The orientation and vibrational states of H2O in synthetic alkali-free beryl

 The polarized single-crystal Raman spectra of synthetic H₂O-containing alkali-free beryl were recorded at room and low temperatures, and the polarized single-crystal IR spectra at room temperature. The H₂O molecule in the channel cavities is characterized by a Raman-active symmetric stretching vibration (ν₁) at 3607 cm⁻¹ and an IR-active asymmetric stretch (ν₃) at 3700 cm⁻¹ at room temperature. At low temperatures this ν₃ mode is observed in the Raman. Weak ν₁ and ν₃ modes of a second type of H₂O are also observed in the Raman spectra but only at 5 K. The H⋯·H vector of the most abundant type of H₂O is parallel to the channel axis of beryl along [0 0 0 1]. The components of the polarizability tensor of the ν₁ mode of H₂O are similar to, but not exactly the same as, those of a free H₂O molecule. The Raman measurements indicate that the H₂O molecule is rotationally disordered around [0 0 0 1]. External translation and librational modes of H₂O could be observed as overtones with the internal H₂O-stretching modes. In the case of the librational motions, normal modes could also be observed directly in the Raman spectra at ∼200 cm⁻¹. The energies of the translational modes can be determined from an analysis of the overtones and are about 9 cm⁻¹ in energy (i.e., T_z). The energies of the librational modes are about 210 cm⁻¹ for R_x and 190 cm⁻¹ for R_y. Received: 8 April 1999 / Accepted: 5 April 2000     

Vibrational analysis of dioptase Cu6Si6O18 · 6(H2O) and its puckered six-membered ring

The normal modes of vibration and their frequencies are calculated for dioptase, a mineral whose crystal structure (space group R or C _3i ² ) consists of puckered six-membered silicate rings (Si₆O₁₈) linked by Cu²⁺ ions and H₂O groups. The calculation employs a valence force potential consisting of central interactions between nearest neighbors and bond-bending interactions centered at the Si⁴⁺ and Cu²⁺ ions. The force constants are determined by fitting the calculated frequencies to values obtained by measuring the single-crystal Raman spectra. The calculated frequencies are in reasonable agreement with experiment, permitting assignment of normal modes to the observed spectral frequencies. Considerable mixing of Cu and H₂O motions with those of the ring is found for the Raman-active modes below 430 cm^-1. The normal modes and frequencies of the hypothetical isolated ring with C _3i symmetry are determined by neglecting all interactions between the rings and the surrounding Cu and H₂O. The identification of normal modes characteristic of the puckered six-membered silicate rings and the effect of the environment on these modes may prove useful in the interpretation of the Raman spectra of amorphous silicates.     

Molecular force constants in dynamical model of α-quartz

Ab initio force constants of structural fragments of -quart, Si-O-Si bridge and SiO₄ tetrahedron, are calculated by the gradient (force) method for molecules accessible to spectroscopic investigation, disiloxane and tetramethoxysilane respectively. The comparison of theoretical frequencies with experimental ones enables the empirical scaling of quantum chemical force constants. A generalized approach to the inverse vibrational problem in spectroscopy of solids is outlined. It consists of a joint treatment of vibrational spectra and properties of a crystal related to its homogeneous deformation, namely compressibility and elastic constants. The importance of analyzing the microscopic structure of compressibility for testing the force field model is emphasized. The scaled molecular force constants complemented by the force constants of nonbonded O...O interactions at shortest distances after slight empirical correction are found to be sufficient to reproduce all mechanical properties of -quartz accessible to experimental determination. A discussion of results in terms of structure and bonding including the analysis of various versions of a force field model is presented. The calculated shapes of normal coordinates and uniform strains are validated by satisfactory reproduction of IR intensities and piezoelectric constants.     

Lattice dynamics and inelastic neutron scattering from forsterite,Mg2SiO4: Phonon dispersion relation,density of states and specific heat

Magnesium-rich olivine (Mg_0.9Fe_0.1)₂SiO₄ is considered to be a major constituent of the Earth's upper mantle. Because of its major geophysical importance, the temperature and pressure dependence of its crystal structure, elastic and dielectric constants, long-wavelength phonon modes and specific heat have been measured using a variety of experimental techniques. Theoretical study of lattice dynamics provides a means of analyzing and understanding a host of such experimental data in a unified manner. A detailed study of the lattice dynamics of forsterite, Mg₂SiO₄, has been made using a crystal potential function consisting of Coulombic and short-range terms. Quasiharmonic lattice dynamical calculations based on a rigid molecular-ion model have provided theoretical estimates of elastic constants, long-wavelength modes, phonon dispersion relation for external modes along the three high symmetry directions in the Brillouin zone, total and partial density of states and inelastic neutron scattering cross-sections. The neutron cross-sections were used as guides for the coherent inelastic neutron scattering experiment on a large single crystal using a triple axis spectrometer in the constant Q mode. The observed and predicted phonon dispersion relation show excellent agreement. The inelastically scattered neutron spectra from a powder sample have been analyzed on the basis of a phonon density of states calculated from a rigid-ion model, which includes both external and internal modes. The experimental data from a powder sample show good agreement with the calculated spectra, which include a multiphonon contribution in the incoherent approximation. The computed phonon densities of states are used to calculate the specific heat as a function of temperature using both the rigid molecular-ion and rigid ion models. These results are in very good agreement with the calorimetric measurement of the specific heat. The interatomic potential developed here can be used with some confidence to study physical properties of forsterite as a function of pressure and temperature.     

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 C ₃₃ and C ₁₁ + C ₁₂ 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.     

Single crystal Raman spectrum of uvarovite, Ca3Cr2Si3O12

Single-crystal Raman spectra of synthetic end-member uvarovite (Ca₃Cr₂Si₃O₁₂) and of a binary solution (59% uvarovite, 41% andradite) have been measured using single crystal techniques. For each of these garnets, 22 and 21 of the 25 Raman modes were located, respectively. The spectra for uvarovite garnets closely resemble those of the other calcic garnets, grossular, and andradite. The modes for uvarovites do not fit into the same trends as established by the other five anhydrous end-member garnets: the high energy “internal” Si–O modes do not depend on lattice constant in uvarovite. They exceed frequencies for both andradite and grossular. This is likely due to the large crystal field stabilization energy of trivalent chromium. The low energy and midrange modes are at similar frequencies to the other calcic garnets.     

High-temperature Raman spectroscopy and quasi-harmonic lattice dynamic simulation of diopside

We investigated the lattice vibrational properties and lattice dynamical behaviour of diopside by combining laser micro-Raman spectroscopic measurements with quasi-harmonic lattice dynamic simulation using a transferable interatomic potential. We obtained polarized Raman spectra from a Fe-poor natural diopside and the temperature dependencies of the Raman modes to 1125?K from high-temperature Raman spectra of a Fe-poor and a Fe-rich natural diopside. The various modes display different temperature dependencies: from ?0.021?cm^?1/K to ?0.004?cm^?1/K. The temperature shift of low frequency modes is generally higher. A comparison of experimentally determined frequencies and symmetries of vibrational modes of the optical type (Raman and infrared) obtained in this and earlier studies with those calculated by us suggests that a consistent characterization of the vibrational properties was achieved. The good agreement between the experimental and simulated data on the temperature-dpendencies of the Raman modes (within 5%), crystal structure (2%), bulk modulus (5%), volume thermal expansivity (6%), and constant volume heat capacity (0.2%) testifies to the applicability of the transferable interatomic potential and the lattice dynamic model to predicting the vibrational, physical, and thermodynamic properties. The simulated properties from the lattice dynamic calculations are very similar to those obtained by molecular dynamic calculations with the same potential model.     

Lattice dynamics and Raman spectroscopy of protoenstatite Mg2Si2O6

Enstatites (Mg₂Si₂O₆) are important rock forming silicates of the pyroxene group whose structures are characterised by double MgO₆ octahedral bands and single silicate chains. Orthoenstatite transforms to protoenstatite above 1273 K with a doubling of the a axis and a rearrangement of the silicate chains with respect to the Mg₂₊ ions. Lattice dynamical calculations based on a rigid-ion model in the quasi-harmonic approximation provide theoretical estimates of elastic constants, long wavelength phonon modes, phonon dispersion relations, total and partial density of states and inelastic neutron scattering cross-sections of protoenstatite. The computed elastic constants are in good agreement with experimental data. The computed density of states of a chain silicate such as protoenstatite is distinct from that of olivines (forsterite, Mg₂SiO₄ and fayalite, Fe₂-SiO₄) with isolated silicate tetrahedra. The band gaps in the density of states in forsterite are largely due to the separation in the frequency ranges of the external and internal vibrations of the isolated silicate group, whereas in protoenstatite these gaps are filled by the vibrations of the bridging oxygens of the silicate chain. The computed density of states is used to calculate the specific heat, the mean square atomic displacements and temperature factors. Validity of these calculations are supported by Raman scattering measurements. Polarised and unpolarised Raman spectra are obtained from small single crystals of protoenstatite (Li,Sc)_0.6Mg_1.4Si₂O₆ stable at room temperature using the 488 nm or 514.5 nm lines of an Ar⁺ ion laser and a micro-Raman spectrometer with backscattering geometry. The Raman spectra were analysed and interpreted based on the lattice dynamical model. The experimental Raman frequencies and mode assignments (based on polarised single crystal spectra) are in good agreement with those obtained from lattice dynamical calculations.     

OH incorporation in nearly pure MgAl2O4 natural and synthetic spinels

Four nearly pure MgAl₂O₄ spinels, of both natural and synthetic occurrence, have been studied by means of X-ray single crystal diffraction and FTIR spectroscopy in order to detect their potential OH content. Absorption bands that can be assigned to OH incorporated in the spinel structure were only observed in spectra of a non-stoichiometric synthetic sample. The absorption intensity of two bands occurring at 3350 and 3548 cm⁻¹ indicate an OH content of 90 ppm H₂O. Based on correlations of OH vibrational frequencies and O-H?O distances, the observed absorption bands correspond to O-H?O distances of 2.77 and 2.99 Å, respectively, which is close to the values obtained by the structure refinements for ^VIO-O_unsh (2.825 Å) and ^IVO-O (3.001 Å). This indicates that one probable local position for hydrogen incorporation is the oxygens coordinating a vacant tetrahedral site. The present spectra demonstrate that the detection limit for OH in Fe-free spinels is in the range 10-20 ppm H₂O. However, at appreciable Fe²⁺ levels, the detection of OH bands becomes hampered due to overlap with strong absorption bands caused by electronic d-d transitions in Fe²⁺ in the tetrahedral position.     

Elastic, mechanical, and thermodynamical properties of superionic lithium oxide for high pressures

The elastic and thermodynamic properties of Li₂O for high pressures are presented. For cubic Li₂O, model effective interatomic interaction potential incorporating long-range Coulomb, charge transfer interactions, covalency effect, Hafemeister and Flygare type short-range overlap repulsion extended up to the second neighbor ions and van der Waals interactions is formulated. Both charge transfer interactions and covalency effect apart from long-range Coulomb are important in revealing high-pressure-induced associated volume collapse, elastic, and thermodynamical properties. The elastic constants, Debye temperature, and thermal expansion coefficient obtained are in good agreement with the available experimental data and other theoretical results. The Li₂O is mechanically stiffened, thermally softened, and brittle in nature as inferred from the pressure-dependent elastic constants behavior. To our knowledge, this is the first quantitative theoretical prediction of the pressure dependence of elastic, thermal, and thermodynamical properties of Li₂O and still awaits experimental confirmation.     

Combined inelastic neutron scattering and solid-state DFT study of dynamics of hydrogen atoms in trioctahedral 1M phlogopite

Inelastic neutron scattering (INS) was used to study the vibrational dynamics of the hydrogen atoms in natural trioctahedral phlogopite, K_0.93Na_0.03(Mg_2.47Fe_0.22Al_0.16Fe_0.04Tl_0.06)[Si_2.84Al_1.16]O₁₀OH_1.71F_0.28Cl_0.01, within the 50–1,000?cm^?1 energy range. The INS spectra collected using direct geometry spectrometer SEQUOIA (ORNL) were interpreted by means of the solid-state DFT calculations covering both normal mode analysis and molecular dynamics. To optimize the structure and to calculate the vibrational modes under harmonic approximation, both a hybrid PBE0 and the AM05 functional were used, while the molecular dynamics calculations (60?ps/1?fs) were performed only with the computationally less-demanding AM05 functional. The main contributions to the dominant band within ~750–550?cm^?1 are symmetric and antisymmetric Mg–O–H bending modes, overlapping with the skeletal stretching and bending modes causing weaker secondary movements of H atoms of inner hydroxyl groups. Signatures of the Mg–O–H bending modes appear down to ~400?cm^?1, where a region of octahedra deformation modes starts. These deformations cause just shallow movements of the hydrogen atoms and are mirrored by the modes with close vibrational energies. The region from ~330?cm^?1 down to the low-energy end of the spectrum portrays induced vibrations of the H atoms caused by deformation of individual polyhedra, translational vibrations of the parts of the 2:1 layer relative one to another, and librational and translational vibrations of the layer. The main difference between the INS spectrum of dioctahedral Al-muscovite and trioctahedral Mg-phlogopite is that the Mg–O–H modes are all assigned to in-plane vibrations of the respective hydrogen atoms.     

Ab initio valence force field calculations for quartz

We have derived valence force constants for the tetrahedral SiO₄ unit and the inter-tetrahedral SiOSi linkage from previous ab initio molecular orbital calculations on H₄SiO₄ and H₆Si₂O₇ using a split-valence polarized Gaussian basis set (6-31G^*), and used these to calculate the infrared and Raman active vibrational modes of α-quartz. The calculation gives frequencies approximately 15% greater than experiment, as expected from harmonic force constants obtained at this level of Hartree-Fock theory, but the calculation gives the correct distribution of modes within each frequency range. Calculated 28–30 Si and 16–18 O isotope shifts and pressure shifts to 6 GPa are also in reasonable agreement with experiment. We have also used our ab initio force field to calculate the vibrational spectrum for β-quartz. The results suggest either that inclusion of a torsional force constant is important for determining the stability of this high temperature polymorph, or that the β-quartz has a disordered structure with lower symmetry (P6₂) domains, as suggested by earlier diffraction studies.     

Polarized electronic absorption spectra of Co2+ ions in the kieserite-type compounds CoSO4 · H2O and CoSeO4 · H2O

Polarized electronic absorption spectra of the kieserite-type compounds CoSO₄ · H₂O and CoSeO₄ · H₂O have been obtained at room temperature (spectral range 35 000-5000 cm^-1) and at liquid nitrogen temperature (visible spectral region), using microscope-spectrometric techniques. The spectra are interpreted and evaluated in terms of a tetragonal crystal field formalism for the d⁷ configuration, in regard to the pseudotetragonal elongation of the CoO₄(H₂O)₂ octahedra, known from previous X-ray structure investigations, employing the tetragonal parameters Dq, Dt, and Ds, and the Racah parameters B and C. The observed and calculated energy levels are in good agreement for the following parameter sets: CoSO₄ · H₂O: Dq=826, Dt=40, Ds=350, B=856, C=3580 cm^-1; CoSeO₄· H₂O: Dq=817, Dt=44, Ds=406, B=841, C=3490 cm^-1; corresponding ‘cubic’ crystal field strengths Dq_cub are 803 and 792 cm^-1, respectively. The values of Dq_(cub), Racah B and C are in the common range for Co²⁺ ions in (pseudo) octahedral fields of oxygen ligands, and their differences in CoSO₄· H₂O compared to CoSeO₄ · H₂O are consistent with somewhat different mean Co-O bond lengths and with a slightly higher covalent contribution to Co-O bonding in the selenate compound. The values found for the parameter Dt, which is directly correlated to the extent of tetragonal distortion, are much lower than expected from purely geometrical considerations, thus confirming a significantly higher position of H₂O ligands in the spectrochemical series compared to oxygen ligands belonging to SO₄ or SeO₄ groups.     

Shock effects on hydrous minerals and implications for carbonaceous meteorites

New infrared absorption spectra, thermo-gravimetric analyses and optical-and scanning electron microscopy of shock-recovered specimens of antigorite serpentine (Mg₃Si₂O₅(OH)₄) from the pressure range between 25 to 59 GPa are reported. The infrared spectra show systematic changes in absorption peaks related to structural and molecular surface absorbed water. H₂O absorption peaks increase at the expense of OH peaks with increasing shock pressure. Changes in SiO bond vibrational modes with increasing shock pressure parallel those seen for other, non-hydrous minerals. Thermogravimetric analyses of shock-recovered samples determine the amount of shock-induced water loss. For samples shocked in vented assemblies, the data define a relation between shock-induced water loss versus shock pressure. Results for samples shocked in sealed assemblies demonstrate a dependence of water loss on shock pressure and target confinement. For the vented assembly samples, a linear relation between shock pressure and both the length of dehydration interval and the effective activation energy for releasing post-shock structural water in antigorite is found. Optical and scanning electron miscroscopy of shocked antigorite reveal a number of textures thought to be unique to shock loading of volatile-bearing minerals. Gas bubbles, which probably are the result of shock-released H₂O appear to be injected into zones of partial melting. This process may produce the vesicular dark veins which are distributed throughout heavily shocked samples. The present observations suggest several criteria which may constrain possible shock histories of the hydrous matrix phases of carbonaceous condrites. A model is proposed for explaining hydrous alteration processes occurring on carbonaceous chondrite parent bodies in the course of their accretion. We speculate that shock loading of hydrous minerals would release and redistribute free water in the regoliths of carbonaceous chondrite parent bodies giving rise to the observed hydrous alterations.     

Raman spectroscopy of water tracer diffusion in zeolite single crystals

The water tracer diffusion in single crystals of natrolite, scolecite, mesolite, heulandite, and chabazite has been studied by Raman micro-spectroscopy. A model of water tracer diffusion is proposed. The H₂O, HDO, and D₂O molecule concentrations are calculated for a crystal of orthorhombic symmetry on deuteration of the initial H₂O-sample. A way is shown to find the diffusion coefficients, the constant of equilibrium, and the deuteron-proton exchange rate from experimental data. The water diffusion coefficients for natrolite placed in liquid D₂O appeared to be 1.5–2 times higher than those for a sample in vaporous D₂O. For natrolite at room temperature, 1.5–1.6 times higher water diffusion occurs along [001] than along [110].     

Ab initio calculation of H, O, Al and Si NMR parameters, vibrational frequencies and bonding energetics in hydrous silica and Na-aluminosilicate glasses

Ab initio, molecular orbital (MO) calculations were performed on model systems of SiO₂, NaAlSi₃O₈ (albite), H₂O-SiO₂ and H₂O-NaAlSi₃O₈ glasses. Model nuclear magnetic resonance (NMR) isotropic chemical shifts (δ_iso) for ¹H, ¹⁷O, ²⁷Al and ²⁹Si are consistent with experimental data for the SiO₂, NaAlSi₃O₈, H₂O-SiO₂ systems where structural interpretations of the NMR peak assignments are accepted. For H₂O-NaSi₃AlO₈ glass, controversy has surrounded the interpretation of NMR and infrared (IR) spectra. Calculated δ_iso¹H, δ_iso¹⁷O, δ_iso²⁷Al and δ_iso²⁹Si are consistent with the interpretation of Kohn et al. (1992) that Si-(OH)-Al linkages are responsible for the observed peaks in hydrous Na-aluminosilicate glasses. In addition, a theoretical vibrational frequency associated with the Kohn et al. (1992) model agrees well with the observed shoulder near 900 cm⁻¹ in the IR and Raman spectra of hydrous albite glasses. MO calculations suggest that breaking this Si-(OH)-Al linkage requires ∼+56 to +82 kJ/mol which is comparable to the activation energies for viscous flow in hydrous aluminosilicate melts.     

Vibrational spectroscopy of aluminate spinels at 1 atm and of MgAl2O4 to over 200 kbar

Single-crystal Raman and infrared reflectivity data including high pressure results to over 200 kbar on a natural, probably fully ordered MgAl₂O₄ spinel reveal that many of the reported frequencies from spectra of synthetic spinels are affected by disorder at the cation sites. The spectra are interpreted in terms of factor group analysis and show that the high energy modes are due to the octahedral internal modes, in contrast to the behavior of silicate spinels, but in agreement with previous data based on isotopic and chemical cation substitutions and with new Raman data on gahnite (～ ZnAl₂O₄) and new IR reflectivity data on both gahnite and hercynite (～Fe_0.58Mg_0.42Al₂O₄). Therefore, aluminate spinels are inappropriate as elastic or thermodynamic analogs for silicate spinels. Fluorescence sideband spectra yield complementary information on the vibrational modes and provide valuable information on the acoustic modes at high pressure. The transverse acoustic modes are nearly pressure independent, which is similar to the behavior of the shear modes previously measured by ultrasonic techniques. The pressure derivative of all acoustic modes become negative above 110 kbar, indicating a lattice instability, in agreement with previous predictions. This lattice instability lies at approximately the same pressure as the disproportionation of spinel to MgO and Al₂O₃ reported in high temperature, high pressure work.     

Dehydration process and structural development of cordierite ceramic precursors derived from FTIR spectroscopic investigations

 Cordierite precursors were prepared by a sol-gel process using tetraethoxysilane, aluminum sec.-butoxide, and Mg metal flakes as starting materials. The precursors were treated by 15-h heating steps in intervals of 100 °C from 200 to 900 °C; they show a continuous decrease in the analytical water content with increasing preheating temperatures. The presence of H₂O and (Si,Al)–OH combination modes in the FTIR powder spectra prove the presence of both H₂O molecules and OH groups as structural components, with invariable OH concentrations up to preheating temperatures of 500 °C. The deconvolution of the absorptions in the (H₂O,OH)-stretching vibrational region into four bands centred at 3584, 3415, 3216 and 3047 cm⁻¹ reveals non-bridging and bridging H₂O molecules and OH groups. The precursor powders remain X-ray amorphous up to preheating temperatures of 800 °C. Above this temperature the precursors crystallize to μ-cordierite; at 1000 °C the structure transforms to α-cordierite. Close similarities exist in the pattern of the 1400–400 cm⁻¹ lattice vibrational region for precursors preheated up to 600 °C. Striking differences are evident at preheating temperatures of 800 °C, where the spectrum of the precursor powder corresponds to that of conventional cordierite glass. Bands centred in the “as-prepared” precursor at 1137 and 1020 cm⁻¹ are assigned to Si–O-stretching vibrations. A weak absorption at 872 cm⁻¹ is assigned to stretching modes of AlO₄ tetrahedral units and the same assignment holds for a band at 783 cm⁻¹ which appears in precursors preheated at 600 °C. With increasing temperatures, these bands show a significant shift to higher wavenumbers and the Al–O stretching modes display a strong increase in their intensities. (Si,Al)–O–(Si,Al)-bending modes occur at 710 cm⁻¹ and the band at 572 cm⁻¹ is assigned to stretching vibrations of AlO₆ octahedral units. A strong band around 440 cm⁻¹ is essentially attributed to Mg–O-stretching vibrations. The strongly increasing intensity of the 872 and 783 cm⁻¹ bands demonstrates a clear preference of Al for a fourfold-coordinated structural position in the precursors preheated at high temperatures. The observed band shift is a strong indication for increasing tetrahedral network condensation along with changes in the Si–O and Al–O distances to tetrahedra dimensions similar to those occurring in crystalline cordierite. These structural changes are correlated to the dehydration process starting essentially above 500 °C, clearly demonstrating the inhibiting role of H₂O molecules and especially of OH groups. Received: 1 March 2002 / Accepted: 26 June 2002     

Raman Spectroscopy of Garnet—group Minerals

The Raman spectra of the natural end members of the garnet-group minerals,which include pyrope, almandine and spessarite of Fe-Al garnet series and grossularite ,andradite and uvarovite of Ca-Fe garnet series, have been strdied.Measured Raman spectra of these minerals are reasonably and qualitatively assigned to the internal modes, translational and rotatory modes of SiO4 tetrahedra, as well as the translational motion of bivalent cations in the X site.The stretch and rotatory A1g modes for the Fe-Al garnet series show obvious Raman shifts as compared with those for the Ca-Fe garnet series ,owing to the cations residing in the Xsite connected with SiO4 tetrahedra by sharing the two edges.The Raman shifts of all members within either of the series are attributed mainly to the properties of cations in the X site for the Fe-Al garnet series andin the Y site for the Ca-Fe garnet series.     

Natrolite,part I: Refinement of high-order data,separation of internal and external vibrational amplitudes from displacement parameters

A single crystal of natrolite, Na₂Al₂Si₃O₁₀·2H₂O, was studied by X-ray diffraction methods at room temperature. The intensities were measured with MoKα radiation (λ = 0.7107 Å) in a complete sphere of reflection up to sin θ/λ = 0.903 Å^?1. The structure was refined in the orthorhombic space group Fdd2 with a = 18.2929 (7) Å, b = 18.6407(9) Å, c = 6.5871(6) Å, V = 2246 ų, Z = 8. A refinement of high-order diffraction data yielded reliability factors of R(F) = 0.9%, R _w(F) = 0.8%, GoF = 1.40 for 1856 high-angle reflections (0.7 ?in θ/λ <0.903 Å^?1) and R(F) = 1.0%, R _W(F) = 1.2%, GoF = 3.07 for all 3471 independent reflections in the complete sphere of reflection. The T-O distances as well as the T-O-T angles were found to be strongly influenced by the different bond strengths received by the individual oxygen atoms. The T O distances calculated using Baur's extended valence rule agree on average within 0.003 Å with the observed values. An analysis of the mean square displacement amplitudes allowed a separation of the external and internal vibrational amplitudes along the T-O bonds as well as along the Na O and H₂O-O bond directions and the calculation of force constants. The internal vibrational amplitudes (ΔU) of the T-O vibrations are in the range of 5 to 11 × 10^-4 Ų, that is about one order of magnitude smaller than the mean square displacement amplitudes of the external vibrations. The corresponding force constants are F = 354 to 824 Nm^?1. The values of the force constants of the motion of the Na-ion and the water molecule against the framework oxygen atoms lie in the range between F = 57 and 293 Nm^?1. This is the first instance where displacement amplitudes from a zeolite structure refinement could be apportioned between contributions from internal and external vibrations for individual bonds.