The vibrational spectrum of calcite (CaCO<Subscript>3</Subscript>): an ab initio quantum-mechanical calculation

The vibrational spectrum of calcite (CaCO₃) is evaluated at an ab initio periodic quantum-mechanical level by using the CRYSTAL package. A localized basis set of Gaussian-type functions and the B3LYP hybrid Hamiltonian are adopted. The dynamical matrix is obtained by differentiating numerically the analytical first derivatives of the energy. The accuracy with respect to all computational parameters is documented. The calculated frequencies are compared with available IR and RAMAN data (16 and 5 peaks, respectively), the mean absolute error being less than 12 cm^–1 (frequencies range from 100 to 1600 cm^–1). Overall, the agreement with experiment is very satisfactory, and shows that simulation can produce at a relatively low cost the full spectra of crystalline compounds of mineralogical interest.     

First-principles simulation of high-pressure polymorphs in MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript>

We have used density functional theory to investigate the stability of MgAl₂O₄ polymorphs under pressure. Our results can reasonably explain the transition sequence of MgAl₂O₄ polymorphs observed in previous experiments. The spinel phase (stable at ambient conditions) dissociates into periclase and corundum at 14 GPa. With increasing pressure, a phase change from the two oxides to a calcium-ferrite phase occurs, and finally transforms to a calcium-titanate phase at 68 GPa. The calcium-titanate phase is stable up to at least 150 GPa, and we did not observe a stability field for a hexagonal phase or periclase + Rh₂O₃(II)-type Al₂O₃. The bulk moduli of the phases calculated in this study are in good agreement with those measured in high-pressure experiments. Our results differ from those of a previous study using similar methods. We attribute this inconsistency to an incomplete optimization of a cell shape and ionic positions at high pressures in the previous calculations.     

Raman spectra of bixbyite,Mn<Subscript>2</Subscript>O<Subscript>3</Subscript>, up to 40 GPa

The Raman spectra of bixbyite, Mn₂O₃, were measured up to 40 GPa at room temperature. Mn₂O₃ undergoes a phase transition from the C-type rare earth structure to the CaIrO₃-type (post-perovskite) structure at 16–25 GPa. The transition pressure measured in Raman spectroscopy is significantly lower than the pressure reported previously by an X-ray diffraction study. This could be due to the greater polarizability in the CaIrO₃-type structure, consistent with high-pressure observation on the CaIrO₃ type in MgGeO₃, although it is still possible that experimental differences may cause the discrepancy. Unlike the change at the perovskite to CaIrO₃-type transition, the spectroscopic Grüneisen parameter does not decrease at the C-type to CaIrO₃-type transition. The spectroscopic Grüneisen parameter of the low-pressure phase (C type) is significantly lower than thermodynamic Grüneisen parameter, suggesting significant magnetic contributions to the thermodynamic property of this material. Our Raman measurements on CaIrO₃-type Mn₂O₃ contribute to building systematic knowledge about this structure, which has emerged as one of the common structures found in geophysically important materials.     

High-pressure thermo-elastic properties of beryl (Al<Subscript>4</Subscript>Be<Subscript>6</Subscript>Si<Subscript>12</Subscript>O<Subscript>36</Subscript>) from ab initio calculations,and observations about the source of thermal expansion

Ab initio calculations of thermo-elastic properties of beryl (Al₄Be₆Si₁₂O₃₆) have been carried out at the hybrid HF/DFT level by using the B3LYP and WC1LYP Hamiltonians. Static geometries and vibrational frequencies were calculated at different values of the unit cell volume to get static pressure and mode-γ Grüneisen’s parameters. Zero point and thermal pressures were calculated by following a standard statistical-thermodynamics approach, within the limit of the quasi-harmonic approximation, and added to the static pressure at each volume, to get the total pressure (P) as a function of both temperature (T) and cell volume (V). The resulting P(V, T) curves were fitted by appropriate EoS’, to get bulk modulus (K ₀) and its derivative (K′), at different temperatures. The calculation successfully reproduced the available experimental data concerning compressibility at room temperature (the WC1LYP Hamiltonian provided K ₀ and K′ values of 180.2 Gpa and 4.0, respectively) and the low values observed for the thermal expansion coefficient. A zone-centre soft mode \( P6/mcc \to P\bar{1} \) phase transition was predicted to occur at a pressure of about 14 GPa; the reduction of the frequency of the soft vibrational mode, as the pressure is increased, and the similar behaviour of the majority of the low-frequency modes, provided an explanation of the thermal behaviour of the crystal, which is consistent with the RUM model (Rigid Unit Model; Dove et al. in Miner Mag 59:629–639, 1995), where the negative contribution to thermal expansion is ascribed to a geometric effect connected to the tilting of rigid polyhedra in framework silicates.     

Insights into oxygen-cation bonding in fresnoite-type structures from O <Emphasis Type="Italic">K</Emphasis>- and Ti <Emphasis Type="Italic">L</Emphasis><Subscript>23</Subscript>-electron energy-loss spectra and ab initio calculations of the electronic structure

O K- and Ti L₂₃-core-loss spectra of fresnoite Ba₂TiSi₂O₈ (BTS) and Sr₂TiSi₂O₈ (STS), which is isotypic to BTS, have been measured by electron energy-loss spectroscopy (EELS). The energy-loss near-edge structures (ELNES) of the O K edge have been identified on the basis of theoretical simulations and interpretations of the X-ray absorption near-edge structures (XANES), which have been modelled in the framework of self-consistent full multiple-scattering (FMS) theory using FEFF8. Herewith, the K-absorption spectra of oxygen (E) and the local partial electron density of states (DOS) of all atoms have been calculated. For BTS, the observed spectral features in the O K-edge spectra are interpreted in terms of mixing between the central O p and neighbouring Ba 5d and 4f, Si 3p and 3d, and Ti 3d orbitals. The observed differences in the O K-edge spectra for STS and BTS can mainly be attributed to three properties: (1) The lack of high local partial Sr unoccupied DOS with 4f symmetry near the Fermi level compared to the high Ba 4f unoccupied DOS results in differences of overlapping O 2p – cation orbitals. (2) The differences in the ionic radii of Sr and Ba result in a larger unit cell for BTS and, thus, in larger oxygen-cation bonding distances. (3) In comparison to STS, the strength of the incommensurate 2-D structural modulation is significantly weaker in BTS, i.e. distortions of coordination polyhedra occur to a much lesser extent. All these effects alter the oxygen-cation hybridization and, hence, result in a variation of the O 1s p transition and consequently of the O K-edge spectral shape. The observed peak broadening in Ti L₂₃ ELNES of STS compared to BTS is correlated with strong displacive modulations hosted in STS.     

Minerals at high pressure. Mechanics of compression from quantum mechanical calculations in a case study: the beryl (Al<Subscript>4</Subscript>Be<Subscript>6</Subscript>Si<Subscript>12</Subscript>O<Subscript>36</Subscript>)

The Bader topological analysis has been applied to ab initio computed electron densities of beryl, in order to clarify its mechanism of compression. Full structural optimization and total energy (E) calculations were performed at different cell volumes (V _c). The pressure at each volume and the equation of state were estimated from the first and second derivatives of the resultant E(V _c) curve. The total (negative) potential energy of the crystal, sum of both attractive and repulsive electrostatic terms, was found to systematically decrease (i.e., it moved to more negative values) up to the highest pressure considered (28.4 GPa), indicating that interelectronic and internuclear repulsions are not the only terms controlling the compressibility, at least in the pressure range investigated. Electronic kinetic energy increases as the cell volume is reduced, leading to a parallel increase of the total energy. Both structure at equilibrium and compressibility are therefore due to the balance between the opposing kinetic and potential energy terms. The Bader theory has been used to identify the topological atoms within the structure and to calculate their properties, with particular attention to the forces driving the structural relaxation at high pressure. On a qualitative basis, the obtained results are expected to be transferable to the discussion of compressibility of other mineral phases.     

Experimental multipole-refined and theoretical charge density study of LiGaSi<Subscript>2</Subscript>O<Subscript>6</Subscript> clinopyroxene at ambient conditions

The synthetic LiGaSi₂O₆ clinopyroxene is monoclinic C2/c at room-T. Its experimental electron density, ρ(r), has been derived starting from accurate room-T single-crystal diffraction data. Topological analysis confirms an intermediate ionic-covalent character for Si–O bonding, as found by previous electron-density studies on other silicates such as diopside, coesite and stishovite. The non-bridging Si–O bonds have more covalent character than the bridging ones. The Ga–O bonds have different bonding characters, the Ga–O2 bond being more covalent than the two Ga–O1 bonds. Li–O bonds are classified as pure closed-shell ionic interactions. Similar to spodumene (LiAlSi₂O₆), Li has sixfold coordination, but the bond critical points associated to the two longest bonds are characterized by very low electron density values. Similar to what previously found in spodumene and diopside, O···O interactions were detected from the topological analysis of ρ(r), and indicate a cooperative interaction among the lone pairs of neighbouring oxygen atoms. In particular, this kind of interaction has been obtained for the O1···O1 edge shared between two Ga octahedra. Integration over the atomic basins gives net charges of −1.39(10), 2.82(10), 1.91(10) and 0.82(8) e for O (averaged), Si, Ga and Li atoms, respectively. Periodic Hartree–Fock and DFT calculations confirm the results obtained by multipole refinement of the experimental data. Moreover, the theoretical topological properties of the electron density distribution on the Si₂O₆ group are very similar to those calculated for spodumene. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Low-temperature heat capacities of MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript> and spinels of the MgCr<Subscript>2</Subscript>O<Subscript>4</Subscript>–MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript> solid solution

We present results from low-temperature heat capacity measurements of spinels along the solid solution between MgAl₂O₄ and MgCr₂O₄. The data also include new low-temperature heat capacity measurements for MgAl₂O₄ spinel. Heat capacities were measured between 1.5 and 300 K, and thermochemical functions were derived from the results. No heat capacity anomaly was observed for MgAl₂O₄ spinel; however, we observe a low-temperature heat capacity anomaly for Cr-bearing spinels at temperatures below 15 K. From our data we calculate standard entropies (298.15 K) for Mg(Cr,Al)₂O₄ spinels. We suggest a standard entropy for MgAl₂O₄ of 80.9 ± 0.6 J mol⁻¹ K⁻¹. For the solid solution between MgAl₂O₄ and MgCr₂O₄, we observe a linear increase of the standard entropies from 80.9 J mol⁻¹ K⁻¹ for MgAl₂O₄ to 118.3 J mol⁻¹ K⁻¹ for MgCr₂O₄.     

Discussion of “Thermodynamic parameters of CaMgSi<Subscript>2</Subscript>O<Subscript>6</Subscript>-Mg<Subscript>2</Subscript>Si<Subscript>2</Subscript>O<Subscript>6</Subscript> pyroxenes based on regular solution and cooperative disordering models” by Holland,Navrotsky, and Newton

Phase equilibria in the join CaMgSi₂O₆-CaFeAlSiO₆-CaTiAl₂O₆ have been determined in air at 1 atm by the ordinary quenching method. Clinopyroxene_ss, forsterite, perovskite, magnetite_ss, spinel_ss, hibonite and an unknown phase X are present at liquidus temperatures (ss: solid solution). At subsolidus temperatures the following phase assemblages were encountered; clinopyroxene_ss+perovskite, clinopyroxene_ss +perovskite+spinel_ss, clinopyroxene_ss +perovskite+melilite (+anorthite), clinopyroxene_ss +perovskite+melilite+spinel_ss+anorthite, clinopyroxene_ss +perovskite+anorthite+spinel_ss, and clinopyroxene_ss +perovskite+anorthite+hibonite. At subsolidus temperatures the single phase field of clinopyroxene_ss extends up to 19 wt.% CaTiAl₂O₆. Even in the field of clinopyroxene_ss+perovskite, the TiO₂ content in clinopyroxene_ss continues to increase and attains 9.2 wt.% TiO₂ with 24.8 wt.% Al₂O₃. An interesting fact is that unusual clinopyroxenes which contain more Al^IV than Si^IV are present in the CaFe-AlSiO₆-rich region. The liquid coexisting with pyroxene is richer in Ti, Al, and Fe³⁺ than the coexisting pyroxene. The clinopyroxenes_ss coexisting with liquid contain less TiO₂, Al₂O₃ and Fe₂O₃ than those crystallized at subsolidus temperatures. The petrological significance of the join and the crystallization of Ti- and Al-rich clinopyroxenes are discussed on the basis of the experimental results of the join.     

Atomistic simulation of the structure and segregation to the (0001) and surfaces of Fe<Subscript>2</Subscript>O<Subscript>3</Subscript>

The segregation of ten isovalent impurities (Al³⁺ Cr³⁺, Eu³⁺, Gd³⁺, Ho³⁺, La³⁺, Lu³⁺, Nd³⁺, Tb³⁺, Y³⁺) to the and the (0001) surfaces of haematite (-Fe₂O₃) have been studied using atomistic simulation where the forces between the atoms are modelled using the Born model of solids. Segregation is found to be energetically favoured in virtually every case. The results for the surface show that the most favourable impurity surface concentration is 33.33%. The (0001) surface has two possible terminations, one terminated by iron atoms and the other by oxygen. No minimum is calculated for the Fe termination of the (0001) surface at low temperatures, but when the effect of raising the temperature is considered, an energy minimum is found, also at 33.33% impurity coverage. In contrast, the O terminated (0001) surface has a minimum in the segregation energy for between 16.67 and 33.33% depending on the cation being considered.     

Magnetic phase diagrams of Mg-, Fe-, (Cu + Ti)- and Cu-substituted braunite Mn<Superscript>2+</Superscript>Mn<Subscript>6</Subscript><Superscript>3+</Superscript>SiO<Subscript>12</Subscript>

 The magnetic behavior of the Jahn-Teller structure braunite, (Mn²⁺ _1−yM _y )(Mn³⁺ _{6− x} M_x)SiO₁₂, is strongly influenced by the incorporation of elements substituting manganese. Magnetic properties of well-defined synthetic samples were investigated in dependence on the composition. The final results are presented in magnetic phase diagrams. To derive the necessary data, ac susceptibility and magnetization of braunites with the substitutional elements M = Mg, Fe, (Cu+Ti) and Cu were measured. Whereas the antiferromagnetic ordering temperature, T _N , of pure braunite is hardly affected by the substitution of nonmagnetic Mg, it is rapidly suppressed by the substitution of magnetic atoms at the Mn positions. Typically for a concentration (x, y) ≥ 0.7 of the substituted elements, a spin glass phase occurs in the magnetic phase diagrams. Additionally, for the braunite system with Fe³⁺ substitutions, we observe in the concentration range 0.2 < x< 0.7 a double transition from the paramagnetic state, first to the antiferromagnetic state, followed by a transition to a spin glass state at lower temperatures. The unusual change of the magnetic properties with magnetic substitution at the Mn positions is attributed to the peculiar antiferromagnetic structure of braunite, which has been resolved recently. Received: 19 April 2001 / Accepted: 6 September 2001     

Ab-initio calculations of the proton location in topaz-OH,Al<Subscript>2</Subscript>SiO<Subscript>4</Subscript>(OH)<Subscript>2</Subscript>

The position of hydrogen in the structure of topaz-OH was determined by means of ab-initio quantum-mechanic calculations. Static lattice energy calculations predict the existence of four non-equivalent positions of protons, which are characterized by O4–H1... O1, O4–H2... O2, O4–H3... O3 and O4–H4... O4 hydrogen bonds. The distribution of the protons between positions of local equilibrium is controlled by the proton–proton avoidance rule and the strength of the hydrogen bonds. The most favourable configuration of hydrogen atoms is achieved for adjacent protons, which form O4–H3... O3 and O4–H4... O4 hydrogen bonds, respectively. The thermal excitation of atoms at a temperature of 55 K is large enough for the hydrogen atoms occasionally to change their positions to form O4–H1... O1 and O4–H2... O2 bonds. At ambient pressures and higher temperatures the protons are in a dynamic exchange between the allowed positions of local minima. As a consequence, for nearly room-temperature conditions, the dynamic change between different structural configurations leads to the violation of all possible symmetry elements and with that to space group #E5/E5#1. The flipping of the protons between different sites is achieved by simple rotation of the OH-dipole and does not produce any significant distortion of the framework of topaz, whose symmetry remains that of the space group Pbnm. Therefore, no reduction of symmetry has been observed in former X-ray studies on topaz-OH. Calculated IR absorption spectra of topaz-OH were found to be in good agreement with measured spectra. According to the calculations, the two favourable configurations of protons might correspond to the measured peak splitting within the OH-stretching range. An experimentally observed low-frequency band at 3520 cm^–1 was assigned to the OH-stretching of the O4–H3... O3 bond, while the band at 3600 cm^–1 was attributed to OH-stretching of the O4–H4... O4 hydrogen bond. The broad peak in FAR-IR frequency range at 100–150 cm^–1 is attributed to the stretching of H3... O3 and H4... O4 contacts. The rate of proton exchange at 670 K among different sites was estimated by ab-inito molecular dynamic simulations. The calculations predict that flipping of adjacent protons between O4–H3... O3 and O4–H4... O4 bonds at 670 K occur at a rate of about 1.96 THz.     

Adsorption behaviors of Cd^2＋ on Fe2O3/MnO2 and the effects of coexisting ions under alkaline conditions

This study describes the adsorption features of cadmium on Fe2O3 and MnO2 in alkaline saline conditions. The adsorption reached equilibrium in 6 hours under alkaline conditions. The absorption of cadmium on Fe2O3 and MnO2 was consistent with Freundlich absorption isotherms, and the corresponding adsorption capacities were 16.3 and 16.7 mg·g-1, respectively. Moreover, the adsorption quantity of cadmium on Fe2O3 and MnO2 rose with increasing pH from acidic to neutral, and reached the maximum at pH= 9. The coexisting chlorides reduced the adsorption capacity of Fe2O3 and MnO2. The influence intensities of different cations follow the order of CaCl2>>KCl>NaCl. However, the influence of sodium salts on the capacities of Fe2O3 and MnO2 to adsorb cadmium appeared more complicated: the relatively low concentrations of sodium salts could reduce the adsorption capacity; with increasing concentrations of sodium salts, e.g. NaCl and NaNO3. The adsorption capacity decreased continually. Moreover, due to the competition adsorption and precipitation effects, the adsorption capabilities of Na2CO3, NaH2PO4 and Na2HSO4 could also be reduced and cadmium concentrations in the solution were reduced as well.     

Structure and phase transition of CaGe<Subscript>2</Subscript>O<Subscript>5</Subscript> revisited

The structure of CaGe₂O₅ between room temperature and 923 K has been determined by X-ray powder diffraction. A continuous phase transition from triclinic C1¯ to monoclinic C2/c symmetry at T_c=714±3 K is observed. The transition is accompanied by a weak heat capacity anomaly. This anomaly and the strain analysis based on the measured lattice parameters indicate a classical second-order phase transition. The order parameter, as measured by the strain component e₂₃, is associated with the displacement of the Ca cation. Electronic structure optimization by density functional methods is used to verify the centric space group of the low-temperature structure of CaGe₂O₅.     

High-pressure phase behavior of MnTiO<Subscript>3</Subscript>: decomposition of perovskite into MnO and MnTi<Subscript>2</Subscript>O<Subscript>5</Subscript>

The phase relations and compression behavior of MnTiO₃ perovskite were examined using a laser-heated diamond-anvil cell, X-ray diffraction, and analytical transmission electron microscopy. The results show that MnTiO₃ perovskite becomes unstable and decomposes into MnO and orthorhombic MnTi₂O₅ phases at above 38 GPa and high temperature. This is the first example of ABO₃ perovskite decomposing into AO + AB₂O₅ phases at high pressure. The compression behavior of volume, axes, and the tilting angle of TiO₆ octahedron of MnTiO₃ perovskite are consistent with those of other A²⁺B⁴⁺O₃ perovskites, although no such decomposition was observed in other perovskites. FeTiO₃ is also known to decompose into two phases, instead of transforming into the CaIrO₃-type post-perovskite phase and we argue that one of the reasons for the peculiar behavior of titanate is the weak covalency of the Ti–O chemical bonds.