Effective potentials for 6 - coordinated Boron : structural geometry approach

– We have built a database of ab-initio total energies for elemental Boron in over 60 hypothetical crystal structures of varying coordination Z, such that every atom is equivalent. Fitting to each subset with a particular Z, we extract a classical effective potential, written as a sum over coordination shells and dominated by three-atom (bond angle dependent) terms. In the case Z = 6 (lowest in energy and most relevant), the classical potential has a typical error of 0.1 eV/atom, and favours the " inverted-umbrells " environment seen in real Boron. Introduction. – Boron stands out among the elements for the complexity and polymorphous variety of its structures [1]. The structures are networks built from icosahedrally symmetric clusters, and the typical " inverted-umbrella " coordination shell is asymmetrical, containing five neighbors on one side and one on the other. The stable phase (β-B) is currently modeled with 320 atoms/unit cell. Of the metastable allomorphs [1], only α 12 and T 50 have solved structures [2], the latter of which is stabilized by 4% N atoms [3]. The simplest phase α 12 contains 3-centered bonds both within and between icosahedra [4]. It was thought that bonding within icosahedra is metallic and weaker, while inter-icosahedral bonds are covalent and strong [5, 6]; however, recent experiments have questioned this behavior [7, 8]. Boron is the only plausible candidate for a single-element or covalent quasicrystal, which can be speculatively modeled [9, 10] on either α 12-B or β-B. This idea inspired the discovery of a new Boron phase [11], as well as the prediction of Boron nanotubes [12]. Our motivation is to compare the energies of alternate Boron structures. Selected crystal structures [3, 13], finite icosahedral clusters [9], microtube segments, or sheet fragments [12] were compared by direct ab-initio calculations. Such computations, however, are limited to O(10 2) atoms whereas real Boron has more atoms per unit cell, and quasicrystal models require ∼ 10 5 atoms. Furthermore Monte Carlo and/or molecular dynamics simulations are desirable, especially for the liquid [14].