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J. Phys. Chem. B 2001, 105, 5099-5105

5099

ARTICLES Atomistic Modeling of Gibbsite: Cation Incorporation Sean D. Fleming,†,‡ Andrew L. Rohl,†,* Steve C. Parker,§ and Gordon M. Parkinson† A. J. Parker CooperatiVe Research Centre for Hydrometallurgy, School of Applied Chemistry, Curtin UniVersity of Technology, GPO Box U1987, Perth, WA 6845, Australia, and Department of Chemistry, UniVersity of Bath, Bath BA2 7AY, U.K.

Computer modeling techniques provide a useful mechanism with which to model the morphology of defect crystals. In this work, a study of the incorporation of sodium and potassium cations into the morphologically important surfaces of gibbsite was conducted. Computation of the resulting changes in surfaces energies was achieved with the aid of a Born-Haber cycle. These calculations were then employed to determine the defect influenced morphologies for both cations. The resulting habits suggest that cation incorporation contributes to the elongation of the prismatic faces and also to the formation of diamond morphologies.

1. Introduction The incorporation of foreign species into crystalline materials has received much attention in the literature. Many studies have involved computing the surface segregation energy, defined as the preference for a defect in the bulk to migrate to the surface.1 It has been shown that segregation tends to be highly dependent on the crystal face and the percentage of defect coverage selected.2 Researchers have also investigated the effect of cationic defects on the surface energy and, thus, the influence on the morphology of calcite.3 Further studies on this system have yielded information concerning nucleation and crystal growth.4 This work was concerned with predicting morphology changes in gibbsite due to the incorporation of cationic defects. Consequently, the development of a computational technique for examining the structural characteristics of surface defect sites was of considerable importance. In the work by Wesolowski et al.,5 the phenomena of cationic binding to the surface of magnetite was examined. Some of the issues addressed by the authors concern the surface to labile ion potential model, the precise nature and likelihood of surface complexation reactions, and the importance of estimating the total reactive surface area. It is conceivable that the methods employed in our work may be applied to such problems in the future. The most commonly used industrial process for the production of alumina from bauxite is the Bayer process. The process is essentially one of recrystallization, in which the precipitation of gibbsite (a polymorph of Al(OH)3), from a supersaturated sodium aluminate liquor, is the rate-limiting step

Al(OH)4- h Al (OH)3 + OHSodium is incorporated in the gibbsite during production, and * Corresponding author. † Curtin University of Technology. ‡ Current address: Laboratory for Process Equipment, Technical University of Delft, 2628 CA Delft, The Netherlands. § University of Bath.

this is a serious form of contamination, as the soda is retained in the product after calcination to alumina. This causes subsequent problems during smelting to aluminum, as high levels of sodium accelerate the degradation of the bath mixture and damage the electrolytic cells. It is thus important for alumina refineries to be operated in such a way as to minimize the level of sodium incorporation in gibbsite while maximizing productivity, two conditions that are not necessarily mutually compatible. As an initial step towards controlling the level of sodium incorporation in gibbsite, it is important to understand how and where it is incorporated. This is very difficult to achieve experimentally, and hence, complementary studies by computer molecular modeling have particular value. It has been shown that an equilibrium model is sufficient to predict all experimentally observed gibbsite surfaces.6 However, these calculations underestimate the morphological importance (MI) of the (200) and (110) prismatic faces, possibly due to the assumption of vacuum growth conditions. It is therefore of further interest to include some effects of solution upon the equilibrium morphology of the gibbsite. One important modifier is the disruption of the lattice resulting from defects. Solution studies have shown that the cationic species Na+ and K+ tend to be closely linked with clusters of aluminate monomers.7 It is therefore possible that incorporation occurs when growth units (accompanied by associated cations) dock into the surface of gibbsite. It has also been suggested that the sodium cation acts as a substitution impurity by replacing a proton.8 Furthermore, quantitative experimental evidence of cation incorporation and of the associated elongation of the prismatic faces was presented in the work of Lee et al.9 and Mensah.10 2. Background Surface Modeling. All modeling calculations were performed using the computer code MARVIN.11 With this program, surfaces are treated as being composed of a stack of interacting layers. These layers are classified as belonging to one of two possible region types. The uppermost layers, labeled (1..n), are allowed to move until the net force acting upon the atoms

10.1021/jp003136s CCC: $20.00 © 2001 American Chemical Society Published on Web 05/11/2001

5100 J. Phys. Chem. B, Vol. 105, No. 22, 2001

Fleming et al.

TABLE 1: Accessibility of Unique Surface Hydrogens in Gibbsite to a Sodium Cationa hydrogen accessibilities (%) candidate 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 surface sites

(002) (200) (110) 32.46 30.85 30.41 28.80 8.48 2.05

4

49.27 39.62 30.85 15.35 3.36 0.00

49.12 47.66 46.78 39.91 29.09 27.34 21.49 17.84 12.87 10.23 2.34 0.15 0.00

3

(101h)

(101) 37.87 37.87 36.70 36.70 22.37 22.37 0.15 0.15

5

38.60 38.45 37.43 37.43 23.39 23.39 0.00 0.00

6

41.67 41.67 32.60 32.02 15.94 15.94 0.00 0.00

6

(112) (112h)

41.81 41.81 33.19 33.19 13.30 13.30 3.95 3.95

4

4

44.44 41.96 37.57 37.13 36.40 34.94 34.80 26.90 23.98 22.37 14.33 12.72 3.65 3.07 0.00 9

43.86 40.94 38.60 38.01 34.06 32.46 30.99 29.82 20.18 16.96 16.08 9.06 2.78 0.58 0.15 8

a

The values represent the percentage of the total spherical surface area. The two columns for the (101) and (101h) faces list the results for the two possible cleavage planes. The bold entries correspond to those sites that have been deemed accessible by the algorithm given in the text.

TABLE 2: Accessibility of Unique Surface Hydrogens in Gibbsite to a Potassium Cationa hydrogen accessibility (%) candidate 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 surface sites

(002) (200) (110)

(101h)

(101)

29.24 47.22 43.71 33.33 33.04 25.58 34.94 41.37 32.60 33.04 26.02 23.39 40.50 31.58 33.04 24.12 5.26 33.92 31.14 32.31 1.32 3.36 22.95 17.11 17.11 0.73 0.44 20.76 17.11 17.11 13.45 0.00 0.00 11.11 7.02 1.17 0.44 0.00

4

2

4

6

38.60 38.60 27.49 26.75 9.94 9.94 0.00

6

4

(112) (112h)

38.45 38.16 27.78 26.61 3.80 3.65 0.00

4

41.08 36.55 32.89 32.31 32.16 31.29 30.41 21.93 17.84 16.96 8.63 2.49 1.02 0.44 0.00 8

39.18 34.94 33.19 31.87 30.85 27.63 26.90 25.88 14.47 11.84 13.30 1.32 0.15 0.00 8

a

The values represent the percentage of the total spherical surface area. The two columns for the (101) and (101h) faces list the results for the two possible cleavage planes.

converges to zero. These are designated as belonging to region 1. Region 2 is comprised of all the slices beneath region 1 and simulates the effect of the bulk crystal on the surface region. Hence, all atoms in region 2 are held fixed. It is straightforward to extend this concept to define the surface energy for some plane (hkl) n

Ehkl surf

)

∑ i)1

Eislice - Ebulk slice Ahkl

(1)

where Eislice is the energy of the ith slice in region 1, Ebulk slice is the energy of an equivalent slice in the bulk, and Ahkl is the surface area. Using a Langmuir relation, we can write the defect surface defe energy Esurf for each face in the morphology as4 pure Edefe surf ) Esurf + χEs

(2)

pure where the term Esurf represents the surface energy of the pure

Figure 1. Contact and re-entrant surface of the (002) face of gibbsite for a cationic sodium probe. Four surface repeat units are shown (2 × 2 construction), with the original surface cell outlined in white. Element colors are white for hydrogen, orange for oxygen, and green for aluminum. The re-entrant surface is magenta.

crystal. The fractional quantity χ is the defect surface coverage, and Es is the extra energy (per unit surface area) required to form a maximally covered defective surface from a pure surface. Thus, Es is the sum of the energies of all possible defect sites. In such a scheme, if a value for χ were selected so that only one defect per unit surface area were formed, the change in surface energy would be the average expected if all candidate sites were equally likely to contain the defect. Defect Surface Coverage. Unfortunately, the Langmuir isotherm often proves insufficient in its unmodified form. The possibility of deviation from Langmuir behavior was emphasized in the work by Tasker et al.,12 in which the authors demonstrate a linear relationship between the logarithm of surface coverage and the reciprocal temperature for several metal oxide systems. Furthermore, it has been observed that the relationship between defect energy and surface coverage can be strongly dependent on the crystal face under consideration.13,14 This is of vital importance to morphology prediction and requires that some modification of expression 2 be made. An atomistic approach was taken in which the term Es was replaced with a new quantity Erep. Erep is defined as the energy required to replace a particular hydrogen on the surface of gibbsite with a cation from solution. Naturally, a given surface coverage value may correspond to a noninteger number of defect sites. For example, 30% coverage on a face with 8 defect sites implies 2.4 occupied sites. In this case, an effective E* rep can be calculated so that χE* rep is the energy per unit surface area required to replace the two hydrogens with the lowest associated Erep, plus a weighted (0.4) contribution from the third lowest. However, this scheme still requires that the defects be isolated. Thus, it was necessary to impose a minimum surface area requirement per defect in order to ensure negligible interaction. In the defect calculations to date, the crystal structures of the substances considered have been of very high symmetry, i.e., cubic or hexagonal. This leads to highly symmetric surfaces in which the surface sites can easily be identified. In contrast, the surface structure of gibbsite is quite complex, and for most faces, it is not clear which protons should be considered as surface sites. However, it is imperative to determine the total number of surface sites. This is because candidates for the substitution calculations must obviously be known and because the percentage of surface coverage must also be assessed. In this work, a modified version of the method of Connolly15 has been adopted in order to analyze the surfaces in the calculated morphology of gibbsite. The essential idea is to determine how accessible the hydrogen atoms are to a given probe atom. A program was written in Perl to accomplish this and is available on request. The code determines how much of the surface of a

Atomistic Modeling of Gibbsite

J. Phys. Chem. B, Vol. 105, No. 22, 2001 5101

Figure 2. Contact and re-entrant surface of the (200) face of gibbsite for a cationic sodium probe.

Figure 3. Contact and re-entrant surface of the (110) face of gibbsite for a cationic sodium probe.

Figure 4. Contact and re-entrant surface of the (101) face of gibbsite for a cationic sodium probe.

probe atom can be brought into contact with each hydrogen, without penetrating the surface of any other atom. The size of each atom in the gibbsite surface was taken to be the appropriate van der Waals radius, while the ionic radius was used to simulate a cationic probe. Analysis of the percentage accessible area was performed with both a sodium and a potassium probe. 3. Results Surface Coverage. A general scheme was applied to differentiate between surface and bulk hydrogens. A list of

accessibilities of all unique hydrogens was constructed and sorted from highest to lowest (Tables 1 and 2). The tabulated values indicate how much of the total area of the hydrogen’s van der Waals surface may be touched by the probe ion. The accessibilities of a sodium ion are larger than those of a potassium ion, as expected from their relative ionic radii. Inaddition, the largest accessibility values are a little under 50%, with most being in the 30-40% range. The contact surface for each face in the gibbsite morphology is largely formed from a few of the uppermost hydrogen atoms. However, oxygen and aluminum atoms also contribute. Figures 1-7 illustrate the van der Waals surface for each of the faces of interest in the gibbsite morphology. In each diagram, the contact surface for a given atom is color coded according to element type, with white for hydrogen, orange for oxygen, and green for aluminum. The magenta portions of the figure comprise the re-entrant surface. For clarity, the van der Waals surface has been raised with respect to the gibbsite surface structure, and the face’s surface repeat unit is outlined. A sodium probe was used in order in generate each of the surface representations. It is apparent that one distinguishing character between surface and bulk sites should be a large drop in the percentage accessibility. Given that the highest hydrogen accessibility for most of these surfaces is ∼40%, it is questionable whether a hydrogen on the same surface with less than half this accessibility should also be treated as a true “surface” site. Hence, for each face, the cutoff was calculated to be the accessibility of the most exposed hydrogen, minus 20%. Note that a large drop in accessibility generally occurs after this point. Also, such a cutoff point enables the selection of defect sites for faces that lack a sharp decrease in hydrogen accessibility, such as {112}. The model employed by MARVIN creates a surface by infinitely replicating the corresponding repeat units in two dimensions. Presented in Table 3 are the surface areas corresponding to each repeat unit of all faces in the gibbsite morphology. As any impurity substitution will also be repeated,

Figure 5. Contact and re-entrant surface of the (101h) face of gibbsite for a cationic sodium probe.

5102 J. Phys. Chem. B, Vol. 105, No. 22, 2001

Fleming et al. gated. Finally, a supercell construction was not employed for the (110), (112), and (112h) faces, as the respective surface areas were judged to be sufficiently large. Defect Energy. Calculation of the energy required to form a defect was accomplished with the aid of the following expression: ∆E

nAl(OH)3 (s) + MOH(aq) 98 (n - 1)[Al(OH)3]Al(OH)2MO(s) + H2O(l) Figure 6. Contact and re-entrant surface of the (112) face of gibbsite for a cationic sodium probe.

This reaction represents the energy required for a proton on a gibbsite surface to be replaced by a cation M+ in solution. Separate runs for each face in the morphology and each candidate site were therefore required. The MARVIN code was employed to relax the gibbsite surfaces (with the substituted defect) and compute Edefe R1 , the total energy of region 1. This may be compared to the total energy of region 1 for the pure material Epure R1 . Unfortunately, the difference between the two region 1 energies is not equal to ∆E. To compute this energy, we developed a suitable Born-Haber cycle (Figure 8). The values of each reaction shown in this figure are listed in expression 3 (see Appendix A for their derivations) ∆E1 ) -936.7 kJ mol-1

+ Na+ (g) + OH(g) 98 Na(aq) + OH(aq)

Figure 7. Contact and re-entrant surface of the (112h) face of gibbsite for a cationic sodium probe.

TABLE 3: Surface Areas of a Single Repeat Unit for Each Face in the Gibbsite Morphology (002) (200) (110) (101) (101h) (112) (112h)

(hkl) surface area

(Å2)

44.0

48.9

98.7

69.1

62.3

135.6 128.8

the question of defect interaction must be considered. A surface area of approximately 100 Å2 per defect was judged sufficient in order for the defect to be considered isolated. Thus, for the (002), (200), (101), and (101h) faces, only one defect per four surface repeat units (in a 2 × 2 configuration) was created. This quadruples the surface area and the number of candidate proton sites. In addition, as the (101) and (101h) faces possess two possible cuts with similar surface energies, both were investi-

∆E2 ) -852.9 kJ mol-1

+ K+ (g) + OH(g) 98 K(aq) + OH(aq) ∆E3 ) -523.0 kJ mol-1

0.4 O-1.4 (g) + H(g) 98 OH(g) ∆E4 ) 1133 kJ mol-1

22OH(g) 98 O(g) + H2O(g) ∆E5 ) -44.00 kJ mol-1

H2O(g) 98 H2O(l)

(3)

Defects were created by substituting each candidate proton, and the oxygen it was bonded to with a cationic species (Na+or K+) and an O2- ion, respectively. Replacement of the oxygen was required because of charge neutrality requirements and the partial charge model used for the hydroxyl component of the gibbsite. Impurity substitution was made on the relaxed surfaces from the equilibrium morphology prediction. The defect surfaces constructed were then allowed to relax to a minimum, where

Figure 8. Born-Haber cycle for the evaluation of the replacement energy (Erep ≡ ∆E). The diagram is written so that ∆E is the sum of the quantities on the lower reaction pathway.

Atomistic Modeling of Gibbsite

J. Phys. Chem. B, Vol. 105, No. 22, 2001 5103

TABLE 4: Replacement Energies for the Creation of an Isolated Sodium Defect on the Morphologically Important Faces of Gibbsitea surface site (002) (200) (110) 1 2 3 4 5 6 7 8 9

Erep (kJ mol-1) (101) (101h)

260.0 278.4 322.5 207.1 241.2 292.8 204.7 323.7 207.1 241.2 293.0 134.0 256.9 189.8 205.2 279.7 138.7 189.8 205.2 108.7 199.4 210.2 199.4 210.2

145.2 141.7 218.8 218.8

488.7 502.0 392.2 392.1

(112) (112h) 238.9 198.3 207.7 213.5 221.9 169.4 247.9 463.5 215.2

389.7 443.1 328.0 408.2 374.5 442.5 213.4 194.6

Figure 10. Morphologies of gibbsite for (a) sodium and (b) potassium defect incorporation, assuming 5% defect incorporation into the (002) face and 10% into the others.

TABLE 6: Ranked Defect Replacement Energies (per unit surface area) for Sodiuma γrep (Jm-2)

a

The numbering of the surface defect site involved corresponds to that in Table 1.

TABLE 5: Replacement Energies for the Creation of an Isolated Potassium Defect on the Morphologically Important Faces of Gibbsitea Erep (kJ mol-1) surface site (002) (200) (110) (101) 1 2 3 4 5 6 7 8

762.4 549.4 497.6 316.0 579.8 381.9 300.3 467.1 318.8 597.0 527.8 401.8 510.9 315.7 414.6 326.6 510.8 315.7 654.5 665.8 654.5 665.8

(101h) 420.9 420.9 359.3 359.9

521.7 520.2 418.1 365.3

(112) (112h) 411.6 310.7 301.8 244.9 333.7 429.3 359.9 452.6

401.3 309.0 375.1 396.3 331.4 411.9 519.0 427.2

site (002) (200) (110) 1 2 3 4 5 6 7 8 9

(101)

0.245 0.114 0.183 0.114 0.123 0.264 0.173 0.233 0.114 0.123 0.276 0.236 0.432 0.120 0.126 0.276 0.543 0.120 0.126 0.545 0.124 0.145 0.124 0.145

(101h) 0.0944 0.0968 0.146 0.146

0.261 0.261 0.326 0.335

(112) (112h) 0.207 0.243 0.254 0.261 0.264 0.272 0.293 0.304 0.568

0.251 0.275 0.423 0.483 0.502 0.526 0.570 0.571

a Note that for those faces with 2 × 2 surface constructions, only the defect energies from one surface repeat unit are listed.

a The numbering of the surface defect site involved corresponds to that in Table 2.

Figure 11. Morphologies of gibbsite with (a) 10% selective coverage and (b) 20% selective coverage of sodium defects. Figure 9. Relaxed equilibrium morphology of gibbsite.

the final region 1 energy was recorded. Force field interaction terms for this study were developed in previous work by the authors6. For each face, the region 1 energy was combined with the enthalpies of the reactions shown previously to determine Erep. These values are recorded in Table 4 for sodium and Table 5 for potassium. 3.1. Morphology and Defect Incorporation. The scheme described earlier was applied to calculate E*rep and, thus, the defect surface energy for a range of surface coverage values. For the (101) face, neither of the two likely cleavage planes possessed the lower surface energy for all fractional coverage values of interest. Hence, the mean defect surface energy of the two shifts was used, yielding an estimation of the average morphological importance for the (101) face. This procedure was also required for the (101h) face. In addition, it is notable that for both sodium and potassium, the lowest Erep value for the basal plane is significantly greater (∼50 kJ mol-1 or more) than the minimum Erep of any other face. The sole exception is one of the (101h) configurations. This would suggest that in a low coverage environment, defects would tend to favor sites other than the basal plane. As a result, equilibrium morphologies were calculated using 5% coverage for the basal plane and 10% for all the others. Visualization of the morphologies was accomplished with the JSHAPE program16. Images of the “pure” and “defect” equilibrium morphologies are shown in Figures 9 and 10, respectively. Clearly, the presence of sodium ions has increased the prominence of the prismatic (110) and (200) faces

and reduced the significance of the (112) and (101) chamfered faces compared to the “pure” equilibrium morphology prediction. The resulting elongated crystal is now in excellent agreement with that presented in ref 9. In addition, the effects are more pronounced with potassium incorporation, again in good experimental agreement. Data from Lee et al.9 have indicated that cation incorporation is considerably higher for sodium than for potassium. To estimate the effects of higher concentrations of defects, we divided the replacement energies for sodium (Table 4) by the appropriate surface area. These values, shown in Table 6, are denoted as γrep and are ranked from lowest to highest. The figures given represent the energy per unit surface area required to create an impurity substitution at a given proton site. This provides a means to assess the expected coverage. Consideration of the average defect replacement energies per unit surface area for potassium should not be necessary. This is due to the relatively low level of incorporation, which suggests that defects may be treated as completely isolated to good approximation. For sodium incorporation, the energy per unit surface area required to form (for example) the first four defects is significantly lower for the {200}, {101}, and {101h} faces. Consequently, these surfaces would be expected to experience higher levels of defect incorporation. Two separate morphologies with 10% and 20% coverage for the {101}, {101h}, and {200}, and 5% coverage on the other faces are illustrated in Figure 11. Clearly, the habit is approaching that of a truncated diamond, a morphology that has been observed in gibbsite crystals precipitated from sodium aluminate solutions.9,17,18 For example,

5104 J. Phys. Chem. B, Vol. 105, No. 22, 2001 Lee et al.9 reported agglomerates of hexagonal and diamondshaped crystals; Rossiter et al.18 showed the production of a large number of diamond-shaped secondary nuclei, whereas when primary nuclei were formed,19 hexagonal particles as small as 50 nm were seen. In all these cases, the crystals were produced under conditions of caustic concentration and aluminate supersaturation comparable to those prevailing in the alumina industry. It has been reported that under these conditions, the amount of sodium incorporated increases with the square of the aluminate supersaturation.20 It is possible, therefore, that where diamond-shaped gibbsite crystals are found, these occur as the result of localized conditions of high sodium incorporation (for example, secondary nuclei form at the crystal/ solution interface, at which there may be an increased concentration of sodium ions). The relatively large, diamond-shaped crystals of Sweegers et al.17 match the predicted morphology particularly well, exhibiting the chamfered faces that are shown in Figure 11. It is interesting to note that these crystals were grown from solutions with a much higher sodium ion concentration (6 M, cf. 3.8 M for the other experiments) and, hence, would probably contain higher levels of sodium incorporation.

Fleming et al. TABLE 7: Enthalpy Values Used in the Born-Haber Cycles, Together with Any Intermediate Steps Used to Derive Them quantity

intermediate steps

value (kJ mol-1)

∆Hf[Na+ (aq)] ∆Hf[K+ (aq)] ∆Hf[OH(aq)] ∆H(1) ip [Na] ∆H(1) ip [K] ∆Hsub[Na] ∆Hsub[K] ∆Hf[OH(g)] ∆Heg[OH] ∆Hf[OH(g)] ∆Hf[Al(g)] 3 ∑i)1 ∆H(i) ip [Al] ∆Hf[Al3+ (g) ] ∆Hf[H2O(g)] ∆Hf[H2O(l)] ∆Hf[Al2O3] Elatt[Al2O3]

Hf[Na(g)] Hf[K(g)] ∆Hf[OH(g)] + ∆Heg[OH] 3 ∆Hf[Al(g)] + ∑i)1 ∆H(i) ip [Al] -

-240.34 -252.14 -230.015 495.84 418.81 107.5 89.0 39.3 -176.34 -137.03 330.4 5139.0 5469.4 -241.826 -285.830 -1675.7 15916

All quantities in this table were obtained from Lide [21].

4. Conclusion A new approach for defining defect surface coverage on highly complex, and even rough, surfaces was developed. The scheme was based on the Connolly method and involves determining the accessibility of a particular surface site to a cationic probe. With the aid of this technique, we have established evidence for the modification of gibbsite morphology by the incorporation of cations known to be present in experimental solutions. The predictions of this study are valid in the low to medium surface coverage regime, as the model has been defined such that defects do not interact. If approximately equal surface coverage is assumed, the effect of impurity substitution is to increase the importance of the prismatic faces. These results have assisted in explaining the elongated experimental morphology, which was not reproduced by a normal equilibrium morphology prediction. In addition, the disparity in the levels of incorporation for sodium compared to potassium necessitated a means of estimating the expected surface coverage values in a relatively higher defect density regime. This has yielded a possible explanation for the diamond morphologies observed in sodium aluminate liquors. Acknowledgment. The authors would like to acknowledge the funding of this work by the A.J. Parker Cooperative Research Centre for Hydrometallurgy.

Figure 12. Born-Haber hydration enthalpy cycle, written so that ∆E is equal to the sum of the enthalpies along the lower reaction pathway.

compensation to Epure R1 if one bulk gibbsite hydroxyl is converted to the gas phase without dissociating. The value of ∆E4 was calculated using Elatt

2Al2O3(s) 98 2Al3+ (g) + 3O(g)

Appendix A The enthalpy values employed in this work were determined with the aid of the data given in Table 7. In the table, ∆Hf is the enthalpy of formation, Elatt represents the lattice energy, ∆ Hjip is the jth ionization potential, ∆Heg is the electron gain enthalpy, and ∆Hsub is the sublimation enthalpy. The enthalpies of hydration at infinite dilution were calculated by employing the cycle shown in Figure 12. Hence, ∆E1 and ∆E2 (from the reactions in 3) are evaluated by adding all the quantities along the lower reaction pathway, with Na and K substituted, respectively, for M. The O-H morse potential employed in this work was fitted to gibbsite structural and vibrational parameters.6 Consequently, the dissociation energy for a hydroxyl ion (∆E3) was estimated to be the minimum value of this fitted potential. The error was considered minimal, since ∆E3 may be considered as the energy

which yields

1 3+ ∆Hf[O2(g) ] ) (Elatt[Al2O3] + ∆Hf[Al2O3(s)] - 2∆Hf[Al(g) ]) 3 ) 1100 kJ mol-1 thus ∆E4 ) ∆Hf[O2(g) ] + ∆Hf[H2O(g)] - 2∆Hf[OH(g)]

) 1133 kJ mol-1 Finally, ∆E5 is simply the difference between the enthalpies of formation of gaseous and liquid water

Atomistic Modeling of Gibbsite

∆E5 ) ∆Hf[H2O(g)] - ∆Hf[H2O(l)] ) 44.00 kJ mol-1 References and Notes (1) Kenway, P. R.; Oliver, P. M.; Parker, S. C.; Sayle, D. C.; Sayle, T. X. T.; Titiloye, J. O. Mol. Simul. 1992, 9, 83. (2) Davies, M. J.; Kenway, P. R.; Lawrence, P. J.; Parker, S. C.; Tasker, P. W.; Mackrodt, W. C. J. Chem. Soc., Faraday Trans. 1989, 85, 555. (3) Titiloye, J. O.; Parker, S. C.; Osguthorpe, D. J.; Mann, S. J. Chem. Soc., Chem. Commun. 1991, 1494. (4) Titiloye, J. O.; Parker, S. C.; Mann, S. J. Cryst. Growth 1993, 131, 533. (5) Wesolowski, D. J.; Machesky, M. L.; Palmer, D. A.; Anovitz, L. M. Chem. Geology 2000, 167, 193. (6) Fleming, S.; Rohl, A.; Lee, M.-Y.; Gale, J.; Parkinson, G. J. Cryst. Growth 2000, 209, 159. (7) Watling, H. R.; Fleming, S. D.; van Bronswijk, W.; Rohl, A. L. J. Chem. Soc., Dalton Trans. 1998, 3911. (8) Wefers, K.; Misra, C. Alcoa Technical Paper No. 19, Revised; 1987; p 8.

J. Phys. Chem. B, Vol. 105, No. 22, 2001 5105 (9) Lee, M.-Y.; Rohl, A. L.; Gale, J. D.; Parkinson, G. M.; Lincoln, F. J. Trans. Inst. Chem. Eng. 1996, 739. (10) Addai-Mensah, J. Miner. Eng. 1997, 10, 81. (11) Gay, D. H.; Rohl, A. L. J. Chem. Soc., Faraday Trans. 1995, 91, 925. (12) Mackrodt, W. C.; Tasker, P. W. J. Am. Ceram. Soc. 1989, 72, 1576. (13) Mackrodt, W. C.; Davey, R. J.; Black, S. N.; Doherty, R. J. Cryst. Growth 1987, 80, 441. (14) Mackrodt, W. C. AdVances in Ceramics, Nonstoichiometric Compounds; American Ceramic Society: Westerville, OH, 1988; Vol. 23, p 293. (15) Connolly, M. L. J. Appl. Crystallogr. 1983, 16, 548. (16) http://SAL. KachinaTechnol.COM. (17) Sweegers, C.; van Enckevort, W. J. P.; Meekes, H.; Bennema, P.; Hiralal, I. D. K.; Rijkeboer, A. J. Cryst. Growth 1999, 197, 244. (18) Rossiter, D. S.; Ilievski, D.; Parkinson, G. M. In Fifth International Alumina Quality Workshop; Bunbury, WA, Australia, 1999; 170. (19) Rossiter, D. S.; Fawell, P. D.; Ilievski, D.; Parkinson, G. M. J. Cryst. Growth 1998, 191, 525. (20) Sang, J. V. Light Metals 1988, 147. (21) Lide, D. R., Ed. In CRC Handbook of Chemistry and Physics; CRC Press: Boca Raton, FL, 1995.