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V S Harutyunyan - One of the best experts on this subject based on the ideXlab platform.
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the Madelung Constant and bonding angle as sensors of the high pressure induced amorphization and first order isostructural phase transition in mg oh 2 and ca oh 2
Journal of Solid State Chemistry, 2021Co-Authors: V S HarutyunyanAbstract:Abstract With the use of high-pressure experimental results available in literature, this study theoretically investigates, for M(OH)2 (M= Mg, Ca) compounds, the pressure dependences of the structural parameters (lattice parameters, the Madelung Constant, bonding angle. O-M-O, unit cell volume and its contributions from constituent sublattices) and bulk compressibility. These pressure dependences and their anomalies are analyzed in terms of the amorphization of the H-sublattice and isostructural transition in a compound. It is demonstrated that (i) for Mg(OH)2 and Ca(OH)2, the Madelung Constant and bonding angle O-M-O decrease with increase of pressure, (ii) for Mg(OH)2 and Ca(OH)2, both the Madelung Constant and bonding angle O-M-O achieve a minimum at pressure of the onset of a strong amorphization of the H-sublattice, and (iii) for Mg(OH)2, the isostructural phase transition and above critical amorphization occur practically at the same pressure. It is assumed that the critical amorphization is mainly responsible for isostructural phase transition.
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correlation of the Madelung Constant and i m i bonding angle with cohesive energy contributions in layered metal diiodides mi2 with cdi2 2h polytype structure
Acta Crystallographica Section B Structural Crystallography and Crystal Chemistry, 2020Co-Authors: V S HarutyunyanAbstract:This study uses theoretically methods to investigate, for metal diiodides MI2 (M = Mg, Ca, Mn, Fe, Cd, Pb) with CdI2 (2H polytype) structure, the mutual correlation between the structure-characterizing parameters (the flatness parameter of monolayers f, the Madelung Constant A, and bonding angle I-M-I) and correlation of these parameters with contributions of the Coulomb and covalent energies to cohesive energy. The energy contributions to cohesive energy are determined with the use of empirical atomic potentials. It is demonstrated that the parameters f and A, and the bonding angle I-M-I are strictly correlated and increase in the same order: FeI2 < PbI2 < MnI2 < CdI2 < MgI2 < CaI2. It is found that with an increase of parameter A and bonding angle I-M-I the relative contribution of the Coulomb energy to cohesive energy increases, whereas the relative contribution of the covalent energy decreases. For a hypothetical MX2 layered compound with the CdI2 (2H polytype) structure, composed of regular MX6 octahedra (angle X-M-X = 90°), the flatness parameter and the Madelung Constant are found to be freg = 2.449 and Areg = 2.183, respectively. Correlation of the covalent energy with the type of distortion of MI6 octahedra (elongation or compression) with respect to regular configuration (angle I-M-I = 90°) is also analyzed.
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anomalous behavior of the Madelung Constant and i fe i bonding angle at high pressure induced structural phase transition of fei2
Materials Chemistry and Physics, 2020Co-Authors: V S HarutyunyanAbstract:Abstract This study is devoted to theoretical analysis of the high-pressure experimental results available in literature that are associated with the structural phase transition of FeI2 in the pressure variation range up to ≈20 GPa. To establish the dependence of the interatomic interaction potentials of FeI2 on the pressure, theoretical relationships connecting the Madelung Constant with the pressure-dependent lattice parameters, ionicity parameter, and I–Fe–I bonding angle are obtained. A strong correlation is revealed between the Madelung Constant, ionicity parameter, and the bonding angle in their dependences on pressure. As a result of this correlation, with increase of pressure the Coulomb energy, which depends on the Madelung Constant and ionicity parameter (i.e., ionic partial charges), tends to decrease, whereas the covalent energy dependent on the bonding angle exhibits a trend to increase. It is found that at the pressure of P = 16.9 GPa, the Madelung Constant, ionicity parameter, and the bonding angle of the initial phase of FeI2 achieve their well-expressed minimum values. As a consequence, at above pressure the binding energy of FeI2 contributed by the Coulomb and covalent energies achieves its minimum value of 6.46 eV that results in structure destabilization and partial transition of the initial phase of the FeI2 to a new phase. It is concluded that, for FeI2 and compounds isostructural with this material, analysis of the pressure-dependent variation of the Madelung Constant and bonding angle may be helpful in the prediction of possible structural phase transitions in high-pressure experimental investigations.
Arjan J Berger - One of the best experts on this subject based on the ideXlab platform.
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clifford boundary conditions for periodic systems the Madelung Constant of cubic crystals in 1 2 and 3 dimensions
Theoretical Chemistry Accounts, 2021Co-Authors: Nicolas Tavernier, Gian Luigi Bendazzoli, Veronique Brumas, Stefano Evangelisti, Arjan J BergerAbstract:In this work we demonstrate the robustness of a real-space approach for the treatment of infinite systems described with periodic boundary conditions that we have recently proposed (Tavernier et al in J Phys Chem Lett 17:7090, 2000). In our approach we extract a fragment, i.e., a supercell, out of the infinite system, and then modifying its topology into the that of a Clifford torus which is a flat, finite and border-less manifold. We then renormalize the distance between two points by defining it as the Euclidean distance in the embedding space of the Clifford torus. With our method we have been able to calculate the reference results available in the literature with a remarkable accuracy, and at a very low computational effort. In this work we show that our approach is robust with respect to the shape of the supercell. In particular, we show that the Madelung Constants converge to the same values but that the convergence properties are different. Our approach scales linearly with the number of atoms. The calculation of Madelung Constants only takes a few seconds on a laptop computer for a relative precision of about 10 $$^{-6}$$ .
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clifford boundary conditions for periodic systems the Madelung Constant of cubic crystals in 1 2 and 3 dimensions
arXiv: Materials Science, 2021Co-Authors: Nicolas Tavernier, Gian Luigi Bendazzoli, Veronique Brumas, Stefano Evangelisti, Arjan J BergerAbstract:In this work we demonstrate the robustness of a real-space approach for the treatment of infinite systems described with periodic boundary conditions that we have recently proposed [J. Phys. Chem. Lett. 17, 7090]. In our approach we extract a fragment, i.e., a supercell, out of the infinite system, and then modifying its topology into the that of a Clifford torus which is a flat, finite and border-less manifold. We then renormalize the distance between two points by defining it as the Euclidean distance in the embedding space of the Clifford torus. With our method we have been able to calculate the reference results available in the literature with a remarkable accuracy, and at a very low computational effort. In this work we show that our approach is robust with respect to the shape of the supercell. In particular, we show that the Madelung Constants converge to the same values but that the convergence properties are different. Our approach scales linearly with the number of atoms. The calculation of Madelung Constants only takes a few seconds on a laptop computer for a relative precision of about 10$^{-6}$.
Sheng Gui - One of the best experts on this subject based on the ideXlab platform.
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Madelung Constant and computer aided computation of ionic crystal lattice energy
Computers and Applied Chemistry, 1999Co-Authors: Sheng GuiAbstract:Firstly a mistake in deducing Madelung Constant was pointed out in this paper.The mistake has remained in some present works of crystal chemistry.Then an effective method of calculating ionic lattice energy was given by using of nunmber theory and computer technique in this paper.
Nicolas Tavernier - One of the best experts on this subject based on the ideXlab platform.
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clifford boundary conditions for periodic systems the Madelung Constant of cubic crystals in 1 2 and 3 dimensions
Theoretical Chemistry Accounts, 2021Co-Authors: Nicolas Tavernier, Gian Luigi Bendazzoli, Veronique Brumas, Stefano Evangelisti, Arjan J BergerAbstract:In this work we demonstrate the robustness of a real-space approach for the treatment of infinite systems described with periodic boundary conditions that we have recently proposed (Tavernier et al in J Phys Chem Lett 17:7090, 2000). In our approach we extract a fragment, i.e., a supercell, out of the infinite system, and then modifying its topology into the that of a Clifford torus which is a flat, finite and border-less manifold. We then renormalize the distance between two points by defining it as the Euclidean distance in the embedding space of the Clifford torus. With our method we have been able to calculate the reference results available in the literature with a remarkable accuracy, and at a very low computational effort. In this work we show that our approach is robust with respect to the shape of the supercell. In particular, we show that the Madelung Constants converge to the same values but that the convergence properties are different. Our approach scales linearly with the number of atoms. The calculation of Madelung Constants only takes a few seconds on a laptop computer for a relative precision of about 10 $$^{-6}$$ .
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clifford boundary conditions for periodic systems the Madelung Constant of cubic crystals in 1 2 and 3 dimensions
arXiv: Materials Science, 2021Co-Authors: Nicolas Tavernier, Gian Luigi Bendazzoli, Veronique Brumas, Stefano Evangelisti, Arjan J BergerAbstract:In this work we demonstrate the robustness of a real-space approach for the treatment of infinite systems described with periodic boundary conditions that we have recently proposed [J. Phys. Chem. Lett. 17, 7090]. In our approach we extract a fragment, i.e., a supercell, out of the infinite system, and then modifying its topology into the that of a Clifford torus which is a flat, finite and border-less manifold. We then renormalize the distance between two points by defining it as the Euclidean distance in the embedding space of the Clifford torus. With our method we have been able to calculate the reference results available in the literature with a remarkable accuracy, and at a very low computational effort. In this work we show that our approach is robust with respect to the shape of the supercell. In particular, we show that the Madelung Constants converge to the same values but that the convergence properties are different. Our approach scales linearly with the number of atoms. The calculation of Madelung Constants only takes a few seconds on a laptop computer for a relative precision of about 10$^{-6}$.
Stefano Evangelisti - One of the best experts on this subject based on the ideXlab platform.
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clifford boundary conditions for periodic systems the Madelung Constant of cubic crystals in 1 2 and 3 dimensions
Theoretical Chemistry Accounts, 2021Co-Authors: Nicolas Tavernier, Gian Luigi Bendazzoli, Veronique Brumas, Stefano Evangelisti, Arjan J BergerAbstract:In this work we demonstrate the robustness of a real-space approach for the treatment of infinite systems described with periodic boundary conditions that we have recently proposed (Tavernier et al in J Phys Chem Lett 17:7090, 2000). In our approach we extract a fragment, i.e., a supercell, out of the infinite system, and then modifying its topology into the that of a Clifford torus which is a flat, finite and border-less manifold. We then renormalize the distance between two points by defining it as the Euclidean distance in the embedding space of the Clifford torus. With our method we have been able to calculate the reference results available in the literature with a remarkable accuracy, and at a very low computational effort. In this work we show that our approach is robust with respect to the shape of the supercell. In particular, we show that the Madelung Constants converge to the same values but that the convergence properties are different. Our approach scales linearly with the number of atoms. The calculation of Madelung Constants only takes a few seconds on a laptop computer for a relative precision of about 10 $$^{-6}$$ .
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clifford boundary conditions for periodic systems the Madelung Constant of cubic crystals in 1 2 and 3 dimensions
arXiv: Materials Science, 2021Co-Authors: Nicolas Tavernier, Gian Luigi Bendazzoli, Veronique Brumas, Stefano Evangelisti, Arjan J BergerAbstract:In this work we demonstrate the robustness of a real-space approach for the treatment of infinite systems described with periodic boundary conditions that we have recently proposed [J. Phys. Chem. Lett. 17, 7090]. In our approach we extract a fragment, i.e., a supercell, out of the infinite system, and then modifying its topology into the that of a Clifford torus which is a flat, finite and border-less manifold. We then renormalize the distance between two points by defining it as the Euclidean distance in the embedding space of the Clifford torus. With our method we have been able to calculate the reference results available in the literature with a remarkable accuracy, and at a very low computational effort. In this work we show that our approach is robust with respect to the shape of the supercell. In particular, we show that the Madelung Constants converge to the same values but that the convergence properties are different. Our approach scales linearly with the number of atoms. The calculation of Madelung Constants only takes a few seconds on a laptop computer for a relative precision of about 10$^{-6}$.
