Comparison of analytic and numerical bond-order potentials for W and Mo

Area of Science:

• Computational Materials Science
• Condensed Matter Physics
• Atomistic Simulations

Background:

• Bond-order potentials (BOPs) are essential for atomistic simulations, derived from the tight-binding approximation.
• Both numerical and analytic formalisms exist for BOPs, impacting energy and force calculations.
• Accurate force calculations are critical for reliable predictions of material properties.

Purpose of the Study:

• To conduct a detailed comparison between numerical and analytic Bond-Order Potentials (BOPs).
• To evaluate the performance of both BOPs in predicting energies and forces for refractory metals.
• To assess the suitability of analytic BOPs for dynamical simulations and defect property predictions.

Main Methods:

• Utilized established parametrizations for body-centered cubic (bcc) refractory metals: tungsten (W) and molybdenum (Mo).
• Calculated structural energy differences, deformation paths (tetragonal, trigonal, hexagonal, orthorhombic), point defect formation energies, and phonon dispersion relations.
• Compared results obtained from numerical BOPs against those from analytic BOPs.

Main Results:

• Numerical and analytic BOPs show strong agreement for energy calculations across various configurations and properties.
• Analytic BOPs provide forces that precisely match the negative energy gradients, unlike numerical BOPs.
• Analytic BOPs demonstrate superior accuracy in predicting defect energies and phonon dispersion relations.

Conclusions:

• Analytic BOPs are advantageous for dynamical simulations due to exact force calculations.
• The analytic BOP formalism leads to improved predictions of material properties, particularly defect energies and phonons.
• This study validates the utility of analytic BOPs for accurate and efficient atomistic simulations in materials science.