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Antiprism
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Jean Galy – One of the best experts on this subject based on the ideXlab platform.

Coherent view of crystal chemistry and ab initio analyses of Pb(II) and Bi(III) Lone Pair in square planar coordination
Progress in Solid State Chemistry, 2015CoAuthors: Samir F. Matar, Jean GalyAbstract:Abstract The stereochemistry of 6s 2 (E) lone pair of divalent Pb and trivalent Bi (PbII and BiIII designated by M ∗ ) in structurally related PbO, PbFX (X = Cl, Br, I), BiOX (X = F, Cl, Br, I) and Bi 2 NbO 5 F is rationalized. The lone pair LP presence determined by its sphere of influence E, equal to those of oxygen or fluorine anions, was settled by its center then giving M ∗ –E directions and distances. Detailed description of structural features of both elements in the above cited compounds characterized by [PbEO] n and [BiEO] n layers allowed to show the evolution of M ∗ –E distance versus the changes with the square pyramidal SP coordination polyhedra. All are different, in red PbO one finds {PbEO 4 E 4 } square Antiprism, a {[Bi.E]O 4 X 4 X apical } monocapped square Antiprism in PbFX and BiOX and {BiEO 4 F 4 }square Antiprism in Bi 2 NbO 5 F. To analyze the crystal chemistry results, the electronic structures of these compounds were calculated within density functional theory DFT. Real space analyses of electron localization illustrate a full volume development of the lone pair on Pb(II) within {PbEO 4 E 4 } in PbOE, {PbEF 4 X 4 } in PbFXE and Bi(III) within {BiEO 4 X 4 } square Antiprisms, contrary to Bi(III) within {[Bi.E]O 4 F 4 F apical } monocapped square Antiprism. Larger hardness (larger bulk modules B 0 ) and band gap characterize BiOF versus PbO due to the presence of fluorine which brings antibonding Bi–F interactions oppositely to mainly bonding Bi–O. In PbFX and BiOX series there is a systematic decrease of B 0 with the increasing volume following the nature and size of X which is decreasingly electronegative and increasingly large. The electronic densities of states mirror these effects through the relative energy position and relative electronegativities of F/X and O/X leading to decrease the band gap.

Coherent view of crystal chemistry and ab initio analyses of Pb(II) and Bi(III) Lone Pair in square planar coordination
Progress in Solid State Chemistry, 2015CoAuthors: Samir F. Matar, Jean GalyAbstract:The stereochemistry of 6s2 (E) lone pair of divalent Pb and trivalent Bi (PbII and BiIII designated by M*) in structurally related PbO, PbFX (X= Cl, Br, I), BiOX (X= F, Cl, Br, I) and Bi2NbO5F is rationalized. The lone pair LP presence determined by its sphere of influence E, equal to those of oxygen or fluorine anions, was settled by its center then giving M*E directions and distances. Detailed description of structural features of both elements in the title compounds characterized by [PbEO]n and [BiEO]n layers allowed to show the evolution of M*E distance versus the changes with the square pyramidal SP coordination polyhedra. All are different, in red PbO one finds {PbEO4E4} square Antiprism, a {[Bi.E]O4X4Xapical} monocapped square Antiprism in PbFX and BiOX and {BiEO4F4}square Antiprism in Bi2NbO5F. To analyze the crystal chemistry results, the electronic structures of these compounds were calculated within density functional theory DFT. Real space analyses of electron localization illustrate a full volume development of the lone pair on PbII within {PbEO4E4} in PbOE, {PbEF4X4} in PbFXE and Bi(III) within {BiEO4X4} square Antiprisms, contrary to Bi(III) within {[Bi.E]O4F4Fapical} monocapped square Antiprism. Larger hardness (larger bulk modules B0) and band gap characterize BiOF versus PbO due to the presence of F which brings antibonding BiF interactions oppositely to mainly bonding BiO. In PbFX and BiOX series there is a systematic decrease of B0 with the increasing volume following the nature and size of X which is decreasingly electronegative and increasingly large. The electronic densities of states mirror these effects through the relative energy position and relative electronegativities of F/X and O/X leading to decrease the band gap.

6s2 Lone Pair Effects in related structures PbO, BiOF and Bi2NbO5F: Crystal chemistry and DFT investigations
, 2014CoAuthors: Samir F. Matar, Jean GalyAbstract:Based on the stereochemistry of 6s 2 (E) lone pair elements Pb II and Bi III , designated by M*, the related PbO, BiOF and Bi2NbO5F crystal structures were revisited. Lone pair presence determined by its sphere of influence E, equal to those of oxygen or fluorine anions, was settled by its center then giving M*E directions and distances. Detailed description of structural features of both elements in these three compounds characterized by [PbEO]n and [BiEO]n layers allowed to show the evolution of M*E versus the coordination polyhedra. All are different, in red PbO one finds {PbEO4E4} square Antiprism, a {[Bi.E]O4F4Fapical} monocapped square Antiprism in BiOF and {BiEO4F4}square Antiprism in Bi2NbO5F. To analyze the crystal chemistry results, the electronic structures of these compounds were calculated within density functional theory DFT. Real space analyses of electron localization illustrate a full volume development of the lone pair on Pb II within {PbEO4E4} and Bi III within {BiEO4F4} square Antiprisms, contrary to Bi III within {[Bi.E]O4F4Fapical} monocapped square Antiprism. Larger hardness and band gap characterize BiOF versus PbO due to the presence of F which brings antibonding BiF interactions oppositely to mainly bonding BiO. 2014 Elsevier Ltd. All rights reserved.
Samir F. Matar – One of the best experts on this subject based on the ideXlab platform.

Coherent view of crystal chemistry and ab initio analyses of Pb(II) and Bi(III) Lone Pair in square planar coordination
Progress in Solid State Chemistry, 2015CoAuthors: Samir F. Matar, Jean GalyAbstract:Abstract The stereochemistry of 6s 2 (E) lone pair of divalent Pb and trivalent Bi (PbII and BiIII designated by M ∗ ) in structurally related PbO, PbFX (X = Cl, Br, I), BiOX (X = F, Cl, Br, I) and Bi 2 NbO 5 F is rationalized. The lone pair LP presence determined by its sphere of influence E, equal to those of oxygen or fluorine anions, was settled by its center then giving M ∗ –E directions and distances. Detailed description of structural features of both elements in the above cited compounds characterized by [PbEO] n and [BiEO] n layers allowed to show the evolution of M ∗ –E distance versus the changes with the square pyramidal SP coordination polyhedra. All are different, in red PbO one finds {PbEO 4 E 4 } square Antiprism, a {[Bi.E]O 4 X 4 X apical } monocapped square Antiprism in PbFX and BiOX and {BiEO 4 F 4 }square Antiprism in Bi 2 NbO 5 F. To analyze the crystal chemistry results, the electronic structures of these compounds were calculated within density functional theory DFT. Real space analyses of electron localization illustrate a full volume development of the lone pair on Pb(II) within {PbEO 4 E 4 } in PbOE, {PbEF 4 X 4 } in PbFXE and Bi(III) within {BiEO 4 X 4 } square Antiprisms, contrary to Bi(III) within {[Bi.E]O 4 F 4 F apical } monocapped square Antiprism. Larger hardness (larger bulk modules B 0 ) and band gap characterize BiOF versus PbO due to the presence of fluorine which brings antibonding Bi–F interactions oppositely to mainly bonding Bi–O. In PbFX and BiOX series there is a systematic decrease of B 0 with the increasing volume following the nature and size of X which is decreasingly electronegative and increasingly large. The electronic densities of states mirror these effects through the relative energy position and relative electronegativities of F/X and O/X leading to decrease the band gap.

Coherent view of crystal chemistry and ab initio analyses of Pb(II) and Bi(III) Lone Pair in square planar coordination
Progress in Solid State Chemistry, 2015CoAuthors: Samir F. Matar, Jean GalyAbstract:The stereochemistry of 6s2 (E) lone pair of divalent Pb and trivalent Bi (PbII and BiIII designated by M*) in structurally related PbO, PbFX (X= Cl, Br, I), BiOX (X= F, Cl, Br, I) and Bi2NbO5F is rationalized. The lone pair LP presence determined by its sphere of influence E, equal to those of oxygen or fluorine anions, was settled by its center then giving M*E directions and distances. Detailed description of structural features of both elements in the title compounds characterized by [PbEO]n and [BiEO]n layers allowed to show the evolution of M*E distance versus the changes with the square pyramidal SP coordination polyhedra. All are different, in red PbO one finds {PbEO4E4} square Antiprism, a {[Bi.E]O4X4Xapical} monocapped square Antiprism in PbFX and BiOX and {BiEO4F4}square Antiprism in Bi2NbO5F. To analyze the crystal chemistry results, the electronic structures of these compounds were calculated within density functional theory DFT. Real space analyses of electron localization illustrate a full volume development of the lone pair on PbII within {PbEO4E4} in PbOE, {PbEF4X4} in PbFXE and Bi(III) within {BiEO4X4} square Antiprisms, contrary to Bi(III) within {[Bi.E]O4F4Fapical} monocapped square Antiprism. Larger hardness (larger bulk modules B0) and band gap characterize BiOF versus PbO due to the presence of F which brings antibonding BiF interactions oppositely to mainly bonding BiO. In PbFX and BiOX series there is a systematic decrease of B0 with the increasing volume following the nature and size of X which is decreasingly electronegative and increasingly large. The electronic densities of states mirror these effects through the relative energy position and relative electronegativities of F/X and O/X leading to decrease the band gap.

6s2 Lone Pair Effects in related structures PbO, BiOF and Bi2NbO5F: Crystal chemistry and DFT investigations
, 2014CoAuthors: Samir F. Matar, Jean GalyAbstract:Based on the stereochemistry of 6s 2 (E) lone pair elements Pb II and Bi III , designated by M*, the related PbO, BiOF and Bi2NbO5F crystal structures were revisited. Lone pair presence determined by its sphere of influence E, equal to those of oxygen or fluorine anions, was settled by its center then giving M*E directions and distances. Detailed description of structural features of both elements in these three compounds characterized by [PbEO]n and [BiEO]n layers allowed to show the evolution of M*E versus the coordination polyhedra. All are different, in red PbO one finds {PbEO4E4} square Antiprism, a {[Bi.E]O4F4Fapical} monocapped square Antiprism in BiOF and {BiEO4F4}square Antiprism in Bi2NbO5F. To analyze the crystal chemistry results, the electronic structures of these compounds were calculated within density functional theory DFT. Real space analyses of electron localization illustrate a full volume development of the lone pair on Pb II within {PbEO4E4} and Bi III within {BiEO4F4} square Antiprisms, contrary to Bi III within {[Bi.E]O4F4Fapical} monocapped square Antiprism. Larger hardness and band gap characterize BiOF versus PbO due to the presence of F which brings antibonding BiF interactions oppositely to mainly bonding BiO. 2014 Elsevier Ltd. All rights reserved.
Yuyun Mintarsih – One of the best experts on this subject based on the ideXlab platform.

On the strong metric dimension of Antiprism graph, king graph, and Km ? Kn graph
, 2018CoAuthors: Yuyun MintarsihAbstract:Abstract. Let G be a connected graph with a set of vertices V (G) and a set of edges E(G).The interval I[u; v] between u and v to be the collection of all vertices that belong to someshortest uv path. A vertex s ∈ V (G) is said to be strongly resolved for vertices u, v ∈ V (G)if v ∈ I[u; s] or u ∈ I[v; s]. A vertex set S ⊆ V (G) is a strong resolving set for G if every twodistinct vertices of G are strongly resolved by some vertices of S. The strong metric dimensionof G, denoted by sdim(G), is de ned as the smallest cardinality of a strong resolving set. Inthis paper, we determine the strong metric dimension of an Antiprism An graph, a king Km;ngraph, and a Km ? Kn graph. We obtain the strong metric dimension of an antiprim graphAn are n for n odd and n + 1 for n even. The strong metric dimension of King graph Km;n ism+n−1. The strong metric dimension of Km ?Kn graph are n for m = 1, n ≥ 1 and mn−1for m ≥ 2, n ≥ 1.

on the strong metric dimension of Antiprism graph king graph and km kn graph
, 2018CoAuthors: Yuyun MintarsihAbstract:Abstract. Let G be a connected graph with a set of vertices V (G) and a set of edges E(G).The interval I[u; v] between u and v to be the collection of all vertices that belong to someshortest uv path. A vertex s ∈ V (G) is said to be strongly resolved for vertices u, v ∈ V (G)if v ∈ I[u; s] or u ∈ I[v; s]. A vertex set S ⊆ V (G) is a strong resolving set for G if every twodistinct vertices of G are strongly resolved by some vertices of S. The strong metric dimensionof G, denoted by sdim(G), is de ned as the smallest cardinality of a strong resolving set. Inthis paper, we determine the strong metric dimension of an Antiprism An graph, a king Km;ngraph, and a Km ? Kn graph. We obtain the strong metric dimension of an antiprim graphAn are n for n odd and n + 1 for n even. The strong metric dimension of King graph Km;n ism+n−1. The strong metric dimension of Km ?Kn graph are n for m = 1, n ≥ 1 and mn−1for m ≥ 2, n ≥ 1.