Mauro Prencipe

On the elastic properties of lithium, sodium and potassium oxide. An ab initio study

Abstract The binding energy, equilibrium lattice parameter, elastic constants and central zone phonon frequencies of Li2O, Na2O and K2O have been calculated at an ab initio level with CRYSTAL, a Hartree-Fock linear combination of atomic orbitals (LCAO) program for periodic compounds. The variational basis set has been optimized for each compound, and is reported for future reference and work. A quite satisfactory agreement with very recent experimental data is obtained for Li2O. With regard to Na2O and K2O no experimental data exist, to our knowledge, for the elastic constants and the central zone phonon frequencies, so that the present data represent the first determination of these quantities.

The Raman spectrum of diopside: a comparison between ab initio calculated and experimentally measured frequencies

The Raman spectrum of diopside has been calculated by using three purely Density Functional Theory (DFT) Hamiltonians (PBE, WCPBE, LDA), the Hartree-Fock Hamiltonian (HF) and three hybrid HF/DFT ones (B3LYP, WC1LYP, PBE0). A comparison has been done between the calculated frequencies with those measured by Raman spectroscopy on a natural sample, along with several different orientations and beam polarizations, or retrieved from literature; such a comparison demonstrated the excellent performances of the hybrid Hamiltonians in reproducing the vibrational spectrum of the mineral, in line with what it is generally observed in literature concerning other mineral phases. In particular, the mean average absolute discrepancies of the calculated frequencies with respect to the experimental data were: 3.2 (WC1LYP), 4.7 (B3LYP), 6.5 (PBE0), 18.0 (PBE), 9.7 (WCPBE), 7.3 (LDA), and 40.6 cm −1 (HF). The very good quality of the WC1LYP results allowed for a reliable assignment of all of the experimentally observed Raman signals, and the corresponding assignments to specific patterns of atomic vibrational motion (normal modes).

Olivine with diamond-imposed morphology included in diamonds. Syngenesis or protogenesis?

The identification of syngenetic inclusions in diamond (i.e. inclusions of minerals that crystallized at the same time and by the same genesis as their host) has long been of paramount importance in diamond studies. However, the widespread assumption that many or most inclusions in diamonds are syngenetic is based on qualitative morphological criteria and few direct measurements. In order to provide statistically significant information on inclusion–host genetic relations for at least one kimberlite, we have determined the crystallographic orientations of 43 olivine inclusions with diamond-imposed morphology, a feature generally interpreted to indicate syngenesis, in 20 diamonds from the Udachnaya kimberlite (Siberia). Our unprecedented large data set indicates no overall preferred orientation of these olivines in diamond. However, multiple inclusions within a single diamond frequently exhibit similar orientations, implying that they were derived from original single monocrystals. Therefore, regardless of the possible chemical re-equilibration during diamond-forming processes, at least some of the olivines may have existed prior to the diamond (i.e. they are protogenetic). Our results imply that a diamond-imposed morphology alone cannot be considered as unequivocal proof of syngenicity of mineral inclusions in diamonds.

The vibrational spectrum of lizardite-1T [Mg3Si2O5(OH)4] at the Γ point: A contribution from an ab initio periodic B3LYP calculation

Abstract The vibrational spectrum of lizardite at the Γ point has been calculated with ab initio methods, using a hybrid HF/DFT Hamiltonian (B3LYP). Apart from a few bending modes involving hydrogen motion, very good agreement has been found between calculated and experimental infrared and Raman spectra of the mineral. The anharmonic correction to the OH-stretching modes proved to be crucial for a correct evaluation of their frequencies and, on average, it amounts to a lowering of about 150 cm-1 with respect to the values computed within the harmonic approximation. LO-TO splitting effects had to be taken into account for a correct interpretation of the data obtained from infrared spectra on powder samples. The calculation can be used either to confidently identify which bands in the experimental spectra do correspond to fundamental vibrational transitions or to unequivocally assign them to specific normal modes.

Ab initio quantum-mechanical calculation of CaCO 3 aragonite at high pressure: thermodynamic properties and comparison with experimental data

Structure and vibrational frequencies (at the Γ point) of CaCO 3 aragonite have been calculated from first principles, by using the hybrid Hartree-Fock/DFT B3LYP Hamiltonian, at different unit-cell volumes in the 185–242 A 3 range. By using the frequencies evaluated at such different volumes, the mode- γ Gruneisen’s parameters were estimated for each vibrational mode, and the zero point and thermal pressure contributions to the total pressure, at each volume and temperature, have then been determined by means of standard thermodynamic formulas, within the limits of the quasi-harmonic approximation. This allowed for the determination of ( i ) the equation of state at different temperatures; ( ii ) the thermal expansion as a function of pressure and temperature, and ( iii ) the evaluation of some thermodynamic properties (entropy and specific heat) together with their temperature dependences. Results were directly compared with relevant experimental data. The agreement of the calculated frequencies with the experimental data, at variable pressure, shows that the ab initio simulation can reproduce, at a relatively low computational cost, the full vibrational spectra of crystalline compounds of mineralogical interest. Moreover, the elastic properties (bulk modulus in particular), thermal expansion and thermodynamic properties, which play an important role in the characterization and in the understanding of the stability relations between carbonate phases, at high-pressure and high-temperature conditions, can be satisfactorily estimated. Precisely, at room temperature and pressure conditions, the calculated bulk modulus was 64.7 GPa, to be compared with an experimental value of 65(1) GPa (mean of three different experimental determinations); the estimated thermal expansion was about 6.1 · 10 −5 K −1 , which is only slightly underestimated with respect to the experimental datum [6.3(2) · 10 −5 K −1 ]; the calculated entropy ( S ) and the constant-pressure specific heat ( C P ) were 87.5 and 83.1 J mol −1 K −1 respectively, which are in close agreement with the experimental data [84(6) and 82.6 J mol −1 K −1 , for S and C P respectively].

Hydroxylclinohumite, a new member of the humite group: Twinning, crystal structure and crystal chemistry of the clinohumite subgroup

Hydroxylclinohumite Mg9[SiO4]4(OH, F)2, a new mineral from Zelentsovskaya mine near Magnitka (Zlatoust district, Southwestern Urals), is the OH-dominant equivalent of clinohumite Mg9[SiO4]4(F,OH)2. The crystal structure of hydroxylclinohumite has been refined from single-crystal X-ray data to R = 0.026 for the 1912 observed unique reflections [Fo > 4σ(Fo): a = 4.7480(3) Å, b = 10.2730(7) Å, c = 13.6894(2) Å, α = 100.72(1)°, V = 656.1(1) Å3, P21/b (No. 14), Z = 2]. Twinning on {001}, which apparently doubles the c axis, was detected and a ratio of 0.94:0.06 between the volumes of the two twin components has been obtained by least-squares refinement. The crystal structure of hydroxylclinohumite corresponds to that of clinohumite except for the positions of the hydrogen atoms. The crystal chemistry of the clinohumite subgroup is discussed and a general formula M2+8(M2+, M4+) (SiO4)4(OH, F, O)2 (M2+ and M4+ mainly Mg and Ti, respectively) is proposed for it.

Stoppaniite, (Fe,Al,Mg)4(Be6Si12O36)*(H2O)2(Na,□) a new mineral of the beryl group from Latium (Italy)

This paper relates the finding of stoppaniite, a new mineral of the beryl group, at Capranica, Vico volcanic complex, Latium, Italy. Stoppaniite occurs inside the miarolitic cavities of a volcanic ejectum, as very rare, transparent, light-blue, hexagonal-prismatic euhedral crystals, up to 0.5 mm in length. It is optically uniaxial (-), and shows a weak pleochroism from colourless to very light blue. The refraction indices are: e = 1.619(3) and ω = 1.625(3); the density is: Dobs = 2.79(3) g/cm3. Dcalc = 2.811 g/cm3. Stoppaniite is hexagonal, s.g. P 6/ mcc, with a (A) = 9.397(1), c (A) = 9.202(2). Strongest X-ray powder diffraction lines (Gandolfi camera) are (d in A, intensities visually estimated): 3.278 (vS), 8.12 (S), 2.903 (S), 4.00 (m), 2.553 (mw), 1.752 (mw). The empirical crystal-chemical formula is: \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[(Fe^{3{+}}\_{2.70}Mg\_{0.64}Al\_{0.42}Mn\_{0.06}Ti\_{0.02}Sc\_{0.02})(Be\_{6.88}Si\_{11.60})O\_{36}*2H\_{2}O(Na\_{0.94}K\_{0.02}Cs_{0.02})\] \end{document} compatible with the simplified formula: \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[(Fe^{3{+}})\_{3}(Mg,Fe^{2{+}})Na(Be\_{6}Si\_{12}O\_{36})*2H\_{2}O,\ or\ ideally\ Fe^{3{+}}\_{4}Be\_{6}Si\_{12}O_{36}.\] \end{document} A rational classification of beryl group minerals based on the octahedral occupancy is proposed.

The (100), (111) and (110) surfaces of diamond: an ab initio B3LYP study

We present an accurate ab initio study of the structure and surface energy of the low-index (100), (111) and (110) diamond faces, by using the hybrid Hartree–Fock/density functional B3LYP Hamiltonian and a localised all-electron Gaussian-type basis set. A two-dimensional periodic slab model has been adopted, for which convergence on both structural and energetic parameters has been thoroughly investigated. For all the three surfaces, possible relaxations and reconstructions have been considered; a detailed geometrical characterisation is provided for the most stable structure of each orientation. Surface energy is discussed for all the investigated faces.

Toward an accurate ab initio estimation of compressibility and thermal expansion of diamond in the [0, 3000 K] temperature and [0, 30 GPa] pressures ranges, at the hybrid HF/DFT theoretical level

Abstract The isothermal bulk modulus, together with its temperature dependence, and the thermal expansion of diamond at various pressures were calculated from first principles in the [0, 30 GPa] and [0, 3000 K] pressure and temperature ranges, within the limits of the quasi-harmonic approximation (QHA). The hybrid HF/DFT functional employed (WC1LYP) proved to be particularly effective in providing a very close agreement between the calculated and the available experimental data. In particular, the bulk modulus at 300 K was estimated to be 444.6 GPa (K′ = 3.60); at the same temperature, the (volume) thermal expansion coefficient was 3.19×10-6 K-1. To the authors’ knowledge, among the theoretical papers devoted to the subject, the present one provides the most accurate thermo-elastic data in high-pressure and temperature ranges. Such data can confidently be used in the determination of the pressure of formation using the “elastic method” for minerals found as inclusions in diamonds (recently applied on different minerals included in diamonds), thus shedding light upon the genesis of diamonds in the Earth’s upper mantle.

Ab-initio determination of high-pressure and high-temperature thermoelastic and thermodynamic properties of low-spin (Mg1−xFex)O ferropericlase with x in the range [0.06, 0.59]

Abstract In this work, we calculate the thermo-elastic properties of (Mg1-xFex)O ferropericlase, with x in the [0.06, 0.59] range, and the thermodynamic properties of ferropericlase having the specific stoichiometric composition (Mg0.54Fe0.46)O, at pressures and temperatures, which are those typical of the Earth’s lower mantle. We follow an ab-initio quantum-mechanical approach, with the use of the WC1LYP hybrid Hartree-Fock/density functional theory (HF/DFT) functional, within the framework of the quasiharmonic approximation. Iron is assumed to be in the low-spin configuration, as it proved to be the most stable spin arrangement at the thermo-baric conditions of the deepest lower mantle. The choice of the low-spin configuration, and the use of an ab-initio approach, make this work unique as it is the first time that such a technique is applied for the calculation of the vibrational and thermodynamic properties of the low-spin ferropericlase. We observe a linear increase of the bulk modulus and a linear decrease of the cell volume as iron content increases. More precisely, for x = 0.46, at ambient condition KT = 205.57 GPa, K′T = 4.242, and VT = 72.216 Å3; for x = 0.03, at the same conditions, KT = 167.42 GPa, K′T = 4.085, and VT = 75.145 Å3. Some thermodynamic parameters and the thermal expansion (CV, CP, S, α) for (Mg0.54Fe0.46)O are calculated both at ambient condition [CV = 36.11 J/(mol K), CP = 36.38 J/(mol K), S = 26.62 J/(mol K), α = 1.97×10−5 K−1], and at simultaneous high-pressure and high-temperature conditions as a function of the geobar and geotherm curves. The data here proposed can be seen as possible bounds to the values of thermoelastic and thermodynamic parameters employed in the construction of geophysical models and the same data could be used to revise the velocity of the seismic waves in the lower mantle