X-ray determination of electron distributions in forsterite, fayalite and tephroite

Fujino, Kiyoshi; Sasaki, Shin; Takéuchi, Yoshio; Sadanaga, Ryôichi

doi:10.1107/s0567740881003506

Cited by 169 publications

(68 citation statements)

References 6 publications

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“…The symmetry of the olivine structutre allows these two chains to undergo retractable tilting and the b -axis has the largest facility of variarion among three axes. Then, the steric facility of variarion is in the order, Table 3 ( Fujino et al, 1981;Takeuchi et al, 1984). This is also consistent to the experimental results that the variations of unit cell constants with pressure (Hazen, 1976;Kudoh and Takeuchi, 1985), temperature (Takeuchi et al, 1984) and with composition of hydrous forsterite in Table 3 ( Kudoh et al, 2006;Smyth et al, 2006) are in the order, ∂b…”

Section: Variation Of the Unit-cell Dimensionssupporting

confidence: 78%

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Crystal structural features of hydrous forsterite: Effect of Fe on the M-site vacancies, possible hydrogen positions and variation of the unit cell dimensions

Kudoh

2008

Journal of Mineralogical and Petrological Sciences

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A qualitative understanding of the incorporation of hydrogen atoms in forsterite and corresponding octahedral vacancies are given from the inspection of the crystal structure with the view point of minimum strain configuration. In the case of Fe -free hydrous forsterite, the structural strain from the ideal size is larger in the M1 site than in the M2 site. Two H atoms may replace the Mg atom predominantly at the M1 site to reduce the structural strain, giving the vacancy at the M1 site. In the case of Fe -bearing hydrous forsterite, two H atoms may replace the Mg atom predominantly at the M2 site to avoid the combination of Fe in M1 site and Mg in M2 site for the reduction of the structural strain, giving the vacancy at the M2 site. In both cases, the most probable H atom locations are near to the edges of MO 6 octahedra. Variation of the unit cell dimensions (-∂bwith the incorporation of hydrogen atom is interpreted in terms of retractable and unretractable chains in the part of olivine structure.

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Section: Variation Of the Unit-cell Dimensionssupporting

confidence: 78%

“…In order to reduce the (7) Å (Takeuchi et al, 1984). 3 For fayalite, a = 4.8195(6) Å, b = 10.4788(17) Å, c = 6.0873(8) Å (Fujino et al, 1981). structural strain, two H atoms may replace the Mg atom predominantly at the M2 site to avoid the combination of Fe -Mg for M1 -M2 sites, giving the vacancy at the M2 site.…”

Section: Fe-bearing Hydrous Forsteritementioning

confidence: 99%

Crystal structural features of hydrous forsterite: Effect of Fe on the M-site vacancies, possible hydrogen positions and variation of the unit cell dimensions

Kudoh

2008

Journal of Mineralogical and Petrological Sciences

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“…The dispersion terms were not included. Using the model of Fujino et al (1981), the appropriate atomic positional and isotropic thermal parameters were refined, along with the lattice parameters, the zero point, three half-width parameters, the mixing parameter for the pseudo-Voigt function, and the background parameters. There was no correction for preferred orientation, and the radiation was assumed to be 100% polarized in the plane of the synchrotron orbit.…”

Section: Discussionmentioning

confidence: 99%

A two-circle powder diffractometer for synchrotron radiation with a closed loop encoder feedback system

Cernik¹,

Murray²,

Pattison³

et al. 1990

J Appl Cryst

100

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A high-angular-resolution two-circle powder diffractometer equipped with long diffracted-beam collimators has been built at Daresbury Laboratory. The diffractometer has encoders mounted directly on the 20 and to axes. These give a nominal angular resolution of 0-1 and 1.0 mdeg respectively. Repeated scans of single powder peaks have demonstrated a reproducibility of 0.1 mdeg 20. Measurements on five independent peaks of tungsten give a self consistency of l(1) x 10-sA. An example data set from synthetic olivine Mg2SiO4 has been refined using the Rietveld method and the results compare very well with single-crystal structure refinements.

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“…Thus there remain four energy parameters, qo, Ro, RMg and Rca. These four parameters were derived from the two known crystal structures, Mg olivine (Fujino, Sasaki, Tak6uchi & Sadanaga;1981) and Ca olivine (Czaya, 1971), with a least-squares fit. We minimize the expression…”

Section: Derivation Of the Potential Parametersmentioning

confidence: 99%

“…Thus from the two structures a total of 16 observations is available. The minimization of F was performed with the SIMPLEX method (Nelder & Mead, 1965 +2.11 (3)lel for Si, -1.29--1.52 (7)lel for O from the EDR (effective distribution radii) method, and 1.8 (1)lel for Si, -1.6--1.9 (1)lel for O from the L1 method; Fujino et al, 1981], and the relative magnitudes of the repulsive radii follow the expected trend: RMg < Rca < R o. It is to be noted that the Rca value of 1.581 A is almost identical to that obtained from the crystal structure of a-calcium formate (1.591A; Matsui & Watanab6, 1981a), in spite of the different …”

Section: Derivation Of the Potential Parametersmentioning

confidence: 99%

An interatomic potential-function model for Mg, Ca and CaMg olivines

Matsui¹,

Matsumotο²

1982

Acta Cryst Sect A

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The structures of Mg(forsterite), Ca and CaMg(monticellite) olivines have been investigated by lattice energy calculations, where the silicate ions are treated as rigid bodies. The lattice energy was approximated to be the sum of electrostatic and repulsive terms. The net charges on the Si and O atoms in the silicate ion and the repulsive radii of the atoms concerned were derived using the two known crystal structures, Mg and Ca olvines, by a least-squares fit. The results are as follows: qo(lel) = -1.569, qsi = +2.276, R o (A) = 1.998, Rug = 1.164, and Rca = 1.581. The repulsive interactions of the Si atoms were neglected, since the Si atom would be screened by the outermost four O atoms of the silicate ion. The reliability and the transferability of the potential model presented were tested by the calculation of the energy-minimized structure for CaMg olivine, with the result that the observed structure was very well reproduced.

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X-ray determination of electron distributions in forsterite, fayalite and tephroite

Cited by 169 publications

References 6 publications

Crystal structural features of hydrous forsterite: Effect of Fe on the M-site vacancies, possible hydrogen positions and variation of the unit cell dimensions

Crystal structural features of hydrous forsterite: Effect of Fe on the M-site vacancies, possible hydrogen positions and variation of the unit cell dimensions

A two-circle powder diffractometer for synchrotron radiation with a closed loop encoder feedback system

An interatomic potential-function model for Mg, Ca and CaMg olivines

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