Bond-Order Potentials in Transition Metal Alloys

Bond-order potentials constitute a class of semi-empirical interatomic potentials rooted in tight-binding theory and tailored to capture the directionality and electronic character of bonding in transition metals. By expressing the cohesive energy as a function of pairwise and many-body interactions modulated by bond orders, these potentials bridge the gap between computationally demanding quantum-mechanical methods and more approximate schemes such as the embedded-atom method. In transition-metal alloys, where d-electron contributions govern mechanical strength, defect energetics and phase stability, bond-order potentials provide a transparent framework to incorporate orbital symmetries, magnetism and bond-strength variations with local environment. Recent advances have extended the formalism to multicomponent systems, improved transferability across lattice types and refined parameter optimisation strategies to reproduce energies, forces and elastic constants simultaneously. This combination of physical insight and computational efficiency has enabled large-scale simulations of plastic deformation, grain-boundary segregation and phase transformations in technologically relevant alloys. The predictive capability of bond-order potentials underpins the design of high-strength steels, superalloys and emerging high-entropy materials, offering quantitative guidance on composition–structure–property relations under extreme conditions. By capturing both the local electronic structure and the emergent collective behaviour of atoms, bond-order potentials remain an indispensable tool in the computational materials scientist’s repertoire.

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Bond-Order Potentials in Transition Metal Alloys publication trend

The graph below shows the total number of articles in bond-order potentials in transition metal alloys across all publications each year (not limited to Nature Index journals).

Technical terms

Bond-order potential: A semi-empirical framework in which the cohesive energy depends on pairwise bond energies weighted by bond orders derived from tight-binding theory.

Tight-binding approximation: A quantum-mechanical model that represents electrons as hopping between atomic orbitals, capturing the electronic structure of solids with limited basis functions.

Density of states (DOS): A distribution function describing the number of electronic states available at each energy level, whose moments inform bond-order characteristics.

Moments theorem: A mathematical relation between powers of the Hamiltonian and sums over electronic states, used to compute structural descriptors without full diagonalisation.

Topologically close-packed (TCP) phases: Complex intermetallic structures characterised by high coordination numbers and intricate atomic arrangements common in high-performance alloys.

Transferability: The ability of a potential’s parameter set to predict energies and forces accurately across diverse compositions, phases and defect configurations.

References

1. Crystal-Structure Analysis with Moments of the Density-of-States: Application to Intermetallic Topologically Close-Packed Phases. Crystals (2016).
2. Topologically close-packed phases in binary transition-metal compounds: matching high-throughput ab initio calculations to an empirical structure map. New Journal of Physics (2013).
3. Development of data-driven spd tight-binding models of Fe—parameterisation based on QSGW and DFT calculations including information about higher-order elastic constants. Modelling and Simulation in Materials Science and Engineering (2021).