Mean bond-length variations in crystals for ions bonded to oxygen

Gagné, Olivier Charles; Hawthorne, Frank C.

doi:10.1107/s2052520617014548

Cited by 19 publications

(63 citation statements)

References 42 publications

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“…The a priori bond-valences for spinel, grossular and forsterite are equal to the Pauling bond-strengths (Tables 1, 2 and 4) and there are no bond-valence requirements driving any distortion of the bond lengths via the effect of the distortion theorem (Brown, 2016;Urusov, 2014;Gagné & Hawthorne, 2017a). Nevertheless, there are significant differences between the a priori bond-lengths and those observed experimentally.…”

Section: Structures In Which the A Priori Bond-valences Obey The Equamentioning

confidence: 69%

“…Today, bond lengths are routinely predicted and rationalized via the addition of the constituent ionic radii (Shannon, 1976) based on the assumption that these values are transferable between crystal structures (see Gagné & Hawthorne 2017a for a discussion of the effect of structure type on mean bond-length).…”

Section: Predicting Bond Length Via Bond-strength Methodsmentioning

confidence: 99%

“…In particular, the observed mean bond-lengths are greater than the mean a priori bond-lengths for all olivine-group minerals, for spinel and for the Al and Si polyhedra in grossular. Gagné & Hawthorne (2017a) showed that there is a significant effect of structure type on the agreement between a priori and observed bond-lengths and mean bond-lengths. In particular, they…”

Section: Structures In Which the A Priori Bond-valences Obey The Equamentioning

confidence: 99%

“…On the other hand, Gagné & Hawthorne (2016a) showed good correlation (R 2 = 0.65) between GII and BSI for fourteen milarite-group minerals, all having the same bond topology. Gagné & Hawthorne (2017a) have suggested that the principal reason for the variation in mean bondlength in structures for a specific ion-pair is the result of strain in those structures. If this is the case, it is important to understand the differences between GSI and BII.…”

Section: Strain In Crystal Structuresmentioning

confidence: 99%

“…It is a calculation that allows quantitative assessment of the strain in a crystal structure, an important quantity that Gagné & Hawthorne (2017a) suggest is strongly related to the variation in mean bond-length for ion pairs in crystal structures.…”

Section: Agreement Between Observed and A Priori Bond-lengthsmentioning

confidence: 99%

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A Priori Bond-Valence and Bond-Length Calculations in Rock-Forming Minerals

Gagné¹,

Mercier²,

Hawthorne³

2018

Preprint

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Synopsis A priori bond-valences and bond-lengths are calculated for a series of rock-forming minerals. Comparison of a priori and observed bond-lengths allows structural strain to be assessed for those minerals.Abstract Within the framework of the bond-valence model, one may write equations describing the valence-sum rule and the loop rule in terms of the constituent bond-valences. These are collectively called the network equations, and can be solved for a specific bond topology to calculate its a priori bond-valences. A priori bond-valences are the ideal values of bond strengths intrinsic to a given bond topology that depend strictly on the formal valences (oxidation state) of the ion at each site in the structure, and the bond-topological characteristics of the structure (i.e., the ion connectivity). The a priori bond-valences are calculated for selected rock-forming minerals, beginning with a simple example (spinel, = 1.379 bits/atom) and progressing through a series of gradually more complex minerals (grossular, diopside, forsterite, fluoro-phlogopite, phlogopite, fluoro-tremolite, tremolite, albite) to finish with epidote ( = 4.187 bits/atom). The effects of weak bonds (hydrogen bonds, long between the a priori and observed bond-lengths is small, whereas for cations of low Lewis acidity, the range of differences between the a priori and observed bond-lengths is large. These calculations allow assessment of the strain in a crystal structure and provide a way to examine the effect of bond topology on variation in observed bond-lengths for the same ion-pair in different bond topologies.

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Section: Structures In Which the A Priori Bond-valences Obey The Equamentioning

confidence: 69%

Section: Predicting Bond Length Via Bond-strength Methodsmentioning

confidence: 99%

Section: Structures In Which the A Priori Bond-valences Obey The Equamentioning

confidence: 99%

Section: Strain In Crystal Structuresmentioning

confidence: 99%

Section: Agreement Between Observed and A Priori Bond-lengthsmentioning

confidence: 99%

See 3 more Smart Citations

A Priori Bond-Valence and Bond-Length Calculations in Rock-Forming Minerals

Gagné¹,

Mercier²,

Hawthorne³

2018

Preprint

Self Cite

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Rational Design of Biaxial Tensile Strain for Boosting Electronic and Ionic Conductivities of Na₂MnSiO₄ for Rechargeable Sodium‐Ion Batteries

et al. 2022

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Using first‐principles calculations, biaxial tensile (ϵ=2 and 4 %) and compressive (ϵ=−2 and −4 %) straining of Na 2 MnSiO 4 lattices resulted into radial distance cut offs of 1.65 and 2 Å, respectively, in the first and second nearest neighbors shell from the center. The Si−O and Mn−O bonds with prominent probability density peaks validated structural stability. Wide‐band gap of 2.35 (ϵ=0 %) and 2.54 eV (ϵ=−4 %), and narrow bandgap of 2.24 eV (ϵ=+4 %) estimated with stronger coupling of p–d σ bond than that of the p–d π bond, mainly contributed from the oxygen p‐state and manganese d‐state. Na + ‐ion diffusivity was found to be enhanced by three orders of magnitude as the applied biaxial strain changed from compressive to tensile. According to the findings, the rational design of biaxial strain would improve the ionic and electronic conductivity of Na 2 MnSiO 4 cathode materials for advanced rechargeable sodium‐ion batteries.

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The Floppiness of It All: Bond Lengths Change with Atomic Displacement Parameters and the Flexibility of Various Coordination Tetrahedra in Zeolitic Frameworks. An Empirical Structural Study of Bond Lengths and Angles

Baur

Fischer

2019

Chem. Mater.

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We have evaluated more than 7000 crystal structures of zeolites in terms of the values of their bondlengths T−O (T = Si, Al, P, Zn, Be, Ge, B, As, Ga, Co) and their variability as well as the flexibility of their bond angles O−T−O. Out of these known crystal structure descriptions of zeolites, we have selected 1179 which have estimated standard deviations of their T−O bond lengths of 0.01 Å or less. For the most common bond lengths, we obtain 1.603(11) Å for 1323 mean tetrahedral Si−O, 1.736(8) Å for 416 Al−O, and 1.522(9) Å for 228 P−O. It is unsettling that the spread of each of these values is large: about 0.07 Å within the population studied by us. Furthermore, these values disagree by several hundredths of an Ångstrom from some of the mean values of Si−O, Al−O, and P−O compiled from nonzeolitic types of compounds. This is at variance with the widespread conviction that such T−O distance values should be relatively constant across different types of inorganic compounds. Ever since Cruickshank (Acta Crystallogr. 1956, 9, 757), it has been known that high atomic displacement factors shorten observed bond lengths. Corrections for this effect were applied in the past but have become lately rarer. We find that much of the variance observed by us in the bond lengths is due to the fact that topologically different zeolite framework types have different atomic displacement parameters of their oxygen atoms. Thus, it makes no sense to search for mean tetrahedral bond lengths in TO 4 tetrahedra. Instead, a particular mean bond length, e.g., Si−O, can be only characteristic for a Si−O bond for one given framework type as we show for the topologically different framework types CAN, FER, MFI, NAT, and SOD. Even after bond length corrections for differing displacement parameters, the mean Si−O bonds range from 1.601 Å for FER to 1.629 Å for SOD. The observed angles O−T−O cover a range from 94.5 to 129.1°averaging around a tetrahedral angle of 109.5°. The largest deviations from the tetrahedral angle occur for tetrahedra with long mean T−O distances of the T-atoms. Our results, properly applied, can be useful as an input for distance least squares calculations on zeolites and for checking on the results of crystal structure refinements or of theoretical calculations.

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Mean bond-length variations in crystals for ions bonded to oxygen

Cited by 19 publications

References 42 publications

A Priori Bond-Valence and Bond-Length Calculations in Rock-Forming Minerals

A Priori Bond-Valence and Bond-Length Calculations in Rock-Forming Minerals

Rational Design of Biaxial Tensile Strain for Boosting Electronic and Ionic Conductivities of Na₂MnSiO₄ for Rechargeable Sodium‐Ion Batteries

The Floppiness of It All: Bond Lengths Change with Atomic Displacement Parameters and the Flexibility of Various Coordination Tetrahedra in Zeolitic Frameworks. An Empirical Structural Study of Bond Lengths and Angles

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Mean bond-length variations in crystals for ions bonded to oxygen

Cited by 19 publications

References 42 publications

A Priori Bond-Valence and Bond-Length Calculations in Rock-Forming Minerals

A Priori Bond-Valence and Bond-Length Calculations in Rock-Forming Minerals

Rational Design of Biaxial Tensile Strain for Boosting Electronic and Ionic Conductivities of Na2MnSiO4 for Rechargeable Sodium‐Ion Batteries

The Floppiness of It All: Bond Lengths Change with Atomic Displacement Parameters and the Flexibility of Various Coordination Tetrahedra in Zeolitic Frameworks. An Empirical Structural Study of Bond Lengths and Angles

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Rational Design of Biaxial Tensile Strain for Boosting Electronic and Ionic Conductivities of Na₂MnSiO₄ for Rechargeable Sodium‐Ion Batteries