The bond-order potentials (BOPs) idea employs the orthogonal two-centre tight-binding (TB) representation for the bond energy and the Harris–Foulkes approximation for the repulsive pairwise contribution. In the last ten years, although many efforts have been focused on theoretical calculations of the bond order expression, the BOPs still suffers from the uncertainty of how best to choose the semi-empirical TB parameters that enter the scheme. In this paper, we review recent developments to obtain the reliable and transferable BOPs which help to extend the accuracy and applicability to technologically important multicomponent systems. Firstly, we have found that a simple pair potential is unsuitable for describing the environmental screening effects due to the 𝑠 and 𝑝 orbital overlap repulsion in transition metal alloys and therefore the inability to reproduce the negative Cauchy pressures exhibiting in strong covalent systems. By adding the environmental dependent repulsive term, the Cauchy pressure problem has been removed and we are now able to get the BOPs for studying dislocations, extended defects and mechanical properties of hightemperature intermetallic Ti–Al alloys. In particular, new results on the core structures and possible dissociation of different type of dislocations will be discussed. Secondly, we present the first derivation of explicit analytic expressions for environmental dependence of 𝜎, 𝜋 and 𝛿 bond integrals by inverting the non-orthogonal matrix. We illustrate the power of this new formalism by showing that it not only captures the transferability of bond integrals between Mo, Si and MoSi2 but also predicts the large discontinuities between first and second nearest neighbours for $pp\sigma, pp\pi$ and $dd\pi$ even though absence of any discontinuity for the $dd\sigma$ bond integral. A new environmentally dependent BOPs has been developed for bcc-Mo indicating that the core structure of 1/2$\langle$111$\rangle$ screw dislocations is narrower than structures found in previous studies in agreement with recent ab initio calculations. Finally, the new formalism will allow us to study the problem of medium range order found recently in amorphous materials with covalent bonding at large and realistic nanoscale. For the case of 𝑎-C where the issue of $sp^2$ vs $sp^3$ is very crucial for modelling amorphous structure we found that the 𝜎 and 𝜋 bond integrals are not only transferable between graphite and diamond structures but they are also strongly anisotropic due to inter-plan bonding between graphite sheets.
Volume 43, 2020
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