Michele Catti

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.

Lithium location in NASICON-type Li+ conductors by neutron diffraction. I. Triclinic α′-LiZr2(PO4)3

Abstract High-resolution powder neutron diffraction data have been collected at room temperature on the triclinic α′ phase of LiZr2(PO4)3 (HRPD, ISIS Facility, U.K.). Rietveld refinement analysis (space group C1; Z=4; a=15.0718(2), b=8.8556(1), c=9.1234(1) A, α=89.660(1), β=123.912(1), γ=90.429(1)°) and Fourier difference maps have revealed the presence of monoclinic pseudo-symmetry −x, y, 1/2−z for all atoms but lithium, which is disordered over two sites Li1 and Li2 with occupancies 0.71(3) and 0.29(3), respectively. The final agreement indexes are Rp=0.0672, wRp=0.0919, R(F2)=0.0603 for 92 refined parameters. Both Li1 and Li2 are in distorted tetrahedral coordinations, with 〈Li–O〉=2.09 and 2.18 A, respectively. Pairs of centrosymmetrical Li1 sites are located within half of the available M′ holes of the NASICON structure, which are split into two independent sets by triclinic breaking of symmetry. This accounts for the lower conductivity of the triclinic phase.

Lithium location in NASICON-type Li+ conductors by neutron diffraction: II. Rhombohedral α-LiZr2(PO4)3 at T=423 K

Abstract High-resolution powder neutron diffraction data have been collected T =423 K on the rhombohedral α phase of LiZr 2 (PO 4 ) 3 (HRPD, ISIS Facility, UK). By Rietveld refinement analysis (space group R 3 c; Z =6; a =8.85493(3), c =22.1440(1) A) and Fourier difference maps, lithium was found to be disordered over six positions related by 3 symmetry in the large M′ hole of the NASICON structure with centre at 0 0 0. The final agreement indexes are R p =0.0352, wR p =0.0436, R ( F 2 )=0.1289 for 46 refined parameters. Li shows a very distorted tetrahedral coordination, with =2.27 A; this result, together with the large number of empty sites available for hopping, due to disorder, accounts for the high Li + mobility in the α phase. The order–disorder nature of the α–α′ phase transition of LiZr 2 (PO 4 ) 3 is discussed, and structural relations between NASICON and corundum α-Al 2 O 3 are pointed out.

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.

Nuclear quantum effects in ab initio dynamics: Theory and experiments for lithium imide

Owing to their small mass, hydrogen atoms exhibit strong quantum behavior even at room temperature. Including these effects in first-principles calculations is challenging because of the huge computational effort required by conventional techniques. Here we present the first ab initio application of a recently developed stochastic scheme, which allows to approximate nuclear quantum effects inexpensively. The proton momentum distribution of lithium imide, a material of interest for hydrogen storage, was experimentally measured by inelastic neutron-scattering experiments and compared with the outcome of quantum thermostatted ab initio dynamics. We obtain favorable agreement between theory and experiments for this purely quantum-mechanical property, thereby demonstrating that it is possible to improve the modeling of complex hydrogen-containing materials without additional computational effort.

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).

Tetragonal superstructure and thermal history of Li0.3La0.567TiO3 (LLTO) solid electrolyte by neutron diffraction

High-resolution time-of-flight neutron powder diffraction data (ISIS facility, Rutherford Appleton Laboratory, U. K.) were collected on sample I, prepared by slow cooling from 1300 °C, of the Li0.3La0.567TiO3 (LLTO) lithium ion conductor, and on sample II quenched in liquid N2. Patterns were obtained at room temperature (RT), 400 and 700 °C on sample I, and at 550 °C on sample II, studied at RT in previous work. The structure was resolved and Rietveld refined in the tetragonal P4/nbm space group with √2ap × √2ap × 2ap unit-cell [a = 5.48162(1), c = 7.74646(1) A at RT, Z = 4; ap is the cell edge of cubic perovskite] in all cases except 700 °C, where a P4/mmm (ap × ap × 2ap) structure was determined and refined [a = 3.89827(2), c = 7.8002(1) A, Z = 2]. In both space groups lanthanum ordering over two La1 and La2 sites is present, but only in P4/nbm can an additional anti-phase octahedral tilting of type a0a0c− be observed, similar to what occurs in the I4/mcm RT metastable phase of the quenched sample. The two distortions are associated to hkl superlattice reflections with h + k even, l odd, and h + k odd, l odd, respectively. Lithium atoms were located in highly disordered sites within the less populated La1 hollows, with short Li–Li′ distances accounting for the high ionic mobility. Possible ordering schemes indicate a mainly (001) two-dimensional mechanism of ion hopping among Li sites.

Quantum-mechanical Hartree-Fock study of calcite (CaCO3) at variable pressure, and comparison with magnesite (MgCO3)

The static crystal energy of calcite and its structure configuration as functions of pressure were determined by ab initio all-electron periodic Hartree-Fock calculations (CRYSTAL code). Ca, O and C atoms were represented by 22, 18 and 14 atomic orbitals, respectively, in form of contracted Gaussian-type functions. Comparison between theoretical and experimental data was performed for binding energy, equilibrium unit-cell and bond lengths, bulk modulus and C33 and C11 + C12 elastic constants, and vibrational frequency of the symmetrical C-O stretching mode. The agreement is generally satisfactory. A larger compressibility is observed for structural parameters of calcite than for those of magnesite coming from a similar calculation. The Ca-O and C-O chemical bonding was characterized by electron density maps and by Mulliken atomic charges; these are discussed and compared to values determined by empirical fitting of Born-type interatomic potentials.

Theoretical equilibrium and growth morphology of anhydrite (CaSO4) crystals

Theoretical equilibrium and growth morphology of CaSO4 (anhydrite) are obtained by applying the Hartman-Perdok method and computing surface and attachment energies with a Born interatomic potential (electrostatic + dispersive + exponential repulsive terms). Dispersive coefficients derive from experimental refractivity data and the other parameters have been fitted to structural and elastic properties of the anhydrite crystal. A comparison is made with the morphology of natural samples, where the three fundamental pinacoids {100}, {010} and {001} prevail on other S forms. Finally the equilibrium shape of 2D nuclei which can form on F faces is calculated.