Related results were published in npj Computational Materials.

The popular used density functional theory based on the generalized gradient approximation (DFT-GGA) fails to describe the formation energies of copper-based transition metal (Cu-TM) intermetallic alloys. For instance, the calculated formation energies of Cu₃Au and CuAu are approximately 40% lower than their experimental counterparts. These discrepancies significantly hinder the practical application of DFT-GGA calculations in Cu-TM intermetallic alloy research.

In this study, researchers investigated the formation energies of 20 Cu-TM alloys and the ground state structures of Cu-Au alloys using first principles and cluster expansion methods. The physical mechanism of the incorrect prediction of the formation energy and structural stability was elucidated by analyzing the electronic structure of the compound.

They examined seven ordered alloys and observed that in alloys with fewer d-electrons in the transition metal (TM), GGA overestimates formation energies, while in alloys with more d-electrons, it underestimates them. This highlights the sensitivity of GGA-calculated formation energies to the distribution of d-band energy levels.

Further research revealed that while GGA accurately models d-band energy distributions of transition metals with d-electron contributions at the Fermi energy level, it fails for those with deeper distributions. By using the Hubbard U correction to adjust Cu-d bands to experimentally reported energy range, which accurately calculated the interactions between the Cu and Au atoms in the alloys, allowing for precise calculation of formation energies in the alloys. In addition, the researchers found that the addition of the U correction to 19 other Cu-TMs alloys produced results closer to the experimental values.

Their work underscores the effectiveness of GGA+U in improving the predictive capabilities of DFT-GGA for alloy properties and provides valuable insights for future applications in materials science.

Formation energies of Cu-based transition metal intermetallic alloys. (Image by ZHAO Jing)