Abstract
The bonding of atoms is described as function of the electrostatic forces, covalent bonding, mixed bonding van der Waals bonding hydrogen and metallic bonding, and Born repulsion, yielding equilibrium distance and ionic or atomic radii that are tabulated. Repulsive potential softness parameters and Mohs hardness are tabulated Close packing of ions/atoms determine ordering preferences. Compressibility and Madelung constants, lattice constants and bond length are discussed and tabulated (Table 1.2). Electronegativity, ionicity and effective charges for numerous AB-compounds are listed. Atomic electron density profiles are given.
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Notes
- 1.
A better fit for the Born repulsion is obtained by the sum of a power and an exponential law:
$$ V_{\mathrm{Born}}= \frac{\beta}{r^{m}}+\gamma\exp\biggl(-\frac{r}{r_{0}}\biggr). $$(1.2)r 0 is the softness parameter, listed for ions in Table 1.7. For more sophisticated repulsion potentials, see Shanker and Kumar (1987). β is the force constant (see Eq. (1.1)) and m is an empirical exponent. For ionic crystals the exponent m lies between 6 and 10.
- 2.
β can be eliminated from the minimum condition \(\{dV/dr| _{r_{e}} = 0\}\). One obtains \(\beta = e^{2} r_{e}^{m-1}/ (4\pi \varepsilon _{0}m)\) and as cohesive energy \(eV_{\min} = - e^{2} (m-1)/(4\pi \varepsilon_{0} m_{r_{e}})\).
- 3.
The promotion energy is 4.3, 3.5, and 3.3 eV for C, Si, and α-Sn, respectively. However, when forming bonds by establishing electron bridges to neighboring atoms, a substantially larger energy is gained, therefore resulting in net binding forces. Diamond has the highest cohesive energy in this series, despite the fact that its promotion energy is the largest because its sp 3–sp 3 C–C bonds are the strongest (see Harrison 1980).
- 4.
Meaning compounds between one element of group III and one element of group V on the periodic system of elements.
- 5.
This empirical quantity can be defined in several ways (e.g., as Mohs, Vickers, or Brinell hardness) and is a macroscopic mechanical representation of the cohesive strength of the lattice. In Table 1.9 the often used Mohs hardness is listed, which orders the listed minerals according to the ability of the higher-numbered one to scratch the lower-numbered minerals.
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Böer, K.W. (2013). Crystal Bonding. In: Handbook of the Physics of Thin-Film Solar Cells. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36748-9_1
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