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Charles A Geiger - One of the best experts on this subject based on the ideXlab platform.
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cation order disorder in fe bearing pyrope and Grossular garnets a 27al and 29si mas nmr and 57fe mossbauer spectroscopy study
American Mineralogist, 2015Co-Authors: Aaron C Palke, Charles A Geiger, Jonathan F Stebbins, Gerold TippeltAbstract:A suite of Fe-bearing natural and synthetic Grossular-rich [(Ca,Fe)3(Al,Fe)2Si3O12] and pyrope-rich [(Mg,Fe)3Al2Si3O12] garnets were investigated using 27Al and 29Si MAS NMR and 57Fe Mossbauer spectroscopy. This was done to study the state of cation order-disorder in garnet solid solutions by analyzing paramagnetically shifted resonances in high-resolution NMR spectra. The Mossbauer spectra, along with electron microprobe results, give the concentrations of Fe2+ and Fe3+ and their site occupancies, even in Grossular samples with very low concentrations of Fe. MAS NMR spectra were collected on Fe2+-bearing Grossular- and pyrope-rich garnets with up to 25 mol% almandine component and on other Fe3+-bearing Grossular samples with up to 9 mol% andradite component. Despite peak broadening and signal loss, structural information was even obtained from garnet with relatively high Fe contents (25 mol% almandine component). Paramagnetically shifted NMR peaks, related to the presence of Fe2+, were observed in Grossular samples and are similar in nature to those reported previously for natural, relatively low-Fe2+ pyrope garnets by Stebbins and Kelsey (2009). Additional NMR peaks appear as the concentration of Fe2+ increases, reflecting an increase in the average number of neighboring Fe2+ cations around AlO6 and SiO4 groups. These newly observed peaks hold potential to provide information concerning the presence or absence of short-range ordering in certain Fe-bearing silicate garnets. The effect of Fe3+ on the MAS NMR spectra of garnet appears to be less pronounced, because it does not produce any observable paramagnetically shifted resonances.
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Grossular a crystal chemical calorimetric and thermodynamic study
American Mineralogist, 2012Co-Authors: Edgar Dachs, Charles A Geiger, Artur Benisek, Klausdieter GrevelAbstract:In spite of the amount of research that has been done on Grossular, Ca3Al2Si3O12, there is still uncertainty regarding its exact thermodynamic properties. Because of insufficient sample characterization in the various published calorimetric studies, it is difficult to analyze conflicting C P and S ∘ results. To resolve the discrepancies, a detailed and systematic multi-method investigation was undertaken. Three synthetic Grossular samples and four natural Grossular-rich garnets were characterized by optical microscopy, electron microprobe analysis, IR, and MAS 29Si and 27Al NMR spectroscopy, and X-ray powder diffraction methods. Two of the natural Grossulars, crystallized at relatively low temperatures, are optically anisotropic and two from the higher temperature amphibolite faces are isotropic. The natural garnets have between 94 and 97 mol% Grossular with minor fractions of other garnet components, as well as small amounts of OH in solid solution. 29Si and 27Al MAS NMR spectra indicate that synthetic Grossular crystallized at high- P and high- T conditions is ordered with respect to Al and Si. Heat-capacity measurements between 5 and 300 K were made using relaxation calorimetry and between 282 and 764 K using DSC methods. For the three synthetic Grossulars, the C P data yield an average S ∘ value of 260.23 ± 2.10 J/(mol·K). The S ∘ values for the four natural Grossular-rich garnets, adjusted to end-member Grossular composition, range between 253.0 ± 1.2 and 255.2 ± 1.2 J/(mol·K). The results of this work thus confirm earlier low-temperature adiabatic calorimetric studies that show small, but experimentally significant, differences in S ∘ between natural and synthetic Grossular samples. The difference in terms of heat-capacity behavior between synthetic and natural samples is that the latter have lower C P values at temperatures between 20 and 100 K by up to about 20%. Above 298 K, C P for Grossular is given by C P J / ( mol · K ) = 556.18 ( ± 12 ) - 1289.97 ( ± 394 ) · T - 0.5 - 2.44014 ( ± 0.24 ) · 10 7 · T - 2 + 3.30386 ( ± 0.39 ) · 10 9 · T - 3 . Applying mathematical programming, published high- P-T results on the reaction 3anorthite = Grossular + 2kyanite + quartz were analyzed thermodynamically. The calculations yield best-fit values of Δf H ∘ = −6627.0 kJ/mol and S ∘ = 258.8 J/(mol·K) for Grossular. It is concluded that S ∘ ≈ 260 J/(mol·K) is the best value for end-member Grossular. Variations in structural state and composition in natural samples, as well as assumptions used in correcting for solid-solution and OH groups, appear to be the most important factors that could account for the smaller S ∘ values of 253–257 J/(mol·K).
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microscopic strain in synthetic pyrope Grossular solid solutions determined by synchrotron x ray powder diffraction at 5 k the relationship to enthalpy of mixing behavior
American Mineralogist, 2005Co-Authors: Monica Dapiaggi, Charles A Geiger, Gilberto ArtioliAbstract:A series of synthetic pyrope-Grossular garnets (Mg3Al2,Si3O12-Ca3Al2Si3O12) were investigated by powder X-ray synchrotron radiation at 5 K to determine their microscopic structural strain, which may be responsible for the observed excess enthalpy of mixing for this binary. This substitutional solid solution provides an excellent system for investigating microscopic-macroscopic relationships and the physical nature behind non-ideal thermodynamic mixing behavior in silicates, because of the measurable nonidealities shown by its enthalpy and volume of mixing. An analysis of the X-ray refection profiles, based on theoretical considerations of X-ray line broadening, permits for the first time a direct experimental determination of crystallite size and the root-mean-square structural strain for a mineral solid solution. The measured microscopic strain shows positive and asymmetric deviations from linearity across the join with the largest excess in pyrope-rich compositions. There is a good correlation between the structural strain and the macroscopic enthalpy of mixing behavior for pyrope-Grossular garnets as measured by calorimetry.
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local structural heterogeneity mixing behaviour and saturation effects in the Grossular spessartine solid solution
Physics and Chemistry of Minerals, 2004Co-Authors: U Rodehorst, Michael A Carpenter, Boffa T Ballaran, Charles A GeigerAbstract:Local structural heterogeneities in crystals of the binary Grossular-spessartine solid solution have been analyzed using powder IR absorption spectroscopy. Wavenurnber shifts of the highest energy Si-O stretching mode in spectra collected at room temperature are consistent with variations in Si-O bond length from structural data. They show a smaller positive deviation from linearity across the Join than is seen for the Grossular-pyrope and Grossular-almandine binaries. The effective line widths, Deltacorr, of three selected wavenumber regions all deviate positively from linear behaviour. An empirical calibration of this excess spectroscopic property, obtained by comparison with calorimetric enthalpy of mixing data, gives an estimate for the symmetric Margules parameter of W-spec(H) = 14.4(7) kJ mol(-1) in DeltaH(mix) = W-spec(H) XGrXSp. W-spec(H) values derived on the same basis four aluminosilicate garnet solid solutions analyzed by IR spectroscopy vary with DeltaV(2), where DeltaV represents the difference in molar volume between the end members of each binary system. Measurements of lattice parameters and IR spectra were made over a range of temperatures for seven samples with different compositions. Positive excess molar volumes of mixing at low temperature (30 K) may be larger than the excess molar volumes at room temperature. The saturation temperatures of the molar volumes show no correlation with composition, however, in contrast with what had been expected on the basis of data for the Grossular-pyrope binary. Saturation temperatures for spectroscopic parameters and lattice parameters of samples with compositions Gr15Sp85 and Gr60Sp40 seem to be outliers in all experiments. It is concluded that the data hint at systematic changes in saturation temperatures across the solid solution, with implications for both the excess entropy of mixing and the excess volume of mixing, but more precise data or further sample characterization are needed to prove that this composition dependence is real in garnet solid solutions.
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The crystal structures of Grossular and spessartine between 100 and 600 K and the crystal chemistry of Grossular-spessartine solid solutions
American Mineralogist, 2002Co-Authors: Uta Rodehorst, Charles A Geiger, Thomas ArmbrusterAbstract:Spessartine (Mn3Al2Si3O12)-Grossular (Ca3Al2Si3O12) solid solutions were synthesized at high pressures and temperatures. Compositionally homogeneous garnets are obtained by crystallizing solid-solution glasses prepared from oxides. The unit-cell parameter. a, for the different solid solutions was determined by X-ray powder diffraction methods and the results give positive deviations from ideal volumes of mixing that can be described with a symmetric mixing model with W-v = 0.80 (+/-0.04) cm(3)/mol. The degree of non-ideality is a function of the difference in size between the Ca2+ and Mn2+ cations and is consistent with the range of those observed for the other aluminosilicate garnet binary joins. The crystal structures of synthetic Grossular and spessartine were collected at 50 K intervals between 103 K and 498/648 K using single-crystal X-ray diffraction methods. The rotation of the rigid SiO4 tetrahedra changes slightly by 0.3(1)degrees for Grossular and 0.2(1)degrees for spessartine between 103 and 648 K. The volume expansions of the polyhedra were calculated and their distortions in Grossular and spessartine were analyzed as a function of temperature. The linear thermal expansion coefficients of the Al-O and two X-O bond were also calculated for almandine, pyrope, Grossular, and spessartine. The thermal expansion of spessartine is similar to that of Grossular. In terms of polyhedral distortion and bond-valence values, spessartine has the most ideal structure of the aluminosilicate garnets. This could explain its large P-T stability field and the ease of synthesis at low pressures.
Roberta Oberti - One of the best experts on this subject based on the ideXlab platform.
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Magnesium K-edge EXAFS study of bond-length behavior in synthetic pyrope-Grossular garnet solid solutions
American Mineralogist, 2008Co-Authors: Simona Quartieri, Federico Boscherini, Chiara Dalconi, Gianluca Iezzi, Carlo Meneghini, Roberta ObertiAbstract:Direct structural characterization of the changes in the local environment of Mg occurring in the garnet structure as a function of the Ca content are determined by Mg K -edge X-ray absorption fine structure on synthetic samples along the pyrope-Grossular join. With increasing Ca content, the short Mg-O2 distance of the dodecahedron slightly decreases, while the long Mg-O4 distance tends to increase, so that the dodecahedron is more distorted in Grossular-rich garnets than in end-member pyrope. This quantitative direct description of the changes in the local environment of Mg in the pyrope-Grossular solid solution confirms and better defines previous experimental and recent computational results.
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scandium 45 nmr of pyrope Grossular garnets resolution of multiple scandium sites and comparison with x ray diffraction and x ray absorption spectroscopy
American Mineralogist, 2007Co-Authors: N Kim, Jonathan F Stebbins, Simona Quartieri, Roberta ObertiAbstract:Here we present 45 Sc and 27 Al NMR results on Sc-doped pyrope (Mg 3 Al 2 Si 3 O 12 ), Grossular (Ca 3 Al 2 Si 3 O 12 ), and an 80% Grossular-20% pyrope garnet (grs80) that have recently been well-studied by X-ray diffraction and X-ray spectroscopies. Clearly distinct NMR peaks are observed for Sc in the eight-coordinated X site (pyrope and grs80) and in the six-coordinated Y site (Grossular and grs80). X-ray and NMR data agree that only eight-coordinated Sc is present in pyrope and that six-coordinated Sc is predominant in Grossular; however, the XRD results also indicated significant X and Z site (four-coordinated) Sc in the Ca-rich garnet. Possible reasons for this apparent discrepancy are discussed. We demonstrate that 45 Sc NMR is potentially a useful new method for studies of the site occupancies of Sc 3+ in oxides and silicates, at least in experimental systems where its concentration is a few percent or greater.
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distinct local environments for ca along the non ideal pyrope Grossular solid solution a new model based on crystallographic and exafs analysis
Chemical Geology, 2006Co-Authors: Roberta Oberti, Simona Quartieri, Federico Boscherini, Gianluca Iezzi, Maria Chiara Dalconi, Massimo BoiocchiAbstract:Abstract A multi-technique approach (based on electron microprobe analysis, structure refinement, and EXAFS analysis at the Ca K-edge) was used to characterise the local geometry of Ca in synthetic and natural garnet compositions referable to the pyrope–Grossular solid solution. Multi-shell fits of the EXAFS data indicate that Ca assumes the standard [4 + 4]-fold coordination (the polyhedral shape being a triangular dodecahedron with Ca1–O = 2.30–2.31(1) and Ca2–O = 2.45–2.46(1) A) when Ca > 1.50 atoms per formula unit (apfu), but assumes a nearly regular [8]-fold coordination with Ca–O = 2.35–2.36 (1) A when (Mg, Fe2+, Mn2+) > 1.50 apfu. Therefore, in the pyrope-dominant structure the Ca1–O distance lengthens and the Ca2–O distance shortens to converge towards the value observed for the Mg2–O bond in pyrope. This finding is consistent with many distinct structural features observed in solid solution terms with (Mg, Fe2+, Mn2+) > 1.50 apfu or Ca > 1.50 apfu, as well as with the anomalous properties of the intermediate terms observed both in the short-range and in the long-range perspective. The presence of two distinct Ca coordinations in the pyrope (almandine, spessartine)-like and in the Grossular-like structure, and thus of an isosymmetric transition at the intermediate composition, can help to explain both the strong and asymmetric non-ideality of the solid solution between pyrope (almandine) and Grossular, as well as the differences in the ability to incorporate some trace elements (such as REE and actinides) which are commonly used as process-specific indicators. This feature must be taken into account when building theoretical models of the garnet solid solutions, which are at the moment the most promising approach for calculating thermodynamic properties or for interpreting and predicting trace-element behaviour in this crucial mineral phase.
Thomas Armbruster - One of the best experts on this subject based on the ideXlab platform.
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The crystal structures of Grossular and spessartine between 100 and 600 K and the crystal chemistry of Grossular-spessartine solid solutions
American Mineralogist, 2002Co-Authors: Uta Rodehorst, Charles A Geiger, Thomas ArmbrusterAbstract:Spessartine (Mn3Al2Si3O12)-Grossular (Ca3Al2Si3O12) solid solutions were synthesized at high pressures and temperatures. Compositionally homogeneous garnets are obtained by crystallizing solid-solution glasses prepared from oxides. The unit-cell parameter. a, for the different solid solutions was determined by X-ray powder diffraction methods and the results give positive deviations from ideal volumes of mixing that can be described with a symmetric mixing model with W-v = 0.80 (+/-0.04) cm(3)/mol. The degree of non-ideality is a function of the difference in size between the Ca2+ and Mn2+ cations and is consistent with the range of those observed for the other aluminosilicate garnet binary joins. The crystal structures of synthetic Grossular and spessartine were collected at 50 K intervals between 103 K and 498/648 K using single-crystal X-ray diffraction methods. The rotation of the rigid SiO4 tetrahedra changes slightly by 0.3(1)degrees for Grossular and 0.2(1)degrees for spessartine between 103 and 648 K. The volume expansions of the polyhedra were calculated and their distortions in Grossular and spessartine were analyzed as a function of temperature. The linear thermal expansion coefficients of the Al-O and two X-O bond were also calculated for almandine, pyrope, Grossular, and spessartine. The thermal expansion of spessartine is similar to that of Grossular. In terms of polyhedral distortion and bond-valence values, spessartine has the most ideal structure of the aluminosilicate garnets. This could explain its large P-T stability field and the ease of synthesis at low pressures.
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Mn 3 Al 2 Si 3 O 12 spessartine and Ca 3 Al 2 Si 3 O 12 Grossular garnet; structural dynamic and thermodynamic properties
American Mineralogist, 1997Co-Authors: Charles A Geiger, Thomas ArmbrusterAbstract:The structures of synthetic Mn 3 Al 2 Si 3 O 12 spessartine and Ca 3 Al 2 Si 3 O 12 Grossular garnet have been refined using single-crystal X-ray diffraction methods at 100 K, 293 K, and 500-550 K. The divalent X-site cations, located in large dodecahedral sites, show measurable anisotropic dynamic disorder in contrast to the rigid vibrational behavior of the SiO 4 tetrahedra and AlO 6 octahedra. The amplitudes of vibration of Mn (super 2+) in spessartine are similar to those of Fe (super 2+) of almandine, in the plane of the longer X-O(4) bonds, and both are about twice that of Ca (super 2+) in Grossular, despite the lighter mass of the latter. Heat capacities measured between 300 and 1000 K on synthetic polycrystalline spessartine and two natural nearly end-member spessartine crystals are similar to those of almandine. In addition, the IR active modes of spessartine at low frequencies are very similar to those of almandine suggesting that their heat capacities are also similar at lower temperatures. The low-energy phonon spectra of pyrope and Grossular are probably considerably distinct from the two transition metal-containing garnets as suggested by their different low frequency IR active modes, reflecting the different bonding properties for Mg and Ca in garnet. The large pressure-temperature stability field of spessartine, relative to the other aluminosilicate garnets, does not appear to be due to any sort of intrinsic entropy stabilization.
Simona Quartieri - One of the best experts on this subject based on the ideXlab platform.
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Magnesium K-edge EXAFS study of bond-length behavior in synthetic pyrope-Grossular garnet solid solutions
American Mineralogist, 2008Co-Authors: Simona Quartieri, Federico Boscherini, Chiara Dalconi, Gianluca Iezzi, Carlo Meneghini, Roberta ObertiAbstract:Direct structural characterization of the changes in the local environment of Mg occurring in the garnet structure as a function of the Ca content are determined by Mg K -edge X-ray absorption fine structure on synthetic samples along the pyrope-Grossular join. With increasing Ca content, the short Mg-O2 distance of the dodecahedron slightly decreases, while the long Mg-O4 distance tends to increase, so that the dodecahedron is more distorted in Grossular-rich garnets than in end-member pyrope. This quantitative direct description of the changes in the local environment of Mg in the pyrope-Grossular solid solution confirms and better defines previous experimental and recent computational results.
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scandium 45 nmr of pyrope Grossular garnets resolution of multiple scandium sites and comparison with x ray diffraction and x ray absorption spectroscopy
American Mineralogist, 2007Co-Authors: N Kim, Jonathan F Stebbins, Simona Quartieri, Roberta ObertiAbstract:Here we present 45 Sc and 27 Al NMR results on Sc-doped pyrope (Mg 3 Al 2 Si 3 O 12 ), Grossular (Ca 3 Al 2 Si 3 O 12 ), and an 80% Grossular-20% pyrope garnet (grs80) that have recently been well-studied by X-ray diffraction and X-ray spectroscopies. Clearly distinct NMR peaks are observed for Sc in the eight-coordinated X site (pyrope and grs80) and in the six-coordinated Y site (Grossular and grs80). X-ray and NMR data agree that only eight-coordinated Sc is present in pyrope and that six-coordinated Sc is predominant in Grossular; however, the XRD results also indicated significant X and Z site (four-coordinated) Sc in the Ca-rich garnet. Possible reasons for this apparent discrepancy are discussed. We demonstrate that 45 Sc NMR is potentially a useful new method for studies of the site occupancies of Sc 3+ in oxides and silicates, at least in experimental systems where its concentration is a few percent or greater.
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site preference and local geometry of sc in garnets part i multifarious mechanisms in the pyrope Grossular join
American Mineralogist, 2006Co-Authors: R Oberti, Simona Quartieri, Federico Boscherini, Gianluca Iezzi, Maria Chiara Dalconi, Massimo Boiocchi, Sigrid Griet EeckhoutAbstract:We applied different independent techniques (electron microprobe analysis, structure reÞ nement, and X-ray absorption spectroscopy) to unravel the possible mechanisms of Sc incorporation in the pyrope-Grossular join. Samples were synthesized at elevated pressure and temperature by adding 5 wt% of Sc2O3 to selected nominal compositions (pyrope, pyrope60Grossular40, pyrope20Grossular80, and Grossular). In this way, the site of incorporation was not pre-determined, and only depends on the availability of a mechanism for local charge-balance. The EXAFS spectra of the two end-members could be analyzed by a multi-shell Þ t procedure, whereas the chemical heterogeneity of the Sc-doped solid-solution terms prevented this approach. However, the available information allows detection of different mechanisms of incorporation, which are active as a function of the bulk composition. In pyrope, Sc mainly enters the dodecahedral X site, and the local charge balance is achieved by incorporation of Mg at the adjacent tetrahedral Z site. Local charge-balance requirements suggest that a Z site occupied by Mg bridges two X sites occupied by Sc. When the entrance of Ca provides relaxation of the aver- aged structure, Sc may enter all the three available cation sites via the coupled heterovalent exchange X Sc1 Z Sc1 X Mg-1 Z Si-1 and the homovalent exchange Y Sc1 Y Al-1. In the samples of this work, there is an apparent limit in the Sc incorporation at the Y site, which is in contrast to the favored mechanism of incorporation in Sc-doped andradites. This limit can be explained in terms of relative dimensions of the structural sites when Al is the dominant Y cation. These results must be taken into account when evaluating trace-element behavior in garnets for geochemical purposes. In particular, they explain why DSc can be treated together with DREE in models based on the elastic strain theory in garnets close to the pyrope composition, but deviate from the parabolic Þ t in Grossular-rich garnets.
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distinct local environments for ca along the non ideal pyrope Grossular solid solution a new model based on crystallographic and exafs analysis
Chemical Geology, 2006Co-Authors: Roberta Oberti, Simona Quartieri, Federico Boscherini, Gianluca Iezzi, Maria Chiara Dalconi, Massimo BoiocchiAbstract:Abstract A multi-technique approach (based on electron microprobe analysis, structure refinement, and EXAFS analysis at the Ca K-edge) was used to characterise the local geometry of Ca in synthetic and natural garnet compositions referable to the pyrope–Grossular solid solution. Multi-shell fits of the EXAFS data indicate that Ca assumes the standard [4 + 4]-fold coordination (the polyhedral shape being a triangular dodecahedron with Ca1–O = 2.30–2.31(1) and Ca2–O = 2.45–2.46(1) A) when Ca > 1.50 atoms per formula unit (apfu), but assumes a nearly regular [8]-fold coordination with Ca–O = 2.35–2.36 (1) A when (Mg, Fe2+, Mn2+) > 1.50 apfu. Therefore, in the pyrope-dominant structure the Ca1–O distance lengthens and the Ca2–O distance shortens to converge towards the value observed for the Mg2–O bond in pyrope. This finding is consistent with many distinct structural features observed in solid solution terms with (Mg, Fe2+, Mn2+) > 1.50 apfu or Ca > 1.50 apfu, as well as with the anomalous properties of the intermediate terms observed both in the short-range and in the long-range perspective. The presence of two distinct Ca coordinations in the pyrope (almandine, spessartine)-like and in the Grossular-like structure, and thus of an isosymmetric transition at the intermediate composition, can help to explain both the strong and asymmetric non-ideality of the solid solution between pyrope (almandine) and Grossular, as well as the differences in the ability to incorporate some trace elements (such as REE and actinides) which are commonly used as process-specific indicators. This feature must be taken into account when building theoretical models of the garnet solid solutions, which are at the moment the most promising approach for calculating thermodynamic properties or for interpreting and predicting trace-element behaviour in this crucial mineral phase.
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xafs characterization of the structural site of yb in synthetic pyrope and Grossular garnets ii xanes full multiple scattering calculations at the yb l i and l iii edges
Physics and Chemistry of Minerals, 1999Co-Authors: Simona Quartieri, J Chaboy, G Antonioli, Charles A GeigerAbstract:We present an X-ray absorption near-edge structure study performed at the Yb LI- and LIII-edges on synthetic pyrope (Mg3Al2Si3O12) and Grossular (Ca3Al2Si3O12) garnets containing about 1% wt of Yb. For the first time Yb L-edge XANES spectra are analyzed by full multiple scattering theory using clusters of different sizes and different final-state potentials. A comparison between experimental spectra and model calculations indicates that Yb3+ enters the dodecahedral X-site in both pyrope and Grossular, in agreement with the results of an EXAFS study. Based on the present results, the charge balancing substitution mechanism required by the replacement of divalent Mg and Ca cations with trivalent Yb3+ is discussed in terms of vacancies in dodecahedral sites surrounding the central Yb3+ absorber.
Philippe Darco - One of the best experts on this subject based on the ideXlab platform.
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elasticity of Grossular andradite solid solution an ab initio investigation
Physical Chemistry Chemical Physics, 2014Co-Authors: Valentina Lacivita, Philippe Darco, Roberto Dovesi, Alessandro ErbaAbstract:Grossular and andradite are garnet end-members stable under upper mantle conditions. We perform ab initio simulations to investigate the dependence of the bulk modulus on chemical composition of the Grossular–andradite solid solution, Ca3Fe2−2xAl2x(SiO4)3. All-electron local basis sets of Gaussian-type orbitals and the hybrid B3LYP density functional are used. Our calculations predict a linear modulus-composition trend, in contrast to previous conjectures based on “heterogeneous” experimental measurements. We estimate the largest deviation from linearity to be about 0.5 GPa under ambient conditions, and to progressively reduce to less than 0.2 GPa at pressure P = 20 GPa. The bulk modulus is computed over the whole composition range 0 ≤ x ≤ 1 following two independent approaches: fitting energy–volume data to an equation-of-state and calculating elastic tensors. Results from the two methods are in perfect agreement, assuring consistency and high numerical accuracy of the adopted algorithms.
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anomalous birefringence in andradite Grossular solid solutions a quantum mechanical approach
Pacific Rim Conference on Multimedia, 2013Co-Authors: Valentina Lacivita, Philippe Darco, Roberto Orlando, Roberto Dovesi, Alessio MeyerAbstract:The static linear optical properties (refractive indices, birefringence and axial angle) of andradite–Grossular (Ca3Fe2Si3O12–Ca3Al2Si3O12) solid solutions have been computed at the ab initio quantum-mechanical level through the Coupled Perturbed Kohn–Sham scheme, using an all-electron Gaussian-type basis set. Geometry relaxation after substitution of 1–8 Al for Fe atoms in the primitive cell of andradite yields 23 non-equivalent configurations ranging from cubic to triclinic symmetry. Refractive indices vary quite regularly between the andradite (1.860) and Grossular (1.671) end-members; the birefringence δ and the axial angle 2V at intermediate compositions can be as large as 0.02° and 89°, respectively. Comparison with experiments suffers from inhomogeneities and impurities of natural samples; however, semi-quantitative agreement is observed.
