Semiempirical approximation for atomization energy of bivalent metal halide crystals

Urusov, V. S.; Dudnikova, V. B.

doi:10.1007/bf00945145

Cited by 5 publications

(12 citation statements)

References 15 publications

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“…(14) is a sum of A E(q) over all atoms in a crystal, if q is set equal to Z f, the effective charge of an atom. This way to estimate the charge-transfer energy can be used as a good approximation for monovalent atomic species in the alkali halide crystals (Ferreira 1964) and even for divalent metals in halide molecules (Evans and t-Iuheey 1970) and crystals (Urusov and Dudnikova 1985). The resulting E values are in a good accordance with the experimental values of the atomization energy.…”

Section: Charge-transfer Energy; Example Of Si and 0 Atomssupporting

confidence: 60%

Energy minimum criteria in modeling structures and properties of minerals

Urusov

Eremin

1995

Phys Chem Minerals

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Abstract. The leading principle in modeling procedures is the minimization of structural energy. It is assumed that the calculated minimal energy has to be compared with the experimental estimate of cohesion energy of a crystal. The reference state for structure energy depends on bonding type: the lattice energy for purely ionic crystals consisting of cations and anions, the atomization energy for covalent and metallic crystals consisting of atoms, the sublimation energy for molecular crystals consisting of molecules etc.As is well-known, a majority of minerals can not be correctly described as purely ionic crystals. Moreover, for these crystals lattice energy cannot be determined empirically because free anions, such as 0 2-, S 2-, As 3 -, etc., do not exist. In order to describe crystal structures and properties in a better approximation it is usually proposed that the bonding character of such crystals is intermediate between ionic and covalent, so that effective charges instead of formal ones, and an appropriate covalent contribution, are involved in energy calculations. However, the corresponding calculated structure energies are not comparable to any experimental values. Moreover, they decrease with increasing effective charges and a purely ionic structure seems, as before, to be most stable from energetic point of view.To avoid this "energetic catastrophe" the so-called "charge-transfer energy" has to be taken into account. Estimations of charge-transfer energies were sometimes faced with difficulties because of limitation of knowledge about valence-state energies of atoms. Now it is possible to refine this approach using new data on the average one-electron energies of the valenceshell electrons in ground-state free atoms. It is demonstrated for the examples of Si and O atoms. The successive ionization of mixed s, p valence-shell of silicon atom from Si ~ to Si 4+ states is reconstructed and a new extrapolation procedure to obtain the electron affinity of 0 2-is applied.Correspondence to: V.S. Urusov The structure energy of stishovite SiO 2 as a function of the ionicity degree parameterfis calculated with the aid of pair potential consisting of the effective ionic, the covalent Morse type contributions and the charge transfer correction. The structure energies change from -6.32 eV for the ionic structure (f= 1) to -11.91 eV for the covalent structure (f=0) with minimum value of -15.41 eV for f= 0.49. The latter can be compared to the experimental value of atomization energy (-18.9 eV). The corresponding oxygen atomic coordinate x varies from 0.310 0c= 1) to 0.300 (f=0) being equal to the true value of 0.306 at f=0.75. Atfless than 0.7 the improvement of the simulated elastic and dielectric constants, when compared to the ionic model, is sufficient.

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Section: Charge-transfer Energy; Example Of Si and 0 Atomssupporting

confidence: 60%

Energy minimum criteria in modeling structures and properties of minerals

Urusov

Eremin

1995

Phys Chem Minerals

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“…We have assumed w to be equal to the interlayer distance in bulk PbI 2 , 6.986 Å,43 and w 0 to be the average interlayer distance of bulk PbI 2 and MoS 2 , 6.567 Å 44. The dangling bond energy, ε x , has been roughly estimated from the atomization energy of bulk PbI 2 which equals 0.508 eV atom −1 45. The energy of the weak van der Waals' interaction ε v d W was calculated using a universal force field method (UFF) implemented in a deMon package and equals −8.5 meV Å −2 46…”

Section: Resultsmentioning

confidence: 99%

Synthesis of Core–Shell Inorganic Nanotubes

Kreizman

Enyashin

Deepak

et al. 2010

Adv Funct Materials

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New materials and techniques pertaining to the synthesis of inorganic nanotubes have been ever increasing since the initiation of the field in 1992. Recently, WS2 nanotubes, which are produced now in large amounts, were filled with molten lead iodide salt by a capillary wetting process, resulting in PbI2@WS2 core–shell nanotubes. This work features progress in the synthesis of new core–shell nanotubes, including BiI3@WS2 nanotubes produced in a similar same manner. In addition, two new techniques for obtaining core–shell nanotubes are presented. The first is via electron‐beam irradiation, i.e., in situ synthesis within a transmission electron microscope. This synthesis results in SbI3 nanotubes, observed either in a hollow core of WS2 ones (SbI3@WS2 nanotubes), or atop of them (WS2@SbI3 nanotubes). The second technique involves a gaseous phase reaction, where the layered product employs WS2 nanotubes as nucleation sites. In this case, the MoS2 layers most often cover the WS2 nanotube, resulting in WS2@MoS2 core–shell nanotubes. Notably, superstructures of the form MoS2@WS2@MoS2 are occasionally obtained. Using a semi‐empirical model, it is shown that the PbI2 nanotubes become stable within the core of MoS2 nanotubes only above a critical core diameter of the host (>12 nm); below this diameter the PbI2 crystallizes as nanowires. These model calculations are in agreement with the current experimental observations, providing further support to the growth mechanism of such core–shell nanotubes.

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“…The Coulomb energy of electrostatic interaction per molecule in a 3D bulk crystal of ionic binary compound MX 2 is expressed as ( ) is the permittivity of vacuum, R is the nearest-neighbor interionic distance M −X, and A M is the Madelung constant. As mentioned above, in metal dihalides (MX 2 ) and particularly in MI 2 compounds, the chemical bonds are partially ionic and partially covalent [22][23][24][25][26][27][28]. Therefore, in equation (1), the charge numbers Z c and Z a are fractional and do not coincide with (are smaller than) their corresponding formal values = Z 2…”

Section: Calculation Of the Madelung Constant For 3d Bulk Crystal Andmentioning

confidence: 99%

“…It should be noted that, in above cited publications [22,24,29,40,41] reporting the data for the Madelung constant, equation (1) is expressed in other form in terms of the definition of the Madelung constant:…”

Section: Calculation Of the Madelung Constant For 3d Bulk Crystal Andmentioning

confidence: 99%

“…Especially in applications of the exfoliation methods (through-solution, mechanical, intercalation) for preparation of 2D nanolayers of MI 2 layered compounds [2,16,[19][20][21], it is of technological interest the theoretical quantification of the cohesive energy (intralayer and interlayer) both in 2D layers/nanolayers and parent 3D bulk crystals. In metal dihalides (MX 2 ) and particularly in MI 2 compounds, the chemical bonds are partially ionic and partially covalent, with dominating iconicity [22][23][24][25][26][27][28], and this results in dominating contribution of the Coulomb electrostatic energy to the total cohesive energy (cohesive energy includes also the repulsive, polarization, van der Waals, and covalent energies) [22][23][24][25]29]. In its turn, the evaluation of the Coulomb electrostatic energy assumes, besides the partial (non-formal) ionic charges, also the precise knowledge of the Madelung constant, which characterizes the type of crystallographic arrangement of constituent ions in the crystal lattice [22,24,30].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analytic dependence of the Madelung constant on lattice parameters for 2D and 3D metal diiodides (MI₂) with CdI₂ (2H polytype) layered structure

Harutyunyan¹

2020

Mater. Res. Express

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In this theoretical study, the Madelung constant (A M ) both for a 2D layer and parent 3D bulk crystal of metal diiodides MI 2 (M=Mg, Ca, Mn, Fe, Cd, Pb) with CdI 2 (2 H polytype) structure is calculated on the basis of the lattice summation method proposed in author's earlier work. This method enabled, both for a 2D layer and 3D bulk crystal of these compounds, to obtain an analytic dependence of the Madelung constant, A M (a, c, u), on the main crystallographic parameters a, c, and u. The dependence A M (a, c, u) reproduces with a high accuracy the value of the constant A M not only for metal diiodides MI 2 with CdI 2 (2 H polytype) structure, but also for metal dihalides (MX 2 ) and metal dihydroxides [M(OH) 2 ] with the same structure. With the use of the high-pressure experimental results available in literature particularly for FeI 2 , it is demonstrated that the above analytic dependence A M (a, c, u) is also valid for direct and precise analysis of the pressure-dependent variation of the Madelung constant.

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Semiempirical approximation for atomization energy of bivalent metal halide crystals

Cited by 5 publications

References 15 publications

Energy minimum criteria in modeling structures and properties of minerals

Energy minimum criteria in modeling structures and properties of minerals

Synthesis of Core–Shell Inorganic Nanotubes

Analytic dependence of the Madelung constant on lattice parameters for 2D and 3D metal diiodides (MI₂) with CdI₂ (2H polytype) layered structure

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Semiempirical approximation for atomization energy of bivalent metal halide crystals

Cited by 5 publications

References 15 publications

Energy minimum criteria in modeling structures and properties of minerals

Energy minimum criteria in modeling structures and properties of minerals

Synthesis of Core–Shell Inorganic Nanotubes

Analytic dependence of the Madelung constant on lattice parameters for 2D and 3D metal diiodides (MI2) with CdI2 (2H polytype) layered structure

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Analytic dependence of the Madelung constant on lattice parameters for 2D and 3D metal diiodides (MI₂) with CdI₂ (2H polytype) layered structure