Non-ideal solid-solution in garnet: crystal-structure evidence and modelling

Ungaretti, L.; Leona, Marco; Merli, Marcello; Oberti, Roberta

doi:10.1127/ejm/7/6/1299

Cited by 47 publications

(25 citation statements)

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“…They are fundamental not only from the technological point of view but also represent the main constituents of the Earth's lower crust, upper mantle and transition zone (Anderson 1986(Anderson , 1989Ungaretti et al 1995). For these reasons, the accurate evaluation of the thermodynamic properties of such compounds is of great interest.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics and phonon dispersion of pyrope and grossular silicate garnets from ab initio simulations

et al. 2015

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The phonon dispersion and thermodynamic properties of Mg 3 Al 2 Si 3 O 12 , pyrope, and Ca 3 Al 2 Si 3 O 12 , grossular, have been computed by using an ab initio quantum mechanical approach, an all-electron variational Gaussian type basis set and the B3LYP hybrid functional, as implemented in the CRYSTAL program. Dispersion effects in the phonon bands have been simulated by using supercells of increasing size, containing 80, 160, 320, 640, 1280 and 2160 atoms, corresponding to 1, 2, 4, 8, 16 and 27 k points in the first Brillouin zone. Phonon band structures, density-of-states and corresponding inelastic neutron scattering spectra are reported. Full convergence of the various thermodynamic properties, in particular entropy (S) and specific heat at constant volume (C V ), with the number of k points is achieved with 27 k points. The very regular behavior of the S(T ) and C V (T ) curves as a function of the number of k points, determined by high numerical stability of the code, permits extrapolation to an infinite number of k points. The limiting value differs from the 27-k case by only 0.40% at 100 K for S (the difference decreasing to 0.11% at 1000 K) and by 0.29% (0.05% at 1000 K) for C V . The agreement with the experimental data is rather satisfactory. We also address the problem of the relative entropy of pyrope and grossular, a still debated question. Our lattice dynamical calculations correctly describe the larger entropy of pyrope than grossular by taking into account merely vibrational contributions and without invoking "static disorder" of the Mg ions in dodecahedral sites. However, as the computed entropy difference is found to be larger than the experimental one by a factor of 2-3, present calculations can not exclude possible thermally-

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Section: Introductionmentioning

confidence: 99%

Thermodynamics and phonon dispersion of pyrope and grossular silicate garnets from ab initio simulations

et al. 2015

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“…A sketch of the cubic garnet crystal structure (e.g., Gibbs and Smith 1965;Ungaretti et al 1995) is shown in Fig. 2.…”

Section: Introductionmentioning

confidence: 99%

Quantifying garnet-melt trace element partitioning using lattice-strain theory: new crystal-chemical and thermodynamic constraints

Westrenen

Draper

2007

Contrib Mineral Petrol

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Many geochemical models of major igneous differentiation events on the Earth, the Moon, and Mars invoke the presence of garnet or its high-pressure majoritic equivalent as a residual phase, based on its ability to fractionate critical trace element pairs (Lu/Hf, U/Th, heavy REE/light REE). As a result, quantitative descriptions of mid-ocean ridge and hot spot magmatism, and lunar, martian, and terrestrial magma oceans require knowledge of garnet-melt partition coefficients over a wide range of conditions. In this contribution, we present new crystalchemical and thermodynamic constraints on the partitioning of rare earth elements (REE), Y and Sc between garnet and anhydrous silicate melt as a function of pressure (P), temperature (T), and composition (X). Our approach is based on the interpretation of experimentally determined values of partition coefficients D using lattice-strain theory. In this and a companion paper (Draper and van Westrenen this issue) we derive new predictive equations for the ideal ionic radius of the dodecahedral garnet X-site, r 0 (3+), its apparent Young's modulus E X (3+), and the strain-free partition coefficient D 0 (3+) for a fictive REE element J of ionic radius r 0 (3+). The new calibrations remedy several shortcomings of earlier lattice-strain based attempts to model garnet-melt partitioning. A hitherto irresolvable temperature effect on r 0 (3+) is identified, as is a pronounced decrease in E X (3+) as Al on the garnet Y site is progressively replaced by quadruvalent cations (Si, Ti) as pressure and garnet majorite content increase. D 0 (3+) can be linked to the free energy of fusion of a hypothetical rareearth garnet component JFe 2 Al 3 Si 2 O 12 through simple activity-composition relations. By combining the three lattice-strain parameter models, garnet-anhydrous melt and majorite-anhydrous melt D values for the REE, Y and Sc can be predicted from P, T, garnet major element composition, and melt iron content at pressures from 2.5-25 GPa and temperatures up to 2,573 K, covering virtually the entire P-T range over which igneous garnets are stable in solar system compositions. Standard deviations of the difference between predicted and observed D REE,Y,Sc range from 25% for Er to 70% for Ce, and are not correlated with trace element mass. The maximum error in D prediction (n > 300) is 218% for one measurement of D Dy . This is remarkably low considering the total spread in D values of over four orders of magnitude.

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“…Because of the similar radii of 8-coordinated Li + (r = 0.92 Å) and Mg 2+ (r = 0.89 Å) (Shannon 1976), many geometrical parameters of the X site in LiMGt and pyrope are also comparable, e.g., mean X-O bond length, mean O-O edge distance, and dodecahedral volume (Table 3). Nonetheless, the dodecahedron in LiMGt is the most distorted of all silicate garnets, as measured by the bond-length distortion index (Renner and Lehmann 1986) or, more simply, by the difference between the two crystallographically independent X-O4 and X-O2 bond lengths [Δ(X-O)] (Ungaretti et al 1995) (see Fig. 1 for the atom labels).…”

Section: Resultsmentioning

confidence: 99%

Crystal structure and Raman spectrum of a high-pressure Li-rich majoritic garnet, (Li2Mg)Si2(SiO4)3

Yang

Konzett

Downs

et al. 2009

American Mineralogist

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A Li-rich majoritic garnet (LiMGt), (Li 2 Mg)Si 2 (SiO 4 ) 3 , was synthesized at 15 GPa and 1500 °C and its structure studied with single-crystal X-ray diffraction and Raman spectroscopy. It is cubic with space group Ia3d and unit-cell parameters a = 11.2660(2) Å and V = 1429.91(1) Å 3 . The 8-, 6-, and 4-coordinated cation sites in LiMGt are occupied by (Li + + Mg 2+ ), Si 4+ , and Si 4+ , respectively. Whereas the SiO 6 octahedron is nearly regular, the XO 8 dodecahedron is the most distorted of all known silicate garnets in terms of the bond-length distortion index. All Raman peaks of LiMGt are broader than those of pyrope, due to the substitution of Li + for Mg 2+ at the dodecahedral site. Furthermore, both Si-O symmetric stretching (A 1g -ν 1 ) and O-Si-O symmetric bending (A 1g -ν 2 ) modes of LiMGt shift significantly to higher frequencies relative to the corresponding ones of pyrope. In contrast, the A 1g -(SiO 4 ) rotational mode of LiMGt displays a much lower frequency than that of pyrope. This study represents the first structural report on a garnet with an all-silicate framework and suggests that, like Na incorporation in garnets, the pressure-dependent coupled substitution of (Li + + Si 4+ ) for (Mg 2+ + Al 3+ ) is likely one of the primary mechanisms for Li enrichment in garnets in the mantle and the transition zone.

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Non-ideal solid-solution in garnet: crystal-structure evidence and modelling

Cited by 47 publications

References 0 publications

Thermodynamics and phonon dispersion of pyrope and grossular silicate garnets from ab initio simulations

Thermodynamics and phonon dispersion of pyrope and grossular silicate garnets from ab initio simulations

Quantifying garnet-melt trace element partitioning using lattice-strain theory: new crystal-chemical and thermodynamic constraints

Crystal structure and Raman spectrum of a high-pressure Li-rich majoritic garnet, (Li2Mg)Si2(SiO4)3

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