Dy<sub>2</sub>ScNbO<sub>7</sub>: an unconventional spin ice?

Rutherford, Megan; Mauws, Cole; Haravifard, Sara; Marjerrison, Casey; Luke, G. M.; Beare, J.; Herbert, D C; Ritch, J.; Wiebe, C. R.

doi:10.1107/s0108767318098276

Cited by 2 publications

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“…The prediction of bond lengths in solids has been proposed by drawing a parallel between crystal structures and electrical networks, and by solving the equivalent of Kirchhoff's circuit laws for the network of chemical bonds to obtain a priori bond valences (Mackay & Finney, 1973;Brown, 1977Brown, , 1981Brown, , 1987Rutherford, 1990Rutherford, , 1998O'Keeffe, 1990). These equivalent rules for chemical-bond networks are called the valence-sum rule and the equal-valence rule by Brown (1977Brown ( , 2002Brown ( , 2016.…”

Section: The Effect Of Structure Typementioning

confidence: 99%

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

Gagné

Hawthorne

2017

Acta Crystallogr Sect B

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Variations in mean bond length are examined in oxide and oxysalt crystals for 55 cation configurations bonded to O 2À . Stepwise multiple regression analysis shows that mean bond length is correlated to bond-length distortion in 42 ion configurations at the 95% confidence level, with a mean coefficient of determination (hR 2 i) of 0.35. Previously published correlations between mean bond length and mean coordination number of the bonded anions are found not to be of general applicability to inorganic oxide and oxysalt structures. For two of 11 ions tested for the 95% confidence level, mean bond lengths predicted using a fixed radius for O 2À are significantly more accurate as those predicted using an O 2À radius dependent on coordination number, and are statistically identical otherwise. As a result, the currently accepted ionic radii for O 2À in different coordinations are not justified by experimental data. Previously reported correlation between mean bond length and the mean electronegativity of the cations bonded to the oxygen atoms of the coordination polyhedron is shown to be statistically insignificant; similar results are obtained with regard to ionization energy. It is shown that a priori bond lengths calculated for many ion configurations in a single structure-type leads to a high correlation between a priori and observed mean bond lengths, but a priori bond lengths calculated for a single ion configuration in many different structure-types leads to negligible correlation between a priori and observed mean bond lengths. This indicates that structure type has a major effect on mean bond length, the magnitude of which goes beyond that of the other variables analyzed here.

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Section: The Effect Of Structure Typementioning

confidence: 99%

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

Gagné

Hawthorne

2017

Acta Crystallogr Sect B

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“…The methods of O' Keeffe (1990) and Rutherford (1990) may be reformulated without the introduction of weighting factors (discussed further below). Urusov & Orlov (1999) used this approach to solve for the a priori bond-valences of Ca2B2SiO8 and to calculate its a priori bond-lengths.…”

Section: Amount O'mentioning

confidence: 99%

“…The same method was used by Gagné and Hawthorne (2016a) to solve for the a priori bond-lengths of fourteen milaritegroup minerals. Methods alternative to the use of loop equations include the resonance-bond model (Rutherford, 1998) and the method of maximum entropy (Rao & Brown, 1998), but these have seen little use.…”

Section: Amount O'mentioning

confidence: 99%

“…This rule introduces the idea of directed bond-valences, whereby bonds from a cation to an anion are considered positive and bonds from an anion to a cation are considered negative in sign. The number of linearly-independent loop equations is equal to the difference between the number of crystallographically-distinct bonds and sites in the crystal (Rutherford, 1990).…”

Section: Calculation Of a Priori Bond-valences From The Valence-sum Ementioning

confidence: 99%

“…Brown (1977) proposed an iterative approach in solving for the a priori bond-valences of a crystal structure, which consists of averaging the cation and anion Pauling bond strength of individual bonds, and changing these values by small increments (in cycles) until the valence-sum rule is obeyed for all cation and anions of the structure. O' Keeffe (1990) and Rutherford (1990) proposed a more direct approach to the solution of the network equations that essentially consists of solving a system of equations via matrix manipulations. To deal with negative bond-valences sometimes encountered in structures with very weak bonds (e.g.…”

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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 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 bondvalences are calculated for selected rock-forming minerals, beginning with a simple example (magnesiochromite, = 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 Na + -O 2bonds) on the calculation of a priori bond-valences and bond-lengths are examined. For the selected set of minerals, a priori and observed bond-valences and bond-lengths scatter closely about the 1:1 line with an average deviation of 0.04 v.u. and 0.048 Å and maximum deviations of 0.16 v.u. and 0.620 Å. The scatter of the corresponding a priori and observed bond-lengths is strongly a function of the Lewis acidity of the constituent cation. For cations of high Lewis acidity, the range of differences 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. Keywords: bond valence, bond length, network equations, Lewis acidity, structural strain IntroductionThe Bond-Valence Model (Brown, 2002(Brown, , 2016 is used extensively in Crystallography and Mineralogy to validate structural arrangements in crystals, and to interpret many aspects of crystal structure in terms of constituent chemical composition and bond topology. There are two distinct aspects of the bond-valence model: (1) relating observed bond-lengths to bond valences through experimentally determined bond-valence curves (e.g., Brown & Shannon, 1973;Brown & Altermatt, 1985;Brese & O'Keeffe, 1991;Gagné & Hawthorne, 2015), and (2) using bond-valence theory to understand chemical and topological aspects of atomic arrangements.There are two important theorems in the bond-valence model (Brown, 2002(Brown, , 2016: [1] the valencesum rule, which states that the sum of the bond valences at each atom is equal to the magnitude of the ato...

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Dy₂ScNbO₇: an unconventional spin ice?

Cited by 2 publications

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

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

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

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Dy2ScNbO7: an unconventional spin ice?

Cited by 2 publications

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

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

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

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Dy₂ScNbO₇: an unconventional spin ice?