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δ-Al(OD)3 powders were synthesized from Al(OD)3 bayerite at 4 GPa and 523 K using a cubic press apparatus. Neutron powder diffraction analyses of δ-Al(OD)3 at ambient conditions revealed that the crystals are orthorhombic with space group P212121, not Pnma as reported previously based on X-ray diffraction data. The P212121 δ-Al(OH)3 structure contains seven independent atoms in the asymmetric unit, including one Al, three O, and three H atoms. The initial lattice parameters and the atomic positions of both Al and O were taken from previous X-ray structural analyses of the Pnma structure, while the positions of H were determined in the present study using ab initio calculations to (1) give the least energy among trial structural models for P212121 δ-Al(OH)3, (2) accurately reproduce the measured lattice parameters of δ-Al(OD)3, and (3) show reasonable energetic relations between the Al(OH)3 polymorphs; namely, gibbsite is stable at ambient pressure, δ-Al(OH)3 has the lowest enthalpy at pressure greater than 1.1 GPa, and both bayerite and η-Al(OH)3 are metastable over the entire pressure range. Furthermore, we found that the structure of δ-Al(OH)3 obtained from ab initio calculations is in good agreement with that derived from a Rietveld refinement of δ-Al(OD)3, based on the present powder neutron diffraction data. The δ-Al(OH)3 structure possesses one relatively long and two short O-H···O hydrogen bonds. Ab initio calculations also reveal that δ-Al(OH)3 with space group P212121 transforms to another high-pressure polymorph with space group Pnma at around 67 GPa, and that the two short hydrogen bonds in δ-Al(OH)3 become both symmetric through the P212121 to Pnma transformation, in which the protons are located at the midpoints of the O···O hydrogen bonds.
Aluminum trihydroxide Al(OH)3 has four polymorphs in nature: gibbsite, bayerite, doyleite, and nordstrandite. Of these, gibbsite is the most common, and is an important constituent of bauxite. Both gibbsite and bayerite are monoclinic, whereas doyleite and nordstrandite are triclinic. Using a high-pressure opposed-anvils apparatus, Dachille and Gigl (1983) synthesized two new Al(OH)3 polymorphs, the η (called β′ by the authors) and δ phases. Based on powder X-ray diffraction analyses, the authors reported that the η phase is monoclinic, while the δ phase is orthorhombic with space group Pna21 or Pnam; in the present study, the axis directions are changed from those reported by Dachille and Gigl to give the standard setting, Pnma.
The structure of the high-pressure η phase was much in debate. Huang et al. (1996, 1999) reported that gibbsite transforms to nordstrandite with triclinic unit cell at approximately 3 GPa and room temperature, based on Raman spectra and X-ray diffraction measurements. Subsequently, Liu et al. (2004, 2005) reindexed this high-pressure phase as orthorhombic with space group Pbca, using in situ high-pressure synchrotron X-ray diffraction combined with infrared absorption experiments. However, Komatsu et al. (2007a) successfully obtained a single crystal of this phase (called η) at 3 GPa and determined it to be monoclinic with space group P21/c and a monoclinic β angle of 90.34(6)° at 3 GPa and room temperature, consistent with the earlier report by Dachille and Gigl (1983); here, the axis directions are changed from those reported by Komatsu et al. (2007a) to give the standard setting, P21/c. We note that the P21/c structure of the η phase at 3 GPa, as obtained by Komatsu et al. (2007a), is very similar to the Pbca structure proposed by Liu et al. (2005), with the monoclinic β angle for the former [90.34(6)°] being close to 90°.
A deuterated high-pressure phase, called δ-Al(OD)3, was synthesized at 18 GPa and 973 K using a Kawai-type multi-anvil apparatus (Komatsu et al. 2007b). Based on powder X-ray diffraction at ambient conditions, Komatsu et al. (2007b) confirmed δ-Al(OD)3 is isostructural with δ-Al(OH)3 with space group Pnma, previously synthesized at high temperatures and high pressures by Dachille and Gigl (1983). Based on Rietveld and difference-Fourier analyses using powder X-ray data, Komatsu et al. (2007b) reported a structural model for δ-Al(OD)3 in which positional disorders of the D atoms were proposed in their hydrogen bonds. However, based on the present neutron diffraction measurements of δ-Al(OD)3 at ambient conditions, we found that the real space group of δ-Al(OD)3 is P212121 (not Pnma as reported in X-ray diffraction experiments), suggesting that the positions of D atoms may be ordered in hydrogen bonds in the P212121 structure.
The two high-pressure polymorphs, η- and δ-Al(OH)3, are quenchable at ambient conditions. The crystal structures of the Al(OH)3 polymorphs, except the δ phase, all consist of layers of edge-sharing AlO6 octahedra; they differ in stacking of the layers and in the hydrogen bonding between and within layers (Chao et al. 1985; Clark et al. 1998; Komatsu et al. 2007a). The δ phase is composed of AlO6 octahedra linked together by corner sharing and by hydrogen bonds, and may be considered a member of A-site deficient hydroxyl-perovskites (Komatsu et al. 2007b).
Here, we apply ab initio calculations to the three Al(OH)3 polymorphs (gibbsite, bayerite, and the η phase) to critically assess the reliability and applicability of the ab initio calculations for this system. Subsequently, we use ab initio calculations to determine the crystal structure (e.g., hydrogen positions) of the P212121 δ phase. The calculated cell parameters and the atomic positions of δ-Al(OH)3 are then successfully used as initial parameters for a Rietveld refinement of δ-Al(OD)3 based on the present observed neutron diffraction data.
Pressure-induced phase transformations forming symmetrical hydrogen bonds, where the protons reside midpoints of O···O bonds, were reported to occur in ice at 60–65 GPa (Goncharov et al. 1996; Loubeyre et al. 1999), and in δ-AlO(OH) at ~30 GPa (Tsuchiya and Tsuchiya 2009). δ-Al(OD)3 includes two short O-D···O hydrogen bonds, with the O···O distances of 2.766(1) and 2.738(1) Å, respectively (Komatsu et al. 2007b). Structural changes of δ-Al(OH)3 with pressure are also studied using ab initio calculations to investigate the possible occurrence of hydrogen-bond symmetrization in δ-Al(OH)3 at high pressures.
Experimental and computational methods
Sample preparation and neutron diffraction
δ-Al(OD)3 powder samples were synthesized from Al(OD)3 bayerite with excess D2O as a starting material at 4 GPa and 250 °C for 24 h, using a 700 ton cubic anvil type high-temperature and high-pressure apparatus at the Institute for Solid State Physics, University of Tokyo, Japan. The starting material was loaded into a gold capsule (5.4 mm diameter and 8 mm height) and placed in a cylindrical graphite heater with an insulating sleeve of boron nitride. The loading of samples into the gold capsule and pre-compression were carefully performed in an Ar-loaded glove box to prevent unwanted hydration of the sample.
Neutron diffraction measurements were conducted at D20, at the Institut Laue-Langevin (ILL), Grenoble, France. A vanadium can (diameter = 5 mm) was used as a sample container. The sample (0.214 g), which was synthesized by one run, was put into the vanadium can and held on the sample position. The monochromator was Ge (117) and the take-off angle of the monochromator was 120° (high-resolution configuration), resulting in a wavelength of 1.3588 Å. The measurement conditions and results are summarized in Table 1⇓. The observed neutron diffraction pattern is shown in Figure 1⇓.
Ab initio calculations
Calculations were performed with the Vienna Ab Initio Simulation Package VASP (Kresse and Furthmüller 1996) based on density functional theory (DFT). The projector-augmented wave (PAW) method (Blöchl 1994; Kresse and Joubert 1999) was used in the generalized gradient approximation (GGA) for the exchange-correlation functional (Perdew et al. 1996) based on valence electron configurations of 3s23p1, 2s22p4, and 1s1 for Al, O, and H, respectively. We employed the GGA approach because it generally reproduces the hydrogen bond system more accurately than does the LDA approach (Digne et al. 2002). The planewave cut-off energy was 800 eV, and the k point sampling using a Monkhorst-Pack grid was 4 × 6 × 4, 6 × 4 × 4, 4 × 4 × 6, and 6 × 4 × 6 for gibbsite, bayerite, the η phase, and the δ phase, respectively. Test calculations with a 1500 eV cut-off yielded energies that agreed within 0.003 eV per formula unit with the 800 eV cut-off calculation, and increasing the k-point grid produced essentially the same energies. A quasi-Newton algorithm was used to minimize the enthalpy of the system H = U + PV by optimizing the cell parameters and the atomic coordinates at static conditions (0 K without zero-point vibrations) under observed crystal-symmetry constraints. Here, U is the internal energy, and P and V are the pressure and volume of the system of interest, respectively. Initial structural parameters were taken from Komatsu et al. (2007a) for both gibbsite and the η phase, and from Zigan et al. (1978) for bayerite.
Results and discussion
Gibbsite, bayerite, and the η phase
Table 2⇓ lists the observed and calculated cell parameters and average bond distances for the two Al(OH)3 polymorphs (gibbsite and bayerite) at 0 GPa, and those for the η phase at both 0 and 3 GPa. For comparison, the table also lists the results of previous ab initio calculations using the pseudopotential planewave method (termed PP) and GGA calculation for both gibbsite and bayerite (Gale et al. 2001). The observed data for the three polymorphs were obtained at room temperature, while the present calculated values, as well as the data reported by Gale et al. (2001), were derived at 0 K without zero-point vibrations.
The observed and calculated structures are in good agreement for all three polymorphs. As listed in Table 2⇑, the present calculations systematically overestimate the observed volumes by 1–3% for all three phases. Likewise, the PP calculations overestimate the volumes of gibbsite and bayerite by 1.9% and 3.9%, respectively. Such overestimation is typical for the GGA approximation to the exchange-correlation functionals used in the present study and in the previous PP calculations. The calculated β angle is underestimated by 2.4% for gibbsite, and the errors in the β angle are within 0.5% for the other polymorphs. PP also underestimates the β angle for gibbsite by 2.2%. Each structure contains 14 independent atoms in their asymmetric units, containing 2 Al atoms in octahedral coordination, 6 O atoms, and 6 H atoms. The calculated Al-O distances compare well with experimental results for each structure, with the average Al1-O and Al2-O distances (<Al1-O> and <Al2-O>, respectively, in Table 2⇑) being systematically 0.02–0.03 Å longer than the observed values, reflecting the general tendency of GGA calculations to underbind the interactions between atoms, as described above.
The hydrogen positions in bayerite were determined by neutron diffraction using a deuterated sample, and the calculated <O-H> distance of 0.98 Å for bayerite agrees within error with the observed value of 0.97(1) Å (Table 2⇑). The hydrogen positions in gibbsite were obtained from X-ray analyses, yielding a shorter <O-H> distance than the present calculated value and observed value in bayerite. The <O-H> distance of 1.03 Å in the η phase at 3 GPa, obtained from a molecular dynamics simulation with an empirical potential (Komatsu et al. 2007a), is slightly longer than the present value, as shown in Table 2⇑.
The calculated compression of gibbsite with pressure also compares well with experimental results (Liu et al. 2004), as shown in Figure 2⇓. The DFT calculated bulk modulus and its pressure derivative, using compression data up to 10 GPa and the Vinet equation, were K0 = 53.5(7) GPa and K0′ = 5.84(17), respectively, which again agree well with the value K0 = 55 GPa reported by Gale et al. (2001) using a PP calculation.
We first tried to refine the structure model of the δ phase based on the previously determined space group Pnma [the unit cells reported by Komatsu et al. (2007b) are transformed as follows: a′ = a, b′ = c, c′ = −b] and using the present neutron diffraction data. However, we observed several unexplained peaks for the space group Pnma [e.g., (140), (041), (320), and (023), as shown in Fig. 1⇑]; these peaks were not observed in the X-ray diffraction data (Komatsu et al. 2007b). The systematic absences of observed neutron reflections are as follows: h00; h = 2n, 0k0; k = 2n, and 00l; l = 2n, which suggests the space group of the δ phase is P212121, which is one of the maximal non-isomorphic subgroups of Pnma.
Since our ab initio calculations succeeded in accurately reproducing the available measured structural data of the three Al(OH)3 polymorphs (gibbsite, bayerite, and the η phase) and their pressure dependence, we sought to construct the structure model of the δ phase using ab initio calculations. The asymmetric unit of the δ phase with space group P212121 contains seven independent atoms, including one Al, three O, and three H atoms. The initial lattice parameters and atomic positions of both Al and O were taken from previous X-ray data for the Pnma structure (Komatsu et al. 2007b) with an appropriate origin shift from Pnma to P212121, while the H atom positions were taken to be in ordered configurations and were selected from either one of the two disordered sites in the hydrogen bonds in the Pnma structure (Komatsu et al. 2007b). We tested several initial configurations for H atoms for the calculations, and finally found an energy-minimized structure that (1) has the least energy of the configurations sampled, (2) accurately reproduces the measured lattice parameters of the δ phase, and (3) gives reasonable Al-O, O-H, and hydrogen bond distances. Furthermore, starting from the calculated structure of the δ phase, we undertook a Rietveld refinement of the structure based on the measured neutron data, and found that the observed and calculated neutron diffraction patterns agree very well (Fig. 1⇑; the wRp and RF2 values are listed in Table 1⇑). Tables 3⇓ and 4⇓ provide a structural comparison between δ-Al(OH)3 by the present DFT calculation and δ-Al(OD)3 by Rietveld refinement based on the observed neutron data. (A CIF is on deposit1.)
We note that the atomic coordinates of Al and three O in the P212121 δ-Al(OH)3 are very close to those for the space group Pnma: Al approximately on an inversion center in the Pnma lattice at (0.5, 0.0, 0.75), O1 on a mirror plane at y = 0.25, and O2 and O3 are symmetrically related to each other by a mirror plane at y = 0.25; however, the three H atoms, especially H2 and H3, deviate strongly from the Pnma structure. As hydrogen is a very weak X-ray scatterer, only Pnma reflections, which are dominated by the contribution of the similar Al and O atom positions, were observed in the X-ray diffraction measurements of δ-Al(OD)3 performed by Komatsu et al. (2007b). The DFT calculated crystal structure of δ-Al(OH)3 at 0 GPa is given in Figure 3⇓.
A slight overestimation of the DFT calculated cell parameters and Al-O distances, compared with the Rietveld results (see Tables 3⇑ and 4⇑), is again due to the GGA approximation used in the present study. The δ-Al(OH)3 [or δ-Al(OD)3] structure includes three different hydrogen bonds, with two short distances (O2-H2···O3 and O3-H3···O2) and one relatively long distance (O1-H1···O1), all of which have nearly linear O-H···O (or O-D···O) configurations, as shown in Table 4⇑. The O2-H2 (or D2) distance [1.002 Å by DFT calculation and 0.995(8) Å by Rietveld refinement] and O3-H3(D3) distance [1.000 Å by DFT calculation and 1.028(6) Å by Rietveld refinement] are slightly longer than the O1-H1(D1) distance [0.987 Å by DFT calculation and 0.958(6) Å by Rietveld refinement], which reflects the general trend that the O-H bond length increases with decreasing O···O hydrogen bond distance.
Figure 4⇓ shows the calculated pressure variation in enthalpy difference of the polymorphs with respect to gibbsite. The present calculations show that gibbsite is stable at the ambient pressure, with the energy difference between gibbsite and bayerite at 0 GPa and 0 K being 6.4 kJ/mol, which compares well with the PP calculation of 7.7 kJ/mol (Gale et al. 2001) and with other ab initio calculations using localized basis sets of 4.9 kJ/mol (Demichelis et al. 2008), 6.3 kJ/mol (Gale et al. 2001), and 5.4 kJ/mol (Digne et al. 2002), and is reasonably consistent with the measured free-energy difference between the two phases at 0 GPa and 298 K of 2.9 kJ/mol (Parks 1972) and 3.0 kJ/mol (Liu et al. 1998). Our calculations show that δ-Al(OH)3 becomes more stable than gibbsite above 1.1 GPa, and η-Al(OH)3 is metastable against δ-Al(OH)3 at all pressures (Fig. 4⇓), being consistent with the observations by Dachille and Gigl (1983) that the δ phase was synthesized at high pressures from a wide variety of starting materials, including gibbsite, bayerite, boehmite (AlOOH) + H2O, and corundum (Al2O3) + H2O, whereas the η phase was formed only from gibbsite at relatively low temperatures less than ~473 K, and pressures above 1.5 GPa. This metastable transformation from gibbsite to η-Al(OH)3 at high pressures is explained by the close resemblance of the crystal structures of gibbsite and η-Al(OH)3, both of which are composed of layers of edge-sharing AlO6 octahedra, whereas δ-Al(OH)3 has a completely different structure, containing corner-sharing AlO6 octahedra.
Calculated δ-Al(OH)3 structure at high pressures
The cell parameters and atomic positions of the δ-Al(OH)3 structure were optimized with DFT for several pressures up to 100 GPa. Figures 5a and 5b⇓ shows the pressure dependence of the volume and hydrogen-bond geometry of δ-Al(OH)3, respectively. From the calculated P–V data between 0 and 60 GPa, we obtain V0 = 192.40(12) Å3, K0 = 91.4(9) GPa, and K0′ = 4.97(5) using the Vinet equation of state. At approximately 67 GPa, the P212121 δ-Al(OH)3 phase transforms to a new high-pressure form with space group Pnma [called Pnma-Al(OH)3], in which both Al and H2 occupy inversion centers; O1, H1, and H3 are all on mirror planes; and O2 is on a general position in the space group Pnma; the O2-H2-O3 angle becomes 180°, as shown in Figures 5a and 5b⇓; the O3 atom is symmetrically related to the O2 atom in Pnma-Al(OH)3. We found continuous changes in volume and atomic displacements from the δ structure to Pnma-Al(OH)3 structure at the transition, suggesting a second-order phase transition.
Table 5⇓ gives the structural data of Pnma-Al(OH)3 at 70 GPa and the hydrogen bond geometries of δ-Al(OH)3 and Pnma-Al(OH)3 at selected pressures. With increasing pressure, the two short hydrogen bonds in δ-Al(OH)3 become progressively symmetric, with both the H2 and H3 atoms being located at midpoints of O···O hydrogen bonds at around 67 GPa (Fig. 5b⇑; Table 5⇓); the relatively long hydrogen bond in δ-Al(OH)3, O1-H···O1, remains asymmetric even at 70 GPa. Through this hydrogen-bond symmetrization, both the covalently bonded O2-H2 and O3-H3 distances increase, while the corresponding hydrogen bonded O···O distances decrease, a general trend in short O-H···O hydrogen bonds, as found in the transformation process from ice VII to X at high pressures (Loubeyre et al. 1999).
Based on powder neutron diffraction experiments for δ-AlO(OD) at pressures up to 9.2 GPa, Sano-Furukawa et al. (2008) directly observed that the covalent O-D bond distance in δ-AlO(OD) increases from 0.999(5) Å at 0 GPa to 1.050(6) Å at 9.2 GPa, while the O···O hydrogen-bond distance decreases from 2.564(8) Å at 0 GPa to 2.449(13) Å at 9.2 GPa. The symmetrical hydrogen-bond distance of 2.30 estimated here in Pnma-Al(OH)3 at 70 GPa compares well with calculated symmetrical hydrogen-bond distances of O···O = 2.37 and 2.32 Å at 30 and 70 GPa, respectively, obtained by ab initio calculations for δ-AlO(OH) by Tsuchiya and Tsuchiya (2009), and is also compared with the measured O···O distance of ~2.40 Å reported for a symmetrical hydrogen bond in ice X at 60–65 GPa (Goncharov et al. 1996; Loubeyre et al. 1999).
Finally, it is to be noted that the Pnma-Al(OH)3 structure may be produced by perfect disordering in protons between two potential-minimum sites along the O···O hydrogen bonds, but not the single potential-minimum model as taken here; even the P212121 δ-Al(OH)3 structure may have some degree of disorder between the two sites at higher pressures. Then the transition pressure from δ- to Pnma-Al(OH)3 obtained here, ~67 GPa, is considered to be an upper bound, because we neglect, in this study, the zero-point and thermal vibrations of atoms, and quantum tunneling of the protons, all of which enhance the extent of proton disorder.
We thank Thomas C. Hansen for his help with the neutron diffraction experiments. We also thank Sandro Jahn, Ron Peterson (Technical Editor), Alexandra Friedrich (Associate Editor), and an anonymous reviewer for their kind and constructive suggestions. Figure 3⇑ was drawn by the VESTA program (Momma and Izumi 2008). This work was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology grant no. 19204054 to M.M., and nos. 19GS0205 and 21840024 to K.K.
↵1 Deposit item AM-11-024, CIF. Deposit items are available two ways: For a paper copy contact the Business Office of the Mineralogical Society of America (see inside front cover of recent issue) for price information. For an electronic copy visit the MSA web site at http://www.minsocam.org, go to the American Mineralogist Contents, find the table of contents for the specific volume/issue wanted, and then click on the deposit link there.
Manuscript handled by Alexandra Friedrich
- Manuscript Received August 15, 2010.
- Manuscript Accepted December 14, 2010.