydroxide and temperature on the catalyst surface area, average pore diameter, and total pore volume are shown in Figure 4. Leaching at lower temperatures gave significantly higher surface areas with a correspondingly larger pore volume and smaller average pore diameter. Surface areas are in general larger, and pore size is smaller, than those for skeletal copper leached under similar conditions.15
Figure 2. Optical microscope image of a precursor alloy piece leached to 44% conversion in 6.0 M NaOH at 40 °C (mounted and sectioned). The light area (lower right) is unleached alloy and the dark area (upper left) is void space with the area between being porous cobalt as the leached residue.
3.2. Characteristics of Leaching. The leaching reaction can be represented as follows:
13NaOH(aq) + Al13Co4 (s) + 39H2O f 13NaAl(OH)4(aq) + 39/2H2 (g) + 4Co(s) (1) The reaction conversion can be measured by either determining the amount of dissolved aluminum found in the leach solution or by monitoring the volume of hydrogen gas evolved from the reaction vessel. Both measurements were conducted in several experiments from which H2/Al molar ratios of 1.55 ( 0.04 (at 95% confidence level) were determined. This is slightly higher than the theoretical value of 1.50 as given from the above reaction stoichiometry. This is most likely due to some holdup of aluminum as hydroxide in the leached cobalt catalysts, particularly near the reaction front where the pH is lower than in the bulk. Measurements of the amount of hydrogen evolved for each set of conditions were converted to overall conversion (R). Figures 5-7 show the variation of reaction conversion with respect to changing temperature, particle size range, and NaOH concentration, respectively. 3.3. Rate Equation. On the basis of the sharp reaction front observed during leaching (Figure 2), the potential kinetic models
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Figure 3. Dual-beam FIB image of skeletal cobalt (-165 + 125 µm, 4.0 °C, 6.0 M NaOH, unstirred, and 71% alloy conversion): (A) dark patch is the pore void space and (B) light patch is the pore wall of skeletal cobalt.
will be limited to topochemical ones, where the reacting particle is progressively converted from the outside to the inside. Starting with the generic rate equation,
dR ) k[OH-]xAyexp dt
(2)
it was found that the initial rate varies proportionately with exposed surface area. Varying hydroxide concentration did not show any clear trend and a relatively small influence. Thus, we will set x ) 0 and y ) 1 in eq 2. As leaching progresses, the exposed surface area will be a function of the original surface area (A0) and the overall conversion as the leach front progresses into the alloy particle: 16
Aexp ) A0f(R)
(3)
Thus, the rate equation becomes
dR ) kA0f(R) dt
(4)
Young17 and Pannetier and Souchay18 both summarize the derivation of various kinetic models for the reaction of solids based on a nucleation-and-growth mechanism, including Mampel’s Law as the most general kinetic model for a solidfluid reaction. Starting with the nucleation of active sites, these nuclei grow in number and in size as the reaction proceeds. Depending on their initial number, the speed of conversion to active nuclei, and their rate and direction of growth, a number of models are obtained. The primary ones are given in Table 2 in a common form utilizing overall conversion (R). In this table, if the function f(R) is defined by
dR ) Kf(R) dt
(5)
then g(R) is defined by the integral of this
g(R) ) Koverallt
(6)
where Koverall in eq 6 is a function that contains the Arrhenius equation as well as any dependency on the average initial
Figure 4. Effect of varying sodium hydroxide concentration (at 20.6 °C) and temperature (at 6.0 M NaOH) on (a) the total surface area, (b) the average pore diameter, and (c) the total pore volume of skeletal cobalt catalysts (particle size ) -165 + 125 µm).
particle surface area. For all experiments in this work, the temperature was held constant during each run while the alkali concentration was far in excess of stoichiometry (>20×) so that any change in the bulk concentration was negligible. The difference between models no. 1 and 2 in Table 2 accounts for chain nucleation, where as each nucleus grows it results in the formation of new nuclei. The Prout-Tompkins relationship (model no. 3) considers ingestion of potential nuclei by the growing nuclei. The more complex model no. 4 (Mampel’s Law) allows for the case where potential nuclei are numerous, nucleation is rapid, and their growth involves ingestion of a significant quantity of potential nuclei. Avrami derived a very similar relationship to Mampel’s Law in her series of papers on the kinetics of phase change.19-21 Simplification of the relationship for specific cases where the probability of potential nuclei to become nucleated is either large or small, and consideration of a shape factor describing the growth of the nuclei in either 1, 2, or 3 dimensions, resulted in
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Figure 5. Effect of temperature on reaction conversion (at particle size range ) -211 + 160 µm and 6.0 M NaOH).
relationship through probability considerations, a method predicted to work by Avrami in the first of her series of papers. Erofe’ev’s derivation, however, allows for values of n > 4 depending on the mechanism of nucleus formation. In addition, while integer values of n are characteristic of particular mechanisms, values between 0.54 and 0.62 are indicative of diffusion-controlled mechanisms.23 The shrinking-unreacted core (or envelope) models summarized by Levenspiel7 are a special case of the more generic nucleation-and-growth model no. 4. They are derived based on the progressive reaction of a homogeneous solid with a surrounding fluid, where there is, in effect, a very large number of starting nuclei that grow uniformly to give a shrinking envelope of the same shape as the original particle. On the basis of whether the particles are shrinking in 1, 2, or 3 dimensions, and whether the kinetics are controlled by the surface reaction or by diffusion through the product layer, models no. 6-11 are obtained. The case of film-diffusion control (no product layer) is not considered here, since skeletal cobalt clearly has a product layer. In fitting the models of Table 2 to the leaching rate data for skeletal cobalt formation, the shrinking-core model for reaction control with spherical particles does appear to fit for the initial stages of leaching to low conversions, while the corresponding product-layer diffusion-control model fits midrange conversions. This could be interpreted as a change in controlling mechanism from reaction control to diffusion control as the product layer (skeletal cobalt) forms during leaching and causes a longer diffusion path for the reacting species. A model based on the “combination of resistances”, where both surface reaction control and diffusion control are combined to allow for a change in mechanism during reaction, gives a reasonable fit for the kinetic data. However, the simpler Avrami-Erofe’ev model with n)1
-ln(1 - R) ) Koverallt Figure 6. Effect of particle size range on reaction conversion (6.0 M NaOH and 20.0 °C).
Figure 7. Effect of NaOH concentration on reaction conversion (-211 + 160 µm and 20.0 °C).
a series of simple models that can be described by the form given in model no. 5. In this model, n refers to the shape factor or dimensions of nuclei growth, plus an extra 1 if there is a constantly increasing number of nuclei instead of a constant number (that is, n ) 1, 2, 3, or 4). Erofe’ev22 also derived this
(7)
successfully fits the leaching kinetics for the whole of the reaction up to high conversions and across all conditions (Figures 8-10). Given the excellent fit for the reaction kinetics to this simple model, it is unlikely that the combined shrinking unreacted-core model is the correct one. No other model in Table 2 could provide a similar fit to the kinetic data. In addition to the models listed in Table 2, other alternatives considered included the homogeneous model (fast diffusion throughout the particle followed by slow reaction24), different orders of reaction, and starting with a porous solid. Skeletal catalysts are known to age,25 giving a coarsening product layer; however, allowance for this in the shrinking-core models (affects the diffusion coefficient because of varying tortuosity over the depth of the product layer) did not give an adequate or improved fit to the kinetics. The physical meaning to the kinetic data fitting eq 7 and no other model is that the reaction must be controlled by nucleation and growth. A value of n ) 1 in the Avrami-Erofe’ev equation is unusual. While this value is seldom discussed in most kinetic texts, it was discussed in Avrami’s original work.20 The value refers to the case where there are a large number of nucleation sites, randomly distributed, where their activation is fast and their growth is lineal (1-dimensional). In the case of skeletal cobalt precursor alloy, there exists two intermetallic phases, both high in aluminum concentration and obtained through quenching, giving a random and highly defected microstructure. This provides the large number of potential nuclei. Leaching with 6 M NaOH provides a very strong driver for relatively fast
Ind. Eng. Chem. Res., Vol. 47, No. 5, 2008 1413 Table 2. Rate Equations for the Various Solid-Fluid Reaction Models model Nucleation-Growth 1. power law nucleation, linear growth of nuclei 2. chain nucleation, linear growth of nuclei 3. chain nucleation, overlapping/ingestion of nuclei (Prout-Tompkins) 4. numerous potential nuclei, rapid growth followed by ingestion (Mampel’s Law) 5. Avrami-Erofe’ev 6. one-dimensional flat-plate symmetry 7. two-dimensional cylindrical symmetry 8. three-dimensional spherical symmetry
g(R) ) kt (unless otherwise noted)
ref
R1/n ln(R) ln[R/(1 - R)] -ln(1-R) ) A[e-kt - 1 + kt - 1/2(kt)2 + 1/6(kt)3] [-ln(1 - R)]1/n
18 18 18 18 17, 20, 22
Shrinking Core, Surface-Reaction Control R 1 - (1 - R)0.5 1 - (1 - R)1/3
Shrinking Core, Diffusion Control 9. one-dimensional flat-plate symmetry R2 10. two-dimensional cylindrical symmetry (1 - R)[ln(1 - R)] + R 11. three-dimensional spherical symmetry 1 - 3(1 - R)2/3 + 2(1 - R) 12. three-dimensional spherical symmetry (Jander equation) [1 - (1 - R)1/3]2 13. three-dimensional spherical symmetry (Ginstling-Brounshtein) (1 - 2R/3) - (1 - R)2/3
nucleation of the aluminum sites. As the reaction proceeds, cobalt metal is left behind, either by selective removal of the aluminum and surface diffusion of the cobalt (as for many dealloying systems) or by codissolution of both metals followed by reprecipitation of the cobalt (as seen in skeletal copper13). Regardless of the mechanism of cobalt structure formation, its coalescence surrounding an active, growing nucleus will cause
Figure 8. Plot of -ln(1 - R) vs time for different temperatures (particle size range ) -211 + 160 µm, 6.0 M NaOH).
Figure 9. Plot of -ln(1 - R) vs time for different particle size ranges (6.0 M NaOH and 20 °C). Data for the two finest ranges were measured at different solid loadings of alloys.
7 7 7 7 7 7 28 29
the direction of growth of that nucleus to be hindered. By hindering the growth of pores in all directions except one, as might be expected for the cobalt coalescing on the surface around the active nuclei, the growth of the pore nuclei become lineal, or one-dimensional. Such a mechanism would result in the pore formation seen under the electron microscope (Figure 3). While the Avrami-Erofe’ev equation has traditionally been applied to solid-state phase transformations, there is a precedent for its application to the nucleation and growth of pores within a solid.26 Thus, the model makes physical sense as well as providing an excellent fit to high levels of conversion. The overall rate constant Koverall of eq 6 can be determined as the slope of the straight lines in Figures 8-10. The dependence of this overall rate constant on parameters such as mean particle size, temperature, and viscosity and activity of NaOH will now be considered. 3.4. Effect of Mean Particle Size. Figure 11 shows the linear dependence of Koverall on the inverse of mean size of the precursor alloy for the several ranges of particle size studied. Using a constant amount (weight and volume) of catalyst for each experiment, the initial exposed surface area will be proportional to the initial volume divided by average length, and hence, this inverse relationship of Koverall with average particle size is in agreement with eq 4. 3.5. Effect of NaOH. The value of Koverall initially increases with increasing NaOH concentration to an optimum somewhere around 6 M but then decreases with further increases in NaOH
Figure 10. Plot of -ln(1 - R) vs time for different NaOH concentrations (particle size range ) -211 + 160 µm and 20 °C).
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Ind. Eng. Chem. Res., Vol. 47, No. 5, 2008 Table 4. Table of Activation Energies for Skeletal Cobalt, Copper, and Nickel Formations skeletal system cobalt copper copper nickel nickel nickel
phase or alloy composition
activation energy (kJ mol-1)
ref
Co4Al13 plus Co2Al9 CuAl2 plus CuAl2-Al eutectic CuAl2 plus CuAl2-Al eutectic Ni20Al80 (rapid quench) Ni50Al50 (rapid quench) Ni50Al50
72 ( 4 69 ( 7 69.1 41.98 103 56.6
(this study) 13 8 10 10 5
4). The value for the cobalt system is very close to that determined for copper but differs from that of the nickel system. 3.7. Final Kinetic Model for Skeletal Cobalt Formation. On the basis of the relationship with particle size and temperature, a more complete kinetic model is offered for the leaching of cobalt-aluminum alloy to give skeletal cobalt, Figure 11. Koverall vs the inverse of mean size of alloy particles (6.0 M NaOH and 20 °C, upper axis), and Koverall vs NaOH concentration (particle size range ) -211 + 160 µm and 20 °C, lower axis).
-ln(1 - R) ) k0 exp(-EaR-1T-1)s0-1t
(8)
where R ) overall conversion, k0 ) 3.5 × 1015 (µm‚h-1), Ea ) activation energy (72.5 × 103 J‚mol-1), R ) gas constant (8.314 J‚K-1‚mol-1), T ) temperature (K), so ) initial average particle size (µm), and t ) time (h). The rate constant in eq 8 has a weak, complex dependency on NaOH activity/concentration; however, the relationship is not simple and requires further exploration to fully understand it. 4. Conclusions The structure of skeletal cobalt is similar to that for skeletal copper, although on a finer scale. Leaching progresses with a sharp reaction front and follows Avrami-Erofe’ev kinetics with an exponent of 1, representing rapid nucleation and a large number of potential nuclei throughout the solid, while the growth of the nuclei is one-dimensional because of the buildup of product cobalt metal around the pores. The activation energy and relationship with initial particle size has been determined, but the trend with respect to sodium hydroxide concentration, which is similar to that seen for skeletal copper, is not simple and requires further exploration.
Figure 12. Arrhenius plot for varying temperatures (particle size range ) -211 + 160 µm and 6.0 M NaOH). Table 3. Molar Concentration and Interpolated Mean Activity Coefficients for Sodium Hydroxide Solution at 20 °C27 molar concentration (20 °C)
mean molar activity coefficient, γ (20 °C)
1.5 2.7 6.0 10.4
0.68 0.76 1.42 5.35
concentration; however, the trend is weak and insignificant compared to other parameters of the kinetic equation (Figure 11). This weak trend has also been observed with skeletal copper, although the reasons for it have not been adequately explored. Even allowing for the large change in activity coefficient across the range of concentrations investigated (Table 3),27 or for the increase in solution viscosity with concentration, no clear or significant trend is observed for the value of Koverall. 3.6. Effect of Temperature. The Arrhenius relationship between Koverall and (1/T) is presented in Figure 12. From the slope of this line, the activation energy of the leaching process was found to be 72 ( 4 kJ/mol. Reported activation energies for other skeletal systems are tabulated for comparison (Table
Acknowledgment Financial support from the Australian Research Council is gratefully acknowledged. Literature Cited (1) Faucounau, L. A New Method of Preparation of Metal Catalysts. I. Preparation of Active Copper and Some of Its Dehydrogenation and Hydrogenation Reactions. Bull. Soc. Chim. 1937, 4 (5), 58-67. (2) Aller, B. V. Raney Cobalt Hydrogenation Catalysts. I. The Preparation of the Catalyst. J. Appl. Chem. 1957, 7, 130-134. (3) Aller, B. V. Raney Cobalt Hydrogenation Catalysts. II. The Physical and Chemical Properties of the Catalyst. J. Appl. Chem. 1958, 8, 163167. (4) Aller, B. V. Raney Cobalt Hydrogenation Catalysts. III. Applications and Promoter Effects. J. Appl. Chem. 1958, 8, 492-495. (5) Choudhary, V. R.; Chaudhari, S. K.; Gokarn, A. N. A Kinetic Model for Leaching Process in Preparation of Raney Nickel Catalyst. Ind. Eng. Chem. Res. 1989, 28, 33-37. (6) Wainwright, M. S. Skeletal Metal Catalysts. In Handbook of Heterogeneous Catalysis; Ertl, G., Kno¨zinger, H., Weitkamp, J., Eds.; WileyVCH: Weinheim, Germany, 1998; Vol. 1, pp 64-72. (7) Levenspiel, O. Chemical Reaction Engineering, 2nd ed.; John Wiley & Sons, Inc.: Singapore, 1972; p 372. (8) Ma, L.; Smith, A. J.; Tran, T.; Wainwright, M. S. Development of Skeletal Copper-Chromia Catalysts. II. Kinetics of Leaching Al and Chromia Deposition. Chem. Eng. Process 2001, 40, 59-69.
Ind. Eng. Chem. Res., Vol. 47, No. 5, 2008 1415 (9) Friedrich, J. B.; Young, D. J.; Wainwright, M. S. Caustic Leaching of Al-Cu-Zn Alloys to Produce Raney Catalysts. II. Leaching Kinetics. J. Electrochem. Soc. 1981, 128 (9), 1845-1850. (10) Hu, H.; Qiao, M.; Pei, Y.; Fan, K.; Li, H.; Zong, B.; Zhang, X. Kinetics of Hydrogen Evolution in Alkali Leaching of Rapidly Quenched Ni-Al Alloy. Appl. Catal., A 2003, 252, 173-183. (11) Bakker, M. L.; Young, D. J.; Wainwright, M. S. Selective Leacing of Nickel-Aluminium (NiAl3 and Ni2Al3) Intermetallics to Form Raney Nickels. J. Mater. Sci. 1988, 23, 3921-3926. (12) Cho, M.-H. Microstructure Development of Raney Cobalt Catalysts. Ph.D. Thesis, Purdue University, West Lafayette, Indiana, 2004. (13) Smith, A. J.; Tran, T.; Wainwright, M. S. Kinetics and Mechanism of the Preparation of Raney Copper. J. Appl. Electrochem. 1999, 29 (9), 1085-1094. (14) Massalski, T. B.; Okamoto, H.; Subramanian, P. R.; Kacprzak, L. Binary Alloy Phase Diagrams; ASM International: Materials Park, Ohio, 1990. (15) Tomsett, A. D.; Young, D. J.; Wainwright, M. S. Pore Development During Selective Leaching. J. Electrochem. Soc. 1984, 131 (11), 2476. (16) Sohn, H. Y. Chemical Reaction Engineering in the Chemical Processing of Metals and Inorganic Materials. Part I. Advances in Fluid-Solid Reaction Analysis. Korean J. Chem. Eng. 2003, 20 (2), 185199. (17) Young, D. A. Decomposition of Solids. In The International Encyclopedia of Physical Chemistry and Chemical Physics; Tompkins, F. C., Ed.; Pergammon Press: Oxford, U. K., 1966; Vol. 1, Chapter 2. (18) Pannetier, G.; Souchay, P. Chemical Kinetics; Elsevier: London, 1967; Chapter 9. (19) Avrami, M. Kinetics of Phase Change. I. General Theory. J. Chem. Phys. 1939, 7, 1103-1112.
(20) Avrami, M. Kinetics of Phase Change. II. Transformation-Time Relations for Random Distribution of Nuclei. J. Chem. Phys. 1940, 8, 212224. (21) Avrami, M. Kinetics of Phase Change. III. Granulation, Phase Change, and Microstructure. J. Chem. Phys. 1941, 9, 177-184. (22) Erofe’ev, B. V. A Generalized Equation of Chemical Kinetics and Its Application in Reaction Involving Solids. Compt. Rend. Acad. Sci. USSR 1946, 6, 511-514. (23) Hancock, J. D.; Sharp, J. H. Method of Comparing Solid-State Kinetic Data and Its Application to the Decomposition of Kaolinite, Brucite, and BaCO3. J. Am. Ceram. Soc. 1972, 55 (2), 74-77. (24) Wen, C. Y. Noncatalytic Heterogeneous Solid Fluid Reaction Models. Ind. Eng. Chem. 1968, 60 (9), 34-54. (25) Smith, A. J.; Trimm, D. L. The Preparation of Skeletal Catalysts. Annu. ReV. Mater. Res. 2005, 35, 127-142. (26) Emel’yanov, A. N. Formation of Pores in Granulated Mineral Materials under Firing. Glass Ceram. 2001, 58 (1-2), 34-35. (27) Åkerlo¨f, G.; Kegeles, G. Thermodynamics of Concentrated Aqueous Solutions of Sodium Hydroxide. J. Am. Chem. Soc. 1940, 62, 620-640. (28) Ginstling, A. M.; Brounshtein, B. I. The Diffusion Kinetics of Reactions in Spherical Particles. J. Appl. Chem. USSR 1950, 23 (12), 13271338. (29) Jander, W. Reactions in Solid State at High Temperature. Z. Anorg. Allg. Chem. 1927, 163 (1-2), 1-32.
ReceiVed for reView June 11, 2007 ReVised manuscript receiVed December 10, 2007 Accepted December 23, 2007 IE070801B
