Atomvolumen, Packungsdichte der Atome und chemische Bindung in nichtmetallischen Elementen

Abstract

The atomic volume of crystalline elements is largely determined by the packing density of atoms in the respective modification. The determination of packing density is improved by assuming that the atomic distances depend on bond valences according to Pauling's equation. With the additional assumption of equal valence in different modifications, the experimental atomic volume of an element in any given structure is reduced to its volume in close-packed structures, e.g. f.c.c. The ratio of this reduced atomic volume and the experimental atomic volume is a measure of packing density. Reduced atomic volumes of C, Si, Ge, P, As, S and Se, as calculated from different modifications, correspond in most cases to within less than +/-1% for each element, even if calculated from extremely different structures like diamond and buckminsterfullerene in the case of carbon, or from numerous modifications of sulfur with annular molecules of different sizes. Exceptions (graphite, white phosphorus, tin and selenium) indicate deviating valences.

Recent Developments in the Methods and Applications of the Bond Valence Model

“…Trömel and Hübner 171 , 175 subsequently extended their work on metallic elements to nonmetallic elemental structures with similar results. Here it was found that the values of v D were not always the same for a given element.…”

“…Similarly four-coordinated carbon in diamond with v D = 4.10 Å 3 has a valence of 4 but three-coordinate carbon in graphite has v D = 3.69 Å 3 which corresponds to a valence of 5 vu. Trömel( 175 ) finds that the lengths predicted for multiple C−C bonds, calculated using bond valence parameters based on eq 55 , deviate from those observed, but he attributes the difference to the additional bonds included in the geometric coordination. An examination of the many different high pressure structures of Si show that the values of v D all lie on a smooth curve in which v D decreases monotonically with pressure, even though values of v A vary from one high-pressure structure to another.…”

Electron-Transport Properties of Few-Layer Black Phosphorus

“…The recent successful exfoliation of another new 2D atomic-layer material, namely, layered black phosphorus (BP) or phosphorene from bulk BP, − has attracted immediate attention owing to their remarkable electronic properties. ,− Notably, the monolayer phosphorene possesses a desirable direct bandgap of 1.5 eV , and significant transport anisotropy within the monolayer plane as well as the linear dichorism, − rendering it a potential candidate for future nanoelectronic applications. ,,,,− Few-layer BPs are predicted to have even richer electronic properties and higher tunability compared with the monolayer BP, ,,− such as the high carrier mobility up to 1000 cm 2 V –1 s –1 and layer-dependent direct bandgaps, ranging from 1.51 eV for monolayer BP to 0.59 eV for five-layer BP. The reduction of bandgap in few-layer BPs is largely due to interlayer van der Waals interaction .…”