Alessandro Pavese

Static compression and H disorder in brucite, Mg(OH)2, to 11 GPa: a powder neutron diffraction study

Neutron diffraction data suitable for Rietveld refinements were collected on a powder sample of synthetic Mg(OH)2 by the Polaris time-of-flight spectrometer (ISIS spallation source, U.K.) at 10-4 7.8(3) and 10.9(6) GPa. The Paris-Edinburgh high-pressure cell with WC anvils was used. Pressure calibration and equation-ofstate results were attained by separate runs with an NaCl internal standard. Interpolation of p(V) data by the fourth-order Birch-Murnaghan e.o.s. yields K0=41(2) GPa, K′0=4(2) and K″0=1.1(9) GPa-1. The bulk modulus obtained is smaller than previously reported results. Rietveld refinements (Rprof=1.45% and 2.02% at 10-4 and 10.9 GPa) show that H lies on the threefold axis (1/3, 2/3, z) up to 10.9 GPa, where a model with H disordered in (x, 2x, z) can be refined. In the latter case, a hydrogen bond with O-H=0.902(7), H..O′=2.026(8) Å and <OHO′=145.9 (7)° is observed. Differences with previous results for deuterated brucite are discussed. The onset of H disorder, and a jump of the c/a ratio vs. pressure at 6–7 GPa, may be related to a second-order phase transition consistent with recently reported Raman spectroscopic results.

Interatomic potentials for CaCO3 polymorphs (calcite and aragonite), fitted to elastic and vibrational data

Calcite and aragonite have been modeled using rigid-ion, two-body Born-type potentials, supplemented by O-C-O angular terms inside the CO3 groups. A shell model has also been developed for calcite. Atomic charges, repulsive parameters and force constants have been optimized to reproduce the equilibrium crystal structures, the elastic constants and the Raman and infrared vibrational frequencies. The rigid-ion potential RIM (atomic charges:zO= -0.995e,zC = 0.985e,zCa = 2.0e) fitted to calcite properties is able to account for those of aragonite as well. Experimental unit-cell edges, elastic constants, internal and lattice frequencies are reproduced with average relative errors of 2.1, 5.5, 2.4, 15.1% for calcite and of 0.2, 19.4, 2.5, 11.8% for aragonite, respectively. The RIM potential is suitable for thermodynamic and phase diagram simulations in the CaCO3 system, and is discussed and compared to other potentials.

X-ray single-crystal diffraction study of pyrope in the temperature range 30-973 K

The crystal structures of a synthetic H-bearing aluminous stishovite, containing approximately 1.6 wt% A1203, and a pure-silica stishovite have been refined from threedimensional, single-crystal X-ray diffraction data. The space group of both is P42/mnm, and the unit cell parameters of the aluminous crystal are a = 4.1839(8) and c = 2.6684(6) A, which are slightly larger than those of pure silica [a = 4.1773(4) and c = 2.6652(2) A]. The AI-bearing octahedron is slightly larger and more regular than that of pure-silica stishovite. Unit cell and atom position refinement are consistent with 1.6% substitution of Al for Si. The observation of 1.9% Al substitution for [6ISi,even without clear charge balance, is evidence that this substitution may be significant in many lower mantle silicate phases.

Nature of structural disorder in natural kaolinites : a new model based on computer simulation of powder diffraction data and electrostatic energy calculation

A new model for the description of the structural disorder in natural kaolinite materials is proposed, based on the stacking of two 1:1 layers and their enantiomorphs, and encompassing previously proposed models. The layers, where randomly stacked along the c axis (using probabilistic functions nested in recursive algorithms), correctly describe the observed powder diffraction patterns of natural kaolinites with any density of structural faults. The proposed model was evaluated using electrostatic energy calculations against earlier models of disorder based on layer shift, layer rotation, statistical occupancy of the Al octahedra, or enantiomorphic layers. The present 4-layer model has a minimum of potential energy with respect to the previous models. As expected, the fully ordered triclinic structure of kaolinite possesses the absolute minimum of potential energy.

THERMODYNAMIC PROPERTIES OF CACO3 CALCITE AND ARAGONITE - A QUASI-HARMONIC CALCULATION

A quasi-harmonic model has been used to simulate the thermodynamic behaviour of the CaCO3 polymorphs, by equilibrating their crystal structures as a function of temperature so as to balance the sum of inner static and thermal pressures against the applied external pressure. The vibrational frequencies and elastic properties needed have been computed using interatomic potentials based on two-body Born-type functions, with O-C-O angular terms to account for covalency inside the CO3 molecular ion. A good agreement with experimental data is generally shown by simulated heat capacity and entropy, while the thermal expansion coefficient seems to be more difficult to reproduce. The results obtained for aragonite are less satisfactory than those of calcite, but they are improved by using a potential specifically optimized on properties of that phase itself.

Elastic behavior and phase stability of pollucite, a potential host for nuclear waste

Abstract The elastic behavior and the phase stability of natural pollucite, (Cs,Na)16Al16Si32O96⋅nH2O, were investigated at hydrostatic pressure by in situ single-crystal X-ray diffraction with a diamond-anvil cell. Pollucite experiences a P-induced phase transition, not previously reported in the literature, at P = 0.66 ± 0.12 GPa from cubic (Ia3̅d) to triclinic symmetry (P1̅). The phase transition is completely reversible and without any appreciable hysteresis effect. No further phase transition has been observed up to 9 GPa. Fitting the pressure-volume data of the low-pressure cubic polymorph with a second-order Birch-Murnaghan Equation-of-State (BM-EoS), we obtain V0 = 2558.3(4) Å3, KT0 = 41(2) GPa, and K′T = 4 (fixed). For the high-pressure triclinic polymorph, a third-order BM-EoS fit gives V0 = 2577.5(40) Å3, KT0 = 25.1(9) GPa, and K′T = 6.5(4). The axial bulk moduli of the high-pressure triclinic polymorph were calculated with a third-order “linearized” BM-EoS. The EoS parameters are a0 = 13.699(12) Å, KT0(a) = 25.5(17) GPa, and K′T(a) = 6.8(6) for the a axis; b0 = 13.728(12) Å, KT0(b) = 23.2(15) GPa, and K′T(b) = 7.7(7) for the b axis; c0 = 13.710(7) Å, KT0(c) = 25.2(10) GPa, and K′T(c) = 6.8(4) for the c axis [KT0(a):KT0(b):KT0(c) = 1.10:1:1.09]. Brillouin light-scattering was used to investigate the single-crystal elastic properties of pollucite at ambient conditions. The aggregate adiabatic bulk modulus (Ks) and shear modulus (G), calculated using the Voigt-Reuss-Hill averaging procedures, are Ks = 52.1(10) GPa and G = 31.5(6) GPa. The elastic response of pollucite and other isotypic materials (e.g., analcime, leucite, and wairakite) is compared. The high thermo-elastic stability of pollucite, reflected by the preservation of crystallinity at least up to 9 GPa (at room T) and 1470 K (at room P) in elastic regime, the large amount of Cs hosted in this material (Cs2O ~ 30 wt%), the immobility of Cs at high-temperature and high-pressure conditions, and the extremely low leaching rate of Cs, make of this open-framework silicate a functional material with potential use for fixation and deposition of Cs radioisotopes in high-level nuclear waste.

P-V equation of State, thermal expansion, and P-T stability of synthetic zincochromite (ZnCr2O4 spinel)

Abstract The elastic properties and thermal behavior of synthetic zincochromite (ZnCr2O4) have been studied by combining room-temperature high-pressure (0.0001.21 GPa) synchrotron radiation powder diffraction data with high-temperature (298.1240 K) powder diffraction data. Elastic properties were obtained by fitting two Equations of State (EoS) to the P-V data. A third-order Birch-Murnaghan model, which provides results consistent with those from the Vinet EoS, yields: K0 = 183.1(±3.5) GPa, K’ = 7.9(±0.6), K’’ = .0.1278 GPa-1 (implied value), at V0 = 577.8221 Å3 (fixed). Zincochromite does not exhibit order-disorder reactions at high temperature in the thermal range explored, in agreement with previous studies. The volume thermal expansion was modeled with αV = α0 + α1T + α2/T-2, where only the first coefficient was found to be significant [α0 = 23.0(4) 10-6K-1]. Above 23 GPa diffraction patterns hint at the onset of a phase transition; the high pressure phase is observed at approximately 30 GPa and exhibits orthorhombic symmetry. The elastic and thermal properties of zincochromite were then used to model by thermodynamic calculations the P-T stability field of ZnCr2O4 with respect to its oxide constituents (Cr2O3 and rocksalt-like ZnO). Spinel is expected to decompose into oxides at about 18 GPa and room temperature, in absence of sluggish kinetics.

Further study of the cation ordering in phengite 3T by neutron powder diffraction

Abstract Phengite 3T (Dora-Maira massif, Italian western Alps), with chemical composition K0.96Na0.01Al1.44Mg0.56(Si3.59Al0.41)O10(OH)2 has been investigated using powder neutron diffraction, at the ILL (Institut Laue-Langevin) Facility, on the D2B diffractometer. Data sets were collected at 293 and 873 K, and the present results are compared with those obtained previously using the time-of-flight (TOF) technique, on the same compound. In the octahedral sheet, Al tends to order into the M2 site, in accordance with the measurements mentioned above, whereas the Al/Si tetrahedral ordering we observe (i.e. Si fully into T1 site) is at variance with that determined previously. These discrepancies are ascribed to the presence of talc impurities in the sample used previously (~6 wt.%), which affected the results obtained.

Theoretical equilibrium and growth morphology of CaCO3 polymorphs. I. Aragonite

Abstract Periodic bond chain (PBC) analysis is performed using a potential function fitted to elastic, structural and vibrational properties of aragonite. The resulting equilibrium form of the crystal, bounded by six forms having F character, is dominated by {0 1 1}, {1 1 0} and {1 0 2}, other forms being {1 1 1}, {0 1 0} and {0 0 1}, the corresponding specific surface energy γ has a mean value of ≈940erg/cm 2 . The theoretical growth shape is defined by five F-forms: {1 1 0}, {0 1 0}, {0 1 1}, {0 0 1}, {1 0 2} and a stepped one, {0 2 1}. Its habit depends on what value of the attachment energy of {0 1 1} is considered. The agreement between the theoretical growth morphology and that of natural crystals is not fully satisfactory: as a matter of fact three out of the eight forms bounding the averaged natural morphology (i.e., {1 1 1}, {0 1 2} and {1 2 1}) are missing in the theoretical growth morphology. From the observation of the natural gypsum/aragonite epitaxy, a simple model is proposed to explain the striking morphological difference between the pseudo-symmetrical zones [0 1 0] and [1 1 0] in natural aragonite crystals. The variation on the attachment energy of {0 1 0}, induced by water adsorption, improves the fit between theory and observation around these zones, especially when the distribution of their vicinal faces is considered. The same reasoning on water adsorption is extended to the specific surface energy of the crystal: a theoretical value of 330 erg/cm 2 is calculated for γ erystal/water of the face (0 1 0).

Leucite at high pressure: Elastic behavior, phase stability, and petrological implications

Abstrac Elastic and structural behavior of a natural tetragonal leucite from the volcanic Lazium district (Italy) were investigated at high pressure by in situ single-crystal X-ray diffraction with a diamond anvil cell under hydrostatic conditions. A first-order phase transition, never reported in the literature, was observed at P = 2.4 ± 0.2 GPa from tetragonal (I41/a) to triclinic symmetry (analysis of diffraction intensities suggests the space group P1), accompanied by a drastic increase in density of about 4.7%. The transition pressure was bracketed by several measurements in compression and decompression. No further phase-transition has been observed up to 7 GPa. Fitting a second-order Birch-Murnaghan equation of state (BM-EoS) to the pressure-volume data of the tetragonal polymorph, we obtain K0 = 41.9(6) GPa and K′ = 4 (fixed). In the case of the triclinic polymorph, a second-order BM-EoS gives K0 = 33.2(5) GPa. The eulerian finite strain (fe) vs. normalized stress (Fe) curves were calculated for the low- and high-P polymorphs, providing Fe(0) = 42(1) and Fe(0) = 33.2(4) GPa, respectively. The axial bulk modulus values of the tetragonal polymorph, calculated with a linearized BM-EoS, are K0(a) = 34.5(5) and K0(c) = 78(1) GPa. For the triclinic polymorph, we obtain K0(a) = 35.9(5), K0(b) = 34.9(7), and K0(c) = 35.5(7) GPa. The elastic behavior of the low-P polymorph appears to be more anisotropic than that of the high-P polymorph. The HP-crystal structure evolution of the tetragonal polymorph of leucite was studied on the basis of six structural refinements at different pressures between 0.0001 and 1.8 GPa. The main deformation mechanisms at high-pressure are due to tetrahedral tilting, giving rise to an increase of the ellipticity of the four- and six-membered rings of the tetrahedral framework. The T-O bond distances are practically invariant within the stability field of the tetragonal polymorph. The complex P-induced twinning, due to the tetragonal → triclinic phase-transition, and the low quality of the diffraction data at pressure above the phase-transition, did not allow the refinement of the crystal structure of the triclinic polymorph.