Lanthanide Contraction in <i>Ln</i>F<sub>3</sub> (<i>Ln</i> = Ce-Lu) and Its Chemical and Structural Consequences: Part 2: Specialized Empirical System of <i>R</i><sup>3+</sup> (<i>R</i> = Y, La, and 14 <i>Ln</i>) and F<sup>1−</sup> Ionic Radii for <i>R</i>F<sub>3</sub> Series

Lanthanide Contraction in <i>Ln</i>F<sub>3</sub> (<i>Ln</i> = Ce-Lu) and Its Chemical and Structural Consequences: Part 2: Specialized Empirical System of <i>R</i><sup>3+</sup> (<i>R</i> = Y, La, and 14 <i>Ln</i>) and F<sup>1−</sup> Ionic Radii for <i>R</i>F<sub>3</sub> Series

A <i>specialized empirical</i> (<i><b>Spec-zd Emp</b></i>) <i>system of ionic radii</i> (<b>SIR</b>) for <i><b>R</b></i> = Y<sup>3+</sup>, La<sup>3+</sup>, <i>Ln</i><sup>3+&l...

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Main Authors: Boris P. Sobolev, Elena A. Sulyanova
Format: Article
Language:English
Published: MDPI AG 2023-12-01
Series:International Journal of Molecular Sciences
Subjects:
lanthanide contraction
ionic radii
empirical system of ionic radii
rare earth elements
lanthanide trifluorides
fluorine anion radius
Online Access:https://www.mdpi.com/1422-0067/24/23/17080
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author Boris P. Sobolev
Elena A. Sulyanova
author_facet Boris P. Sobolev
Elena A. Sulyanova
author_sort Boris P. Sobolev
collection DOAJ
description A <i>specialized empirical</i> (<i><b>Spec-zd Emp</b></i>) <i>system of ionic radii</i> (<b>SIR</b>) for <i><b>R</b></i> = Y<sup>3+</sup>, La<sup>3+</sup>, <i>Ln</i><sup>3+</sup>, and F<sup>1−</sup> (<i>R</i> rare earth elements (<b>REE</b>)) was derived from the dependence of <i>lanthanide contraction</i> (<b>LC</b>) on the <i>atomic number</i> (<b>Z</b>) of <i>lanthanides</i> (<i><b>Ln</b></i>). LC decreased the radius of the cation with increasing Z. The structures of <b><i>t</i></b>-<i>R</i>F<sub>3</sub> (LaF<sub>3</sub>-NdF<sub>3</sub>, “<i>pseudo</i> <b><i>t</i></b>-SmF<sub>3</sub>”) of the LaF<sub>3</sub> type, 11 <b><i>β</i></b>-<i>Ln</i>F<sub>3</sub> (<i>Ln</i> = Sm-Lu), and <b><i>β</i></b>-YF<sub>3</sub> of the β-YF<sub>3</sub> type were studied. The empirical basis of the shortest (F-F)<sub>min</sub> and (<i>R</i>-F)<sub>min</sub> distances was calculated from the structural data for the <i>R</i>F<sub>3</sub> complete series. The dependence of (F-F)<sub>min</sub> on Z reached saturation at Z = 67 (Ho). The base F<sup>1−</sup> radius <i><b>r</b></i><sub>−</sub> = 1.2539(16) Å was calculated as the arithmetic mean of five (F-F)<sub>min</sub> in <i>Ln</i>F<sub>3</sub> with <i>Ln</i> = Ho-Lu. For the <i>Ln</i>F<sub>3</sub> series with <i>Ln</i> contributions up to 75 % wt., the dependence of (<i>Ln</i>-F)<sub>min</sub> on Z reflected the non-uniformity of the 4<i>f</i> orbital filling. SIR was calculated as the difference in the empirical constants of <i>R</i>F<sub>3</sub> (<i>ionic radii</i> of (<i>R</i>,<i>Ln</i>)<sup>3+</sup> (<i><b>r</b></i><sub>+</sub>) and F<sup>1−</sup> (<i><b>r</b></i><sub>−</sub>)), the change in which was continuous over the series and did not depend on the type of structure: <i><b>r</b></i><sub>+</sub> = (<sub>Z</sub><i>R</i>-F)<sub>min</sub> − ½(F-F)<sub>min</sub> (Z = 57–71). The changes in LC in the <i>Ln</i>F<sub>3</sub> series were described by a third-degree polynomial. LC reduced <b><i>r</i></b><sub>+</sub> by 24% (percentage relative to less) from 1.1671(16) Å (La<sup>3+</sup>) to 0.9439(17) Å (Lu<sup>3+</sup>). In the <i>Spec-zd Emp</i> SIR, <i><b>r</b></i><sub>+</sub> were constants that did not require corrections for a <i>coordination number</i> (<b>CN</b>). A comparison of <i><b>r</b></i><sub>+</sub> in the <i>Spec-zd Emp</i> SIR with other SIRs was performed.
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spelling doaj.art-d93797e182f346a096c93ffc41296fb42023-12-08T15:18:19ZengMDPI AGInternational Journal of Molecular Sciences1661-65961422-00672023-12-0124231708010.3390/ijms242317080Lanthanide Contraction in <i>Ln</i>F<sub>3</sub> (<i>Ln</i> = Ce-Lu) and Its Chemical and Structural Consequences: Part 2: Specialized Empirical System of <i>R</i><sup>3+</sup> (<i>R</i> = Y, La, and 14 <i>Ln</i>) and F<sup>1−</sup> Ionic Radii for <i>R</i>F<sub>3</sub> SeriesBoris P. Sobolev0Elena A. Sulyanova1Shubnikov Institute of Crystallography, Federal Scientific Research Centre “Crystallography and Photonics”, Russian Academy of Sciences, Leninskiy Prospekt 59, 119333 Moscow, RussiaShubnikov Institute of Crystallography, Federal Scientific Research Centre “Crystallography and Photonics”, Russian Academy of Sciences, Leninskiy Prospekt 59, 119333 Moscow, RussiaA <i>specialized empirical</i> (<i><b>Spec-zd Emp</b></i>) <i>system of ionic radii</i> (<b>SIR</b>) for <i><b>R</b></i> = Y<sup>3+</sup>, La<sup>3+</sup>, <i>Ln</i><sup>3+</sup>, and F<sup>1−</sup> (<i>R</i> rare earth elements (<b>REE</b>)) was derived from the dependence of <i>lanthanide contraction</i> (<b>LC</b>) on the <i>atomic number</i> (<b>Z</b>) of <i>lanthanides</i> (<i><b>Ln</b></i>). LC decreased the radius of the cation with increasing Z. The structures of <b><i>t</i></b>-<i>R</i>F<sub>3</sub> (LaF<sub>3</sub>-NdF<sub>3</sub>, “<i>pseudo</i> <b><i>t</i></b>-SmF<sub>3</sub>”) of the LaF<sub>3</sub> type, 11 <b><i>β</i></b>-<i>Ln</i>F<sub>3</sub> (<i>Ln</i> = Sm-Lu), and <b><i>β</i></b>-YF<sub>3</sub> of the β-YF<sub>3</sub> type were studied. The empirical basis of the shortest (F-F)<sub>min</sub> and (<i>R</i>-F)<sub>min</sub> distances was calculated from the structural data for the <i>R</i>F<sub>3</sub> complete series. The dependence of (F-F)<sub>min</sub> on Z reached saturation at Z = 67 (Ho). The base F<sup>1−</sup> radius <i><b>r</b></i><sub>−</sub> = 1.2539(16) Å was calculated as the arithmetic mean of five (F-F)<sub>min</sub> in <i>Ln</i>F<sub>3</sub> with <i>Ln</i> = Ho-Lu. For the <i>Ln</i>F<sub>3</sub> series with <i>Ln</i> contributions up to 75 % wt., the dependence of (<i>Ln</i>-F)<sub>min</sub> on Z reflected the non-uniformity of the 4<i>f</i> orbital filling. SIR was calculated as the difference in the empirical constants of <i>R</i>F<sub>3</sub> (<i>ionic radii</i> of (<i>R</i>,<i>Ln</i>)<sup>3+</sup> (<i><b>r</b></i><sub>+</sub>) and F<sup>1−</sup> (<i><b>r</b></i><sub>−</sub>)), the change in which was continuous over the series and did not depend on the type of structure: <i><b>r</b></i><sub>+</sub> = (<sub>Z</sub><i>R</i>-F)<sub>min</sub> − ½(F-F)<sub>min</sub> (Z = 57–71). The changes in LC in the <i>Ln</i>F<sub>3</sub> series were described by a third-degree polynomial. LC reduced <b><i>r</i></b><sub>+</sub> by 24% (percentage relative to less) from 1.1671(16) Å (La<sup>3+</sup>) to 0.9439(17) Å (Lu<sup>3+</sup>). In the <i>Spec-zd Emp</i> SIR, <i><b>r</b></i><sub>+</sub> were constants that did not require corrections for a <i>coordination number</i> (<b>CN</b>). A comparison of <i><b>r</b></i><sub>+</sub> in the <i>Spec-zd Emp</i> SIR with other SIRs was performed.https://www.mdpi.com/1422-0067/24/23/17080lanthanide contractionionic radiiempirical system of ionic radiirare earth elementslanthanide trifluoridesfluorine anion radius
spellingShingle Boris P. Sobolev
Elena A. Sulyanova
Lanthanide Contraction in <i>Ln</i>F<sub>3</sub> (<i>Ln</i> = Ce-Lu) and Its Chemical and Structural Consequences: Part 2: Specialized Empirical System of <i>R</i><sup>3+</sup> (<i>R</i> = Y, La, and 14 <i>Ln</i>) and F<sup>1−</sup> Ionic Radii for <i>R</i>F<sub>3</sub> Series
International Journal of Molecular Sciences
lanthanide contraction
ionic radii
empirical system of ionic radii
rare earth elements
lanthanide trifluorides
fluorine anion radius
title Lanthanide Contraction in <i>Ln</i>F<sub>3</sub> (<i>Ln</i> = Ce-Lu) and Its Chemical and Structural Consequences: Part 2: Specialized Empirical System of <i>R</i><sup>3+</sup> (<i>R</i> = Y, La, and 14 <i>Ln</i>) and F<sup>1−</sup> Ionic Radii for <i>R</i>F<sub>3</sub> Series
title_full Lanthanide Contraction in <i>Ln</i>F<sub>3</sub> (<i>Ln</i> = Ce-Lu) and Its Chemical and Structural Consequences: Part 2: Specialized Empirical System of <i>R</i><sup>3+</sup> (<i>R</i> = Y, La, and 14 <i>Ln</i>) and F<sup>1−</sup> Ionic Radii for <i>R</i>F<sub>3</sub> Series
title_fullStr Lanthanide Contraction in <i>Ln</i>F<sub>3</sub> (<i>Ln</i> = Ce-Lu) and Its Chemical and Structural Consequences: Part 2: Specialized Empirical System of <i>R</i><sup>3+</sup> (<i>R</i> = Y, La, and 14 <i>Ln</i>) and F<sup>1−</sup> Ionic Radii for <i>R</i>F<sub>3</sub> Series
title_full_unstemmed Lanthanide Contraction in <i>Ln</i>F<sub>3</sub> (<i>Ln</i> = Ce-Lu) and Its Chemical and Structural Consequences: Part 2: Specialized Empirical System of <i>R</i><sup>3+</sup> (<i>R</i> = Y, La, and 14 <i>Ln</i>) and F<sup>1−</sup> Ionic Radii for <i>R</i>F<sub>3</sub> Series
title_short Lanthanide Contraction in <i>Ln</i>F<sub>3</sub> (<i>Ln</i> = Ce-Lu) and Its Chemical and Structural Consequences: Part 2: Specialized Empirical System of <i>R</i><sup>3+</sup> (<i>R</i> = Y, La, and 14 <i>Ln</i>) and F<sup>1−</sup> Ionic Radii for <i>R</i>F<sub>3</sub> Series
title_sort lanthanide contraction in i ln i f sub 3 sub i ln i ce lu and its chemical and structural consequences part 2 specialized empirical system of i r i sup 3 sup i r i y la and 14 i ln i and f sup 1 sup ionic radii for i r i f sub 3 sub series
topic lanthanide contraction
ionic radii
empirical system of ionic radii
rare earth elements
lanthanide trifluorides
fluorine anion radius
url https://www.mdpi.com/1422-0067/24/23/17080
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