High-pressure single-crystal X-ray diffraction study of katoite hydrogarnet: Evidence for a phase transition from Ia3d ÆI43d symmetry at 5 GPa

The crystal structure of katoite hydrogarnet has been refined at 0.0001, 2.15, 4.21, 5.09, 6.00, 7.09, and 7.78 GPa from single-crystal X-ray diffraction data using a 4:1 methanol:ethanol mixture as pressure medium in a Merrill-Bassett diamond-anvil cell. Below ~5 GPa, the katoite structure has Ia3d symmetry and compresses by bond shortening rather than bond bending, in agreement with recent quantum mechanical calculations. An unconstrained third-order Birch-Murnaghan fit to the unit-cell volumes and pressures for Ia3d symmetry gave the following equation of state parameters: Vo = 1987.6(1) Å, Ko = 58(1) GPa and K ' = 4.0(7). Above this pressure, the structure undergoes a phase transition to space group I4–3d, a non-centric subgroup of Ia3d. In the I4–3d structure, there are two non-equivalent (O4H4) groups. Both the Ca and Al atoms are displaced along a relative to their positions in Ia3d. It is proposed that compression of the short H-H distance between (O4H4) groups destabilizes the structure and may initiate the observed phase transition. Corroboration of this model will require accurate information on the hydrogen atom positions at pressures above 5 GPa. ric mixture of Al foil (in the form of strips) (Aldrich 35,685-0, 0.05 mm thick, 99.8%) and reagent-grade lime (CaO). After seven days at 423 K, this method produced relatively large single crystals (up to 800 mm) in a matrix of fine-grained material (<10 mm). A crystal fragment with dimensions 120 ¥ 100 ¥ 50 mm was first examined in air outside the diamond-anvil cell on a Picker automated four-circle diffractometer (45 kV; 40 mA; unfiltered, non-monochromatic MoKa radiation). Reflection profiles (w scans) were sharp (FWHM = 0.08∞) with no indication of twinning. A small subset of reflections, e.g., (400), showed significant thermal diffuse scattering. Intensity data were collected in air assuming space group symmetry Ia3d and the structure was refined using RFINE4 (Finger and Prince 1975). The unit-cell parameter and atomic coordinates were consistent with the single-crystal X-ray results of Lager et al. (1987) and are not reported in this study. High-pressure experiments were carried out using a 4-pin Merrill-Bassett diamond-anvil cell with 600 mm culets. The crystal was mounted in a 350 mm diameter sample hole drilled into an Inconel steel gasket (250 mm thickness; preindented to 100 mm) with an electrostatic discharge machine. A 4:1 methanol:ethanol mixture was used as pressure-transmitting medium. The pressure was determined from the shift in the fluorescence lines of a small ruby chip mounted in the sample hole. The R1 and R2 peaks at each pressure were fit with Lorentzian functions; pressure was calculated using the relationship given by Mao et al. (1978). Errors in the pressure are estimated to be ±0.05 GPa. Unit-cell parameters at ten pressures up to 7.78 GPa were determined from least-squares refinement of 25 reflections (8∞ LAGER ET AL.: HIGH-PRESSURE PHASE TRANSITION IN HYDROGARNET 643 £ 2q £ 48∞) using an eight-reflection centering technique (King and Finger 1979) (Table 1). Generally, in a high-pressure experiment, a full sphere of intensity data is collected because of the limited number of reflections accessible through the diamond-anvil cell. However, given the large unit cell of garnet (>3000 reflections), this is impractical because of the diffractometer time required. Hazen and Finger (1989) previously tried to address this problem in their study of andradite and pyrope by including in the data set only those reflections that strongly influenced the variation in structural parameters (leverage analysis). This method requires few high-quality data, and may not be feasible with the diamond-anvil cell because of restricted access to reciprocal space and systematic absorption problems [see, for example, Merli et al. (2000) and references therein]. In this study, a new approach was used. First, all accessible reflections were ordered into equivalence classes. Several symmetry equivalent reflections (usually four) with the lowest diamond-anvil cell absorption were then chosen from each class and used as input to the data-collection routine. In the fixed-f mode that is typically used for single-crystal diffraction experiments at high pressures (Angel et al. 2000), the reflections with the smallest |w| values will suffer from the least amount of diamond cell absorption. Intensity data were collected with w scans to sinq/l = 0.7 Å [2q < 60∞] at seven pressures up to 7.78 GPa. Scan width, step size and counting time were 1∞, 0.025∞, and 6s per step, respectively. Each peak was integrated with backgrounds determined by fits to Gaussian functions. Data were corrected for the effects of diamond-anvil cell absorption; symmetryequivalent reflections were averaged and converted to structure factors using in-house software modified from the suite of programs used at the Geophysical Laboratory. Refinements were carried out with RFINE4. Structure factors were weighted by [sF + (pF)], where sF was obtained from counting statistics and p was chosen to ensure that the errors were normally distributed. It was possible to locate the hydrogen atom in the Ia3d structure and refine its position at high pressure. However, the O-H vector exhibited a significant and non-systematic rotation with pressure, which is chemically unreasonable. As a result, atomic fractional coordinates and anisotropic displacement parameters were refined for all atoms except hydrogen, which was omitted from the refinement models. All refinements below 6.0 GPa converged to weighted R values between 0.020 and 0.034 in space group Ia3d. However, the refinement at 6 GPa resulted in a significantly higher R value (Rw = 0.078). In addition, the Ca displacement ellipsoid at this pressure became highly anisotropic with the major axis parallel to a. A search for all reflections [h, k, l > 0] violating Ia3d symmetry revealed weak reflections of the type hk0 with h π 2n, indicating loss of the a glide. Multiple diffraction effects were discounted based on the results from y scans. Unconstrained unit-cell refinement showed no deviation from cubic geometry. On decompression of the cell to 5.38 GPa, the same hk0 reflections were observed but their intensities were significantly weaker (Fig. 1). The pressure was then lowered to 3.08 GPa, and the unit-cell parameter was determined. Reflections violating Ia3d symmetry were not found (Fig. 1). Based on the quality of the refinement at 5.09 GPa, the transition pressure is assumed to lie between 5.09 and 5.38 GPa. The structures at 6.00, 7.09, and 7.78 GPa were refined in space group I4–3d, a non-centric subgroup of Ia3d. Refinement of these structures in Ia3d resulted in systematically high R values (~0.10). In space group I4 – 3d, the Ca and Al atoms occupy positions [x, 0, 1/4] and [x, x, x], respectively. There are two non-equivalent O and H positions, i.e., two non-equivalent (O4H4) units. The strong pseudosymmetry above the transition pressure resulted in high correlations (r ~ 0.75) between the fractional coordinates of the two O atoms and between b22 and b33 of the Ca atom. Attempts to decouple the O positions, e.g., by randomly offsetting the coordinates, or by alternately refining the two positions, were not successful. Refinement results, atomic fractional coordinates, and displacement parameters are given in Tables 2 and 3. Selected interatomic distances and angles, polyhedral volumes, and distortion parameters are presented in Tables 4 and 5. RESULTS AND DISCUSSION Hydrogarnet structure The general formula of hydrogarnet can be represented as X3Y2(SiO4)3–x(O4H4)x, where the superscripts in brackets refer to the O coordination of the three types of cations in the structure. The O coordination of the X site can be defined as a triangular dodecahedron (distorted cube) that shares two edges with tetrahedra, four with octahedra (Y site), and four with other TABLE 1. Unit-cell parameter and volume for katoite at pressure P (GPa) a (Å) V (Å3) 0.0001 12.5731(2) 1987.6(1) 1.24(5) 12.4866(3) 1946.8(1) 2.15(5) 12.4286(3) 1919.8(1) 3.08(5) 12.3719(3) 1893.7(1) 4.21(5) 12.3094(3) 1865.2(1) 5.09(5) 12.2595(3) 1842.5(1) 5.38(5) 12.2442(3) 1835.6(1) 6.00(5) 12.2145(2) 1822.3(1) 7.09(5) 12.1623(4) 1799.0(2) 7.78(5) 12.1267(3) 1783.3(1) FIGURE 1. Variation in the intensity profiles of the (710) reflection as a function of pressure. Profiles represent w scans of 1∞ width, 0.025∞ step size and 6 s per step counting time. LAGER ET AL.: HIGH-PRESSURE PHASE TRANSITION IN HYDROGARNET 644 to an H atom. In space group Ia3d, the hydrogarnet structure is uniquely defined by the fractional coordinates of the O and H atoms and by the unit-cell parameter. The cation positions are fixed by symmetry. As noted above, there are two non-equivalent O and H positions and two non-equivalent (O4H4) tetrahedra in space group I4 – 3d. One tetrahedron is quite regular (d1) whereas the other is distorted (d2) (Table 5). Just above the transition pressure the Ca atom is displaced by 0.112 Å along a in the direction of d1, which has the longer shared edge (Table 5). The Al atom is also displaced relative to its position in Ia3d and moves 0.051 Å along the threefold axis. TABLE 2. Refinement conditions and atom parameters for katoite in Ia 3d P (GPa) 0.0001 2.15(5) 4.21(5) 5.09(5) 6.00(5) Rw 0.032 0.034 0.024 0.018 0.078 p 0.011 0.010 0.0 0.0 0.065 c 1.13 1.19 1.14 1.17 1.09 No. obs. 250 250 250 248 247 Ca b(1,1) 0.0021(1) 0.0021(1) 0.0027(1) 0.0034(1) 0.0040(1) Ca b(2,2) 0.00151(7) 0.00125(7) 0.00148(6) 0.00163(6) 0.0015(1) Ca b(2,3) 0.0000(1) 0.0001(1) 0.0002(1) –0.0001(1) –0.0004(1) Biso 1.09(3) 0.95(3) 1.14(2) 1.33(3) 1.41(6) Al b(1,1) 0.00138(7) 0.00133(7) 0.00144(6) 0.00172(7) 0.0019(2) Al b(1,2) –0.0000(1) 0.0001(1) 0.0000(1) 0.0001(1) 0.0002(2) Biso 0.88(2) 0.82(2) 0.87(1) 1.03(1) 1.13(3) O x 0.0285(2) 0.0289(2) 0.0299(2) 0.0306(2) 0.0310(4) y 0.0522(2) 0.0530(2) 0.0529(2) 0.0528(2) 0.0527(4) z 0.6402(3) 0.6410(2) 0.6414(2) 0.6421(2) 0.6423(4) b(1,1) 0.0026(3) 0.0023(3) 0.0025(2) 0.0028(3) 0.0026(4) b(2,2) 0.0020(2) 0.0022(2) 0.0019(2) 0.0023(2) 0.0022(4) b(3,3) 0.0016(2) 0.0013(2) 0.0016(2) 0.0020(2) 0.0019(4) b(1,2) –0.0001(2) –0.0004(2) –0.0003(1) –0.0003(1) –0.0005(3) b(1,3) 0.0001(2) –0.0001(1) –0.0002(1) –0.0005(1) 0.0002(3) b(2,3) –0.0002(2) –0.0002(2) –0.0003(1) –0.0003(2) –0.0004(3) Biso 1.31(7) 1.20(6) 1.21(5) 1.41(6) 1.4(1) Note: The Ca atom is located at [1/8, 0, 1/4], with b(3,3) = b(2,2), b(1,2) = b(1,3) = 0; the Al atom is located at [0, 0, 0], with b(1,1) = b(2,2) = b(3,3), b(1,2) = b(1,3) = b(2,3). TABLE 5. Selected interatomic distances and angles for katoite in I 4 – 3d P (GPa) 6.00(5) 7.09(5) 7.78(5) Ca1-O4a 2.366(9) 2.350(8) 2.340(7) Ca1-O4b 2.443(9) 2.434(7) 2.432(6) Ca2-O4a 2.428(9) 2.438(7) 2.405(6) Ca2-O4b 2.481(10) 2.445(8) 2.450(7) Mean 2.430 2.417 2.407 V (CaO8) 24.11 23.74 23.42 Al-O1 1.877(9) 1.873(7) 1.891(7) Al-O2 1.905(10) 1.904(6) 1.892(6) Mean 1.891 1.888 1.892 O1◊◊◊O4 2.573(17) 2.571(10) 2.590(11) O1◊◊◊O5 2.730(10) 2.709(7) 2.720(7) V (AlO6) 8.96 8.92 8.97 Angle Var* 12.53 15.76 15.08 d1-O† 1.869(10) 1.866(6) 1.845(7) O1a◊◊◊O2a 3.004(22) 3.004(11) 2.986(13) O1a◊◊◊O3a 3.077(16) 3.068(10) 3.026(11) V (d O4) 3.35 3.33 3.22 Angle Var* 3.88 3.04 1.27 d-O-Al 132.5(6) 130.4(3) 131.5(3) d 2-O 1.850 1.833(7) 1.840(7) O1b◊◊◊O2b 2.847(22) 2.809(14) 2.805(14) O1b◊◊◊O3b 3.104(17) 3.082(13) 3.100(12) V (d O4) 3.19 3.10 3.12 Angle Var* 48.05 55.42 63.44 d-O-Al 129.9(5) 131.4(4) 129.4(3) * Bond angle variance as defined by Robinson et al. (1971). † d is Wyckoff notation for the position with point symmetry 4 – in space group Ia 3d (occupied by Si in silicate garnets); d 1 and d 2 are located at [3/8,0,1/4] and [3/4,5/8,0], respectively, in space group I4–3d. TABLE 4. Selected interatomic distances and angles for katoite in Ia 3d P (GPa) 0.0001 2.15(5) 4.21(5) 5.09(5) Ca1-O1 2.462(3) 2.434(3) 2.417(3) 2.410(3) Ca2-O4 2.520(3) 2.482(3) 2.463(2) 2.455(3) Mean 2.491 2.459 2.440 2.429 V (CaO8) 25.96 24.97 24.41 24.22 Al-O 1.914(3) 1.906(3) 1.895(2) 1.896(2) O1◊◊◊O4 2.599(5) 2.587(5) 2.583(4) 2.593(3) O1◊◊◊O5 2.813(6) 2.801(6) 2.772(4) 2.767(5) V (AlO6) 9.28 9.15 9.00 9.03 Angle Var.* 22.47 22.59 17.84 14.85 d1-O† 1.952(3) 1.922(3) 1.893(3) 1.873(2) O1◊◊◊O2 3.057(6) 3.013(6) 2.974(5) 2.945(4) O1◊◊◊O3 3.250(5) 3.201(5) 3.147(4) 3.114(4) Angle Var.* 24.67 24.21 21.22 20.50 V (d O4) 3.78 3.61 3.45 3.35 d-O-Al 130.7(2) 130.3(2) 130.6(1) 130.8(2) * Bond angle variance as defined by Robinson et al. (1971). † d is Wyckoff notation for the position with point symmetry 4– in space group Ia 3d (occupied by Si at [3/8,0,1/4] in silicate garnets). TABLE 3. Refinement conditions and atom parameters for katoite in I 43d P (GPa) 6.00(5) 7.09(5) 7.78(5) Rw 0.050 0.023 0.021 p 0.030 0.0 0.010 c 1.15 1.12 1.06 No. obs. 495 478 474 Ca x 0.1342(3) 0.1354(3) 0.1370(2) Ca b(1,1) 0.0022(2) 0.0022(2) 0.0016(2) Ca b(2,2) 0.0012(2) 0.0015(2) 0.0014(2) Ca b(3,3) 0.0019(2) 0.0016(2) 0.0015(2) Ca b(2,3) –0.0000(1) 0.0004(1) 0.0004(1) Biso 1.08(4) 1.03(4) 0.88(4) Al x 0.0024(4) 0.0039(3) 0.0032(3) Al b(1,1) 0.00163(8) 0.00118(8) 0.00127(7) Al b(1,2) –0.0000(1) –0.0003(1) –0.0001(1) Biso 0.97(2) 0.70(2) 0.75(1) O1 x 0.0339(6) 0.0340(5) 0.0356(5) y 0.0510(8) 0.0533(5) 0.0528(5) z 0.6381(8) 0.6386(5) 0.6388(5) b(1,1) 0.0012(5) 0.0023(4) 0.0021(4) b(2,2) 0.0029(6) 0.0013(4) 0.0016(4) b(3,3) 0.0018(6) 0.0013(5) 0.0014(5) b(1,2) –0.0005(4) –0.0001(4) –0.0007(3) b(1,3) 0.0005(4) –0.0008(4) 0.0002(3) b(2,3) 0.0001(4) 0.0004(3) 0.0002(3) Biso 1.2(1) 1.0(1) 1.0(1) O2 x 0.1465(9) 0.1468(6) 0.1476(5) y 0.9717(7) 0.9719(6) 0.9732(5) z 0.0536(7) 0.0518(6) 0.0538(5) b(1,1) 0.0018(5) 0.0014(5) 0.0017(4) b(2,2) 0.0044(7) 0.0029(5) 0.0027(5) b(3,3) 0.0016(6) 0.0030(4) 0.0019(4) b(1,2) 0.0003(5) –0.0009(4) 0.0001(4) b(1,3) –0.0006(4) –0.0004(4) –0.0008(3) b(2,3) 0.0001(5) –0.0003(4) –0.0002(4) Biso 1.6(2) 1.4(1) 1.2(1) Note: The Ca atom is located at [x, 0, 1/4], with b(1,2) = b(1,3) = 0; Al is located at [x, x, x ], with b(1,1) = b(2,2) = b(3,3), b(1,2) = b(1,3) = b(2,3). dodecahedra. The dodecahedral cavities are located within a framework composed of corner sharing octahedra and tetrahedra (Novak and Gibbs 1971). When Si does not occupy the tetrahedron, each O atom surrounding the vacancy is bonded LAGER ET AL.: HIGH-PRESSURE PHASE TRANSITION IN HYDROGARNET 645