An alternative definition of ionicity on a microscopic scale

doi:10.1016/0375-9601(84)90655-8

Physics Letters A

Volume 105, Issue 3, 8 October 1984, Pages 139-144

https://doi.org/10.1016/0375-9601(84)90655-8 Get rights and content

Abstract

A decomposition of the electronic charge density of a crystal in terms of the density correlation function and the bare ion pseudopotential is achieved in such a way that the charge bound to the different ion species in the appropriate sublattices can unambiguously be defined. By means of this decomposition a general microscopic ionicity can be established being constructed from the valence charges and the longitudinal effective charges. The latter can also be expressed by experimentally well defined quantities, i.e. the transverse effective charges and the macroscopic dielectric constant. Explicit values for a large class of crystals are given and compared with the other ionicity scales (Phillips, Harrison, Pauling, Coulson).

References (18)

J.C. Phillips
Phys. Rev. Lett.
(1968)
J.C. Phillips
Rev. Mod. Phys.
(1970)
J.A. Van Vechten
Phys. Rev.
(1969)
D.R. Penn
Phys. Rev.
(1962)
R.M. Martin
Phys. Rev.
(1970)
H.B. Callen
Phys. Rev.
(1949)
M. Born et al.
Z. Phys.
(1924)
C. Falter, M. Selmke, A.A. Maradudin, W. Ludwig and W. Zierau, to be...
C. Falter et al.
J. Phys.
(1984)

There are more references available in the full text version of this article.

Cited by (42)

Extant ionic charge theory for bond orbital model based on the tight-binding method: A semi-empirical model applied to wide-bandgap II-VI and III-V semiconductors
2015, Materials Science in Semiconductor Processing
Citation Excerpt :
The trends of C12/C11 versus covalency αc, are shown in Fig. 7, which are similar to that given by Kitamura et al. [13]. Falter et al. [30] have given the ratio of the non-central (bond-bending) force constant β to the central (bond-stretching) force constant α as a function of polarity. This ratio is a measure of the importance of the covalent bond in stabilizing the tetrahedral structure.
In order to enhance the viability of this review for that issue, I suggest adding this to the beginning of the Abstract: "Binary semiconductors with II-VI and III-V composition, owing to their direct and typically rather wide gap, are technologically important materials. The recent successful fabrication of the blue-green laser diode based on these compounds has renewed interest in their physical properties In this review the correlations are presented for the bond polarity (α_p), hybrid covalent energy (V₂) and elastic constants (C_ij) and may be represented by linear equations. These are simple function of product of ionic charges of cation and anion (Z₁Z₂) and nearest neighbour distance (d in Å). On the basis of this result a bond orbital calculations based on the tight-binding method is used to estimate the hybrid covalency (α_c), hybrid polar energy (V₃), effective charge, transverse effective charge (e_T), Kleinman׳s internal displacement parameter (ζ), bulk modulus (B), shear constant (C₁₁−C₁₂)/2, shear modulus (G), Young׳s modulus (Y), bond stretching force constants (α), bond bending force constants (β) of a number of ordered A^NB^8−N semiconductors. The proposed expressions can be applied to a broad selection of covalent materials and their predictions are in good agreement with the experimental data and those from ab initio calculations.
Tight-binding simulations for bulk and low dimensional properties of SiC
2012, Superlattices and Microstructures
Based on an orthogonal ${sp}^{3} s^{*}$ basis set, we report a tight-binding model and its transferable Si–C, C–C and Si–Si interatomic parameters. Our calculations are performed to study the structural properties of SiC in different configurations, namely, bulk, surface, clusters, and point defects. It is essential to involve the two-center intra-atomic parameters and the local environment dependent on-site atomic energy levels to get more accurate results for bulk and low dimensional configurations of SiC. In addition, the structural and electronic properties of higher-coordinated metallic structures are well described besides to those of lower-coordinated covalent structures. The parametrization of tight-binding model is found by a simultaneous fit to the structural and electronic structures of SiC in various bulk crystal configurations and its transferability to low dimensional systems. In this scheme, the results for surface energies, native formation energies, and stacking fault energies, as well as some medium size clusters are in reasonable accordance with the available experimental and theoretical calculations.
Electronic and optical properties of CdTe under hydrostatic pressure effect
2002, Superlattices and Microstructures
Predictions of the bonding properties in Cd<inf>1-x</inf>Zn<inf>x</inf>Te
2001, Superlattices and Microstructures
The electronic, optical and elastic properties of the ternary II–VI semiconductor alloys Cd_1 − x Zn _xTe are calculated by thesp³s^* semi-empirical tight-binding theory and the bond-orbital model. We found a nonlinear decrease of the transverse effective charge and refractive index and a nonlinear increase of the bandgap and elastic constants with increasing Zn composition x. For all these behaviours, the corresponding bowing factors are predicted. The results are compared with previous theoretical estimates and experiments.
Calculation of the elastic properties of CuCl
1997, Physics Letters, Section A: General, Atomic and Solid State Physics
The elastic constants of CuCl with zinc-blende structure are calculated by means of two processes. By using, first, a classical bond-orbital model based on the tight-binding method, and secondly, an approach which combines the latter model with an adjusted empirical pseudopotential method. The bond length d, bond polarity α_p, bulk modulus B, elastic shear constants $(C_{11} -C_{12}) 2$ , bond-stretching force constant α, bond-bending force constant β, internal displacement parameter ξ, effective atomic charge $Z^{∗}$ , transfer parameter $β^{∗}$ , transverse charge $e_{T}^{∗}$ , and piezoelectric charge $e_{p}^{∗}$ are calculated with both methods. The results are compared, with previous theoretical estimates and experiments.
Calculation of elastic constants of Al<inf>x</inf>Ga<inf>1-x</inf>As alloys
1995, Solid State Communications
The elastic constants of Al_xGa_1−xAs alloys are calculated from the bond-orbital model based on the tight-binding method. The results are compared with previous theoretical estimates and experiments. It shoes an approximately linear decrease with increasing Al composition x and the decrease found is dominated by the change in polarity of the valence bonds in Al_xGa_1−xAs alloys. This is a qualitative agreement with the trends determined by near infrared Brillouin scattering. All of the results obtained by experiment are explained by the theory.

View all citing articles on Scopus

View full text

An alternative definition of ionicity on a microscopic scale

Abstract

Phys. Rev. Lett.

Rev. Mod. Phys.

Phys. Rev.

Phys. Rev.

Phys. Rev.

Phys. Rev.

Z. Phys.

J. Phys.