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

2018 ◽  
Author(s):  
Olivier Charles Gagné ◽  
Patrick H.J. Mercier ◽  
Frank Christopher Hawthorne
Keyword(s):  
Bond Length ◽  
A Priori ◽  
Bond Valence ◽  
Bond Lengths ◽  
Structural Strain

<i>A priori </i>bond-valences and bond-lengths are calculated for a series of rock-forming minerals. Comparison of <i>a priori </i>and observed bond-lengths allows structural strain to be assessed for those minerals.

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

2018 ◽  
Author(s):  
Olivier Charles Gagné ◽  
Patrick H.J. Mercier ◽  
Frank Christopher Hawthorne
Keyword(s):  
Bond Length ◽  
A Priori ◽  
Bond Valence ◽  
Bond Lengths ◽  
Structural Strain

<i>A priori </i>bond-valences and bond-lengths are calculated for a series of rock-forming minerals. Comparison of <i>a priori </i>and observed bond-lengths allows structural strain to be assessed for those minerals.

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

2018 ◽  
Author(s):  
Olivier Charles Gagné ◽  
Patrick H.J. Mercier ◽  
Frank Christopher Hawthorne
Keyword(s):  
Bond Length ◽  
A Priori ◽  
Bond Valence ◽  
Bond Lengths ◽  
Structural Strain

<i>A priori </i>bond-valences and bond-lengths are calculated for a series of rock-forming minerals. Comparison of <i>a priori </i>and observed bond-lengths allows structural strain to be assessed for those minerals.

scholarly journals Survey of Bond Lengths in the Solid State for Oxides: Results and Applications

2014 ◽  
Vol 70 (a1) ◽  
pp. C1103-C1103
Author(s):  
Olivier Gagne ◽  
Frank Hawthorne
Keyword(s):  
Solid State ◽  
Bond Length ◽  
Crystal Structures ◽  
A Priori ◽  
Bond Valence ◽  
Inorganic Crystal Structure Database ◽  
Ionic Radii ◽  
Coordination Polyhedra ◽  
Coordination Numbers ◽  
Bond Lengths

A complete survey of bond lengths from the Inorganic Crystal Structure Database (ICSD) is presented for all atoms of the Periodic Table of Elements, bonded to oxygen and in different oxidation states and coordination numbers. From over 135,000 crystal structures, a total of 33,343 coordination polyhedra and 188,462 bond distances were collected after passing a rigorous filtering process. One hundred thirty-six (136) ions in four hundred seventy-three (473) different configurations (coordination numbers) resulted. First, the bondlength distributions are visually inspected. This leads to (1) the observation and visual interpretation of known phenomena (e.g. Jahn-Teller effect), and (2) the isolation of new phenomena, as trends that are less obvious in smaller case-studies become more noticeable. Next, different applications of the data are investigated. The completeness of the survey allows the reassessment of important parameters of the solid state: ionic radii, and bond-valence parameters. Of the 473 ionic radii derived in this study, 329 revisions are made to Shannon's list of radii [1] (of which 176 were estimates), and 144 new ionic radii are derived. Next, a systematic evaluation of all bond-valence parameters published to date is done for oxides. Furthermore, using a new method of derivation, 136 new pairs of bond-valence parameters are obtained. In comparison to the previous-best published bond-valence parameters, an overall average decrease in the r.m.s.d. to the valence-sum rule of 20.7% (12.6% when weighted) is observed for the 33,343 coordination polyhedra, using the new parameters. New equations to describe the bond-length to bond-valence relation are also investigated. From an optimization between the experimental and a priori bond-valences of 54 carefully-selected crystal structures, roughly 20 relatively simple equations were selected for testing. Following a rigorous evaluation, the current exponential equation was found to be a viable choice in describing the relation. Finally, bond-length and bond-valence ranges are assigned to the 473 configurations of the atoms. Whereas the bondlength ranges are a useful aid in structure refinement, the assignment of a bond-valence range to ions allows a priori analysis of site occupancy in crystal structures.

Mean bond-length variation in crystal structures: a bond-valence approach

2014 ◽  
Vol 70 (4) ◽  
pp. 697-704 ◽  
Author(s):  
Ferdinando Bosi
Keyword(s):  
Bond Length ◽  
Crystal Structures ◽  
Coordination Sphere ◽  
Distortion Theorem ◽  
Bond Valence ◽  
Algebraic Expression ◽  
Length Variation ◽  
Bond Lengths ◽  
Valence Theory ◽  
New Equation

The distortion theorem of the bond-valence theory predicts that the mean bond length 〈D〉 increases with increasing deviation of the individual bond lengths from their mean value according to the equation 〈D〉 = (D′ + ΔD), whereD′ is the length found in a polyhedron having equivalent bonds and ΔDis the bond distortion. For a given atom,D′ is expected to be similar from one structure to another, whereas 〈D〉 should vary as a function of ΔD. However, in several crystal structures 〈D〉 significantly varies without any relevant contribution from ΔD. In accordance with bond-valence theory, 〈D〉 variation is described here by a new equation: 〈D〉 = (DRU + ΔDtop + ΔDiso + ΔDaniso + ΔDelec), whereDRUis a constant related to the type of cation and coordination environment, ΔDtopis the topological distortion related to the way the atoms are linked, ΔDisois an isotropic effect of compression (or stretching) in the bonds produced by steric strain and represents the same increase (or decrease) in all the bond lengths in the coordination sphere, ΔDanisois the distortion produced by compression and stretching of bonds in the same coordination sphere, ΔDelecis the distortion produced by electronic effects. If present, ΔDeleccan be combined with ΔDanisobecause they lead to the same kind of distortions in line with the distortion theorem. EachD-index, in the new equation, corresponds to an algebraic expression containing experimental and theoretical bond valences. On the basis of this study, the ΔDindex defined in bond valence theory is a result of both the bond topology and the distortion theorem (ΔD= ΔDtop + ΔDaniso + ΔDelec), andD′ is a result of the compression, or stretching, of bonds (D′ =DRU + ΔDiso). The deficiencies present in the bond-valence theory in explaining mean bond-length variations can therefore be overcome, and the observed variations of 〈D〉 in crystal structures can be described by a self-consistent model.

A priori bond-valence and bond-length calculations in rock-forming minerals

2018 ◽  
Vol 74 (6) ◽  
pp. 470-482 ◽  
Author(s):  
Olivier Charles Gagné ◽  
Patrick H. J. Mercier ◽  
Frank Christopher Hawthorne
Keyword(s):  
A Priori ◽  
Bond Valence ◽  
Lewis Acidity ◽  
Average Deviation ◽  
Bond Lengths ◽  
Bond Topology ◽  
Bond Strengths ◽  
Topological Characteristics ◽  
Bond Valence Model ◽  
The Ideal

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 bond valences are calculated for selected rock-forming minerals, beginning with a simple example (magnesiochromite, = 1.379 bits per 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 per atom). The effects of weak bonds (hydrogen bonds, long Na+—O2− bonds) 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.

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

2017 ◽  
Vol 73 (6) ◽  
pp. 1019-1031 ◽  
Author(s):  
Olivier Charles Gagné ◽  
Frank Christopher Hawthorne
Keyword(s):  
Bond Length ◽  
Coordination Number ◽  
Confidence Level ◽  
A Priori ◽  
Structure Type ◽  
Stepwise Multiple Regression ◽  
Coefficient Of Determination ◽  
General Applicability ◽  
Ionic Radii ◽  
Bond Lengths

Variations in mean bond length are examined in oxide and oxysalt crystals for 55 cation configurations bonded to O2−. 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 (〈R 2〉) 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 O2− are significantly more accurate as those predicted using an O2− radius dependent on coordination number, and are statistically identical otherwise. As a result, the currently accepted ionic radii for O2− 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.

scholarly journals Bond-length distributions for ions bonded to oxygen: results for the non-metals and discussion of lone-pair stereoactivity and the polymerization of PO4

2018 ◽  
Vol 74 (1) ◽  
pp. 79-96 ◽  
Author(s):  
Olivier Charles Gagné ◽  
Frank Christopher Hawthorne
Keyword(s):  
Metal Ions ◽  
Bond Length ◽  
Oxidation State ◽  
Lone Pair ◽  
Bond Valence ◽  
Group 14 ◽  
Coordination Polyhedra ◽  
Bond Lengths ◽  
Secondary Bonds ◽  
Lone Pair Electrons

Bond-length distributions are examined for three configurations of the H+ ion, 16 configurations of the group 14–16 non-metal ions and seven configurations of the group 17 ions bonded to oxygen, for 223 coordination polyhedra and 452 bond distances for the H+ ion, 5957 coordination polyhedra and 22 784 bond distances for the group 14–16 non-metal ions, and 248 coordination polyhedra and 1394 bond distances for the group 17 non-metal ions. H...O and O—H + H...O distances correlate with O...O distance (R 2 = 0.94 and 0.96): H...O = 1.273 × O...O – 1.717 Å; O—H + H...O = 1.068 × O...O – 0.170 Å. These equations may be used to locate the hydrogen atom more accurately in a structure refined by X-ray diffraction. For non-metal elements that occur with lone-pair electrons, the most observed state between the n versus n+2 oxidation state is that of highest oxidation state for period 3 cations, and lowest oxidation state for period 4 and 5 cations when bonded to O2−. Observed O—X—O bond angles indicate that the period 3 non-metal ions P3+, S4+, Cl3+ and Cl5+ are lone-pair seteroactive when bonded to O2−, even though they do not form secondary bonds. There is no strong correlation between the degree of lone-pair stereoactivity and coordination number when including secondary bonds. There is no correlation between lone-pair stereoactivity and bond-valence sum at the central cation. In synthetic compounds, PO4 polymerizes via one or two bridging oxygen atoms, but not by three. Partitioning our PO4 dataset shows that multi-modality in the distribution of bond lengths is caused by the different bond-valence constraints that arise for Obr = 0, 1 and 2. For strongly bonded cations, i.e. oxyanions, the most probable cause of mean bond length variation is the effect of structure type, i.e. stress induced by the inability of a structure to follow its a priori bond lengths. For ions with stereoactive lone-pair electrons, the most probable cause of variation is bond-length distortion.

scholarly journals Complex transition metal hydrides: linear correlation of countercation electronegativity versus T–D bond lengths

2015 ◽  
Vol 51 (56) ◽  
pp. 11248-11251 ◽  
Author(s):  
T. D. Humphries ◽  
D. A. Sheppard ◽  
C. E. Buckley
Keyword(s):  
Transition Metal ◽  
Bond Length ◽  
Linear Correlation ◽  
Metal Hydrides ◽  
Bond Lengths ◽  
Transition Metal Hydrides ◽  
Complex Hydrides

For homoleptic 18-electron complex hydrides, an inverse linear correlation has been established between the T–deuterium bond length and the average electronegativity of the metal countercations.

scholarly journals Bond-Length Distributions for Ions Bonded to Oxygen: Results for the Transition Metals and Quantification of the Factors Underlying Bond-Length Variation in Inorganic Solids

2020 ◽  
Author(s):  
Olivier Charles Gagné ◽  
Frank Christopher Hawthorne
Keyword(s):  
Transition Metal ◽  
Bond Length ◽  
A Priori ◽  
Bond Formation ◽  
Length Variation ◽  
Electronic Effects ◽  
Coordination Polyhedra ◽  
Jahn Teller ◽  
Jahn Teller Effect ◽  
Non Local

Bond-length distributions are examined for 63 transition-metal ions bonded to O2- in 147 configurations, for 7522 coordination polyhedra and 41,488 bond distances, providing baseline statistical knowledge of bond lengths for transi-tion metals bonded to O2-. A priori bond valences are calculated for 140 crystal structures containing 266 coordination poly-hedra for 85 transition-metal ion configurations with anomalous bond-length distributions. Two new indices, Δ𝑡𝑜𝑝𝑜𝑙 and Δ𝑐𝑟𝑦𝑠𝑡, are proposed to quantify bond-length variation arising from bond-topological and crystallographic effects in extended solids. Bond-topological mechanisms of bond-length variation are [1] non-local bond-topological asymmetry, and [2] multi-ple-bond formation; crystallographic mechanisms are [3] electronic effects (with inherent focus on coupled electronic-vibra-tional degeneracy in this work), and [4] crystal-structure effects. The Δ𝑡𝑜𝑝𝑜𝑙 and Δ𝑐𝑟𝑦𝑠𝑡 indices allow one to determine the primary cause(s) of bond-length variation for individual coordination polyhedra and ion configurations, quantify the dis-torting power of cations via electronic effects (by subtracting the bond-topological contribution to bond-length variation), set expectation limits regarding the extent to which functional properties linked to bond-length variations may be optimized in a given crystal structure (and inform how optimization may be achieved), and more. We find the observation of multiple bonds to be primarily driven by the bond-topological requirements of crystal structures in solids. However, we sometimes observe multiple bonds to form as a result of electronic effects (e.g. the pseudo Jahn-Teller effect); resolution of the origins of multiple-bond formation follows calculation of the Δ𝑡𝑜𝑝𝑜𝑙 and Δ𝑐𝑟𝑦𝑠𝑡 indices on a structure-by-structure basis. Non-local bond-topological asymmetry is the most common cause of bond-length variation in transition-metal oxides and oxysalts, followed closely by the pseudo Jahn-Teller effect (PJTE). Non-local bond-topological asymmetry is further suggested to be the most widespread cause of bond-length variation in the solid state, with no a priori limitations with regard to ion identity. Overall, bond-length variations resulting from the PJTE are slightly larger than those resulting from non-local bond-topological asym-metry, comparable to those resulting from the strong JTE, and less than those induced by π-bond formation. From a compar-ison of a priori and observed bond valences for ~150 coordination polyhedra in which the strong JTE or the PJTE is the main reason underlying bond-length variation, the Jahn-Teller effect is found not to have a symbiotic relation with the bond-topo-logical requirements of crystal structures. The magnitude of bond-length variations caused by the PJTE decreases in the fol-lowing order for octahedrally coordinated d0 transition metals oxyanions: Os8+ > Mo6+ > W6+ >> V5+ > Nb5+ > Ti4+ > Ta5+ > Hf4+ > Zr4+ > Re7+ >> Y3+ > Sc3+. Such ranking varies by coordination number; for [4], it is Re7+ > Ti4+ > V5+ > W6+ > Mo6+ > Cr6+ > Os8+ >> Mn7+; for [5], it is Os8+ > Re7+ > Mo6+ > Ti4+ > W6+ > V5+ > Nb5+. We conclude that non-octahedral coordinations of d0 ion configurations are likely to occur with bond-length variations that are similar in magnitude to their octahedral counterparts. However, smaller bond-length variations are expected from the PJTE for non-d0 transition-metal oxyanions.<br>

Reaktionen von Azacoronanden mit Quecksilber(II)iodid: Kristallstrukturen zweier Komplexe von Hgl2 mit Diaza-15-krone-5 und Diaza-18-krone-6 /Reactions of Azacoronands with Mercury(II) Iodide: Crystal Structures of Two Complexes of Hgl2 with Diaza-15-crown-5, and Diaza-18-crown-6

1997 ◽  
Vol 52 (7) ◽  
pp. 847-850 ◽  
Author(s):  
Joachim Pickardt ◽  
Sven Wiese
Keyword(s):  
Bond Length ◽  
Crystal Structures ◽  
Iodine Atom ◽  
Bond Lengths ◽  
The Mean ◽  
Iodide Crystal

The reactions of diaza-15-crown-5 (“2.1”), and diaza-18-crown-6 (“2.2”), resp., with HgI2 in methanol afford the compounds [Hg(2.1)I][Hg2I6] (1) and [Hg(2.2)I][Hg2I6] (2), the crystal structures of which were determined. 1 consists of isolated cations [Hg(2.1)I]+ and anions [Hg2I6]2-. In the cations Hg is coordinated by one iodine atom, the two N atoms and the three O atoms of the ligand; the Hg-I distance is 262.1(3) pm, the Hg-N bond lengths are 221(2) and 238(2) pm; they are significantly shorter than the Hg-O distances, which are in the range between 262 and 271 pm. 2 consists of cations [Hg(2.2)I]+, which are bridged by the anions. In the cations of 2 Hg is coordinated by an iodine atom and by the two N atoms of the ligand, but by only three of the four O atoms. The Hg-I distance is 275.8(5) pm, the mean Hg-N bond length 234(4) pm, and the Hg-O distances vary between 285 and 304 pm. The Hg-I distance to the bridging I atom of the anion is 388.6(6) pm. The Hg-I bond lengths within the anions are slightly widened by this coordination.

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