982
Ind. Eng. Chem. Res. 1989, 28, 982-987
Coals in Hydrogen Donor Media. Fuel 1980,59, 803-805. Guin, J. A.; Tarrer, A. R.; Prather, J. W.; Johnson, D. R.; Lee, J. M. Effects of Coal Minerals on the Hydrogenation, Desulphurization and Solvent Extraction of Coal. Ind. Eng. Chem. Process Des. Dev. 1978, 17, 118-126. Guin, J. A.; Tarrer, A. R.; Lee, J. M.; Van Backle, H. F.; Curtis, C. W. Further Studies of Catalytic Activity of Coal Minerals in Coal Liquefaction. Ind. Eng. Chem. Process Des. Deu. 1979, 18, 631-637. Habermehl, D.; Orywel, F.; Beyer, H. D. Plastic Properties of Coal. In Chemistry of Coal Utilization;Elliot, M. A., Ed.; Wiley: New York, 1981; 2nd Sup. Vol., p 354. Hill, G. R.; Hariri, H.; Redd, R. I.; Anderson, L. L. Adu. Chem. Ser. 1966, No. 55, 427. Hombach, H. P. General Aspects of Coal Solubility. Fuel 1980,59, 465-470. Kuhlmann, E.; Boerwinkle, E.; Orchin, M. Solubilization of Illinois Bituminous Coal: The Critical Importance of Methylene Group Cleavage. Fuel 1981, 60, 1002-1004. Liebenberg, F. J., Pitgieter, H. Fuel 1973, 52, 130. McElroy, R. British Columbia Research Ltd., Internal Report, 1982. Mochida, I.; Takarabe, A,; Takeshita, K. Solvolytic Liquefaction of Coals with a Series of Solvents. Fuel 1979, 58, 17-23. Mohan, G.; Silla, H. Kinetics of Donor Solvent Liquefaction of Bituminous Coals in Nonisothermal Experiments. Ind. Eng. Chem. Process Des. Dev. 1981, 20, 349-358. Painter, P. C.; Yamada, Y.; Jenkins, R. G.; Coleman, M. M.; Walker, P. L. Investigation of Retrogressive Reactions Leading to Carbonization of Solvent-Refined Coal. Fuel 1979, 58, 293-297. Petrakis, L.; Grandy, D. W. Free Radicals in Coals and Coal Conversion. 2. Effect of Liquefaction Processing Conditions on the Formation and Quenching of Coal Free Radicals. Fuel 1980,59, 227-232. Reid, R. c.; Prausnitz, J. M.; Sherwood, T. K. The Properties of Gases and Liquids, 3rd, ed.; McGraw-Hill: New York, 1977. Ross, D. S.; Blessing, J. E. Alcohols as H-Donor Media in Coal Conversion. Fuel 1979, 58, 433-437. Rudnick, L. R.; Whitehurst, D. D. The Effect of Solvent Composition on the Liquefaction Behavior of Western Sub-bituminous Coal. A m . Chem. SOC.S y m p . Ser. 1981, 169 (New Approaches to Coal Chem,). 153-1 71.
Shalabi, M. A.; Baldwin, R. M.; Bain, R. L.; Gary, J. H.; Golden, J. D. Noncatalytic Coal Liquefaction in a Donor Solvent. Rate of Formation of Oil, Asphaltenes, and Preasphaltenes. Ind. Eng. Chem. Process Des. Deu. 1979, 18,474-479. Shaw, J. M. A Correlation for Hydrogen Solubility in Alicyclic and Aromatic Solvents. C.J.Ch.E. 1987, 65, 293-298. Shaw, J. M.; Peters, E. The Role of Initial Reaction Conditions in Direct-Coal-Liquefaction. Ind. Eng. Chem. Res. 1989, submitted. Shibaoka, M.; Stephens, J. F.; Russel, N. J. Microscopic Observations of the Swelling of a High-Volatile Bituminous Coal in Response to Organic Solvents. Fuel 1979, 58, 515-522. Singh, C. P. P.; Shah, Y. T.; Carr, N. L.; Prudich, M. E. Liquefaction of Coal by SRC-I1 Process (I). Can. J . Chem. Eng. 1982, 60, 248-260. Smith, G. C.; Cook, A. C. Coalification Paths of Exinite, Vitrinite, and Inertite. Fuel 1980, 59, 641-646. Szladow, A. J.; Given, P. H. Models and Activation Energies for Coal Liquefaction Reactions. Ind. Eng. Chem. Process. Des. Dew. 1981, 20, 27-33. Taverides, L. L.; Stamatoudis, M. The Analysis of Interphase Reactions and Mass Transfer in Liquid-Liquid Dispersions. Adv. Chem. Eng. 1980,2, 199-268. Thurgood, J. R.; Hanks, R. W.; Oswald, G. E.; Youngblood, E. L. The Rheological Characterization of Coal Liquefaction Pre-heater Slurries. AZCHE J . 1982, 28, 111-116. Vernon, L. W. Free Radical Chemistry of Coal Liquefaction: Role of Molecular Hydrogen. Fuel 1980,59, 102-106. Weigold, H. Behavior of Co-Mo-Al,03 Catalysis in the Hydrodeoxygenation of Phenols. Fuel 1980, 61, 1021-1026. Weinberg, V. L.; Yen, T. F. Solubility Parameters in Coal and Coal Liquefaction Products. Fuel 1980, 59, 287-289. Whitehurst, D. D.; Mitchell, T. 0.;Farcasiu, M. Coal Liquefaction. The Chemistry and Technology of Thermal Processes;Academic Press: New York, 1980. Yarzab, R. F.; Given, P. H.; Spackman, W.; Davies, A. Dependence of Coal Liquefaction Behavior on Coal Characteristics. 4. Cluster Analysis for Characteristics of 104 Coals. Fuel 1980, 59, 81-92. Yoshida, R.; Maekawa, Y.; Ishii, T.; Takeya, G. Fuel 1976,55, 337.
Received for review May 11, 1987 Accepted July 22, 1988
MATERIALS AND INTERFACES Effective Boundary Area of Decomposition and Dissolution of Agglomerated Lead Carbonate Kenichi Miyasaka, Kanako Ueda, and Mamoru Senna* Faculty of Science and Technology, Keio University, Hiyoshi, Yokohama 223, Japan
Mechanically activated, fine powdered aggregates were additionally compressed into agglomerates to examine the effective boundary area of the dissolution and decomposition reactions. The effective boundary area for the dissolution reaction was confirmed to be the external area around the aggregates or agglomerates, which tended to disintegrate themselves during the reaction. T h e decomposition reaction, on the other hand, was not restricted by the external surface area. Instead, the limiting extensive dimension was similar t o the intercrystallite boundary area. Energy storage as a result of mechanical activation is well-known (Heinicke, 1984; Miyasaka and Senna, 1985). The reactivity of such mechanically activated fine powders is often predominated by the availability of the stored energy (Miyasaka and Senna, 1987). The effective boundary area is of no less importance, as was already discussed (Miyasaka and Senna, 1986). In spite of the 0888-5885/89/2628-0982$01.50/0
general recognition of the above-mentioned, experimental studies aimed at the separation of parameters affecting the rate of solid-state reaction are scarce. A real rate process of the solid-state reaction using mechanically activated, fine powdery materials can never be expressed by any models comprising an ensemble of separated spherical particles. Existence of agglomerates
6 1989 American Chemical Society
Ind. Eng. Chem. Res., Vol. 28, No. 7, 1989 983 Table I. Preparative Conditions of Agglomerates powders P, GPa dA, pm symbol as-received 0 115 N-0-115 ground 0 115 M-0-115 as-received 0.1 N-0.1-115 115 505 N-0.1-505 ground M-0.1-115 0.1 115 M-0.1-505 505 as-received 0.5 N-0.5-115 115 N-0.5-505 505 ground M-0.5-115 0.5 115 M-0.5-505 505 as-received 1.0 N-1.0-115 115 N-1.0-505 505 ground 1.0 115 M- 1.O-115 M- 1.0-505 505 as-received 2.0 115 N-2.0-115 N-2.0-505 505 ground 2.0 115 M-2.0-115 M-2.0-505 505
is almost always unavoidable and plays an important role. In the course of a solid-state reaction, agglomerates may be disintegrated into smaller fractions, making the process even more complicated. This kind of change in the granulometrical morphology alters the effective boundary area of the surface during the reaction. The change depends on the density of the agglomerates. The role of the surface area on the solid-state reaction was extensively studied. Most of them were dedicated, however, to the solid-solid addition reactions, where the significant contact is more or less point like (Blum and Li, 1961; Nagai et al., 1976). The reaction partner of the dissolution or decomposition, on the contrary, is a continuum, so the effective boundary area for a reaction is to be discussed more thoroughly from a microscopic point of view. Dissolution processes of mechanically activated materials were extensively studied (Grizina, 1978; Steinike et al., 1982). A common conclusion is that the enhanced rate of dissolution is chiefly attributed to the structural change, rather than the simple increase of the geometrical surface area. Grizina (1978) showed it for activated V209 Steinike et al. also showed a correlation between the rate of dissolution of quartz and the amorphous portion (Steinike et al., 1982). The role of the effective boundary was discussed recently on mechanically activated Mg(OH)2(Inoue and Senna, 1988). The purpose of the present study is to elucidate the role of the effective boundary for the dissolution reaction of mechanically activated fine powders. For this purpose, a series of agglomerates of activated and nonactivated materials were prepared with varying compressive stress. Thermal decomposition was also carried out on the same samples in order to discuss the specificity of the effective area for a particular reaction.
Experimental Section Commercial lead carbonate (Merck, pro analysi) was used as a starting material. For the purpose of mechanical activation, a laboratory-sized vitration mill was used in air for 1 h. The amplitude was kept constant a t 50 mm. Details of grinding conditions were given elsewhere (Miyasaka and Senna, 1985). Compression of the powders was carried out to obtain different agglomerates. The powder (0.5 g) was put into a cylinder of 4.3-mm i.d. and compressed uniaxially for 5 min. The tablets obtained were subjected to fragmentation by a hand mortar. Care was taken not to give any additional mechanical activation during the subsequent fragmentation. The obtained agglomerates were sieved into
Table 11. Terminology and Granunometric Properties terminology symbol crystallite primary particle aggregate agglomerate intraaggregate pore interaggregate pore volid fraction of agglomerate
diameter D dB dP
specific surface area U
SB SP
SA d! median radius volume VI TI r2 c
v2
Figure 1. Scanning electron micrographs of nonactivated (A) [N0-1151 and activated (B) [M-0-1151 materials.
two fractions, i.e., 28/35 mesh (average 505 pm) and 120/150 mesh (average 115 pm). All specimens used are tabulated in Table I. Powders and agglomerates were characterized by using an air permeability method (Shimadzu, SS-100) to obtain the external area, S,, and mercury porosimetry (Carlo Erba, Porosimeter 2000). The intercrystallite boundary area, 0 , was calculated from the crystallite size obtained by conventional X-ray diffractometry. The void fraction, E , of agglomerates was calculated from the geometry of the compressed tablets. The rate of dissolution in 0.1 M acetic acid-ethanol (l:l, w/w) was monitored by a pH meter. A 20-mg specimen was put into 50 cm3 of the solvent in Ar atmosphere. Mixing conditions such as the size of the stirring rods and the rate of revolution were carefully chosen in order to avoid the dependence of dissolution kinetics on the rate of mixing. Based on the preliminary experiments, we used a small vessel (a beaker of 43-mm inner diameter) with a large magnetic rod (40 mm long) where the mixing is good enough. Since the rate of dissolution remained always constant for a specimen when the rate of revolution of the stirrer was above 200 rpm, the latter was kept constant at 200 rpm. An electrothermobalance equipped with a line-focused infrared furnace (Rigaku, Thermoflex) was used for the measurement of the rate of decomposition. All the reactions were carried out a t a nitrogen flow of 50 cm3 min-'. Details of the experimental conditions for the decomposition reaction are given elsewhere (Miyasaka and Senna, 1986). The parameters used in the present study are summarized in Table 11, together with the terminology of the associated particles.
Results and Discussion Granulometrical Properties. Micrographs of the starting materials and agglomerates are shown in Figures 1and 2. It is recognized from Figure 1 that the starting material, particularly after mechanical activation, was highly aggregated even before the compression. The micrographs of classified agglomerates are shown in Figure 2.
984 Ind. Eng. Chem. Res., Vol. 28, No. 7,1989
0.6
-
H
420pm
0.L
-
CI
w
w
590pm
105pm
I
125pm
c
0.2
Figure 2. Optical micrographs of the classified agglomerates (C) [N-1.0-5051 and (D)[M-1.0-1151.
N-0.1-505
1oa
0 0
0.05
0.1
0.5
5
1
P / GPa
-0.5 - 5 0 5 _ _ _N_ _- -_- -_- ---
0, n
E
E
50
\
>
I
I
N-1 -505
001
0.1
LO
10
1 r / pm
Figure 3. Pore size distribution curves for different agglomerates. For the notation, see Table I. 300 2 sa 20c
'0,
20
th
0
0
0.05 0.1
0.5
1
N
M
O
A 5
P / GPa
Figure 5. (a, top) Relationship between the noncrystallinity, 1 - I,, and P. (b, bottom) Relationship between the crystallite size, D,and P.
75
E E \ N
?
30
10
1 oc
n
'
\
n
5c
>-
2:
0 J-
'
0
0.5
0.05 0.1 P /
1
5
GPa
Figure 4. Variation of partial void volumes, VI and V,, with compressive stress, P.
As shown in Figure 3, the pore size distriubtion was always bimodal, reflecting the existence of agglomerates (Imai and Kuno, 1986; Dimilia and Reed, 1983; StanleyWood and Shubair, 1979). The median radius and the cumulative volume of smaller intraaggregate pores were denoted by rl and Vl, respectively. Those for the larger interaggregate pores were denoted with subscript 2. The variation of void volumes V1 and V2 with compressive
stress is shown in Figure 4. The median pore radius showed a similar decrease with compressive stress. From Figure 4, it was concluded that the interaggregate pores preferentially disappeared after compression. The change was a little more remarkable for the mechanically activated materials. The insensitivity of rl and Vl to the compressive stress would suggest that no significant disintegration of the unit aggregate took place during compression. Structural Properties. As shown in Figure 5a, the noncrystallinity, 1 - If,remained eventually unchanged when the compressive stress was below 0.5 and 1 GPa for samples N and M, respectively. After exceeding the critical stress, the increase in 1 - If became significant. The crystallite size, D, decreased with stress, in contrast to that of 1 - If, as shown in Figure 5b. Application of the compressive stress on the PbC03 powders thus gives rise to the simple compression a t lower stress, followed by the structural degradation a t higher stress. The critical stress of the structural degradation was higher for the sample, which was preliminarily activated, in which structural defects were already contained. Kinetic Process of Dissolution. A modified firstorder kinetic equation, (1-
- 1 = kdt
(1)
where CY is the fraction dissolved, kd is the apparent rate constant of dissolution and t is time, was applied. Equa-
Ind. Eng. Chem. Res., Vol. 28, No. 7, 1989 985 t
/
S
60
30
0
90
120 1
N
M
d, = 1 1 5u m O
A
@
A
293 K
- I P
i
i
l R
= . i 32
N-01-115 0 M-01-115 A
1 P / GPa
Figure 7. Relationship between the apparent rate constant of dissolution, kd, and P.
M - 2 -115 A
i 0
120 t
/
n 360
2LO
La6
a!
'
S
Figure 6. Relationship between (1-
- 1 and t for dissolution.
i
tion 1 was derived by accounting for the specific surface area, S ( t ) ,as d a / d t = k S ( t ) ( l- a ) (2) By integrating eq 2, we obtain (1 -
- 1=
2 -kSot = k d t 3
(3)
where So is the initial surface area. Details of the rate analysis using eq 1 are given elsewhere (Miyasaka and Senna, 1986). The dissolution process was expressed with a straight line for those samples preliminary compressed under relatively small stress, as shown in Figure 6. For the dense agglomerates, on the other hand, the dissolution kinetic process showed two different steps, the first, slower one and the second, faster one. The reason for this will be discussed later on. The apparent rate constant of dissolution was obtained from the slope of the first linear portion of the curve shown in Figure 6. The apparent rate constant, k d , of dissolution decreased markedly with increasing compressive stress, as shown in Figure 7. The dissolution rate of the nonactivated samples was always larger than that of activated samples, compared at the same compressive stress. The apparent rate depended also on the size or the external area of the agglomerates; i.e., the smaller agglomerates gave rise to the faster dissolution. The apparent rate constant of dissolution is divided by the external surface area of the aggregates. When the rate of dissolution of the uncompressed materials, kdO, was divided by the external surface, S,, the rate constants per unit external area, kdO/Sp, for nonactivated [N-0-1151 and activated [M-0-115] materials, respectively, were almost identical, i.e., 56.8 and 57.0 mg m-2 s-l. This leads to the inference that S , is a common extensive factor predominating the dissolution, and the structural change did not play a significant role in enhancing the rates of dissolution. Similar results were already argued for different experiments (Miyasaka and Senna, 1986). Effects of Surface Area and Size of Agglomerates for Dissolution Reaction. In order to discuss the effect
I
'%---" 0 0 5 01
05
1
5
P/GFb
Figure 8. Variation of
Qd
and
8, with P.
of the external surface area of the agglomerates, S A , on the dissolution rate, the apparent rate constant of dissolution of smaller agglomerates, kdl115, was divided by that of larger agglomerates, kd/505, to obtain the ratio Q d (=kd/115/kd/505). If the rate constant of dissolution is solely dominated by the external surface of the agglomerates, Qd should be 505/115 or 4.4. As shown in Figure 8, Q d was 1for sample N as well as M when the compressive stress was as low as 0.1 GPa. &d increased thereafter with increasing P. If the reactive solution penetrates into the agglomerate easily and the agglomerates disintegrate themselves during the reaction, the effective boundary area must increase. The lower value of Qd for the loose agglomerate could thus be explained by assuming the disintegration of the agglomerates into their construction unit, i.e., aggregates. The increase in Q d with compressive stress will be explained by the same manner. The difference in the rate of increase of Qdwith respect to the stress between samples N and M may be attributed to the difference in the rate of densification with respect to the compressive stress as shown in Figure 4. The limiting void fraction, e, for the beginning of the increase in Q d was about 0.17. Change in the Effective Area during Dissolution. The change in the effective surface during the dissolution reaction as a result of the disintegration of agglomerates should now be expressed quantitatively. The effective particle size and corresponding surface area of the ag-
986 Ind. Eng. Chem. Res., Vol. 28, No. 7, 1989 1.0
I
i
-
E
u 06-
4 \
R
M-2-115
A
-535
Figure 9. Relationship between the effective diameter of agglomerates, d * , and P.
glomerates are denoted d* and S * , respectively. If no change in the reaction rates per unit effective surface area takes place during a dissolution reaction, eq 4 should hold.
33
3
60
12C
93
-C' 152
t / s
Figure 10. Relationship between -(ln (1 - a))or a and t for decomposition reaction, showing the applicability of the first-order kinetics.
Since kd is the rate constant of dissolution for compressed lead carbonate, the ratio at the left-hand side of eq 4 expresses the rate constant per unit effective area. By rearranging eq 4,we obtain d* =
(kdo/kd)dp
(5)
where d, is the initial diameter of the aggregates. The variation of d * , defined above, against the compressive stress is shown in Figure 9. Compression of the nonactivated sample, N, under stress as slow as 0.5 GPa brought about nearly complete disintegration of the agglomerates. An increase in the effective particle size, d*, with compressive stress was obvious for nonactivated as well as activated materials. The increase was particularly remarkable above 0.5 GPa. When sample M was compressed at 2 GPa, d* for larger agglomerates was 422 pm, Le., near the agglomerate size, 505 pm. In the case of smaller agglomerates made under the same compressive stress, the value of d*, 61 pm, was appreciably smaller than the agglomerate size, 115 pm. The easier disintegration of smaller agglomerates may be attributed to the easier absorption of liquid in the case of smaller agglomerates, because of larger contact area per unit volume of agglomerates. The value of &d that is larger than the calculated value of 4.4,shown in Figure 8, will also be explained by assuming the easier disintegration for smaller agglomerates. Thus, the difference in the apparent dissolution behavior between the dense and loose agglomerates is explained by the change in the effective boundary area available for the dissolution reaction. Kinetic Process of Decomposition. As reported elsewhere (Miyasaka and Senna, 1986), the initial step of the decomposition of lead carbonate is expressed by
0
P /
1
5
GPa
Figure 11. Relationship between the apparent rate constant of decomposition, k,, and P.
of kd (Figure 7). This again confirms our idea that the controlling factors for dissolution and decomposition reactions are substantially different from each other. Effect of Intercrystallite Boundary Area a n d Density of Agglomerates for Decomposition. The ratio Q, was defined for the decomposition reaction, as in the same manner as Qd. As shown in Figure 8, Q, remained almost unchanged, i.e., within the range between 1.0 and 1.2. This is an indication that the decomposition reaction is insensitive to the external surface area of agglomerates. The rate constant was divided by the intercrystallite boundary area, and the ratio RpIDwas defined as Rp/D
The kinetic analysis was carried out only for this initial step. First-order kinetics applied fairly well to the isothermal decomposition, as shown in Figure 10. As shown in Figure 11, the apparent first-order rate constants, k,, changed in a manner almost opposite to that
05
0.05 0.1
=
(kp/
.)/
(kpO/
uO)
(7)
where Kpo and a. are the initial values of k and a for nonactivated materials before compression. A s shown in Figure 12, the value of R,lD varied only within the range between 1and 1.5, in spite of the fact that the rate constant of sample M was ca. twice as large as that for sample N.
Ind. Eng. Chem. Res., Vol. 28, No. 7, 1989 987 2c
= kd of larger agglomerates, s-l k , = rate constant of decomposition, s-' kPo = k , for nonactivated materials before compression, s-' kp/115 = k , of smaller agglomerates, s-' kp/505 = k , of larger agglomerates, s-' P = compressive stress, GPa kd/505
A 15
Qd Qp
2
kd/115/kd/505 kp/iidkp/~05
r = pore radius, pm r1 = median radius of intraaggregate pore, pm r2 = median radius of interaggregate pore, pm S * = effective surface area of agglomerates during dissolution,
0
(L
= =
10
m2 g-' 05 N
M
dA=115pm
A
d,=505pm
A
0 0
0.05 0.1
05
1
5
P / GPa
Figure 12. Relationship between R,,D and 1 - I p
It is therefore reasonable to assume that the effective area for the decomposition reaction was nearer to the intercrystallite boundary area than to any other areas including B E T specific surface. This was also the case for mechanically activated Mg(OH), (Inoue and Senna, 1988). RpIDincreased with increasing compressive stress, passing through a maximum, and decreased again above 1 GPa. The decrease in RplD for very dense agglomerates, in spite of larger noncrystallinity, should be explained by an alternative mechanism. One of the most probable mechanisms will be the reluctant outgassing of the decomposed product, C 0 2 . This increases the local partial pressure of COz, which, in turn, would enhance the rate of reverse reaction, shifting the local equilibrium. The turning point, Le., the critical void fraction in this case, was 0.17 or 0.09 for nonactivated or activated materials, respectively.
Conclusions The effective boundary area for the dissolution reaction changes from the external area of the agglomerates of that of aggregates, depending on the density of the agglomerate. When the void fraction exceeded 0.17, the agglomerates tended to disintegrate themselves to give an effective boundary area larger than that of the external area of the agglomerates, approaching to a limiting value, i.e., that of unit aggregates. The decomposition reaction, on the other hand, was restricted by the intercrystallite boundary area. The effect of the reverse reaction became significant, however, in the case of agglomerates, with their void fraction being smaller than a critical value. Nomenclature D = diameter of crystallite, nm d* = effective diameter of agglomerate during dissolution,pm dA = diameter of agglomerate, pm d B = diameter of primary particle, wm d, = diameter of aggregates, pm If = relative intensity ratio of X-ray diffraction 1 - If = noncrystallinity k = general rate constant, in eq 2 and 3 k d = rate constant of dissolution, s-l k d O = k d of aggregates before compression, s-' k d / 1 1 5 = k d of smaller agglomerates, s-l
SA= specific surface area of agglomerates, m2 g-' S B = specific surface area of primary particles, m2 g-' So = specific surface area at the beginning of the reaction, in eq 3 S , = external surface area of aggregates, m2 g-' S ( t ) = general specific surface area, in eq 2 t = time, s V = pore volume, mm3 g-' V1 = intraaggregate pore volume, mm3 g-' V 2 = interaggregate pore volume, mm3 g-' Greek Symbols a = fraction dissolved E = void fraction u = intercrystallite boundary area, m2 g-' uo = u for nonactivated materials before compression, m2g-'
Registry No. PbCO,, 598-63-0.
Literature Cited Blum, S. L.; Li, P. C. Kinetics of nickel ferrite formation. J. Am. Ceram. SOC.1961, 44, 611. Dimilia, R. A.; Reed, J. S. Dependence of compaction on the glass transition temperature of the binder phase. Am. Ceram. SOC. Bull. 1983, 62, 484. Grizina, K. Grundlagenuntersuchungen zur Mahlaktivierung kristalliner Feststoffe unter besonderer Berucksichtigung der Losungkinetik am Beispiel von Vanadiumpentoxid (Fundamental studies on the mechanical activation of crystalline solids with particular reference to the dissolution kinetics of vanadium pentoxide). Ph.D. Dissertation, T. H. Aachen, F.R.G., 1978. Heinicke, G. Tribochemistry; Akademie-Verlag: Berlin, 1984. Imai, H.; Kuno, H. Change in intra- and inter-granular pores with compaction process. Funtai oyobi Funmatsu Yakin 1986,33,11. Inoue, S.; Senna, M. Differences between the dissolution and the decomposition kinetics of mechanically activated magnesium hydroxide. React. Solids 1988,5, 155. Miyasaka, K.; Senna, M. Calorimetric and thermoanalytical assessment of mechanically activated PbC03. Thermochim. Acta 1985, 83, 225. Miyasaka, K.; Senna, M. Correlation between excess enthalpy and the rates of decomposition and dissolution of mechanically activated lead carbonate. React. Solids 1986, 2, 135. Miyasaka, K.; Senna, M. Effects of strontium incorporation on the rate of decomposition of mechanically activated lead carbonate. React. Solids 1987, 4, 151. Nagai, H.; Cho, S. H.; Yamaguchi, T.; Kuno, H. Effects of aggregation of reactant powder particles on the kinetics and mechanism of solid state reaction between BaCO, and Ti02. Funtai oyobi Funmatsu Yakin 1976,23, 68. Stanley-Wood, N. G.; Shubair, M. S. The influence of binder concentration on the intra- and inter-granular porosity of pharmaceutical granules. Powder Technol. 1979, 22, 153. Steinike, U.; Hennig, H.-P.;Richter-Mandau, J. R.; Kretzschmar, U. Investigations of dissolving mechanically processed quartz grains. Crystal Res. Technol. 1982, 17, 1585. Received for review August 4 , 1988 Revised manuscript received March 14, 1989 Accepted April 11, 1989
