J. Phys. Chem. C 2009, 113, 6785–6791
6785
Structure and Stability of the Al(OH)3 Polymorphs Doyleite and Nordstrandite: A Quantum Mechanical ab Initio Study with the CRYSTAL06 Code Raffaella Demichelis,*,† Michele Catti,‡ and Roberto Dovesi†,§ Dipartimento di Chimica IFM, UniVersita` di Torino, Via Pietro Giuria 7, 10125 Torino, Italy, Dipartimento di Scienza dei Materiali, UniVersita` di Milano Bicocca, Via Cozzi 53, 20125 Milano, Italy, and Nanostructured Interfaces and Surfaces (NIS), Centre of Excellence, Via Pietro Giuria 7, 10125 Torino, Italy ReceiVed: NoVember 17, 2008; ReVised Manuscript ReceiVed: January 16, 2009
The crystal structures and relative energies of doyleite and nordstrandite, two of the four aluminum trihydroxide polymorphs, were investigated at the periodic ab initio quantum-mechanical level with the CRYSTAL06 computer program, by using an all-electron Gaussian-type basis set and the hybrid B3LYP Hamiltonian. By least-energy optimizations of different starting arrangements of H atoms, a noncentrosymmetrical P1 structure model was proved to be slightly more stable than a P1j one in doyleite. The primitive P1j unit cell of nordstrandite was confirmed to contain four formula units, unlike doyleite (Z ) 2). The layered structures of nordstrandite and doyleite were shown to be closely related to that of bayerite, differing from one another by the interlayer shift vectors only. From the optimized positions of H atoms, the hydrogen bonding schemes and geometries were fully determined for both polymorphs. The computed Gibbs free energies at 298 K of bayerite, doyleite, and nordstrandite, referred to that of gibbsite, are 3.9, 4.4, and 15.2 kJ mol-1 per formula unit, respectively. Nordstrandite was then predicted to be largely the less stable of all four Al(OH)3 polymorphs. I. Introduction Doyleite, nordstrandite, bayerite, and gibbsite are the four known polymorphs of Al(OH)3, belonging to the wider family of Al2O3 · nH2O aluminum hydroxides.1-4 Gibbsite is the most diffuse phase in natural ores, and with bayerite it is widely used in industry.4,5 Nordstrandite and doyleite, discovered in 19566 and 1985,7 respectively, are rarely observed as natural minerals, and although they can be readily synthesized as chemical products,5,8,9 their commercial importance is lower than that of bayerite and gibbsite. Nordstrandite, however, is the starting phase for the production of many catalyst-supporting materials.8 The four polymorphs share several common structural features.4 In particular, their structures are different stacking sequences of basically the same kind of layer, which is built up by Al(OH)6 distorted octahedra sharing edges. One Al atom out of three is missing in the layer, leaving an empty cavity and thus giving rise to a two-dimensional pseudohexagonal pattern of octahedra and hollows. Hydrogen atoms are strongly bonded to oxygens on the layer surfaces, and they provide the crystal cohesion by means of interlayer hydrogen bonding. Some intralayer hydrogen bonds are present as well. The main differences among the four polymorphs concern: (1) orientation and translation relationships between adjacent parallel layers, (2) minor changes of the intralayer structure, and (3) location, geometry, and strength of hydrogen bonding. In this respect, the structures of doyleite10 and nordstrandite11 have been characterized experimentally much less completely than those of gibbsite and bayerite. In particular, no neutron diffraction studies are reported for them, so that the H atoms were never located in the case of nordstrandite, and they were * To whom correspondence should be addressed. Tel.: +39 011 670 7560. Fax: +39 011 670 7855. E-mail:
[email protected]. † Universita` di Torino. ‡ Universita` di Milano Bicocca. § NIS.
located approximately in a disordered configuration for doyleite. Further, P1j triclinic unit cells of different sizes were proposed for nordstrandite,11-14 and also the most reliable X-ray investigation11 is obsolete with respect to modern techniques. In the case of doyleite, there is also an ambiguity of space group, because both P1 and P1j were suggested in previous work.7,10,15-17 Two simulation studies of doyleite and nordstrandite are reported in the literature. In the first one,16 the structures of both polymorphs were optimized by force-field-like (empirical potentials) methods; yet only the unit cell constants and average Al-O and O-H distances are given, and the doyleite study is limited to the P1j structural model.16 In the second article,18 an ab initio optimization (CASTEP code) is reported for nordstrandite only. Further, the nordstrandite structure is investigated in both cases within the constraint of the smallest triclinic unit cell given in the literature,12 although the full experimental structural data refer to a cell with double volume.11 Following previous work on other members of the aluminum hydroxide family, namely akdalaite3 (n ) 0.2), diaspore1 and boehmite2 (n ) 1), and bayerite and gibbsite (n ) 3),4 a computational investigation of the structures and stabilities of doyleite and nordstrandite is presented here. The ab initio periodic approach is based on an all-electron Gaussian-type basis set and on the hybrid B3LYP Hamiltonian, as implemented in the CRYSTAL06 code.19 This work has several aims. First, we want to employ an accurate, state-of-the-art quantum-mechanical computational tool to possibly resolve the problems that are still open with the crystal structures of both polymorphs: (i) the true space group of doyleite and (ii) the true unit cell of nordstrandite. The second purpose is to determine the positions of hydrogen atoms in the nordstrandite structure, where there are no corresponding data from experiment, and to check the H locations in ordered arrangements of doyleite as functions of the space group. In this way, the hydrogen bonding providing interlayer cohesion should be fully characterized in the whole series of polymorphs.
10.1021/jp810084c CCC: $40.75 2009 American Chemical Society Published on Web 03/25/2009
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TABLE 1: Electronic Energy per Formula Unit of the Optimized Doyleite and Nordstrandite Structuresa P1-doyleite P1j-doyleite P1j-nordstrandite
E/Ha
∆E/kJ mol-1
-470.130057 -470.128592 -470.125963
0 3.84 10.74
TABLE 2: Unit Cell Constants and (Maximum, Minimum, and Average) Bond Distances for the P1 and P1j Structures of Doyleite, Compared to Experimental Results10 a
a In the last column, the difference with respect to P1-doyleite is given in kilojoules per mole (1 Ha ) 2625.5 kJ mol-1).
Finally, by comparing the ground-state total energies of the optimized structures, the relative stabilities of doyleite and nordstrandite with each other and with the other Al(OH)3 polymorphs will be predicted, so as to obtain a complete thermodynamic insight of this system. The article is organized as follows. In section II, the computational method employed for all calculations is summarized. The optimized equilibrium geometries are presented, discussed, and compared to experiment in section III, separately for doyleite and nordstrandite. A final section (IV) is devoted to discussing the structural and energetic relationships between the two polymorphs. II. Computational Details 19
The present calculations were performed with CRYSTAL06, a periodic ab initio all-electron program that uses a Gaussiantype function basis set. For Al, O, and H, the 8-621G(d), 8-411G(d), and 211G(p) contractions were adopted, respectively, as in previous calculations.1-4,20-22 The B3LYP Hamiltonian, widely and successfully used in molecular quantum chemistry as well as in solid-state calculations,23-26 was employed. The level of accuracy in evaluating the Coulomb and Hartree-Fock exchange series is controlled by five parameters (see the TOLINTEG keyword in the CRYSTAL06 manual),19 for which the 7 7 7 7 16 values were used. The threshold on the SCF energy was set to 10-9 Ha. The reciprocal space was sampled according to a regular sublattice with shrinking factor 6,19 corresponding to the choice of 112 independent k vectors in the irreducible part of the Brillouin zone for both doyleite and nordstrandite. The DFT exchange-correlation contribution is evaluated by numerical integration over the unit cell volume. The corresponding accuracy can be estimated by quoting the error of the integrated electronic charge density in the unit cell: ∆e is in the order of 10-4|e| for a total of 80 and 160 electrons in doyleite and nordstrandite, respectively. Further information about the grid generation and its influence on the accuracy and cost of calculation can be found in refs 24, 25, and 27. Structure optimizations were performed by use of analytical energy gradients with respect to atomic coordinates and unit cell constants28-30 and the Broyden-Fletcher-Goldfarb-Shanno scheme for Hessian updating.31-34 Convergence was checked on both gradient components and nuclear displacements (TOLDEG and TOLDEX, cf. the CRYSTAL06 manual,19 were set to 3.0 × 10-5 Ha/Bohr and 1.2 × 10-4 Bohr, respectively). As the structures of doyleite and nordstrandite are not unambiguously and completely defined by experimental results, they were optimized with more severe thresholds than those used in previous studies on aluminum hydroxides.1-4 In particular, the thresholds on gradient, atom displacements, and SCF convergence were decreased by a factor 10 in the present calculations. The Γ-point vibrational frequencies23 were computed for each optimized structure, so as to discriminate between a true energy
a b c R β γ V Z (O-H)max (O-H)min (O-H)av (H- - -O)max (H- - -O)min (H- - -O)av (Al-O)max (Al-O)min (Al-O)av
P1
P1j
expt (P1j)10
5.145 5.227 4.965 98.59 118.06 103.39 109.3 2 0.980 0.967 0.972 2.296 1.837 2.075 1.960 1.869 1.916
5.080 5.384 5.041 99.96 118.79 105.11 109.1 2 0.977 0.964 0.971 2.352 1.884 2.174 1.937 1.894 1.917
5.000 5.168 4.983 97.44 118.69 104.66 104.4 2 0.971 0.887 0.930 2.282 1.854 1.968 1.909 1.858 1.885
a Distances are in angstroms, angles are in degrees, and volume is in cubic angstroms.
minimum (all real frequencies) and a saddle point due to artificial symmetry constraints (one or more imaginary frequencies). Further, by use of the obtained vibrational spectra and of the standard formulas of statistical thermodynamics, the thermal contributions to the Gibbs free energy could be estimated in all cases. III. Results and Discussion A. Doyleite. The mineral doyleite was identified as a new Al(OH)3 polymorph on the basis of X-ray diffraction (XRD), microprobe analysis, and optical studies.7 It was found to be triclinic with two Al(OH)3 formula units (fu) in the primitive cell, and the P1j rather than the P1 space group was proposed on the basis of crystal morphology and IR absorption spectrum. In fact, the simplicity of the doyleite spectrum with respect to those of the other Al trihydroxides suggests that only one symmetry-independent Al(OH)3 group is present in the unit cell, whereas two of them are contained in the other hydroxides. Also, the Raman spectrum was interpreted according to the P1j symmetry.17 The crystal structure of doyleite was determined by a singlecrystal XRD study in the P1j space group, and it was also characterized by atomic force microscopy and Raman spectroscopy techniques.10 The three independent hydrogen atoms were found to be disordered over six positions with 0.5 occupancy. Among them, two sets of three interlayer (Ha) and three intralayer (Hb) half atoms can be distinguished. In the present work, an ordered structure had to be devised as the starting point for the least-energy optimization, on the basis of the experimental atomic coordinates of the quoted study.10 This was accomplished by selecting six H atoms out of 12 disordered positions per unit cell, so as to comply with the principle of maximum distance between pairs of them. Four ordered configuration with acceptable H-H spacings were obtained: two of them in the P1 and two in the P1j space group. The optimizations yielded a P1 least-energy structure, and a second P1j solution with slightly higher energy (Table 1). This energy difference is due to H-H distances shorter in P1j than those in P1 (4 H-H at 1.89 and two at 2.20 Å in P1j vs two H-H at 1.98 and six at 2.03-2.18 Å in P1) and to hydrogen bonds longer in P1j than those in P1 (two O- - -H at
Al(OH)3 Polymorphs Doyleite and Nordstrandite
J. Phys. Chem. C, Vol. 113, No. 16, 2009 6787
TABLE 3: Fractional Coordinates of the Symmetry-Independent Atoms of Doyleite for Experimental10 and Calculated Resultsa x expt (P1j)10 Al Al′ O1 O1′ O2 O2′ O3 O3′ H1a H1a′ H2b H2b′ H3a H3b
0.3269
H1b H2a H3a
0.16 0.88 0.56
a
0.0868 0.7223 0.4672 0.16 0.88 0.56 0.32
y P1j
expt (P1j)10
0.3333
-0.0006
0.0937
0.2090
0.7294
0.2149
0.4781
0.2107
P1 0.3314 0.6872 0.0933 0.9290 0.7196 0.2965 0.4785 0.5471 0.1761 0.8462 0.8785 0.1200 0.5567 0.3229
0.40 0.18 0.40 0.18 0.0806 0.7795 0.6283
0.18 0.40 0.40
z P1j
expt (P1j)10
0.0016
0.1670
0.2074
0.2016
0.2132
0.5663
0.2155
0.9450
P1 -0.0009 0.0016 0.2104 0.7999 0.2207 0.7874 0.2238 0.8002 0.4117 0.5979 0.2162 0.7722 0.6206 0.2395
0.30 0.52 0.00 0.74 0.2008 0.4094 0.4042
P1j
P1 0.1705 0.8467 0.2265 0.8007 0.5760 0.4392 0.9582 0.0629 0.2824 0.7284 0.5244 0.4674 0.0826 0.7592
0.40 0.64 0.00
0.1714 0.2269 0.5872 0.9015
0.4118 0.6664 0.0985
Primed atoms of the P1 structure correspond to centrosymmetrical atoms of the P1j cases.
1.89 and four at 2.29-2.36 Å in P1j vs three at 1.84-1.96 and three at 2.23-2.29 Å in P1). No gain in energy and no structural differences are observed if the 1j operator is removed from the P1j structural arrangement. The Gibbs free energies of the two minimum structures were calculated, on the basis of their Γ-point vibrational frequencies, to estimate the most probable (and stable) structure at 298 K and 1 bar. The ∆G value between the P1j and P1 structures varies from 3.7 to 3.5 kJ/mol per formula unit in the range 100-400 K: the noncentrosymmetrical configuration, then, can be considered the most stable at any temperature in that range. The ratio between the populations of the P1 and P1j phases (p1 and p2, respectively) can be used to estimate the probability of the P1j structure with
(
∆G21(T) p2 ) exp p1 kT
)
(1)
respect to P1: where k is the Boltzmann constant. The ratio is about 0.05 at T ) 298 K; this confirms that P1 is the most probable structure of doyleite at room temperature. In Table 2, the unit cell constants and bond distances of the two optimized structures are compared to the corresponding experimental10 values. The maximum differences between the lattice constants of the experimental and P1 optimized structures are of the order of 0.1 Å and 1°, but for b and R of the P1j optimized case larger deviations are observed (0.2 Å and 2°, respectively). An increase of unit cell volume with respect to experiment is observed for both computed structures, according to the well-known overestimate of lattice distances by the B3LYP functional. This is also reflected by the slightly larger Al-O bond lengths appearing in the calculated results. The hydrogen bond lengths H- - -O of the P1 computed structure agree better with experiment than the P1j ones. This confirms what was already observed for the unit cell constants. The fractional atomic coordinates of the two optimized structures are reported and compared to experimental values10 in Table 3. The Al and O coordinates are similar in the two calculated configurations, whereas large differences are observed
TABLE 4: Optimized Lattice Constants of Nordstrandite, Compared to the Corresponding Experimental Values and to Those of Bayeritea bayerite 36
expt space group a b c R β γ V Z
P21/n 5.063 8.672 9.425 90 90.26 90 413.81 8
nordstrandite 11
expt P1j 5.069 8.752 6.155 127.73 80.97 91.66 212.48 4
calcd P1j 5.056 8.869 6.302 127.75 81.34 88.98 218.67 4
a A unit cell similar to that of bayerite was chosen for nordstrandite. Cell edges are in angstroms, volume is in cubic angstroms, and angles are in degrees.
for H positions. For this reason, the H section of Table 3 was split into two parts. In the case of P1, six H positions are shown: primed atoms correspond to centrosymmetrical ones in the P1j structure. The x and z optimized coordinates closely correspond to the experimental values, whereas larger differences appear for the y coordinates of H2b, H2b′, H3b, and particularly H3a, which is moved to the other side of the interlayer region. The P1 structure is shown in Figure 1. Optimization of the other two selected starting configurations gave the following results. The second P1j configuration, with H(1a), H(2b), and H(3b) hydrogen positions, converged to a saddle point (transition state) rather than to a minimum (equilibrium state) of the energy hypersurface. This appeared as a negative eigenvalue of the Hessian matrix, corresponding to an imaginary vibrational eigenfrequency. On removing the 1j symmetry constraint, the P1 structure previously described was recovered. The second P1 starting configuration, with hydrogen atoms in the H1a, H2a, H3a, H2b, H2b′, and H3b positions, converged to a stable structure with much higher energy (51 kJ mol-1) than the P1 least-energy structure. Further, its geometrical features were not fully consistent with those of the other aluminum hydroxides, so as to be disregarded. B. Nordstrandite. The crystal structure of nordstrandite was determined by single-crystal XRD (Weissenberg and precession
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Figure 1. Least-energy structure of P1-doyleite. The Al(OH)6 octahedra are emphasized; dashed lines indicate the hydrogen bonds.
Figure 2. Projections of the least-energy crystal structure of nordstrandite.
Figure 3. Projections of the experimental36 crystal structure of bayerite.
photographic data),11 in the triclinic space group I1j, with the following unit cell: a ) 8.752, b ) 5.069, c ) 10.244 Å, R ) 109.33, β ) 97.66, γ ) 88.34° (Z ) 8). This structure was also later confirmed,35 but the H atoms were not located. In another study based on XRD powder data,12 a structural model based on a smaller P1j unit cell (a ) 5.114, b ) 5.082, c ) 5.127 Å, R ) 70.26, β ) 74.00, γ ) 58.47°, Z ) 2) was refined, proving to be a substructure of the previous one with incorrectly higher translational symmetry. It seems thus likely that a subset of weak Bragg peaks were missed in the powder data, with respect to those measured on the nordstrandite single crystal. However, taking also into account that a simulation study of nordstrandite had been performed on the basis of the latter incorrect results by using classical ionic potential and DFT simulation techniques,18 at first we decided to test this simpler
P1j structural model. The optimization was started from the experimental12 cell parameters and Al and O coordinates and from the simulated18 coordinates of H atoms. A structure isoenergetic to the doyleite transition state described in the previous section was obtained. Differences of 0.1-0.2 Å were obtained between calculated and experimental cell edges and about 7° cm-1 for R and 5° for γ. The difference with respect to calculated Al-O distances is of the order of 10-2 Å. This optimized structure is quite similar to that obtained by the CASTEP study with GGA functional,18 but it corresponds actually to a saddle point (transition state), because by computing the set of vibrational frequencies a negative eigenvalue (-169.4 cm-1) of the Hessian matrix was obtained. The corresponding frequency can be assigned to a H-bending mode, breaking the symmetry center that relates a pair of H atoms. After the 1j
Al(OH)3 Polymorphs Doyleite and Nordstrandite
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TABLE 5: Atomic Fractional Coordinates of the Experimental and Least-Energy-Optimized P1j Structures of Nordstrandite expt11 Al1 Al2 O1 O2 O3 O4 O5 O6 H1 H2 H3 H4 H5 H6
calcd
x
y
z
x
y
z
0.0028 0.4842 0.2497 0.8083 0.3399 0.8276 0.7640 0.3116
0.3344 0.1699 0.7952 0.2610 0.1042 0.5734 0.9071 0.4078
0.0034 0.0020 0.2306 0.1988 0.2268 0.1986 0.2302 0.1870
-0.0218 0.5312 0.2426 0.8128 0.3128 0.8235 0.7270 0.3027 0.2018 0.7662 0.1229 0.7842 0.6392 0.4062
0.3361 0.1658 0.7834 0.2689 0.0998 0.5846 0.9022 0.4147 0.8705 0.3755 0.1195 0.6738 0.8879 0.4982
-0.0010 -0.0012 0.2103 0.2044 0.2014 0.2062 0.2335 0.2138 0.4088 0.4013 0.1991 0.4054 0.3665 0.1937
operator was removed, the structure was then reoptimized in the P1 space group. The resulting geometry corresponds to a true minimum of the energy hypersurface (no imaginary frequencies). This new P1 arrangement is now very similar to the experimental structure from XRD powder data,12 based on the “small” unit cell, and the differences for the R and γ angles are reduced to about 5 and 2°, respectively. The present P1 “small cell” optimized structure of nordstrandite is isoenergetic to the P1-doyleite minimum structure (Table 1). Bond lengths, cell volume, and cell parameters are also very similar to those calculated for doyleite, with differences of the order of 10-3 to 10-2 Å for the latter values. Frequency calculations, too, provided very similar vibrational spectra in the two cases, confirming that within the constraint of the “small” unit cell12 the structure of nordstrandite converges to the same P1 arrangement optimized for doyleite. A new optimization was then performed starting from the primitive cell content (Z ) 4) of the I1j experimental structure11 (“large” unit cell). At first, the heavy atoms were kept fixed, and the positions of H atoms were optimized; then all structural parameters were fully relaxed, obtaining finally a well-converged least-energy structure. The total electronic energy is reported in Table 1, and it shows that nordstrandite is predicted to be significantly less stable than doyleite. During the analysis of this structural model, and by comparing it with the structures of the other Al(OH)3 polymorphs, we realized that the nordstrandite structure is actually closely related to that of bayerite. To appreciate this point, it is necessary to transform the I1j unit cell according to the following matrix, where the columns give the components of the new basis vectors in terms of the old ones:
[ ] 0 -1
1
0
0
0
1 2 1 2 1 2
A primitive triclinic unit cell is obtained, whose (001) face is very similar to the (001) face of the monoclinic unit cell of bayerite (Table 4). This face has a double area with respect to the (010) face of the doyleite unit cell (Figure 1). In the
Figure 4. Two-dimensional layer unit cells of doyleite (bold line, (010) plane) and nordstrandite (gray, (001) plane).
following, all the discussion will refer to the cell obtained with such a transformation. The atomic coordinates of the experimental11 and least-energy optimized structures of nordstrandite were then transformed correspondingly, according to the relationships x′ ) y - z + 1 /2, y′ ) -x + z + 1/2, z′ ) 2z, where an origin shift by 1/2,1/2,0 is included, and they are reported in this form in Table 5. The asymmetric unit was chosen so as to have all atoms belonging to the same (001) layer. The calculated and experimental coordinates are very similar. Computed Al-O bond lengths range from 1.883 to 1.956 Å (average 1.919), against 1.814 to 2.042 Å (average 1.909) for the measured values. The optimized crystal structure of nordstrandite is shown in Figure 2. A different minimum-energy structure was also obtained, by starting the optimization from the experimental nordstrandite structure11 without previously relaxing the H positions. The corresponding electronic energy was 6.2 kJ mol-1/fu lower than that of the previous nordstrandite structure, and 4.7 and 0.8 kJ mol-1 higher, respectively, than the P1 and P1j doyleite energies (Table 1). It could then be easily shown that this structure was quite similar to that of P1j doyleite and was then discarded as a secondary minimum of the energy hypersurface. To appreciate the close similarity between the structures of triclinic nordstrandite and monoclinic bayerite, the latter is shown in Figure 3. IV. Comparison of Doyleite and Nordstrandite It was shown in the previous section that the (001) layers of nordstrandite and bayerite have essentially the same structure (Figures 2 and 3), which is shared also by the corresponding layers of gibbsite. This structure has a two-dimensional ≈ 5.06 × 5.063 Å rectangular unit cell (Table 4), with P1j symmetry and P21/a pseudosymmetry. It corresponds to a distorted supercell of the ideal 5.06 × 5.06 Å hexagonal (γ ) 120°) lattice of a close-packed arrangement of O atoms, whose cell area is doubled by removal of half-lattice vectors. The layers of doyleite are based on a slightly distorted area-conserving version of the hexagonal cell itself (cf. Table 2 and Figure 4), with P1 symmetry and P2/m pseudosymmetry. They then correspond to a different symmetry lowering of the ideal hexagonal lattice, with no loss of translational symmetry at variance with the nordstrandite/bayerite/gibbsite case. Adjacent layers are simply translated by a lattice vector in the case of nordstrandite (c vector) and doyleite (b). In bayerite, they are related by an n glide plane, yet are quasi-translationally equivalent because of their internal P21/a pseudosymmetry. On the other hand, adjacent layers in gibbsite are rotated by a parallel twofold axis with respect to each other. The geometrical features of hydrogen bonds (HB) in doyleite and nordstrandite are shown in Table 6. As shown in Figures 1
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TABLE 6: Interatomic Distances and Angles Involving Hydrogen Atoms in Least-Energy Doyleite and Nordstranditea Doyleite O1-H1a O1′-H1a′ O3′-H3a O2-H2b O2′-H2b′ O3-H3b
0.980 0.979 0.968 0.969 0.970 0.967
H1a- - -O2′ H1a′- - -O2 H3a- - -O3 H2b- - -O1 H2b′- - -O1′ H3b- - -O1
1.837 1.839 1.960 2.225 2.291 2.296
(inter) (inter) (inter) (intra) (intra) (intra)
O1-H1a- - -O2′ O1′-H1a′- - -O2 O3′-H3a- - -O3 O2-H2b- - -O1 O2′-H2b′- - -O1′ O3-H3b- - -O1
168.2 173.8 159.7 157.4 149.4 154.7
(inter) (inter) (inter) (intra) (intra)
O1-H1- - -O5 O2-H2- - -O6 O4-H4- - -O3 O3-H3- - -O2 O6-H6- - -O4 O5-H5 · · · O1 O5-H5 · · · O4
150.9 176.5 166.6 150.5 140.2 93.5 105.1
Nordstrandite O1-H1 O2-H2 O4-H4 O3-H3 O6-H6 O5-H5 a
0.968 0.978 0.972 0.977 0.973 0.967
H1- - -O5 H2- - -O6 H4- - -O3 H3- - -O2 H6- - -O4 H5 · · · O1 H5 · · · O4
1.996 1.915 1.982 2.019 2.253 2.322 2.329
Distances are in angstroms, and angles are in degrees. “Inter” and “intra” denote inter- and intralayer hydrogen bonds, respectively.
and 2, two kinds of HBs are present: interlayer HBs, responsible for the cohesion between adjacent layers, and intralayer HBs, bridging O atoms across the cavities within the layers. Interlayer HBs are stronger than intralayer HBs in both structures, as shown by the corresponding lengths. The former ones fall at the upper limit of the range found for aluminum trihydroxide HBs4 (1.8-2.0 Å), whereas the latter are similar to values obtained for bayerite and gibbsite4 (2.0-2.3 Å). Interlayer HBs in doyleite are shorter than those in nordstrandite, although the interlayer spacing is larger by about 0.1 Å (5.085 Å in doyleite and 4.983 Å in nordstrandite). As usual, HB lengths correlate with the bonding angles, which are more bent in the intra- than in the interlayer cases, with the exception of the quite bent interlayer O1-H1- - -O5 bond in nordstrandite. In the same polymorph, the behavior of H5 is noteworthy: it shows two nearly symmetrical contacts with O1 and O4, which could be considered as a weak “bifurcated” intralayer hydrogen bonding, but the corresponding angles are too bent to be acceptable for HBs. Taking into account the relative energies obtained for doyleite and nordstrandite in this work (Table 1) and the values previously calculated for gibbsite and bayerite,4 we can order the four polymorphs according to ∆E ) 4.14, 4.94, and 14.89 kJ mol-1 (per formula unit) for doyleite, bayerite, and nordstrandite with respect to gibbsite. It is quite remarkable that nordstrandite has a significantly higher energy than all other polymorphs at T ) 0 K. To include the contribution of thermal effects in the relative stability of these phases, we calculated the vibrational parts of the G function at 298 K for all four polymorphs (within the harmonic approximations and neglecting dispersion of the γ-point frequencies). The ∆G differences obtained with respect to gibbsite were 4.41, 3.87, and 15.21 kJ mol-1 for doyleite, bayerite, and nordstrandite, respectively. Therefore, the relative stabilities of doyleite and nordstrandite with respect to each other and to gibbsite are completely confirmed; on the other hand, bayerite turns out to be more stable than both doyleite and nordstrandite at room temperature. Experimental data5,37,38 are available for the formation Gibbs energy at 298 K of bayerite and gibbsite, and they agree with the computed energy difference between the two polymorphs.4 The ∆fG values of doyleite and nordstrandite are reported in only one article37 to our knowledge, leading to ∆G ) 4.39 and 3.39 kJ mol-1 with respect to gibbsite; this would imply that nordstrandite should be more stable than doyleite, at variance with our theoretical results. However, such data were not directly measured but are just presented as “estimates based upon model
calculations”, without further details. We then conclude that our theoretical result (doyleite is more stable than nordstrandite by 10.8 kJ mol-1/fu) can be considered to be quite reliable and that it contributes significantly to insight into the thermodynamics of the Al(OH)3 polymorphs. Acknowledgment. M.C. and R.D. acknowledge Italian MURST for financial support (Cofin07 Project 200755ZKR3_004 coordinated by Prof. C. Giacovazzo). Computer support from the CINECA supercomputing centre is kindly acknowledged. References and Notes (1) Demichelis, R.; Noel, Y.; Civalleri, B.; Roetti, C.; Ferrero, M.; Dovesi, R. J. Phys. Chem. B 2007, 111, 9337. (2) Noel, Y.; Demichelis, R.; Pascale, F.; Ugliengo, P.; Orlando, R.; Dovesi, R. Phys. Chem. Miner. 2009, 36, 47. (3) Demichelis, R.; Noel, Y.; Zicovich-Wilson, C. M.; Roetti, C.; Valenzano, L.; Dovesi, R. J. Phys.: Conf. Ser. 2008, 117, 012013. (4) Demichelis, R.; Civalleri, B.; Noel, Y.; Meyer, A.; Dovesi, R. Chem. Phys. Lett. 2008, 465, 220. (5) Oxides and Hydroxides of Aluminium; Werfers, K., Bell, G. M., Eds.; Technical Paper 19; ALCOA Laboratories: Alcoa Center, PA, 1987. (6) Nordstrand, R. A. V.; Hettinger, W. P.; Keith, C. D. Nature 1956, 177, 713. (7) Chao, G. Y.; Baker, J.; Sabina, A. P.; Roberts, A. C. Can. Mineral. 1985, 23, 21. (8) Lipin, V. A. Russ. J. Appl. Chem. 2001, 74, 181. (9) Alumina as a Ceramic Material; Gitzen, W. H., Ed.; American Ceramic Society: Columbus, OH, 1970. (10) Clark, G. R.; Rodgers, K. A.; Henderson, G. S. Z. Kristallogr. 1998, 213, 96. (11) Saalfeld, H.; Jarchow, O. Neues Jahrb. Mineral. 1968, 109, 185. (12) Bosmans, H. J. Acta Crystallogr. 1970, B26, 649. (13) Hathaway, J. C.; Schlanger, S. O. Am. Mineral. 1965, 50, 1029. (14) Schoen, R.; Robertson, C. E. Am. Mineral. 1970, 55, 43. (15) Chao, G. Y.; Baker, J. Mineral. Rec. 1979, 10, 99. (16) Chroneos, A.; Desai, K.; Redfern, S. E.; Zacate, M. O.; Grimes, R. W. J. Mater. Sci. 2006, 41, 675. (17) Rodgers, K. A. Clay Miner. 1993, 28, 85. (18) Chroneos, A.; Ashley, N. J.; Desai, K.; Maguire, J. F.; Grimes, R. W. J. Mater. Sci. 2007, 42, 2024. (19) Dovesi, R.; Saunders, V. R.; Roetti, C.; Orlando, R.; ZicovichWilson, C. M.; Pascale, F.; Civalleri, B.; Doll, K.; Harrison, N. M.; Bush, I. J.; D’Arco, P.; Llunell, M. CRYSTAL 2006 User’s Manual; University of Torino: Torino, Italy, 2006. (20) Montanari, B.; Civalleri, B.; Zicovich-Wilson, C. M.; Dovesi, R. Int. J. Quantum Chem. 2006, 106, 1703. (21) Orlando, R.; Torres, F. J.; Pascale, F.; Ugliengo, P.; ZicovichWilson, C.; Dovesi, R. J. Phys. Chem. B 2006, 110, 692. (22) Pascale, F.; Tosoni, S.; Zicovich-Wilson, C.; Ugliengo, P.; Orlando, R.; Dovesi, R. Chem. Phys. Lett. 2004, 396, 308. (23) Pascale, F.; Zicovich-Wilson, C. M.; Gejo, F. L.; Civalleri, B.; Orlando, R.; Dovesi, R. J. Comput. Chem. 2004, 25, 888. (24) Prencipe, M.; Pascale, F.; Zicovich-Wilson, C. M.; Saunders, V. R.; Orlando, R.; Dovesi, R. Phys. Chem. Miner. 2004, 31, 559.
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